Finite Group Databasebeta

← #7632242

Subgroups — #7632242

Order 512.

4936 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36564C213yesmaximal, complemented
2Q8×#125C211yesmaximal, characteristic, complemented
3#36479C213yesmaximal, complemented
4#36475C211yesmaximal, characteristic, complemented
5#36445C211yesmaximal, characteristic
6#36431C211yesmaximal, characteristic
7#36425C213yesmaximal, complemented
8#36407C213yesmaximal, complemented
9#35957C211yesmaximal, characteristic, complemented
10#35937C211yesmaximal, characteristic, complemented
11#35934C213yesmaximal, complemented
12#35934C213yesmaximal, complemented
13#35816C211yesmaximal, characteristic
14#35788C213yesmaximal, complemented
15#35748C211yesmaximal, characteristic
16#35708C213yesmaximal, complemented
17#35581C213yesmaximal, complemented
18#35580C213yesmaximal, complemented
19#35579C213yesmaximal, complemented
20#35578C213yesmaximal, complemented
21#35282C213yesmaximal, complemented
22#35176C213yesmaximal, complemented
23#34893C213yesmaximal, complemented
24#34882C213yesmaximal, complemented
25#34337C211yesmaximal, characteristic, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic
29#34263C211yesmaximal, characteristic
30C4×Q82C211yesmaximal, characteristic, complemented
31C4×#520C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2864C2213yes—
40#2859C2213yes—
41#2857C2216yes—
42#2857C2213yes—
43#2855C2216yes—
44#2851C2213yes—
45#2667C2216yes—
46#2667C2216yes—
47#2660C2213yes—
48#2660C2213yes—
49#2629C2213yes—
50#2628C2213yes—
51#2608C2216yes—
52#2607C2216yes—
53#2590C2216yes—
54#2589C2216yes—
55#2588C2216yes—
56#2587C2216yes—
57#2586C2213yes—
58#2586C2213yes—
59#2586C2216yes—
60#2585C2213yes—
61#2585C2213yes—
62#2585C2216yes—
63#2584C2213yes—
64#2584C2213yes—
65#2580C2213yes—
66#2580C2213yes—
67#2574C2213yes—
68#2574C2216yes—
69#2574C2213yes—
70#2570C2213yes—
71#2570C2213yes—
72#2567C2213yes—
73#2566C2213yes—
74#2566C2213yes—
75#2556C2216yes—
76#2556C2216yes—
77#2556C2213yes—
78#2556C2213yes—
79#2556C2216yes—
80#2552C2213yes—
81#2552C2213yes—
82#2552C2213yes—
83#2552C2213yes—
84#2551C2213yes—
85#2551C2213yes—
86#2550C2213yes—
87#2550C2213yes—
88#2550C2213yes—
89#2550C2213yes—
90#2549C2216yes—
91#2549C2216yes—
92#2546C2213yes—
93#2542C2213yes—
94#2542C2213yes—
95#2538C2213yes—
96#2538C2213yes—
97#2522C2213yes—
98#2522C2213yes—
99#2522C2216yes—
100#2522C2216yes—
101#2520C2213yes—
102#2520C2213yes—
103#2509C2213yes—
104#2508C2213yes—
105#2507C2213yes—
106#2507C2213yes—
107#2507C2213yes—
108#2507C2213yes—
109#2507C2216yes—
110#2507C2213yes—
111#2506C2213yes—
112#2465C2213yes—
113#2465C2213yes—
114#2465C2216yes—
115#2465C2216yes—
116#2462C2211yescharacteristic
117#2462C2213yes—
118#2462C2216yes—
119#2454C2213yes—
120#2454C2213yes—
121#2454C2213yes—
122#2454C2213yes—
123#2452C2213yes—
124#2452C2213yes—
125#2452C2213yes—
126#2452C2213yes—
127#2451C2216yes—
128#2442C2213yes—
129#2441C2216yes—
130#2441C2213yes—
131#2441C2213yes—
132#2441C2213yes—
133#2440C2213yes—
134#2440C2213yes—
135#2440C2213yes—
136#2439C2216yes—
137#2439C2213yes—
138#2438C2216yes—
139#2438C2216yes—
140#2429C2216yes—
141#2423C2216yes—
142#2399C2213yes—
143#2399C2213yes—
144#2396C2213yes—
145#2396C2213yes—
146#2396C2216yes—
147#2396C2216yes—
148#2370C2213yes—
149#2370C2213yes—
150#2370C2213yes—
151#2370C2213yes—
152#2370C2213yes—
153#2370C2213yes—
154#2369C2213yes—
155#2369C2213yes—
156#2369C2213yes—
157#2369C2213yes—
158#2369C2213yes—
159#2365C2213yes—
160#2357C2213yes—
161#2357C2213yes—
162#2355C2213yes—
163#2355C2213yes—
164#2354C2213yes—
165#2354C2213yes—
166#2351C2211yescharacteristic
167#2351C2211yescharacteristic
168#2351C2211yescharacteristic
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172Q8×C4⋊C4C2211yescharacteristic
173Q8×C4⋊C4C2211yescharacteristic
174Q8×C4⋊C4C2211yescharacteristic
175Q8×C4⋊C4C2213yes—
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2213yes—
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184#2345C2213yes—
185#2345C2213yes—
186#2344C2213yes—
187#2344C2213yes—
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2211yescharacteristic
192#2331C2213yes—
193#2331C2213yes—
194#2330C2213yes—
195#2330C2213yes—
196#2330C2213yes—
197#2330C2213yes—
198#2319C2213yes—
199#2319C2213yes—
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×C22⋊Q8C2213yes—
211C4×C22⋊Q8C2213yes—
212C4×C22⋊Q8C2216yes—
213#2298C2213yes—
214#2298C2213yes—
215#2296C2216yes—
216#2295C2213yes—
217#2295C2213yes—
218#2295C2213yes—
219#2293C2213yes—
220#2293C2213yes—
221#2276C2211yescharacteristic
222#2276C2211yescharacteristic
223#2276C2211yescharacteristic
224#2276C2211yescharacteristic
225#2275C2213yes—
226#2275C2213yes—
227#2274C2213yes—
228#2274C2213yes—
229C42×Q8C2211yescharacteristic
230C42×Q8C2211yescharacteristic
231C42×Q8C2211yescharacteristic
232C42×Q8C2213yes—
233C42×Q8C2211yescharacteristic
234C42×D4C2213yes—
235C42×D4C2213yes—
236C4×#117C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239Q82—28no—
240#557—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⋊Q8C2316yes—
250C2×#125C2311yescharacteristic
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2316yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2316yes—
265#520—28no—
266#520Q8116yescomplemented
267C4×#41—28no—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2316yes—
285C2×C4×Q8C2316yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C2×#117C2316yes—
299C2×#117C2316yes—
300C2×#117C2313yes—
301C22×C4⋊C4C2313yes—
302C22×C4⋊C4C2313yes—
303C22×C42C2313yes—
304C22×C42C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2313yes—
309#399C2316yes—
310#399C2316yes—
311#399C2316yes—
312#399C2313yes—
313#399C2316yes—
314#399C2313yes—
315#398C2316yes—
316#398C2316yes—
317#398C2313yes—
318#398C2313yes—
319#398C2316yes—
320#398C2316yes—
321#398C2313yes—
322#398C2313yes—
323#398C2313yes—
324#398C2316yes—
325#398C2313yes—
326#398C2313yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2311yescharacteristic
333#398C2311yescharacteristic
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#396C2313yes—
338#396C2316yes—
339#396C2316yes—
340#396C2316yes—
341#396C2313yes—
342#396C2316yes—
343#396C2313yes—
344#396C2316yes—
345#396C2316yes—
346#396C2313yes—
347#395C2313yes—
348#395C2316yes—
349#395C2313yes—
350#395C2313yes—
351#395C2316yes—
352#395C2313yes—
353#395C2313yes—
354#395C2316yes—
355#395C2313yes—
356#395C2316yes—
357#395C2311yescharacteristic
358#395C2313yes—
359#395C2311yescharacteristic
360#395C2313yes—
361#393C2313yes—
362#393C2316yes—
363#393C2313yes—
364#393C2316yes—
365#391C2313yes—
366#391C2316yes—
367#391C2316yes—
368#391C2316yes—
369#391C2316yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2316yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2316yes—
378#391C2316yes—
379#391C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2316yes—
403#389C2316yes—
404#389C2316yes—
405#389C2313yes—
406#389C2313yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2316yes—
419#389C2316yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2311yescharacteristic
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2316yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2316yes—
440#389C2316yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2311yescharacteristic
447#388C2316yes—
448#388C2316yes—
449#388C2316yes—
450#388C2316yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#387C2311yescharacteristic
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2316yes—
468#387C2316yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2311yescharacteristic
477#387C2316yes—
478#387C2316yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2311yescharacteristic
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2316yes—
488#387C2313yes—
489#387C2316yes—
490#387C2313yes—
491#387C2313yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2311yescharacteristic
496#387C2311yescharacteristic
497#387C2313yes—
498#387C2316yes—
499#387C2313yes—
500#387C2313yes—
501#387C2316yes—
502#387C2313yes—
503#387C2313yes—
504#387C2311yescharacteristic
505#385C2313yes—
506#385C2316yes—
507#385C2316yes—
508#385C2316yes—
509#385C2316yes—
510#385C2313yes—
511#385C2313yes—
512#385C2316yes—
513#385C2316yes—
514#385C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2316yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#381C2316yes—
535#381C2316yes—
536#380C2313yes—
537#380C2313yes—
538#380C2313yes—
539#380C2313yes—
540#380C2313yes—
541#380C2316yes—
542#380C2313yes—
543#380C2316yes—
544#380C2316yes—
545#380C2316yes—
546C4×C4⋊C4C2313yes—
547C4×C4⋊C4C2313yes—
548C4×C4⋊C4C2313yes—
549C4×C4⋊C4C2313yes—
550C4×C4⋊C4C2313yes—
551C4×C4⋊C4C2316yes—
552C4×C4⋊C4C2316yes—
553C4×C4⋊C4C2316yes—
554C4×C4⋊C4C2313yes—
555C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
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⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2311yescharacteristic
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2316yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620C2×#95C2316yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41C2×Q818yes—
628C22×Q8C2411yescharacteristic
629C22×Q8C2413yes—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2416yes—
633C22×Q8C2411yescharacteristic
634C22×D4C2413yes—
635C23×C4C2413yes—
636C23×C4C2413yes—
637C23×C4C2416yes—
638C23×C4C2413yes—
639C23×C4C2416yes—
640C4⋊Q8—212no—
641C4⋊Q8—212no—
642C4⋊Q8—212no—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—86no—
647#125—212no—
648#125—212no—
649#125—212no—
650#125—212no—
651#125—24no—
652#125—212no—
653#125—212no—
654#125—46no—
655#125—86no—
656C22⋊Q8—212no—
657C22⋊Q8—46no—
658C22⋊Q8—86no—
659C22⋊Q8—86no—
660C22⋊Q8—86no—
661C22⋊Q8—86no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8—212no—
676C4×Q8—212no—
677C4×Q8—46no—
678C4×Q8—86no—
679C4×Q8—86no—
680C4×Q8C2×Q818yes—
681C4×Q8C2×Q818yes—
682C4×Q8#4118yes—
683C4×Q8#4118yes—
684C4×D4—212no—
685C4×D4—212no—
686C4×D4—212no—
687C4×D4—212no—
688C4×D4C2×Q8124yes—
689C4×D4C2×Q8124yes—
690#117—212no—
691#117—212no—
692#117—412no—
693#117—86no—
694#117C2×Q8124yes—
695C2×C4⋊C4—212no—
696C2×C4⋊C4C2×Q8124yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C42—212no—
790C2×C42—86no—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2413yes—
809C2×C42C2416yes—
810C2×C42C2416yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2416yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2416yes—
830#95C2416yes—
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2416yes—
856#95C2416yes—
857#95C2411yescharacteristic
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2416yes—
862#95C2413yes—
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2413yes—
867#95C2411yescharacteristic
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2416yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893C24C2513yes—
894#41—232no—
895C2×Q8—22no—
896C2×Q8—26no—
897C2×Q8—26no—
898C2×Q8—26no—
899C2×Q8—212no—
900C2×Q8—22no—
901C2×Q8—26no—
902C2×Q8—22no—
903C2×Q8—43no—
904C2×Q8—46no—
905C2×Q8—43no—
906C2×Q8—43no—
907C2×Q8—43no—
908C2×Q8—46no—
909C2×Q8—43no—
910C2×Q8C22×Q814yes—
911C2×Q8C2×#4114yes—
912C2×Q8C2×#4114yes—
913C2×D4—26no—
914C2×D4—26no—
915C2×D4C22×Q8112yes—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—212no—
922C22×C4—43no—
923C22×C4—46no—
924C22×C4—46no—
925C22×C4—46no—
926C22×C4—43no—
927C22×C4—46no—
928C22×C4—43no—
929C22×C4C22×Q8112yes—
930C22×C4C22×Q8124yes—
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2511yescharacteristic
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C22×C4C2513yes—
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—22no—
964C4⋊C4—26no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
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—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—212no—
986C4⋊C4—212no—
987C4⋊C4—212no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—46no—
1002C4⋊C4—43no—
1003C4⋊C4—46no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—46no—
1008C4⋊C4—46no—
1009C4⋊C4—46no—
1010C4⋊C4—46no—
1011C4⋊C4—46no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—46no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4C22×Q8112yes—
1030C4⋊C4C22×Q8112yes—
1031C4⋊C4C22×Q8112yes—
1032C4⋊C4C22×Q814yes—
1033C4⋊C4C2×#41112yes—
1034C4⋊C4C2×#41112yes—
1035C4⋊C42−1+414yes—
1036C22⋊C4—26no—
1037C22⋊C4—212no—
1038C22⋊C4—26no—
1039C22⋊C4—26no—
1040C22⋊C4—26no—
1041C22⋊C4—26no—
1042C22⋊C4—46no—
1043C22⋊C4—43no—
1044C22⋊C4—46no—
1045C22⋊C4—43no—
1046C22⋊C4—46no—
1047C22⋊C4—46no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4C22×Q8112yes—
1052C22⋊C4C22×Q8112yes—
1053C42—22no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—22no—
1066C42—22no—
1067C42—22no—
1068C42—22no—
1069C42—26no—
1070C42—43no—
1071C42—43no—
1072C42—46no—
1073C42—46no—
1074C42—46no—
1075C42—43no—
1076C42—46no—
1077C42—43no—
1078C42—43no—
1079C42—43no—
1080C42—43no—
1081C42—43no—
1082C42—43no—
1083C42—43no—
1084C42—43no—
1085C42C22×Q8112yes—
1086C42C22×Q8112yes—
1087C42C2×#41112yes—
1088C42C2×#41112yes—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23C23×Q816yes—
1096C23C2611yescharacteristic
1097Q8—28no—
1098Q8—412no—
1099Q8—86no—
1100Q8—86no—
1101Q8—812no—
1102Q8#533116yes—
1103D4—224no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—21no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—224no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—23no—
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—23no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—424no—
1180C2×C4—412no—
1181C2×C4—86no—
1182C2×C4—812no—
1183C2×C4C23×Q812yes—
1184C2×C4C23×Q812yes—
1185C2×C4C23×Q816yes—
1186C2×C4C23×Q816yes—
1187C2×C4C23×Q812yes—
1188C2×C4C23×Q816yes—
1189C2×C4C22×#4112yes—
1190C2×C4C22×#4116yes—
1191C2×C4C22×#4112yes—
1192C2×C4C22×#4116yes—
1193C2×C4C22×#4116yes—
1194C2×C4C22×#4116yes—
1195C2×C4C2×2−1+412yes—
1196C2×C4C2×2−1+412yes—
1197C2×C4C2×2−1+412yes—
1198C2×C4#58512yes—
1199C22—26no—
1200C22—26no—
1201C22—26no—
1202C22—43no—
1203C22—43no—
1204C22—43no—
1205C22—43no—
1206C22C24×Q811yescharacteristic
1207C22C23×#4111yescharacteristic
1208C22C23×#4111yescharacteristic
1209C22C22×2−1+411yescharacteristic
1210C22C2×#58511yescharacteristic
1211C22H(7,𝔽2)11yescharacteristic
1212C22H(7,𝔽2)11yescharacteristic
1213C4—26no—
1214C4—26no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—26no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—26no—
1225C4—22no—
1226C4—41no—
1227C4—41no—
1228C4—43no—
1229C4—41no—
1230C4—43no—
1231C4—43no—
1232C4—43no—
1233C4—43no—
1234C4—41no—
1235C4—41no—
1236C4—43no—
1237C4—43no—
1238C4—43no—
1239C4—43no—
1240C4—43no—
1241C4—41no—
1242C4C2×#533112yes—
1243C2—46no—
1244C2C22×#53311yescharacteristic
1245C2#6278811yescharacteristic
1246C2#6285811yescharacteristic
1247C2#6298911yescharacteristic
1248C2Q8×2−1+411yescharacteristic
1249C2#6300011yescharacteristic
1250C2#6300611yescharacteristic
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. #36564C2semidirect
2. Q8×#125C2semidirect
3. #36479C2semidirect
4. #36475C2semidirect
7. #36425C2semidirect
8. #36407C2semidirect
9. #35957C2semidirect
10. #35937C2semidirect
11. #35934C2semidirect
12. #35934C2semidirect
14. #35788C2semidirect
16. #35708C2semidirect
17. #35581C2semidirect
18. #35580C2semidirect
19. #35579C2semidirect
20. #35578C2semidirect
21. #35282C2semidirect
22. #35176C2semidirect
23. #34893C2semidirect
24. #34882C2semidirect
25. #34337C2semidirect
26. #34336C2semidirect
27. #34336C2semidirect
30. C4×Q82C2semidirect
266. #520Q8semidirect

Maximal subgroups

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

subgroupindex
#365642
Q8×#1252
#364792
#364752
#364452
#364312
#364252
#364072
#359572
#359372
#359342
#358162
#357882
#357482
#357082
#355812
#355802
#355792
#355782
#352822
#351762
#348932
#348822
#343372
#343362
#342632
C4×Q822
C4×#5202