Finite Group Databasebeta

← #7632241

Subgroups — #7632241

Order 512.

4778 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36565C213yesmaximal, complemented
2Q8×C22⋊Q8C211yesmaximal, characteristic
3#36478C213yesmaximal
4#36475C211yesmaximal, characteristic, complemented
5#36447C211yesmaximal, characteristic, complemented
6#36435C211yesmaximal, characteristic
7#36288C213yesmaximal
8#36283C213yesmaximal, complemented
9#35958C213yesmaximal, complemented
10#35937C211yesmaximal, characteristic, complemented
11#35937C211yesmaximal, characteristic, complemented
12#35936C213yesmaximal, complemented
13#35819C213yesmaximal
14#35786C211yesmaximal, characteristic
15#35747C213yesmaximal
16#35711C211yesmaximal, characteristic
17#35583C213yesmaximal, complemented
18#35582C213yesmaximal, complemented
19#35578C213yesmaximal
20#35577C213yesmaximal
21#35282C213yesmaximal
22#35199C213yesmaximal, complemented
23#34920C213yesmaximal, complemented
24#34882C213yesmaximal
25#34336C211yesmaximal, characteristic, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34335C211yesmaximal, characteristic, complemented
28#34262C211yesmaximal, characteristic
29#34262C211yesmaximal, characteristic
30C4×Q82C211yesmaximal, characteristic, complemented
31C4×#519C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2864C2213yes—
40#2863C2216yes—
41#2862C2216yes—
42#2859C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2666C2216yes—
46#2666C2216yes—
47#2660C2213yes—
48#2660C2213yes—
49#2629C2213yes—
50#2628C2213yes—
51#2612C2216yes—
52#2612C2216yes—
53#2606C2216yes—
54#2606C2216yes—
55#2605C2216yes—
56#2605C2216yes—
57#2590C2216yes—
58#2589C2216yes—
59#2588C2216yes—
60#2587C2216yes—
61#2586C2213yes—
62#2586C2213yes—
63#2586C2216yes—
64#2586C2216yes—
65#2586C2216yes—
66#2585C2213yes—
67#2585C2213yes—
68#2585C2216yes—
69#2584C2213yes—
70#2584C2213yes—
71#2582C2213yes—
72#2582C2213yes—
73#2581C2213yes—
74#2581C2213yes—
75#2574C2213yes—
76#2574C2213yes—
77#2574C2216yes—
78#2571C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2568C2213yes—
82#2567C2213yes—
83#2565C2213yes—
84#2565C2213yes—
85#2556C2213yes—
86#2556C2213yes—
87#2556C2216yes—
88#2552C2213yes—
89#2551C2213yes—
90#2551C2213yes—
91#2551C2213yes—
92#2551C2213yes—
93#2550C2213yes—
94#2550C2213yes—
95#2550C2213yes—
96#2550C2213yes—
97#2550C2216yes—
98#2550C2216yes—
99#2546C2213yes—
100#2546C2213yes—
101#2522C2213yes—
102#2522C2213yes—
103#2520C2213yes—
104#2520C2213yes—
105#2520C2216yes—
106#2520C2216yes—
107#2509C2213yes—
108#2508C2213yes—
109#2508C2213yes—
110#2508C2213yes—
111#2507C2213yes—
112#2506C2213yes—
113#2506C2213yes—
114#2506C2213yes—
115#2492C2216yes—
116#2465C2211yescharacteristic
117#2465C2213yes—
118#2465C2216yes—
119#2462C2213yes—
120#2462C2213yes—
121#2462C2216yes—
122#2462C2216yes—
123#2453C2213yes—
124#2453C2213yes—
125#2451C2213yes—
126#2451C2213yes—
127#2451C2213yes—
128#2451C2216yes—
129#2451C2213yes—
130#2451C2213yes—
131#2451C2213yes—
132#2446C2216yes—
133#2442C2213yes—
134#2441C2213yes—
135#2440C2213yes—
136#2440C2213yes—
137#2440C2213yes—
138#2439C2213yes—
139#2439C2213yes—
140#2439C2213yes—
141#2429C2216yes—
142#2402C2216yes—
143#2399C2213yes—
144#2399C2213yes—
145#2399C2216yes—
146#2396C2213yes—
147#2396C2213yes—
148#2370C2213yes—
149#2370C2213yes—
150#2370C2213yes—
151#2370C2213yes—
152#2369C2213yes—
153#2369C2213yes—
154#2369C2213yes—
155#2369C2213yes—
156#2369C2213yes—
157#2369C2213yes—
158#2365C2213yes—
159#2365C2213yes—
160#2356C2213yes—
161#2356C2213yes—
162#2355C2213yes—
163#2355C2213yes—
164#2355C2213yes—
165#2355C2213yes—
166#2355C2213yes—
167#2351C2211yescharacteristic
168#2351C2211yescharacteristic
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2213yes—
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184#2347C2213yes—
185#2347C2213yes—
186#2346C2213yes—
187#2346C2213yes—
188Q8×C22⋊C4C2211yescharacteristic
189Q8×C22⋊C4C2211yescharacteristic
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192#2331C2213yes—
193#2331C2213yes—
194#2331C2213yes—
195#2331C2213yes—
196#2330C2213yes—
197#2330C2213yes—
198#2320C2213yes—
199#2320C2213yes—
200#2314C2213yes—
201#2314C2213yes—
202C4×C4⋊Q8C2213yes—
203C4×C4⋊Q8C2213yes—
204C4×C4⋊Q8C2213yes—
205C4×C4⋊Q8C2213yes—
206C4×#125C2213yes—
207C4×#125C2213yes—
208C4×#125C2213yes—
209C4×#125C2213yes—
210C4×#125C2216yes—
211C4×C22⋊Q8C2213yes—
212C4×C22⋊Q8C2213yes—
213#2298C2213yes—
214#2298C2213yes—
215#2295C2213yes—
216#2295C2213yes—
217#2295C2213yes—
218#2295C2216yes—
219#2295C2213yes—
220#2295C2213yes—
221#2276C2211yescharacteristic
222#2276C2211yescharacteristic
223#2276C2211yescharacteristic
224#2276C2213yes—
225#2276C2211yescharacteristic
226#2276C2213yes—
227#2274C2213yes—
228#2274C2213yes—
229C42×Q8C2211yescharacteristic
230C42×Q8C2211yescharacteristic
231C42×Q8C2211yescharacteristic
232C42×Q8C2213yes—
233C42×Q8C2211yescharacteristic
234C42×Q8C2213yes—
235C42×Q8C2213yes—
236C4×#117C2213yes—
237C4×#117C2213yes—
238C23×Q8C2311yescharacteristic
239Q82—28no—
240Q82—28no—
241#557—28no—
242#557—28no—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2316yes—
252C2×C4⋊Q8C2316yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2316yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2316yes—
263#519—28no—
264#519Q8116yescomplemented
265C2×C4×Q8—28no—
266C2×C4×Q8C2313yes—
267C2×C4×Q8C2313yes—
268C2×C4×Q8C2313yes—
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×Q8C2313yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2316yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2316yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×#117C2313yes—
295C2×#117C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C22×C4⋊C4C2313yes—
299C22×C42C2313yes—
300#400C2313yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#399C2313yes—
309#399C2313yes—
310#398C2313yes—
311#398C2316yes—
312#398C2316yes—
313#398C2316yes—
314#398C2316yes—
315#398C2316yes—
316#398C2316yes—
317#398C2313yes—
318#398C2313yes—
319#398C2313yes—
320#398C2316yes—
321#398C2316yes—
322#398C2316yes—
323#398C2313yes—
324#398C2313yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2313yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2313yes—
333#398C2313yes—
334#396C2313yes—
335#396C2316yes—
336#396C2313yes—
337#396C2313yes—
338#396C2311yescharacteristic
339#395C2316yes—
340#395C2316yes—
341#395C2313yes—
342#395C2313yes—
343#395C2316yes—
344#395C2313yes—
345#395C2316yes—
346#395C2313yes—
347#395C2313yes—
348#395C2313yes—
349#395C2313yes—
350#395C2316yes—
351#395C2316yes—
352#395C2316yes—
353#395C2311yescharacteristic
354#395C2311yescharacteristic
355#395C2316yes—
356#395C2313yes—
357#393C2313yes—
358#393C2316yes—
359#393C2311yescharacteristic
360#391C2316yes—
361#391C2316yes—
362#391C2316yes—
363#391C2316yes—
364#391C2313yes—
365#391C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2316yes—
373#391C2316yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2316yes—
378#391C2311yescharacteristic
379#391C2316yes—
380#391C2316yes—
381#391C2316yes—
382#391C2316yes—
383#391C2316yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2316yes—
388#391C2316yes—
389#391C2313yes—
390#389C2311yescharacteristic
391#389C2313yes—
392#389C2316yes—
393#389C2316yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2316yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2316yes—
411#389C2313yes—
412#389C2313yes—
413#389C2316yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2316yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2316yes—
449#388C2316yes—
450#388C2311yescharacteristic
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2311yescharacteristic
456#387C2311yescharacteristic
457#387C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2316yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2316yes—
465#387C2313yes—
466#387C2313yes—
467#387C2316yes—
468#387C2316yes—
469#387C2316yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2316yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2311yescharacteristic
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2316yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2313yes—
507#387C2313yes—
508#387C2311yescharacteristic
509#385C2311yescharacteristic
510#385C2313yes—
511#385C2313yes—
512#385C2316yes—
513#385C2313yes—
514#384C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#383C2316yes—
523#383C2316yes—
524#382C2313yes—
525#382C2313yes—
526#382C2316yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2316yes—
535#382C2316yes—
536#382C2313yes—
537#380C2313yes—
538#380C2313yes—
539#380C2313yes—
540#380C2313yes—
541#380C2313yes—
542#380C2313yes—
543C4×C4⋊C4C2313yes—
544C4×C4⋊C4C2316yes—
545C4×C4⋊C4C2316yes—
546C4×C4⋊C4C2313yes—
547C4×C4⋊C4C2313yes—
548C4×C4⋊C4C2316yes—
549C4×C4⋊C4C2313yes—
550C4×C4⋊C4C2313yes—
551C4×C4⋊C4C2313yes—
552C4×C4⋊C4C2313yes—
553C4×C4⋊C4C2316yes—
554C4×C4⋊C4C2316yes—
555C4×C4⋊C4C2316yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2316yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2316yes—
584C4×C4⋊C4C2316yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2316yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2311yescharacteristic
612C4×C22⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2316yes—
617#376C2316yes—
618#376C2316yes—
619#376C2313yes—
620C43C2313yes—
621C43C2313yes—
622C43C2313yes—
623C43C2316yes—
624C43C2313yes—
625C22×Q8—24no—
626C22×Q8—24no—
627C22×Q8C2×Q818yes—
628C22×Q8C2411yescharacteristic
629C22×Q8C2411yescharacteristic
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2416yes—
633C22×Q8C2413yes—
634C22×Q8C2416yes—
635C22×Q8C2411yescharacteristic
636C23×C4C2411yescharacteristic
637C23×C4C2413yes—
638C23×C4C2413yes—
639C4⋊Q8—212no—
640C4⋊Q8—212no—
641C4⋊Q8—212no—
642C4⋊Q8—212no—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—212no—
647C4⋊Q8—86no—
648C4⋊Q8—86no—
649#125—212no—
650#125—212no—
651#125—212no—
652#125—212no—
653#125—212no—
654#125—46no—
655#125—86no—
656C22⋊Q8—24no—
657C22⋊Q8—46no—
658C22⋊Q8—86no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—212no—
670C4×Q8—212no—
671C4×Q8—24no—
672C4×Q8—212no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8—212no—
676C4×Q8—212no—
677C4×Q8—212no—
678C4×Q8—412no—
679C4×Q8—46no—
680C4×Q8—86no—
681C4×Q8C2×Q8124yes—
682C4×Q8C2×Q8124yes—
683C4×Q8C2×Q818yes—
684C4×Q8C2×Q818yes—
685C4×Q8#4118yes—
686C4×Q8#4118yes—
687#117—212no—
688#117—212no—
689#117C2×Q8124yes—
690#117C2×Q8124yes—
691C2×C4⋊C4—212no—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2416yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2413yes—
777C2×C42—212no—
778C2×C42C2413yes—
779C2×C42C2416yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2416yes—
801C2×C42C2413yes—
802C2×C42C2416yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2416yes—
806C2×C42C2413yes—
807C2×C42C2411yescharacteristic
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2416yes—
811C2×C42C2413yes—
812C2×C42C2416yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816#95C2413yes—
817#95C2411yescharacteristic
818#95C2413yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2416yes—
829#95C2413yes—
830#95C2413yes—
831#95C2416yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2416yes—
839#95C2416yes—
840#95C2416yes—
841#95C2416yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2411yescharacteristic
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2416yes—
856#95C2416yes—
857#95C2411yescharacteristic
858#95C2413yes—
859#95C2413yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2411yescharacteristic
867#95C2413yes—
868#95C2413yes—
869#95C2416yes—
870#95C2416yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2416yes—
878#95C2416yes—
879#95C2413yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888C24C2511yescharacteristic
889C2×Q8—232no—
890C2×Q8—22no—
891C2×Q8—26no—
892C2×Q8—26no—
893C2×Q8—22no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—212no—
897C2×Q8—212no—
898C2×Q8—22no—
899C2×Q8—22no—
900C2×Q8—22no—
901C2×Q8—41no—
902C2×Q8—46no—
903C2×Q8—46no—
904C2×Q8—43no—
905C2×Q8—46no—
906C2×Q8—43no—
907C2×Q8—43no—
908C2×Q8—43no—
909C2×Q8—46no—
910C2×Q8C22×Q8112yes—
911C2×Q8C22×Q814yes—
912C2×Q8C2×#4114yes—
913C2×Q8C2×#4114yes—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—26no—
919C22×C4—41no—
920C22×C4—43no—
921C22×C4—43no—
922C22×C4C22×Q8112yes—
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2513yes—
926C22×C4C2511yescharacteristic
927C22×C4C2513yes—
928C22×C4C2511yescharacteristic
929C22×C4C2513yes—
930C22×C4C2513yes—
931C22×C4C2513yes—
932C22×C4C2511yescharacteristic
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2513yes—
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2513yes—
953C4⋊C4—212no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—212no—
979C4⋊C4—212no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—22no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—46no—
1002C4⋊C4—46no—
1003C4⋊C4—46no—
1004C4⋊C4—46no—
1005C4⋊C4—43no—
1006C4⋊C4—46no—
1007C4⋊C4—46no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—46no—
1014C4⋊C4—46no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4C22×Q8112yes—
1020C4⋊C4C22×Q8112yes—
1021C4⋊C4C22×Q8112yes—
1022C4⋊C4C22×Q8112yes—
1023C4⋊C4C2×#41112yes—
1024C4⋊C4C2×#41112yes—
1025C4⋊C42−1+414yes—
1026C22⋊C4—26no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—41no—
1032C22⋊C4—43no—
1033C22⋊C4—43no—
1034C22⋊C4—43no—
1035C22⋊C4—43no—
1036C22⋊C4C22×Q814yes—
1037C22⋊C4C22×Q8112yes—
1038C42—26no—
1039C42—26no—
1040C42—26no—
1041C42—212no—
1042C42—26no—
1043C42—26no—
1044C42—26no—
1045C42—26no—
1046C42—26no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—22no—
1052C42—22no—
1053C42—22no—
1054C42—26no—
1055C42—26no—
1056C42—43no—
1057C42—43no—
1058C42—43no—
1059C42—46no—
1060C42—41no—
1061C42—43no—
1062C42—43no—
1063C42—46no—
1064C42—46no—
1065C42—43no—
1066C42—43no—
1067C42—43no—
1068C42—43no—
1069C42—43no—
1070C42—46no—
1071C42C22×Q8124yes—
1072C42C22×Q8112yes—
1073C42C22×Q8112yes—
1074C42C2×#41112yes—
1075C42C2×#41112yes—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23C23×Q812yes—
1083C23C2611yescharacteristic
1084Q8—28no—
1085Q8—224no—
1086Q8—44no—
1087Q8—86no—
1088Q8—812no—
1089Q8—86no—
1090Q8—812no—
1091Q8#533116yes—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—21no—
1099C2×C4—23no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—23no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—224no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—44no—
1168C2×C4—86no—
1169C2×C4C23×Q812yes—
1170C2×C4C23×Q816yes—
1171C2×C4C23×Q816yes—
1172C2×C4C23×Q812yes—
1173C2×C4C23×Q816yes—
1174C2×C4C23×Q816yes—
1175C2×C4C22×#4112yes—
1176C2×C4C22×#4116yes—
1177C2×C4C22×#4116yes—
1178C2×C4C22×#4112yes—
1179C2×C4C22×#4116yes—
1180C2×C4C22×#4116yes—
1181C2×C4C2×2−1+412yes—
1182C2×C4C2×2−1+412yes—
1183C2×C4C2×2−1+412yes—
1184C2×C4#58512yes—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22C24×Q811yescharacteristic
1193C22C23×#4111yescharacteristic
1194C22C23×#4111yescharacteristic
1195C22C22×2−1+411yescharacteristic
1196C22C2×#58511yescharacteristic
1197C22H(7,𝔽2)11yescharacteristic
1198C222−1+611yescharacteristic
1199C4—26no—
1200C4—22no—
1201C4—26no—
1202C4—22no—
1203C4—22no—
1204C4—22no—
1205C4—26no—
1206C4—22no—
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—26no—
1211C4—26no—
1212C4—43no—
1213C4—43no—
1214C4—43no—
1215C4—43no—
1216C4—41no—
1217C4—41no—
1218C4—43no—
1219C4—41no—
1220C4—43no—
1221C4—41no—
1222C4—43no—
1223C4—41no—
1224C4—43no—
1225C4—43no—
1226C4—43no—
1227C4—41no—
1228C4C2×#533112yes—
1229C2—42no—
1230C2C22×#53311yescharacteristic
1231C2#6278811yescharacteristic
1232C2#6285711yescharacteristic
1233C2#6299411yescharacteristic
1234C2Q8×2−1+411yescharacteristic
1235C2#6299811yescharacteristic
1236C2#6300411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36565C2semidirect
4. #36475C2semidirect
5. #36447C2semidirect
8. #36283C2semidirect
9. #35958C2semidirect
10. #35937C2semidirect
11. #35937C2semidirect
12. #35936C2semidirect
17. #35583C2semidirect
18. #35582C2semidirect
22. #35199C2semidirect
23. #34920C2semidirect
25. #34336C2semidirect
26. #34336C2semidirect
27. #34335C2semidirect
30. C4×Q82C2semidirect
264. #519Q8semidirect

Maximal subgroups

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

subgroupindex
#365652
Q8×C22⋊Q82
#364782
#364752
#364472
#364352
#362882
#362832
#359582
#359372
#359362
#358192
#357862
#357472
#357112
#355832
#355822
#355782
#355772
#352822
#351992
#349202
#348822
#343362
#343352
#342622
C4×Q822
C4×#5192