Finite Group Databasebeta

← #30617202

Subgroups — #30617202

Order 15616.

844 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462306C211yesmaximal, characteristic
2#21462257C211yesmaximal, characteristic
3#21461899C211yesmaximal, characteristic, complemented
4#21461898C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic
8#21461770C211yesmaximal, characteristic
9#21461723C211yesmaximal, characteristic
10#21461635C211yesmaximal, characteristic, complemented
11#106×#6923C211yesmaximal, characteristic, complemented
12#21461592C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic
15#483×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×#14519856C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23D61⋊(C22⋊C8)C2211yescharacteristic
24C2×#14519831C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26(C2×#6923)⋊Q8C2211yescharacteristic
27#16840713—21no—
28#16840713C2211yescharacteristic
29#16840712—21no—
30#16840712—21no—
31#16840711—21no—
32#16840704C2211yescharacteristic
33C4⋊C4×#6923—21no—
34C4⋊C4×#6923—21no—
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C4×C22⋊#6923—21no—
41C4×C22⋊#6923—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C22⋊Q8×D61C2211yescharacteristic
53C2×C4⋊C4×D61C2211yescharacteristic
54#16840094C411yescharacteristic, complemented
55#16840094C411yescharacteristic, complemented
56#16840093C411yescharacteristic, complemented
57#16840092C411yescharacteristic, complemented
58#16840091C411yescharacteristic, complemented
59#16840091C411yescharacteristic, complemented
60#16840090C411yescharacteristic, complemented
61#106×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65C22⋊C8×D61C2211yescharacteristic
66C61×#483C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71#14519856—22no—
72#14519856—22no—
73#14519856—22no—
74#14519856—22no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923D411yescharacteristic
78C2×C4⋊#6923D411yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923D411yescharacteristic
86C2×C22⋊#6923D411yescharacteristic
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—22no—
97#14519845—22no—
98#14519840—22no—
99#14519840—22no—
100#14519834—21no—
101C22⋊#92420—21no—
102#14519831—22no—
103C8×#6923—22no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113C2×Q8×D61C2311yescharacteristic
114C22×C4×D61—21no—
115C22×C4×D61C2311yescharacteristic
116C2×C8×D61C2311yescharacteristic
117C2×C8×D61C2311yescharacteristic
118#14519757C2×C411yescharacteristic
119#14519756C2×C411yescharacteristic
120#14519755—21no—
121#14519754—21no—
122#14519753C2×C411yescharacteristic
123C2×C4⋊Dic61C2×C411yescharacteristic
124C2×#11758196—21no—
125C4⋊C4×D61—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2×C411yescharacteristic
129C4⋊C4×D61C2×C411yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C4⋊C4×D61C2311yescharacteristic
132C4⋊C4×D61C2311yescharacteristic
133C22⋊C4×D61—21no—
134#14519709C2×C411yescharacteristic
135#14519709C2×C411yescharacteristic
136#14519708C2×C411yescharacteristic
137#14519708C2×C411yescharacteristic
138#14519708C2×C411yescharacteristic
139#14519708C2×C411yescharacteristic
140#14519702C2×C411yescharacteristic
141#14519702C2×C411yescharacteristic
142#14519701C2×C411yescharacteristic
143#14519701C2×C411yescharacteristic
144#14519700C2×C411yescharacteristic
145#14519700C2×C411yescharacteristic
146C22⋊#92418C2×C411yescharacteristic
147#14519689C2×C411yescharacteristic
148#14519689C2×C411yescharacteristic
149C22⋊Q8×C61C2×C411yescharacteristic
150C2×C4⋊C4×C61C2×C411yescharacteristic
151#106×C61C2×C411yescharacteristic
152#106×C61C2×C411yescharacteristic
153#103×C61C2×C411yescharacteristic
154#103×C61C2×C411yescharacteristic
155C22⋊C8×C61C2×C411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923C2×D411yescharacteristic
162C22×#6923C2×D411yescharacteristic
163C22×#6923C2×D411yescharacteristic
164C22×#6923C2×D411yescharacteristic
165C2×Q8×C61C22×C411yescharacteristic
166C22×C4×C61—21no—
167C22×C4×C61C22×C411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61#4111yescharacteristic
170Q8×D61—21no—
171Q8×D61—21no—
172Q8×D61—21no—
173Q8×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61C22×C411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61#4111yescharacteristic
189C2×C4×D61C2411yescharacteristic
190C2×Dic122—21no—
191C2×Dic122C22×C411yescharacteristic
192C22⋊#6923—24no—
193C22⋊#6923—22no—
194C22⋊#6923—22no—
195C22⋊#6923—81no—
196C2×#92420—21no—
197C2×#92420—21no—
198C4⋊#6923—22no—
199C4⋊#6923—22no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—42no—
207C4⋊#6923—81no—
208C4⋊#6923#4112yes—
209C4⋊#6923#4112yes—
210C4×#6923—24no—
211C4×#6923—21no—
212C4×#6923—21no—
213C4×#6923—42no—
214C4×#6923—81no—
215C4×#6923—81no—
216C4×#6923—81no—
217C4×#6923—81no—
218C4×#6923—81no—
219C4×#6923#4112yes—
220C4×#6923#4112yes—
221D61⋊C8—21no—
222D61⋊C8—21no—
223D61⋊C8—21no—
224D61⋊C8—21no—
225C2×C8×C61C22×C411yescharacteristic
226C2×C8×C61C22×C411yescharacteristic
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C22×C411yescharacteristic
230C4⋊C4×C61C22×C411yescharacteristic
231C4⋊C4×C61C22×C411yescharacteristic
232C22⋊C4×C61—21no—
233C22⋊Dic61—21no—
234#11758198—21no—
235#11758198—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C22×C411yescharacteristic
239C4⋊Dic61C22×C411yescharacteristic
240C4⋊Dic61C22×C411yescharacteristic
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244#11758196—21no—
245#11758196—21no—
246#11758196—21no—
247#11758196—21no—
248C2×#92418C22×C411yescharacteristic
249C2×#92418C22×C411yescharacteristic
250C8×D61—21no—
251C8×D61—21no—
252C8×D61—21no—
253C8×D61—21no—
254C23×C61C4×D411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61C4×D411yescharacteristic
262C22×D61C22×D411yescharacteristic
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—22no—
270C2×#6923—22no—
271C2×#6923—21no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923#12312yes—
286C2×#6923#12312yes—
287Q8×C61—21no—
288Q8×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—81no—
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—81no—
305C2×Dic61C4×D411yescharacteristic
306C2×Dic61C2×#4111yescharacteristic
307C4×D61—21no—
308C4×D61—21no—
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—21no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—81no—
322C4×D61—81no—
323C4×D61C2×#4111yescharacteristic
324C4×D61C2×#4111yescharacteristic
325C4×D61C2×#4111yescharacteristic
326C4×D61C2×#4111yescharacteristic
327Dic122—21no—
328Dic122—21no—
329Dic122—41no—
330Dic122—41no—
331#92420—41no—
332#92420—41no—
333C8×C61—21no—
334C8×C61—21no—
335#92418—21no—
336#92418—21no—
337#21587—611nomaximal, Sylow
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61C2×C4×D411yescharacteristic
342C2×D61—21no—
343C2×D61—21no—
344C2×D61—21no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61C2×#12311yescharacteristic
350C2×D61#52511yescharacteristic
351C2×D61#57711yescharacteristic
352C2×D61#57711yescharacteristic
353C2×D61#57711yescharacteristic
354C2×D61#57811yescharacteristic
355#6923—22no—
356#6923—22no—
357#6923—41no—
358#6923—41no—
359#6923—42no—
360#6923—42no—
361#6923—81no—
362#6923—81no—
363C4×C61—21no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61C4×#4111yescharacteristic
369C4×C61C4×#4111yescharacteristic
370Dic61—21no—
371Dic61—41no—
372Dic61—41no—
373Dic61—41no—
374Dic61—41no—
375Dic61#52911yescharacteristic
376Dic61#52911yescharacteristic
377C2×#483—611no—
378#2323—611no—
379#2274—611no—
380#1928—611no—
381#1927—611no—
382#1920—611no—
383#1919—611no—
384#1873—611no—
385#1854—611no—
386#1824—611no—
387#1776—611no—
388C4×#106—611no—
389#1763—611no—
390C4×#103—611no—
391#1750—611no—
392C2×C61—41no—
393C2×C61C4×#12311yescharacteristic
394C2×C61#294711yescharacteristic
395C2×C61#294911yescharacteristic
396D61—41no—
397D61#309711yescharacteristic
398D61#309911yescharacteristic
399D61#312011yescharacteristic
400D61#312511yescharacteristic
401C2×C22⋊Q8—611no—
402C2×C4×Q8—611no—
403C2×#117—611no—
404C2×#117—611no—
405C22×C4⋊C4—611no—
406#483—611no—
407#483—611no—
408#483—611no—
409#483—611no—
410#483—611no—
411#483—611no—
412#483—611no—
413#483#692311yescharacteristic, complemented
414C2×#107—611no—
415C2×#106—611no—
416C2×#106—611no—
417C2×#106—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×#97—611no—
425C2×C4×C8—611no—
426#391—611no—
427#389—611no—
428#389—1221no—
429#388—1221no—
430#388—1221no—
431#387—1221no—
432#380—611no—
433C4×C4⋊C4—611no—
434C4×C4⋊C4—611no—
435C4×C4⋊C4—611no—
436C4×C4⋊C4—611no—
437C4×C4⋊C4—611no—
438C4×C4⋊C4—1221no—
439C4×C4⋊C4—1221no—
440C4×C22⋊C4—1221no—
441C4×C22⋊C4—1221no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#336—611no—
451#336—611no—
452C61#2158711yescharacteristic, complemented, Sylow
453C22×Q8—611no—
454C23×C4—611no—
455C23×C4—1221no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22⋊Q8—611no—
461C22⋊Q8—611no—
462C22⋊Q8—611no—
463C22⋊Q8—1221no—
464C22⋊Q8—1221no—
465C22⋊Q8C2×#692311yescharacteristic
466C4×Q8—1222no—
467C4×Q8—1222no—
468#117—1222no—
469#117—1222no—
470#117—1222no—
471#117—1222no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4C2×#692311yescharacteristic
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505#107—1222no—
506#106—611no—
507#106—611no—
508#106—611no—
509#106—611no—
510#106—611no—
511#106—611no—
512#106—1222no—
513#106C2×#692311yescharacteristic
514#106C2×#692311yescharacteristic
515#103—611no—
516#103—611no—
517#103—611no—
518#103—611no—
519#103—611no—
520#103—611no—
521#103—1222no—
522#103—1222no—
523#103C2×#692311yescharacteristic
524#103C2×#692311yescharacteristic
525C22⋊C8—611no—
526C22⋊C8—611no—
527C22⋊C8—611no—
528C22⋊C8—1221no—
529C22⋊C8—1221no—
530C22⋊C8C2×#692311yescharacteristic
531#97—1222no—
532C4×C8—1222no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542C24—611no—
543C2×Q8—611no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8C22×#692311yescharacteristic
550C22×C4—21no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—4881no—
576C22×C4—4881no—
577C22×C4C22×#692311yescharacteristic
578C2×C8—611no—
579C2×C8—611no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8C22×#692311yescharacteristic
591C2×C8C22×#692311yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—612no—
595C4⋊C4—612no—
596C4⋊C4—611no—
597C4⋊C4—611no—
598C4⋊C4—611no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1222no—
609C4⋊C4—1222no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—4881no—
617C4⋊C4—2442no—
618C4⋊C4C22×#692311yescharacteristic
619C4⋊C4C22×#692311yescharacteristic
620C4⋊C4C22×#692311yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—1221no—
623C22⋊C4—1221no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1224no—
627C22⋊C4—1221no—
628C22⋊C4—4881no—
629C42—612no—
630C42—612no—
631C42—1221no—
632C42—1221no—
633C42—1224no—
634C42—4881no—
635C42—4881no—
636C42—4881no—
637C42—4881no—
638C42—4881no—
639C42—2442no—
640C23—611no—
641C23—611no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23D4×#692311yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—1221no—
652Q8—1221no—
653Q8—2441no—
654Q8—2441no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—81no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—611no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—4881no—
695C2×C4—4881no—
696C2×C4—4881no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4D4×#692311yescharacteristic
716C2×C4C23×#692311yescharacteristic
717C8—21no—
718C8—21no—
719C8—1221no—
720C8—1221no—
721C8—2441no—
722C8—2441no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—611no—
727C22—611no—
728C22—611no—
729C22—611no—
730C22—611no—
731C22—611no—
732C22—1221no—
733C22—1221no—
734C22—1221no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22C2×D4×#692311yescharacteristic
740C4—21no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—611no—
746C4—611no—
747C4—1222no—
748C4—1222no—
749C4—1221no—
750C4—4881no—
751C4—4881no—
752C4—2441no—
753C4—2441no—
754C4—2442no—
755C4—2442no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4—2441no—
760C4#41×#692311yescharacteristic
761C4#41×#692311yescharacteristic
762C2—41no—
763C2—611no—
764C2—611no—
765C2—611no—
766C2—611no—
767C2—2441no—
768C2#123×#692311yescharacteristic
769C2#2146257711yescharacteristic
770C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#483C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#483#6923
hypocenterC61#21587
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #21461899C2semidirect
4. #21461898C2semidirect
5. #21461882C2semidirect
6. #21461881C2semidirect
10. #21461635C2semidirect
11. #106×#6923C2semidirect
12. #21461592C2semidirect
13. #103×#6923C2semidirect
54. #16840094C4semidirect
55. #16840094C4semidirect
56. #16840093C4semidirect
57. #16840092C4semidirect
58. #16840091C4semidirect
59. #16840091C4semidirect
60. #16840090C4semidirect
66. C61×#483C4semidirect
413. #483#6923semidirect
452. C61#21587semidirect

Maximal subgroups

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

subgroupindex
#214623062
#214622572
#214618992
#214618982
#214618822
#214618812
#214618052
#214617702
#214617232
#214616352
#106×#69232
#214615922
#103×#69232
#214615502
#483×D612
#2158761