Finite Group Databasebeta

← #29646679

Subgroups — #29646679

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459112C211yesmaximal, characteristic
2C2×#16839818C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444290C212yesmaximal, complemented
5#21444286C212yesmaximal, complemented
6#21444278C212yesmaximal, complemented
7#21444276C212yesmaximal, complemented
8#21444207C211yesmaximal, characteristic, complemented
9#21444206C211yesmaximal, characteristic, complemented
10#21444204C211yesmaximal, characteristic, complemented
11C61×#1477C211yesmaximal, characteristic, complemented
12#16840316C411yescharacteristic
13#16840316C2211yescharacteristic
14#16840315C411yescharacteristic
15#16840309C411yescharacteristic
16#16840309C2211yescharacteristic
17#16840308C411yescharacteristic
18#16840299C411yescharacteristic
19#16840299C2211yescharacteristic
20#16840294C411yescharacteristic
21#16840294C2211yescharacteristic
22#16840292—21no—
23#16840292—21no—
24#16840290—21no—
25#16840290—21no—
26#16840274C411yescharacteristic
27#16840271—21no—
28#16840271—21no—
29#16840269C411yescharacteristic
30C4×#11758222—21no—
31C4×#11758222—21no—
32C4×#11758222C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839818—21no—
35#16839818—21no—
36#16839818C2212yes—
37#16839818C2212yes—
38#16839815C2211yescharacteristic
39#16839814—21no—
40#16839813C2212yes—
41#16839812—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C4⋊C8×D61—21no—
44C2×#14519689—21no—
45C22⋊C8×D61—21no—
46C2×#14519687—21no—
47C4×C8×D61C2212yes—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C61×#431C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×#92418—21no—
66C2×C8×D61—22no—
67#14519776C2×C411yescharacteristic
68#14519776C2×C411yescharacteristic
69#14519775C2×C411yescharacteristic
70#14519773C2×C411yescharacteristic
71#14519772—21no—
72#14519772—21no—
73#14519770—21no—
74#14519770—21no—
75#14519768C2×C411yescharacteristic
76#14519768C2×C411yescharacteristic
77#14519767—21no—
78#14519767—21no—
79#14519766C2×C411yescharacteristic
80#14519764C2×C411yescharacteristic
81#14519763—21no—
82#14519763—21no—
83#14519762—21no—
84#14519762—21no—
85#14519761—21no—
86#14519759—21no—
87#14519759—21no—
88#14519758—21no—
89#14519757C2×C411yescharacteristic
90#14519757C2×C411yescharacteristic
91#14519755—21no—
92#14519755—21no—
93#14519754—21no—
94#14519754—21no—
95#14519753C2×C411yescharacteristic
96#14519753C2×C411yescharacteristic
97#14519752C2×C411yescharacteristic
98#14519752C2×C411yescharacteristic
99#14519750—21no—
100#14519750—21no—
101#14519749—21no—
102#14519749—21no—
103#14519748C2×C411yescharacteristic
104#14519748C2×C411yescharacteristic
105#14519747—21no—
106#14519745—21no—
107C4×Dic122—21no—
108C4×Dic122—21no—
109C4×Dic122—21no—
110C4×Dic122—21no—
111C4×Dic122C2×C411yescharacteristic
112C4×Dic122C2311yescharacteristic
113C4×D244—21no—
114C4×D244—21no—
115C4×D244—21no—
116C4×D244—21no—
117C4×D244C2×C411yescharacteristic
118C4×D244C2311yescharacteristic
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129#14519736—21no—
130#14519736—21no—
131#14519736C2×C411yescharacteristic
132#14519734—21no—
133#14519734—21no—
134#14519734—21no—
135#14519734—21no—
136#14519734—21no—
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C2×C4×Dic61D411yescharacteristic
140C42×D61—21no—
141C42×D61C2×C411yescharacteristic
142C42×D61C2×C411yescharacteristic
143C42×D61D411yescharacteristic
144C42×D61D411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61C2311yescharacteristic
148C42×D61C2311yescharacteristic
149C4⋊#92418—21no—
150C4⋊#92418—21no—
151C4⋊#92418C2312yes—
152#14519706—22no—
153C22⋊#92418—21no—
154#14519689—22no—
155#14519689—22no—
156#14519689—22no—
157#14519687—22no—
158#14519687—22no—
159C4×#92418C2312yes—
160C8×Dic61—22no—
161C2×#41×C61C2×C411yescharacteristic
162C22×C8×C61—21no—
163C4×Q8×C61C2×C411yescharacteristic
164C4×Q8×C61C2311yescharacteristic
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61C2×C411yescharacteristic
168C4×D4×C61C2311yescharacteristic
169#117×C61—21no—
170#117×C61C2×C411yescharacteristic
171C2×C42×C61—21no—
172C2×C42×C61C2311yescharacteristic
173C4⋊C8×C61—21no—
174C4⋊C8×C61—21no—
175C4⋊C8×C61C2312yes—
176C22⋊C8×C61—21no—
177C4×C8×C61C2312yes—
178C23×D61C22⋊C411yescharacteristic
179#41×C61—22no—
180#41×C61—22no—
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198#11758222—22no—
199#11758222—22no—
200#11758222—44no—
201#11758222—42no—
202#11758222—42no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244C22×C411yescharacteristic
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—41no—
212C2×C4×D61—41no—
213C2×C4×D61—42no—
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22×C411yescharacteristic
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122C22×C411yescharacteristic
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61—42no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C22×C411yescharacteristic
235C4⋊C4×C61C22×C411yescharacteristic
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61C22×C411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2411yescharacteristic
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22×C411yescharacteristic
266C4⋊Dic61C22×C411yescharacteristic
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22×C411yescharacteristic
287C4×Dic61C22×C411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C4×Dic61C2×D411yescharacteristic
291C4×Dic61C2×D411yescharacteristic
292C2×#92418—22no—
293C2×#92418—22no—
294C2×#92418—42no—
295C8×D61—44no—
296C23×C61—21no—
297C23×C61C2×C22⋊C411yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—21no—
301C22×D61—41no—
302C22×D61C2×C22⋊C411yescharacteristic
303C22×D61C2×C22⋊C411yescharacteristic
304Q8×C61—21no—
305Q8×C61—21no—
306D4×C61—21no—
307D4×C61—21no—
308D4×C61—42no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—41no—
315C2×C4×C61—42no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61#13112yes—
323C2×C4×C61#13112yes—
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C22⋊D61—42no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C22⋊D61—42no—
331C22⋊D61—42no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344D244—21no—
345D244—21no—
346D244—42no—
347D244—42no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—42no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—42no—
368Dic122—21no—
369Dic122—21no—
370Dic122—42no—
371Dic122—42no—
372C8×C61—42no—
373C8×C61—42no—
374#92418—42no—
375#92418—42no—
376#17482—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61#40812yes—
383C22×C61C22×C22⋊C411yescharacteristic
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—44no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61#42112yes—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61#40812yes—
401C4×C61C2×#13111yescharacteristic
402C4×C61C2×#13111yescharacteristic
403C4×C61#57511yescharacteristic
404C4×C61#57511yescharacteristic
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—41no—
412Dic61—41no—
413Dic61—41no—
414#3444—611no—
415C2×#432—611no—
416C2×#431—611no—
417#1497—612no—
418#1496—612no—
419#1494—612no—
420#1494—612no—
421#1477—611no—
422#1477—611no—
423#1477—611no—
424#1477D6111yescharacteristic, complemented
425C2×C61—22no—
426C2×C61—81no—
427C2×C61C2×#40811yescharacteristic
428C2×C61#289611yescharacteristic
429C2×C61C2×#42111yescharacteristic
430D61—22no—
431D61—41no—
432D61—81no—
433#533—611no—
434#533—611no—
435#533—611no—
436#532—611no—
437#532—611no—
438#532—611no—
439#529—611no—
440#529—611no—
441#529—611no—
442#529—611no—
443#529—1221no—
444#529—1221no—
445#529—1221no—
446#529—1221no—
447#525—611no—
448#525—611no—
449#525—1221no—
450#525—1221no—
451C4×#41—611no—
452C4×#41—1221no—
453C4×#41—1221no—
454C4×#41C2×D6111yescharacteristic
455C22×C42—611no—
456#432—612no—
457#432—612no—
458#432—1221no—
459#432—1221no—
460#431—611no—
461#431—612no—
462#431—1221no—
463#431—1221no—
464#431C2×D6111yescharacteristic
465C2×C4⋊C8—611no—
466C2×C4⋊C8—1221no—
467C2×C4⋊C8C2×D6111yescharacteristic
468C2×C22⋊C8—1221no—
469C2×C22⋊C8—1221no—
470C2×#97—1221no—
471C2×C4×C8—612no—
472Q8⋊C8—612no—
473Q8⋊C8—612no—
474Q8⋊C8—612no—
475Q8⋊C8C2×D6112yescomplemented
476D4⋊C8—612no—
477D4⋊C8—612no—
478D4⋊C8—612no—
479D4⋊C8C2×D6112yescomplemented
480C61#1748211yescharacteristic, complemented, Sylow
481C2×#41—611no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41C4×D6111yescharacteristic
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C22×C8—21no—
489C22×C8—1222no—
490C22×C8—1221no—
491C4⋊Q8—611no—
492C4⋊Q8—611no—
493C4⋊Q8—611no—
494#127—611no—
495#126—1221no—
496#126—1221no—
497#126—1221no—
498#126—1221no—
499#125—611no—
500#125—611no—
501#125—1221no—
502#125—1221no—
503#124—611no—
504#124—611no—
505#124—1221no—
506#124—1221no—
507#123—1221no—
508#123—1221no—
509#123—1221no—
510#123—1221no—
511#123—1221no—
512#123—1221no—
513C22⋊Q8—611no—
514C22⋊Q8—611no—
515C22⋊Q8—611no—
516C22⋊Q8—611no—
517C22⋊Q8—1221no—
518C22⋊Q8—1221no—
519C22⋊Q8—1221no—
520C22⋊Q8—1221no—
521#121—611no—
522#121—611no—
523#121—611no—
524#121—611no—
525#121—1221no—
526#121—1221no—
527#121—1221no—
528#121—1221no—
529#120—1221no—
530#120—1221no—
531C4×Q8—611no—
532C4×Q8—611no—
533C4×Q8—1221no—
534C4×Q8—1221no—
535C4×Q8—1221no—
536C4×Q8—1221no—
537C4×Q8C4×D6111yescharacteristic
538C4×Q8C22×D6111yescharacteristic
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—611no—
542C4×D4—611no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4—1221no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C4×D4—1221no—
554C4×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4C4×D6111yescharacteristic
558C4×D4C22×D6111yescharacteristic
559#117—21no—
560#117—611no—
561#117—1221no—
562#117—1221no—
563#117—1221no—
564#117—1221no—
565#117—1221no—
566#117—1221no—
567#117—1221no—
568#117C4×D6111yescharacteristic
569C2×C42—21no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—1221no—
582C2×C42C22×D6111yescharacteristic
583C4⋊C8—21no—
584C4⋊C8—21no—
585C4⋊C8—612no—
586C4⋊C8—1222no—
587C4⋊C8—1221no—
588C4⋊C8—1221no—
589C4⋊C8C22×D6112yes—
590C22⋊C8—21no—
591C22⋊C8—1222no—
592C22⋊C8—1222no—
593C22⋊C8—1222no—
594C22⋊C8—1221no—
595#97—1222no—
596#97—1222no—
597C4×C8—612no—
598C4×C8—1222no—
599C4×C8C22×D6112yes—
600C24—611no—
601#41—22no—
602#41—22no—
603#41—1222no—
604#41—1222no—
605#41—2444no—
606#41—2442no—
607#41—2442no—
608C2×Q8—611no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8C2×C4×D6111yescharacteristic
612C2×D4—21no—
613C2×D4—611no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4C2×C4×D6111yescharacteristic
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—2441no—
646C22×C4—2441no—
647C22×C4—2442no—
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4D4×D6111yescharacteristic
650C22×C4D4×D6111yescharacteristic
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—42no—
654C2×C8—1222no—
655C2×C8—1222no—
656C2×C8—2444no—
657C2×C8—2442no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—611no—
661C4⋊C4—611no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4C2×C4×D6111yescharacteristic
677C4⋊C4C2×C4×D6111yescharacteristic
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—1221no—
712C42—1221no—
713C42—1221no—
714C42C2×C4×D6111yescharacteristic
715C42D4×D6111yescharacteristic
716C42D4×D6111yescharacteristic
717C42C23×D6111yescharacteristic
718C23—21no—
719C23—611no—
720C23—611no—
721C23—1222no—
722C23—1222no—
723C23—1221no—
724C23—2441no—
725C23C22⋊C4×D6111yescharacteristic
726Q8—21no—
727Q8—21no—
728Q8—1221no—
729Q8—1221no—
730Q8—2442no—
731Q8—2442no—
732D4—21no—
733D4—21no—
734D4—42no—
735D4—1221no—
736D4—1221no—
737D4—2442no—
738D4—2442no—
739D4—2442no—
740D4—2442no—
741D4—2442no—
742D4—2442no—
743D4—2442no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2442no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2442no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4C22⋊C4×D6111yescharacteristic
787C2×C4C22⋊C4×D6111yescharacteristic
788C2×C4C22⋊C4×D6111yescharacteristic
789C2×C4#1451978312yes—
790C2×C4#1451978512yes—
791C2×C4C22×C4×D6111yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×D4×D6111yescharacteristic
794C8—42no—
795C8—42no—
796C8—2442no—
797C8—2442no—
798C22—21no—
799C22—21no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—612no—
804C22—1221no—
805C22—1221no—
806C22—1221no—
807C22—1221no—
808C22—1221no—
809C22—2444no—
810C22—2441no—
811C22—2441no—
812C22—2441no—
813C22#1683972712yes—
814C22C2×C22⋊C4×D6111yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—1221no—
822C4—1221no—
823C4—1221no—
824C4—1221no—
825C4—1221no—
826C4—1221no—
827C4—2441no—
828C4—2441no—
829C4—2441no—
830C4#1683972712yes—
831C4C2×#1451978311yescharacteristic
832C4C2×#1451978511yescharacteristic
833C4#1684055811yescharacteristic
834C4#1684056111yescharacteristic
835C2—22no—
836C2—81no—
837C2—1222no—
838C2—4881no—
839C2—2441no—
840C2C2×#1683972711yescharacteristic
841C2#2145433511yescharacteristic
842C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1477C2
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC42×C61C24
hypercenter#1477D61
hypocenterC61#17482
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. C2×#16839818C2semidirect
3. #431×D61C2semidirect
4. #21444290C2semidirect
5. #21444286C2semidirect
6. #21444278C2semidirect
7. #21444276C2semidirect
8. #21444207C2semidirect
9. #21444206C2semidirect
10. #21444204C2semidirect
11. C61×#1477C2semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
424. #1477D61semidirect
475. Q8⋊C8C2×D61semidirect
479. D4⋊C8C2×D61semidirect
480. C61#17482semidirect

Maximal subgroups

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

subgroupindex
#214591122
C2×#168398182
#431×D612
#214442902
#214442862
#214442782
#214442762
#214442072
#214442062
#214442042
C61×#14772
#1748261