Finite Group Databasebeta

← #36521349

Subgroups — #36521349

Order 22784.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26029219C211yesmaximal, characteristic, complemented
2#26028918C211yesmaximal, characteristic, complemented
3#26018725C211yesmaximal, characteristic, complemented
4#26018717C211yesmaximal, characteristic, complemented
5#26018712C211yesmaximal, characteristic, complemented
6#26018695C211yesmaximal, characteristic, complemented
7#26018691C211yesmaximal, characteristic, complemented
8#26018686C211yesmaximal, characteristic, complemented
9#26018673C211yesmaximal, characteristic, complemented
10#26018665C211yesmaximal, characteristic, complemented
11#26018660C211yesmaximal, characteristic, complemented
12#26018643C211yesmaximal, characteristic, complemented
13#26018639C211yesmaximal, characteristic, complemented
14#26018634C211yesmaximal, characteristic, complemented
15C89×#3475C211yesmaximal, characteristic
16#19151729—21no—
17#19151676—21no—
18#19151670—21no—
19#19151670—21no—
20#19151659—21no—
21#19151659—21no—
22#19151655C2211yescharacteristic
23#19151655C2211yescharacteristic, complemented
24#19151651C2211yescharacteristic
25#19151651C2211yescharacteristic
26#19151651C2211yescharacteristic, complemented
27#19151651C2211yescharacteristic, complemented
28#19151651C2211yescharacteristic, complemented
29#19151622C2211yescharacteristic, complemented
30C2×C4⋊#10623494C2211yescharacteristic, complemented
31#19151565—21no—
32#19151554—21no—
33C4×#13083558C2211yescharacteristic
34C4×#13083558C2211yescharacteristic, complemented
35C2×C4×#10623494C2211yescharacteristic, complemented
36Q8⋊#10623494C2211yescharacteristic, complemented
37Q8⋊#10623494C2211yescharacteristic, complemented
38Q8⋊#10623494C2211yescharacteristic, complemented
39Q8⋊#10623494C2211yescharacteristic, complemented
40Q8⋊#10623494C2211yescharacteristic, complemented
41Q8⋊#10623494C2211yescharacteristic, complemented
42Q8⋊#10623494C2211yescharacteristic, complemented
43Q8⋊#10623494C2211yescharacteristic, complemented
44D4⋊#10623494C2211yescharacteristic
45D4⋊#10623494C2211yescharacteristic
46D4⋊#10623494C2211yescharacteristic
47D4⋊#10623494C2211yescharacteristic
48D4⋊#10623494C2211yescharacteristic
49D4⋊#10623494C2211yescharacteristic
50D4⋊#10623494C2211yescharacteristic
51D4⋊#10623494C2211yescharacteristic
52#556×C89C411yescharacteristic
53#555×C89C411yescharacteristic
54#554×C89C411yescharacteristic
55#553×C89—21no—
56#552×C89—21no—
57#552×C89C411yescharacteristic
58#552×C89C411yescharacteristic
59#551×C89—21no—
60#551×C89—21no—
61#547×C89C411yescharacteristic
62#546×C89C411yescharacteristic
63#546×C89C411yescharacteristic
64#533×C89C2211yescharacteristic
65#529×C89—21no—
66#529×C89—21no—
67#529×C89C2211yescharacteristic
68#529×C89C2211yescharacteristic
69#525×C89—21no—
70C4×#41×C89C2211yescharacteristic
71C4×#41×C89C2211yescharacteristic
72C4×#41×C89C2211yescharacteristic
73C2×C4×D4×C89C2211yescharacteristic
74C2×#117×C89—21no—
75C2×#13083558—21no—
76C2×#13083558—21no—
77C2×#13083558—21no—
78C22×#10623494—21no—
79C22×#10623494—21no—
80C4⋊#10623494—21no—
81C4⋊#10623494—21no—
82C4⋊#10623494—21no—
83C4⋊#10623494—21no—
84C4⋊#10623494—21no—
85C4⋊#10623494C2311yescharacteristic
86C4⋊#10623494C2311yescharacteristic
87C4⋊#10623494C2311yescharacteristic
88C4⋊#10623494C2311yescharacteristic
89C22⋊#10623494—21no—
90C22⋊#10623494—21no—
91C22⋊#10623494—21no—
92C22⋊#10623494—21no—
93C22⋊#10623494—21no—
94C22⋊#10623494—21no—
95C22⋊#10623494—21no—
96#15667923—21no—
97#15667923—21no—
98#15667923—21no—
99#15667923—21no—
100C4×#10623494—21no—
101C4×#10623494—21no—
102C4×#10623494—21no—
103C4×#10623494C2311yescharacteristic
104C4×#10623494C2311yescharacteristic
105C4×#10623494C2311yescharacteristic
106C4×#10623494C2311yescharacteristic
107C2×#41×C89C2×C411yescharacteristic
108C2×#41×C89C2×C411yescharacteristic
109C2×#41×C89D411yescharacteristic
110C22×D4×C89C2×C411yescharacteristic
111C23×C4×C89—21no—
112C4⋊Q8×C89C2×C411yescharacteristic
113C4⋊Q8×C89C2×C411yescharacteristic
114#126×C89—21no—
115#126×C89—21no—
116#126×C89—21no—
117#126×C89—21no—
118#126×C89—21no—
119#126×C89—21no—
120#125×C89—21no—
121#125×C89—21no—
122#125×C89—21no—
123#125×C89C2×C411yescharacteristic
124#125×C89C2×C411yescharacteristic
125#124×C89—21no—
126#124×C89—21no—
127#124×C89C2×C411yescharacteristic
128#124×C89C2×C411yescharacteristic
129#123×C89—21no—
130#123×C89—21no—
131#123×C89—21no—
132#123×C89—21no—
133#123×C89—21no—
134#123×C89—21no—
135#123×C89—21no—
136#123×C89—21no—
137C22⋊Q8×C89—21no—
138C22⋊Q8×C89—21no—
139C22⋊Q8×C89—21no—
140C22⋊Q8×C89—21no—
141C22⋊Q8×C89—21no—
142C22⋊Q8×C89C2×C411yescharacteristic
143C22⋊Q8×C89C2×C411yescharacteristic
144C22⋊Q8×C89C2×C411yescharacteristic
145C22⋊Q8×C89C2×C411yescharacteristic
146#121×C89—21no—
147#121×C89—21no—
148#121×C89—21no—
149#121×C89—21no—
150#121×C89C2×C411yescharacteristic
151#121×C89C2×C411yescharacteristic
152#120×C89—21no—
153#120×C89—21no—
154C4×Q8×C89—21no—
155C4×Q8×C89C2×C411yescharacteristic
156C4×Q8×C89C2×C411yescharacteristic
157C4×Q8×C89C2×C411yescharacteristic
158C4×Q8×C89D411yescharacteristic
159C4×Q8×C89C2311yescharacteristic
160C4×Q8×C89C2311yescharacteristic
161C4×D4×C89—21no—
162C4×D4×C89—21no—
163C4×D4×C89—21no—
164C4×D4×C89—21no—
165C4×D4×C89—21no—
166C4×D4×C89—21no—
167C4×D4×C89—21no—
168C4×D4×C89—21no—
169C4×D4×C89C2×C411yescharacteristic
170C4×D4×C89C2×C411yescharacteristic
171C4×D4×C89C2×C411yescharacteristic
172C4×D4×C89C2×C411yescharacteristic
173C4×D4×C89C2×C411yescharacteristic
174C4×D4×C89C2×C411yescharacteristic
175C4×D4×C89C2×C411yescharacteristic
176C4×D4×C89D411yescharacteristic
177C4×D4×C89D411yescharacteristic
178C4×D4×C89D411yescharacteristic
179C4×D4×C89C2311yescharacteristic
180C4×D4×C89C2311yescharacteristic
181#117×C89—21no—
182#117×C89—21no—
183#117×C89—21no—
184#117×C89—21no—
185#117×C89—21no—
186#117×C89—21no—
187#117×C89—21no—
188#117×C89—21no—
189#117×C89—21no—
190#117×C89C2×C411yescharacteristic
191#117×C89C2×C411yescharacteristic
192#117×C89D411yescharacteristic
193#117×C89D411yescharacteristic
194#117×C89D411yescharacteristic
195C2×C4⋊C4×C89—21no—
196C2×C4⋊C4×C89—21no—
197C2×C4⋊C4×C89C2×C411yescharacteristic
198C2×C22⋊C4×C89—21no—
199C2×C22⋊C4×C89—21no—
200C2×C22⋊C4×C89—21no—
201C2×C42×C89—21no—
202C2×C42×C89—21no—
203C2×C42×C89C2311yescharacteristic
204C2×C42×C89C2311yescharacteristic
205C2×C42×C89C2311yescharacteristic
206#13083558—42no—
207#13083558—42no—
208#13083558—42no—
209C2×#10623494—21no—
210C2×#10623494—21no—
211C2×#10623494—21no—
212C2×#10623494—21no—
213C2×#10623494—21no—
214C2×#10623494—21no—
215C2×#10623494—21no—
216C2×#10623494—21no—
217C2×#10623494—42no—
218C2×#10623494—42no—
219C24×C89—21no—
220#41×C89—22no—
221#41×C89—22no—
222#41×C89—41no—
223#41×C89—41no—
224#41×C89—41no—
225#41×C89—41no—
226C2×Q8×C89—21no—
227C2×Q8×C89C22⋊C411yescharacteristic
228C2×Q8×C89C22×C411yescharacteristic
229C2×Q8×C89C22×C411yescharacteristic
230C2×D4×C89—22no—
231C2×D4×C89—21no—
232C2×D4×C89—21no—
233C2×D4×C89—21no—
234C2×D4×C89—21no—
235C2×D4×C89—21no—
236C2×D4×C89—41no—
237C2×D4×C89C22⋊C411yescharacteristic
238C2×D4×C89C22⋊C411yescharacteristic
239C2×D4×C89C22⋊C411yescharacteristic
240C2×D4×C89C22×C411yescharacteristic
241C2×D4×C89C22×C411yescharacteristic
242C22×C4×C89—21no—
243C22×C4×C89—21no—
244C22×C4×C89—21no—
245C22×C4×C89—21no—
246C22×C4×C89—21no—
247C22×C4×C89—21no—
248C22×C4×C89—21no—
249C22×C4×C89—21no—
250C22×C4×C89—21no—
251C22×C4×C89—42no—
252C22×C4×C89—42no—
253C22×C4×C89C22×C411yescharacteristic
254C22×C4×C89C22×C411yescharacteristic
255C22×C4×C89C22×C411yescharacteristic
256C22×C4×C89C2×D411yescharacteristic
257C22×C4×C89C2×D411yescharacteristic
258C22×C4×C89C2×D411yescharacteristic
259C22×C4×C89C2×D411yescharacteristic
260C22×C4×C89C2×D411yescharacteristic
261C22×C4×C89C2×D411yescharacteristic
262C4⋊C4×C89—21no—
263C4⋊C4×C89—21no—
264C4⋊C4×C89—21no—
265C4⋊C4×C89—21no—
266C4⋊C4×C89—21no—
267C4⋊C4×C89—21no—
268C4⋊C4×C89—21no—
269C4⋊C4×C89—21no—
270C4⋊C4×C89—21no—
271C4⋊C4×C89—21no—
272C4⋊C4×C89—21no—
273C4⋊C4×C89—21no—
274C4⋊C4×C89—21no—
275C4⋊C4×C89—21no—
276C4⋊C4×C89—21no—
277C4⋊C4×C89—21no—
278C4⋊C4×C89C22⋊C411yescharacteristic
279C4⋊C4×C89C22⋊C411yescharacteristic
280C4⋊C4×C89C22⋊C411yescharacteristic
281C4⋊C4×C89C22⋊C411yescharacteristic
282C4⋊C4×C89C22⋊C411yescharacteristic
283C4⋊C4×C89C22⋊C411yescharacteristic
284C4⋊C4×C89C22×C411yescharacteristic
285C4⋊C4×C89C22×C411yescharacteristic
286C4⋊C4×C89C22×C411yescharacteristic
287C4⋊C4×C89C22×C411yescharacteristic
288C22⋊C4×C89—21no—
289C22⋊C4×C89—21no—
290C22⋊C4×C89—21no—
291C22⋊C4×C89—21no—
292C22⋊C4×C89—21no—
293C22⋊C4×C89—21no—
294C22⋊C4×C89—21no—
295C22⋊C4×C89—21no—
296C22⋊C4×C89—21no—
297C22⋊C4×C89—21no—
298C22⋊C4×C89—21no—
299C22⋊C4×C89—21no—
300C22⋊C4×C89—21no—
301C22⋊C4×C89—21no—
302C22⋊C4×C89—21no—
303C22⋊C4×C89—21no—
304C22⋊C4×C89—21no—
305C22⋊C4×C89—21no—
306C22⋊C4×C89C22⋊C411yescharacteristic
307C22⋊C4×C89C22⋊C411yescharacteristic
308C22⋊C4×C89C22⋊C411yescharacteristic
309C22⋊C4×C89C22⋊C411yescharacteristic
310C22⋊C4×C89C22⋊C411yescharacteristic
311C22⋊C4×C89C22⋊C411yescharacteristic
312C42×C89—21no—
313C42×C89—21no—
314C42×C89—21no—
315C42×C89—21no—
316C42×C89—21no—
317C42×C89—21no—
318C42×C89C22×C411yescharacteristic
319C42×C89C22×C411yescharacteristic
320C42×C89C22×C411yescharacteristic
321C42×C89C2×D411yescharacteristic
322C42×C89C2×D411yescharacteristic
323C42×C89C2×D411yescharacteristic
324C42×C89C2×D411yescharacteristic
325C42×C89C2×D411yescharacteristic
326C42×C89C2×D411yescharacteristic
327C42×C89C2411yescharacteristic
328C23×C89—21no—
329C23×C89—21no—
330C23×C89—42no—
331C23×C89—42no—
332C23×C89—81no—
333C23×C89C2×C22⋊C411yescharacteristic
334C23×C89C2×C22⋊C411yescharacteristic
335C23×C89C2×C22⋊C411yescharacteristic
336Q8×C89—21no—
337Q8×C89—21no—
338Q8×C89—21no—
339Q8×C89—21no—
340Q8×C89—41no—
341Q8×C89—81no—
342D4×C89—21no—
343D4×C89—21no—
344D4×C89—21no—
345D4×C89—41no—
346D4×C89—41no—
347D4×C89—41no—
348D4×C89—42no—
349D4×C89—42no—
350D4×C89—42no—
351D4×C89—81no—
352D4×C89—81no—
353D4×C89#13112yes—
354C2×C4×C89—21no—
355C2×C4×C89—21no—
356C2×C4×C89—21no—
357C2×C4×C89—21no—
358C2×C4×C89—21no—
359C2×C4×C89—21no—
360C2×C4×C89—21no—
361C2×C4×C89—21no—
362C2×C4×C89—21no—
363C2×C4×C89—21no—
364C2×C4×C89—21no—
365C2×C4×C89—21no—
366C2×C4×C89—21no—
367C2×C4×C89—21no—
368C2×C4×C89—21no—
369C2×C4×C89—21no—
370C2×C4×C89—21no—
371C2×C4×C89—21no—
372C2×C4×C89—41no—
373C2×C4×C89—41no—
374C2×C4×C89—41no—
375C2×C4×C89—42no—
376C2×C4×C89—42no—
377C2×C4×C89—42no—
378C2×C4×C89—42no—
379C2×C4×C89—42no—
380C2×C4×C89—41no—
381C2×C4×C89—41no—
382C2×C4×C89—41no—
383C2×C4×C89—41no—
384C2×C4×C89—81no—
385C2×C4×C89—81no—
386C2×C4×C89C2×C22⋊C411yescharacteristic
387C2×C4×C89C2×C22⋊C411yescharacteristic
388C2×C4×C89C2×C22⋊C411yescharacteristic
389C2×C4×C89C2×C22⋊C411yescharacteristic
390C2×C4×C89C2×C22⋊C411yescharacteristic
391C2×C4×C89C2×C22⋊C411yescharacteristic
392C2×C4×C89C2×C22⋊C411yescharacteristic
393C2×C4×C89C2×C22⋊C411yescharacteristic
394C2×C4×C89C2×C22⋊C411yescharacteristic
395C2×C4×C89C23×C411yescharacteristic
396C2×C4×C89C22×D411yescharacteristic
397C2×C4×C89C22×D411yescharacteristic
398#10623494—22no—
399#10623494—41no—
400#10623494—41no—
401#10623494—41no—
402#10623494—41no—
403#10623494—41no—
404#10623494—41no—
405#10623494—41no—
406C22×C89—21no—
407C22×C89—21no—
408C22×C89—21no—
409C22×C89—22no—
410C22×C89—21no—
411C22×C89—21no—
412C22×C89—21no—
413C22×C89—21no—
414C22×C89—21no—
415C22×C89—21no—
416C22×C89—41no—
417C22×C89—41no—
418C22×C89—41no—
419C22×C89—41no—
420C22×C89—41no—
421C22×C89—84no—
422C22×C89C22×C22⋊C411yescharacteristic
423C4×C89—21no—
424C4×C89—21no—
425C4×C89—21no—
426C4×C89—21no—
427C4×C89—21no—
428C4×C89—21no—
429C4×C89—21no—
430C4×C89—21no—
431C4×C89—21no—
432C4×C89—21no—
433C4×C89—41no—
434C4×C89—41no—
435C4×C89—41no—
436C4×C89—41no—
437C4×C89—41no—
438C4×C89—41no—
439C4×C89C2×#13111yescharacteristic
440C4×C89#56811yescharacteristic
441C4×C89#57511yescharacteristic
442C4×C89#57511yescharacteristic
443#17513—891nomaximal, Sylow
444C2×C89—41no—
445C2×C89—41no—
446C2×C89—41no—
447C2×C89—42no—
448C2×C89—81no—
449C2×C89#288011yescharacteristic
450C2×C89#289611yescharacteristic
451C2×C89#290111yescharacteristic
452#3475D8911yescharacteristic
453#2965—891no—
454#2925—891no—
455#1497—891no—
456#1495—891no—
457#1494—891no—
458#1490—891no—
459#1489—891no—
460#1488—891no—
461#1485—891no—
462#1483—891no—
463#1482—891no—
464#1478—891no—
465#1477—891no—
466#1476—891no—
467C89#1751311yescharacteristic, complemented, Sylow
468#556Dic8911yescharacteristic
469#555Dic8911yescharacteristic
470#554Dic8911yescharacteristic
471#553—21no—
472#552—21no—
473#552Dic8911yescharacteristic
474#552Dic8911yescharacteristic
475#551—21no—
476#551—21no—
477#547Dic8911yescharacteristic
478#546Dic8911yescharacteristic
479#546Dic8911yescharacteristic
480#533C2×D8911yescharacteristic
481#529—21no—
482#529—21no—
483#529C2×D8911yescharacteristic
484#529C2×D8911yescharacteristic
485#525—21no—
486C4×#41C2×D8911yescharacteristic
487C4×#41C2×D8911yescharacteristic
488C4×#41C2×D8911yescharacteristic
489C2×C4×D4C2×D8911yescharacteristic
490C2×#117—21no—
491#446—1781no—
492#436—1781no—
493#435—1781no—
494#435—1781no—
495#433—1781no—
496#433—1781no—
497#432—891no—
498#432—891no—
499#431—891no—
500#431—891no—
501#431—891no—
502#431—891no—
503#431—891no—
504#423—891no—
505C2×C4⋊C8—891no—
506#408—1781no—
507#405—1781no—
508C4×M16—891no—
509C4×M16—891no—
510C2×C4×C8—891no—
511Q8⋊C8—891no—
512Q8⋊C8—891no—
513Q8⋊C8—891no—
514Q8⋊C8—891no—
515Q8⋊C8—891no—
516Q8⋊C8—891no—
517Q8⋊C8—891no—
518Q8⋊C8—891no—
519D4⋊C8—891no—
520D4⋊C8—891no—
521D4⋊C8—891no—
522D4⋊C8—891no—
523D4⋊C8—891no—
524D4⋊C8—891no—
525D4⋊C8—891no—
526D4⋊C8—891no—
527C2×#41C2×Dic8911yescharacteristic
528C2×#41C2×Dic8911yescharacteristic
529C2×#41C22⋊D8911yescharacteristic
530C22×D4C2×Dic8911yescharacteristic
531C23×C4—21no—
532C2×M16—1781no—
533C2×M16—1781no—
534C2×M16—1781no—
535C22×C8—1781no—
536C22×C8—1781no—
537C4⋊Q8C2×Dic8911yescharacteristic
538C4⋊Q8C2×Dic8911yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#125—21no—
546#125—21no—
547#125—21no—
548#125C2×Dic8911yescharacteristic
549#125C2×Dic8911yescharacteristic
550#124—21no—
551#124—21no—
552#124C2×Dic8911yescharacteristic
553#124C2×Dic8911yescharacteristic
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8C2×Dic8911yescharacteristic
568C22⋊Q8C2×Dic8911yescharacteristic
569C22⋊Q8C2×Dic8911yescharacteristic
570C22⋊Q8C2×Dic8911yescharacteristic
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121C2×Dic8911yescharacteristic
576#121C2×Dic8911yescharacteristic
577#120—21no—
578#120—21no—
579C4×Q8—21no—
580C4×Q8C2×Dic8911yescharacteristic
581C4×Q8C2×Dic8911yescharacteristic
582C4×Q8C2×Dic8911yescharacteristic
583C4×Q8C22⋊D8911yescharacteristic
584C4×Q8C22×D8911yescharacteristic
585C4×Q8C22×D8911yescharacteristic
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4C2×Dic8911yescharacteristic
595C4×D4C2×Dic8911yescharacteristic
596C4×D4C2×Dic8911yescharacteristic
597C4×D4C2×Dic8911yescharacteristic
598C4×D4C2×Dic8911yescharacteristic
599C4×D4C2×Dic8911yescharacteristic
600C4×D4C2×Dic8911yescharacteristic
601C4×D4C22⋊D8911yescharacteristic
602C4×D4C22⋊D8911yescharacteristic
603C4×D4C22⋊D8911yescharacteristic
604C4×D4C22×D8911yescharacteristic
605C4×D4C22×D8911yescharacteristic
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117C2×Dic8911yescharacteristic
616#117C2×Dic8911yescharacteristic
617#117C22⋊D8911yescharacteristic
618#117C22⋊D8911yescharacteristic
619#117C22⋊D8911yescharacteristic
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4C2×Dic8911yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42C22×D8911yescharacteristic
629C2×C42C22×D8911yescharacteristic
630C2×C42C22×D8911yescharacteristic
631C4⋊C8—891no—
632C4⋊C8—891no—
633C4⋊C8—891no—
634C4⋊C8—891no—
635C4⋊C8—1781no—
636C4⋊C8—1781no—
637C4⋊C8—1781no—
638C4⋊C8—1781no—
639C4⋊C8—1781no—
640C22⋊C8—1781no—
641C22⋊C8—1781no—
642C22⋊C8—1781no—
643C22⋊C8—1781no—
644C22⋊C8—1781no—
645C22⋊C8—1781no—
646C22⋊C8—1781no—
647#97—1781no—
648#97—1781no—
649#97—1781no—
650#97—1781no—
651C4×C8—891no—
652C4×C8—891no—
653C4×C8—891no—
654C4×C8—891no—
655C4×C8—1781no—
656C4×C8—1781no—
657C4×C8—1781no—
658C24—21no—
659#41—22no—
660#41—22no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665C2×Q8—21no—
666C2×Q8C22⋊Dic8911yescharacteristic
667C2×Q8C22×Dic8911yescharacteristic
668C2×Q8C22×Dic8911yescharacteristic
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—41no—
676C2×D4C22⋊Dic8911yescharacteristic
677C2×D4C22⋊Dic8911yescharacteristic
678C2×D4C22⋊Dic8911yescharacteristic
679C2×D4C22×Dic8911yescharacteristic
680C2×D4C22×Dic8911yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4C22×Dic8911yescharacteristic
693C22×C4C22×Dic8911yescharacteristic
694C22×C4C22×Dic8911yescharacteristic
695C22×C4C2×C22⋊D8911yescharacteristic
696C22×C4C2×C22⋊D8911yescharacteristic
697C22×C4C2×C22⋊D8911yescharacteristic
698C22×C4C2×C22⋊D8911yescharacteristic
699C22×C4C2×C22⋊D8911yescharacteristic
700C22×C4C2×C22⋊D8911yescharacteristic
701M16—3562no—
702M16—3562no—
703M16—3562no—
704C2×C8—3562no—
705C2×C8—3562no—
706C2×C8—1781no—
707C2×C8—1781no—
708C2×C8—1781no—
709C2×C8—1781no—
710C2×C8—1781no—
711C2×C8—1781no—
712C2×C8—1781no—
713C2×C8—1781no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C22⋊Dic8911yescharacteristic
731C4⋊C4C22⋊Dic8911yescharacteristic
732C4⋊C4C22⋊Dic8911yescharacteristic
733C4⋊C4C22⋊Dic8911yescharacteristic
734C4⋊C4C22⋊Dic8911yescharacteristic
735C4⋊C4C22⋊Dic8911yescharacteristic
736C4⋊C4C22×Dic8911yescharacteristic
737C4⋊C4C22×Dic8911yescharacteristic
738C4⋊C4C22×Dic8911yescharacteristic
739C4⋊C4C22×Dic8911yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4C22⋊Dic8911yescharacteristic
759C22⋊C4C22⋊Dic8911yescharacteristic
760C22⋊C4C22⋊Dic8911yescharacteristic
761C22⋊C4C22⋊Dic8911yescharacteristic
762C22⋊C4C22⋊Dic8911yescharacteristic
763C22⋊C4C22⋊Dic8911yescharacteristic
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42C22×Dic8911yescharacteristic
771C42C22×Dic8911yescharacteristic
772C42C22×Dic8911yescharacteristic
773C42C2×C22⋊D8911yescharacteristic
774C42C2×C22⋊D8911yescharacteristic
775C42C2×C22⋊D8911yescharacteristic
776C42C2×C22⋊D8911yescharacteristic
777C42C2×C22⋊D8911yescharacteristic
778C42C2×C22⋊D8911yescharacteristic
779C42C23×D8911yescharacteristic
780C23—21no—
781C23—21no—
782C23—42no—
783C23—42no—
784C23—81no—
785C23C2×C22⋊Dic8911yescharacteristic
786C23C2×C22⋊Dic8911yescharacteristic
787C23C2×C22⋊Dic8911yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—41no—
793Q8—81no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4#1566801912yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C2×C22⋊Dic8911yescharacteristic
839C2×C4C2×C22⋊Dic8911yescharacteristic
840C2×C4C2×C22⋊Dic8911yescharacteristic
841C2×C4C2×C22⋊Dic8911yescharacteristic
842C2×C4C2×C22⋊Dic8911yescharacteristic
843C2×C4C2×C22⋊Dic8911yescharacteristic
844C2×C4C2×C22⋊Dic8911yescharacteristic
845C2×C4C2×C22⋊Dic8911yescharacteristic
846C2×C4C2×C22⋊Dic8911yescharacteristic
847C2×C4C23×Dic8911yescharacteristic
848C2×C4C22×C22⋊D8911yescharacteristic
849C2×C4C22×C22⋊D8911yescharacteristic
850C8—3561no—
851C8—3561no—
852C8—3561no—
853C8—3561no—
854C8—3561no—
855C8—3561no—
856C8—3561no—
857C8—1782no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—84no—
874C22C22×C22⋊Dic8911yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4C2×#1566801911yescharacteristic
892C4#1915236511yescharacteristic
893C4#1915239611yescharacteristic
894C4#1915239611yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—42no—
899C2—81no—
900C2#2602870111yescharacteristic
901C2#2602877111yescharacteristic
902C2#2602879911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
Fitting, prime radicalC89×#3475C2
socleC22×C89C22×C22⋊C4
cosocleC42×C89C24
hypercenter#3475D89
hypocenterC89#17513
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #26029219C2semidirect
2. #26028918C2semidirect
3. #26018725C2semidirect
4. #26018717C2semidirect
5. #26018712C2semidirect
6. #26018695C2semidirect
7. #26018691C2semidirect
8. #26018686C2semidirect
9. #26018673C2semidirect
10. #26018665C2semidirect
11. #26018660C2semidirect
12. #26018643C2semidirect
13. #26018639C2semidirect
14. #26018634C2semidirect
23. #19151655C22semidirect
26. #19151651C22semidirect
27. #19151651C22semidirect
28. #19151651C22semidirect
29. #19151622C22semidirect
30. C2×C4⋊#10623494C22semidirect
34. C4×#13083558C22semidirect
35. C2×C4×#10623494C22semidirect
36. Q8⋊#10623494C22semidirect
37. Q8⋊#10623494C22semidirect
38. Q8⋊#10623494C22semidirect
39. Q8⋊#10623494C22semidirect
40. Q8⋊#10623494C22semidirect
41. Q8⋊#10623494C22semidirect
42. Q8⋊#10623494C22semidirect
43. Q8⋊#10623494C22semidirect
467. C89#17513semidirect

Maximal subgroups

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

subgroupindex
#260292192
#260289182
#260187252
#260187172
#260187122
#260186952
#260186912
#260186862
#260186732
#260186652
#260186602
#260186432
#260186392
#260186342
C89×#34752
#1751389