Finite Group Databasebeta

← #30610806

Subgroups — #30610806

Order 15616.

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#21462631C211yesmaximal, characteristic, complemented
2#21462514C211yesmaximal, characteristic, complemented
3#21461181C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461171C211yesmaximal, characteristic, complemented
6#21461158C211yesmaximal, characteristic, complemented
7#21461154C211yesmaximal, characteristic, complemented
8#21461151C211yesmaximal, characteristic, complemented
9#21461141C211yesmaximal, characteristic, complemented
10#21461134C211yesmaximal, characteristic, complemented
11#21461131C211yesmaximal, characteristic, complemented
12#21461118C211yesmaximal, characteristic, complemented
13#21461114C211yesmaximal, characteristic, complemented
14#21461111C211yesmaximal, characteristic, complemented
15#21459370C211yesmaximal, characteristic
16#16840812—21no—
17#16840797—21no—
18#16840794—21no—
19#16840794—21no—
20#16840787—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic, complemented
23#16840783C2211yescharacteristic
24#16840781C2211yescharacteristic, complemented
25#16840781C2211yescharacteristic, complemented
26#16840778C2211yescharacteristic
27#16840778C2211yescharacteristic
28#16840778C2211yescharacteristic, complemented
29#16840765C2211yescharacteristic, complemented
30C2×C4⋊#92420C2211yescharacteristic, complemented
31#16840735—21no—
32#16840726—21no—
33C4×#11758217C2211yescharacteristic
34C4×#11758217C2211yescharacteristic, complemented
35C4×D61⋊C8C2211yescharacteristic, complemented
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42Q8⋊#92420C2211yescharacteristic, complemented
43Q8⋊#92420C2211yescharacteristic, complemented
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840481C411yescharacteristic
53#16840476C411yescharacteristic
54#16840471C411yescharacteristic
55#16840455—21no—
56#16840454C411yescharacteristic
57#16840452C411yescharacteristic
58#16840449—21no—
59#16840443—21no—
60#16840438—21no—
61#16840411C411yescharacteristic
62#16840406C411yescharacteristic
63#16840314C2211yescharacteristic
64#16840293—21no—
65#16840293C2211yescharacteristic
66#16840291C2211yescharacteristic
67#16840289—21no—
68#16840268—21no—
69#41×Dic61C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C4×#11758224C2211yescharacteristic
72C2×D4×Dic61C2211yescharacteristic
73C2×#14519733—21no—
74C61×#546C411yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80#14519844—21no—
81C4⋊#92420—21no—
82C4⋊#92420—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758224C2×C411yescharacteristic
108C2×#11758224D411yescharacteristic
109C23×Dic61—21no—
110#14519776C2×C411yescharacteristic
111#14519775C2×C411yescharacteristic
112#14519772—21no—
113#14519770—21no—
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519769C2×C411yescharacteristic
119#14519768—21no—
120#14519768C2×C411yescharacteristic
121#14519767—21no—
122#14519767—21no—
123#14519764—21no—
124#14519764C2×C411yescharacteristic
125#14519763—21no—
126#14519761—21no—
127#14519760—21no—
128#14519759—21no—
129#14519758—21no—
130#14519758—21no—
131#14519758—21no—
132#14519758—21no—
133#14519756—21no—
134#14519756C2×C411yescharacteristic
135#14519756C2×C411yescharacteristic
136#14519754—21no—
137#14519754—21no—
138#14519754—21no—
139#14519754—21no—
140#14519753C2×C411yescharacteristic
141#14519749—21no—
142#14519749—21no—
143#14519749—21no—
144#14519748C2×C411yescharacteristic
145#14519746—21no—
146Q8×Dic61C2×C411yescharacteristic
147Q8×Dic61C2311yescharacteristic
148C4×Dic122C2×C411yescharacteristic
149C4×Dic122C2×C411yescharacteristic
150#14519742—21no—
151#14519742D411yescharacteristic
152#14519742C2311yescharacteristic
153D4×Dic61—21no—
154D4×Dic61—21no—
155D4×Dic61—21no—
156D4×Dic61—21no—
157D4×Dic61—21no—
158D4×Dic61C2×C411yescharacteristic
159D4×Dic61C2×C411yescharacteristic
160D4×Dic61C2×C411yescharacteristic
161D4×Dic61D411yescharacteristic
162D4×Dic61C2311yescharacteristic
163D4×Dic61C2311yescharacteristic
164C4×C22⋊D61—21no—
165C4×C22⋊D61C2×C411yescharacteristic
166C4×C22⋊D61C2×C411yescharacteristic
167#14519737—21no—
168#14519737—21no—
169#14519737D411yescharacteristic
170#14519737D411yescharacteristic
171#14519736—21no—
172#14519736C2×C411yescharacteristic
173#14519735C2×C411yescharacteristic
174#14519735D411yescharacteristic
175#14519733—21no—
176#14519733—21no—
177#14519733—21no—
178#14519733—21no—
179#14519733—21no—
180#14519733—21no—
181#14519733—21no—
182#14519733—21no—
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C2×C4⋊Dic61C2×C411yescharacteristic
186C2×#11758196—21no—
187C2×#11758196—21no—
188C2×C22⋊Dic61—21no—
189C2×C22⋊Dic61—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#124×C61C2×C411yescharacteristic
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#120×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C22⋊C4×C61—21no—
206C24×C61—21no—
207#41×C61—22no—
208#41×C61—41no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—22no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—41no—
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61C22⋊C411yescharacteristic
225C2×C22⋊D61C22⋊C411yescharacteristic
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—42no—
234C22×Dic61—42no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239#11758224—22no—
240#11758224—41no—
241#11758224—41no—
242#11758224—41no—
243C2×C4×D61C22×C411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×Dic122—21no—
247C2×Dic122C22⋊C411yescharacteristic
248C2×Dic122C22×C411yescharacteristic
249#11758217—42no—
250#11758217—42no—
251#11758217—42no—
252C2×#92420—21no—
253C2×#92420—21no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—42no—
261D61⋊C8—42no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C22⋊C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61C22⋊C411yescharacteristic
271C22⋊C4×C61C22⋊C411yescharacteristic
272C42×C61C22×C411yescharacteristic
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61C22⋊C411yescharacteristic
285C22⋊Dic61C22⋊C411yescharacteristic
286#11758198—21no—
287#11758198—21no—
288#11758198C22⋊C411yescharacteristic
289#11758198C22⋊C411yescharacteristic
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61C22⋊C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297C4⋊Dic61C22×C411yescharacteristic
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2411yescharacteristic
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61—81no—
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C2×C22⋊C411yescharacteristic
335C22×D61C2×C22⋊C411yescharacteristic
336Q8×C61—21no—
337Q8×C61—21no—
338D4×C61—21no—
339D4×C61—21no—
340D4×C61—21no—
341D4×C61—41no—
342D4×C61—42no—
343D4×C61—42no—
344D4×C61—81no—
345D4×C61#13112yes—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—42no—
353C2×C4×C61—81no—
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C23×C411yescharacteristic
359C22⋊D61—41no—
360C22⋊D61—41no—
361C22⋊D61—42no—
362C22⋊D61—81no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—81no—
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C22×D411yescharacteristic
388C2×Dic61C22×D411yescharacteristic
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—41no—
394Dic122—21no—
395Dic122—21no—
396Dic122—41no—
397Dic122—81no—
398#92420—22no—
399#92420—41no—
400#92420—41no—
401#92420—41no—
402#92420—41no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#17513—611nomaximal, Sylow
407C22×C61—22no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—84no—
420C22×C61C22×C22⋊C411yescharacteristic
421C2×D61—21no—
422C2×D61—21no—
423C2×D61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61C2×#13111yescharacteristic
431C4×C61#56811yescharacteristic
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—41no—
439Dic61—41no—
440Dic61—41no—
441Dic61—41no—
442Dic61#57511yescharacteristic
443Dic61#57511yescharacteristic
444#3475—611no—
445#2965—611no—
446#2925—611no—
447#1497—611no—
448#1495—611no—
449#1494—611no—
450#1490—611no—
451#1489—611no—
452#1488—611no—
453#1485—611no—
454#1483—611no—
455#1482—611no—
456#1478—611no—
457#1477—611no—
458#1476—611no—
459C2×C61—41no—
460C2×C61—41no—
461C2×C61—42no—
462C2×C61—81no—
463C2×C61#288011yescharacteristic
464C2×C61#289611yescharacteristic
465C2×C61#290111yescharacteristic
466D61—41no—
467#556—611no—
468#555—611no—
469#554—611no—
470#553—1221no—
471#552—611no—
472#552—611no—
473#552—1221no—
474#551—1221no—
475#551—1221no—
476#547—611no—
477#546—611no—
478#546#692311yescharacteristic
479#533—611no—
480#529—611no—
481#529—611no—
482#529—1221no—
483#529—1221no—
484#525—1221no—
485C4×#41—611no—
486C4×#41—611no—
487C4×#41—611no—
488C2×C4×D4—611no—
489C2×#117—1221no—
490#446—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494#433—1221no—
495#433—1221no—
496#432—611no—
497#432—611no—
498#431—611no—
499#431—611no—
500#431—611no—
501#431—611no—
502#431—611no—
503#423—611no—
504C2×C4⋊C8—611no—
505#408—1221no—
506#405—1221no—
507C4×M16—611no—
508C4×M16—611no—
509C2×C4×C8—611no—
510Q8⋊C8—611no—
511Q8⋊C8—611no—
512Q8⋊C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517Q8⋊C8—611no—
518D4⋊C8—611no—
519D4⋊C8—611no—
520D4⋊C8—611no—
521D4⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526C61#1751311yescharacteristic, complemented, Sylow
527C2×#41—611no—
528C2×#41—611no—
529C2×#41C2×#692311yescharacteristic
530C22×D4C2×#692311yescharacteristic
531C23×C4—1221no—
532C2×M16—1221no—
533C2×M16—1221no—
534C2×M16—1221no—
535C22×C8—1221no—
536C22×C8—1221no—
537C4⋊Q8—611no—
538C4⋊Q8—611no—
539#126—1221no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#125—611no—
546#125—611no—
547#125—1221no—
548#125—1221no—
549#125—1221no—
550#124—611no—
551#124—1221no—
552#124—1221no—
553#124C2×#692311yescharacteristic
554#123—21no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562C22⋊Q8—611no—
563C22⋊Q8—611no—
564C22⋊Q8—611no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8C2×#692311yescharacteristic
571#121—21no—
572#121—611no—
573#121—1221no—
574#121—1221no—
575#121—1221no—
576#121C2×#692311yescharacteristic
577#120—21no—
578#120—1221no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—1221no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4C2×#692311yescharacteristic
605C4×D4C2×#692311yescharacteristic
606#117—611no—
607#117—611no—
608#117—611no—
609#117—611no—
610#117—611no—
611#117—1221no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618#117—1221no—
619#117—1221no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C42—611no—
627C2×C42—611no—
628C2×C42—611no—
629C2×C42—1221no—
630C2×C42—1221no—
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—611no—
634C4⋊C8—611no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637C4⋊C8—1221no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640C22⋊C8—1221no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643C22⋊C8—1221no—
644C22⋊C8—1221no—
645C22⋊C8—1221no—
646C22⋊C8—1221no—
647#97—1221no—
648#97—1221no—
649#97—1221no—
650#97—1221no—
651C4×C8—611no—
652C4×C8—611no—
653C4×C8—611no—
654C4×C8—611no—
655C4×C8—1221no—
656C4×C8—1221no—
657C4×C8—1221no—
658C24—21no—
659#41—22no—
660#41—41no—
661#41—1222no—
662#41—2441no—
663#41—2441no—
664#41—2441no—
665C2×Q8—611no—
666C2×Q8—611no—
667C2×Q8—1221no—
668C2×Q8C22×#692311yescharacteristic
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—41no—
674C2×D4—611no—
675C2×D4—611no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4C22⋊#692311yescharacteristic
679C2×D4C22×#692311yescharacteristic
680C2×D4C22×#692311yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—2442no—
698C22×C4—2442no—
699C22×C4C22×#692311yescharacteristic
700C22×C4C22×#692311yescharacteristic
701M16—2442no—
702M16—2442no—
703M16—2442no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—611no—
716C4⋊C4—611no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4C22⋊#692311yescharacteristic
739C4⋊C4C22×#692311yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—611no—
746C22⋊C4—611no—
747C22⋊C4—611no—
748C22⋊C4—611no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4C22⋊#692311yescharacteristic
763C22⋊C4C22⋊#692311yescharacteristic
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—611no—
772C42—611no—
773C42—1221no—
774C42—1221no—
775C42—1221no—
776C42—1221no—
777C42—1221no—
778C42—1221no—
779C42C22×#692311yescharacteristic
780C23—21no—
781C23—21no—
782C23—42no—
783C23—42no—
784C23—81no—
785C23—611no—
786C23C2×C22⋊#692311yescharacteristic
787C23C2×C22⋊#692311yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—1221no—
791Q8—1221no—
792Q8—4881no—
793Q8—2441no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—81no—
801D4—4881no—
802D4—2441no—
803D4—2441no—
804D4—2442no—
805D4#1451986412yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—42no—
813C2×C4—81no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—4881no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4C2×C22⋊#692311yescharacteristic
846C2×C4C2×C22⋊#692311yescharacteristic
847C2×C4C2×C22⋊#692311yescharacteristic
848C2×C4C2×C22⋊#692311yescharacteristic
849C2×C4C23×#692311yescharacteristic
850C8—1222no—
851C8—2441no—
852C8—2441no—
853C8—2441no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C8—2441no—
858C22—21no—
859C22—21no—
860C22—22no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—84no—
871C22—1221no—
872C22—1221no—
873C22—1221no—
874C22C22×C22⋊#692311yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—41no—
880C4—41no—
881C4—611no—
882C4—611no—
883C4—1221no—
884C4—1221no—
885C4—1221no—
886C4—1221no—
887C4—1221no—
888C4—1221no—
889C4—2441no—
890C4—2441no—
891C4—2441no—
892C4—2441no—
893C4C2×#1451986411yescharacteristic
894C4#1684084011yescharacteristic
895C2—41no—
896C2—41no—
897C2—42no—
898C2—81no—
899C2—2441no—
900C2#2146240711yescharacteristic
901C2#2146243911yescharacteristic
902C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459370C2
cosocleC4×Dic61C24
hypercenter#546#6923
hypocenterC61#17513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462631C2semidirect
2. #21462514C2semidirect
3. #21461181C2semidirect
4. #21461174C2semidirect
5. #21461171C2semidirect
6. #21461158C2semidirect
7. #21461154C2semidirect
8. #21461151C2semidirect
9. #21461141C2semidirect
10. #21461134C2semidirect
11. #21461131C2semidirect
12. #21461118C2semidirect
13. #21461114C2semidirect
14. #21461111C2semidirect
22. #16840784C22semidirect
24. #16840781C22semidirect
25. #16840781C22semidirect
28. #16840778C22semidirect
29. #16840765C22semidirect
30. C2×C4⋊#92420C22semidirect
34. C4×#11758217C22semidirect
35. C4×D61⋊C8C22semidirect
36. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
42. Q8⋊#92420C22semidirect
43. Q8⋊#92420C22semidirect
526. C61#17513semidirect

Maximal subgroups

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

subgroupindex
#214626312
#214625142
#214611812
#214611742
#214611712
#214611582
#214611542
#214611512
#214611412
#214611342
#214611312
#214611182
#214611142
#214611112
#214593702
#1751361