Finite Group Databasebeta

← #7688385

Subgroups — #7688385

Order 512.

5045 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59769C214yesmaximal, complemented
3#59489C214yesmaximal, complemented
4#59427C212yesmaximal, complemented
5#59421C212yesmaximal, complemented
6#59078C212yesmaximal, complemented
7#45090C214yesmaximal, complemented
8#44371C218yesmaximal, complemented
9#40031C214yesmaximal, complemented
10#39226C214yesmaximal, complemented
11#39200C212yesmaximal, complemented
12#39193C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36577C212yesmaximal, complemented
15#36560C211yesmaximal, characteristic, complemented
16#36555C212yesmaximal, complemented
17#36406C212yesmaximal, complemented
18#36314C212yesmaximal, complemented
19#36127C211yesmaximal, characteristic
20#35726C214yesmaximal, complemented
21#34955C212yesmaximal, complemented
22#34954C211yesmaximal, characteristic, complemented
23#34322C212yesmaximal, complemented
24#34316C212yesmaximal, complemented
25C4×#556C211yesmaximal, characteristic, complemented
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#556C2212yes—
29C2×#556C2211yescharacteristic
30C2×D4×Q8C2211yescharacteristic
31C2×#547C2212yes—
32C2×#532C2212yes—
33C22×C4×Q8C2212yes—
34#2868C2211yescharacteristic
35#2864C2214yes—
36#2862C2212yes—
37#2859C2212yes—
38#2857C2212yes—
39#2857C2214yes—
40#2796C2218yes—
41#2783C2218yes—
42#2781C2218yes—
43#2779C2218yes—
44#2773C2218yes—
45#2757C2218yes—
46#2754C2218yes—
47#2741C2218yes—
48#2727C2214yes—
49#2711C2218yes—
50#2702C2218yes—
51#2652C2218yes—
52#2625C2214yes—
53#2593C2214yes—
54#2592C2214yes—
55#2592C2214yes—
56#2591C2218yes—
57#2589C2218yes—
58#2587C2218yes—
59#2582C2212yes—
60#2582C2214yes—
61#2582C2211yescharacteristic
62#2577C2218yes—
63#2571C2212yes—
64#2571C2211yescharacteristic
65#2570C2214yes—
66#2568C2214yes—
67#2568C2212yes—
68#2568C2212yes—
69#2565C2214yes—
70#2560C2218yes—
71#2553C2218yes—
72#2553C2218yes—
73#2548C2211yescharacteristic
74#2548C2211yescharacteristic
75#2548C2212yes—
76#2547C2212yes—
77#2546C2212yes—
78#2546C2212yes—
79#2545C2214yes—
80#2542C2212yes—
81#2538C2212yes—
82#2537C2212yes—
83#2537C2212yes—
84#2533C2218yes—
85#2532C2218yes—
86#2531C2218yes—
87#2530C2218yes—
88#2523C2218yes—
89#2522C2218yes—
90#2513C2212yes—
91#2513C2212yes—
92#2512C2214yes—
93#2511C2214yes—
94#2511C2214yes—
95#2506C2214yes—
96#2506C2214yes—
97#2504C2214yes—
98#2499C2214yes—
99#2497C2214yes—
100#2495C2214yes—
101#2495C2214yes—
102#2492C2214yes—
103#2490C2214yes—
104#2460C2218yes—
105#2454C2214yes—
106#2453C2218yes—
107#2453C2214yes—
108#2448C2214yes—
109#2448C2214yes—
110#2448C2212yes—
111#2448C2212yes—
112#2446C2214yes—
113#2442C2214yes—
114#2442C2218yes—
115#2439C2214yes—
116#2436C2214yes—
117#2432C2214yes—
118#2432C2214yes—
119#2427C2214yes—
120#2427C2214yes—
121#2426C2214yes—
122#2423C2214yes—
123#2422C2214yes—
124#2422C2214yes—
125#2421C2214yes—
126#2415C2214yes—
127#2398C2218yes—
128#2395C2214yes—
129#2374C2218yes—
130#2373C2218yes—
131#2373C2214yes—
132#2367C2214yes—
133#2367C2212yes—
134#2365C2212yes—
135#2365C2211yescharacteristic
136#2365C2211yescharacteristic
137#2365C2212yes—
138#2365C2212yes—
139#2365C2212yes—
140#2363C2214yes—
141#2362C2214yes—
142#2362C2212yes—
143#2360C2214yes—
144#2360C2214yes—
145#2360C2212yes—
146#2360C2214yes—
147#2356C2214yes—
148#2356C2212yes—
149#2355C2212yes—
150#2355C2211yescharacteristic
151#2355C2212yes—
152#2354C2211yescharacteristic
153#2354C2212yes—
154#2351C2214yes—
155Q8×C4⋊C4C2211yescharacteristic
156Q8×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2211yescharacteristic
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161#2347C2212yes—
162#2346C2214yes—
163#2345C2214yes—
164#2341C2214yes—
165Q8×C22⋊C4C2214yes—
166Q8×C22⋊C4C2212yes—
167#2335C2218yes—
168#2334C2218yes—
169#2324C2214yes—
170#2323C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×#127C2211yescharacteristic
177C4×#126C2214yes—
178C4×#124C2214yes—
179C4×#124C2212yes—
180C4×#124C2212yes—
181C4×#124C2212yes—
182C4×#124C2214yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2214yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187#2297C2214yes—
188#2297C2214yes—
189#2295C2214yes—
190#2293C2212yes—
191#2293C2212yes—
192#2274C2214yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2314yes—
200C23×Q8C2312yes—
201#557—48no—
202#556—216no—
203#556—28no—
204D4×Q8—28no—
205#547—216no—
206#532—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#123C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×C4×Q8—48no—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2311yescharacteristic
263C2×#117C2314yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C42C2312yes—
271C22×C42C2314yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2318yes—
279#400C2318yes—
280#399C2314yes—
281#399C2318yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2318yes—
289#397C2318yes—
290#397C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2314yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#394C2318yes—
303#394C2314yes—
304#394C2318yes—
305#394C2314yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#393C2318yes—
310#393C2318yes—
311#391C2318yes—
312#391C2312yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2312yes—
332#390C2318yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2318yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2318yes—
362#389C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2314yes—
376#389C2318yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2318yes—
392#388C2314yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2314yes—
421#387C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2312yes—
438#384C2311yescharacteristic
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2312yes—
444#383C2314yes—
445#383C2318yes—
446#382C2314yes—
447#382C2314yes—
448#382C2318yes—
449#382C2314yes—
450#382C2314yes—
451#382C2312yes—
452#382C2312yes—
453#382C2312yes—
454#380C2318yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2314yes—
463#380C2318yes—
464#380C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2318yes—
520#376C2318yes—
521#376C2314yes—
522C43C2314yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C43C2312yes—
526C2×#41—216no—
527C2×#41—48no—
528C2×#41—48no—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8—44no—
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2414yes—
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2411yescharacteristic
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2412yes—
542C22×D4C2418yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2418yes—
549C23×C4C2414yes—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—28no—
554C4⋊Q8—44no—
555C4⋊Q8—48no—
556C4⋊Q8#4118yescomplemented
557#127—24no—
558#126—232no—
559#126—216no—
560#125—48no—
561#125—416no—
562#124—216no—
563#124—28no—
564#124—28no—
565#124—44no—
566#124—48no—
567#123—232no—
568C22⋊Q8—28no—
569C22⋊Q8—216no—
570C22⋊Q8—28no—
571C22⋊Q8—216no—
572C22⋊Q8—216no—
573C22⋊Q8—48no—
574#121—216no—
575#121—48no—
576#121—48no—
577C4×Q8—216no—
578C4×Q8—24no—
579C4×Q8—28no—
580C4×Q8—24no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—28no—
585C4×Q8—24no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—44no—
589C4×Q8—44no—
590C4×Q8—44no—
591C4×Q8—48no—
592C4×Q8—42no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—24no—
598C4×D4—28no—
599C4×D4—44no—
600C4×D4—42no—
601C4×D4—48no—
602C4×D4—48no—
603C4×D4—44no—
604C4×D4#4118yes—
605#117—28no—
606#117—216no—
607#117—48no—
608#117—44no—
609C2×C4⋊C4—216no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C42—28no—
692C2×C42—48no—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2414yes—
696C2×C42C2418yes—
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2412yes—
738#95C2414yes—
739#95C2412yes—
740#95C2418yes—
741#95C2412yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2412yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768C24C2514yes—
769C24C2512yes—
770#41—832no—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—28no—
776C2×Q8—28no—
777C2×Q8—24no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—28no—
786C2×Q8—44no—
787C2×Q8—432no—
788C2×Q8C2×#4118yes—
789C2×Q82−1+414yes—
790C2×D4—216no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—48no—
803C2×D4—48no—
804C2×D4C2×#4114yes—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—216no—
816C22×C4—24no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—48no—
820C22×C4—42no—
821C22×C4—44no—
822C22×C4—42no—
823C22×C4—44no—
824C22×C4—48no—
825C22×C4C2×#4118yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2511yescharacteristic
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2518yes—
837C22×C4C2512yes—
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2514yes—
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C4⋊C4—28no—
851C4⋊C4—216no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—216no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—22no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—24no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—42no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—42no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4C2×#4114yes—
900C4⋊C4C2×#4118yes—
901C4⋊C4C2×#4118yes—
902C22⋊C4—28no—
903C22⋊C4—216no—
904C22⋊C4—28no—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—24no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—216no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—42no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4C2×#4118yes—
929C42—216no—
930C42—28no—
931C42—24no—
932C42—24no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—28no—
939C42—24no—
940C42—24no—
941C42—22no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—22no—
946C42—24no—
947C42—22no—
948C42—44no—
949C42—44no—
950C42—41no—
951C42—42no—
952C42—42no—
953C42—44no—
954C42—44no—
955C42—42no—
956C42—48no—
957C42—44no—
958C42—48no—
959C42C2×#4114yes—
960C42C2×#4114yes—
961C42H(5,𝔽2)14yes—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23C22×#4114yes—
976C23C2611yescharacteristic
977Q8—28no—
978Q8—216no—
979Q8—416no—
980Q8—48no—
981Q8—44no—
982Q8—416no—
983D4—28no—
984D4—48no—
985D4—48no—
986D4—48no—
987D4—816no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—24no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—216no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—28no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—28no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—28no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—416no—
1047C2×C4—416no—
1048C2×C4—48no—
1049C2×C4—84no—
1050C2×C4—816no—
1051C2×C4—88no—
1052C2×C4C22×#4118yes—
1053C2×C4C22×#4114yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×2−1+414yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4#58512yes—
1066C2×C4#58512yes—
1067C22—24no—
1068C22—24no—
1069C22—24no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22C23×#4111yescharacteristic
1082C22C23×#4111yescharacteristic
1083C22C22×H(5,𝔽2)11yescharacteristic
1084C22C22×2−1+411yescharacteristic
1085C22C2×#58511yescharacteristic
1086C22C2×#58511yescharacteristic
1087C222−1+611yescharacteristic
1088C4—22no—
1089C4—22no—
1090C4—24no—
1091C4—28no—
1092C4—24no—
1093C4—22no—
1094C4—42no—
1095C4—44no—
1096C4—42no—
1097C4—42no—
1098C4—48no—
1099C4—42no—
1100C4—42no—
1101C4—42no—
1102C4—41no—
1103C4—42no—
1104C4—42no—
1105C4—44no—
1106C4—42no—
1107C4—44no—
1108C4—44no—
1109C4#348014yes—
1110C4#351414yes—
1111C4#352014yes—
1112C2—44no—
1113C2—84no—
1114C2C2×#348011yescharacteristic
1115C2C2×#352011yescharacteristic
1116C2C2×#351411yescharacteristic
1117C2#6292511yescharacteristic
1118C2#6300111yescharacteristic
1119C2#6300711yescharacteristic
1120C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59769C2semidirect
3. #59489C2semidirect
4. #59427C2semidirect
5. #59421C2semidirect
6. #59078C2semidirect
7. #45090C2semidirect
8. #44371C2semidirect
9. #40031C2semidirect
10. #39226C2semidirect
11. #39200C2semidirect
12. #39193C2semidirect
13. #36598C2semidirect
14. #36577C2semidirect
15. #36560C2semidirect
16. #36555C2semidirect
17. #36406C2semidirect
18. #36314C2semidirect
20. #35726C2semidirect
21. #34955C2semidirect
22. #34954C2semidirect
23. #34322C2semidirect
24. #34316C2semidirect
25. C4×#556C2semidirect
26. C4×D4×Q8C2semidirect
556. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598212
#597692
#594892
#594272
#594212
#590782
#450902
#443712
#400312
#392262
#392002
#391932
#365982
#365772
#365602
#365552
#364062
#363142
#361272
#357262
#349552
#349542
#343222
#343162
C4×#5562
C4×D4×Q82