Finite Group Databasebeta

← C89×#62025 #36439873

Subgroups — C89×#62025 #36439873

Order 22784.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3554C211yesmaximal, characteristic, complemented
2C89×#3524C211yesmaximal, characteristic, complemented
3C89×#3403C211yesmaximal, characteristic, complemented
4C89×#3400C211yesmaximal, characteristic, complemented
5C89×#3374C211yesmaximal, characteristic, complemented
6C89×#3371C211yesmaximal, characteristic, complemented
7C89×#3321C211yesmaximal, characteristic, complemented
8C89×#3320C211yesmaximal, characteristic, complemented
9C89×#3315C211yesmaximal, characteristic, complemented
10C89×#3309C211yesmaximal, characteristic, complemented
11C89×#3303C211yesmaximal, characteristic, complemented
12C89×#3300C211yesmaximal, characteristic, complemented
13C89×#3285C211yesmaximal, characteristic, complemented
14C89×#3284C211yesmaximal, characteristic, complemented
15C89×#3271C211yesmaximal, characteristic, complemented
16C89×#3271C211yesmaximal, characteristic, complemented
17C89×#3270C211yesmaximal, characteristic, complemented
18C89×#3269C211yesmaximal, characteristic, complemented
19C89×#3263C211yesmaximal, characteristic, complemented
20C89×#3257C211yesmaximal, characteristic, complemented
21C89×#3248C211yesmaximal, characteristic, complemented
22C89×#3225C211yesmaximal, characteristic, complemented
23C89×#3221C211yesmaximal, characteristic, complemented
24C89×#3219C211yesmaximal, characteristic, complemented
25C89×#3124C211yesmaximal, characteristic, complemented
26C89×#3121C211yesmaximal, characteristic, complemented
27C89×#3116C211yesmaximal, characteristic, complemented
28C89×#3046C211yesmaximal, characteristic, complemented
29C89×#3044C211yesmaximal, characteristic, complemented
30C89×#3035C211yesmaximal, characteristic, complemented
31C89×#2992C211yesmaximal, characteristic, complemented
32C2×#137×C89C2211yescharacteristic
33C2×#137×C89C2211yescharacteristic
34C2×#135×C89C2211yescharacteristic
35C2×#135×C89C2211yescharacteristic
36C2×#135×C89C2211yescharacteristic
37C22×Q16×C89C2211yescharacteristic
38#562×C89—21no—
39#562×C89—21no—
40#559×C89—21no—
41#559×C89—21no—
42#559×C89C2211yescharacteristic
43#559×C89C2211yescharacteristic
44#557×C89C2211yescharacteristic
45#557×C89C2211yescharacteristic
46#555×C89—21no—
47#555×C89C2211yescharacteristic
48#554×C89—21no—
49#553×C89—21no—
50#553×C89C2211yescharacteristic
51#552×C89—21no—
52#552×C89C2211yescharacteristic
53#550×C89C2211yescharacteristic
54#550×C89C2211yescharacteristic
55D4×Q8×C89C2211yescharacteristic
56#548×C89C2211yescharacteristic
57#548×C89C2211yescharacteristic
58#548×C89C2211yescharacteristic
59#548×C89C2211yescharacteristic
60#547×C89C2211yescharacteristic
61#547×C89C2211yescharacteristic
62#542×C89—21no—
63#542×C89—21no—
64#542×C89C2211yescharacteristic
65#542×C89C2211yescharacteristic
66#542×C89C2211yescharacteristic
67#540×C89—21no—
68#540×C89—21no—
69#540×C89C2211yescharacteristic
70#539×C89—21no—
71#539×C89—21no—
72#536×C89C2211yescharacteristic
73#536×C89C2211yescharacteristic
74#533×C89C2211yescharacteristic
75#532×C89C2211yescharacteristic
76#529×C89—21no—
77#529×C89—21no—
78#529×C89C2211yescharacteristic
79#529×C89C2211yescharacteristic
80#520×C89C2211yescharacteristic
81#519×C89C2211yescharacteristic
82C4×#41×C89C2211yescharacteristic
83#497×C89C2211yescharacteristic
84#497×C89C2211yescharacteristic
85#496×C89C2211yescharacteristic
86#496×C89C2211yescharacteristic
87#495×C89C2211yescharacteristic
88#492×C89C2211yescharacteristic
89#491×C89C2211yescharacteristic
90#491×C89C2211yescharacteristic
91#490×C89C2211yescharacteristic
92#489×C89C2211yescharacteristic
93#488×C89C2211yescharacteristic
94#487×C89C2211yescharacteristic
95#485×C89C2211yescharacteristic
96#485×C89C2211yescharacteristic
97#485×C89C2211yescharacteristic
98#484×C89C2211yescharacteristic
99#482×C89C2211yescharacteristic
100#480×C89C2211yescharacteristic
101#479×C89C2211yescharacteristic
102#479×C89C2211yescharacteristic
103#479×C89C2211yescharacteristic
104#478×C89C2211yescharacteristic
105#477×C89C2211yescharacteristic
106#476×C89C2211yescharacteristic
107#476×C89C2211yescharacteristic
108#475×C89C2211yescharacteristic
109#475×C89C2211yescharacteristic
110#474×C89C2211yescharacteristic
111#470×C89C2211yescharacteristic
112#469×C89C2211yescharacteristic
113#469×C89C2211yescharacteristic
114#468×C89C2211yescharacteristic
115#467×C89C2211yescharacteristic
116#467×C89C2211yescharacteristic
117#466×C89C2211yescharacteristic
118#465×C89C2211yescharacteristic
119#465×C89C2211yescharacteristic
120#465×C89C2211yescharacteristic
121#465×C89C2211yescharacteristic
122#465×C89C2211yescharacteristic
123#464×C89C2211yescharacteristic
124#464×C89C2211yescharacteristic
125#464×C89C2211yescharacteristic
126#464×C89C2211yescharacteristic
127#464×C89C2211yescharacteristic
128#464×C89C2211yescharacteristic
129#464×C89C2211yescharacteristic
130#464×C89C2211yescharacteristic
131#464×C89C2211yescharacteristic
132#464×C89C2211yescharacteristic
133#463×C89C2211yescharacteristic
134#463×C89C2211yescharacteristic
135#463×C89C2211yescharacteristic
136#463×C89C2211yescharacteristic
137#463×C89C2211yescharacteristic
138#463×C89C2211yescharacteristic
139#462×C89C2211yescharacteristic
140#462×C89C2211yescharacteristic
141#462×C89C2211yescharacteristic
142#462×C89C2211yescharacteristic
143#462×C89C2211yescharacteristic
144#462×C89C2211yescharacteristic
145#461×C89C2211yescharacteristic
146#461×C89C2211yescharacteristic
147#461×C89C2211yescharacteristic
148#461×C89C2211yescharacteristic
149#460×C89C2211yescharacteristic
150#460×C89C2211yescharacteristic
151#459×C89C2211yescharacteristic
152#459×C89C2211yescharacteristic
153#452×C89C2211yescharacteristic
154#452×C89C2211yescharacteristic
155#452×C89C2211yescharacteristic
156#452×C89C2211yescharacteristic
157#452×C89C2211yescharacteristic
158#452×C89C2211yescharacteristic
159#451×C89C2211yescharacteristic
160#451×C89C2211yescharacteristic
161#449×C89C2211yescharacteristic
162#449×C89C2211yescharacteristic
163#449×C89C2211yescharacteristic
164#449×C89C2211yescharacteristic
165#449×C89C2211yescharacteristic
166#449×C89C2211yescharacteristic
167#448×C89C2211yescharacteristic
168#448×C89C2211yescharacteristic
169#448×C89C2211yescharacteristic
170#448×C89C2211yescharacteristic
171#446×C89C2211yescharacteristic
172#446×C89C2211yescharacteristic
173#441×C89C2211yescharacteristic
174#441×C89C2211yescharacteristic
175#441×C89C2211yescharacteristic
176#440×C89C2211yescharacteristic
177#440×C89C2211yescharacteristic
178#440×C89C2211yescharacteristic
179#440×C89C2211yescharacteristic
180#440×C89C2211yescharacteristic
181C4×Q16×C89C2211yescharacteristic
182C4×Q16×C89C2211yescharacteristic
183C4×SD16×C89C2211yescharacteristic
184C4×D8×C89C2211yescharacteristic
185#435×C89C2211yescharacteristic
186#435×C89C2211yescharacteristic
187#435×C89C2211yescharacteristic
188#435×C89C2211yescharacteristic
189C8×D4×C89C2211yescharacteristic
190C8×D4×C89C2211yescharacteristic
191#433×C89C2211yescharacteristic
192#433×C89C2211yescharacteristic
193#432×C89C2211yescharacteristic
194#424×C89C2211yescharacteristic
195#424×C89C2211yescharacteristic
196C2×C4⋊C8×C89C2211yescharacteristic
197#419×C89C2211yescharacteristic
198#417×C89C2211yescharacteristic
199#416×C89C2211yescharacteristic
200#416×C89C2211yescharacteristic
201#416×C89C2211yescharacteristic
202C2×#103×C89C2211yescharacteristic
203C2×#41×C89C2311yescharacteristic
204C2×#41×C89C2311yescharacteristic
205C2×#41×C89C2311yescharacteristic
206C2×#41×C89C2311yescharacteristic
207C2×#41×C89C2311yescharacteristic
208C2×#41×C89C2311yescharacteristic
209C22×Q8×C89C2311yescharacteristic
210C22×Q8×C89C2311yescharacteristic
211C22×Q8×C89C2311yescharacteristic
212#137×C89—42no—
213#137×C89—42no—
214#135×C89—42no—
215#135×C89—42no—
216#135×C89—42no—
217C2×Q16×C89—42no—
218C2×Q16×C89C2311yescharacteristic
219C2×Q16×C89C2311yescharacteristic
220C2×Q16×C89C2311yescharacteristic
221C2×Q16×C89C2311yescharacteristic
222C2×Q16×C89C2311yescharacteristic
223C2×Q16×C89C2311yescharacteristic
224C2×Q16×C89C2311yescharacteristic
225C2×Q16×C89C2311yescharacteristic
226C2×SD16×C89C2311yescharacteristic
227C2×SD16×C89C2311yescharacteristic
228C2×SD16×C89C2311yescharacteristic
229C2×SD16×C89C2311yescharacteristic
230C2×SD16×C89C2311yescharacteristic
231C2×SD16×C89C2311yescharacteristic
232C2×SD16×C89C2311yescharacteristic
233C2×SD16×C89C2311yescharacteristic
234C2×SD16×C89C2311yescharacteristic
235C2×SD16×C89C2311yescharacteristic
236C2×SD16×C89C2311yescharacteristic
237C2×SD16×C89C2311yescharacteristic
238C2×D8×C89C2311yescharacteristic
239C2×D8×C89C2311yescharacteristic
240C2×D8×C89C2311yescharacteristic
241C2×D8×C89C2311yescharacteristic
242C2×M16×C89C2311yescharacteristic
243C2×M16×C89C2311yescharacteristic
244C22×C8×C89C2311yescharacteristic
245C22×C8×C89C2311yescharacteristic
246C22×C8×C89C2311yescharacteristic
247C22×C8×C89C2311yescharacteristic
248C4⋊Q8×C89—21no—
249C4⋊Q8×C89—21no—
250C4⋊Q8×C89C2311yescharacteristic
251C4⋊Q8×C89C2311yescharacteristic
252C4⋊Q8×C89C2311yescharacteristic
253C4⋊Q8×C89C2311yescharacteristic
254C4⋊Q8×C89C2311yescharacteristic
255C4⋊Q8×C89C2311yescharacteristic
256#127×C89—21no—
257#127×C89—21no—
258#127×C89C2311yescharacteristic
259#127×C89C2311yescharacteristic
260#126×C89—21no—
261#126×C89—21no—
262#126×C89—21no—
263#126×C89—21no—
264#126×C89—21no—
265#126×C89—21no—
266#126×C89D411yescharacteristic
267#126×C89D411yescharacteristic
268#125×C89—21no—
269#125×C89—21no—
270#125×C89—21no—
271#125×C89—21no—
272#125×C89—21no—
273#125×C89—21no—
274#125×C89—21no—
275#125×C89D411yescharacteristic
276#125×C89C2311yescharacteristic
277#125×C89C2311yescharacteristic
278#124×C89—21no—
279#124×C89—21no—
280#124×C89—21no—
281#124×C89—21no—
282#124×C89—21no—
283#124×C89—21no—
284#124×C89—21no—
285#124×C89—21no—
286#124×C89—21no—
287#124×C89—21no—
288#124×C89—21no—
289#124×C89D411yescharacteristic
290#124×C89C2311yescharacteristic
291#124×C89C2311yescharacteristic
292#124×C89C2311yescharacteristic
293#124×C89C2311yescharacteristic
294#124×C89C2311yescharacteristic
295#124×C89C2311yescharacteristic
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×C89—21no—
305#123×C89—21no—
306#123×C89—21no—
307#123×C89—21no—
308#123×C89—21no—
309#123×C89—21no—
310#123×C89—21no—
311#123×C89—21no—
312#123×C89—21no—
313#123×C89—21no—
314#123×C89—21no—
315#123×C89—21no—
316#123×C89D411yescharacteristic
317#123×C89D411yescharacteristic
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×C89—21no—
326C22⋊Q8×C89—21no—
327C22⋊Q8×C89—21no—
328C22⋊Q8×C89—21no—
329C22⋊Q8×C89—21no—
330C22⋊Q8×C89—21no—
331C22⋊Q8×C89—21no—
332C22⋊Q8×C89D411yescharacteristic
333C22⋊Q8×C89C2311yescharacteristic
334C22⋊Q8×C89C2311yescharacteristic
335C22⋊Q8×C89C2311yescharacteristic
336C22⋊Q8×C89C2311yescharacteristic
337C22⋊Q8×C89C2311yescharacteristic
338C22⋊Q8×C89C2311yescharacteristic
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×C89—21no—
348#121×C89—21no—
349#121×C89—21no—
350#121×C89—21no—
351#121×C89—21no—
352#121×C89—21no—
353#121×C89—21no—
354#121×C89—21no—
355#121×C89D411yescharacteristic
356#121×C89C2311yescharacteristic
357#121×C89C2311yescharacteristic
358#121×C89C2311yescharacteristic
359#121×C89C2311yescharacteristic
360#121×C89C2311yescharacteristic
361#121×C89C2311yescharacteristic
362C4×Q8×C89—21no—
363C4×Q8×C89—21no—
364C4×Q8×C89—21no—
365C4×Q8×C89—21no—
366C4×Q8×C89—21no—
367C4×Q8×C89C2311yescharacteristic
368C4×Q8×C89C2311yescharacteristic
369C4×Q8×C89C2311yescharacteristic
370C4×Q8×C89C2311yescharacteristic
371C4×Q8×C89C2311yescharacteristic
372C4×Q8×C89C2311yescharacteristic
373C4×Q8×C89C2311yescharacteristic
374C4×Q8×C89C2311yescharacteristic
375C4×Q8×C89C2311yescharacteristic
376C4×Q8×C89C2311yescharacteristic
377C4×Q8×C89C2311yescharacteristic
378C4×D4×C89—21no—
379C4×D4×C89—21no—
380C4×D4×C89—21no—
381C4×D4×C89—21no—
382C4×D4×C89—21no—
383C4×D4×C89—21no—
384C4×D4×C89—21no—
385C4×D4×C89—21no—
386C4×D4×C89—21no—
387C4×D4×C89—21no—
388C4×D4×C89—21no—
389C4×D4×C89—21no—
390C4×D4×C89—21no—
391C4×D4×C89—21no—
392C4×D4×C89—21no—
393C4×D4×C89—21no—
394C4×D4×C89—21no—
395C4×D4×C89C2311yescharacteristic
396C4×D4×C89C2311yescharacteristic
397C4×D4×C89C2311yescharacteristic
398C4×D4×C89C2311yescharacteristic
399C4×D4×C89C2311yescharacteristic
400C4×D4×C89C2311yescharacteristic
401C4×D4×C89C2311yescharacteristic
402C4×D4×C89C2311yescharacteristic
403C4×D4×C89C2311yescharacteristic
404#117×C89—21no—
405#117×C89—21no—
406#117×C89—21no—
407#117×C89—21no—
408#117×C89—21no—
409#117×C89—21no—
410#117×C89—21no—
411#117×C89—21no—
412#117×C89C2311yescharacteristic
413#117×C89C2311yescharacteristic
414#117×C89C2311yescharacteristic
415#117×C89C2311yescharacteristic
416C2×C4⋊C4×C89—21no—
417C2×C4⋊C4×C89—21no—
418C2×C4⋊C4×C89—21no—
419C2×C4⋊C4×C89C2311yescharacteristic
420C2×C42×C89—21no—
421C2×C42×C89C2311yescharacteristic
422#107×C89C2311yescharacteristic
423#107×C89C2311yescharacteristic
424#107×C89C2311yescharacteristic
425#107×C89C2311yescharacteristic
426#106×C89C2311yescharacteristic
427#106×C89C2311yescharacteristic
428#106×C89C2311yescharacteristic
429#106×C89C2311yescharacteristic
430C4⋊C8×C89C2311yescharacteristic
431C4⋊C8×C89C2311yescharacteristic
432C4⋊C8×C89C2311yescharacteristic
433C4⋊C8×C89C2311yescharacteristic
434C4⋊C8×C89C2311yescharacteristic
435C4⋊C8×C89C2311yescharacteristic
436C4⋊C8×C89C2311yescharacteristic
437C4⋊C8×C89C2311yescharacteristic
438C4⋊C8×C89C2311yescharacteristic
439C4⋊C8×C89C2311yescharacteristic
440#103×C89C2311yescharacteristic
441#103×C89C2311yescharacteristic
442#103×C89C2311yescharacteristic
443#103×C89C2311yescharacteristic
444#103×C89C2311yescharacteristic
445#103×C89C2311yescharacteristic
446#103×C89C2311yescharacteristic
447#103×C89C2311yescharacteristic
448#103×C89C2311yescharacteristic
449#103×C89C2311yescharacteristic
450#103×C89C2311yescharacteristic
451#103×C89C2311yescharacteristic
452#103×C89C2311yescharacteristic
453#103×C89C2311yescharacteristic
454#103×C89C2311yescharacteristic
455#103×C89C2311yescharacteristic
456#103×C89C2311yescharacteristic
457#103×C89C2311yescharacteristic
458#103×C89C2311yescharacteristic
459#103×C89C2311yescharacteristic
460#102×C89C2311yescharacteristic
461#102×C89C2311yescharacteristic
462#102×C89C2311yescharacteristic
463#102×C89C2311yescharacteristic
464#102×C89C2311yescharacteristic
465#102×C89C2311yescharacteristic
466#102×C89C2311yescharacteristic
467#102×C89C2311yescharacteristic
468#102×C89C2311yescharacteristic
469#102×C89C2311yescharacteristic
470#102×C89C2311yescharacteristic
471#102×C89C2311yescharacteristic
472C22⋊C8×C89C2311yescharacteristic
473C22⋊C8×C89C2311yescharacteristic
474C22⋊C8×C89C2311yescharacteristic
475C22⋊C8×C89C2311yescharacteristic
476C22⋊C8×C89C2311yescharacteristic
477C22⋊C8×C89C2311yescharacteristic
478#97×C89C2311yescharacteristic
479#97×C89C2311yescharacteristic
480#97×C89C2311yescharacteristic
481#97×C89C2311yescharacteristic
482C4×C8×C89C2311yescharacteristic
483C4×C8×C89C2311yescharacteristic
484#41×C89—22no—
485#41×C89—22no—
486#41×C89—41no—
487#41×C89—41no—
488#41×C89—41no—
489#41×C89—41no—
490#41×C89—41no—
491#41×C89—41no—
492#41×C89—41no—
493#41×C89—41no—
494#41×C89—41no—
495#41×C89—41no—
496C2×Q8×C89—21no—
497C2×Q8×C89—21no—
498C2×Q8×C89—21no—
499C2×Q8×C89—21no—
500C2×Q8×C89—21no—
501C2×Q8×C89—22no—
502C2×Q8×C89—41no—
503C2×Q8×C89—41no—
504C2×Q8×C89—41no—
505C2×Q8×C89—41no—
506C2×Q8×C89—41no—
507C2×Q8×C89C2×D411yescharacteristic
508C2×Q8×C89C2411yescharacteristic
509C2×Q8×C89C2411yescharacteristic
510C2×Q8×C89C2411yescharacteristic
511C2×Q8×C89C2411yescharacteristic
512C2×Q8×C89C2411yescharacteristic
513C2×Q8×C89C2411yescharacteristic
514C2×D4×C89—21no—
515C2×D4×C89—21no—
516C2×D4×C89—21no—
517C2×D4×C89—21no—
518C2×D4×C89—21no—
519C2×D4×C89—21no—
520C2×D4×C89—21no—
521C2×D4×C89—21no—
522C2×D4×C89—21no—
523C2×D4×C89—21no—
524C2×D4×C89—21no—
525C2×D4×C89—21no—
526C2×D4×C89—21no—
527C2×D4×C89—21no—
528C2×D4×C89—21no—
529C2×D4×C89—21no—
530C2×D4×C89C2×D411yescharacteristic
531C2×D4×C89C2×D411yescharacteristic
532C2×D4×C89C2×D411yescharacteristic
533C2×D4×C89C2411yescharacteristic
534C2×D4×C89C2411yescharacteristic
535C2×D4×C89C2411yescharacteristic
536C2×D4×C89C2411yescharacteristic
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×C89—21no—
544C22×C4×C89—21no—
545C22×C4×C89—21no—
546C22×C4×C89—21no—
547C22×C4×C89—21no—
548C22×C4×C89—21no—
549C22×C4×C89—21no—
550C22×C4×C89—21no—
551C22×C4×C89—21no—
552C22×C4×C89—21no—
553C22×C4×C89C2×D411yescharacteristic
554C22×C4×C89C2×D411yescharacteristic
555C22×C4×C89C2411yescharacteristic
556C22×C4×C89C2411yescharacteristic
557C22×C4×C89C2411yescharacteristic
558Q16×C89—22no—
559Q16×C89—22no—
560Q16×C89—22no—
561Q16×C89—22no—
562Q16×C89—41no—
563Q16×C89—41no—
564Q16×C89—41no—
565Q16×C89—41no—
566SD16×C89—22no—
567SD16×C89—22no—
568SD16×C89—41no—
569SD16×C89—41no—
570SD16×C89—41no—
571SD16×C89—41no—
572SD16×C89—41no—
573SD16×C89—41no—
574SD16×C89—41no—
575SD16×C89—41no—
576SD16×C89—41no—
577SD16×C89—41no—
578D8×C89—41no—
579D8×C89—41no—
580D8×C89—41no—
581D8×C89—41no—
582M16×C89—41no—
583M16×C89—41no—
584C2×C8×C89—41no—
585C2×C8×C89—41no—
586C2×C8×C89—41no—
587C2×C8×C89—41no—
588C2×C8×C89C2411yescharacteristic
589C2×C8×C89C2411yescharacteristic
590C2×C8×C89C2411yescharacteristic
591C2×C8×C89C2411yescharacteristic
592C2×C8×C89C2411yescharacteristic
593C2×C8×C89C2411yescharacteristic
594C2×C8×C89C2411yescharacteristic
595C2×C8×C89C2411yescharacteristic
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×C89—21no—
609C4⋊C4×C89—21no—
610C4⋊C4×C89—21no—
611C4⋊C4×C89—21no—
612C4⋊C4×C89—21no—
613C4⋊C4×C89—21no—
614C4⋊C4×C89—21no—
615C4⋊C4×C89—21no—
616C4⋊C4×C89—21no—
617C4⋊C4×C89—21no—
618C4⋊C4×C89—21no—
619C4⋊C4×C89—21no—
620C4⋊C4×C89—21no—
621C4⋊C4×C89—21no—
622C4⋊C4×C89—21no—
623C4⋊C4×C89—21no—
624C4⋊C4×C89—21no—
625C4⋊C4×C89—21no—
626C4⋊C4×C89—21no—
627C4⋊C4×C89C2×D411yescharacteristic
628C4⋊C4×C89C2×D411yescharacteristic
629C4⋊C4×C89C2×D411yescharacteristic
630C4⋊C4×C89C2×D411yescharacteristic
631C4⋊C4×C89C2×D411yescharacteristic
632C4⋊C4×C89C2×D411yescharacteristic
633C4⋊C4×C89C2×D411yescharacteristic
634C4⋊C4×C89C2×D411yescharacteristic
635C4⋊C4×C89C2×D411yescharacteristic
636C4⋊C4×C89C2×D411yescharacteristic
637C4⋊C4×C89C2411yescharacteristic
638C4⋊C4×C89C2411yescharacteristic
639C4⋊C4×C89C2411yescharacteristic
640C4⋊C4×C89C2411yescharacteristic
641C4⋊C4×C89C2411yescharacteristic
642C4⋊C4×C89C2411yescharacteristic
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×C89—21no—
659C22⋊C4×C89—21no—
660C22⋊C4×C89—21no—
661C22⋊C4×C89—21no—
662C22⋊C4×C89—21no—
663C22⋊C4×C89—21no—
664C22⋊C4×C89—21no—
665C22⋊C4×C89—21no—
666C22⋊C4×C89—21no—
667C22⋊C4×C89—21no—
668C22⋊C4×C89—21no—
669C22⋊C4×C89—21no—
670C22⋊C4×C89—21no—
671C22⋊C4×C89—21no—
672C22⋊C4×C89—21no—
673C22⋊C4×C89—21no—
674C22⋊C4×C89—21no—
675C22⋊C4×C89C2×D411yescharacteristic
676C22⋊C4×C89C2×D411yescharacteristic
677C22⋊C4×C89C2×D411yescharacteristic
678C22⋊C4×C89C2×D411yescharacteristic
679C22⋊C4×C89C2×D411yescharacteristic
680C22⋊C4×C89C2×D411yescharacteristic
681C22⋊C4×C89C2×D411yescharacteristic
682C22⋊C4×C89C2×D411yescharacteristic
683C22⋊C4×C89C2×D411yescharacteristic
684C22⋊C4×C89C2×D411yescharacteristic
685C42×C89—21no—
686C42×C89—21no—
687C42×C89—21no—
688C42×C89—21no—
689C42×C89—21no—
690C42×C89—21no—
691C42×C89—21no—
692C42×C89—21no—
693C42×C89—21no—
694C42×C89—21no—
695C42×C89—21no—
696C42×C89—21no—
697C42×C89C2×D411yescharacteristic
698C42×C89C2×D411yescharacteristic
699C42×C89C2411yescharacteristic
700C42×C89C2411yescharacteristic
701C42×C89C2411yescharacteristic
702C42×C89C2411yescharacteristic
703C23×C89—21no—
704C23×C89—21no—
705C23×C89—21no—
706C23×C89—21no—
707C23×C89C22×D411yescharacteristic
708C23×C89C22×D411yescharacteristic
709C23×C89C22×D411yescharacteristic
710Q8×C89—21no—
711Q8×C89—21no—
712Q8×C89—21no—
713Q8×C89—21no—
714Q8×C89—21no—
715Q8×C89—21no—
716Q8×C89—21no—
717Q8×C89—21no—
718Q8×C89—21no—
719Q8×C89—21no—
720Q8×C89—21no—
721Q8×C89—41no—
722Q8×C89—42no—
723Q8×C89—81no—
724Q8×C89—81no—
725Q8×C89—81no—
726Q8×C89—81no—
727Q8×C89H(5,𝔽2)12yes—
728D4×C89—21no—
729D4×C89—21no—
730D4×C89—21no—
731D4×C89—21no—
732D4×C89—21no—
733D4×C89—21no—
734D4×C89—21no—
735D4×C89—21no—
736D4×C89—41no—
737D4×C89—41no—
738D4×C89—41no—
739D4×C89—42no—
740D4×C89—42no—
741D4×C89—42no—
742D4×C89—81no—
743D4×C89—81no—
744D4×C89—81no—
745D4×C89—81no—
746D4×C89—81no—
747D4×C89—81no—
748D4×C89—81no—
749D4×C89—81no—
750D4×C89—81no—
751D4×C89—81no—
752D4×C89—81no—
753D4×C89—81no—
754D4×C89—81no—
755C2×C4×C89—21no—
756C2×C4×C89—21no—
757C2×C4×C89—21no—
758C2×C4×C89—21no—
759C2×C4×C89—21no—
760C2×C4×C89—21no—
761C2×C4×C89—21no—
762C2×C4×C89—21no—
763C2×C4×C89—21no—
764C2×C4×C89—21no—
765C2×C4×C89—21no—
766C2×C4×C89—21no—
767C2×C4×C89—21no—
768C2×C4×C89—21no—
769C2×C4×C89—21no—
770C2×C4×C89—21no—
771C2×C4×C89—21no—
772C2×C4×C89—21no—
773C2×C4×C89—41no—
774C2×C4×C89—41no—
775C2×C4×C89—42no—
776C2×C4×C89—42no—
777C2×C4×C89—42no—
778C2×C4×C89—81no—
779C2×C4×C89—81no—
780C2×C4×C89—81no—
781C2×C4×C89—81no—
782C2×C4×C89—81no—
783C2×C4×C89—81no—
784C2×C4×C89—81no—
785C2×C4×C89—81no—
786C2×C4×C89—81no—
787C2×C4×C89—81no—
788C2×C4×C89—81no—
789C2×C4×C89—81no—
790C2×C4×C89—81no—
791C2×C4×C89C22×D411yescharacteristic
792C2×C4×C89C22×D411yescharacteristic
793C2×C4×C89C22×D411yescharacteristic
794C2×C4×C89C22×D411yescharacteristic
795C2×C4×C89C22×D411yescharacteristic
796C2×C4×C89C22×D411yescharacteristic
797C2×C4×C89C22×D411yescharacteristic
798C2×C4×C89C22×D411yescharacteristic
799C2×C4×C89C22×D411yescharacteristic
800C2×C4×C89C22×D411yescharacteristic
801C2×C4×C89C22×D411yescharacteristic
802C2×C4×C89C2511yescharacteristic
803C8×C89—21no—
804C8×C89—21no—
805C8×C89—21no—
806C8×C89—21no—
807C8×C89—21no—
808C8×C89—21no—
809C8×C89—21no—
810C8×C89—21no—
811C22×C89—21no—
812C22×C89—21no—
813C22×C89—21no—
814C22×C89—21no—
815C22×C89—21no—
816C22×C89—21no—
817C22×C89—21no—
818C22×C89—21no—
819C22×C89—21no—
820C22×C89—41no—
821C22×C89—41no—
822C22×C89—41no—
823C22×C89—41no—
824C22×C89—41no—
825C22×C89—41no—
826C22×C89—41no—
827C22×C89—41no—
828C22×C89—41no—
829C22×C89—41no—
830C22×C89—41no—
831C22×C89—41no—
832C22×C89C23×D411yescharacteristic
833C4×C89—21no—
834C4×C89—21no—
835C4×C89—21no—
836C4×C89—21no—
837C4×C89—21no—
838C4×C89—21no—
839C4×C89—21no—
840C4×C89—21no—
841C4×C89—21no—
842C4×C89—21no—
843C4×C89—21no—
844C4×C89—22no—
845C4×C89—41no—
846C4×C89—41no—
847C4×C89—41no—
848C4×C89—41no—
849C4×C89—41no—
850C4×C89—41no—
851C4×C89—41no—
852C4×C89—41no—
853C4×C89—41no—
854C4×C89—41no—
855C4×C89—41no—
856C4×C89C2×H(5,𝔽2)11yescharacteristic
857C4×C89#58511yescharacteristic
858#62025C8911yesmaximal, characteristic, direct product factor, Sylow
859C2×C89—41no—
860C2×C89—41no—
861C2×C89—41no—
862C2×C89—81no—
863C2×C89—81no—
864C2×C89—81no—
865C2×C89—81no—
866C2×C89#348811yescharacteristic
867C2×C89#358411yescharacteristic
868C2×C89#358611yescharacteristic
869#3554C2×C8911yescharacteristic, complemented
870#3524C2×C8911yescharacteristic, complemented
871#3403C2×C8911yescharacteristic, complemented
872#3400C2×C8911yescharacteristic, complemented
873#3374C2×C8911yescharacteristic, complemented
874#3371C2×C8911yescharacteristic, complemented
875#3321C2×C8911yescharacteristic, complemented
876#3320C2×C8911yescharacteristic, complemented
877#3315C2×C8911yescharacteristic, complemented
878#3309C2×C8911yescharacteristic, complemented
879#3303C2×C8911yescharacteristic, complemented
880#3300C2×C8911yescharacteristic, complemented
881#3285C2×C8911yescharacteristic, complemented
882#3284C2×C8911yescharacteristic, complemented
883#3271C2×C8911yescharacteristic, complemented
884#3271C2×C8911yescharacteristic, complemented
885#3270C2×C8911yescharacteristic, complemented
886#3269C2×C8911yescharacteristic, complemented
887#3263C2×C8911yescharacteristic, complemented
888#3257C2×C8911yescharacteristic, complemented
889#3248C2×C8911yescharacteristic, complemented
890#3225C2×C8911yescharacteristic, complemented
891#3221C2×C8911yescharacteristic, complemented
892#3219C2×C8911yescharacteristic, complemented
893#3124C2×C8911yescharacteristic, complemented
894#3121C2×C8911yescharacteristic, complemented
895#3116C2×C8911yescharacteristic, complemented
896#3046C2×C8911yescharacteristic, complemented
897#3044C2×C8911yescharacteristic, complemented
898#3035C2×C8911yescharacteristic, complemented
899#2992C2×C8911yescharacteristic, complemented
900C89#6202511yescharacteristic, direct product factor, Sylow
901C2×#137C22×C8911yescharacteristic
902C2×#137C22×C8911yescharacteristic
903C2×#135C22×C8911yescharacteristic
904C2×#135C22×C8911yescharacteristic
905C2×#135C22×C8911yescharacteristic
906C22×Q16C22×C8911yescharacteristic
907#562—21no—
908#562—21no—
909#559—21no—
910#559—21no—
911#559C22×C8911yescharacteristic
912#559C22×C8911yescharacteristic
913#557C22×C8911yescharacteristic
914#557C22×C8911yescharacteristic
915#555—21no—
916#555C22×C8911yescharacteristic
917#554—21no—
918#553—21no—
919#553C22×C8911yescharacteristic
920#552—21no—
921#552C22×C8911yescharacteristic
922#550C22×C8911yescharacteristic
923#550C22×C8911yescharacteristic
924D4×Q8C22×C8911yescharacteristic
925#548C22×C8911yescharacteristic
926#548C22×C8911yescharacteristic
927#548C22×C8911yescharacteristic
928#548C22×C8911yescharacteristic
929#547C22×C8911yescharacteristic
930#547C22×C8911yescharacteristic
931#542—21no—
932#542—21no—
933#542C22×C8911yescharacteristic
934#542C22×C8911yescharacteristic
935#542C22×C8911yescharacteristic
936#540—21no—
937#540—21no—
938#540C22×C8911yescharacteristic
939#539—21no—
940#539—21no—
941#536C22×C8911yescharacteristic
942#536C22×C8911yescharacteristic
943#533C22×C8911yescharacteristic
944#532C22×C8911yescharacteristic
945#529—21no—
946#529—21no—
947#529C22×C8911yescharacteristic
948#529C22×C8911yescharacteristic
949#520C22×C8911yescharacteristic
950#519C22×C8911yescharacteristic
951C4×#41C22×C8911yescharacteristic
952#497C22×C8911yescharacteristic
953#497C22×C8911yescharacteristic
954#496C22×C8911yescharacteristic
955#496C22×C8911yescharacteristic
956#495C22×C8911yescharacteristic
957#492C22×C8911yescharacteristic
958#491C22×C8911yescharacteristic
959#491C22×C8911yescharacteristic
960#490C22×C8911yescharacteristic
961#489C22×C8911yescharacteristic
962#488C22×C8911yescharacteristic
963#487C22×C8911yescharacteristic
964#485C22×C8911yescharacteristic
965#485C22×C8911yescharacteristic
966#485C22×C8911yescharacteristic
967#484C22×C8911yescharacteristic
968#482C22×C8911yescharacteristic
969#480C22×C8911yescharacteristic
970#479C22×C8911yescharacteristic
971#479C22×C8911yescharacteristic
972#479C22×C8911yescharacteristic
973#478C22×C8911yescharacteristic
974#477C22×C8911yescharacteristic
975#476C22×C8911yescharacteristic
976#476C22×C8911yescharacteristic
977#475C22×C8911yescharacteristic
978#475C22×C8911yescharacteristic
979#474C22×C8911yescharacteristic
980#470C22×C8911yescharacteristic
981#469C22×C8911yescharacteristic
982#469C22×C8911yescharacteristic
983#468C22×C8911yescharacteristic
984#467C22×C8911yescharacteristic
985#467C22×C8911yescharacteristic
986#466C22×C8911yescharacteristic
987#465C22×C8911yescharacteristic
988#465C22×C8911yescharacteristic
989#465C22×C8911yescharacteristic
990#465C22×C8911yescharacteristic
991#465C22×C8911yescharacteristic
992#464C22×C8911yescharacteristic
993#464C22×C8911yescharacteristic
994#464C22×C8911yescharacteristic
995#464C22×C8911yescharacteristic
996#464C22×C8911yescharacteristic
997#464C22×C8911yescharacteristic
998#464C22×C8911yescharacteristic
999#464C22×C8911yescharacteristic
1000#464C22×C8911yescharacteristic
1001#464C22×C8911yescharacteristic
1002#463C22×C8911yescharacteristic
1003#463C22×C8911yescharacteristic
1004#463C22×C8911yescharacteristic
1005#463C22×C8911yescharacteristic
1006#463C22×C8911yescharacteristic
1007#463C22×C8911yescharacteristic
1008#462C22×C8911yescharacteristic
1009#462C22×C8911yescharacteristic
1010#462C22×C8911yescharacteristic
1011#462C22×C8911yescharacteristic
1012#462C22×C8911yescharacteristic
1013#462C22×C8911yescharacteristic
1014#461C22×C8911yescharacteristic
1015#461C22×C8911yescharacteristic
1016#461C22×C8911yescharacteristic
1017#461C22×C8911yescharacteristic
1018#460C22×C8911yescharacteristic
1019#460C22×C8911yescharacteristic
1020#459C22×C8911yescharacteristic
1021#459C22×C8911yescharacteristic
1022#452C22×C8911yescharacteristic
1023#452C22×C8911yescharacteristic
1024#452C22×C8911yescharacteristic
1025#452C22×C8911yescharacteristic
1026#452C22×C8911yescharacteristic
1027#452C22×C8911yescharacteristic
1028#451C22×C8911yescharacteristic
1029#451C22×C8911yescharacteristic
1030#449C22×C8911yescharacteristic
1031#449C22×C8911yescharacteristic
1032#449C22×C8911yescharacteristic
1033#449C22×C8911yescharacteristic
1034#449C22×C8911yescharacteristic
1035#449C22×C8911yescharacteristic
1036#448C22×C8911yescharacteristic
1037#448C22×C8911yescharacteristic
1038#448C22×C8911yescharacteristic
1039#448C22×C8911yescharacteristic
1040#446C22×C8911yescharacteristic
1041#446C22×C8911yescharacteristic
1042#441C22×C8911yescharacteristic
1043#441C22×C8911yescharacteristic
1044#441C22×C8911yescharacteristic
1045#440C22×C8911yescharacteristic
1046#440C22×C8911yescharacteristic
1047#440C22×C8911yescharacteristic
1048#440C22×C8911yescharacteristic
1049#440C22×C8911yescharacteristic
1050C4×Q16C22×C8911yescharacteristic
1051C4×Q16C22×C8911yescharacteristic
1052C4×SD16C22×C8911yescharacteristic
1053C4×D8C22×C8911yescharacteristic
1054#435C22×C8911yescharacteristic
1055#435C22×C8911yescharacteristic
1056#435C22×C8911yescharacteristic
1057#435C22×C8911yescharacteristic
1058C8×D4C22×C8911yescharacteristic
1059C8×D4C22×C8911yescharacteristic
1060#433C22×C8911yescharacteristic
1061#433C22×C8911yescharacteristic
1062#432C22×C8911yescharacteristic
1063#424C22×C8911yescharacteristic
1064#424C22×C8911yescharacteristic
1065C2×C4⋊C8C22×C8911yescharacteristic
1066#419C22×C8911yescharacteristic
1067#417C22×C8911yescharacteristic
1068#416C22×C8911yescharacteristic
1069#416C22×C8911yescharacteristic
1070#416C22×C8911yescharacteristic
1071C2×#103C22×C8911yescharacteristic
1072C2×#41C23×C8911yescharacteristic
1073C2×#41C23×C8911yescharacteristic
1074C2×#41C23×C8911yescharacteristic
1075C2×#41C23×C8911yescharacteristic
1076C2×#41C23×C8911yescharacteristic
1077C2×#41C23×C8911yescharacteristic
1078C22×Q8C23×C8911yescharacteristic
1079C22×Q8C23×C8911yescharacteristic
1080C22×Q8C23×C8911yescharacteristic
1081#137—42no—
1082#137—42no—
1083#135—42no—
1084#135—42no—
1085#135—42no—
1086C2×Q16—42no—
1087C2×Q16C23×C8911yescharacteristic
1088C2×Q16C23×C8911yescharacteristic
1089C2×Q16C23×C8911yescharacteristic
1090C2×Q16C23×C8911yescharacteristic
1091C2×Q16C23×C8911yescharacteristic
1092C2×Q16C23×C8911yescharacteristic
1093C2×Q16C23×C8911yescharacteristic
1094C2×Q16C23×C8911yescharacteristic
1095C2×SD16C23×C8911yescharacteristic
1096C2×SD16C23×C8911yescharacteristic
1097C2×SD16C23×C8911yescharacteristic
1098C2×SD16C23×C8911yescharacteristic
1099C2×SD16C23×C8911yescharacteristic
1100C2×SD16C23×C8911yescharacteristic
1101C2×SD16C23×C8911yescharacteristic
1102C2×SD16C23×C8911yescharacteristic
1103C2×SD16C23×C8911yescharacteristic
1104C2×SD16C23×C8911yescharacteristic
1105C2×SD16C23×C8911yescharacteristic
1106C2×SD16C23×C8911yescharacteristic
1107C2×D8C23×C8911yescharacteristic
1108C2×D8C23×C8911yescharacteristic
1109C2×D8C23×C8911yescharacteristic
1110C2×D8C23×C8911yescharacteristic
1111C2×M16C23×C8911yescharacteristic
1112C2×M16C23×C8911yescharacteristic
1113C22×C8C23×C8911yescharacteristic
1114C22×C8C23×C8911yescharacteristic
1115C22×C8C23×C8911yescharacteristic
1116C22×C8C23×C8911yescharacteristic
1117C4⋊Q8—21no—
1118C4⋊Q8—21no—
1119C4⋊Q8C23×C8911yescharacteristic
1120C4⋊Q8C23×C8911yescharacteristic
1121C4⋊Q8C23×C8911yescharacteristic
1122C4⋊Q8C23×C8911yescharacteristic
1123C4⋊Q8C23×C8911yescharacteristic
1124C4⋊Q8C23×C8911yescharacteristic
1125#127—21no—
1126#127—21no—
1127#127C23×C8911yescharacteristic
1128#127C23×C8911yescharacteristic
1129#126—21no—
1130#126—21no—
1131#126—21no—
1132#126—21no—
1133#126—21no—
1134#126—21no—
1135#126D4×C8911yescharacteristic
1136#126D4×C8911yescharacteristic
1137#125—21no—
1138#125—21no—
1139#125—21no—
1140#125—21no—
1141#125—21no—
1142#125—21no—
1143#125—21no—
1144#125D4×C8911yescharacteristic
1145#125C23×C8911yescharacteristic
1146#125C23×C8911yescharacteristic
1147#124—21no—
1148#124—21no—
1149#124—21no—
1150#124—21no—
1151#124—21no—
1152#124—21no—
1153#124—21no—
1154#124—21no—
1155#124—21no—
1156#124—21no—
1157#124—21no—
1158#124D4×C8911yescharacteristic
1159#124C23×C8911yescharacteristic
1160#124C23×C8911yescharacteristic
1161#124C23×C8911yescharacteristic
1162#124C23×C8911yescharacteristic
1163#124C23×C8911yescharacteristic
1164#124C23×C8911yescharacteristic
1165#123—21no—
1166#123—21no—
1167#123—21no—
1168#123—21no—
1169#123—21no—
1170#123—21no—
1171#123—21no—
1172#123—21no—
1173#123—21no—
1174#123—21no—
1175#123—21no—
1176#123—21no—
1177#123—21no—
1178#123—21no—
1179#123—21no—
1180#123—21no—
1181#123—21no—
1182#123—21no—
1183#123—21no—
1184#123—21no—
1185#123D4×C8911yescharacteristic
1186#123D4×C8911yescharacteristic
1187C22⋊Q8—21no—
1188C22⋊Q8—21no—
1189C22⋊Q8—21no—
1190C22⋊Q8—21no—
1191C22⋊Q8—21no—
1192C22⋊Q8—21no—
1193C22⋊Q8—21no—
1194C22⋊Q8—21no—
1195C22⋊Q8—21no—
1196C22⋊Q8—21no—
1197C22⋊Q8—21no—
1198C22⋊Q8—21no—
1199C22⋊Q8—21no—
1200C22⋊Q8—21no—
1201C22⋊Q8D4×C8911yescharacteristic
1202C22⋊Q8C23×C8911yescharacteristic
1203C22⋊Q8C23×C8911yescharacteristic
1204C22⋊Q8C23×C8911yescharacteristic
1205C22⋊Q8C23×C8911yescharacteristic
1206C22⋊Q8C23×C8911yescharacteristic
1207C22⋊Q8C23×C8911yescharacteristic
1208#121—21no—
1209#121—21no—
1210#121—21no—
1211#121—21no—
1212#121—21no—
1213#121—21no—
1214#121—21no—
1215#121—21no—
1216#121—21no—
1217#121—21no—
1218#121—21no—
1219#121—21no—
1220#121—21no—
1221#121—21no—
1222#121—21no—
1223#121—21no—
1224#121D4×C8911yescharacteristic
1225#121C23×C8911yescharacteristic
1226#121C23×C8911yescharacteristic
1227#121C23×C8911yescharacteristic
1228#121C23×C8911yescharacteristic
1229#121C23×C8911yescharacteristic
1230#121C23×C8911yescharacteristic
1231C4×Q8—21no—
1232C4×Q8—21no—
1233C4×Q8—21no—
1234C4×Q8—21no—
1235C4×Q8—21no—
1236C4×Q8C23×C8911yescharacteristic
1237C4×Q8C23×C8911yescharacteristic
1238C4×Q8C23×C8911yescharacteristic
1239C4×Q8C23×C8911yescharacteristic
1240C4×Q8C23×C8911yescharacteristic
1241C4×Q8C23×C8911yescharacteristic
1242C4×Q8C23×C8911yescharacteristic
1243C4×Q8C23×C8911yescharacteristic
1244C4×Q8C23×C8911yescharacteristic
1245C4×Q8C23×C8911yescharacteristic
1246C4×Q8C23×C8911yescharacteristic
1247C4×D4—21no—
1248C4×D4—21no—
1249C4×D4—21no—
1250C4×D4—21no—
1251C4×D4—21no—
1252C4×D4—21no—
1253C4×D4—21no—
1254C4×D4—21no—
1255C4×D4—21no—
1256C4×D4—21no—
1257C4×D4—21no—
1258C4×D4—21no—
1259C4×D4—21no—
1260C4×D4—21no—
1261C4×D4—21no—
1262C4×D4—21no—
1263C4×D4—21no—
1264C4×D4C23×C8911yescharacteristic
1265C4×D4C23×C8911yescharacteristic
1266C4×D4C23×C8911yescharacteristic
1267C4×D4C23×C8911yescharacteristic
1268C4×D4C23×C8911yescharacteristic
1269C4×D4C23×C8911yescharacteristic
1270C4×D4C23×C8911yescharacteristic
1271C4×D4C23×C8911yescharacteristic
1272C4×D4C23×C8911yescharacteristic
1273#117—21no—
1274#117—21no—
1275#117—21no—
1276#117—21no—
1277#117—21no—
1278#117—21no—
1279#117—21no—
1280#117—21no—
1281#117C23×C8911yescharacteristic
1282#117C23×C8911yescharacteristic
1283#117C23×C8911yescharacteristic
1284#117C23×C8911yescharacteristic
1285C2×C4⋊C4—21no—
1286C2×C4⋊C4—21no—
1287C2×C4⋊C4—21no—
1288C2×C4⋊C4C23×C8911yescharacteristic
1289C2×C42—21no—
1290C2×C42C23×C8911yescharacteristic
1291#107C23×C8911yescharacteristic
1292#107C23×C8911yescharacteristic
1293#107C23×C8911yescharacteristic
1294#107C23×C8911yescharacteristic
1295#106C23×C8911yescharacteristic
1296#106C23×C8911yescharacteristic
1297#106C23×C8911yescharacteristic
1298#106C23×C8911yescharacteristic
1299C4⋊C8C23×C8911yescharacteristic
1300C4⋊C8C23×C8911yescharacteristic
1301C4⋊C8C23×C8911yescharacteristic
1302C4⋊C8C23×C8911yescharacteristic
1303C4⋊C8C23×C8911yescharacteristic
1304C4⋊C8C23×C8911yescharacteristic
1305C4⋊C8C23×C8911yescharacteristic
1306C4⋊C8C23×C8911yescharacteristic
1307C4⋊C8C23×C8911yescharacteristic
1308C4⋊C8C23×C8911yescharacteristic
1309#103C23×C8911yescharacteristic
1310#103C23×C8911yescharacteristic
1311#103C23×C8911yescharacteristic
1312#103C23×C8911yescharacteristic
1313#103C23×C8911yescharacteristic
1314#103C23×C8911yescharacteristic
1315#103C23×C8911yescharacteristic
1316#103C23×C8911yescharacteristic
1317#103C23×C8911yescharacteristic
1318#103C23×C8911yescharacteristic
1319#103C23×C8911yescharacteristic
1320#103C23×C8911yescharacteristic
1321#103C23×C8911yescharacteristic
1322#103C23×C8911yescharacteristic
1323#103C23×C8911yescharacteristic
1324#103C23×C8911yescharacteristic
1325#103C23×C8911yescharacteristic
1326#103C23×C8911yescharacteristic
1327#103C23×C8911yescharacteristic
1328#103C23×C8911yescharacteristic
1329#102C23×C8911yescharacteristic
1330#102C23×C8911yescharacteristic
1331#102C23×C8911yescharacteristic
1332#102C23×C8911yescharacteristic
1333#102C23×C8911yescharacteristic
1334#102C23×C8911yescharacteristic
1335#102C23×C8911yescharacteristic
1336#102C23×C8911yescharacteristic
1337#102C23×C8911yescharacteristic
1338#102C23×C8911yescharacteristic
1339#102C23×C8911yescharacteristic
1340#102C23×C8911yescharacteristic
1341C22⋊C8C23×C8911yescharacteristic
1342C22⋊C8C23×C8911yescharacteristic
1343C22⋊C8C23×C8911yescharacteristic
1344C22⋊C8C23×C8911yescharacteristic
1345C22⋊C8C23×C8911yescharacteristic
1346C22⋊C8C23×C8911yescharacteristic
1347#97C23×C8911yescharacteristic
1348#97C23×C8911yescharacteristic
1349#97C23×C8911yescharacteristic
1350#97C23×C8911yescharacteristic
1351C4×C8C23×C8911yescharacteristic
1352C4×C8C23×C8911yescharacteristic
1353#41—22no—
1354#41—22no—
1355#41—41no—
1356#41—41no—
1357#41—41no—
1358#41—41no—
1359#41—41no—
1360#41—41no—
1361#41—41no—
1362#41—41no—
1363#41—41no—
1364#41—41no—
1365C2×Q8—21no—
1366C2×Q8—21no—
1367C2×Q8—21no—
1368C2×Q8—21no—
1369C2×Q8—21no—
1370C2×Q8—22no—
1371C2×Q8—41no—
1372C2×Q8—41no—
1373C2×Q8—41no—
1374C2×Q8—41no—
1375C2×Q8—41no—
1376C2×Q8C2×D4×C8911yescharacteristic
1377C2×Q8C24×C8911yescharacteristic
1378C2×Q8C24×C8911yescharacteristic
1379C2×Q8C24×C8911yescharacteristic
1380C2×Q8C24×C8911yescharacteristic
1381C2×Q8C24×C8911yescharacteristic
1382C2×Q8C24×C8911yescharacteristic
1383C2×D4—21no—
1384C2×D4—21no—
1385C2×D4—21no—
1386C2×D4—21no—
1387C2×D4—21no—
1388C2×D4—21no—
1389C2×D4—21no—
1390C2×D4—21no—
1391C2×D4—21no—
1392C2×D4—21no—
1393C2×D4—21no—
1394C2×D4—21no—
1395C2×D4—21no—
1396C2×D4—21no—
1397C2×D4—21no—
1398C2×D4—21no—
1399C2×D4C2×D4×C8911yescharacteristic
1400C2×D4C2×D4×C8911yescharacteristic
1401C2×D4C2×D4×C8911yescharacteristic
1402C2×D4C24×C8911yescharacteristic
1403C2×D4C24×C8911yescharacteristic
1404C2×D4C24×C8911yescharacteristic
1405C2×D4C24×C8911yescharacteristic
1406C22×C4—21no—
1407C22×C4—21no—
1408C22×C4—21no—
1409C22×C4—21no—
1410C22×C4—21no—
1411C22×C4—21no—
1412C22×C4—21no—
1413C22×C4—21no—
1414C22×C4—21no—
1415C22×C4—21no—
1416C22×C4—21no—
1417C22×C4—21no—
1418C22×C4—21no—
1419C22×C4—21no—
1420C22×C4—21no—
1421C22×C4—21no—
1422C22×C4C2×D4×C8911yescharacteristic
1423C22×C4C2×D4×C8911yescharacteristic
1424C22×C4C24×C8911yescharacteristic
1425C22×C4C24×C8911yescharacteristic
1426C22×C4C24×C8911yescharacteristic
1427Q16—22no—
1428Q16—22no—
1429Q16—22no—
1430Q16—22no—
1431Q16—41no—
1432Q16—41no—
1433Q16—41no—
1434Q16—41no—
1435SD16—22no—
1436SD16—22no—
1437SD16—41no—
1438SD16—41no—
1439SD16—41no—
1440SD16—41no—
1441SD16—41no—
1442SD16—41no—
1443SD16—41no—
1444SD16—41no—
1445SD16—41no—
1446SD16—41no—
1447D8—41no—
1448D8—41no—
1449D8—41no—
1450D8—41no—
1451M16—41no—
1452M16—41no—
1453C2×C8—41no—
1454C2×C8—41no—
1455C2×C8—41no—
1456C2×C8—41no—
1457C2×C8C24×C8911yescharacteristic
1458C2×C8C24×C8911yescharacteristic
1459C2×C8C24×C8911yescharacteristic
1460C2×C8C24×C8911yescharacteristic
1461C2×C8C24×C8911yescharacteristic
1462C2×C8C24×C8911yescharacteristic
1463C2×C8C24×C8911yescharacteristic
1464C2×C8C24×C8911yescharacteristic
1465C4⋊C4—21no—
1466C4⋊C4—21no—
1467C4⋊C4—21no—
1468C4⋊C4—21no—
1469C4⋊C4—21no—
1470C4⋊C4—21no—
1471C4⋊C4—21no—
1472C4⋊C4—21no—
1473C4⋊C4—21no—
1474C4⋊C4—21no—
1475C4⋊C4—21no—
1476C4⋊C4—21no—
1477C4⋊C4—21no—
1478C4⋊C4—21no—
1479C4⋊C4—21no—
1480C4⋊C4—21no—
1481C4⋊C4—21no—
1482C4⋊C4—21no—
1483C4⋊C4—21no—
1484C4⋊C4—21no—
1485C4⋊C4—21no—
1486C4⋊C4—21no—
1487C4⋊C4—21no—
1488C4⋊C4—21no—
1489C4⋊C4—21no—
1490C4⋊C4—21no—
1491C4⋊C4—21no—
1492C4⋊C4—21no—
1493C4⋊C4—21no—
1494C4⋊C4—21no—
1495C4⋊C4—21no—
1496C4⋊C4C2×D4×C8911yescharacteristic
1497C4⋊C4C2×D4×C8911yescharacteristic
1498C4⋊C4C2×D4×C8911yescharacteristic
1499C4⋊C4C2×D4×C8911yescharacteristic
1500C4⋊C4C2×D4×C8911yescharacteristic
1501C4⋊C4C2×D4×C8911yescharacteristic
1502C4⋊C4C2×D4×C8911yescharacteristic
1503C4⋊C4C2×D4×C8911yescharacteristic
1504C4⋊C4C2×D4×C8911yescharacteristic
1505C4⋊C4C2×D4×C8911yescharacteristic
1506C4⋊C4C24×C8911yescharacteristic
1507C4⋊C4C24×C8911yescharacteristic
1508C4⋊C4C24×C8911yescharacteristic
1509C4⋊C4C24×C8911yescharacteristic
1510C4⋊C4C24×C8911yescharacteristic
1511C4⋊C4C24×C8911yescharacteristic
1512C22⋊C4—21no—
1513C22⋊C4—21no—
1514C22⋊C4—21no—
1515C22⋊C4—21no—
1516C22⋊C4—21no—
1517C22⋊C4—21no—
1518C22⋊C4—21no—
1519C22⋊C4—21no—
1520C22⋊C4—21no—
1521C22⋊C4—21no—
1522C22⋊C4—21no—
1523C22⋊C4—21no—
1524C22⋊C4—21no—
1525C22⋊C4—21no—
1526C22⋊C4—21no—
1527C22⋊C4—21no—
1528C22⋊C4—21no—
1529C22⋊C4—21no—
1530C22⋊C4—21no—
1531C22⋊C4—21no—
1532C22⋊C4—21no—
1533C22⋊C4—21no—
1534C22⋊C4—21no—
1535C22⋊C4—21no—
1536C22⋊C4—21no—
1537C22⋊C4—21no—
1538C22⋊C4—21no—
1539C22⋊C4—21no—
1540C22⋊C4—21no—
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4C2×D4×C8911yescharacteristic
1545C22⋊C4C2×D4×C8911yescharacteristic
1546C22⋊C4C2×D4×C8911yescharacteristic
1547C22⋊C4C2×D4×C8911yescharacteristic
1548C22⋊C4C2×D4×C8911yescharacteristic
1549C22⋊C4C2×D4×C8911yescharacteristic
1550C22⋊C4C2×D4×C8911yescharacteristic
1551C22⋊C4C2×D4×C8911yescharacteristic
1552C22⋊C4C2×D4×C8911yescharacteristic
1553C22⋊C4C2×D4×C8911yescharacteristic
1554C42—21no—
1555C42—21no—
1556C42—21no—
1557C42—21no—
1558C42—21no—
1559C42—21no—
1560C42—21no—
1561C42—21no—
1562C42—21no—
1563C42—21no—
1564C42—21no—
1565C42—21no—
1566C42C2×D4×C8911yescharacteristic
1567C42C2×D4×C8911yescharacteristic
1568C42C24×C8911yescharacteristic
1569C42C24×C8911yescharacteristic
1570C42C24×C8911yescharacteristic
1571C42C24×C8911yescharacteristic
1572C23—21no—
1573C23—21no—
1574C23—21no—
1575C23—21no—
1576C23C22×D4×C8911yescharacteristic
1577C23C22×D4×C8911yescharacteristic
1578C23C22×D4×C8911yescharacteristic
1579Q8—21no—
1580Q8—21no—
1581Q8—21no—
1582Q8—21no—
1583Q8—21no—
1584Q8—21no—
1585Q8—21no—
1586Q8—21no—
1587Q8—21no—
1588Q8—21no—
1589Q8—21no—
1590Q8—41no—
1591Q8—42no—
1592Q8—81no—
1593Q8—81no—
1594Q8—81no—
1595Q8—81no—
1596Q8H(5,𝔽2)×C8912yes—
1597D4—21no—
1598D4—21no—
1599D4—21no—
1600D4—21no—
1601D4—21no—
1602D4—21no—
1603D4—21no—
1604D4—21no—
1605D4—41no—
1606D4—41no—
1607D4—41no—
1608D4—42no—
1609D4—42no—
1610D4—42no—
1611D4—81no—
1612D4—81no—
1613D4—81no—
1614D4—81no—
1615D4—81no—
1616D4—81no—
1617D4—81no—
1618D4—81no—
1619D4—81no—
1620D4—81no—
1621D4—81no—
1622D4—81no—
1623D4—81no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—41no—
1643C2×C4—41no—
1644C2×C4—42no—
1645C2×C4—42no—
1646C2×C4—42no—
1647C2×C4—81no—
1648C2×C4—81no—
1649C2×C4—81no—
1650C2×C4—81no—
1651C2×C4—81no—
1652C2×C4—81no—
1653C2×C4—81no—
1654C2×C4—81no—
1655C2×C4—81no—
1656C2×C4—81no—
1657C2×C4—81no—
1658C2×C4—81no—
1659C2×C4—81no—
1660C2×C4C22×D4×C8911yescharacteristic
1661C2×C4C22×D4×C8911yescharacteristic
1662C2×C4C22×D4×C8911yescharacteristic
1663C2×C4C22×D4×C8911yescharacteristic
1664C2×C4C22×D4×C8911yescharacteristic
1665C2×C4C22×D4×C8911yescharacteristic
1666C2×C4C22×D4×C8911yescharacteristic
1667C2×C4C22×D4×C8911yescharacteristic
1668C2×C4C22×D4×C8911yescharacteristic
1669C2×C4C22×D4×C8911yescharacteristic
1670C2×C4C22×D4×C8911yescharacteristic
1671C2×C4C25×C8911yescharacteristic
1672C8—21no—
1673C8—21no—
1674C8—21no—
1675C8—21no—
1676C8—21no—
1677C8—21no—
1678C8—21no—
1679C8—21no—
1680C22—21no—
1681C22—21no—
1682C22—21no—
1683C22—21no—
1684C22—21no—
1685C22—21no—
1686C22—21no—
1687C22—21no—
1688C22—21no—
1689C22—41no—
1690C22—41no—
1691C22—41no—
1692C22—41no—
1693C22—41no—
1694C22—41no—
1695C22—41no—
1696C22—41no—
1697C22—41no—
1698C22—41no—
1699C22—41no—
1700C22—41no—
1701C22C23×D4×C8911yescharacteristic
1702C4—21no—
1703C4—21no—
1704C4—21no—
1705C4—21no—
1706C4—21no—
1707C4—21no—
1708C4—21no—
1709C4—21no—
1710C4—21no—
1711C4—21no—
1712C4—21no—
1713C4—22no—
1714C4—41no—
1715C4—41no—
1716C4—41no—
1717C4—41no—
1718C4—41no—
1719C4—41no—
1720C4—41no—
1721C4—41no—
1722C4—41no—
1723C4—41no—
1724C4—41no—
1725C4C2×H(5,𝔽2)×C8911yescharacteristic
1726C4#585×C8911yescharacteristic
1727C2—41no—
1728C2—41no—
1729C2—41no—
1730C2—81no—
1731C2—81no—
1732C2—81no—
1733C2—81no—
1734C2C89×#348811yescharacteristic
1735C2C89×#358411yescharacteristic
1736C2C89×#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×#3554C2semidirect
2. C89×#3524C2semidirect
3. C89×#3403C2semidirect
4. C89×#3400C2semidirect
5. C89×#3374C2semidirect
6. C89×#3371C2semidirect
7. C89×#3321C2semidirect
8. C89×#3320C2semidirect
9. C89×#3315C2semidirect
10. C89×#3309C2semidirect
11. C89×#3303C2semidirect
12. C89×#3300C2semidirect
13. C89×#3285C2semidirect
14. C89×#3284C2semidirect
15. C89×#3271C2semidirect
16. C89×#3271C2semidirect
17. C89×#3270C2semidirect
18. C89×#3269C2semidirect
19. C89×#3263C2semidirect
20. C89×#3257C2semidirect
21. C89×#3248C2semidirect
22. C89×#3225C2semidirect
23. C89×#3221C2semidirect
24. C89×#3219C2semidirect
25. C89×#3124C2semidirect
26. C89×#3121C2semidirect
27. C89×#3116C2semidirect
28. C89×#3046C2semidirect
29. C89×#3044C2semidirect
30. C89×#3035C2semidirect
31. C89×#2992C2semidirect
858. #62025C89direct (N × H)
869. #3554C2×C89semidirect
870. #3524C2×C89semidirect
871. #3403C2×C89semidirect
872. #3400C2×C89semidirect
873. #3374C2×C89semidirect
874. #3371C2×C89semidirect
875. #3321C2×C89semidirect
876. #3320C2×C89semidirect
877. #3315C2×C89semidirect
878. #3309C2×C89semidirect
879. #3303C2×C89semidirect
880. #3300C2×C89semidirect
881. #3285C2×C89semidirect
882. #3284C2×C89semidirect
883. #3271C2×C89semidirect
884. #3271C2×C89semidirect
885. #3270C2×C89semidirect
886. #3269C2×C89semidirect
887. #3263C2×C89semidirect
888. #3257C2×C89semidirect
889. #3248C2×C89semidirect
890. #3225C2×C89semidirect
891. #3221C2×C89semidirect
892. #3219C2×C89semidirect
893. #3124C2×C89semidirect
894. #3121C2×C89semidirect
895. #3116C2×C89semidirect
896. #3046C2×C89semidirect
897. #3044C2×C89semidirect
898. #3035C2×C89semidirect
899. #2992C2×C89semidirect
900. C89#62025direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#35542
C89×#35242
C89×#34032
C89×#34002
C89×#33742
C89×#33712
C89×#33212
C89×#33202
C89×#33152
C89×#33092
C89×#33032
C89×#33002
C89×#32852
C89×#32842
C89×#32712
C89×#32702
C89×#32692
C89×#32632
C89×#32572
C89×#32482
C89×#32252
C89×#32212
C89×#32192
C89×#31242
C89×#31212
C89×#31162
C89×#30462
C89×#30442
C89×#30352
C89×#29922
#6202589