Finite Group Databasebeta

← #7690497

Subgroups — #7690497

Order 512.

4891 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59918C213yesmaximal, complemented
2#59666C213yesmaximal, complemented
3#59664C213yesmaximal, complemented
4#59325C213yesmaximal, complemented
5#59324C213yesmaximal, complemented
6#45409C213yesmaximal, complemented
7#45279C213yesmaximal, complemented
8#45278C213yesmaximal, complemented
9#45190C213yesmaximal, complemented
10#39629C213yesmaximal, complemented
11#39603C213yesmaximal, complemented
12#38101C213yesmaximal
13#38099C213yesmaximal
14#36571C213yesmaximal, complemented
15Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
16#36474C211yesmaximal, characteristic, complemented
17#36435C211yesmaximal, characteristic, complemented
18#36435C211yesmaximal, characteristic, complemented
19#36435C211yesmaximal, characteristic, complemented
20#36191C213yesmaximal
21#35971C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35786C211yesmaximal, characteristic, complemented
24#35711C211yesmaximal, characteristic, complemented
25#34772C213yesmaximal
26#34336C211yesmaximal, characteristic, complemented
27#34291C211yesmaximal, characteristic
28#34291C211yesmaximal, characteristic
29#34182C211yesmaximal, characteristic, complemented
30C4×D4×Q8C211yesmaximal, characteristic
31C2×#2351C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2862C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2851C2213yes—
46#2851C2213yes—
47#2806C2216yes—
48#2806C2216yes—
49#2805C2216yes—
50#2805C2216yes—
51#2802C2216yes—
52#2802C2216yes—
53#2792C2216yes—
54#2791C2216yes—
55#2788C2216yes—
56#2774C2216yes—
57#2768C2216yes—
58#2755C2216yes—
59#2742C2216yes—
60#2704C2216yes—
61#2647C2213yes—
62#2647C2213yes—
63#2629C2213yes—
64#2628C2213yes—
65#2590C2216yes—
66#2588C2216yes—
67#2586C2216yes—
68#2585C2216yes—
69#2583C2216yes—
70#2582C2213yes—
71#2582C2213yes—
72#2581C2213yes—
73#2581C2213yes—
74#2581C2213yes—
75#2581C2213yes—
76#2574C2216yes—
77#2574C2216yes—
78#2571C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2568C2213yes—
82#2567C2213yes—
83#2567C2213yes—
84#2565C2213yes—
85#2565C2213yes—
86#2565C2213yes—
87#2565C2213yes—
88#2552C2213yes—
89#2550C2216yes—
90#2550C2213yes—
91#2550C2213yes—
92#2550C2213yes—
93#2550C2213yes—
94#2549C2216yes—
95#2546C2213yes—
96#2522C2213yes—
97#2522C2213yes—
98#2520C2213yes—
99#2520C2216yes—
100#2520C2216yes—
101#2520C2216yes—
102#2520C2216yes—
103#2520C2213yes—
104#2511C2213yes—
105#2509C2213yes—
106#2509C2213yes—
107#2508C2213yes—
108#2508C2216yes—
109#2508C2213yes—
110#2507C2216yes—
111#2507C2213yes—
112#2507C2213yes—
113#2507C2213yes—
114#2506C2213yes—
115#2506C2213yes—
116#2505C2216yes—
117#2505C2213yes—
118#2505C2213yes—
119#2502C2213yes—
120#2497C2213yes—
121#2492C2213yes—
122#2487C2213yes—
123#2473C2216yes—
124#2453C2213yes—
125#2453C2213yes—
126#2453C2213yes—
127#2453C2213yes—
128#2451C2213yes—
129#2451C2213yes—
130#2451C2213yes—
131#2451C2213yes—
132#2451C2213yes—
133#2451C2213yes—
134#2451C2213yes—
135#2451C2213yes—
136#2450C2213yes—
137#2450C2216yes—
138#2450C2211yescharacteristic
139#2442C2213yes—
140#2442C2213yes—
141#2442C2213yes—
142#2441C2213yes—
143#2440C2213yes—
144#2440C2213yes—
145#2440C2213yes—
146#2440C2213yes—
147#2440C2213yes—
148#2440C2213yes—
149#2439C2213yes—
150#2439C2213yes—
151#2439C2213yes—
152#2417C2213yes—
153#2402C2213yes—
154#2402C2213yes—
155#2396C2213yes—
156#2396C2213yes—
157#2370C2213yes—
158#2370C2216yes—
159#2370C2213yes—
160#2369C2213yes—
161#2368C2216yes—
162#2368C2216yes—
163#2365C2213yes—
164#2365C2213yes—
165#2365C2213yes—
166#2362C2213yes—
167#2362C2213yes—
168#2360C2213yes—
169#2360C2213yes—
170#2360C2213yes—
171#2360C2213yes—
172#2355C2213yes—
173#2352C2213yes—
174#2352C2213yes—
175#2351C2213yes—
176#2351C2213yes—
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2213yes—
183#2351C2211yescharacteristic
184#2351C2213yes—
185#2351C2213yes—
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2213yes—
191Q8×C4⋊C4C2213yes—
192Q8×C4⋊C4C2213yes—
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199D4×C4⋊C4C2213yes—
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2331C2213yes—
207#2330C2213yes—
208#2327C2213yes—
209#2327C2213yes—
210#2323C2213yes—
211#2323C2213yes—
212#2316C2213yes—
213#2316C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×#125C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×C22⋊Q8C2213yes—
223C4×C22⋊Q8C2213yes—
224C4×C22⋊Q8C2213yes—
225#2295C2213yes—
226C2×#389C2213yes—
227C2×#389C2213yes—
228#2290C2213yes—
229#2290C2213yes—
230#2285C2213yes—
231#2285C2213yes—
232C2×#382C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C23×Q8C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—44no—
241#557—28no—
242#557—44no—
243D4×Q8Q8116yescomplemented
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2316yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263#519—44no—
264#519—44no—
265C2×C4×Q8—28no—
266C2×C4×Q8—28no—
267C2×C4×Q8—44no—
268C2×C4×Q8—44no—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2313yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×#117C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C22×C4⋊C4C2313yes—
305C22×C4⋊C4C2313yes—
306C22×C4⋊C4C2313yes—
307C22×C4⋊C4C2313yes—
308C22×C4⋊C4C2313yes—
309C22×C4⋊C4C2313yes—
310C22×C42C2313yes—
311C22×C42C2313yes—
312C22×C42C2313yes—
313C22×C42C2313yes—
314#400C2313yes—
315#400C2316yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2316yes—
327#400C2316yes—
328#400C2311yescharacteristic
329#400C2313yes—
330#400C2313yes—
331#399C2313yes—
332#399C2313yes—
333#398C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2316yes—
343#398C2316yes—
344#398C2313yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2316yes—
349#398C2313yes—
350#398C2313yes—
351#398C2316yes—
352#398C2313yes—
353#398C2316yes—
354#398C2313yes—
355#398C2311yescharacteristic
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2316yes—
360#396C2313yes—
361#396C2316yes—
362#396C2313yes—
363#396C2311yescharacteristic
364#396C2313yes—
365#395C2316yes—
366#395C2316yes—
367#395C2316yes—
368#395C2316yes—
369#395C2316yes—
370#395C2313yes—
371#395C2316yes—
372#395C2316yes—
373#395C2316yes—
374#395C2313yes—
375#393C2313yes—
376#393C2316yes—
377#393C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2316yes—
391#391C2313yes—
392#391C2313yes—
393#391C2316yes—
394#391C2316yes—
395#391C2316yes—
396#391C2313yes—
397#391C2316yes—
398#391C2313yes—
399#391C2316yes—
400#391C2313yes—
401#391C2316yes—
402#391C2316yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2316yes—
409#389C2316yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2316yes—
437#389C2313yes—
438#389C2316yes—
439#389C2316yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2316yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2316yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2316yes—
459#389C2316yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#387C2313yes—
472#387C2316yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2316yes—
492#387C2316yes—
493#387C2313yes—
494#387C2313yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2311yescharacteristic
510#387C2313yes—
511#387C2313yes—
512#386C2313yes—
513#386C2313yes—
514#386C2311yescharacteristic
515#386C2311yescharacteristic
516#385C2313yes—
517#385C2316yes—
518#385C2313yes—
519#385C2313yes—
520#385C2316yes—
521#385C2316yes—
522#385C2313yes—
523#385C2316yes—
524#385C2316yes—
525#385C2313yes—
526#385C2313yes—
527#385C2313yes—
528#385C2313yes—
529#385C2313yes—
530#385C2311yescharacteristic
531#385C2311yescharacteristic
532#385C2311yescharacteristic
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2316yes—
551#382C2316yes—
552#382C2316yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2313yes—
557#380C2316yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2311yescharacteristic
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2316yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2316yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622#376C2313yes—
623#376C2313yes—
624C2×#95C2313yes—
625C2×#95C2316yes—
626C2×#95C2311yescharacteristic
627C43C2313yes—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8C2×Q818yes—
633C22×Q8C2×Q818yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2413yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2416yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2411yescharacteristic
642C23×C4C2413yes—
643C23×C4C2411yescharacteristic
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2411yescharacteristic
651C23×C4C2413yes—
652C4⋊Q8—212no—
653C4⋊Q8—46no—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658C4⋊Q8C2×Q8124yes—
659#125—212no—
660#125—212no—
661#125—46no—
662#125—46no—
663#125—412no—
664C22⋊Q8—24no—
665C22⋊Q8—212no—
666C22⋊Q8—412no—
667C22⋊Q8—46no—
668C22⋊Q8—46no—
669C22⋊Q8C2×Q8124yes—
670C22⋊Q8C2×Q8124yes—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—212no—
683C4×Q8—212no—
684C4×Q8—212no—
685C4×Q8—212no—
686C4×Q8—212no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—46no—
696C4×Q8—46no—
697C4×Q8C2×Q818yes—
698C4×Q8#4118yes—
699C4×D4—24no—
700C4×D4—46no—
701C4×D4C2×Q8124yes—
702#117—46no—
703#117—46no—
704#117—46no—
705#117—46no—
706C2×C4⋊C4—212no—
707C2×C4⋊C4—212no—
708C2×C4⋊C4—46no—
709C2×C4⋊C4—46no—
710C2×C4⋊C4—46no—
711C2×C4⋊C4—46no—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2416yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2411yescharacteristic
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C42—212no—
803C2×C42—212no—
804C2×C42—46no—
805C2×C42—46no—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2411yescharacteristic
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2416yes—
823C2×C42C2416yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2416yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2416yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835#95C2413yes—
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2416yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2416yes—
845#95C2416yes—
846#95C2416yes—
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2413yes—
875#95C2416yes—
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2416yes—
890#95C2416yes—
891#95C2416yes—
892#95C2413yes—
893#95C2416yes—
894#95C2416yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2416yes—
904C24C2511yescharacteristic
905C24C2511yescharacteristic
906C2×Q8—232no—
907C2×Q8—232no—
908C2×Q8—26no—
909C2×Q8—26no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—26no—
913C2×Q8—22no—
914C2×Q8—26no—
915C2×Q8—22no—
916C2×Q8—41no—
917C2×Q8—43no—
918C2×Q8—43no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—46no—
922C2×Q8—46no—
923C2×Q8—46no—
924C2×Q8C22×Q8112yes—
925C2×Q8C22×Q8112yes—
926C2×Q8C22×Q814yes—
927C2×Q8C2×#4114yes—
928C2×Q8H(5,𝔽2)14yes—
929C2×D4—22no—
930C2×D4—22no—
931C2×D4C22×Q814yes—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—26no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—26no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—43no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4C22×Q8112yes—
961C22×C4C22×Q8112yes—
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C22×C4C2511yescharacteristic
966C22×C4C2513yes—
967C22×C4C2513yes—
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2511yescharacteristic
972C22×C4C2513yes—
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2513yes—
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2513yes—
991C4⋊C4—212no—
992C4⋊C4—212no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—22no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—212no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—22no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4—46no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—41no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—41no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—41no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—46no—
1048C4⋊C4—43no—
1049C4⋊C4—46no—
1050C4⋊C4—46no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—46no—
1054C4⋊C4—46no—
1055C4⋊C4—46no—
1056C4⋊C4—46no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4C22×Q8112yes—
1060C4⋊C4C22×Q8112yes—
1061C4⋊C4C22×Q8124yes—
1062C4⋊C4C2×#41112yes—
1063C22⋊C4—22no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—22no—
1067C22⋊C4—26no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—43no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—43no—
1078C22⋊C4C22×Q8112yes—
1079C22⋊C4C22×Q8112yes—
1080C22⋊C42−1+414yes—
1081C42—26no—
1082C42—26no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—26no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—22no—
1097C42—43no—
1098C42—43no—
1099C42—43no—
1100C42—43no—
1101C42—43no—
1102C42—46no—
1103C42—46no—
1104C42—46no—
1105C42—43no—
1106C42—46no—
1107C42—43no—
1108C42C22×Q8112yes—
1109C42C2×#41112yes—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23C23×Q812yes—
1121C23C23×Q812yes—
1122C23C2×2−1+412yes—
1123C23#58512yes—
1124C23C2611yescharacteristic
1125Q8—224no—
1126Q8—224no—
1127Q8—44no—
1128Q8—86no—
1129Q8—86no—
1130Q8—166no—
1131Q8#554116yes—
1132D4—28no—
1133C2×C4—21no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—23no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—224no—
1152C2×C4—224no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—44no—
1213C2×C4—412no—
1214C2×C4—44no—
1215C2×C4—86no—
1216C2×C4—86no—
1217C2×C4—86no—
1218C2×C4C23×Q812yes—
1219C2×C4C23×Q816yes—
1220C2×C4C23×Q816yes—
1221C2×C4C23×Q816yes—
1222C2×C4C23×Q816yes—
1223C2×C4C22×#4112yes—
1224C2×C4C22×#4116yes—
1225C2×C4C22×#4116yes—
1226C2×C4C2×H(5,𝔽2)16yes—
1227C2×C4C2×2−1+412yes—
1228C2×C4C2×2−1+412yes—
1229C2×C4#58512yes—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22#350214yes—
1244C22C24×Q811yescharacteristic
1245C22C23×#4111yescharacteristic
1246C22C22×H(5,𝔽2)11yescharacteristic
1247C22C22×2−1+411yescharacteristic
1248C22C2×#58511yescharacteristic
1249C22C2×#58511yescharacteristic
1250C222−1+611yescharacteristic
1251C4—22no—
1252C4—22no—
1253C4—26no—
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—26no—
1258C4—26no—
1259C4—26no—
1260C4—41no—
1261C4—43no—
1262C4—41no—
1263C4—41no—
1264C4—43no—
1265C4—43no—
1266C4—41no—
1267C4—43no—
1268C4—43no—
1269C4—43no—
1270C4—43no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—43no—
1276C4—43no—
1277C4—43no—
1278C4—43no—
1279C4C2×#554112yes—
1280C2—24no—
1281C2—42no—
1282C2C22×#55411yescharacteristic
1283C2C2×#350211yescharacteristic
1284C2#6281611yescharacteristic
1285C2#6291911yescharacteristic
1286C2#6299811yescharacteristic
1287C2#6300411yescharacteristic
1288C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59918C2semidirect
2. #59666C2semidirect
3. #59664C2semidirect
4. #59325C2semidirect
5. #59324C2semidirect
6. #45409C2semidirect
7. #45279C2semidirect
8. #45278C2semidirect
9. #45190C2semidirect
10. #39629C2semidirect
11. #39603C2semidirect
14. #36571C2semidirect
15. Q8×C22⋊Q8C2semidirect
16. #36474C2semidirect
17. #36435C2semidirect
18. #36435C2semidirect
19. #36435C2semidirect
21. #35971C2semidirect
22. #35868C2semidirect
23. #35786C2semidirect
24. #35711C2semidirect
26. #34336C2semidirect
29. #34182C2semidirect
31. C2×#2351C2semidirect
243. D4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#599182
#596662
#596642
#593252
#593242
#454092
#452792
#452782
#451902
#396292
#396032
#381012
#380992
#365712
Q8×C22⋊Q82
#364742
#364352
#361912
#359712
#358682
#357862
#357112
#347722
#343362
#342912
#341822
C4×D4×Q82
C2×#23512