Finite Group Databasebeta

← C89×#62566 #36440414

Subgroups — C89×#62566 #36440414

Order 22784.

1712 conjugacy classes of subgroups.

The subgroup lattice has 1696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3562C211yesmaximal, characteristic, complemented
2C89×#3552C211yesmaximal, characteristic, complemented
3C89×#3377C211yesmaximal, characteristic, complemented
4C89×#3373C211yesmaximal, characteristic, complemented
5C89×#3371C211yesmaximal, characteristic, complemented
6C89×#3367C211yesmaximal, characteristic, complemented
7C89×#3333C211yesmaximal, characteristic, complemented
8C89×#3331C211yesmaximal, characteristic, complemented
9C89×#3326C211yesmaximal, characteristic, complemented
10C89×#3322C211yesmaximal, characteristic, complemented
11C89×#3316C211yesmaximal, characteristic, complemented
12C89×#3314C211yesmaximal, characteristic, complemented
13C89×#3313C211yesmaximal, characteristic, complemented
14C89×#3311C211yesmaximal, characteristic, complemented
15C89×#3309C211yesmaximal, characteristic, complemented
16C89×#3308C211yesmaximal, characteristic, complemented
17C89×#3307C211yesmaximal, characteristic, complemented
18C89×#3306C211yesmaximal, characteristic, complemented
19C89×#3242C211yesmaximal, characteristic, complemented
20C89×#3241C211yesmaximal, characteristic, complemented
21C89×#3238C211yesmaximal, characteristic, complemented
22C89×#3225C211yesmaximal, characteristic, complemented
23C89×#3224C211yesmaximal, characteristic, complemented
24C89×#3219C211yesmaximal, characteristic, complemented
25C89×#3183C211yesmaximal, characteristic, complemented
26C89×#3179C211yesmaximal, characteristic, complemented
27C89×#3178C211yesmaximal, characteristic, complemented
28C89×#3141C211yesmaximal, characteristic, complemented
29C89×#3137C211yesmaximal, characteristic, complemented
30C89×#3136C211yesmaximal, characteristic, complemented
31C89×#2967C211yesmaximal, characteristic, complemented
32#563×C89—21no—
33#563×C89—21no—
34#562×C89—21no—
35#560×C89—21no—
36#559×C89C2211yescharacteristic
37#557×C89C2211yescharacteristic, complemented
38#556×C89C2211yescharacteristic
39#556×C89C2211yescharacteristic
40#554×C89C2211yescharacteristic
41#554×C89C2211yescharacteristic, complemented
42#553×C89—21no—
43#553×C89C2211yescharacteristic
44#553×C89C2211yescharacteristic, complemented
45#551×C89—21no—
46#550×C89C2211yescharacteristic
47D4×Q8×C89—21no—
48D4×Q8×C89C2211yescharacteristic, complemented
49#548×C89—21no—
50#548×C89C2211yescharacteristic
51#548×C89C2211yescharacteristic
52#547×C89C2211yescharacteristic
53#547×C89C2211yescharacteristic
54#546×C89C2211yescharacteristic
55#546×C89C2211yescharacteristic
56#544×C89C2211yescharacteristic
57#544×C89C2211yescharacteristic, complemented
58#542×C89C2211yescharacteristic
59#542×C89C2211yescharacteristic, complemented
60#541×C89—21no—
61#541×C89C2211yescharacteristic
62#540×C89—21no—
63#540×C89C2211yescharacteristic
64#539×C89—21no—
65#539×C89—21no—
66#539×C89—21no—
67#538×C89—21no—
68#538×C89—21no—
69#536×C89—21no—
70#536×C89C2211yescharacteristic
71#535×C89C2211yescharacteristic
72#532×C89C2211yescharacteristic
73C2×C4⋊Q8×C89C2211yescharacteristic, complemented
74#529×C89C2211yescharacteristic
75#529×C89C2211yescharacteristic
76#529×C89C2211yescharacteristic, complemented
77#501×C89C2211yescharacteristic, complemented
78#501×C89C2211yescharacteristic, complemented
79#499×C89C2211yescharacteristic, complemented
80#497×C89C2211yescharacteristic, complemented
81#496×C89C2211yescharacteristic
82#495×C89C2211yescharacteristic
83#491×C89C2211yescharacteristic, complemented
84#491×C89C2211yescharacteristic, complemented
85#490×C89C2211yescharacteristic
86#490×C89C2211yescharacteristic
87#489×C89C2211yescharacteristic
88#489×C89C2211yescharacteristic
89#489×C89C2211yescharacteristic
90#489×C89C2211yescharacteristic
91#489×C89C2211yescharacteristic
92#489×C89C2211yescharacteristic
93#489×C89C2211yescharacteristic, complemented
94#489×C89C2211yescharacteristic, complemented
95#488×C89C2211yescharacteristic
96#488×C89C2211yescharacteristic
97#488×C89C2211yescharacteristic
98#488×C89C2211yescharacteristic, complemented
99#487×C89C2211yescharacteristic, complemented
100#487×C89C2211yescharacteristic, complemented
101#487×C89C2211yescharacteristic, complemented
102#486×C89C2211yescharacteristic
103#486×C89C2211yescharacteristic
104#486×C89C2211yescharacteristic
105#485×C89C2211yescharacteristic
106#485×C89C2211yescharacteristic
107#484×C89C2211yescharacteristic
108#483×C89C2211yescharacteristic
109#483×C89C2211yescharacteristic, complemented
110#483×C89C2211yescharacteristic, complemented
111#482×C89C2211yescharacteristic
112#482×C89C2211yescharacteristic, complemented
113#481×C89C2211yescharacteristic
114#480×C89C2211yescharacteristic
115#480×C89C2211yescharacteristic
116#480×C89C2211yescharacteristic, complemented
117#479×C89C2211yescharacteristic, complemented
118#479×C89C2211yescharacteristic, complemented
119#478×C89C2211yescharacteristic
120#478×C89C2211yescharacteristic, complemented
121#477×C89C2211yescharacteristic, complemented
122#477×C89C2211yescharacteristic, complemented
123#477×C89C2211yescharacteristic, complemented
124#476×C89C2211yescharacteristic
125#476×C89C2211yescharacteristic
126#476×C89C2211yescharacteristic, complemented
127#475×C89C2211yescharacteristic, complemented
128#474×C89C2211yescharacteristic
129#470×C89C2211yescharacteristic
130#470×C89C2211yescharacteristic, complemented
131#469×C89C2211yescharacteristic
132#469×C89C2211yescharacteristic
133#468×C89C2211yescharacteristic
134#468×C89C2211yescharacteristic
135#468×C89C2211yescharacteristic, complemented
136#468×C89C2211yescharacteristic, complemented
137#467×C89C2211yescharacteristic
138#466×C89C2211yescharacteristic, complemented
139#465×C89C2211yescharacteristic
140#465×C89C2211yescharacteristic
141#464×C89C2211yescharacteristic
142#464×C89C2211yescharacteristic
143#464×C89C2211yescharacteristic
144#464×C89C2211yescharacteristic, complemented
145#463×C89C2211yescharacteristic
146#463×C89C2211yescharacteristic
147#463×C89C2211yescharacteristic
148#463×C89C2211yescharacteristic, complemented
149#462×C89C2211yescharacteristic, complemented
150#461×C89C2211yescharacteristic, complemented
151#460×C89C2211yescharacteristic
152#459×C89C2211yescharacteristic
153#452×C89C2211yescharacteristic
154#452×C89C2211yescharacteristic
155#452×C89C2211yescharacteristic
156#452×C89C2211yescharacteristic, complemented
157#451×C89C2211yescharacteristic, complemented
158#450×C89C2211yescharacteristic
159#449×C89C2211yescharacteristic
160#449×C89C2211yescharacteristic
161#449×C89C2211yescharacteristic
162#449×C89C2211yescharacteristic, complemented
163#448×C89C2211yescharacteristic, complemented
164#447×C89C2211yescharacteristic
165#446×C89C2211yescharacteristic, complemented
166#446×C89C2211yescharacteristic, complemented
167#442×C89C2211yescharacteristic
168#442×C89C2211yescharacteristic, complemented
169#441×C89C2211yescharacteristic, complemented
170#441×C89C2211yescharacteristic, complemented
171#440×C89C2211yescharacteristic
172#440×C89C2211yescharacteristic
173#440×C89C2211yescharacteristic, complemented
174#440×C89C2211yescharacteristic, complemented
175C4×Q16×C89C2211yescharacteristic, complemented
176C4×SD16×C89C2211yescharacteristic, complemented
177C4×SD16×C89C2211yescharacteristic, complemented
178C4×D8×C89C2211yescharacteristic
179#436×C89C2211yescharacteristic
180#436×C89C2211yescharacteristic, complemented
181#435×C89C2211yescharacteristic
182#435×C89C2211yescharacteristic
183#435×C89C2211yescharacteristic
184#435×C89C2211yescharacteristic, complemented
185#433×C89C2211yescharacteristic
186#433×C89C2211yescharacteristic, complemented
187#432×C89C2211yescharacteristic, complemented
188#419×C89C2211yescharacteristic, complemented
189#418×C89C2211yescharacteristic
190#417×C89C2211yescharacteristic
191#417×C89C2211yescharacteristic
192#417×C89C2211yescharacteristic
193#417×C89C2211yescharacteristic
194#417×C89C2211yescharacteristic, complemented
195#417×C89C2211yescharacteristic, complemented
196#416×C89C2211yescharacteristic
197#416×C89C2211yescharacteristic
198C2×#103×C89C2211yescharacteristic, complemented
199C2×#102×C89C2211yescharacteristic
200#405×C89C2211yescharacteristic
201#405×C89C2211yescharacteristic, complemented
202C4×M16×C89C2211yescharacteristic, complemented
203C2×#41×C89—21no—
204C2×#41×C89C2311yescharacteristic
205C2×#41×C89C2311yescharacteristic
206C2×#41×C89C2311yescharacteristic
207C2×#41×C89C2311yescharacteristic
208C22×Q8×C89—21no—
209C22×Q8×C89—21no—
210C22×Q8×C89C2311yescharacteristic
211C22×D4×C89C2311yescharacteristic
212C2×Q16×C89C2311yescharacteristic
213C2×Q16×C89C2311yescharacteristic
214C2×Q16×C89C2311yescharacteristic
215C2×SD16×C89C2311yescharacteristic
216C2×SD16×C89C2311yescharacteristic
217C2×SD16×C89C2311yescharacteristic
218C2×SD16×C89C2311yescharacteristic
219C2×SD16×C89C2311yescharacteristic
220C2×SD16×C89C2311yescharacteristic
221C2×D8×C89C2311yescharacteristic
222C2×D8×C89C2311yescharacteristic
223C2×D8×C89C2311yescharacteristic
224C2×M16×C89C2311yescharacteristic
225C2×M16×C89C2311yescharacteristic
226C2×M16×C89C2311yescharacteristic
227C2×M16×C89C2311yescharacteristic
228C22×C8×C89C2311yescharacteristic
229C22×C8×C89C2311yescharacteristic
230C4⋊Q8×C89—21no—
231C4⋊Q8×C89—21no—
232C4⋊Q8×C89—21no—
233C4⋊Q8×C89—21no—
234C4⋊Q8×C89—21no—
235C4⋊Q8×C89C2311yescharacteristic
236C4⋊Q8×C89C2311yescharacteristic
237C4⋊Q8×C89C2311yescharacteristic
238C4⋊Q8×C89C2311yescharacteristic
239C4⋊Q8×C89C2311yescharacteristic
240C4⋊Q8×C89C2311yescharacteristic
241C4⋊Q8×C89C2311yescharacteristic
242C4⋊Q8×C89C2311yescharacteristic
243#127×C89—21no—
244#127×C89C2311yescharacteristic
245#127×C89C2311yescharacteristic
246#126×C89—21no—
247#126×C89—21no—
248#126×C89—21no—
249#126×C89—21no—
250#126×C89—21no—
251#126×C89—21no—
252#126×C89—21no—
253#126×C89—21no—
254#126×C89—21no—
255#126×C89—21no—
256#126×C89—21no—
257#126×C89—21no—
258#126×C89D411yescharacteristic
259#126×C89D411yescharacteristic
260#125×C89—21no—
261#125×C89—21no—
262#125×C89—21no—
263#125×C89—21no—
264#125×C89—21no—
265#125×C89—21no—
266#125×C89—21no—
267#125×C89—21no—
268#125×C89D411yescharacteristic
269#125×C89C2311yescharacteristic
270#125×C89C2311yescharacteristic
271#125×C89C2311yescharacteristic
272#125×C89C2311yescharacteristic
273#124×C89—21no—
274#124×C89—21no—
275#124×C89—21no—
276#124×C89—21no—
277#124×C89—21no—
278#124×C89—21no—
279#124×C89D411yescharacteristic
280#124×C89C2311yescharacteristic
281#124×C89C2311yescharacteristic
282#124×C89C2311yescharacteristic
283#124×C89C2311yescharacteristic
284#124×C89C2311yescharacteristic
285#124×C89C2311yescharacteristic
286#123×C89—21no—
287#123×C89—21no—
288#123×C89—21no—
289#123×C89—21no—
290#123×C89—21no—
291#123×C89—21no—
292#123×C89—21no—
293#123×C89—21no—
294#123×C89—21no—
295#123×C89—21no—
296#123×C89—21no—
297#123×C89—21no—
298#123×C89—21no—
299#123×C89—21no—
300#123×C89—21no—
301#123×C89—21no—
302#123×C89—21no—
303#123×C89—21no—
304#123×C89D411yescharacteristic
305#123×C89D411yescharacteristic
306C22⋊Q8×C89—21no—
307C22⋊Q8×C89—21no—
308C22⋊Q8×C89—21no—
309C22⋊Q8×C89—21no—
310C22⋊Q8×C89—21no—
311C22⋊Q8×C89—21no—
312C22⋊Q8×C89—21no—
313C22⋊Q8×C89—21no—
314C22⋊Q8×C89—21no—
315C22⋊Q8×C89—21no—
316C22⋊Q8×C89—21no—
317C22⋊Q8×C89—21no—
318C22⋊Q8×C89—21no—
319C22⋊Q8×C89—21no—
320C22⋊Q8×C89—21no—
321C22⋊Q8×C89—21no—
322C22⋊Q8×C89—21no—
323C22⋊Q8×C89—21no—
324C22⋊Q8×C89—21no—
325C22⋊Q8×C89D411yescharacteristic
326C22⋊Q8×C89C2311yescharacteristic
327C22⋊Q8×C89C2311yescharacteristic
328C22⋊Q8×C89C2311yescharacteristic
329C22⋊Q8×C89C2311yescharacteristic
330C22⋊Q8×C89C2311yescharacteristic
331C22⋊Q8×C89C2311yescharacteristic
332#121×C89—21no—
333#121×C89—21no—
334#121×C89—21no—
335#121×C89—21no—
336#121×C89—21no—
337#121×C89—21no—
338#121×C89—21no—
339#121×C89—21no—
340#121×C89—21no—
341#121×C89—21no—
342#121×C89—21no—
343#121×C89—21no—
344#121×C89—21no—
345#121×C89—21no—
346#121×C89—21no—
347#121×C89D411yescharacteristic
348#121×C89C2311yescharacteristic
349#121×C89C2311yescharacteristic
350#121×C89C2311yescharacteristic
351#121×C89C2311yescharacteristic
352#121×C89C2311yescharacteristic
353#121×C89C2311yescharacteristic
354#120×C89—21no—
355#120×C89—21no—
356#120×C89—21no—
357#120×C89—21no—
358C4×Q8×C89—21no—
359C4×Q8×C89—21no—
360C4×Q8×C89C2311yescharacteristic
361C4×Q8×C89C2311yescharacteristic
362C4×Q8×C89C2311yescharacteristic
363C4×Q8×C89C2311yescharacteristic
364C4×Q8×C89C2311yescharacteristic
365C4×Q8×C89C2311yescharacteristic
366C4×Q8×C89C2311yescharacteristic
367C4×D4×C89—21no—
368C4×D4×C89—21no—
369C4×D4×C89—21no—
370C4×D4×C89—21no—
371C4×D4×C89—21no—
372C4×D4×C89—21no—
373C4×D4×C89—21no—
374C4×D4×C89—21no—
375C4×D4×C89—21no—
376C4×D4×C89—21no—
377C4×D4×C89—21no—
378C4×D4×C89—21no—
379C4×D4×C89C2311yescharacteristic
380C4×D4×C89C2311yescharacteristic
381C4×D4×C89C2311yescharacteristic
382C4×D4×C89C2311yescharacteristic
383C4×D4×C89C2311yescharacteristic
384C4×D4×C89C2311yescharacteristic
385C4×D4×C89C2311yescharacteristic
386C4×D4×C89C2311yescharacteristic
387C4×D4×C89C2311yescharacteristic
388#117×C89—21no—
389#117×C89—21no—
390#117×C89—21no—
391#117×C89C2311yescharacteristic
392#117×C89C2311yescharacteristic
393#117×C89C2311yescharacteristic
394#117×C89C2311yescharacteristic
395C2×C4⋊C4×C89—21no—
396C2×C4⋊C4×C89—21no—
397C2×C4⋊C4×C89C2311yescharacteristic
398C2×C4⋊C4×C89C2311yescharacteristic
399C2×C4⋊C4×C89C2311yescharacteristic
400C2×C4⋊C4×C89C2311yescharacteristic
401C2×C22⋊C4×C89—21no—
402C2×C22⋊C4×C89—21no—
403C2×C42×C89C2311yescharacteristic
404#107×C89C2311yescharacteristic
405#107×C89C2311yescharacteristic
406#107×C89C2311yescharacteristic
407#107×C89C2311yescharacteristic
408#107×C89C2311yescharacteristic
409#107×C89C2311yescharacteristic
410#106×C89C2311yescharacteristic
411#106×C89C2311yescharacteristic
412#106×C89C2311yescharacteristic
413#106×C89C2311yescharacteristic
414#106×C89C2311yescharacteristic
415#106×C89C2311yescharacteristic
416C4⋊C8×C89C2311yescharacteristic
417C4⋊C8×C89C2311yescharacteristic
418C4⋊C8×C89C2311yescharacteristic
419C4⋊C8×C89C2311yescharacteristic
420C4⋊C8×C89C2311yescharacteristic
421C4⋊C8×C89C2311yescharacteristic
422#103×C89C2311yescharacteristic
423#103×C89C2311yescharacteristic
424#103×C89C2311yescharacteristic
425#103×C89C2311yescharacteristic
426#103×C89C2311yescharacteristic
427#103×C89C2311yescharacteristic
428#103×C89C2311yescharacteristic
429#103×C89C2311yescharacteristic
430#103×C89C2311yescharacteristic
431#103×C89C2311yescharacteristic
432#103×C89C2311yescharacteristic
433#103×C89C2311yescharacteristic
434#103×C89C2311yescharacteristic
435#103×C89C2311yescharacteristic
436#103×C89C2311yescharacteristic
437#103×C89C2311yescharacteristic
438#103×C89C2311yescharacteristic
439#103×C89C2311yescharacteristic
440#103×C89C2311yescharacteristic
441#103×C89C2311yescharacteristic
442#102×C89C2311yescharacteristic
443#102×C89C2311yescharacteristic
444#102×C89C2311yescharacteristic
445#102×C89C2311yescharacteristic
446#102×C89C2311yescharacteristic
447#102×C89C2311yescharacteristic
448#102×C89C2311yescharacteristic
449#102×C89C2311yescharacteristic
450#102×C89C2311yescharacteristic
451#102×C89C2311yescharacteristic
452#102×C89C2311yescharacteristic
453#102×C89C2311yescharacteristic
454#102×C89C2311yescharacteristic
455#102×C89C2311yescharacteristic
456#102×C89C2311yescharacteristic
457#102×C89C2311yescharacteristic
458#102×C89C2311yescharacteristic
459#102×C89C2311yescharacteristic
460#102×C89C2311yescharacteristic
461#102×C89C2311yescharacteristic
462C22⋊C8×C89C2311yescharacteristic
463C22⋊C8×C89C2311yescharacteristic
464C22⋊C8×C89C2311yescharacteristic
465C22⋊C8×C89C2311yescharacteristic
466C22⋊C8×C89C2311yescharacteristic
467C22⋊C8×C89C2311yescharacteristic
468#97×C89C2311yescharacteristic
469#97×C89C2311yescharacteristic
470#97×C89C2311yescharacteristic
471#97×C89C2311yescharacteristic
472#97×C89C2311yescharacteristic
473#97×C89C2311yescharacteristic
474C4×C8×C89C2311yescharacteristic
475C4×C8×C89C2311yescharacteristic
476C4×C8×C89C2311yescharacteristic
477C4×C8×C89C2311yescharacteristic
478C24×C89—21no—
479#41×C89—41no—
480#41×C89—41no—
481#41×C89—41no—
482#41×C89—41no—
483#41×C89—41no—
484#41×C89—41no—
485#41×C89—41no—
486#41×C89—41no—
487#41×C89—82no—
488C2×Q8×C89—21no—
489C2×Q8×C89—21no—
490C2×Q8×C89—21no—
491C2×Q8×C89—21no—
492C2×Q8×C89—21no—
493C2×Q8×C89—21no—
494C2×Q8×C89—21no—
495C2×Q8×C89—41no—
496C2×Q8×C89—41no—
497C2×Q8×C89—82no—
498C2×Q8×C89—82no—
499C2×Q8×C89C2×D411yescharacteristic
500C2×Q8×C89C2411yescharacteristic
501C2×Q8×C89C2411yescharacteristic
502C2×Q8×C89C2411yescharacteristic
503C2×Q8×C89C2411yescharacteristic
504C2×D4×C89—21no—
505C2×D4×C89—21no—
506C2×D4×C89—21no—
507C2×D4×C89—21no—
508C2×D4×C89—21no—
509C2×D4×C89—21no—
510C2×D4×C89—21no—
511C2×D4×C89—21no—
512C2×D4×C89—21no—
513C2×D4×C89—21no—
514C2×D4×C89—21no—
515C2×D4×C89—21no—
516C2×D4×C89—21no—
517C2×D4×C89—21no—
518C2×D4×C89—21no—
519C2×D4×C89—41no—
520C2×D4×C89—41no—
521C2×D4×C89C2×D411yescharacteristic
522C2×D4×C89C2×D411yescharacteristic
523C2×D4×C89C2×D411yescharacteristic
524C2×D4×C89C2411yescharacteristic
525C2×D4×C89C2411yescharacteristic
526C2×D4×C89C2411yescharacteristic
527C2×D4×C89C2411yescharacteristic
528C22×C4×C89—21no—
529C22×C4×C89—21no—
530C22×C4×C89—21no—
531C22×C4×C89—21no—
532C22×C4×C89—21no—
533C22×C4×C89—21no—
534C22×C4×C89—21no—
535C22×C4×C89—21no—
536C22×C4×C89—21no—
537C22×C4×C89—21no—
538C22×C4×C89—21no—
539C22×C4×C89—21no—
540C22×C4×C89—21no—
541C22×C4×C89—21no—
542C22×C4×C89—21no—
543C22×C4×C89C2×D411yescharacteristic
544C22×C4×C89C2×D411yescharacteristic
545C22×C4×C89C2411yescharacteristic
546C22×C4×C89C2411yescharacteristic
547C22×C4×C89C2411yescharacteristic
548Q16×C89—41no—
549Q16×C89—41no—
550Q16×C89—41no—
551SD16×C89—41no—
552SD16×C89—41no—
553SD16×C89—41no—
554SD16×C89—41no—
555SD16×C89—41no—
556SD16×C89—41no—
557D8×C89—41no—
558D8×C89—41no—
559D8×C89—41no—
560M16×C89—41no—
561M16×C89—41no—
562M16×C89—41no—
563M16×C89—41no—
564C2×C8×C89—41no—
565C2×C8×C89—41no—
566C2×C8×C89C2411yescharacteristic
567C2×C8×C89C2411yescharacteristic
568C2×C8×C89C2411yescharacteristic
569C2×C8×C89C2411yescharacteristic
570C2×C8×C89C2411yescharacteristic
571C2×C8×C89C2411yescharacteristic
572C2×C8×C89C2411yescharacteristic
573C2×C8×C89C2411yescharacteristic
574C4⋊C4×C89—21no—
575C4⋊C4×C89—21no—
576C4⋊C4×C89—21no—
577C4⋊C4×C89—21no—
578C4⋊C4×C89—21no—
579C4⋊C4×C89—21no—
580C4⋊C4×C89—21no—
581C4⋊C4×C89—21no—
582C4⋊C4×C89—21no—
583C4⋊C4×C89—21no—
584C4⋊C4×C89—21no—
585C4⋊C4×C89—21no—
586C4⋊C4×C89—21no—
587C4⋊C4×C89—21no—
588C4⋊C4×C89—21no—
589C4⋊C4×C89—21no—
590C4⋊C4×C89—21no—
591C4⋊C4×C89—21no—
592C4⋊C4×C89—21no—
593C4⋊C4×C89—21no—
594C4⋊C4×C89—21no—
595C4⋊C4×C89—21no—
596C4⋊C4×C89—21no—
597C4⋊C4×C89—21no—
598C4⋊C4×C89—21no—
599C4⋊C4×C89—21no—
600C4⋊C4×C89—21no—
601C4⋊C4×C89—21no—
602C4⋊C4×C89—21no—
603C4⋊C4×C89—21no—
604C4⋊C4×C89—21no—
605C4⋊C4×C89—21no—
606C4⋊C4×C89—21no—
607C4⋊C4×C89—21no—
608C4⋊C4×C89C2×D411yescharacteristic
609C4⋊C4×C89C2×D411yescharacteristic
610C4⋊C4×C89C2×D411yescharacteristic
611C4⋊C4×C89C2×D411yescharacteristic
612C4⋊C4×C89C2×D411yescharacteristic
613C4⋊C4×C89C2×D411yescharacteristic
614C4⋊C4×C89C2×D411yescharacteristic
615C4⋊C4×C89C2×D411yescharacteristic
616C4⋊C4×C89C2×D411yescharacteristic
617C4⋊C4×C89C2×D411yescharacteristic
618C4⋊C4×C89C2411yescharacteristic
619C4⋊C4×C89C2411yescharacteristic
620C4⋊C4×C89C2411yescharacteristic
621C4⋊C4×C89C2411yescharacteristic
622C4⋊C4×C89C2411yescharacteristic
623C4⋊C4×C89C2411yescharacteristic
624C4⋊C4×C89C2411yescharacteristic
625C4⋊C4×C89C2411yescharacteristic
626C22⋊C4×C89—21no—
627C22⋊C4×C89—21no—
628C22⋊C4×C89—21no—
629C22⋊C4×C89—21no—
630C22⋊C4×C89—21no—
631C22⋊C4×C89—21no—
632C22⋊C4×C89—21no—
633C22⋊C4×C89—21no—
634C22⋊C4×C89—21no—
635C22⋊C4×C89—21no—
636C22⋊C4×C89—21no—
637C22⋊C4×C89—21no—
638C22⋊C4×C89—21no—
639C22⋊C4×C89—21no—
640C22⋊C4×C89—21no—
641C22⋊C4×C89—21no—
642C22⋊C4×C89—21no—
643C22⋊C4×C89—21no—
644C22⋊C4×C89—21no—
645C22⋊C4×C89—21no—
646C22⋊C4×C89—21no—
647C22⋊C4×C89—21no—
648C22⋊C4×C89—21no—
649C22⋊C4×C89—21no—
650C22⋊C4×C89—21no—
651C22⋊C4×C89—21no—
652C22⋊C4×C89—21no—
653C22⋊C4×C89—21no—
654C22⋊C4×C89—21no—
655C22⋊C4×C89—21no—
656C22⋊C4×C89—21no—
657C22⋊C4×C89—21no—
658C22⋊C4×C89C2×D411yescharacteristic
659C22⋊C4×C89C2×D411yescharacteristic
660C22⋊C4×C89C2×D411yescharacteristic
661C22⋊C4×C89C2×D411yescharacteristic
662C22⋊C4×C89C2×D411yescharacteristic
663C22⋊C4×C89C2×D411yescharacteristic
664C22⋊C4×C89C2×D411yescharacteristic
665C22⋊C4×C89C2×D411yescharacteristic
666C22⋊C4×C89C2×D411yescharacteristic
667C22⋊C4×C89C2×D411yescharacteristic
668C42×C89—21no—
669C42×C89—21no—
670C42×C89—21no—
671C42×C89—21no—
672C42×C89—21no—
673C42×C89—21no—
674C42×C89—21no—
675C42×C89—21no—
676C42×C89C2×D411yescharacteristic
677C42×C89C2×D411yescharacteristic
678C42×C89C2411yescharacteristic
679C42×C89C2411yescharacteristic
680C42×C89C2411yescharacteristic
681C42×C89C2411yescharacteristic
682C23×C89—21no—
683C23×C89—21no—
684C23×C89—21no—
685C23×C89—21no—
686C23×C89—81no—
687C23×C89—81no—
688C23×C89—81no—
689C23×C89C22×D411yescharacteristic
690C23×C89C22×D411yescharacteristic
691C23×C89C22×D411yescharacteristic
692Q8×C89—21no—
693Q8×C89—21no—
694Q8×C89—21no—
695Q8×C89—21no—
696Q8×C89—21no—
697Q8×C89—21no—
698Q8×C89—21no—
699Q8×C89—21no—
700Q8×C89—41no—
701Q8×C89—42no—
702Q8×C89—42no—
703Q8×C89—81no—
704Q8×C89—81no—
705Q8×C89—81no—
706Q8×C89—81no—
707Q8×C89—81no—
708D4×C89—21no—
709D4×C89—21no—
710D4×C89—21no—
711D4×C89—21no—
712D4×C89—21no—
713D4×C89—21no—
714D4×C89—21no—
715D4×C89—21no—
716D4×C89—41no—
717D4×C89—41no—
718D4×C89—41no—
719D4×C89—42no—
720D4×C89—81no—
721D4×C89—81no—
722D4×C89—81no—
723D4×C89—81no—
724D4×C89—81no—
725D4×C89—81no—
726D4×C89—81no—
727D4×C89—81no—
728D4×C89—81no—
729D4×C89—81no—
730D4×C89—81no—
731D4×C89—81no—
732D4×C89—81no—
733D4×C89—81no—
734C2×C4×C89—21no—
735C2×C4×C89—21no—
736C2×C4×C89—21no—
737C2×C4×C89—21no—
738C2×C4×C89—21no—
739C2×C4×C89—21no—
740C2×C4×C89—21no—
741C2×C4×C89—21no—
742C2×C4×C89—21no—
743C2×C4×C89—21no—
744C2×C4×C89—21no—
745C2×C4×C89—21no—
746C2×C4×C89—21no—
747C2×C4×C89—21no—
748C2×C4×C89—21no—
749C2×C4×C89—21no—
750C2×C4×C89—21no—
751C2×C4×C89—21no—
752C2×C4×C89—41no—
753C2×C4×C89—41no—
754C2×C4×C89—42no—
755C2×C4×C89—81no—
756C2×C4×C89—81no—
757C2×C4×C89—81no—
758C2×C4×C89—81no—
759C2×C4×C89—81no—
760C2×C4×C89—81no—
761C2×C4×C89—81no—
762C2×C4×C89—81no—
763C2×C4×C89—81no—
764C2×C4×C89—81no—
765C2×C4×C89—81no—
766C2×C4×C89—81no—
767C2×C4×C89—81no—
768C2×C4×C89—81no—
769C2×C4×C89C22×D411yescharacteristic
770C2×C4×C89C22×D411yescharacteristic
771C2×C4×C89C22×D411yescharacteristic
772C2×C4×C89C22×D411yescharacteristic
773C2×C4×C89C22×D411yescharacteristic
774C2×C4×C89C22×D411yescharacteristic
775C2×C4×C89C22×D411yescharacteristic
776C2×C4×C89C22×D411yescharacteristic
777C2×C4×C89C22×D411yescharacteristic
778C2×C4×C89C22×D411yescharacteristic
779C2×C4×C89C22×D411yescharacteristic
780C2×C4×C89C2511yescharacteristic
781C8×C89—21no—
782C8×C89—21no—
783C8×C89—21no—
784C8×C89—21no—
785C8×C89—21no—
786C8×C89—21no—
787C8×C89—21no—
788C8×C89—21no—
789C22×C89—21no—
790C22×C89—21no—
791C22×C89—21no—
792C22×C89—21no—
793C22×C89—21no—
794C22×C89—21no—
795C22×C89—21no—
796C22×C89—21no—
797C22×C89—21no—
798C22×C89—41no—
799C22×C89—41no—
800C22×C89—41no—
801C22×C89—41no—
802C22×C89—41no—
803C22×C89—41no—
804C22×C89—41no—
805C22×C89—41no—
806C22×C89—41no—
807C22×C89—41no—
808C22×C89—41no—
809C22×C89—41no—
810C22×C89—162no—
811C22×C89C23×D411yescharacteristic
812C4×C89—21no—
813C4×C89—21no—
814C4×C89—21no—
815C4×C89—21no—
816C4×C89—21no—
817C4×C89—21no—
818C4×C89—21no—
819C4×C89—21no—
820C4×C89—21no—
821C4×C89—21no—
822C4×C89—21no—
823C4×C89—41no—
824C4×C89—41no—
825C4×C89—41no—
826C4×C89—41no—
827C4×C89—41no—
828C4×C89—41no—
829C4×C89—41no—
830C4×C89—41no—
831C4×C89—41no—
832C4×C89—41no—
833C4×C89—41no—
834C4×C89—41no—
835C4×C89#58511yescharacteristic
836C4×C89#58511yescharacteristic
837#62566C8911yesmaximal, characteristic, direct product factor, Sylow
838C2×C89—41no—
839C2×C89—41no—
840C2×C89—41no—
841C2×C89—81no—
842C2×C89—81no—
843C2×C89—81no—
844C2×C89—81no—
845C2×C89#350011yescharacteristic
846C2×C89#358511yescharacteristic
847C2×C89#358611yescharacteristic
848#3562C2×C8911yescharacteristic, complemented
849#3552C2×C8911yescharacteristic, complemented
850#3377C2×C8911yescharacteristic, complemented
851#3373C2×C8911yescharacteristic, complemented
852#3371C2×C8911yescharacteristic, complemented
853#3367C2×C8911yescharacteristic, complemented
854#3333C2×C8911yescharacteristic, complemented
855#3331C2×C8911yescharacteristic, complemented
856#3326C2×C8911yescharacteristic, complemented
857#3322C2×C8911yescharacteristic, complemented
858#3316C2×C8911yescharacteristic, complemented
859#3314C2×C8911yescharacteristic, complemented
860#3313C2×C8911yescharacteristic, complemented
861#3311C2×C8911yescharacteristic, complemented
862#3309C2×C8911yescharacteristic, complemented
863#3308C2×C8911yescharacteristic, complemented
864#3307C2×C8911yescharacteristic, complemented
865#3306C2×C8911yescharacteristic, complemented
866#3242C2×C8911yescharacteristic, complemented
867#3241C2×C8911yescharacteristic, complemented
868#3238C2×C8911yescharacteristic, complemented
869#3225C2×C8911yescharacteristic, complemented
870#3224C2×C8911yescharacteristic, complemented
871#3219C2×C8911yescharacteristic, complemented
872#3183C2×C8911yescharacteristic, complemented
873#3179C2×C8911yescharacteristic, complemented
874#3178C2×C8911yescharacteristic, complemented
875#3141C2×C8911yescharacteristic, complemented
876#3137C2×C8911yescharacteristic, complemented
877#3136C2×C8911yescharacteristic, complemented
878#2967C2×C8911yescharacteristic, complemented
879C89#6256611yescharacteristic, direct product factor, Sylow
880#563—21no—
881#563—21no—
882#562—21no—
883#560—21no—
884#559C22×C8911yescharacteristic
885#557C22×C8911yescharacteristic, complemented
886#556C22×C8911yescharacteristic
887#556C22×C8911yescharacteristic
888#554C22×C8911yescharacteristic
889#554C22×C8911yescharacteristic, complemented
890#553—21no—
891#553C22×C8911yescharacteristic
892#553C22×C8911yescharacteristic, complemented
893#551—21no—
894#550C22×C8911yescharacteristic
895D4×Q8—21no—
896D4×Q8C22×C8911yescharacteristic, complemented
897#548—21no—
898#548C22×C8911yescharacteristic
899#548C22×C8911yescharacteristic
900#547C22×C8911yescharacteristic
901#547C22×C8911yescharacteristic
902#546C22×C8911yescharacteristic
903#546C22×C8911yescharacteristic
904#544C22×C8911yescharacteristic
905#544C22×C8911yescharacteristic, complemented
906#542C22×C8911yescharacteristic
907#542C22×C8911yescharacteristic, complemented
908#541—21no—
909#541C22×C8911yescharacteristic
910#540—21no—
911#540C22×C8911yescharacteristic
912#539—21no—
913#539—21no—
914#539—21no—
915#538—21no—
916#538—21no—
917#536—21no—
918#536C22×C8911yescharacteristic
919#535C22×C8911yescharacteristic
920#532C22×C8911yescharacteristic
921C2×C4⋊Q8C22×C8911yescharacteristic, complemented
922#529C22×C8911yescharacteristic
923#529C22×C8911yescharacteristic
924#529C22×C8911yescharacteristic, complemented
925#501C22×C8911yescharacteristic, complemented
926#501C22×C8911yescharacteristic, complemented
927#499C22×C8911yescharacteristic, complemented
928#497C22×C8911yescharacteristic, complemented
929#496C22×C8911yescharacteristic
930#495C22×C8911yescharacteristic
931#491C22×C8911yescharacteristic, complemented
932#491C22×C8911yescharacteristic, complemented
933#490C22×C8911yescharacteristic
934#490C22×C8911yescharacteristic
935#489C22×C8911yescharacteristic
936#489C22×C8911yescharacteristic
937#489C22×C8911yescharacteristic
938#489C22×C8911yescharacteristic
939#489C22×C8911yescharacteristic
940#489C22×C8911yescharacteristic
941#489C22×C8911yescharacteristic, complemented
942#489C22×C8911yescharacteristic, complemented
943#488C22×C8911yescharacteristic
944#488C22×C8911yescharacteristic
945#488C22×C8911yescharacteristic
946#488C22×C8911yescharacteristic, complemented
947#487C22×C8911yescharacteristic, complemented
948#487C22×C8911yescharacteristic, complemented
949#487C22×C8911yescharacteristic, complemented
950#486C22×C8911yescharacteristic
951#486C22×C8911yescharacteristic
952#486C22×C8911yescharacteristic
953#485C22×C8911yescharacteristic
954#485C22×C8911yescharacteristic
955#484C22×C8911yescharacteristic
956#483C22×C8911yescharacteristic
957#483C22×C8911yescharacteristic, complemented
958#483C22×C8911yescharacteristic, complemented
959#482C22×C8911yescharacteristic
960#482C22×C8911yescharacteristic, complemented
961#481C22×C8911yescharacteristic
962#480C22×C8911yescharacteristic
963#480C22×C8911yescharacteristic
964#480C22×C8911yescharacteristic, complemented
965#479C22×C8911yescharacteristic, complemented
966#479C22×C8911yescharacteristic, complemented
967#478C22×C8911yescharacteristic
968#478C22×C8911yescharacteristic, complemented
969#477C22×C8911yescharacteristic, complemented
970#477C22×C8911yescharacteristic, complemented
971#477C22×C8911yescharacteristic, complemented
972#476C22×C8911yescharacteristic
973#476C22×C8911yescharacteristic
974#476C22×C8911yescharacteristic, complemented
975#475C22×C8911yescharacteristic, complemented
976#474C22×C8911yescharacteristic
977#470C22×C8911yescharacteristic
978#470C22×C8911yescharacteristic, complemented
979#469C22×C8911yescharacteristic
980#469C22×C8911yescharacteristic
981#468C22×C8911yescharacteristic
982#468C22×C8911yescharacteristic
983#468C22×C8911yescharacteristic, complemented
984#468C22×C8911yescharacteristic, complemented
985#467C22×C8911yescharacteristic
986#466C22×C8911yescharacteristic, complemented
987#465C22×C8911yescharacteristic
988#465C22×C8911yescharacteristic
989#464C22×C8911yescharacteristic
990#464C22×C8911yescharacteristic
991#464C22×C8911yescharacteristic
992#464C22×C8911yescharacteristic, complemented
993#463C22×C8911yescharacteristic
994#463C22×C8911yescharacteristic
995#463C22×C8911yescharacteristic
996#463C22×C8911yescharacteristic, complemented
997#462C22×C8911yescharacteristic, complemented
998#461C22×C8911yescharacteristic, complemented
999#460C22×C8911yescharacteristic
1000#459C22×C8911yescharacteristic
1001#452C22×C8911yescharacteristic
1002#452C22×C8911yescharacteristic
1003#452C22×C8911yescharacteristic
1004#452C22×C8911yescharacteristic, complemented
1005#451C22×C8911yescharacteristic, complemented
1006#450C22×C8911yescharacteristic
1007#449C22×C8911yescharacteristic
1008#449C22×C8911yescharacteristic
1009#449C22×C8911yescharacteristic
1010#449C22×C8911yescharacteristic, complemented
1011#448C22×C8911yescharacteristic, complemented
1012#447C22×C8911yescharacteristic
1013#446C22×C8911yescharacteristic, complemented
1014#446C22×C8911yescharacteristic, complemented
1015#442C22×C8911yescharacteristic
1016#442C22×C8911yescharacteristic, complemented
1017#441C22×C8911yescharacteristic, complemented
1018#441C22×C8911yescharacteristic, complemented
1019#440C22×C8911yescharacteristic
1020#440C22×C8911yescharacteristic
1021#440C22×C8911yescharacteristic, complemented
1022#440C22×C8911yescharacteristic, complemented
1023C4×Q16C22×C8911yescharacteristic, complemented
1024C4×SD16C22×C8911yescharacteristic, complemented
1025C4×SD16C22×C8911yescharacteristic, complemented
1026C4×D8C22×C8911yescharacteristic
1027#436C22×C8911yescharacteristic
1028#436C22×C8911yescharacteristic, complemented
1029#435C22×C8911yescharacteristic
1030#435C22×C8911yescharacteristic
1031#435C22×C8911yescharacteristic
1032#435C22×C8911yescharacteristic, complemented
1033#433C22×C8911yescharacteristic
1034#433C22×C8911yescharacteristic, complemented
1035#432C22×C8911yescharacteristic, complemented
1036#419C22×C8911yescharacteristic, complemented
1037#418C22×C8911yescharacteristic
1038#417C22×C8911yescharacteristic
1039#417C22×C8911yescharacteristic
1040#417C22×C8911yescharacteristic
1041#417C22×C8911yescharacteristic
1042#417C22×C8911yescharacteristic, complemented
1043#417C22×C8911yescharacteristic, complemented
1044#416C22×C8911yescharacteristic
1045#416C22×C8911yescharacteristic
1046C2×#103C22×C8911yescharacteristic, complemented
1047C2×#102C22×C8911yescharacteristic
1048#405C22×C8911yescharacteristic
1049#405C22×C8911yescharacteristic, complemented
1050C4×M16C22×C8911yescharacteristic, complemented
1051C2×#41—21no—
1052C2×#41C23×C8911yescharacteristic
1053C2×#41C23×C8911yescharacteristic
1054C2×#41C23×C8911yescharacteristic
1055C2×#41C23×C8911yescharacteristic
1056C22×Q8—21no—
1057C22×Q8—21no—
1058C22×Q8C23×C8911yescharacteristic
1059C22×D4C23×C8911yescharacteristic
1060C2×Q16C23×C8911yescharacteristic
1061C2×Q16C23×C8911yescharacteristic
1062C2×Q16C23×C8911yescharacteristic
1063C2×SD16C23×C8911yescharacteristic
1064C2×SD16C23×C8911yescharacteristic
1065C2×SD16C23×C8911yescharacteristic
1066C2×SD16C23×C8911yescharacteristic
1067C2×SD16C23×C8911yescharacteristic
1068C2×SD16C23×C8911yescharacteristic
1069C2×D8C23×C8911yescharacteristic
1070C2×D8C23×C8911yescharacteristic
1071C2×D8C23×C8911yescharacteristic
1072C2×M16C23×C8911yescharacteristic
1073C2×M16C23×C8911yescharacteristic
1074C2×M16C23×C8911yescharacteristic
1075C2×M16C23×C8911yescharacteristic
1076C22×C8C23×C8911yescharacteristic
1077C22×C8C23×C8911yescharacteristic
1078C4⋊Q8—21no—
1079C4⋊Q8—21no—
1080C4⋊Q8—21no—
1081C4⋊Q8—21no—
1082C4⋊Q8—21no—
1083C4⋊Q8C23×C8911yescharacteristic
1084C4⋊Q8C23×C8911yescharacteristic
1085C4⋊Q8C23×C8911yescharacteristic
1086C4⋊Q8C23×C8911yescharacteristic
1087C4⋊Q8C23×C8911yescharacteristic
1088C4⋊Q8C23×C8911yescharacteristic
1089C4⋊Q8C23×C8911yescharacteristic
1090C4⋊Q8C23×C8911yescharacteristic
1091#127—21no—
1092#127C23×C8911yescharacteristic
1093#127C23×C8911yescharacteristic
1094#126—21no—
1095#126—21no—
1096#126—21no—
1097#126—21no—
1098#126—21no—
1099#126—21no—
1100#126—21no—
1101#126—21no—
1102#126—21no—
1103#126—21no—
1104#126—21no—
1105#126—21no—
1106#126D4×C8911yescharacteristic
1107#126D4×C8911yescharacteristic
1108#125—21no—
1109#125—21no—
1110#125—21no—
1111#125—21no—
1112#125—21no—
1113#125—21no—
1114#125—21no—
1115#125—21no—
1116#125D4×C8911yescharacteristic
1117#125C23×C8911yescharacteristic
1118#125C23×C8911yescharacteristic
1119#125C23×C8911yescharacteristic
1120#125C23×C8911yescharacteristic
1121#124—21no—
1122#124—21no—
1123#124—21no—
1124#124—21no—
1125#124—21no—
1126#124—21no—
1127#124D4×C8911yescharacteristic
1128#124C23×C8911yescharacteristic
1129#124C23×C8911yescharacteristic
1130#124C23×C8911yescharacteristic
1131#124C23×C8911yescharacteristic
1132#124C23×C8911yescharacteristic
1133#124C23×C8911yescharacteristic
1134#123—21no—
1135#123—21no—
1136#123—21no—
1137#123—21no—
1138#123—21no—
1139#123—21no—
1140#123—21no—
1141#123—21no—
1142#123—21no—
1143#123—21no—
1144#123—21no—
1145#123—21no—
1146#123—21no—
1147#123—21no—
1148#123—21no—
1149#123—21no—
1150#123—21no—
1151#123—21no—
1152#123D4×C8911yescharacteristic
1153#123D4×C8911yescharacteristic
1154C22⋊Q8—21no—
1155C22⋊Q8—21no—
1156C22⋊Q8—21no—
1157C22⋊Q8—21no—
1158C22⋊Q8—21no—
1159C22⋊Q8—21no—
1160C22⋊Q8—21no—
1161C22⋊Q8—21no—
1162C22⋊Q8—21no—
1163C22⋊Q8—21no—
1164C22⋊Q8—21no—
1165C22⋊Q8—21no—
1166C22⋊Q8—21no—
1167C22⋊Q8—21no—
1168C22⋊Q8—21no—
1169C22⋊Q8—21no—
1170C22⋊Q8—21no—
1171C22⋊Q8—21no—
1172C22⋊Q8—21no—
1173C22⋊Q8D4×C8911yescharacteristic
1174C22⋊Q8C23×C8911yescharacteristic
1175C22⋊Q8C23×C8911yescharacteristic
1176C22⋊Q8C23×C8911yescharacteristic
1177C22⋊Q8C23×C8911yescharacteristic
1178C22⋊Q8C23×C8911yescharacteristic
1179C22⋊Q8C23×C8911yescharacteristic
1180#121—21no—
1181#121—21no—
1182#121—21no—
1183#121—21no—
1184#121—21no—
1185#121—21no—
1186#121—21no—
1187#121—21no—
1188#121—21no—
1189#121—21no—
1190#121—21no—
1191#121—21no—
1192#121—21no—
1193#121—21no—
1194#121—21no—
1195#121D4×C8911yescharacteristic
1196#121C23×C8911yescharacteristic
1197#121C23×C8911yescharacteristic
1198#121C23×C8911yescharacteristic
1199#121C23×C8911yescharacteristic
1200#121C23×C8911yescharacteristic
1201#121C23×C8911yescharacteristic
1202#120—21no—
1203#120—21no—
1204#120—21no—
1205#120—21no—
1206C4×Q8—21no—
1207C4×Q8—21no—
1208C4×Q8C23×C8911yescharacteristic
1209C4×Q8C23×C8911yescharacteristic
1210C4×Q8C23×C8911yescharacteristic
1211C4×Q8C23×C8911yescharacteristic
1212C4×Q8C23×C8911yescharacteristic
1213C4×Q8C23×C8911yescharacteristic
1214C4×Q8C23×C8911yescharacteristic
1215C4×D4—21no—
1216C4×D4—21no—
1217C4×D4—21no—
1218C4×D4—21no—
1219C4×D4—21no—
1220C4×D4—21no—
1221C4×D4—21no—
1222C4×D4—21no—
1223C4×D4—21no—
1224C4×D4—21no—
1225C4×D4—21no—
1226C4×D4—21no—
1227C4×D4C23×C8911yescharacteristic
1228C4×D4C23×C8911yescharacteristic
1229C4×D4C23×C8911yescharacteristic
1230C4×D4C23×C8911yescharacteristic
1231C4×D4C23×C8911yescharacteristic
1232C4×D4C23×C8911yescharacteristic
1233C4×D4C23×C8911yescharacteristic
1234C4×D4C23×C8911yescharacteristic
1235C4×D4C23×C8911yescharacteristic
1236#117—21no—
1237#117—21no—
1238#117—21no—
1239#117C23×C8911yescharacteristic
1240#117C23×C8911yescharacteristic
1241#117C23×C8911yescharacteristic
1242#117C23×C8911yescharacteristic
1243C2×C4⋊C4—21no—
1244C2×C4⋊C4—21no—
1245C2×C4⋊C4C23×C8911yescharacteristic
1246C2×C4⋊C4C23×C8911yescharacteristic
1247C2×C4⋊C4C23×C8911yescharacteristic
1248C2×C4⋊C4C23×C8911yescharacteristic
1249C2×C22⋊C4—21no—
1250C2×C22⋊C4—21no—
1251C2×C42C23×C8911yescharacteristic
1252#107C23×C8911yescharacteristic
1253#107C23×C8911yescharacteristic
1254#107C23×C8911yescharacteristic
1255#107C23×C8911yescharacteristic
1256#107C23×C8911yescharacteristic
1257#107C23×C8911yescharacteristic
1258#106C23×C8911yescharacteristic
1259#106C23×C8911yescharacteristic
1260#106C23×C8911yescharacteristic
1261#106C23×C8911yescharacteristic
1262#106C23×C8911yescharacteristic
1263#106C23×C8911yescharacteristic
1264C4⋊C8C23×C8911yescharacteristic
1265C4⋊C8C23×C8911yescharacteristic
1266C4⋊C8C23×C8911yescharacteristic
1267C4⋊C8C23×C8911yescharacteristic
1268C4⋊C8C23×C8911yescharacteristic
1269C4⋊C8C23×C8911yescharacteristic
1270#103C23×C8911yescharacteristic
1271#103C23×C8911yescharacteristic
1272#103C23×C8911yescharacteristic
1273#103C23×C8911yescharacteristic
1274#103C23×C8911yescharacteristic
1275#103C23×C8911yescharacteristic
1276#103C23×C8911yescharacteristic
1277#103C23×C8911yescharacteristic
1278#103C23×C8911yescharacteristic
1279#103C23×C8911yescharacteristic
1280#103C23×C8911yescharacteristic
1281#103C23×C8911yescharacteristic
1282#103C23×C8911yescharacteristic
1283#103C23×C8911yescharacteristic
1284#103C23×C8911yescharacteristic
1285#103C23×C8911yescharacteristic
1286#103C23×C8911yescharacteristic
1287#103C23×C8911yescharacteristic
1288#103C23×C8911yescharacteristic
1289#103C23×C8911yescharacteristic
1290#102C23×C8911yescharacteristic
1291#102C23×C8911yescharacteristic
1292#102C23×C8911yescharacteristic
1293#102C23×C8911yescharacteristic
1294#102C23×C8911yescharacteristic
1295#102C23×C8911yescharacteristic
1296#102C23×C8911yescharacteristic
1297#102C23×C8911yescharacteristic
1298#102C23×C8911yescharacteristic
1299#102C23×C8911yescharacteristic
1300#102C23×C8911yescharacteristic
1301#102C23×C8911yescharacteristic
1302#102C23×C8911yescharacteristic
1303#102C23×C8911yescharacteristic
1304#102C23×C8911yescharacteristic
1305#102C23×C8911yescharacteristic
1306#102C23×C8911yescharacteristic
1307#102C23×C8911yescharacteristic
1308#102C23×C8911yescharacteristic
1309#102C23×C8911yescharacteristic
1310C22⋊C8C23×C8911yescharacteristic
1311C22⋊C8C23×C8911yescharacteristic
1312C22⋊C8C23×C8911yescharacteristic
1313C22⋊C8C23×C8911yescharacteristic
1314C22⋊C8C23×C8911yescharacteristic
1315C22⋊C8C23×C8911yescharacteristic
1316#97C23×C8911yescharacteristic
1317#97C23×C8911yescharacteristic
1318#97C23×C8911yescharacteristic
1319#97C23×C8911yescharacteristic
1320#97C23×C8911yescharacteristic
1321#97C23×C8911yescharacteristic
1322C4×C8C23×C8911yescharacteristic
1323C4×C8C23×C8911yescharacteristic
1324C4×C8C23×C8911yescharacteristic
1325C4×C8C23×C8911yescharacteristic
1326C24—21no—
1327#41—41no—
1328#41—41no—
1329#41—41no—
1330#41—41no—
1331#41—41no—
1332#41—41no—
1333#41—41no—
1334#41—41no—
1335#41—82no—
1336C2×Q8—21no—
1337C2×Q8—21no—
1338C2×Q8—21no—
1339C2×Q8—21no—
1340C2×Q8—21no—
1341C2×Q8—21no—
1342C2×Q8—21no—
1343C2×Q8—41no—
1344C2×Q8—41no—
1345C2×Q8—82no—
1346C2×Q8—82no—
1347C2×Q8C2×D4×C8911yescharacteristic
1348C2×Q8C24×C8911yescharacteristic
1349C2×Q8C24×C8911yescharacteristic
1350C2×Q8C24×C8911yescharacteristic
1351C2×Q8C24×C8911yescharacteristic
1352C2×D4—21no—
1353C2×D4—21no—
1354C2×D4—21no—
1355C2×D4—21no—
1356C2×D4—21no—
1357C2×D4—21no—
1358C2×D4—21no—
1359C2×D4—21no—
1360C2×D4—21no—
1361C2×D4—21no—
1362C2×D4—21no—
1363C2×D4—21no—
1364C2×D4—21no—
1365C2×D4—21no—
1366C2×D4—21no—
1367C2×D4—41no—
1368C2×D4—41no—
1369C2×D4C2×D4×C8911yescharacteristic
1370C2×D4C2×D4×C8911yescharacteristic
1371C2×D4C2×D4×C8911yescharacteristic
1372C2×D4C24×C8911yescharacteristic
1373C2×D4C24×C8911yescharacteristic
1374C2×D4C24×C8911yescharacteristic
1375C2×D4C24×C8911yescharacteristic
1376C22×C4—21no—
1377C22×C4—21no—
1378C22×C4—21no—
1379C22×C4—21no—
1380C22×C4—21no—
1381C22×C4—21no—
1382C22×C4—21no—
1383C22×C4—21no—
1384C22×C4—21no—
1385C22×C4—21no—
1386C22×C4—21no—
1387C22×C4—21no—
1388C22×C4—21no—
1389C22×C4—21no—
1390C22×C4—21no—
1391C22×C4C2×D4×C8911yescharacteristic
1392C22×C4C2×D4×C8911yescharacteristic
1393C22×C4C24×C8911yescharacteristic
1394C22×C4C24×C8911yescharacteristic
1395C22×C4C24×C8911yescharacteristic
1396Q16—41no—
1397Q16—41no—
1398Q16—41no—
1399SD16—41no—
1400SD16—41no—
1401SD16—41no—
1402SD16—41no—
1403SD16—41no—
1404SD16—41no—
1405D8—41no—
1406D8—41no—
1407D8—41no—
1408M16—41no—
1409M16—41no—
1410M16—41no—
1411M16—41no—
1412C2×C8—41no—
1413C2×C8—41no—
1414C2×C8C24×C8911yescharacteristic
1415C2×C8C24×C8911yescharacteristic
1416C2×C8C24×C8911yescharacteristic
1417C2×C8C24×C8911yescharacteristic
1418C2×C8C24×C8911yescharacteristic
1419C2×C8C24×C8911yescharacteristic
1420C2×C8C24×C8911yescharacteristic
1421C2×C8C24×C8911yescharacteristic
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
1428C4⋊C4—21no—
1429C4⋊C4—21no—
1430C4⋊C4—21no—
1431C4⋊C4—21no—
1432C4⋊C4—21no—
1433C4⋊C4—21no—
1434C4⋊C4—21no—
1435C4⋊C4—21no—
1436C4⋊C4—21no—
1437C4⋊C4—21no—
1438C4⋊C4—21no—
1439C4⋊C4—21no—
1440C4⋊C4—21no—
1441C4⋊C4—21no—
1442C4⋊C4—21no—
1443C4⋊C4—21no—
1444C4⋊C4—21no—
1445C4⋊C4—21no—
1446C4⋊C4—21no—
1447C4⋊C4—21no—
1448C4⋊C4—21no—
1449C4⋊C4—21no—
1450C4⋊C4—21no—
1451C4⋊C4—21no—
1452C4⋊C4—21no—
1453C4⋊C4—21no—
1454C4⋊C4—21no—
1455C4⋊C4—21no—
1456C4⋊C4C2×D4×C8911yescharacteristic
1457C4⋊C4C2×D4×C8911yescharacteristic
1458C4⋊C4C2×D4×C8911yescharacteristic
1459C4⋊C4C2×D4×C8911yescharacteristic
1460C4⋊C4C2×D4×C8911yescharacteristic
1461C4⋊C4C2×D4×C8911yescharacteristic
1462C4⋊C4C2×D4×C8911yescharacteristic
1463C4⋊C4C2×D4×C8911yescharacteristic
1464C4⋊C4C2×D4×C8911yescharacteristic
1465C4⋊C4C2×D4×C8911yescharacteristic
1466C4⋊C4C24×C8911yescharacteristic
1467C4⋊C4C24×C8911yescharacteristic
1468C4⋊C4C24×C8911yescharacteristic
1469C4⋊C4C24×C8911yescharacteristic
1470C4⋊C4C24×C8911yescharacteristic
1471C4⋊C4C24×C8911yescharacteristic
1472C4⋊C4C24×C8911yescharacteristic
1473C4⋊C4C24×C8911yescharacteristic
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—21no—
1479C22⋊C4—21no—
1480C22⋊C4—21no—
1481C22⋊C4—21no—
1482C22⋊C4—21no—
1483C22⋊C4—21no—
1484C22⋊C4—21no—
1485C22⋊C4—21no—
1486C22⋊C4—21no—
1487C22⋊C4—21no—
1488C22⋊C4—21no—
1489C22⋊C4—21no—
1490C22⋊C4—21no—
1491C22⋊C4—21no—
1492C22⋊C4—21no—
1493C22⋊C4—21no—
1494C22⋊C4—21no—
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—21no—
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—21no—
1503C22⋊C4—21no—
1504C22⋊C4—21no—
1505C22⋊C4—21no—
1506C22⋊C4C2×D4×C8911yescharacteristic
1507C22⋊C4C2×D4×C8911yescharacteristic
1508C22⋊C4C2×D4×C8911yescharacteristic
1509C22⋊C4C2×D4×C8911yescharacteristic
1510C22⋊C4C2×D4×C8911yescharacteristic
1511C22⋊C4C2×D4×C8911yescharacteristic
1512C22⋊C4C2×D4×C8911yescharacteristic
1513C22⋊C4C2×D4×C8911yescharacteristic
1514C22⋊C4C2×D4×C8911yescharacteristic
1515C22⋊C4C2×D4×C8911yescharacteristic
1516C42—21no—
1517C42—21no—
1518C42—21no—
1519C42—21no—
1520C42—21no—
1521C42—21no—
1522C42—21no—
1523C42—21no—
1524C42C2×D4×C8911yescharacteristic
1525C42C2×D4×C8911yescharacteristic
1526C42C24×C8911yescharacteristic
1527C42C24×C8911yescharacteristic
1528C42C24×C8911yescharacteristic
1529C42C24×C8911yescharacteristic
1530C23—21no—
1531C23—21no—
1532C23—21no—
1533C23—21no—
1534C23—81no—
1535C23—81no—
1536C23—81no—
1537C23C22×D4×C8911yescharacteristic
1538C23C22×D4×C8911yescharacteristic
1539C23C22×D4×C8911yescharacteristic
1540Q8—21no—
1541Q8—21no—
1542Q8—21no—
1543Q8—21no—
1544Q8—21no—
1545Q8—21no—
1546Q8—21no—
1547Q8—21no—
1548Q8—41no—
1549Q8—42no—
1550Q8—42no—
1551Q8—81no—
1552Q8—81no—
1553Q8—81no—
1554Q8—81no—
1555Q8—81no—
1556D4—21no—
1557D4—21no—
1558D4—21no—
1559D4—21no—
1560D4—21no—
1561D4—21no—
1562D4—21no—
1563D4—21no—
1564D4—41no—
1565D4—41no—
1566D4—41no—
1567D4—42no—
1568D4—81no—
1569D4—81no—
1570D4—81no—
1571D4—81no—
1572D4—81no—
1573D4—81no—
1574D4—81no—
1575D4—81no—
1576D4—81no—
1577D4—81no—
1578D4—81no—
1579D4—81no—
1580D4—81no—
1581D4—81no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—41no—
1601C2×C4—41no—
1602C2×C4—42no—
1603C2×C4—81no—
1604C2×C4—81no—
1605C2×C4—81no—
1606C2×C4—81no—
1607C2×C4—81no—
1608C2×C4—81no—
1609C2×C4—81no—
1610C2×C4—81no—
1611C2×C4—81no—
1612C2×C4—81no—
1613C2×C4—81no—
1614C2×C4—81no—
1615C2×C4—81no—
1616C2×C4—81no—
1617C2×C4C22×D4×C8911yescharacteristic
1618C2×C4C22×D4×C8911yescharacteristic
1619C2×C4C22×D4×C8911yescharacteristic
1620C2×C4C22×D4×C8911yescharacteristic
1621C2×C4C22×D4×C8911yescharacteristic
1622C2×C4C22×D4×C8911yescharacteristic
1623C2×C4C22×D4×C8911yescharacteristic
1624C2×C4C22×D4×C8911yescharacteristic
1625C2×C4C22×D4×C8911yescharacteristic
1626C2×C4C22×D4×C8911yescharacteristic
1627C2×C4C22×D4×C8911yescharacteristic
1628C2×C4C25×C8911yescharacteristic
1629C8—21no—
1630C8—21no—
1631C8—21no—
1632C8—21no—
1633C8—21no—
1634C8—21no—
1635C8—21no—
1636C8—21no—
1637C22—21no—
1638C22—21no—
1639C22—21no—
1640C22—21no—
1641C22—21no—
1642C22—21no—
1643C22—21no—
1644C22—21no—
1645C22—21no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—41no—
1658C22—162no—
1659C22C23×D4×C8911yescharacteristic
1660C4—21no—
1661C4—21no—
1662C4—21no—
1663C4—21no—
1664C4—21no—
1665C4—21no—
1666C4—21no—
1667C4—21no—
1668C4—21no—
1669C4—21no—
1670C4—21no—
1671C4—41no—
1672C4—41no—
1673C4—41no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—41no—
1681C4—41no—
1682C4—41no—
1683C4#585×C8911yescharacteristic
1684C4#585×C8911yescharacteristic
1685C2—41no—
1686C2—41no—
1687C2—41no—
1688C2—81no—
1689C2—81no—
1690C2—81no—
1691C2—81no—
1692C2C89×#350011yescharacteristic
1693C2C89×#358511yescharacteristic
1694C2C89×#358611yescharacteristic
subgroupG/H
center, socleC22×C89C23×D4
commutator, Frattini, cosocleC2×C4C25×C89
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C89 ◁ #529×C89 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C89×#3562C2semidirect
2. C89×#3552C2semidirect
3. C89×#3377C2semidirect
4. C89×#3373C2semidirect
5. C89×#3371C2semidirect
6. C89×#3367C2semidirect
7. C89×#3333C2semidirect
8. C89×#3331C2semidirect
9. C89×#3326C2semidirect
10. C89×#3322C2semidirect
11. C89×#3316C2semidirect
12. C89×#3314C2semidirect
13. C89×#3313C2semidirect
14. C89×#3311C2semidirect
15. C89×#3309C2semidirect
16. C89×#3308C2semidirect
17. C89×#3307C2semidirect
18. C89×#3306C2semidirect
19. C89×#3242C2semidirect
20. C89×#3241C2semidirect
21. C89×#3238C2semidirect
22. C89×#3225C2semidirect
23. C89×#3224C2semidirect
24. C89×#3219C2semidirect
25. C89×#3183C2semidirect
26. C89×#3179C2semidirect
27. C89×#3178C2semidirect
28. C89×#3141C2semidirect
29. C89×#3137C2semidirect
30. C89×#3136C2semidirect
31. C89×#2967C2semidirect
37. #557×C89C22semidirect
41. #554×C89C22semidirect
44. #553×C89C22semidirect
48. D4×Q8×C89C22semidirect
57. #544×C89C22semidirect
59. #542×C89C22semidirect
73. C2×C4⋊Q8×C89C22semidirect
76. #529×C89C22semidirect
77. #501×C89C22semidirect
78. #501×C89C22semidirect
79. #499×C89C22semidirect
80. #497×C89C22semidirect
83. #491×C89C22semidirect
84. #491×C89C22semidirect
93. #489×C89C22semidirect
94. #489×C89C22semidirect
98. #488×C89C22semidirect
99. #487×C89C22semidirect
100. #487×C89C22semidirect
101. #487×C89C22semidirect
109. #483×C89C22semidirect
110. #483×C89C22semidirect
112. #482×C89C22semidirect
116. #480×C89C22semidirect
117. #479×C89C22semidirect
118. #479×C89C22semidirect
120. #478×C89C22semidirect
121. #477×C89C22semidirect
122. #477×C89C22semidirect
123. #477×C89C22semidirect
126. #476×C89C22semidirect
127. #475×C89C22semidirect
130. #470×C89C22semidirect
135. #468×C89C22semidirect
136. #468×C89C22semidirect
138. #466×C89C22semidirect
144. #464×C89C22semidirect
148. #463×C89C22semidirect
149. #462×C89C22semidirect
150. #461×C89C22semidirect
156. #452×C89C22semidirect
157. #451×C89C22semidirect
162. #449×C89C22semidirect
163. #448×C89C22semidirect
165. #446×C89C22semidirect
166. #446×C89C22semidirect
168. #442×C89C22semidirect
169. #441×C89C22semidirect
170. #441×C89C22semidirect
173. #440×C89C22semidirect
174. #440×C89C22semidirect
175. C4×Q16×C89C22semidirect
176. C4×SD16×C89C22semidirect
177. C4×SD16×C89C22semidirect
180. #436×C89C22semidirect
184. #435×C89C22semidirect
186. #433×C89C22semidirect
187. #432×C89C22semidirect
188. #419×C89C22semidirect
194. #417×C89C22semidirect
195. #417×C89C22semidirect
198. C2×#103×C89C22semidirect
201. #405×C89C22semidirect
202. C4×M16×C89C22semidirect
837. #62566C89direct (N × H)
848. #3562C2×C89semidirect
849. #3552C2×C89semidirect
850. #3377C2×C89semidirect
851. #3373C2×C89semidirect
852. #3371C2×C89semidirect
853. #3367C2×C89semidirect
854. #3333C2×C89semidirect
855. #3331C2×C89semidirect
856. #3326C2×C89semidirect
857. #3322C2×C89semidirect
858. #3316C2×C89semidirect
859. #3314C2×C89semidirect
860. #3313C2×C89semidirect
861. #3311C2×C89semidirect
862. #3309C2×C89semidirect
863. #3308C2×C89semidirect
864. #3307C2×C89semidirect
865. #3306C2×C89semidirect
866. #3242C2×C89semidirect
867. #3241C2×C89semidirect
868. #3238C2×C89semidirect
869. #3225C2×C89semidirect
870. #3224C2×C89semidirect
871. #3219C2×C89semidirect
872. #3183C2×C89semidirect
873. #3179C2×C89semidirect
874. #3178C2×C89semidirect
875. #3141C2×C89semidirect
876. #3137C2×C89semidirect
877. #3136C2×C89semidirect
878. #2967C2×C89semidirect
879. C89#62566direct (N × H)
885. #557C22×C89semidirect
889. #554C22×C89semidirect
892. #553C22×C89semidirect
896. D4×Q8C22×C89semidirect
905. #544C22×C89semidirect
907. #542C22×C89semidirect
921. C2×C4⋊Q8C22×C89semidirect
924. #529C22×C89semidirect
925. #501C22×C89semidirect
926. #501C22×C89semidirect
927. #499C22×C89semidirect
928. #497C22×C89semidirect
931. #491C22×C89semidirect
932. #491C22×C89semidirect
941. #489C22×C89semidirect
942. #489C22×C89semidirect
946. #488C22×C89semidirect
947. #487C22×C89semidirect
948. #487C22×C89semidirect
949. #487C22×C89semidirect
957. #483C22×C89semidirect
958. #483C22×C89semidirect
960. #482C22×C89semidirect
964. #480C22×C89semidirect
965. #479C22×C89semidirect
966. #479C22×C89semidirect
968. #478C22×C89semidirect
969. #477C22×C89semidirect
970. #477C22×C89semidirect
971. #477C22×C89semidirect
974. #476C22×C89semidirect
975. #475C22×C89semidirect
978. #470C22×C89semidirect
983. #468C22×C89semidirect
984. #468C22×C89semidirect
986. #466C22×C89semidirect
992. #464C22×C89semidirect
996. #463C22×C89semidirect
997. #462C22×C89semidirect
998. #461C22×C89semidirect
1004. #452C22×C89semidirect
1005. #451C22×C89semidirect
1010. #449C22×C89semidirect
1011. #448C22×C89semidirect
1013. #446C22×C89semidirect
1014. #446C22×C89semidirect
1016. #442C22×C89semidirect
1017. #441C22×C89semidirect
1018. #441C22×C89semidirect
1021. #440C22×C89semidirect
1022. #440C22×C89semidirect
1023. C4×Q16C22×C89semidirect
1024. C4×SD16C22×C89semidirect
1025. C4×SD16C22×C89semidirect
1028. #436C22×C89semidirect
1032. #435C22×C89semidirect
1034. #433C22×C89semidirect
1035. #432C22×C89semidirect
1036. #419C22×C89semidirect
1042. #417C22×C89semidirect
1043. #417C22×C89semidirect
1046. C2×#103C22×C89semidirect
1049. #405C22×C89semidirect
1050. C4×M16C22×C89semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C89×#35622
C89×#35522
C89×#33772
C89×#33732
C89×#33712
C89×#33672
C89×#33332
C89×#33312
C89×#33262
C89×#33222
C89×#33162
C89×#33142
C89×#33132
C89×#33112
C89×#33092
C89×#33082
C89×#33072
C89×#33062
C89×#32422
C89×#32412
C89×#32382
C89×#32252
C89×#32242
C89×#32192
C89×#31832
C89×#31792
C89×#31782
C89×#31412
C89×#31372
C89×#31362
C89×#29672
#6256689