Finite Group Databasebeta

← #7985253

Subgroups — #7985253

Order 512.

4941 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59459C212yesmaximal, complemented
3#59144C212yesmaximal, complemented
4#59036C212yesmaximal, complemented
5#47987C218yesmaximal, complemented
6#45503C214yesmaximal, complemented
7#45358C214yesmaximal, complemented
8#44923C214yesmaximal, complemented
9#42954C214yesmaximal, complemented
10#42491C214yesmaximal, complemented
11#39659C214yesmaximal, complemented
12#39609C212yesmaximal, complemented
13#39596C212yesmaximal, complemented
14#39498C212yesmaximal, complemented
15#38967C212yesmaximal, complemented
16#36599C212yesmaximal, complemented
17#36560C211yesmaximal, characteristic, complemented
18#36445C212yesmaximal, complemented
19#36134C211yesmaximal, characteristic, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35279C212yesmaximal, complemented
22#35173C212yesmaximal, complemented
23#34941C211yesmaximal, characteristic, complemented
24#34929C211yesmaximal, characteristic, complemented
25#34480C212yesmaximal
26C4×#547C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×D4×Q8C2212yes—
29C2×#547C2211yescharacteristic
30C2×#533C2212yes—
31C2×#533C2212yes—
32C22×C4⋊Q8C2212yes—
33C2×C4×#41C2212yes—
34#2868C2211yescharacteristic
35#2859C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2214yes—
39#2857C2214yes—
40#2857C2214yes—
41#2841C2218yes—
42#2807C2218yes—
43#2807C2218yes—
44#2805C2214yes—
45#2805C2218yes—
46#2792C2218yes—
47#2792C2218yes—
48#2788C2218yes—
49#2788C2218yes—
50#2784C2218yes—
51#2774C2218yes—
52#2748C2218yes—
53#2742C2218yes—
54#2742C2218yes—
55#2720C2218yes—
56#2713C2218yes—
57#2692C2218yes—
58#2692C2218yes—
59#2665C2218yes—
60#2659C2218yes—
61#2628C2214yes—
62#2628C2214yes—
63#2628C2218yes—
64#2587C2218yes—
65#2586C2218yes—
66#2585C2218yes—
67#2584C2214yes—
68#2584C2214yes—
69#2584C2218yes—
70#2581C2214yes—
71#2580C2214yes—
72#2574C2214yes—
73#2571C2212yes—
74#2569C2218yes—
75#2568C2212yes—
76#2568C2212yes—
77#2567C2214yes—
78#2567C2214yes—
79#2567C2211yescharacteristic
80#2567C2212yes—
81#2567C2214yes—
82#2565C2214yes—
83#2563C2214yes—
84#2563C2211yescharacteristic
85#2556C2214yes—
86#2552C2212yes—
87#2552C2211yescharacteristic
88#2551C2212yes—
89#2551C2212yes—
90#2551C2211yescharacteristic
91#2550C2214yes—
92#2550C2214yes—
93#2546C2211yescharacteristic
94#2546C2214yes—
95#2546C2212yes—
96#2546C2212yes—
97#2546C2212yes—
98#2542C2212yes—
99#2542C2214yes—
100#2542C2211yescharacteristic
101#2538C2212yes—
102#2538C2211yescharacteristic
103#2538C2214yes—
104#2538C2211yescharacteristic
105#2511C2214yes—
106#2511C2214yes—
107#2509C2214yes—
108#2509C2214yes—
109#2509C2214yes—
110#2508C2212yes—
111#2506C2214yes—
112#2506C2212yes—
113#2506C2214yes—
114#2497C2212yes—
115#2492C2212yes—
116#2492C2214yes—
117#2487C2218yes—
118#2473C2218yes—
119#2465C2218yes—
120#2454C2212yes—
121#2454C2214yes—
122#2454C2218yes—
123#2454C2214yes—
124#2452C2212yes—
125#2451C2214yes—
126#2451C2214yes—
127#2446C2214yes—
128#2442C2214yes—
129#2442C2214yes—
130#2441C2214yes—
131#2441C2214yes—
132#2441C2218yes—
133#2440C2214yes—
134#2440C2214yes—
135#2439C2214yes—
136#2434C2214yes—
137#2434C2214yes—
138#2429C2214yes—
139#2429C2212yes—
140#2423C2214yes—
141#2423C2212yes—
142#2423C2214yes—
143#2409C2214yes—
144#2409C2214yes—
145#2396C2214yes—
146#2396C2214yes—
147#2376C2218yes—
148#2370C2214yes—
149#2365C2212yes—
150#2365C2211yescharacteristic
151#2365C2212yes—
152#2365C2212yes—
153#2365C2212yes—
154#2363C2214yes—
155#2362C2212yes—
156#2361C2212yes—
157#2360C2214yes—
158#2359C2214yes—
159#2355C2212yes—
160#2354C2212yes—
161#2354C2211yescharacteristic
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2214yes—
164Q8×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168#2345C2214yes—
169#2344C2212yes—
170#2341C2214yes—
171Q8×C22⋊C4C2214yes—
172#2339C2212yes—
173#2335C2218yes—
174#2324C2214yes—
175#2323C2214yes—
176#2317C2214yes—
177#2316C2214yes—
178#2316C2214yes—
179#2311C2214yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×#125C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2214yes—
189C4×C22⋊Q8C2212yes—
190C4×#123C2214yes—
191C4×#121C2212yes—
192#2293C2212yes—
193#2293C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2314yes—
201#557—48no—
202D4×Q8—48no—
203#547Q8116yescomplemented
204#533—48no—
205#533—48no—
206C2×C4⋊Q8—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2311yescharacteristic
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#123C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2312yes—
238C2×#121C2312yes—
239C4×#41—48no—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117C2314yes—
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2314yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#400C2314yes—
285#399C2318yes—
286#399C2318yes—
287#399C2314yes—
288#399C2318yes—
289#399C2318yes—
290#399C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2314yes—
303#396C2314yes—
304#396C2314yes—
305#396C2318yes—
306#396C2314yes—
307#396C2318yes—
308#396C2314yes—
309#396C2318yes—
310#395C2318yes—
311#395C2314yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2314yes—
321#393C2314yes—
322#393C2318yes—
323#393C2318yes—
324#393C2318yes—
325#393C2314yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2318yes—
335#391C2312yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2318yes—
340#391C2312yes—
341#391C2312yes—
342#391C2318yes—
343#391C2314yes—
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2318yes—
349#390C2312yes—
350#390C2318yes—
351#390C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2312yes—
383#389C2318yes—
384#389C2318yes—
385#389C2314yes—
386#389C2318yes—
387#389C2318yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2312yes—
395#389C2318yes—
396#389C2312yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#388C2314yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2314yes—
406#388C2318yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#387C2318yes—
425#387C2314yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2314yes—
432#386C2314yes—
433#385C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2314yes—
443#385C2314yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2314yes—
452#384C2314yes—
453#384C2318yes—
454#384C2312yes—
455#384C2312yes—
456#384C2312yes—
457#382C2312yes—
458#382C2314yes—
459#382C2314yes—
460#382C2314yes—
461#382C2314yes—
462#381C2314yes—
463#380C2318yes—
464#380C2318yes—
465#380C2312yes—
466#380C2312yes—
467#380C2318yes—
468#380C2318yes—
469#380C2314yes—
470#380C2318yes—
471#380C2318yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2318yes—
477#380C2312yes—
478#380C2314yes—
479#380C2312yes—
480#380C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2318yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C2×#95C2314yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C2×#41—44no—
527C2×#41—44no—
528C2×#41C2×Q8116yescomplemented
529C22×Q8—48no—
530C22×Q8—48no—
531C22×Q8—48no—
532C22×Q8C2411yescharacteristic
533C22×Q8C2414yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2418yes—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2418yes—
550C23×C4C2414yes—
551C4⋊Q8—24no—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—28no—
555C4⋊Q8—48no—
556C4⋊Q8—48no—
557C4⋊Q8—44no—
558C4⋊Q8—44no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—48no—
564C4⋊Q8C2×Q818yescomplemented
565#125—28no—
566#125—48no—
567#125—48no—
568#125—48no—
569#125—416no—
570#123C2×Q8132yescomplemented
571C22⋊Q8—416no—
572C22⋊Q8—48no—
573C22⋊Q8—44no—
574C22⋊Q8—48no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581C22⋊Q8C2×Q8116yescomplemented
582#121C2×Q8116yes—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—24no—
587C4×Q8—44no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8—42no—
591C4×Q8—44no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—42no—
600C4×D4—44no—
601C4×D4—48no—
602C4×D4—48no—
603C4×D4—48no—
604C4×D4C2×Q818yes—
605C4×D4C2×Q818yescomplemented
606#117—48no—
607#117—48no—
608#117—48no—
609#117—44no—
610#117—48no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4C2×Q8116yescomplemented
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2414yes—
699C2×C42—28no—
700C2×C42—28no—
701C2×C42—48no—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2418yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2412yes—
723C2×C42C2418yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2412yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2412yes—
747#95C2414yes—
748#95C2412yes—
749#95C2412yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24C2512yes—
772C24C2512yes—
773#41—432no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—28no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—28no—
785C2×Q8—24no—
786C2×Q8—42no—
787C2×Q8—42no—
788C2×Q8—44no—
789C2×Q8—48no—
790C2×Q8—48no—
791C2×Q8—44no—
792C2×Q8—48no—
793C2×Q8—44no—
794C2×Q8—832no—
795C2×Q8C22×Q818yes—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4C22×Q814yes—
803C2×D4C22×Q814yes—
804C2×D4C22×Q8116yes—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—44no—
820C22×C4—42no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4C22×Q818yes—
830C22×C4C22×Q818yes—
831C22×C4C22×Q8116yes—
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2518yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—22no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—24no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—42no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4C22×Q814yes—
914C4⋊C4C22×Q818yes—
915C4⋊C4C22×Q8116yes—
916C4⋊C4C22×Q814yes—
917C4⋊C4C22×Q818yes—
918C4⋊C42−1+414yes—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—42no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4C22×Q818yes—
938C22⋊C4C22×Q818yes—
939C22⋊C4C22×Q8116yes—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—28no—
947C42—24no—
948C42—28no—
949C42—24no—
950C42—22no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—22no—
955C42—22no—
956C42—44no—
957C42—44no—
958C42—41no—
959C42—42no—
960C42—48no—
961C42—42no—
962C42—48no—
963C42—48no—
964C42C22×Q814yes—
965C42H(5,𝔽2)14yes—
966C42H(5,𝔽2)14yes—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23C23×Q814yes—
980C23C23×Q814yes—
981C23C2611yescharacteristic
982Q8—216no—
983Q8—48no—
984Q8—44no—
985Q8—416no—
986Q8—48no—
987Q8—88no—
988Q8—816no—
989D4—28no—
990D4—28no—
991D4—416no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—216no—
1007C2×C4—216no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—28no—
1021C2×C4—28no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—21no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—28no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—416no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—48no—
1054C2×C4—84no—
1055C2×C4—88no—
1056C2×C4—816no—
1057C2×C4C23×Q812yes—
1058C2×C4C23×Q814yes—
1059C2×C4C23×Q814yes—
1060C2×C4C23×Q818yes—
1061C2×C4C23×Q812yes—
1062C2×C4C23×Q812yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×H(5,𝔽2)12yes—
1065C2×C4C2×H(5,𝔽2)12yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×2−1+414yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4#58512yes—
1072C2×C4#58512yes—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22C24×Q811yescharacteristic
1088C22C22×H(5,𝔽2)11yescharacteristic
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C22×2−1+411yescharacteristic
1091C22C2×#58511yescharacteristic
1092C22C2×#58511yescharacteristic
1093C222−1+611yescharacteristic
1094C4—22no—
1095C4—24no—
1096C4—28no—
1097C4—24no—
1098C4—22no—
1099C4—22no—
1100C4—24no—
1101C4—42no—
1102C4—42no—
1103C4—44no—
1104C4—48no—
1105C4—42no—
1106C4—41no—
1107C4—42no—
1108C4—44no—
1109C4—42no—
1110C4—44no—
1111C4—44no—
1112C4—42no—
1113C4—42no—
1114C4—44no—
1115C4#350114yes—
1116C4#350314yes—
1117C4#354614yes—
1118C2—44no—
1119C2—44no—
1120C2C2×#354611yescharacteristic
1121C2C2×#350111yescharacteristic
1122C2C2×#350311yescharacteristic
1123C2#6292511yescharacteristic
1124C2#6294211yescharacteristic
1125C2#6300411yescharacteristic
1126C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59459C2semidirect
3. #59144C2semidirect
4. #59036C2semidirect
5. #47987C2semidirect
6. #45503C2semidirect
7. #45358C2semidirect
8. #44923C2semidirect
9. #42954C2semidirect
10. #42491C2semidirect
11. #39659C2semidirect
12. #39609C2semidirect
13. #39596C2semidirect
14. #39498C2semidirect
15. #38967C2semidirect
16. #36599C2semidirect
17. #36560C2semidirect
18. #36445C2semidirect
19. #36134C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35279C2semidirect
22. #35173C2semidirect
23. #34941C2semidirect
24. #34929C2semidirect
203. #547Q8semidirect
528. C2×#41C2×Q8semidirect
564. C4⋊Q8C2×Q8semidirect
570. #123C2×Q8semidirect
581. C22⋊Q8C2×Q8semidirect
605. C4×D4C2×Q8semidirect
614. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598702
#594592
#591442
#590362
#479872
#455032
#453582
#449232
#429542
#424912
#396592
#396092
#395962
#394982
#389672
#365992
#365602
#364452
#361342
D4×C4⋊Q82
#352792
#351732
#349412
#349292
#344802
C4×#5472