Finite Group Databasebeta

← #7710943

Subgroups — #7710943

Order 512.

4742 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic, complemented
2#59870C211yesmaximal, characteristic, complemented
3#59823C211yesmaximal, characteristic, complemented
4#59821C211yesmaximal, characteristic, complemented
5#59451C212yesmaximal, complemented
6#59450C212yesmaximal, complemented
7#46332C214yesmaximal, complemented
8#46286C214yesmaximal, complemented
9#39800C214yesmaximal, complemented
10#39771C212yesmaximal, complemented
11#39754C212yesmaximal, complemented
12#39553C214yesmaximal, complemented
13#39506C212yesmaximal, complemented
14#39490C212yesmaximal, complemented
15#38982C214yesmaximal, complemented
16#38974C214yesmaximal, complemented
17#37615C212yesmaximal, complemented
18#37141C214yesmaximal, complemented
19#36635C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic
21#36587C212yesmaximal
22#36579C212yesmaximal, complemented
23#36552C212yesmaximal, complemented
24#36544C212yesmaximal, complemented
25#35024C214yesmaximal, complemented
26#34384C212yesmaximal, complemented
27C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#554C2212yes—
30C22×C4⋊Q8C2211yescharacteristic
31C2×#529C2212yes—
32C22×C4×Q8C2212yes—
33#2864C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2862C2211yescharacteristic
37#2861C2212yes—
38#2860C2212yes—
39#2860C2212yes—
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2855C2212yes—
48#2855C2212yes—
49#2854C2212yes—
50#2854C2212yes—
51#2851C2212yes—
52#2851C2214yes—
53#2850C2212yes—
54#2850C2214yes—
55#2821C2218yes—
56#2810C2214yes—
57#2805C2214yes—
58#2802C2218yes—
59#2796C2218yes—
60#2787C2218yes—
61#2783C2218yes—
62#2783C2218yes—
63#2777C2218yes—
64#2775C2218yes—
65#2774C2218yes—
66#2773C2218yes—
67#2771C2218yes—
68#2751C2218yes—
69#2745C2218yes—
70#2732C2214yes—
71#2727C2214yes—
72#2689C2218yes—
73#2689C2218yes—
74#2660C2214yes—
75#2643C2218yes—
76#2640C2214yes—
77#2623C2218yes—
78#2621C2214yes—
79#2621C2214yes—
80#2597C2218yes—
81#2596C2218yes—
82#2594C2218yes—
83#2592C2214yes—
84#2590C2218yes—
85#2584C2214yes—
86#2581C2214yes—
87#2581C2214yes—
88#2580C2214yes—
89#2577C2218yes—
90#2575C2218yes—
91#2571C2214yes—
92#2571C2212yes—
93#2570C2214yes—
94#2568C2212yes—
95#2568C2212yes—
96#2568C2212yes—
97#2568C2212yes—
98#2567C2212yes—
99#2552C2212yes—
100#2548C2212yes—
101#2542C2212yes—
102#2542C2212yes—
103#2538C2214yes—
104#2538C2212yes—
105#2538C2212yes—
106#2514C2214yes—
107#2514C2214yes—
108#2514C2214yes—
109#2513C2214yes—
110#2513C2214yes—
111#2513C2214yes—
112#2512C2214yes—
113#2511C2214yes—
114#2511C2214yes—
115#2509C2214yes—
116#2508C2214yes—
117#2508C2214yes—
118#2505C2218yes—
119#2504C2214yes—
120#2503C2214yes—
121#2502C2214yes—
122#2499C2214yes—
123#2489C2214yes—
124#2489C2214yes—
125#2481C2218yes—
126#2469C2218yes—
127#2465C2218yes—
128#2454C2214yes—
129#2453C2214yes—
130#2453C2214yes—
131#2449C2218yes—
132#2448C2214yes—
133#2448C2214yes—
134#2447C2214yes—
135#2447C2214yes—
136#2447C2214yes—
137#2444C2218yes—
138#2423C2214yes—
139#2421C2214yes—
140#2417C2214yes—
141#2415C2214yes—
142#2409C2214yes—
143#2409C2214yes—
144#2383C2218yes—
145#2366C2212yes—
146#2365C2212yes—
147#2362C2214yes—
148#2361C2214yes—
149#2360C2214yes—
150#2360C2214yes—
151#2357C2214yes—
152#2355C2212yes—
153#2355C2214yes—
154#2355C2212yes—
155#2355C2212yes—
156#2355C2212yes—
157#2354C2212yes—
158#2352C2214yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2214yes—
163#2330C2214yes—
164#2326C2214yes—
165#2322C2218yes—
166#2318C2218yes—
167#2317C2214yes—
168#2314C2214yes—
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×#127C2211yescharacteristic
183C4×#125C2212yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2214yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190C4×#121C2214yes—
191#2295C2212yes—
192#2295C2212yes—
193C2×#391C2212yes—
194#2293C2212yes—
195#2293C2212yes—
196C2×#389C2212yes—
197C2×#389C2212yes—
198C2×#384C2211yescharacteristic
199#2283C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204#556—48no—
205#554—48no—
206C2×C4⋊Q8—28no—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216#529—216no—
217C2×#126C2314yes—
218C2×#126C2318yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#123C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2318yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×C4×Q8—48no—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2314yes—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273#401C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#394C2318yes—
311#393C2318yes—
312#393C2318yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2312yes—
382#389C2312yes—
383#389C2314yes—
384#389C2318yes—
385#389C2314yes—
386#389C2312yes—
387#389C2318yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2314yes—
431#387C2318yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2314yes—
436#387C2314yes—
437#387C2318yes—
438#387C2318yes—
439#386C2314yes—
440#386C2318yes—
441#386C2318yes—
442#386C2314yes—
443#386C2318yes—
444#386C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2314yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2314yes—
454#385C2318yes—
455#384C2311yescharacteristic
456#384C2312yes—
457#384C2312yes—
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2312yes—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2314yes—
465#384C2314yes—
466#384C2314yes—
467#383C2314yes—
468#383C2318yes—
469#382C2312yes—
470#382C2314yes—
471#382C2314yes—
472#382C2314yes—
473#382C2314yes—
474#382C2312yes—
475#382C2312yes—
476#382C2318yes—
477#382C2314yes—
478#382C2312yes—
479#382C2318yes—
480#381C2318yes—
481#381C2314yes—
482#381C2318yes—
483#380C2314yes—
484#380C2314yes—
485#380C2318yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2318yes—
518C4×C4⋊C4C2314yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2318yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524#376C2314yes—
525C2×#95C2314yes—
526C2×#95C2314yes—
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C22×Q8—28no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2414yes—
543C22×Q8C2412yes—
544C22×D4C2414yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C23×C4C2414yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2414yes—
556C23×C4C2414yes—
557C23×C4C2411yescharacteristic
558C23×C4C2418yes—
559C4⋊Q8—28no—
560C4⋊Q8—24no—
561C4⋊Q8—24no—
562C4⋊Q8—28no—
563C4⋊Q8—28no—
564C4⋊Q8—24no—
565C4⋊Q8—24no—
566C4⋊Q8—24no—
567#127—24no—
568#126—216no—
569#126—416no—
570#125—28no—
571#125—44no—
572#125—48no—
573#124—28no—
574#124—44no—
575#124—48no—
576#123—216no—
577C22⋊Q8—28no—
578C22⋊Q8—28no—
579C22⋊Q8—44no—
580C22⋊Q8—416no—
581C22⋊Q8—48no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585#121—28no—
586#121—28no—
587#121—44no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8—48no—
593C4×Q8—44no—
594C4×Q8—48no—
595C4×Q8—44no—
596C4×Q8—44no—
597C4×Q8—48no—
598C4×Q8—48no—
599C4×D4—216no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—48no—
603C4×D4—48no—
604C4×D4—44no—
605C4×D4—416no—
606#117—216no—
607#117—48no—
608C2×C4⋊C4—28no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C42—24no—
690C2×C42—24no—
691C2×C42—24no—
692C2×C42—48no—
693C2×C42—42no—
694C2×C42—42no—
695C2×C42—42no—
696C2×C42#4118yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777C24C2514yes—
778C24C2511yescharacteristic
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—432no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—42no—
809C2×D4—42no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—28no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—22no—
825C22×C4—28no—
826C22×C4—22no—
827C22×C4—28no—
828C22×C4—44no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4C2×#4114yes—
840C22×C4C2×#4114yes—
841C22×C4C2×#4114yes—
842C22×C42−1+414yes—
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—44no—
901C4⋊C4—42no—
902C4⋊C4—44no—
903C4⋊C4—42no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—42no—
909C4⋊C4—48no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C42—28no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—28no—
947C42—28no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—28no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—28no—
961C42—41no—
962C42—41no—
963C42—41no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—41no—
969C42—44no—
970C42—44no—
971C42—48no—
972C42—48no—
973C42—48no—
974C42C2×#4114yes—
975C42C2×#4114yes—
976C42C2×#4114yes—
977C42C2×#4114yes—
978C42H(5,𝔽2)14yes—
979C422−1+414yes—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23C22×#4112yes—
992C23C2×2−1+412yes—
993C23#58512yes—
994C23C2611yescharacteristic
995Q8—416no—
996Q8—48no—
997Q8—48no—
998Q8—48no—
999Q8—48no—
1000Q8—84no—
1001D4—416no—
1002D4—48no—
1003D4—48no—
1004D4—84no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—28no—
1020C2×C4—28no—
1021C2×C4—28no—
1022C2×C4—28no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—21no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—21no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—21no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—416no—
1072C2×C4—416no—
1073C2×C4—88no—
1074C2×C4—168no—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C2×H(5,𝔽2)12yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4C2×2−1+412yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4#58512yes—
1090C2×C4#58512yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22#350714yes—
1105C22C23×#4111yescharacteristic
1106C22C22×H(5,𝔽2)11yescharacteristic
1107C22C22×2−1+411yescharacteristic
1108C22C22×2−1+411yescharacteristic
1109C22C2×#58511yescharacteristic
1110C22C2×#58511yescharacteristic
1111C22C2×#58511yescharacteristic
1112C4—22no—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—44no—
1120C4—44no—
1121C4—41no—
1122C4—41no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—41no—
1129C4—44no—
1130C4—44no—
1131C4—44no—
1132C4—44no—
1133C4—41no—
1134C4#350614yes—
1135C4#350714yes—
1136C4#355214yes—
1137C2—24no—
1138C2—84no—
1139C2C2×#355211yescharacteristic
1140C2#6276111yescharacteristic
1141C2C2×#350611yescharacteristic
1142C2C2×#350711yescharacteristic
1143C2C2×#350711yescharacteristic
1144C2#6283011yescharacteristic
1145C2#6283111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59875C2semidirect
2. #59870C2semidirect
3. #59823C2semidirect
4. #59821C2semidirect
5. #59451C2semidirect
6. #59450C2semidirect
7. #46332C2semidirect
8. #46286C2semidirect
9. #39800C2semidirect
10. #39771C2semidirect
11. #39754C2semidirect
12. #39553C2semidirect
13. #39506C2semidirect
14. #39490C2semidirect
15. #38982C2semidirect
16. #38974C2semidirect
17. #37615C2semidirect
18. #37141C2semidirect
19. #36635C2semidirect
22. #36579C2semidirect
23. #36552C2semidirect
24. #36544C2semidirect
25. #35024C2semidirect
26. #34384C2semidirect
27. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598752
#598702
#598232
#598212
#594512
#594502
#463322
#462862
#398002
#397712
#397542
#395532
#395062
#394902
#389822
#389742
#376152
#371412
#366352
#366312
#365872
#365792
#365522
#365442
#350242
#343842
C2×C4×C4⋊Q82