Finite Group Databasebeta

← #29658030

Subgroups — #29658030

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457192C211yesmaximal, characteristic, complemented
2#21457013C211yesmaximal, characteristic, complemented
3#21456374C211yesmaximal, characteristic, complemented
4#21445103C211yesmaximal, characteristic, complemented
5#21445089C211yesmaximal, characteristic, complemented
6#21445012C211yesmaximal, characteristic, complemented
7#21444998C211yesmaximal, characteristic, complemented
8#21444991C211yesmaximal, characteristic, complemented
9#21444970C211yesmaximal, characteristic, complemented
10#21444946C211yesmaximal, characteristic, complemented
11#21444935C211yesmaximal, characteristic, complemented
12#21444541C211yesmaximal, characteristic, complemented
13#21444279C211yesmaximal, characteristic, complemented
14#21444270C211yesmaximal, characteristic, complemented
15C61×#3546C211yesmaximal, characteristic
16#16840319C2211yescharacteristic, complemented
17#16840168—21no—
18#16840158C2211yescharacteristic, complemented
19#16840134C2211yescharacteristic
20#16840126—21no—
21#16840114C2211yescharacteristic, complemented
22#16840108C2211yescharacteristic
23#16840083—21no—
24#16840083—21no—
25#16840066—21no—
26#16840057C2211yescharacteristic, complemented
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic
29#16840052C2211yescharacteristic, complemented
30#16840042C2211yescharacteristic
31#16840042C2211yescharacteristic, complemented
32#16840018—21no—
33#16840006—21no—
34#16839989—22no—
35#16839981—21no—
36#16839972C2211yescharacteristic, complemented
37#16839967C2211yescharacteristic
38C4×#11758200—22no—
39#16839819C2211yescharacteristic, complemented
40#16839786C2211yescharacteristic, complemented
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839508C2211yescharacteristic, complemented
43#16839508C2211yescharacteristic, complemented
44#16839506C2211yescharacteristic
45#16839506C2211yescharacteristic
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C61×#560—22no—
55C61×#556C2211yescharacteristic
56C61×#553—21no—
57C61×#550—21no—
58C61×#550C2211yescharacteristic
59C61×#547C2211yescharacteristic
60C61×#546—21no—
61C61×#546—21no—
62D42×C61C2211yescharacteristic
63C61×#542—21no—
64C61×#538—22no—
65C61×#537—21no—
66C61×#535—21no—
67C61×#535—21no—
68C61×#532C2211yescharacteristic
69C61×#532C2211yescharacteristic
70C61×#529C2211yescharacteristic
71C2×#11758202—21no—
72C2×#11758200—22no—
73C2×#11758200—21no—
74C2×#11758194—21no—
75C22×#92418—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519769—21no—
79#14519756—21no—
80#14519756—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83#14519736—21no—
84#14519710—21no—
85#14519710—21no—
86#14519710—21no—
87#14519708—22no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519701—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—22no—
100#14519698—21no—
101#14519698—22no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106C22⋊#92418—21no—
107#14519688—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C4⋊Q8×C61D411yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#127×C61—22no—
120#127×C61—21no—
121#127×C61D411yescharacteristic
122#127×C61C2311yescharacteristic
123#126×C61—22no—
124#126×C61—22no—
125#126×C61—21no—
126#125×C61D411yescharacteristic
127#124×C61—22no—
128#124×C61—21no—
129#124×C61—21no—
130#124×C61—21no—
131#124×C61D411yescharacteristic
132#123×C61—22no—
133#123×C61—22no—
134#123×C61—21no—
135#123×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61D411yescharacteristic
140#121×C61—22no—
141#121×C61—22no—
142#121×C61—22no—
143#121×C61—22no—
144#121×C61—22no—
145#121×C61—21no—
146#121×C61—22no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61D411yescharacteristic
153#121×C61D411yescharacteristic
154#121×C61D412yes—
155#121×C61D411yescharacteristic
156#120×C61—22no—
157#120×C61—22no—
158#120×C61—22no—
159#120×C61—22no—
160C4×Q8×C61—21no—
161C4×Q8×C61C2311yescharacteristic
162C4×D4×C61—22no—
163C4×D4×C61—21no—
164C4×D4×C61—21no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61D412yes—
168C4×D4×C61C2311yescharacteristic
169C4×D4×C61C2311yescharacteristic
170C4×D4×C61C2311yescharacteristic
171#117×C61—21no—
172#117×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C22⋊C4×C61—22no—
175C2×C42×C61C2311yescharacteristic
176C24×C61—22no—
177#41×C61—81no—
178#41×C61—81no—
179#41×C61—81no—
180#41×C61—81no—
181#41×C61—81no—
182#41×C61—81no—
183#41×C61—81no—
184#41×C61—81no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61C2×D411yescharacteristic
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—81no—
202C2×D4×C61—81no—
203C2×D4×C61—81no—
204C2×D4×C61—81no—
205C2×D4×C61C2×D411yescharacteristic
206C2×D4×C61C2×D411yescharacteristic
207C2×D4×C61C2×D411yescharacteristic
208C2×D4×C61C2×D412yes—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—22no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C2×Dic122—21no—
219C2×Dic122—21no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61C2×D411yescharacteristic
229C4⋊C4×C61C2×D411yescharacteristic
230C4⋊C4×C61C2×D411yescharacteristic
231C4⋊C4×C61C2×D412yes—
232C4⋊C4×C61C2×D411yescharacteristic
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C42×C61—22no—
250C42×C61—21no—
251C42×C61C2×D411yescharacteristic
252C42×C61C2×D411yescharacteristic
253C42×C61C2×D411yescharacteristic
254C42×C61C2411yescharacteristic
255C22⋊Dic61—41no—
256#11758202—81no—
257#11758200—44no—
258#11758200—81no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263#11758196—41no—
264#11758196—41no—
265C4×Dic61—41no—
266#11758194—81no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—42no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—22no—
277C23×C61—21no—
278C23×C61—82no—
279C23×C61—82no—
280C23×C61—82no—
281C23×C61#12011yescharacteristic
282Q8×C61—21no—
283Q8×C61—21no—
284Q8×C61—41no—
285Q8×C61—41no—
286Q8×C61—81no—
287D4×C61—21no—
288D4×C61—21no—
289D4×C61—21no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—42no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—41no—
298D4×C61—81no—
299D4×C61—81no—
300D4×C61—81no—
301D4×C61—82no—
302D4×C61—81no—
303D4×C61—81no—
304D4×C61—82no—
305D4×C61—82no—
306D4×C61—82no—
307D4×C61—82no—
308D4×C61—82no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—82no—
327C2×C4×C61—82no—
328C2×C4×C61—82no—
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×Dic61—41no—
336C2×Dic61—41no—
337Dic122—42no—
338Dic122—41no—
339Dic122—41no—
340#92418—22no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#18705—611nomaximal, Sylow
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—42no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—42no—
357C22×C61—41no—
358C22×C61—42no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—164no—
363C22×C61C2×#12011yescharacteristic
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—41no—
369C4×C61—42no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61#57611yescharacteristic
375C4×C61#57711yescharacteristic
376C4×C61#57711yescharacteristic
377C4×C61#57711yescharacteristic
378Dic61—81no—
379Dic61—81no—
380#3546D6111yescharacteristic
381#3252—611no—
382#3235—611no—
383#3167—611no—
384#1654—611no—
385#1652—611no—
386#1641—611no—
387#1639—611no—
388#1638—611no—
389#1635—611no—
390#1631—611no—
391#1629—611no—
392#1557—611no—
393#1494—611no—
394#1492—611no—
395C2×C61—41no—
396C2×C61—81no—
397C2×C61—82no—
398C2×C61—81no—
399C2×C61—81no—
400C2×C61#300911yescharacteristic
401C2×C61#301211yescharacteristic
402C2×C61#301811yescharacteristic
403#560—22no—
404#556C2×D6111yescharacteristic
405#553—21no—
406#550—21no—
407#550C2×D6111yescharacteristic
408#547C2×D6111yescharacteristic
409#546—21no—
410#546—21no—
411D42C2×D6111yescharacteristic
412#542—21no—
413#538—22no—
414#537—21no—
415#535—21no—
416#535—21no—
417#533—611no—
418#532C2×D6111yescharacteristic
419#532C2×D6111yescharacteristic
420#529C2×D6111yescharacteristic
421#501—1221no—
422#498—611no—
423#492—611no—
424#490—1221no—
425#487—611no—
426#486—611no—
427#482—1221no—
428#482—1221no—
429#479—1221no—
430#477—611no—
431#476—611no—
432#476—611no—
433#476—611no—
434#474—611no—
435#474—611no—
436#470—1221no—
437#468—1221no—
438#465—1222no—
439#464—1221no—
440#462—611no—
441#461—611no—
442C4×SD16—1222no—
443#432—611no—
444#423—611no—
445C2×C4×C8—611no—
446#332—611no—
447#332—611no—
448#331—611no—
449#331—611no—
450Q8⋊C8—611no—
451Q8⋊C8—611no—
452D4⋊C8—611no—
453D4⋊C8—611no—
454D4⋊C8—611no—
455D4⋊C8—611no—
456D4⋊C8—611no—
457D4⋊C8—611no—
458C61#1870511yescharacteristic, complemented, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—1221no—
466C2×SD16—1221no—
467C2×SD16—1222no—
468C2×M16—1221no—
469C22×C8—1221no—
470C4⋊Q8—611no—
471C4⋊Q8—611no—
472C4⋊Q8C22⋊D6111yescharacteristic
473C4⋊Q8C22×D6111yescharacteristic
474#127—22no—
475#127—21no—
476#127C22⋊D6111yescharacteristic
477#127C22×D6111yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—1221no—
482#125C22⋊D6111yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124C22⋊D6111yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—1221no—
496C22⋊Q8—1221no—
497C22⋊Q8C22⋊D6111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121C22⋊D6111yescharacteristic
511#121C22⋊D6111yescharacteristic
512#121C22⋊D6111yescharacteristic
513#121C22⋊D6112yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—1221no—
520C4×Q8—1221no—
521C4×Q8C22×D6111yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4C22⋊D6112yes—
528C4×D4C22×D6111yescharacteristic
529C4×D4C22×D6111yescharacteristic
530C4×D4C22×D6111yescharacteristic
531#117—21no—
532#117—21no—
533#117—1221no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C22×D6111yescharacteristic
537#107—1221no—
538#107—1221no—
539#107—1221no—
540#106—1222no—
541#106—1221no—
542#106—1221no—
543#106—1221no—
544C4⋊C8—611no—
545C4⋊C8—611no—
546C4⋊C8—611no—
547C4⋊C8—611no—
548C4⋊C8—1221no—
549#103—1221no—
550#103—1222no—
551#103—1221no—
552#103—1221no—
553#102—1222no—
554#102—1221no—
555#102—1221no—
556#102—1221no—
557#102—1221no—
558#102—1221no—
559C22⋊C8—1221no—
560#97—1221no—
561C4×C8—611no—
562C4×C8—611no—
563C4×C8—1221no—
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8C2×C22⋊D6111yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×C22⋊D6111yescharacteristic
596C2×D4C2×C22⋊D6111yescharacteristic
597C2×D4C2×C22⋊D6111yescharacteristic
598C2×D4C2×C22⋊D6112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608Q16—4881no—
609SD16—4881no—
610SD16—2444no—
611M16—4881no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—2442no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—2441no—
632C4⋊C4—2441no—
633C4⋊C4C2×C22⋊D6111yescharacteristic
634C4⋊C4C2×C22⋊D6112yes—
635C4⋊C4C2×C22⋊D6111yescharacteristic
636C4⋊C4C2×C22⋊D6111yescharacteristic
637C4⋊C4C2×C22⋊D6111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—2441no—
655C42—22no—
656C42—21no—
657C42—2441no—
658C42C2×C22⋊D6111yescharacteristic
659C42C2×C22⋊D6111yescharacteristic
660C42C2×C22⋊D6111yescharacteristic
661C42C23×D6111yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#1451974611yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—41no—
673Q8—41no—
674Q8—81no—
675Q8—2442no—
676Q8—2441no—
677Q8—2441no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—82no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4#1451974611yescharacteristic
723C2×C4#1451974611yescharacteristic
724C2×C4#1451974611yescharacteristic
725C2×C4C22×C22⋊D6111yescharacteristic
726C2×C4C22×C22⋊D6111yescharacteristic
727C2×C4C22×C22⋊D6111yescharacteristic
728C8—1222no—
729C8—2441no—
730C8—2441no—
731C8—2441no—
732C8—2441no—
733C8—2441no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—41no—
749C22—164no—
750C22C2×#1451974611yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—4881no—
762C4—4881no—
763C4#1684056511yescharacteristic
764C4#1684057311yescharacteristic
765C4#1684057311yescharacteristic
766C4#1684057311yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2#2145509611yescharacteristic
773C2#2145512311yescharacteristic
774C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3546C2
socleC22×C61C2×#120
hypercenter#3546D61
hypocenterC61#18705
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3546

Complements

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

NH ≅ G/Ntype
1. #21457192C2semidirect
2. #21457013C2semidirect
3. #21456374C2semidirect
4. #21445103C2semidirect
5. #21445089C2semidirect
6. #21445012C2semidirect
7. #21444998C2semidirect
8. #21444991C2semidirect
9. #21444970C2semidirect
10. #21444946C2semidirect
11. #21444935C2semidirect
12. #21444541C2semidirect
13. #21444279C2semidirect
14. #21444270C2semidirect
16. #16840319C22semidirect
18. #16840158C22semidirect
21. #16840114C22semidirect
26. #16840057C22semidirect
29. #16840052C22semidirect
31. #16840042C22semidirect
36. #16839972C22semidirect
39. #16839819C22semidirect
40. #16839786C22semidirect
41. C2×C4×#92418C22semidirect
42. #16839508C22semidirect
43. #16839508C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
458. C61#18705semidirect

Maximal subgroups

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

subgroupindex
#214571922
#214570132
#214563742
#214451032
#214450892
#214450122
#214449982
#214449912
#214449702
#214449462
#214449352
#214445412
#214442792
#214442702
C61×#35462
#1870561