Finite Group Databasebeta

← #485×#6923 #30617192

Subgroups — #485×#6923 #30617192

Order 15616.

888 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
1C22⋊Q8×#6923C211yesmaximal, characteristic
2#117×#6923C211yesmaximal, characteristic
3#21461899C211yesmaximal, characteristic, complemented
4#21461898C211yesmaximal, characteristic, complemented
5#21461881C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic
8#21461770C211yesmaximal, characteristic
9#21461724C211yesmaximal, characteristic
10#107×#6923C211yesmaximal, characteristic, complemented
11#106×#6923C211yesmaximal, characteristic, complemented
12#103×#6923C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14C22⋊C8×#6923C211yesmaximal, characteristic
15#485×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×#14519856C2211yescharacteristic
18C22×C4×#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23D61⋊(C22⋊C8)C2211yescharacteristic
24C2×C8×#6923C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26(C2×#6923)⋊Q8C2211yescharacteristic
27#16840713C2211yescharacteristic
28#16840711—21no—
29#16840709—21no—
30#16840704C2211yescharacteristic
31C4⋊C4×#6923—21no—
32C4⋊C4×#6923C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C22⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C22⋊C4×#6923—21no—
40#16840698—21no—
41C42×#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
53#117×D61C2211yescharacteristic
54#16840106C411yescharacteristic, complemented
55#16840105C411yescharacteristic, complemented
56#16840104C411yescharacteristic, complemented
57#16840103C411yescharacteristic, complemented
58#16840102C411yescharacteristic, complemented
59#16840101C411yescharacteristic, complemented
60#16840100C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65C22⋊C8×D61C2211yescharacteristic
66C61×#485C411yescharacteristic, complemented
67C23×#6923D411yescharacteristic
68C23×#6923D411yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71Q8×#6923—22no—
72Q8×#6923—22no—
73#14519856—22no—
74#14519856—22no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—22no—
85C2×C4×#6923—22no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923D411yescharacteristic
93C2×C4×#6923D411yescharacteristic
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—22no—
97#14519845—22no—
98#14519840—22no—
99#14519840—22no—
100#14519834—21no—
101C22⋊#92420—21no—
102C8×#6923—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×D61C2311yescharacteristic
115C2×C8×D61C2311yescharacteristic
116C2×C8×D61C2311yescharacteristic
117#14519757C2×C411yescharacteristic
118#14519756C2×C411yescharacteristic
119#14519755—21no—
120#14519754—21no—
121#14519753C2×C411yescharacteristic
122#14519736C2×C411yescharacteristic
123#14519735C2×C411yescharacteristic
124#14519735C2×C411yescharacteristic
125#14519734—21no—
126#14519733—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C22⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C42×D61—21no—
134#14519711C2×C411yescharacteristic, complemented
135#14519710C2×C411yescharacteristic, complemented
136#14519710C2×C411yescharacteristic, complemented
137#14519709C2×C411yescharacteristic, complemented
138#14519708C2×C411yescharacteristic, complemented
139#14519708C2×C411yescharacteristic, complemented
140#14519702C2×C411yescharacteristic, complemented
141#14519702C2×C411yescharacteristic, complemented
142#14519701C2×C411yescharacteristic, complemented
143#14519701C2×C411yescharacteristic, complemented
144#14519700C2×C411yescharacteristic, complemented
145#14519700C2×C411yescharacteristic, complemented
146C22⋊#92418C2×C411yescharacteristic
147#14519689C2×C411yescharacteristic
148#14519689C2×C411yescharacteristic
149C22⋊Q8×C61C2×C411yescharacteristic
150#117×C61C2×C411yescharacteristic
151#107×C61C2×C411yescharacteristic, complemented
152#106×C61C2×C411yescharacteristic, complemented
153#103×C61C2×C411yescharacteristic, complemented
154#103×C61C2×C411yescharacteristic, complemented
155C22⋊C8×C61C2×C411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—22no—
160C22×#6923—22no—
161C22×#6923—22no—
162C22×#6923—22no—
163C22×#6923—22no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—41no—
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C2×Q8×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×Dic61#4111yescharacteristic
174Q8×D61—21no—
175Q8×D61—21no—
176Q8×D61—21no—
177Q8×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—21no—
185C2×C4×D61—21no—
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—42no—
194C2×#92420—21no—
195C2×#92420—21no—
196C4⋊#6923—21no—
197C4⋊#6923—21no—
198C4⋊#6923—21no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—42no—
203C4⋊#6923—42no—
204C4⋊#6923#4112yes—
205C4⋊#6923#4112yes—
206C4×#6923—24no—
207C4×#6923—22no—
208C4×#6923—22no—
209C4×#6923—21no—
210C4×#6923—21no—
211C4×#6923—42no—
212C4×#6923—42no—
213C4×#6923—42no—
214C4×#6923—42no—
215C4×#6923—42no—
216C4×#6923—42no—
217C4×#6923#4112yes—
218C4×#6923#4112yes—
219D61⋊C8—21no—
220D61⋊C8—21no—
221D61⋊C8—21no—
222D61⋊C8—21no—
223C2×C8×C61C22×C411yescharacteristic
224C2×C8×C61C22×C411yescharacteristic
225C4⋊C4×C61—21no—
226C4⋊C4×C61C22×C411yescharacteristic
227C4⋊C4×C61C22×C411yescharacteristic
228C4⋊C4×C61C22×C411yescharacteristic
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C42×C61—21no—
232C22⋊Dic61—21no—
233C22⋊Dic61—21no—
234#11758198—21no—
235#11758198—21no—
236#11758198—21no—
237#11758198—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61C22×C411yescharacteristic
240C4⋊Dic61C22×C411yescharacteristic
241C4⋊Dic61C22×C411yescharacteristic
242#11758196—21no—
243#11758196—21no—
244#11758196—21no—
245#11758196—21no—
246#11758196—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C2×#92418C22×C411yescharacteristic
251C2×#92418C22×C411yescharacteristic
252C8×D61—21no—
253C8×D61—21no—
254C8×D61—21no—
255C8×D61—21no—
256C23×C61C4×D411yescharacteristic
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61C4×D411yescharacteristic
264C22×D61C22×D411yescharacteristic
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—22no—
271C2×#6923—22no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—44no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—44no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—41no—
286C2×#6923#12312yes—
287C2×#6923#12312yes—
288C2×#6923#13512yes—
289C2×#6923#13512yes—
290C2×#6923#13712yes—
291Q8×C61—21no—
292Q8×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61C4×D411yescharacteristic
308C2×Dic61C2×#4111yescharacteristic
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—21no—
313C4×D61—21no—
314C4×D61—21no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
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—
337C4×#485—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×D61C2×#13511yescharacteristic
352C2×D61C2×#13511yescharacteristic
353C2×D61C2×#13711yescharacteristic
354C2×D61#57511yescharacteristic
355#6923—22no—
356#6923—22no—
357#6923—41no—
358#6923—42no—
359#6923—42no—
360#6923—81no—
361#6923—81no—
362#6923#48514yesdirect product factor
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×#485—611no—
378C4×C22⋊Q8—611no—
379C4×#117—611no—
380#1928—611no—
381#1927—611no—
382#1919—611no—
383#1918—611no—
384#1873—611no—
385#1854—611no—
386#1825—611no—
387C4×#107—611no—
388C4×#106—611no—
389C4×#103—611no—
390C4×#103—611no—
391C4×C22⋊C8—611no—
392C2×C61—41no—
393C2×C61C4×#12311yescharacteristic
394C2×C61C4×#13511yescharacteristic
395C2×C61C4×#13711yescharacteristic
396D61—41no—
397D61C2×#48511yescharacteristic
398D61#309111yescharacteristic
399D61#310211yescharacteristic
400D61#310711yescharacteristic
401C2×C22⋊Q8—611no—
402C2×C4×Q8—611no—
403C2×#117—611no—
404C2×#117—611no—
405C22×C42—611no—
406#485—611no—
407#485—611no—
408#485—611no—
409#485—611no—
410#485—611no—
411#485—611no—
412#485—611no—
413#485#692311yescharacteristic, direct product factor
414C2×#107—611no—
415C2×#107—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×C4×C8—611no—
425C2×C4×C8—611no—
426#391—611no—
427#389—611no—
428#387—1221no—
429#385—1221no—
430#380—611no—
431C4×C4⋊C4—611no—
432C4×C4⋊C4—611no—
433C4×C4⋊C4—611no—
434C4×C4⋊C4—611no—
435C4×C4⋊C4—611no—
436C4×C4⋊C4—1221no—
437C4×C22⋊C4—1221no—
438C4×C22⋊C4—1221no—
439C4×C22⋊C4—1221no—
440#376—1221no—
441C43—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—
452C61C4×#48511yescharacteristic, complemented, Sylow
453C22×Q8—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22⋊Q8—611no—
462C22⋊Q8—611no—
463C22⋊Q8—611no—
464C22⋊Q8—1221no—
465C22⋊Q8—1221no—
466C22⋊Q8C2×#692311yescharacteristic
467C4×Q8—1222no—
468C4×Q8—1222no—
469#117—611no—
470#117—611no—
471#117—611no—
472#117—1221no—
473#117—1221no—
474#117—1222no—
475#117—1222no—
476#117C2×#692311yescharacteristic
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×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—1221no—
496C2×C42—1222no—
497C2×C42—1222no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505#107—611no—
506#107—611no—
507#107—611no—
508#107—1222no—
509#107C2×#692311yescharacteristic, complemented
510#106—611no—
511#106—611no—
512#106—611no—
513#106—1222no—
514#106C2×#692311yescharacteristic, complemented
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, complemented
524#103C2×#692311yescharacteristic, complemented
525C22⋊C8—611no—
526C22⋊C8—611no—
527C22⋊C8—611no—
528C22⋊C8—1221no—
529C22⋊C8—1221no—
530C22⋊C8C2×#692311yescharacteristic
531C4×C8—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—611no—
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—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—2441no—
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—612no—
594C4⋊C4—612no—
595C4⋊C4—611no—
596C4⋊C4—611no—
597C4⋊C4—611no—
598C4⋊C4—1221no—
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—1221no—
609C4⋊C4—1221no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C4⋊C4C22×#692311yescharacteristic
613C4⋊C4C22×#692311yescharacteristic
614C4⋊C4C22×#692311yescharacteristic
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—1221no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4—1224no—
622C22⋊C4—1221no—
623C22⋊C4—1221no—
624C22⋊C4—2442no—
625C42—21no—
626C42—612no—
627C42—612no—
628C42—1221no—
629C42—1221no—
630C42—1222no—
631C42—1221no—
632C42—1221no—
633C42—1222no—
634C42—1224no—
635C42—1221no—
636C42—2442no—
637C42—2442no—
638C42—2442no—
639C42—2442no—
640C42—2442no—
641C42—2442no—
642C23—611no—
643C23—611no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23D4×#692311yescharacteristic
651Q8—21no—
652Q8—21no—
653Q8—1221no—
654Q8—1221no—
655Q8—2441no—
656Q8—2441no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—611no—
669C2×C4—611no—
670C2×C4—611no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—611no—
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—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2444no—
704C2×C4—2444no—
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—614no—
746C4—611no—
747C4—611no—
748C4—1222no—
749C4—1222no—
750C4—1221no—
751C4—4881no—
752C4—4881no—
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#135×#692311yescharacteristic
770C2#137×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#485C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#485#6923
hypocenterC61C4×#485
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #21461899C2semidirect
4. #21461898C2semidirect
5. #21461881C2semidirect
6. #21461880C2semidirect
10. #107×#6923C2semidirect
11. #106×#6923C2semidirect
12. #103×#6923C2semidirect
13. #103×#6923C2semidirect
54. #16840106C4semidirect
55. #16840105C4semidirect
56. #16840104C4semidirect
57. #16840103C4semidirect
58. #16840102C4semidirect
59. #16840101C4semidirect
60. #16840100C4semidirect
66. C61×#485C4semidirect
134. #14519711C2×C4semidirect
135. #14519710C2×C4semidirect
136. #14519710C2×C4semidirect
137. #14519709C2×C4semidirect
138. #14519708C2×C4semidirect
139. #14519708C2×C4semidirect
140. #14519702C2×C4semidirect
141. #14519702C2×C4semidirect
142. #14519701C2×C4semidirect
143. #14519701C2×C4semidirect
144. #14519700C2×C4semidirect
145. #14519700C2×C4semidirect
151. #107×C61C2×C4semidirect
152. #106×C61C2×C4semidirect
153. #103×C61C2×C4semidirect
154. #103×C61C2×C4semidirect
362. #6923#485direct (N × H)
413. #485#6923direct (N × H)
452. C61C4×#485semidirect
509. #107C2×#6923semidirect
514. #106C2×#6923semidirect
523. #103C2×#6923semidirect
524. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×#69232
#117×#69232
#214618992
#214618982
#214618812
#214618802
#214618052
#214617702
#214617242
#107×#69232
#106×#69232
#103×#69232
C22⋊C8×#69232
#485×D612
C4×#48561