Finite Group Databasebeta

← #30552362

Subgroups — #30552362

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459209C211yesmaximal, characteristic
2#21457117C214yesmaximal, complemented
3#21457102C214yesmaximal, complemented
4#21457087C214yesmaximal, complemented
5#21457072C214yesmaximal, complemented
6#21456368C211yesmaximal, characteristic, complemented
7#21456361C211yesmaximal, characteristic, complemented
8#21456222C211yesmaximal, characteristic, complemented
9#21456215C211yesmaximal, characteristic, complemented
10#21455750C212yesmaximal, complemented
11#21455742C212yesmaximal, complemented
12#21455637C212yesmaximal, complemented
13#21455628C212yesmaximal, complemented
14#21454457C211yesmaximal, characteristic, complemented
15C2×C61×#544C211yesmaximal, characteristic, complemented
16#16840383C2212yes—
17#16840383C2212yes—
18#16840374C2212yes—
19#16840367C2212yes—
20#16840359—21no—
21#16840359—21no—
22#16840350—21no—
23#16840350—21no—
24#16840319C2211yescharacteristic
25#16840312C2211yescharacteristic
26#16840290—22no—
27#16840290—22no—
28#16840273C2212yes—
29C4×#11758222C2212yes—
30#16840172C2212yescomplemented
31#16840172C2212yescomplemented
32#16840168C2214yescomplemented
33#16840165C2212yescomplemented
34#16840161C2214yescomplemented
35#16840158C2212yescomplemented
36#16840132C2212yescomplemented
37#16840128C2212yescomplemented
38#16840124C2214yescomplemented
39#16840119C2214yescomplemented
40#16840114C2212yescomplemented
41#16840110C2212yescomplemented
42#16840103C2214yes—
43#16840103C2214yes—
44#16840097C2214yes—
45#16840092C2214yes—
46#16840086C2214yes—
47#16840086C2214yes—
48#16840080C2214yes—
49#16840075C2214yes—
50#16840066C2214yescomplemented
51#16840066C2214yescomplemented
52#16840059C2214yescomplemented
53#16840059C2214yescomplemented
54#16840054C2214yescomplemented
55#16840049C2214yescomplemented
56#16840044C2214yescomplemented
57#16840039C2214yescomplemented
58#16839823C2214yes—
59#16839823C2214yes—
60#16839802C2212yes—
61#16839802C2212yes—
62#16839802C2212yes—
63#16839802C2212yes—
64#16839786C2212yes—
65#16839761C2212yes—
66#16839761C2212yes—
67#16839761C2212yes—
68#16839761C2212yes—
69#16839726C2212yes—
70C4×#11758194C2211yescharacteristic
71C4×#11758194C2211yescharacteristic
72C61×#544—22no—
73C61×#544—22no—
74C61×#544C2214yes—
75C61×#544C2214yes—
76C2×C4⋊Q8×C61—21no—
77C2×C4⋊Q8×C61C2211yescharacteristic
78C2×C4⋊Q8×C61C2211yescharacteristic
79C2×#125×C61—21no—
80C2×#125×C61C2211yescharacteristic
81C2×#125×C61C2211yescharacteristic
82C2×C22⋊Q8×C61—21no—
83C2×C22⋊Q8×C61—21no—
84C2×#117×C61C2211yescharacteristic
85C2×#117×C61C2211yescharacteristic
86C22×C4⋊C4×C61C2211yescharacteristic
87C2×#11758222C2312yes—
88C2×#11758194C2312yes—
89C2×#11758194C2312yes—
90#14519777C2311yescharacteristic
91#14519777C2311yescharacteristic
92#14519777C2311yescharacteristic
93#14519774C2311yescharacteristic
94#14519772—22no—
95#14519772—22no—
96#14519770—22no—
97#14519770—22no—
98#14519769C2312yes—
99#14519767—22no—
100#14519767—22no—
101#14519765C2312yes—
102#14519763—22no—
103#14519763—22no—
104#14519762—22no—
105#14519762—22no—
106#14519760—22no—
107#14519759—22no—
108#14519759—22no—
109#14519756—21no—
110#14519756—21no—
111#14519756C2312yes—
112#14519756C2312yes—
113#14519755—22no—
114#14519755—22no—
115#14519751—21no—
116#14519751—21no—
117#14519751C2312yes—
118#14519751C2312yes—
119#14519750—22no—
120#14519750—22no—
121#14519746—22no—
122C4×Dic122—21no—
123C4×Dic122—21no—
124C4×Dic122C2312yes—
125C4×Dic122C2312yes—
126C4×D244—21no—
127C4×D244—21no—
128C4×D244C2312yes—
129C4×D244C2312yes—
130C4×C22⋊D61—22no—
131C4×C22⋊D61—22no—
132C4×C22⋊D61—22no—
133C4×C22⋊D61—22no—
134#14519736C2312yes—
135#14519734—22no—
136C42×D61—22no—
137#14519710C2314yes—
138#14519710C2314yes—
139#14519710C2314yes—
140#14519710C2314yes—
141#14519708C2314yes—
142#14519708C2314yes—
143#14519708C2314yes—
144#14519708C2314yes—
145C4⋊#92418C2314yes—
146C4⋊#92418C2314yes—
147#14519700C2314yes—
148#14519700C2314yes—
149#14519700C2314yes—
150#14519700C2314yes—
151#14519697C2314yes—
152#14519697C2314yes—
153#14519697C2314yes—
154#14519697C2314yes—
155C22⋊#92418C2314yes—
156C22⋊#92418C2314yes—
157#14519688C2312yes—
158#14519688C2312yes—
159C4×#92418C2312yes—
160C4×#92418C2312yes—
161C22×Q8×C61—21no—
162C22×Q8×C61—21no—
163C23×C4×C61—21no—
164C23×C4×C61C2311yescharacteristic
165C4⋊Q8×C61—24no—
166C4⋊Q8×C61—24no—
167C4⋊Q8×C61—22no—
168C4⋊Q8×C61—21no—
169C4⋊Q8×C61—21no—
170C4⋊Q8×C61C2314yes—
171C4⋊Q8×C61C2312yes—
172C4⋊Q8×C61C2312yes—
173#125×C61—24no—
174#125×C61—24no—
175#125×C61—22no—
176#125×C61—21no—
177#125×C61—21no—
178#125×C61C2314yes—
179#125×C61C2312yes—
180#125×C61C2312yes—
181C22⋊Q8×C61—24no—
182C22⋊Q8×C61—24no—
183C22⋊Q8×C61—24no—
184C22⋊Q8×C61—24no—
185#117×C61—22no—
186#117×C61D412yes—
187#117×C61D412yes—
188#117×C61C2314yes—
189#117×C61C2312yes—
190#117×C61C2312yes—
191C2×C4⋊C4×C61—21no—
192C2×C4⋊C4×C61—21no—
193C2×C4⋊C4×C61—21no—
194C2×C4⋊C4×C61—21no—
195C2×C4⋊C4×C61—21no—
196C2×C4⋊C4×C61—22no—
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61—21no—
199C2×C4⋊C4×C61D411yescharacteristic
200C2×C4⋊C4×C61D411yescharacteristic
201C2×C4⋊C4×C61C2311yescharacteristic
202C2×C4⋊C4×C61C2311yescharacteristic
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2314yes—
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61D411yescharacteristic
208C2×C22⋊C4×C61D411yescharacteristic
209C2×C42×C61—21no—
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212C24×C61C2×D411yescharacteristic
213C2×Q8×C61—24no—
214C2×Q8×C61—22no—
215C2×Q8×C61—22no—
216C2×Q8×C61—82no—
217C2×Q8×C61—82no—
218C22×C4×C61—24no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—24no—
224C22×C4×C61—82no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2412yes—
232C22×C4×C61C2411yescharacteristic
233C2×C22⋊D61—22no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236#11758222—28no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C2412yes—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122C2412yes—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C2×D412yes—
261C4⋊C4×C61C2×D412yes—
262C4⋊C4×C61C2×D412yes—
263C4⋊C4×C61C2×D412yes—
264C4⋊C4×C61C2412yes—
265C4⋊C4×C61C2412yes—
266C4⋊C4×C61C2412yes—
267C4⋊C4×C61C2412yes—
268C22⋊C4×C61—24no—
269C22⋊C4×C61C2×D412yes—
270C22⋊C4×C61C2×D412yes—
271C22⋊C4×C61C2×D412yes—
272C22⋊C4×C61C2×D412yes—
273C42×C61—24no—
274C42×C61C2×D412yes—
275C42×C61C2×D411yescharacteristic
276C42×C61C2×D411yescharacteristic
277C42×C61C2411yescharacteristic
278C42×C61C2411yescharacteristic
279C42×C61C2412yes—
280C22⋊Dic61—22no—
281C22⋊Dic61—22no—
282C22⋊Dic61—22no—
283#11758198—22no—
284#11758198—22no—
285#11758198—22no—
286#11758198—22no—
287#11758198—22no—
288#11758198—22no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61C2412yes—
294C4⋊Dic61C2412yes—
295#11758196—22no—
296#11758196—22no—
297#11758196—22no—
298#11758196—22no—
299#11758196—22no—
300#11758196—22no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304#11758194—24no—
305#11758194—24no—
306C2×#92418C2414yes—
307C2×#92418C2414yes—
308C23×C61—22no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61C22×D412yes—
312C23×C61C22×D411yescharacteristic
313C22×D61—22no—
314Q8×C61—82no—
315Q8×C61—84no—
316Q8×C61—82no—
317C2×C4×C61—22no—
318C2×C4×C61—24no—
319C2×C4×C61—24no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61—84no—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D412yes—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C612−1+414yes—
342C2×C4×C61C2511yescharacteristic
343C22⋊D61—44no—
344C22⋊D61—82no—
345C22⋊D61—82no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349D244—24no—
350D244—81no—
351D244—81no—
352C4×D61—44no—
353C4×D61—82no—
354C4×D61—82no—
355Dic122—24no—
356Dic122—81no—
357Dic122—81no—
358#92418—24no—
359#92418—24no—
360#60867—611nomaximal, Sylow
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—44no—
367C22×C61#53612yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C4×C61—21no—
373C4×C61—22no—
374C4×C61—21no—
375C4×C61—21no—
376C4×C61—22no—
377C4×C61—21no—
378C4×C61—22no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61#53612yes—
384C4×C61C2×2−1+412yes—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C2×#544D6111yescharacteristic, complemented
389#3455—611no—
390#3244—614no—
391#3243—614no—
392#3242—614no—
393#3241—614no—
394#3166—611no—
395#3165—611no—
396#3142—611no—
397#3141—611no—
398#3093—612no—
399#3092—612no—
400#3080—612no—
401#3079—612no—
402#2921—611no—
403C2×C61—22no—
404C2×C61—42no—
405C2×C61C2×#53611yescharacteristic
406C2×C61#358511yescharacteristic
407C2×C61#358611yescharacteristic
408D61—82no—
409#544—22no—
410#544—22no—
411#544C2×D6114yes—
412#544C2×D6114yes—
413#542—612no—
414#542—612no—
415#541—612no—
416#540—612no—
417#539—1221no—
418#539—1221no—
419#538—1221no—
420#538—1221no—
421#533—611no—
422#532—611no—
423C2×C4⋊Q8—21no—
424C2×C4⋊Q8C2×D6111yescharacteristic
425C2×C4⋊Q8C2×D6111yescharacteristic
426#529—1222no—
427#529—1222no—
428C2×#125—21no—
429C2×#125C2×D6111yescharacteristic
430C2×#125C2×D6111yescharacteristic
431#525—612no—
432C2×C22⋊Q8—21no—
433C2×C22⋊Q8—21no—
434C4×#41—612no—
435C2×#117C2×D6111yescharacteristic
436C2×#117C2×D6111yescharacteristic
437C22×C4⋊C4C2×D6111yescharacteristic
438#501—614no—
439#501—612no—
440#501—612no—
441#500—612no—
442#499—614no—
443#498—612no—
444#491—612no—
445#490—612no—
446#489—614no—
447#488—614no—
448#487—612no—
449#486—612no—
450#485—614no—
451#485—614no—
452#484—614no—
453#483—614no—
454#482—614no—
455#482—614no—
456#481—614no—
457#480—614no—
458#479—614no—
459#479—614no—
460#478—614no—
461#478—614no—
462#477—614no—
463#476—614no—
464#475—614no—
465#474—614no—
466#433—614no—
467#433—614no—
468#428—612no—
469#428—612no—
470#428—612no—
471#428—612no—
472#423—612no—
473#417—612no—
474#417—612no—
475#417—612no—
476#417—612no—
477#407—612no—
478C4×M16—611no—
479C4×M16—611no—
480C61#6086711yescharacteristic, complemented, Sylow
481C2×#41—612no—
482C22×Q8—21no—
483C22×Q8—21no—
484C23×C4—21no—
485C23×C4C22×D6111yescharacteristic
486C2×M16—612no—
487C2×M16—612no—
488C4⋊Q8—24no—
489C4⋊Q8—24no—
490C4⋊Q8—22no—
491C4⋊Q8—21no—
492C4⋊Q8—21no—
493C4⋊Q8—611no—
494C4⋊Q8—611no—
495C4⋊Q8—611no—
496C4⋊Q8C22×D6114yes—
497C4⋊Q8C22×D6112yes—
498C4⋊Q8C22×D6112yes—
499#127—611no—
500#126—1222no—
501#126—1222no—
502#126—1222no—
503#126—1222no—
504#125—24no—
505#125—24no—
506#125—22no—
507#125—21no—
508#125—21no—
509#125—612no—
510#125—1222no—
511#125—1222no—
512#125C22×D6114yes—
513#125C22×D6112yes—
514#125C22×D6112yes—
515#124—612no—
516#124—1222no—
517#124—1222no—
518#123—1222no—
519#123—1222no—
520#123—1222no—
521#123—1222no—
522#123—1222no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8—612no—
528C22⋊Q8—612no—
529C22⋊Q8—1221no—
530C22⋊Q8—1221no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—612no—
534#121—612no—
535#121—1221no—
536#121—1221no—
537#121—1222no—
538#121—1222no—
539#120—1222no—
540C4×Q8—612no—
541C4×Q8—612no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544C4×D4—612no—
545C4×D4—612no—
546C4×D4—1222no—
547C4×D4—1222no—
548C4×D4—1222no—
549C4×D4—1222no—
550C4×D4—1221no—
551C4×D4—1221no—
552#117—22no—
553#117—612no—
554#117—1222no—
555#117C22⋊D6112yes—
556#117C22⋊D6112yes—
557#117C22×D6114yes—
558#117C22×D6112yes—
559#117C22×D6112yes—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4C22⋊D6111yescharacteristic
569C2×C4⋊C4C22⋊D6111yescharacteristic
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C4⋊C4C22×D6111yescharacteristic
572C2×C4⋊C4C22×D6114yes—
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4C22⋊D6111yescharacteristic
577C2×C22⋊C4C22⋊D6111yescharacteristic
578C2×C42—21no—
579C2×C42—1222no—
580C2×C42C22×D6111yescharacteristic
581C2×C42C22×D6111yescharacteristic
582#107—614no—
583#107—614no—
584#107—614no—
585#107—614no—
586#106—614no—
587#106—614no—
588#106—614no—
589#106—614no—
590C4⋊C8—614no—
591C4⋊C8—614no—
592#103—614no—
593#103—614no—
594#103—614no—
595#103—614no—
596#102—614no—
597#102—614no—
598#102—614no—
599#102—614no—
600C22⋊C8—614no—
601C22⋊C8—614no—
602#97—612no—
603#97—612no—
604C4×C8—612no—
605C4×C8—612no—
606C24C2×C22⋊D6111yescharacteristic
607#41—1228no—
608C2×Q8—24no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—82no—
612C2×Q8—82no—
613C2×Q8—612no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×D4—612no—
617C2×D4—1222no—
618C2×D4—1222no—
619C2×D4—1222no—
620C2×D4—1221no—
621C2×D4—1221no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6112yes—
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C2×C22⋊D6111yescharacteristic
637C22×C4C2×C22⋊D6111yescharacteristic
638C22×C4C23×D6112yes—
639C22×C4C23×D6111yescharacteristic
640M16—1224no—
641M16—1224no—
642C2×C8—614no—
643C2×C8—614no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—612no—
659C4⋊C4—612no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4C2×C22⋊D6112yes—
671C4⋊C4C2×C22⋊D6112yes—
672C4⋊C4C2×C22⋊D6112yes—
673C4⋊C4C2×C22⋊D6112yes—
674C4⋊C4C23×D6112yes—
675C4⋊C4C23×D6112yes—
676C4⋊C4C23×D6112yes—
677C4⋊C4C23×D6112yes—
678C22⋊C4—24no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4C2×C22⋊D6112yes—
689C22⋊C4C2×C22⋊D6112yes—
690C22⋊C4C2×C22⋊D6112yes—
691C22⋊C4C2×C22⋊D6112yes—
692C42—24no—
693C42—1222no—
694C42—1222no—
695C42—1222no—
696C42C2×C22⋊D6112yes—
697C42C2×C22⋊D6111yescharacteristic
698C42C2×C22⋊D6111yescharacteristic
699C42C23×D6111yescharacteristic
700C42C23×D6111yescharacteristic
701C42C23×D6112yes—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—1222no—
706C23C22×C22⋊D6112yes—
707C23C22×C22⋊D6111yescharacteristic
708Q8—84no—
709Q8—82no—
710Q8—82no—
711Q8—1224no—
712Q8—4881no—
713Q8—4881no—
714D4—1224no—
715D4—4881no—
716D4—4881no—
717D4—4882no—
718D4—4882no—
719D4—2444no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—4882no—
740C2×C4—4882no—
741C2×C4—2444no—
742C2×C4C22×C22⋊D6112yes—
743C2×C4C22×C22⋊D6112yes—
744C2×C4C22×C22⋊D6112yes—
745C2×C4C22×C22⋊D6111yescharacteristic
746C2×C4C22×C22⋊D6111yescharacteristic
747C2×C4C22×C22⋊D6111yescharacteristic
748C2×C4C22×C22⋊D6111yescharacteristic
749C2×C4C22×C22⋊D6111yescharacteristic
750C2×C4#1451982514yes—
751C2×C4C24×D6111yescharacteristic
752C8—1224no—
753C8—1224no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22#1684033612yes—
764C22C23×C22⋊D6111yescharacteristic
765C4—22no—
766C4—21no—
767C4—21no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—2442no—
777C4—2442no—
778C4—2442no—
779C4#1684033612yes—
780C4C2×#1451982512yes—
781C2—22no—
782C2—42no—
783C2—4882no—
784C2C2×#1684033611yescharacteristic
785C2#2146059911yescharacteristic
786C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#544C2
socleC22×C61C23×D4
prime radical#21459209C2
hypercenterC2×#544D61
hypocenterC61#60867
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #21457117C2semidirect
3. #21457102C2semidirect
4. #21457087C2semidirect
5. #21457072C2semidirect
6. #21456368C2semidirect
7. #21456361C2semidirect
8. #21456222C2semidirect
9. #21456215C2semidirect
10. #21455750C2semidirect
11. #21455742C2semidirect
12. #21455637C2semidirect
13. #21455628C2semidirect
14. #21454457C2semidirect
15. C2×C61×#544C2semidirect
30. #16840172C22semidirect
31. #16840172C22semidirect
32. #16840168C22semidirect
33. #16840165C22semidirect
34. #16840161C22semidirect
35. #16840158C22semidirect
36. #16840132C22semidirect
37. #16840128C22semidirect
38. #16840124C22semidirect
39. #16840119C22semidirect
40. #16840114C22semidirect
41. #16840110C22semidirect
50. #16840066C22semidirect
51. #16840066C22semidirect
52. #16840059C22semidirect
53. #16840059C22semidirect
54. #16840054C22semidirect
55. #16840049C22semidirect
56. #16840044C22semidirect
57. #16840039C22semidirect
388. C2×#544D61semidirect
480. C61#60867semidirect

Maximal subgroups

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

subgroupindex
#214592092
#214571172
#214571022
#214570872
#214570722
#214563682
#214563612
#214562222
#214562152
#214557502
#214557422
#214556372
#214556282
#214544572
C2×C61×#5442
#6086761