Finite Group Databasebeta

← #29646672

Subgroups — #29646672

Order 15616.

1056 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459112C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3C2×#16839784C211yesmaximal, characteristic, complemented
4#21444283C212yesmaximal, complemented
5#21444281C212yesmaximal, complemented
6#21444272C212yesmaximal, complemented
7#21444268C212yesmaximal, complemented
8#21444207C211yesmaximal, characteristic, complemented
9#21444206C211yesmaximal, characteristic, complemented
10#21444204C211yesmaximal, characteristic, complemented
11C61×#1477C211yesmaximal, characteristic, complemented
12C22×#11758189—21no—
13#16840316C411yescharacteristic
14#16840316C2211yescharacteristic
15#16840315C411yescharacteristic
16#16840309C411yescharacteristic
17#16840309C2211yescharacteristic
18#16840308C411yescharacteristic
19#16840299C411yescharacteristic
20#16840299C2211yescharacteristic
21#16840294C411yescharacteristic
22#16840294C2211yescharacteristic
23#16840292—21no—
24#16840292—21no—
25#16840290—21no—
26#16840290—21no—
27#16840274C411yescharacteristic
28#16840271—21no—
29#16840271—21no—
30#16840269C411yescharacteristic
31C4×#11758222—21no—
32C4×#11758222—21no—
33C4×#11758222C2211yescharacteristic
34C2×C42×D61C2211yescharacteristic
35#16839815C2211yescharacteristic
36#16839814—21no—
37#16839813C2212yes—
38#16839812—21no—
39#16839784—21no—
40#16839784—21no—
41#16839784C2212yes—
42#16839784C2212yes—
43C2×C4⋊#92418C2211yescharacteristic
44C2×#14519706—21no—
45C4⋊C8×D61—21no—
46C22⋊C8×D61—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
65C2×#11758189—22no—
66C2×#11758189—22no—
67C2×#11758189—44no—
68C22×#92418—21no—
69C2×C8×D61—22no—
70#14519776C2×C411yescharacteristic
71#14519776C2×C411yescharacteristic
72#14519775C2×C411yescharacteristic
73#14519773C2×C411yescharacteristic
74#14519772—21no—
75#14519772—21no—
76#14519770—21no—
77#14519770—21no—
78#14519768C2×C411yescharacteristic
79#14519768C2×C411yescharacteristic
80#14519767—21no—
81#14519767—21no—
82#14519766C2×C411yescharacteristic
83#14519764C2×C411yescharacteristic
84#14519763—21no—
85#14519763—21no—
86#14519762—21no—
87#14519762—21no—
88#14519761—21no—
89#14519759—21no—
90#14519759—21no—
91#14519758—21no—
92#14519757C2×C411yescharacteristic
93#14519757C2×C411yescharacteristic
94#14519755—21no—
95#14519755—21no—
96#14519754—21no—
97#14519754—21no—
98#14519753C2×C411yescharacteristic
99#14519753C2×C411yescharacteristic
100#14519752C2×C411yescharacteristic
101#14519752C2×C411yescharacteristic
102#14519750—21no—
103#14519750—21no—
104#14519749—21no—
105#14519749—21no—
106#14519748C2×C411yescharacteristic
107#14519748C2×C411yescharacteristic
108#14519747—21no—
109#14519745—21no—
110C4×Dic122—21no—
111C4×Dic122—21no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122C2×C411yescharacteristic
115C4×Dic122C2311yescharacteristic
116C4×D244—21no—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244—21no—
120C4×D244C2×C411yescharacteristic
121C4×D244C2311yescharacteristic
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—
129C4×C22⋊D61—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132#14519736—21no—
133#14519736—21no—
134#14519736C2×C411yescharacteristic
135#14519734—21no—
136#14519734—21no—
137#14519734—21no—
138#14519734—21no—
139#14519734—21no—
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C42×D61—21no—
144C42×D61C2×C411yescharacteristic
145C42×D61C2×C411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61C2311yescharacteristic
151C42×D61C2311yescharacteristic
152C4⋊#92418—21no—
153C4⋊#92418—21no—
154C4⋊#92418C2312yes—
155#14519706—22no—
156#14519706—22no—
157#14519706—22no—
158C22⋊#92418—21no—
159#14519689—22no—
160C4×#92418C2312yes—
161C8×Dic61—22no—
162C2×#41×C61C2×C411yescharacteristic
163C22×C8×C61—21no—
164C4×Q8×C61C2×C411yescharacteristic
165C4×Q8×C61C2311yescharacteristic
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61C2×C411yescharacteristic
169C4×D4×C61C2311yescharacteristic
170#117×C61—21no—
171#117×C61C2×C411yescharacteristic
172C2×C42×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C4⋊C8×C61—21no—
176C4⋊C8×C61C2312yes—
177C22⋊C8×C61—21no—
178C4×C8×C61C2312yes—
179C23×D61C22⋊C411yescharacteristic
180#41×C61—22no—
181#41×C61—22no—
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198C22×Dic61C22⋊C411yescharacteristic
199#11758222—22no—
200#11758222—22no—
201#11758222—44no—
202#11758222—42no—
203#11758222—42no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244C22×C411yescharacteristic
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122C22×C411yescharacteristic
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61—42no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C22×C411yescharacteristic
236C4⋊C4×C61C22×C411yescharacteristic
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—21no—
243C42×C61C22×C411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2×D411yescharacteristic
246C42×C61C2411yescharacteristic
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251C22⋊Dic61—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—
261#11758198—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61C22×C411yescharacteristic
267C4⋊Dic61C22×C411yescharacteristic
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—
277#11758196—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C22×C411yescharacteristic
288C4×Dic61C22×C411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C4×Dic61C2×D411yescharacteristic
291C4×Dic61C2×D411yescharacteristic
292C4×Dic61C2×D411yescharacteristic
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418—42no—
296#11758189—44no—
297#11758189—44no—
298C8×D61—44no—
299C23×C61—21no—
300C23×C61C2×C22⋊C411yescharacteristic
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—21no—
304C22×D61—41no—
305C22×D61C2×C22⋊C411yescharacteristic
306C22×D61C2×C22⋊C411yescharacteristic
307Q8×C61—21no—
308Q8×C61—21no—
309D4×C61—21no—
310D4×C61—21no—
311D4×C61—42no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61#13112yes—
326C2×C4×C61#13112yes—
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C22⋊D61—42no—
331C22⋊D61—42no—
332C22⋊D61—42no—
333C22⋊D61—42no—
334C22⋊D61—42no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345C2×Dic61C2×C22⋊C411yescharacteristic
346C2×Dic61C2×C22⋊C411yescharacteristic
347D244—21no—
348D244—21no—
349D244—42no—
350D244—42no—
351C4×D61—22no—
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—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—42no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—42no—
369C4×D61AGL(1,ℤ/8)12yes—
370C4×D61#13712yes—
371Dic122—21no—
372Dic122—21no—
373Dic122—42no—
374Dic122—42no—
375C8×C61—42no—
376C8×C61—42no—
377#92418—42no—
378#92418—42no—
379#17481—611nomaximal, Sylow
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61#40812yes—
386C22×C61C22×C22⋊C411yescharacteristic
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—44no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61#41712yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61#40812yes—
404C4×C61C2×#13111yescharacteristic
405C4×C61C2×#13111yescharacteristic
406C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
407C4×C61C2×#13711yescharacteristic
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—41no—
413Dic61—41no—
414Dic61—41no—
415Dic61#41712yes—
416Dic61#42112yes—
417#3444—611no—
418C2×#431—611no—
419C2×#423—611no—
420#1495—612no—
421#1495—612no—
422#1493—612no—
423#1492—612no—
424#1477—611no—
425#1477—611no—
426#1477—611no—
427#1477D6111yescharacteristic, complemented
428C2×C61—22no—
429C2×C61—81no—
430C2×C61C2×#40811yescharacteristic
431C2×C61C2×#41711yescharacteristic
432C2×C61C2×#42111yescharacteristic
433D61—22no—
434D61—41no—
435D61—81no—
436C22×M16—1221no—
437#533—611no—
438#533—611no—
439#533—611no—
440#532—611no—
441#532—611no—
442#532—611no—
443#529—611no—
444#529—611no—
445#529—611no—
446#529—611no—
447#529—1221no—
448#529—1221no—
449#529—1221no—
450#529—1221no—
451#525—611no—
452#525—611no—
453#525—1221no—
454#525—1221no—
455C4×#41—611no—
456C4×#41—1221no—
457C4×#41—1221no—
458C4×#41C2×D6111yescharacteristic
459C22×C42—611no—
460#431—611no—
461#431—612no—
462#431—1221no—
463#431—1221no—
464#431C2×D6111yescharacteristic
465#423—612no—
466#423—612no—
467#423—1221no—
468#423—1221no—
469C2×C4⋊C8—611no—
470C2×C4⋊C8—1221no—
471C2×C4⋊C8—1221no—
472C2×C4⋊C8C2×D6111yescharacteristic
473C2×C22⋊C8—1221no—
474C2×C4×C8—612no—
475Q8⋊C8—612no—
476Q8⋊C8—612no—
477Q8⋊C8—612no—
478Q8⋊C8C2×D6112yescomplemented
479D4⋊C8—612no—
480D4⋊C8—612no—
481D4⋊C8—612no—
482D4⋊C8C2×D6112yescomplemented
483C61#1748111yescharacteristic, complemented, Sylow
484C2×#41—611no—
485C2×#41—1221no—
486C2×#41—1221no—
487C2×#41C4×D6111yescharacteristic
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C2×M16—1222no—
492C2×M16—1222no—
493C2×M16—2444no—
494C22×C8—21no—
495C22×C8—1222no—
496C22×C8—1221no—
497C4⋊Q8—611no—
498C4⋊Q8—611no—
499C4⋊Q8—611no—
500#127—611no—
501#126—1221no—
502#126—1221no—
503#126—1221no—
504#126—1221no—
505#125—611no—
506#125—611no—
507#125—1221no—
508#125—1221no—
509#124—611no—
510#124—611no—
511#124—1221no—
512#124—1221no—
513#123—1221no—
514#123—1221no—
515#123—1221no—
516#123—1221no—
517#123—1221no—
518#123—1221no—
519C22⋊Q8—611no—
520C22⋊Q8—611no—
521C22⋊Q8—611no—
522C22⋊Q8—611no—
523C22⋊Q8—1221no—
524C22⋊Q8—1221no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527#121—611no—
528#121—611no—
529#121—611no—
530#121—611no—
531#121—1221no—
532#121—1221no—
533#121—1221no—
534#121—1221no—
535#120—1221no—
536#120—1221no—
537C4×Q8—611no—
538C4×Q8—611no—
539C4×Q8—1221no—
540C4×Q8—1221no—
541C4×Q8—1221no—
542C4×Q8—1221no—
543C4×Q8C4×D6111yescharacteristic
544C4×Q8C22×D6111yescharacteristic
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—611no—
548C4×D4—611no—
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×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4C4×D6111yescharacteristic
564C4×D4C22×D6111yescharacteristic
565#117—21no—
566#117—611no—
567#117—1221no—
568#117—1221no—
569#117—1221no—
570#117—1221no—
571#117—1221no—
572#117—1221no—
573#117—1221no—
574#117C4×D6111yescharacteristic
575C2×C42—21no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—1221no—
588C2×C42C22×D6111yescharacteristic
589C4⋊C8—21no—
590C4⋊C8—21no—
591C4⋊C8—612no—
592C4⋊C8—1222no—
593C4⋊C8—1222no—
594C4⋊C8—1222no—
595C4⋊C8—1221no—
596C4⋊C8—1221no—
597C4⋊C8C22×D6112yes—
598C22⋊C8—21no—
599C22⋊C8—1222no—
600C22⋊C8—1221no—
601C4×C8—612no—
602C4×C8—1222no—
603C4×C8C22×D6112yes—
604C24—611no—
605#41—22no—
606#41—22no—
607#41—1222no—
608#41—1222no—
609#41—2442no—
610#41—2442no—
611#41—2444no—
612C2×Q8—611no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8C2×C4×D6111yescharacteristic
616C2×D4—21no—
617C2×D4—611no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4C2×C4×D6111yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
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—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—2442no—
652C22×C4C2×C4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655M16—2444no—
656M16—2444no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—42no—
660C2×C8—1222no—
661C2×C8—1222no—
662C2×C8—2444no—
663C2×C8—2442no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—611no—
667C4⋊C4—611no—
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⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4C2×C4×D6111yescharacteristic
683C4⋊C4C2×C4×D6111yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
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—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—1221no—
718C42—1221no—
719C42—1221no—
720C42C2×C4×D6111yescharacteristic
721C42D4×D6111yescharacteristic
722C42D4×D6111yescharacteristic
723C42C23×D6111yescharacteristic
724C23—21no—
725C23—611no—
726C23—611no—
727C23—1222no—
728C23—1222no—
729C23—1221no—
730C23—2441no—
731C23C22⋊C4×D6111yescharacteristic
732Q8—21no—
733Q8—21no—
734Q8—1221no—
735Q8—1221no—
736Q8—2442no—
737Q8—2442no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—1221no—
742D4—1221no—
743D4—2442no—
744D4—2442no—
745D4—2442no—
746D4—2442no—
747D4—2442no—
748D4—2442no—
749D4—2442no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—612no—
763C2×C4—612no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4C22⋊C4×D6111yescharacteristic
793C2×C4C22⋊C4×D6111yescharacteristic
794C2×C4C22⋊C4×D6111yescharacteristic
795C2×C4#1451978312yes—
796C2×C4#1451978512yes—
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C8—42no—
801C8—42no—
802C8—2442no—
803C8—2442no—
804C22—21no—
805C22—21no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—612no—
810C22—1221no—
811C22—1221no—
812C22—1221no—
813C22—1221no—
814C22—1221no—
815C22—2444no—
816C22—2441no—
817C22—2441no—
818C22—2441no—
819C22#1683972712yes—
820C22C2×C22⋊C4×D6111yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—612no—
828C4—612no—
829C4—1221no—
830C4—1221no—
831C4—1221no—
832C4—1221no—
833C4—2441no—
834C4—2441no—
835C4—2441no—
836C4#1683972712yes—
837C4C2×#1451978311yescharacteristic
838C4C2×#1451978511yescharacteristic
839C4AGL(1,ℤ/8)×D6111yescharacteristic
840C4#137×D6111yescharacteristic
841C2—22no—
842C2—81no—
843C2—1222no—
844C2—4881no—
845C2—2441no—
846C2C2×#1683972711yescharacteristic
847C2#417×D6111yescharacteristic
848C2#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#17481
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. #431×D61C2semidirect
3. C2×#16839784C2semidirect
4. #21444283C2semidirect
5. #21444281C2semidirect
6. #21444272C2semidirect
7. #21444268C2semidirect
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
427. #1477D61semidirect
478. Q8⋊C8C2×D61semidirect
482. D4⋊C8C2×D61semidirect
483. C61#17481semidirect

Maximal subgroups

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

subgroupindex
#214591122
#431×D612
C2×#168397842
#214442832
#214442812
#214442722
#214442682
#214442072
#214442062
#214442042
C61×#14772
#1748161