Finite Group Databasebeta

← #30610874

Subgroups — #30610874

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462744C211yesmaximal, characteristic, complemented
2#21462503C211yesmaximal, characteristic, complemented
3#21461181C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461171C211yesmaximal, characteristic, complemented
6#21461162C211yesmaximal, characteristic, complemented
7#21461150C211yesmaximal, characteristic, complemented
8#21461147C211yesmaximal, characteristic, complemented
9#21461135C211yesmaximal, characteristic, complemented
10#21461130C211yesmaximal, characteristic, complemented
11#21461127C211yesmaximal, characteristic, complemented
12#21461121C211yesmaximal, characteristic, complemented
13#21461114C211yesmaximal, characteristic, complemented
14D61⋊(Q8⋊C8)C211yesmaximal, characteristic, complemented
15#21459435C211yesmaximal, characteristic
16#16840814—21no—
17#16840794—21no—
18#16840793—21no—
19#16840789—21no—
20#16840786—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic
23#16840783C2211yescharacteristic
24#16840779C2211yescharacteristic
25#16840779C2211yescharacteristic
26#16840778C2211yescharacteristic
27#16840778C2211yescharacteristic
28#16840778C2211yescharacteristic
29#16840769—21no—
30#16840765C2211yescharacteristic
31D61⋊(C4⋊C8)C2211yescharacteristic
32C2×C4⋊#92420C2211yescharacteristic
33#16840736—21no—
34C4×#11758213C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840488C411yescharacteristic
53#16840481—21no—
54#16840481C411yescharacteristic
55#16840452—21no—
56#16840452C411yescharacteristic
57#16840446—21no—
58#16840446C411yescharacteristic
59Q8×C22⋊D61C411yescharacteristic
60#16840419C411yescharacteristic
61#16840412—21no—
62#16840412C411yescharacteristic
63#16840314—21no—
64#16840314C2211yescharacteristic
65#16840293—21no—
66#16840293C2211yescharacteristic
67#16840291—21no—
68#16840291C2211yescharacteristic
69#41×Dic61C2211yescharacteristic
70C4×#11758224—21no—
71C4×#11758224C2211yescharacteristic
72C2×Q8×Dic61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C61×#548C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91#14519834—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758224—21no—
108C2×#11758224D411yescharacteristic
109C2×Q8×D61C2×C411yescharacteristic
110#14519776—21no—
111#14519776C2×C411yescharacteristic
112#14519775—21no—
113#14519775C2×C411yescharacteristic
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769—21no—
121#14519769C2×C411yescharacteristic
122#14519768—21no—
123#14519768C2×C411yescharacteristic
124#14519767—21no—
125#14519767—21no—
126#14519767—21no—
127#14519764—21no—
128#14519764C2×C411yescharacteristic
129#14519759—21no—
130#14519759—21no—
131#14519759—21no—
132#14519758—21no—
133#14519758—21no—
134#14519758—21no—
135#14519756—21no—
136#14519756—21no—
137#14519756C2×C411yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519754—21no—
140#14519754—21no—
141#14519754—21no—
142#14519753—21no—
143#14519753C2×C411yescharacteristic
144#14519748—21no—
145#14519748C2×C411yescharacteristic
146Q8×Dic61—21no—
147Q8×Dic61—21no—
148Q8×Dic61C2×C411yescharacteristic
149Q8×Dic61C2×C411yescharacteristic
150Q8×Dic61C2×C411yescharacteristic
151Q8×Dic61C2311yescharacteristic
152Q8×Dic61C2311yescharacteristic
153C4×Dic122—21no—
154C4×Dic122—21no—
155C4×Dic122C2×C411yescharacteristic
156C4×Dic122C2×C411yescharacteristic
157#14519742—21no—
158#14519742—21no—
159#14519742D411yescharacteristic
160#14519742C2311yescharacteristic
161D4×Dic61—21no—
162D4×Dic61—21no—
163D4×Dic61—21no—
164D4×Dic61C2×C411yescharacteristic
165D4×Dic61D411yescharacteristic
166D4×Dic61C2311yescharacteristic
167C4×C22⋊D61—21no—
168C4×C22⋊D61—21no—
169C4×C22⋊D61C2×C411yescharacteristic
170C4×C22⋊D61C2×C411yescharacteristic
171#14519737—21no—
172#14519737D411yescharacteristic
173#14519737D411yescharacteristic
174#14519736—21no—
175#14519736C2×C411yescharacteristic
176#14519735—21no—
177#14519735D411yescharacteristic
178#14519733—21no—
179#14519733—21no—
180#14519733—21no—
181#14519733—21no—
182#14519733—21no—
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C2×C4⋊Dic61—21no—
186C2×C4⋊Dic61C2×C411yescharacteristic
187C4⋊C4×D61—21no—
188C4⋊C4×D61C2×C411yescharacteristic
189C2×C4×Dic61—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×Q8×C61C2×C411yescharacteristic
197#124×C61—21no—
198#124×C61C2×C411yescharacteristic
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206#41×C61—22no—
207#41×C61—41no—
208C2×Q8×C61—21no—
209C2×Q8×C61—22no—
210C2×Q8×C61—41no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×Q8×C61C22×C411yescharacteristic
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61C22⋊C411yescharacteristic
223C2×C22⋊D61C22⋊C411yescharacteristic
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231Q8×D61—22no—
232Q8×D61—41no—
233#11758224—42no—
234#11758224—44no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61C22×C411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122C22⋊C411yescharacteristic
243C2×Dic122C22×C411yescharacteristic
244#11758217—81no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—21no—
252C2×#92420—21no—
253C2×#92420—81no—
254#11758213—42no—
255D61⋊C8—42no—
256D61⋊C8—81no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C22⋊C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61C22⋊C411yescharacteristic
266C22⋊C4×C61C22⋊C411yescharacteristic
267C42×C61—21no—
268C42×C61C22×C411yescharacteristic
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61C22⋊C411yescharacteristic
278C22⋊Dic61C22⋊C411yescharacteristic
279#11758198—21no—
280#11758198C22⋊C411yescharacteristic
281#11758198C22⋊C411yescharacteristic
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61C22⋊C411yescharacteristic
290C4⋊Dic61C22×C411yescharacteristic
291C4⋊Dic61C22×C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2411yescharacteristic
326C23×C61—21no—
327C23×C61C2×C22⋊C411yescharacteristic
328C23×C61C2×C22⋊C411yescharacteristic
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—21no—
333Q8×C61—42no—
334Q8×C61#13112yes—
335D4×C61—21no—
336D4×C61—21no—
337D4×C61—41no—
338D4×C61—42no—
339D4×C61—42no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C23×C411yescharacteristic
354C22⋊D61—22no—
355C22⋊D61—22no—
356C22⋊D61—42no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C22×D411yescharacteristic
377C2×Dic61C22×D411yescharacteristic
378C4×D61—22no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—42no—
384C4×D61—42no—
385Dic122—21no—
386Dic122—21no—
387Dic122—41no—
388Dic122—42no—
389Dic122—42no—
390#92420—41no—
391#92420—41no—
392#92420—41no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#92420—41no—
397#92420—41no—
398#17524—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61C22×C22⋊C411yescharacteristic
409C2×D61—21no—
410C2×D61—21no—
411C2×D61#42112yes—
412C4×C61—22no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61C2×#13111yescharacteristic
420C4×C61#56811yescharacteristic
421Dic61—21no—
422Dic61—21no—
423Dic61—21no—
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—41no—
428Dic61—41no—
429Dic61—41no—
430Dic61—41no—
431Dic61#57711yescharacteristic
432Dic61#57811yescharacteristic
433#3482—611no—
434#2990—611no—
435#2922—611no—
436#1497—611no—
437#1495—611no—
438#1494—611no—
439#1491—611no—
440#1488—611no—
441#1487—611no—
442#1483—611no—
443#1482—611no—
444#1481—611no—
445#1479—611no—
446#1477—611no—
447C2×Q8⋊C8—611no—
448C2×C61—41no—
449C2×C61—41no—
450C2×C61—81no—
451C2×C61#288011yescharacteristic
452C2×C61#289811yescharacteristic
453C2×C61C2×#42111yescharacteristic
454D61—22no—
455#557—611no—
456#556—611no—
457#556—1221no—
458#552—611no—
459#552—611no—
460#552—1221no—
461#552—1221no—
462D4×Q8—611no—
463#548—611no—
464#548#692311yescharacteristic
465#547—611no—
466#547—1221no—
467#533—611no—
468#533—1221no—
469#529—611no—
470#529—611no—
471#529—1221no—
472#529—1221no—
473C4×#41—611no—
474C4×#41—611no—
475C4×#41—1221no—
476C2×C4×Q8—611no—
477C2×C4×Q8—611no—
478#446—1221no—
479#435—1221no—
480#435—1221no—
481C8×D4—1221no—
482#433—1221no—
483#433—1221no—
484#432—611no—
485#432—611no—
486#431—611no—
487#431—611no—
488#431—611no—
489#431—611no—
490#431—611no—
491#424—1221no—
492#423—611no—
493C2×C4⋊C8—611no—
494C2×C4⋊C8—611no—
495#408—1221no—
496C4×M16—611no—
497C2×C4×C8—611no—
498Q8⋊C8—611no—
499Q8⋊C8—611no—
500Q8⋊C8—611no—
501Q8⋊C8—611no—
502Q8⋊C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8—611no—
507Q8⋊C8—611no—
508Q8⋊C8—611no—
509Q8⋊C8—611no—
510D4⋊C8—611no—
511D4⋊C8—611no—
512D4⋊C8—611no—
513D4⋊C8—611no—
514C61#1752411yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C2×#41—1221no—
517C2×#41C2×#692311yescharacteristic
518C22×Q8—611no—
519C22×Q8C2×#692311yescharacteristic
520C2×M16—1221no—
521C2×M16—1221no—
522C22×C8—1221no—
523C22×C8—1221no—
524C22×C8—1221no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—1221no—
528C4⋊Q8—1221no—
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#125—611no—
536#125—611no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125—1221no—
541#125—1221no—
542#124—21no—
543#124—611no—
544#124—1221no—
545#124C2×#692311yescharacteristic
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551#123—1221no—
552C22⋊Q8—21no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8C2×#692311yescharacteristic
563#121—21no—
564#121—611no—
565#121—1221no—
566#121C2×#692311yescharacteristic
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—611no—
575C4×Q8—611no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×Q8C2×#692311yescharacteristic
583C4×D4—21no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4C2×#692311yescharacteristic
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117—1221no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C42—611no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619C4⋊C8—611no—
620C4⋊C8—611no—
621C4⋊C8—611no—
622C4⋊C8—611no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C22⋊C8—1221no—
631C22⋊C8—1221no—
632C22⋊C8—1221no—
633C22⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637#97—1221no—
638#97—1221no—
639#97—1221no—
640C4×C8—611no—
641C4×C8—611no—
642C4×C8—611no—
643C4×C8—611no—
644C4×C8—1221no—
645C4×C8—1221no—
646#41—22no—
647#41—41no—
648#41—2442no—
649#41—2444no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—41no—
653C2×Q8—611no—
654C2×Q8—611no—
655C2×Q8—1221no—
656C2×Q8—1221no—
657C2×Q8—1222no—
658C2×Q8—2441no—
659C2×Q8C22×#692311yescharacteristic
660C2×Q8C22×#692311yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—611no—
664C2×D4—611no—
665C2×D4—1221no—
666C2×D4C22⋊#692311yescharacteristic
667C2×D4C22×#692311yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4C22×#692311yescharacteristic
683C22×C4C22×#692311yescharacteristic
684M16—4881no—
685M16—2442no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—4881no—
695C2×C8—4881no—
696C2×C8—2442no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
706C4⋊C4—611no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4C22⋊#692311yescharacteristic
727C4⋊C4C22×#692311yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—611no—
733C22⋊C4—611no—
734C22⋊C4—611no—
735C22⋊C4—611no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4C22⋊#692311yescharacteristic
746C22⋊C4C22⋊#692311yescharacteristic
747C42—21no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42C22×#692311yescharacteristic
766C23—21no—
767C23—611no—
768C23C2×C22⋊#692311yescharacteristic
769C23C2×C22⋊#692311yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—42no—
774Q8—1221no—
775Q8—1221no—
776Q8—2441no—
777Q8—2442no—
778Q8—2442no—
779Q8#1451986412yes—
780D4—21no—
781D4—21no—
782D4—41no—
783D4—42no—
784D4—42no—
785D4—1222no—
786D4—1222no—
787D4—2442no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1222no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2442no—
824C2×C4—2442no—
825C2×C4C2×C22⋊#692311yescharacteristic
826C2×C4C2×C22⋊#692311yescharacteristic
827C2×C4C2×C22⋊#692311yescharacteristic
828C2×C4C2×C22⋊#692311yescharacteristic
829C2×C4C23×#692311yescharacteristic
830C8—2441no—
831C8—2441no—
832C8—2441no—
833C8—2441no—
834C8—2441no—
835C8—2441no—
836C8—2441no—
837C8—2441no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—612no—
848C22—1221no—
849C22—1221no—
850C22C22×C22⋊#692311yescharacteristic
851C4—21no—
852C4—21no—
853C4—22no—
854C4—21no—
855C4—21no—
856C4—41no—
857C4—41no—
858C4—611no—
859C4—611no—
860C4—1221no—
861C4—1221no—
862C4—1221no—
863C4—1221no—
864C4—1221no—
865C4—1221no—
866C4—2441no—
867C4—2441no—
868C4—2441no—
869C4—2441no—
870C4C2×#1451986411yescharacteristic
871C4#1684084011yescharacteristic
872C2—41no—
873C2—41no—
874C2—81no—
875C2—1222no—
876C2#2146240711yescharacteristic
877C2#2146244111yescharacteristic
878C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#21459435C2
cosocleC4×Dic61C24
hypercenter#548#6923
hypocenterC61#17524
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #21462744C2semidirect
2. #21462503C2semidirect
3. #21461181C2semidirect
4. #21461174C2semidirect
5. #21461171C2semidirect
6. #21461162C2semidirect
7. #21461150C2semidirect
8. #21461147C2semidirect
9. #21461135C2semidirect
10. #21461130C2semidirect
11. #21461127C2semidirect
12. #21461121C2semidirect
13. #21461114C2semidirect
14. D61⋊(Q8⋊C8)C2semidirect
514. C61#17524semidirect

Maximal subgroups

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

subgroupindex
#214627442
#214625032
#214611812
#214611742
#214611712
#214611622
#214611502
#214611472
#214611352
#214611302
#214611272
#214611212
#214611142
D61⋊(Q8⋊C8)2
#214594352
#1752461