Finite Group Databasebeta

← #8110002

Subgroups — #8110002

Order 512.

5234 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59302C212yesmaximal, complemented
2#59127C212yesmaximal, complemented
3#53192C214yesmaximal, complemented
4#53183C214yesmaximal, complemented
5#46097C214yesmaximal, complemented
6#45677C214yesmaximal, complemented
7#45633C214yesmaximal, complemented
8#39767C212yesmaximal, complemented
9#39760C212yesmaximal, complemented
10#39734C212yesmaximal, complemented
11#39623C212yesmaximal, complemented
12#39615C212yesmaximal, complemented
13#39596C212yesmaximal, complemented
14#39481C212yesmaximal, complemented
15#39343C212yesmaximal, complemented
16#37852C214yesmaximal, complemented
17#37651C214yesmaximal, complemented
18#37386C212yesmaximal, complemented
19#37324C212yesmaximal, complemented
20#37315C212yesmaximal, complemented
21#37308C212yesmaximal, complemented
22#36729C214yesmaximal, complemented
23#36625C211yesmaximal, characteristic, complemented
24#36624C211yesmaximal, characteristic
25C2×#2857C211yesmaximal, characteristic, complemented
26C2×D4×Q8C2214yes—
27C2×D4×Q8C2212yescomplemented
28C2×#536C2214yes—
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C2×#525C2212yes—
33C22×C22⋊Q8C2212yes—
34C23×C42C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2857C2212yes—
42#2857C2212yes—
43#2857C2212yes—
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2856C2211yescharacteristic
51#2855C2212yes—
52#2855C2212yes—
53#2854C2212yes—
54#2854C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2850C2212yes—
58#2850C2212yes—
59#2848C2212yes—
60#2848C2212yes—
61#2847C2212yes—
62#2847C2212yes—
63#2838C2218yescomplemented
64#2808C2214yescomplemented
65#2808C2214yescomplemented
66#2806C2214yescomplemented
67#2805C2214yescomplemented
68#2805C2214yescomplemented
69#2796C2218yescomplemented
70#2793C2218yescomplemented
71#2792C2218yescomplemented
72#2773C2218yescomplemented
73#2766C2218yescomplemented
74#2759C2218yescomplemented
75#2747C2218yes—
76#2746C2218yes—
77#2742C2218yes—
78#2741C2218yes—
79#2741C2218yes—
80#2737C2218yes—
81#2734C2214yescomplemented
82#2734C2214yescomplemented
83#2734C2214yescomplemented
84#2732C2214yescomplemented
85#2729C2218yescomplemented
86#2727C2214yescomplemented
87#2724C2214yescomplemented
88#2724C2214yescomplemented
89#2720C2218yescomplemented
90#2717C2218yes—
91#2717C2218yes—
92#2702C2218yes—
93#2692C2218yes—
94#2691C2218yes—
95#2681C2218yes—
96#2680C2218yes—
97#2677C2218yes—
98#2677C2218yescomplemented
99#2674C2218yes—
100#2674C2218yescomplemented
101#2672C2218yes—
102#2659C2214yes—
103#2639C2214yes—
104#2628C2214yes—
105#2624C2214yes—
106#2621C2214yes—
107#2616C2214yes—
108#2580C2214yescomplemented
109#2571C2212yescomplemented
110#2570C2214yescomplemented
111#2570C2214yescomplemented
112#2567C2214yescomplemented
113#2564C2218yes—
114#2551C2214yescomplemented
115#2551C2214yescomplemented
116#2546C2212yescomplemented
117#2542C2214yes—
118#2542C2212yescomplemented
119#2538C2212yescomplemented
120#2536C2214yes—
121#2514C2214yescomplemented
122#2513C2214yescomplemented
123#2512C2214yescomplemented
124#2510C2218yes—
125#2507C2214yescomplemented
126#2507C2214yescomplemented
127#2504C2214yes—
128#2499C2214yescomplemented
129#2499C2214yescomplemented
130#2496C2214yescomplemented
131#2495C2214yes—
132#2494C2214yes—
133#2492C2214yescomplemented
134#2491C2214yes—
135#2481C2218yes—
136#2472C2218yes—
137#2452C2214yescomplemented
138#2449C2218yes—
139#2446C2214yescomplemented
140#2445C2214yescomplemented
141#2443C2218yes—
142#2440C2218yes—
143#2440C2214yes—
144#2434C2214yescomplemented
145#2434C2214yescomplemented
146#2429C2214yescomplemented
147#2423C2214yescomplemented
148#2422C2214yes—
149#2418C2218yes—
150#2417C2214yes—
151#2415C2214yes—
152#2415C2214yescomplemented
153#2409C2214yes—
154#2409C2214yes—
155#2409C2214yescomplemented
156#2383C2218yescomplemented
157#2365C2212yescomplemented
158#2361C2214yes—
159#2355C2212yescomplemented
160#2354C2212yescomplemented
161#2352C2214yes—
162#2345C2214yes—
163#2329C2214yes—
164#2325C2214yes—
165#2324C2214yes—
166#2323C2214yes—
167#2314C2214yes—
168C4×C22⋊Q8C2212yes—
169C4×C22⋊Q8C2212yes—
170C4×C22⋊Q8C2212yes—
171C4×C22⋊Q8C2212yes—
172C4×#121C2212yes—
173C4×#121C2212yes—
174C4×#121C2212yes—
175C4×#121C2212yes—
176#2297C2212yes—
177#2296C2212yes—
178C2×#391C2212yes—
179C2×#389C2212yes—
180C2×#389C2212yes—
181#2285C2211yescharacteristic
182#2285C2211yescharacteristic
183C2×#384C2211yescharacteristic
184#2280C2212yes—
185C2×#380C2212yes—
186C2×#380C2212yes—
187C22×#41C2312yes—
188C23×Q8C2312yes—
189C23×Q8C2314yes—
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193D4×Q8—48no—
194D4×Q8—416no—
195#536—416no—
196#533—44no—
197#532—44no—
198C2×C4⋊Q8—44no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2318yes—
209C2×C4⋊Q8C2318yes—
210C2×#127C2311yescharacteristic
211C2×#126C2318yes—
212C2×#125C2312yes—
213C2×#124C2312yes—
214C2×#124C2318yes—
215#525—48no—
216C2×#123C2314yes—
217C2×#123C2318yes—
218C2×#123C2318yes—
219C2×C22⋊Q8—48no—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2318yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#120C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C22⋊C4C2314yes—
268C22×C42—44no—
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281#401C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#393C2318yes—
326#393C2318yes—
327#393C2318yes—
328#393C2318yes—
329#391C2318yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#390C2314yes—
344#390C2318yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2314yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2314yes—
364#389C2318yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#386C2314yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2314yes—
420#386C2314yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#385C2314yes—
437#385C2318yes—
438#385C2318yes—
439#384C2318yes—
440#384C2314yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2312yes—
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2312yes—
447#384C2311yescharacteristic
448#384C2312yes—
449#383C2318yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2312yes—
454#382C2312yes—
455#381C2314yes—
456#380C2312yes—
457#380C2318yes—
458#380C2312yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#379C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C25C2411yescharacteristic
502C2×#41—28no—
503C2×#41—44no—
504C2×#41—44no—
505C22×Q8—28no—
506C22×Q8—44no—
507C22×Q8—44no—
508C22×Q8—48no—
509C22×Q8—48no—
510C22×Q8—48no—
511C22×Q8C2412yes—
512C22×Q8C2414yes—
513C22×Q8C2412yes—
514C22×Q8C2414yes—
515C22×Q8C2412yes—
516C22×Q8C2418yes—
517C22×D4C2414yes—
518C22×D4C2412yes—
519C22×D4C2414yes—
520C22×D4C2412yes—
521C22×D4C2414yes—
522C22×D4C2412yes—
523C23×C4—24no—
524C23×C4—24no—
525C23×C4—24no—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—42no—
530C23×C4—42no—
531C23×C4—42no—
532C23×C4C2411yescharacteristic
533C23×C4C2414yes—
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2414yes—
551C23×C4C2414yes—
552C23×C4C2418yes—
553C23×C4C2411yescharacteristic
554C4⋊Q8—28no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557C4⋊Q8—42no—
558C4⋊Q8—42no—
559C4⋊Q8—48no—
560C4⋊Q8—44no—
561C4⋊Q8—42no—
562C4⋊Q8—48no—
563C4⋊Q8—416no—
564C4⋊Q8—416no—
565#127—42no—
566#126—416no—
567#125—44no—
568#124—44no—
569#124—416no—
570#123—416no—
571#123—48no—
572#123—416no—
573C22⋊Q8—216no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—48no—
578C22⋊Q8—44no—
579C22⋊Q8—416no—
580C22⋊Q8—416no—
581C22⋊Q8—416no—
582C22⋊Q8—48no—
583C22⋊Q8—44no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—48no—
587C22⋊Q8—44no—
588C22⋊Q8—48no—
589C22⋊Q8—48no—
590C22⋊Q8—48no—
591C22⋊Q8—48no—
592#121—28no—
593#121—28no—
594#121—28no—
595#121—44no—
596#121—44no—
597#121—44no—
598#121—44no—
599#121—44no—
600#120—48no—
601C4×Q8—28no—
602C4×Q8—44no—
603C4×Q8—48no—
604C4×D4—216no—
605C4×D4—28no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—44no—
609C4×D4—416no—
610#117—28no—
611#117—44no—
612#117—44no—
613#117—48no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—44no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2418yes—
666C2×C22⋊C4—48no—
667C2×C22⋊C4C2418yes—
668C2×C22⋊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⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—42no—
697C2×C42—42no—
698C2×C42—42no—
699C2×C42—42no—
700C2×C42—42no—
701C2×C42—42no—
702C2×C42—42no—
703C2×C42—42no—
704C2×C42—42no—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2418yes—
718C2×C42C2418yes—
719C2×C42C2418yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—41no—
765C24—41no—
766C24C2514yes—
767C24C2511yescharacteristic
768C24C2511yescharacteristic
769C24C2511yescharacteristic
770#41—816no—
771C2×Q8—24no—
772C2×Q8—28no—
773C2×Q8—28no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—28no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—42no—
781C2×Q8—44no—
782C2×Q8—42no—
783C2×Q8—48no—
784C2×Q8—48no—
785C2×Q8—42no—
786C2×Q8—48no—
787C2×Q8—42no—
788C2×Q8—44no—
789C2×Q8—816no—
790C2×Q8—832no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—44no—
802C2×D4—42no—
803C2×D4—44no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—42no—
809C22×C4—22no—
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—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—416no—
864C22×C4—416no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—416no—
873C22×C4H(5,𝔽2)14yes—
874C22×C4H(5,𝔽2)14yes—
875C22×C42−1+414yes—
876C22×C42−1+414yes—
877C22×C42−1+414yes—
878C22×C4C2511yescharacteristic
879C22×C4C2514yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2514yes—
883C22×C4C2518yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2514yes—
887C22×C4C2518yes—
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—216no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—44no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—48no—
945C22⋊C4—216no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—22no—
977C42—22no—
978C42—22no—
979C42—22no—
980C42—28no—
981C42—28no—
982C42—28no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42—41no—
988C42—41no—
989C42—48no—
990C42—48no—
991C42—48no—
992C42H(5,𝔽2)14yes—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—28no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—44no—
1018C23—44no—
1019C23—44no—
1020C23—44no—
1021C23—44no—
1022C23—44no—
1023C23C2×H(5,𝔽2)12yes—
1024C23C2×H(5,𝔽2)12yes—
1025C23C2×2−1+412yes—
1026C23C2×2−1+412yes—
1027C23C2×2−1+412yes—
1028C23C2611yescharacteristic
1029Q8—48no—
1030Q8—416no—
1031Q8—84no—
1032Q8—88no—
1033Q8—84no—
1034Q8—816no—
1035D4—416no—
1036D4—48no—
1037D4—84no—
1038D4—84no—
1039D4—88no—
1040D4—88no—
1041C2×C4—28no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—28no—
1059C2×C4—28no—
1060C2×C4—28no—
1061C2×C4—28no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—28no—
1072C2×C4—28no—
1073C2×C4—28no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—21no—
1079C2×C4—28no—
1080C2×C4—21no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—28no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—28no—
1094C2×C4—24no—
1095C2×C4—44no—
1096C2×C4—44no—
1097C2×C4—44no—
1098C2×C4—44no—
1099C2×C4—44no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—44no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—416no—
1108C2×C4—44no—
1109C2×C4—88no—
1110C2×C4—88no—
1111C2×C4—816no—
1112C2×C4C2×H(5,𝔽2)12yes—
1113C2×C4C2×H(5,𝔽2)12yes—
1114C2×C4C2×H(5,𝔽2)12yes—
1115C2×C4C2×H(5,𝔽2)12yes—
1116C2×C4C2×H(5,𝔽2)12yes—
1117C2×C4C2×H(5,𝔽2)12yes—
1118C2×C4C2×H(5,𝔽2)12yes—
1119C2×C4C2×2−1+412yes—
1120C2×C4C2×2−1+412yes—
1121C2×C4C2×2−1+412yes—
1122C2×C4C2×2−1+412yes—
1123C2×C4C2×2−1+412yes—
1124C2×C4C2×2−1+412yes—
1125C2×C4#58512yes—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—416no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—44no—
1148C22—44no—
1149C22—44no—
1150C22—44no—
1151C22—44no—
1152C22—44no—
1153C22—44no—
1154C22#355014yes—
1155C22C22×H(5,𝔽2)11yescharacteristic
1156C22C22×H(5,𝔽2)11yescharacteristic
1157C22C22×H(5,𝔽2)11yescharacteristic
1158C22C22×2−1+411yescharacteristic
1159C22C22×2−1+411yescharacteristic
1160C22C22×2−1+411yescharacteristic
1161C22C2×#58511yescharacteristic
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—41no—
1171C4—44no—
1172C4—44no—
1173C4—48no—
1174C4—41no—
1175C4—44no—
1176C4—44no—
1177C4—44no—
1178C4—44no—
1179C4—48no—
1180C4—44no—
1181C4#353714yes—
1182C4#353814yes—
1183C2—24no—
1184C2—42no—
1185C2—42no—
1186C2—84no—
1187C2C2×#353711yescharacteristic
1188C2C2×#353811yescharacteristic
1189C2C2×#355011yescharacteristic
1190C2#6281911yescharacteristic
1191C2#6283311yescharacteristic
1192C2#6283511yescharacteristic
1193C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59302C2semidirect
2. #59127C2semidirect
3. #53192C2semidirect
4. #53183C2semidirect
5. #46097C2semidirect
6. #45677C2semidirect
7. #45633C2semidirect
8. #39767C2semidirect
9. #39760C2semidirect
10. #39734C2semidirect
11. #39623C2semidirect
12. #39615C2semidirect
13. #39596C2semidirect
14. #39481C2semidirect
15. #39343C2semidirect
16. #37852C2semidirect
17. #37651C2semidirect
18. #37386C2semidirect
19. #37324C2semidirect
20. #37315C2semidirect
21. #37308C2semidirect
22. #36729C2semidirect
23. #36625C2semidirect
25. C2×#2857C2semidirect
27. C2×D4×Q8C22semidirect
63. #2838C22semidirect
64. #2808C22semidirect
65. #2808C22semidirect
66. #2806C22semidirect
67. #2805C22semidirect
68. #2805C22semidirect
69. #2796C22semidirect
70. #2793C22semidirect
71. #2792C22semidirect
72. #2773C22semidirect
73. #2766C22semidirect
74. #2759C22semidirect
81. #2734C22semidirect
82. #2734C22semidirect
83. #2734C22semidirect
84. #2732C22semidirect
85. #2729C22semidirect
86. #2727C22semidirect
87. #2724C22semidirect
88. #2724C22semidirect
89. #2720C22semidirect
98. #2677C22semidirect
100. #2674C22semidirect
108. #2580C22semidirect
109. #2571C22semidirect
110. #2570C22semidirect
111. #2570C22semidirect
112. #2567C22semidirect
114. #2551C22semidirect
115. #2551C22semidirect
116. #2546C22semidirect
118. #2542C22semidirect
119. #2538C22semidirect
121. #2514C22semidirect
122. #2513C22semidirect
123. #2512C22semidirect
125. #2507C22semidirect
126. #2507C22semidirect
128. #2499C22semidirect
129. #2499C22semidirect
130. #2496C22semidirect
133. #2492C22semidirect
137. #2452C22semidirect
139. #2446C22semidirect
140. #2445C22semidirect
144. #2434C22semidirect
145. #2434C22semidirect
146. #2429C22semidirect
147. #2423C22semidirect
152. #2415C22semidirect
155. #2409C22semidirect
156. #2383C22semidirect
157. #2365C22semidirect
159. #2355C22semidirect
160. #2354C22semidirect

Maximal subgroups

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

subgroupindex
#593022
#591272
#531922
#531832
#460972
#456772
#456332
#397672
#397602
#397342
#396232
#396152
#395962
#394812
#393432
#378522
#376512
#373862
#373242
#373152
#373082
#367292
#366252
#366242
C2×#28572