Finite Group Databasebeta

← #7680322

Subgroups — #7680322

Order 512.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1133 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59322C212yesmaximal, complemented
2#59321C212yesmaximal, complemented
3#59291C214yesmaximal, complemented
4#59274C214yesmaximal, complemented
5#59259C212yesmaximal, complemented
6#59245C212yesmaximal, complemented
7#45275C214yesmaximal, complemented
8#45273C214yesmaximal, complemented
9#43937C218yesmaximal, complemented
10#39674C214yesmaximal, complemented
11#39673C214yesmaximal, complemented
12#39635C212yesmaximal, complemented
13#39633C212yesmaximal, complemented
14#36563C212yesmaximal, complemented
15#36555C212yesmaximal, complemented
16#35668C212yesmaximal, complemented
17#35575C212yesmaximal
18#35275C211yesmaximal, characteristic, complemented
19#35265C212yesmaximal, complemented
20#34952C211yesmaximal, characteristic
21C2×#2582C211yesmaximal, characteristic, complemented
22#34276C212yesmaximal
23#34183C211yesmaximal, characteristic
24#34182C211yesmaximal, characteristic, complemented
25Q8×#117C211yesmaximal, characteristic, complemented
26C4×#536C211yesmaximal, characteristic
27C2×#544C2212yes—
28C2×#536C2211yescharacteristic
29C2×#520C2212yes—
30C2×#519C2212yes—
31C2×C4×#41C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34#2868C2212yes—
35#2864C2214yes—
36#2859C2214yes—
37#2859C2212yes—
38#2802C2218yes—
39#2802C2218yes—
40#2792C2218yes—
41#2791C2218yes—
42#2790C2218yes—
43#2788C2218yes—
44#2774C2218yes—
45#2768C2218yes—
46#2768C2218yes—
47#2763C2218yes—
48#2755C2218yes—
49#2729C2218yes—
50#2660C2214yes—
51#2647C2214yes—
52#2647C2214yes—
53#2590C2218yes—
54#2589C2218yes—
55#2588C2218yes—
56#2587C2218yes—
57#2586C2218yes—
58#2585C2218yes—
59#2583C2218yes—
60#2582C2212yes—
61#2582C2212yes—
62#2582C2212yes—
63#2582C2212yes—
64#2582C2214yes—
65#2582C2214yes—
66#2582C2211yescharacteristic
67#2582C2211yescharacteristic
68#2581C2212yes—
69#2580C2212yes—
70#2579C2214yes—
71#2568C2214yes—
72#2567C2214yes—
73#2567C2214yes—
74#2565C2214yes—
75#2565C2214yes—
76#2564C2218yes—
77#2556C2218yes—
78#2552C2212yes—
79#2552C2214yes—
80#2552C2212yes—
81#2551C2212yes—
82#2551C2212yes—
83#2550C2218yes—
84#2538C2211yescharacteristic
85#2538C2211yescharacteristic
86#2522C2218yes—
87#2511C2214yes—
88#2511C2214yes—
89#2509C2214yes—
90#2508C2214yes—
91#2507C2214yes—
92#2507C2214yes—
93#2507C2218yes—
94#2507C2214yes—
95#2506C2214yes—
96#2505C2218yes—
97#2502C2214yes—
98#2497C2214yes—
99#2497C2214yes—
100#2492C2214yes—
101#2487C2212yes—
102#2473C2218yes—
103#2473C2218yes—
104#2454C2214yes—
105#2453C2214yes—
106#2453C2214yes—
107#2453C2214yes—
108#2452C2214yes—
109#2451C2214yes—
110#2451C2214yes—
111#2451C2214yes—
112#2442C2214yes—
113#2441C2214yes—
114#2440C2214yes—
115#2440C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2439C2214yes—
119#2438C2218yes—
120#2438C2218yes—
121#2423C2214yes—
122#2417C2218yes—
123#2409C2212yes—
124#2396C2214yes—
125C2×#398C2214yes—
126#2369C2214yes—
127#2362C2214yes—
128#2362C2214yes—
129#2360C2214yes—
130#2360C2214yes—
131#2360C2214yes—
132#2359C2218yes—
133#2359C2218yes—
134#2355C2211yescharacteristic
135#2355C2211yescharacteristic
136#2355C2212yes—
137#2355C2212yes—
138#2355C2214yes—
139#2351C2214yes—
140#2351C2214yes—
141Q8×C4⋊C4C2211yescharacteristic
142Q8×C4⋊C4C2211yescharacteristic
143Q8×C4⋊C4C2212yes—
144Q8×C4⋊C4C2212yes—
145Q8×C4⋊C4C2212yes—
146Q8×C4⋊C4C2212yes—
147Q8×C4⋊C4C2212yes—
148Q8×C4⋊C4C2212yes—
149D4×C4⋊C4C2214yes—
150D4×C4⋊C4C2214yes—
151D4×C4⋊C4C2212yes—
152D4×C4⋊C4C2212yes—
153#2345C2212yes—
154#2345C2214yes—
155#2345C2214yes—
156Q8×C22⋊C4C2212yes—
157#2327C2212yes—
158#2327C2214yes—
159#2326C2212yes—
160#2326C2214yes—
161#2323C2212yes—
162#2323C2212yes—
163#2322C2214yes—
164#2317C2211yescharacteristic
165#2317C2212yes—
166#2317C2214yes—
167#2317C2212yes—
168#2316C2214yes—
169#2316C2212yes—
170#2311C2211yescharacteristic
171#2310C2211yescharacteristic
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2214yes—
174C4×#124C2212yes—
175C4×#124C2214yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×#123C2214yes—
181#2297C2212yes—
182#2296C2212yes—
183#2295C2212yes—
184#2295C2214yes—
185C2×#391C2212yes—
186C2×#391C2212yes—
187C2×#389C2212yes—
188C2×#389C2212yes—
189#2285C2212yes—
190#2285C2211yescharacteristic
191#2285C2212yes—
192#2285C2211yescharacteristic
193#2285C2214yes—
194C2×#384C2211yescharacteristic
195C2×#384C2212yes—
196C42×Q8C2212yes—
197C4×#117C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202#544—48no—
203#536Q8116yescomplemented
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#125C2318yes—
212C2×#124C2312yes—
213C2×#123C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220#520—48no—
221#519—48no—
222C4×#41—28no—
223C2×C4×Q8—28no—
224C2×C4×Q8—28no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2318yes—
249C2×C4×D4C2314yes—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2318yes—
256C2×#117C2314yes—
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C42C2312yes—
270C22×C42C2312yes—
271C22×C42C2312yes—
272C22×C42C2311yescharacteristic
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2318yes—
282#399C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#396C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2314yes—
309#395C2318yes—
310#395C2318yes—
311#393C2318yes—
312#393C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2318yes—
325#391C2318yes—
326#391C2312yes—
327#391C2314yes—
328#391C2318yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2318yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2318yes—
354#389C2312yes—
355#389C2312yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2318yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2318yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2314yes—
383#389C2318yes—
384#389C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#386C2314yes—
420#386C2314yes—
421#386C2314yes—
422#385C2318yes—
423#385C2318yes—
424#385C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2318yes—
436#385C2318yes—
437#384C2312yes—
438#384C2314yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2314yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2314yes—
454#384C2314yes—
455#384C2314yes—
456#382C2312yes—
457#382C2314yes—
458#382C2312yes—
459#382C2312yes—
460#382C2314yes—
461#382C2312yes—
462#382C2312yes—
463#382C2318yes—
464#382C2318yes—
465#381C2314yes—
466#380C2314yes—
467#380C2318yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2314yes—
474#380C2312yes—
475#380C2318yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520#376C2312yes—
521C2×#95C2314yes—
522C2×#95C2314yes—
523C2×#95C2314yes—
524C43C2314yes—
525C43C2312yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41C2×Q818yes—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—42no—
534C22×Q8C2×Q818yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2411yescharacteristic
541C22×Q8C2418yes—
542C22×D4C2412yes—
543C22×D4C2411yescharacteristic
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2418yes—
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C4⋊Q8—48no—
557C4⋊Q8—48no—
558C4⋊Q8—48no—
559C4⋊Q8—84no—
560C4⋊Q8C2×Q8116yescomplemented
561#125—48no—
562#125—48no—
563#125—88no—
564#124C2×Q8116yescomplemented
565#123C2×Q8132yes—
566C22⋊Q8—28no—
567C22⋊Q8—416no—
568C22⋊Q8—44no—
569C22⋊Q8—88no—
570C22⋊Q8C2×Q8116yescomplemented
571C22⋊Q8C2×Q8116yescomplemented
572C4×Q8—28no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—24no—
576C4×Q8—28no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—24no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—44no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—48no—
596C4×D4—416no—
597#117—24no—
598#117—28no—
599#117—28no—
600#117—24no—
601#117—28no—
602#117—416no—
603#117—48no—
604#117C2×Q818yes—
605C2×C4⋊C4—28no—
606C2×C4⋊C4—28no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—84no—
614C2×C4⋊C4—82no—
615C2×C4⋊C4—84no—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C42—28no—
696C2×C42—28no—
697C2×C42—28no—
698C2×C42#4118yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2414yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2412yes—
734#95C2412yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771C24C2512yes—
772C24C2511yescharacteristic
773#41—232no—
774C2×Q8—232no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—24no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—42no—
789C2×Q8—48no—
790C2×Q8—48no—
791C2×Q8—48no—
792C2×Q8—416no—
793C2×Q8C22×Q818yes—
794C2×Q8C22×Q818yes—
795C2×Q8C22×Q814yes—
796C2×Q82−1+414yes—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4C22×Q818yes—
802C2×D4C22×Q814yes—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—41no—
819C22×C4—42no—
820C22×C4—41no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—44no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4C22×Q818yes—
833C22×C4C22×Q818yes—
834C22×C4C22×Q814yes—
835C22×C4C2×#4114yes—
836C22×C4C2×#4114yes—
837C22×C4C2×#4114yes—
838C22×C4H(5,𝔽2)14yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2518yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2512yes—
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—42no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—42no—
922C4⋊C4C22×Q814yes—
923C4⋊C4C22×Q814yes—
924C4⋊C4C22×Q8116yes—
925C4⋊C4C22×Q8116yes—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—28no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4C22×Q818yes—
940C22⋊C4C22×Q8116yes—
941C22⋊C4C22×Q8116yes—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—28no—
946C42—24no—
947C42—24no—
948C42—28no—
949C42—24no—
950C42—24no—
951C42—28no—
952C42—28no—
953C42—24no—
954C42—28no—
955C42—24no—
956C42—24no—
957C42—42no—
958C42—44no—
959C42—48no—
960C42—48no—
961C42—48no—
962C42—44no—
963C42—44no—
964C42—42no—
965C42C22×Q818yes—
966C42C2×#4114yes—
967C42C2×#4114yes—
968C42C2×#4114yes—
969C42C2×#4114yes—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23C23×Q814yes—
981C23C23×Q812yes—
982C23C22×#4112yes—
983C23C2×H(5,𝔽2)12yes—
984C23C2611yescharacteristic
985Q8—216no—
986Q8—216no—
987Q8—28no—
988Q8—28no—
989Q8—48no—
990Q8—44no—
991Q8—168no—
992D4—216no—
993D4—28no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—216no—
1011C2×C4—216no—
1012C2×C4—28no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—28no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—44no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—48no—
1056C2×C4—84no—
1057C2×C4—84no—
1058C2×C4—88no—
1059C2×C4—168no—
1060C2×C4#554116yes—
1061C2×C4C23×Q814yes—
1062C2×C4C23×Q814yes—
1063C2×C4C23×Q818yes—
1064C2×C4C23×Q814yes—
1065C2×C4C23×Q812yes—
1066C2×C4C23×Q812yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×2−1+414yes—
1076C2×C4C2×2−1+412yes—
1077C2×C4#58512yes—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22C2×#55414yes—
1092C22C24×Q811yescharacteristic
1093C22C23×#4111yescharacteristic
1094C22C22×H(5,𝔽2)11yescharacteristic
1095C22C22×2−1+411yescharacteristic
1096C22C2×#58511yescharacteristic
1097C22H(7,𝔽2)11yescharacteristic
1098C222−1+611yescharacteristic
1099C4—24no—
1100C4—24no—
1101C4—22no—
1102C4—24no—
1103C4—22no—
1104C4—22no—
1105C4—24no—
1106C4—28no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—44no—
1113C4—44no—
1114C4—44no—
1115C4—42no—
1116C4—48no—
1117C4—44no—
1118C4—44no—
1119C4—42no—
1120C4C2×#55414yes—
1121C4C2×#55414yes—
1122C4#349514yes—
1123C2—24no—
1124C2—44no—
1125C2C22×#55411yescharacteristic
1126C2C2×#349511yescharacteristic
1127C2#6285611yescharacteristic
1128C2#6294611yescharacteristic
1129C2#6296111yescharacteristic
1130C2Q8×2−1+411yescharacteristic
1131C2#6300411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59322C2semidirect
2. #59321C2semidirect
3. #59291C2semidirect
4. #59274C2semidirect
5. #59259C2semidirect
6. #59245C2semidirect
7. #45275C2semidirect
8. #45273C2semidirect
9. #43937C2semidirect
10. #39674C2semidirect
11. #39673C2semidirect
12. #39635C2semidirect
13. #39633C2semidirect
14. #36563C2semidirect
15. #36555C2semidirect
16. #35668C2semidirect
18. #35275C2semidirect
19. #35265C2semidirect
21. C2×#2582C2semidirect
24. #34182C2semidirect
25. Q8×#117C2semidirect
203. #536Q8semidirect
560. C4⋊Q8C2×Q8semidirect
564. #124C2×Q8semidirect
570. C22⋊Q8C2×Q8semidirect
571. C22⋊Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#593222
#593212
#592912
#592742
#592592
#592452
#452752
#452732
#439372
#396742
#396732
#396352
#396332
#365632
#365552
#356682
#355752
#352752
#352652
#349522
C2×#25822
#342762
#341832
#341822
Q8×#1172
C4×#5362