Finite Group Databasebeta

← #7687953

Subgroups — #7687953

Order 512.

5499 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59641C212yesmaximal, complemented
3#59457C212yesmaximal, complemented
4#59411C214yesmaximal, complemented
5#59084C212yesmaximal, complemented
6#59072C214yesmaximal, complemented
7#45028C214yesmaximal, complemented
8#44075C218yesmaximal, complemented
9#40021C214yesmaximal, complemented
10#39221C214yesmaximal, complemented
11#39147C212yesmaximal, complemented
12#38985C212yesmaximal, complemented
13#36595C211yesmaximal, characteristic, complemented
14#36595C211yesmaximal, characteristic, complemented
15#36591C212yesmaximal, complemented
16#36496C212yesmaximal, complemented
17#36469C212yesmaximal, complemented
18#36128C211yesmaximal, characteristic
19#36117C212yesmaximal, complemented
20#35916C214yesmaximal, complemented
21#34945C211yesmaximal, characteristic, complemented
22#34934C212yesmaximal, complemented
23#34331C212yesmaximal, complemented
24#34236C212yesmaximal, complemented
25C4×Q82C211yesmaximal, characteristic, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#559C2214yes—
29C2×#559C2212yes—
30C2×Q82C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#550C2212yes—
33C2×#532C2212yes—
34C2×#529C2214yes—
35#2867C2211yescharacteristic
36#2861C2214yes—
37#2858C2212yes—
38#2858C2212yes—
39#2856C2212yes—
40#2854C2214yes—
41#2806C2214yes—
42#2801C2218yes—
43#2780C2218yes—
44#2757C2218yes—
45#2731C2218yes—
46#2718C2218yes—
47#2715C2218yes—
48#2710C2218yes—
49#2701C2218yes—
50#2701C2218yes—
51#2700C2218yes—
52#2653C2218yes—
53#2644C2214yes—
54#2602C2218yes—
55#2595C2218yes—
56#2592C2214yes—
57#2584C2214yes—
58#2582C2214yes—
59#2580C2214yes—
60#2573C2214yes—
61#2571C2211yescharacteristic
62#2568C2211yescharacteristic
63#2567C2212yes—
64#2566C2214yes—
65#2566C2214yes—
66#2557C2218yes—
67#2554C2218yes—
68#2552C2212yes—
69#2552C2212yes—
70#2548C2212yes—
71#2548C2212yes—
72#2548C2212yes—
73#2548C2212yes—
74#2548C2212yes—
75#2548C2212yes—
76#2548C2212yes—
77#2547C2211yescharacteristic
78#2544C2214yes—
79#2544C2214yes—
80#2544C2214yes—
81#2541C2212yes—
82#2541C2212yes—
83#2538C2214yes—
84#2538C2211yescharacteristic
85#2516C2218yes—
86#2514C2212yes—
87#2513C2214yes—
88#2512C2214yes—
89#2512C2214yes—
90#2507C2214yes—
91#2501C2214yes—
92#2494C2212yes—
93#2491C2214yes—
94#2491C2214yes—
95#2490C2214yes—
96#2479C2218yes—
97#2470C2218yes—
98#2461C2218yes—
99#2461C2218yes—
100#2455C2218yes—
101#2454C2214yes—
102#2452C2214yes—
103#2452C2214yes—
104#2450C2218yes—
105#2448C2214yes—
106#2448C2214yes—
107#2447C2212yes—
108#2447C2214yes—
109#2445C2214yes—
110#2445C2214yes—
111#2445C2214yes—
112#2445C2214yes—
113#2445C2214yes—
114#2432C2218yes—
115#2431C2214yes—
116#2428C2214yes—
117#2428C2214yes—
118#2427C2218yes—
119#2426C2214yes—
120#2426C2214yes—
121#2426C2214yes—
122#2425C2218yes—
123#2425C2218yes—
124#2422C2218yes—
125#2422C2214yes—
126#2422C2214yes—
127#2421C2212yes—
128#2401C2214yes—
129#2392C2218yes—
130#2370C2212yes—
131#2369C2214yes—
132#2369C2212yes—
133#2369C2211yescharacteristic
134#2369C2212yes—
135#2369C2211yescharacteristic
136#2369C2212yes—
137#2368C2214yes—
138#2367C2214yes—
139#2367C2214yes—
140#2367C2214yes—
141#2366C2212yes—
142#2366C2212yes—
143#2366C2212yes—
144#2366C2212yes—
145#2366C2212yes—
146#2366C2212yes—
147#2365C2212yes—
148#2361C2214yes—
149#2361C2214yes—
150#2361C2214yes—
151#2360C2212yes—
152#2359C2218yes—
153#2357C2214yes—
154#2355C2211yescharacteristic
155#2354C2214yes—
156Q8×C4⋊C4C2211yescharacteristic
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2211yescharacteristic
161#2349C2212yes—
162#2349C2214yes—
163#2349C2214yes—
164D4×C4⋊C4C2211yescharacteristic
165#2345C2212yes—
166#2339C2218yes—
167#2337C2218yes—
168#2335C2218yes—
169#2326C2214yes—
170#2319C2214yes—
171C4×C4⋊Q8C2214yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×#127C2214yes—
178C4×#127C2212yes—
179C4×#127C2212yes—
180C4×#125C2212yes—
181C4×#124C2214yes—
182C4×#124C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×C22⋊Q8C2212yes—
186C4×#121C2214yes—
187C4×#121C2214yes—
188#2295C2212yes—
189#2293C2214yes—
190#2283C2212yes—
191#2275C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2314yes—
200#559—216no—
201#559—416no—
202#559—48no—
203Q82—28no—
204#554—28no—
205#550—48no—
206#532—216no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2314yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#127C2312yes—
221#529—416no—
222C2×#126C2318yes—
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2312yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2318yes—
233C2×#124C2314yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×#123C2318yes—
238C2×#123C2318yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2318yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2318yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2318yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2318yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2318yes—
282C2×C4×D4C2314yes—
283C2×#117C2318yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C42C2312yes—
287C22×C42C2314yes—
288#401C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#399C2318yes—
293#399C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#396C2318yes—
310#396C2318yes—
311#395C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#393C2318yes—
324#393C2318yes—
325#392C2318yes—
326#392C2318yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2312yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2318yes—
340#391C2312yes—
341#391C2314yes—
342#390C2312yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2318yes—
349#390C2318yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2318yes—
392#389C2318yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2314yes—
397#389C2312yes—
398#388C2314yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2318yes—
422#387C2314yes—
423#387C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2314yes—
443#385C2314yes—
444#385C2314yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2314yes—
448#384C2312yes—
449#384C2311yescharacteristic
450#384C2314yes—
451#384C2312yes—
452#384C2314yes—
453#383C2314yes—
454#382C2312yes—
455#382C2312yes—
456#382C2312yes—
457#382C2312yes—
458#381C2314yes—
459#381C2318yes—
460#380C2318yes—
461#380C2318yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2312yes—
466#380C2312yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521C2×#95C2314yes—
522C2×#95C2318yes—
523C43C2312yes—
524C43C2312yes—
525C43C2314yes—
526C43C2311yescharacteristic
527C2×#41—216no—
528C2×#41—48no—
529C2×#41—84no—
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2418yes—
540C22×D4C2411yescharacteristic
541C22×D4C2418yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2418yes—
552C23×C4C2418yes—
553C23×C4C2418yes—
554C4⋊Q8—216no—
555C4⋊Q8—28no—
556C4⋊Q8—28no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8#4118yes—
560#127—216no—
561#127—28no—
562#127—28no—
563#127—28no—
564#127—44no—
565#127—44no—
566#127—44no—
567#127—82no—
568#126—416no—
569#125—28no—
570#125—48no—
571#124—216no—
572#124—216no—
573#124—216no—
574#124—28no—
575#124—216no—
576#124—48no—
577#124—48no—
578#124—416no—
579#124—84no—
580#123—232no—
581#123—416no—
582#123—416no—
583#123—416no—
584#123—416no—
585C22⋊Q8—28no—
586C22⋊Q8—28no—
587C22⋊Q8—216no—
588C22⋊Q8—88no—
589#121—216no—
590#121—216no—
591#121—416no—
592#121—48no—
593#121—48no—
594#121—48no—
595C4×Q8—28no—
596C4×Q8—24no—
597C4×Q8—28no—
598C4×Q8—28no—
599C4×Q8—24no—
600C4×Q8—24no—
601C4×Q8—28no—
602C4×Q8—24no—
603C4×Q8—44no—
604C4×Q8—44no—
605C4×Q8—48no—
606C4×Q8—44no—
607C4×Q8—42no—
608C4×Q8—48no—
609C4×Q8#4118yescomplemented
610C4×D4—24no—
611C4×D4—28no—
612C4×D4—216no—
613C4×D4—216no—
614C4×D4—216no—
615C4×D4—28no—
616C4×D4—24no—
617C4×D4—216no—
618C4×D4—24no—
619C4×D4—416no—
620C4×D4—48no—
621C4×D4—48no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—48no—
626C4×D4—416no—
627C4×D4—88no—
628C4×D4—84no—
629#117—416no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—44no—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C42—28no—
711C2×C42—48no—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2414yes—
728C2×C42C2411yescharacteristic
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2412yes—
734C2×C42C2418yes—
735C2×C42C2412yes—
736C2×C42C2414yes—
737C2×C42C2412yes—
738C2×C42C2414yes—
739C2×C42C2411yescharacteristic
740C2×C42C2412yes—
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2412yes—
758#95C2412yes—
759#95C2414yes—
760#95C2412yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2412yes—
768#95C2412yes—
769#95C2414yes—
770#95C2412yes—
771#95C2412yes—
772#95C2414yes—
773#95C2414yes—
774#95C2412yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2414yes—
781#95C2418yes—
782C24C2518yes—
783C24C2512yes—
784#41—832no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—28no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—42no—
800C2×Q8C2×#4114yes—
801C2×Q8C2×#4118yes—
802C2×Q8H(5,𝔽2)14yes—
803C2×D4—216no—
804C2×D4—216no—
805C2×D4—22no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—216no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—22no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—48no—
821C2×D4—48no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—48no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4H(5,𝔽2)14yes—
833C22×C4—24no—
834C22×C4—28no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—216no—
844C22×C4—216no—
845C22×C4—42no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—44no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2514yes—
871C22×C4C2511yescharacteristic
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2514yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—22no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—22no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—42no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—42no—
919C4⋊C4—44no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4C2×#4114yes—
928C4⋊C4C2×#4118yes—
929C4⋊C4C2×#4118yes—
930C4⋊C4C2×#4118yes—
931C22⋊C4—24no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—216no—
936C22⋊C4—216no—
937C22⋊C4—24no—
938C22⋊C4—28no—
939C22⋊C4—216no—
940C22⋊C4—216no—
941C22⋊C4—216no—
942C22⋊C4—216no—
943C22⋊C4—28no—
944C22⋊C4—216no—
945C22⋊C4—24no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—28no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—28no—
969C42—24no—
970C42—22no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—22no—
975C42—24no—
976C42—24no—
977C42—22no—
978C42—44no—
979C42—44no—
980C42—48no—
981C42—42no—
982C42—44no—
983C42—42no—
984C42—44no—
985C42—42no—
986C42—41no—
987C42C2×#4114yes—
988C42C2×#4118yes—
989C42C2×#4114yes—
990C422−1+414yes—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—28no—
998C23—28no—
999C23—28no—
1000C23—28no—
1001C23—28no—
1002C23—28no—
1003C23—28no—
1004C23C2×H(5,𝔽2)14yes—
1005C23C2611yescharacteristic
1006Q8—28no—
1007Q8—28no—
1008Q8—48no—
1009Q8—48no—
1010Q8—88no—
1011Q8—84no—
1012D4—28no—
1013D4—432no—
1014D4—416no—
1015D4—416no—
1016D4—416no—
1017D4—88no—
1018D4—88no—
1019D4—88no—
1020D4—816no—
1021D4—164no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—24no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—816no—
1082C2×C4—88no—
1083C2×C4—816no—
1084C2×C4—88no—
1085C2×C4—168no—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4118yes—
1088C2×C4C22×#4114yes—
1089C2×C4C22×#4114yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C2×H(5,𝔽2)14yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×H(5,𝔽2)12yes—
1098C2×C4C2×2−1+412yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4C2×2−1+412yes—
1101C2×C4#58512yes—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—48no—
1110C22—48no—
1111C22—48no—
1112C22—48no—
1113C22—48no—
1114C22—48no—
1115C22—48no—
1116C22C23×#4111yescharacteristic
1117C22C23×#4111yescharacteristic
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C22×H(5,𝔽2)11yescharacteristic
1120C22C22×2−1+411yescharacteristic
1121C22C2×#58511yescharacteristic
1122C22H(7,𝔽2)11yescharacteristic
1123C4—22no—
1124C4—28no—
1125C4—24no—
1126C4—22no—
1127C4—24no—
1128C4—22no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—44no—
1134C4—44no—
1135C4—42no—
1136C4—44no—
1137C4—42no—
1138C4—44no—
1139C4—41no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4—42no—
1144C4#348014yes—
1145C4#352214yes—
1146C4#352214yes—
1147C2—44no—
1148C2—88no—
1149C2C2×#348011yescharacteristic
1150C2C2×#352211yescharacteristic
1151C2C2×#352211yescharacteristic
1152C2#6296211yescharacteristic
1153C2#6298311yescharacteristic
1154C2#6298611yescharacteristic
1155C2#6301411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36128C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59641C2semidirect
3. #59457C2semidirect
4. #59411C2semidirect
5. #59084C2semidirect
6. #59072C2semidirect
7. #45028C2semidirect
8. #44075C2semidirect
9. #40021C2semidirect
10. #39221C2semidirect
11. #39147C2semidirect
12. #38985C2semidirect
13. #36595C2semidirect
14. #36595C2semidirect
15. #36591C2semidirect
16. #36496C2semidirect
17. #36469C2semidirect
19. #36117C2semidirect
20. #35916C2semidirect
21. #34945C2semidirect
22. #34934C2semidirect
23. #34331C2semidirect
24. #34236C2semidirect
25. C4×Q82C2semidirect
26. C4×#554C2semidirect
609. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598712
#596412
#594572
#594112
#590842
#590722
#450282
#440752
#400212
#392212
#391472
#389852
#365952
#365912
#364962
#364692
#361282
#361172
#359162
#349452
#349342
#343312
#342362
C4×Q822
C4×#5542