Finite Group Databasebeta

← #7632334

Subgroups — #7632334

Order 512.

4818 conjugacy classes of subgroups.

The subgroup lattice has 1241 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36599C213yesmaximal
2#36577C211yesmaximal, characteristic
3#36564C213yesmaximal
4Q8×C22⋊Q8C211yesmaximal, characteristic
5#36519C213yesmaximal
6#36519C213yesmaximal
7#36435C211yesmaximal, characteristic
8#36435C211yesmaximal, characteristic
9#35972C213yesmaximal, complemented
10#35971C211yesmaximal, characteristic, complemented
11#35958C213yesmaximal, complemented
12#35957C211yesmaximal, characteristic, complemented
13#35937C211yesmaximal, characteristic, complemented
14#35936C213yesmaximal, complemented
15#35868C211yesmaximal, characteristic, complemented
16#35867C213yesmaximal, complemented
17#35643C213yesmaximal, complemented
18#35642C213yesmaximal, complemented
19#35583C213yesmaximal, complemented
20#35582C213yesmaximal, complemented
21#35304C213yesmaximal
22#35239C213yesmaximal
23#34966C213yesmaximal
24#34878C213yesmaximal
25#34337C211yesmaximal, characteristic, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34335C211yesmaximal, characteristic, complemented
29#34192C211yesmaximal, characteristic
30Q8×#117C211yesmaximal, characteristic
31C2×#2276C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2857C2216yes—
40#2857C2213yes—
41#2857C2213yes—
42#2851C2213yes—
43#2851C2213yes—
44#2851C2216yes—
45#2666C2216yes—
46#2666C2216yes—
47#2660C2213yes—
48#2660C2213yes—
49#2647C2213yes—
50#2647C2213yes—
51#2612C2216yes—
52#2612C2213yes—
53#2612C2213yes—
54#2612C2213yes—
55#2612C2213yes—
56#2612C2216yes—
57#2606C2216yes—
58#2606C2216yes—
59#2606C2213yes—
60#2606C2213yes—
61#2605C2213yes—
62#2605C2216yes—
63#2605C2216yes—
64#2605C2213yes—
65#2590C2216yes—
66#2590C2216yes—
67#2588C2216yes—
68#2588C2216yes—
69#2586C2216yes—
70#2586C2216yes—
71#2585C2216yes—
72#2585C2216yes—
73#2584C2213yes—
74#2584C2213yes—
75#2582C2213yes—
76#2582C2213yes—
77#2581C2213yes—
78#2581C2213yes—
79#2571C2213yes—
80#2570C2213yes—
81#2570C2216yes—
82#2570C2213yes—
83#2569C2213yes—
84#2569C2213yes—
85#2569C2216yes—
86#2568C2213yes—
87#2567C2213yes—
88#2567C2213yes—
89#2565C2213yes—
90#2565C2213yes—
91#2552C2213yes—
92#2552C2213yes—
93#2552C2213yes—
94#2551C2213yes—
95#2551C2213yes—
96#2550C2213yes—
97#2550C2213yes—
98#2550C2213yes—
99#2550C2213yes—
100#2550C2216yes—
101#2549C2213yes—
102#2549C2213yes—
103#2549C2216yes—
104#2546C2213yes—
105#2520C2216yes—
106#2520C2216yes—
107#2511C2216yes—
108#2509C2213yes—
109#2509C2213yes—
110#2508C2213yes—
111#2508C2213yes—
112#2507C2213yes—
113#2507C2216yes—
114#2507C2213yes—
115#2506C2213yes—
116#2506C2213yes—
117#2462C2216yes—
118#2462C2216yes—
119#2453C2213yes—
120#2453C2213yes—
121#2453C2213yes—
122#2453C2213yes—
123#2451C2213yes—
124#2451C2213yes—
125#2451C2213yes—
126#2451C2216yes—
127#2451C2213yes—
128#2446C2216yes—
129#2442C2213yes—
130#2442C2213yes—
131#2442C2213yes—
132#2442C2213yes—
133#2440C2213yes—
134#2440C2213yes—
135#2440C2213yes—
136#2440C2213yes—
137#2438C2211yescharacteristic
138#2438C2213yes—
139#2438C2213yes—
140#2438C2213yes—
141#2438C2216yes—
142#2402C2213yes—
143#2402C2213yes—
144#2402C2216yes—
145#2399C2216yes—
146#2399C2213yes—
147#2399C2213yes—
148#2370C2213yes—
149#2370C2213yes—
150#2370C2213yes—
151#2370C2213yes—
152#2370C2213yes—
153#2370C2213yes—
154#2369C2213yes—
155#2369C2213yes—
156#2369C2213yes—
157#2365C2213yes—
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⋊C4C2213yes—
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184#2345C2213yes—
185#2345C2213yes—
186#2345C2213yes—
187#2345C2213yes—
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#2330C2213yes—
199#2330C2213yes—
200#2320C2213yes—
201#2320C2213yes—
202C4×C4⋊Q8C2213yes—
203C4×C4⋊Q8C2213yes—
204C4×#125C2213yes—
205C4×#125C2213yes—
206C4×C22⋊Q8C2213yes—
207C4×C22⋊Q8C2213yes—
208C4×C22⋊Q8C2213yes—
209C4×C22⋊Q8C2213yes—
210C4×C22⋊Q8C2216yes—
211C4×C22⋊Q8C2216yes—
212#2295C2213yes—
213#2295C2213yes—
214#2295C2213yes—
215#2295C2213yes—
216#2295C2213yes—
217#2295C2213yes—
218#2285C2213yes—
219#2283C2213yes—
220#2283C2213yes—
221#2276C2213yes—
222#2276C2211yescharacteristic
223#2276C2211yescharacteristic
224#2276C2211yescharacteristic
225#2276C2211yescharacteristic
226#2276C2211yescharacteristic
227#2276C2213yes—
228#2276C2213yes—
229#2276C2213yes—
230#2276C2211yescharacteristic
231C42×Q8C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C4×#117C2213yes—
234C2×C4×C4⋊C4C2213yes—
235C2×C4×C4⋊C4C2213yes—
236C2×C4×C4⋊C4C2213yes—
237C2×#376C2213yes—
238C23×Q8C2311yescharacteristic
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×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2316yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2316yes—
261C2×C22⋊Q8C2313yes—
262C2×C4×Q8—28no—
263C2×C4×Q8—28no—
264C2×C4×Q8Q8116yescomplemented
265C2×C4×Q8C2313yes—
266C2×C4×Q8C2313yes—
267C2×C4×Q8C2313yes—
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×Q8C2313yes—
283C2×C4×Q8C2316yes—
284C2×C4×Q8C2316yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2313yes—
293C22×C4⋊C4C2313yes—
294C22×C4⋊C4C2313yes—
295C22×C4⋊C4C2313yes—
296C22×C42C2313yes—
297C22×C42C2313yes—
298C22×C42C2316yes—
299C22×C42C2313yes—
300#400C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2316yes—
304#400C2313yes—
305#400C2316yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2316yes—
313#400C2311yescharacteristic
314#400C2313yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2313yes—
320#398C2316yes—
321#398C2313yes—
322#398C2313yes—
323#398C2316yes—
324#398C2313yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2313yes—
332#398C2316yes—
333#398C2313yes—
334#398C2316yes—
335#398C2311yescharacteristic
336#398C2311yescharacteristic
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2316yes—
343#398C2313yes—
344#398C2313yes—
345#395C2313yes—
346#395C2316yes—
347#395C2316yes—
348#395C2316yes—
349#395C2316yes—
350#395C2316yes—
351#395C2313yes—
352#395C2313yes—
353#395C2316yes—
354#395C2311yescharacteristic
355#395C2313yes—
356#395C2313yes—
357#395C2313yes—
358#395C2316yes—
359#395C2313yes—
360#391C2313yes—
361#391C2316yes—
362#391C2313yes—
363#391C2313yes—
364#391C2313yes—
365#391C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2316yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2316yes—
373#391C2313yes—
374#391C2313yes—
375#391C2316yes—
376#391C2316yes—
377#391C2316yes—
378#391C2313yes—
379#391C2313yes—
380#391C2316yes—
381#391C2313yes—
382#391C2316yes—
383#391C2316yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2311yescharacteristic
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2316yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2316yes—
402#389C2313yes—
403#389C2313yes—
404#389C2316yes—
405#389C2316yes—
406#389C2313yes—
407#389C2313yes—
408#389C2316yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2316yes—
419#389C2316yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2311yescharacteristic
446#387C2313yes—
447#387C2313yes—
448#387C2316yes—
449#387C2316yes—
450#387C2313yes—
451#387C2313yes—
452#387C2316yes—
453#387C2316yes—
454#387C2313yes—
455#387C2313yes—
456#387C2316yes—
457#387C2316yes—
458#387C2316yes—
459#387C2316yes—
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2316yes—
469#387C2316yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2313yes—
477#387C2313yes—
478#387C2316yes—
479#387C2316yes—
480#387C2313yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2313yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2313yes—
490#387C2316yes—
491#387C2316yes—
492#387C2313yes—
493#387C2313yes—
494#387C2311yescharacteristic
495#387C2311yescharacteristic
496#385C2311yescharacteristic
497#385C2313yes—
498#385C2313yes—
499#385C2316yes—
500#385C2313yes—
501#385C2313yes—
502#385C2316yes—
503#385C2313yes—
504#385C2313yes—
505#385C2311yescharacteristic
506#384C2313yes—
507#384C2313yes—
508#384C2313yes—
509#384C2316yes—
510#384C2313yes—
511#384C2313yes—
512#384C2313yes—
513#384C2313yes—
514#384C2313yes—
515#383C2316yes—
516#383C2313yes—
517#383C2313yes—
518#382C2313yes—
519#382C2313yes—
520#382C2313yes—
521#382C2313yes—
522#382C2313yes—
523#382C2316yes—
524#382C2313yes—
525#382C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2316yes—
530#381C2311yescharacteristic
531#381C2313yes—
532#380C2313yes—
533#380C2311yescharacteristic
534#380C2313yes—
535#380C2316yes—
536#380C2313yes—
537#380C2313yes—
538#380C2316yes—
539#380C2313yes—
540#380C2313yes—
541#380C2313yes—
542#380C2313yes—
543#380C2313yes—
544C4×C4⋊C4C2313yes—
545C4×C4⋊C4C2313yes—
546C4×C4⋊C4C2313yes—
547C4×C4⋊C4C2316yes—
548C4×C4⋊C4C2316yes—
549C4×C4⋊C4C2316yes—
550C4×C4⋊C4C2316yes—
551C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
561C4×C4⋊C4C2316yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2316yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2316yes—
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⋊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⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2316yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2316yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606#376C2313yes—
607#376C2313yes—
608#376C2313yes—
609#376C2313yes—
610#376C2313yes—
611#376C2313yes—
612#376C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2316yes—
617#376C2313yes—
618#376C2313yes—
619C2×#95C2313yes—
620C2×#95C2313yes—
621C2×#95C2311yescharacteristic
622C2×#95C2313yes—
623C43C2313yes—
624C43C2313yes—
625C22×Q8—24no—
626C22×Q8—24no—
627C22×Q8C2×Q818yes—
628C22×Q8C2413yes—
629C22×Q8C2411yescharacteristic
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2416yes—
633C22×Q8C2413yes—
634C22×Q8C2411yescharacteristic
635C23×C4C2413yes—
636C23×C4C2413yes—
637C23×C4C2411yescharacteristic
638C23×C4C2411yescharacteristic
639C23×C4C2413yes—
640C23×C4C2411yescharacteristic
641C23×C4C2413yes—
642C4⋊Q8—212no—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—212no—
647C4⋊Q8—212no—
648C4⋊Q8—86no—
649#125—212no—
650#125—212no—
651#125—212no—
652#125—212no—
653#125—212no—
654#125—212no—
655#125—86no—
656C22⋊Q8—212no—
657C22⋊Q8—24no—
658C22⋊Q8—412no—
659C22⋊Q8—46no—
660C22⋊Q8—46no—
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—24no—
670C4×Q8—24no—
671C4×Q8—212no—
672C4×Q8—212no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8—212no—
676C4×Q8—212no—
677C4×Q8—212no—
678C4×Q8—212no—
679C4×Q8—86no—
680C4×Q8—86no—
681C4×Q8C2×Q8124yes—
682C4×Q8C2×Q8124yes—
683C4×Q8C2×Q818yes—
684C4×Q8C2×Q818yes—
685C4×Q8#4118yes—
686C4×Q8#4118yes—
687#117—24no—
688#117—46no—
689C2×C4⋊C4—212no—
690C2×C4⋊C4—212no—
691C2×C4⋊C4C2×Q8124yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2416yes—
695C2×C4⋊C4C2416yes—
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
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⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
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⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2411yescharacteristic
772C2×C42—212no—
773C2×C42—212no—
774C2×C42—86no—
775C2×C42C2×Q8124yes—
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2413yes—
779C2×C42C2413yes—
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×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2416yes—
797C2×C42C2416yes—
798C2×C42C2416yes—
799C2×C42C2416yes—
800C2×C42C2416yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2416yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2416yes—
845#95C2416yes—
846#95C2416yes—
847#95C2416yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2416yes—
854#95C2416yes—
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2413yes—
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2411yescharacteristic
868#95C2413yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2413yes—
880#95C2416yes—
881#95C2413yes—
882#95C2416yes—
883#95C2416yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888C24C2511yescharacteristic
889C2×Q8—232no—
890C2×Q8—26no—
891C2×Q8—26no—
892C2×Q8—22no—
893C2×Q8—26no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—212no—
897C2×Q8—22no—
898C2×Q8—26no—
899C2×Q8—43no—
900C2×Q8—41no—
901C2×Q8—46no—
902C2×Q8—43no—
903C2×Q8—43no—
904C2×Q8—46no—
905C2×Q8—43no—
906C2×Q8—43no—
907C2×Q8C22×Q8112yes—
908C2×Q8C22×Q814yes—
909C2×Q8C2×#4114yes—
910C2×Q8C2×#4114yes—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—22no—
917C22×C4—26no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—43no—
924C22×C4—43no—
925C22×C4—43no—
926C22×C4—43no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C22×Q814yes—
930C22×C4C22×Q8112yes—
931C22×C4C22×Q8112yes—
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2513yes—
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2513yes—
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2513yes—
962C4⋊C4—212no—
963C4⋊C4—212no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
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—26no—
986C4⋊C4—212no—
987C4⋊C4—212no—
988C4⋊C4—212no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—26no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—22no—
997C4⋊C4—41no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—46no—
1001C4⋊C4—43no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—46no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—46no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—46no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—46no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4C22×Q8124yes—
1030C4⋊C4C22×Q8112yes—
1031C4⋊C4C22×Q8112yes—
1032C4⋊C4C2×#41112yes—
1033C4⋊C4C2×#41112yes—
1034C22⋊C4—22no—
1035C22⋊C4—26no—
1036C22⋊C4—22no—
1037C22⋊C4—26no—
1038C22⋊C4—26no—
1039C22⋊C4—22no—
1040C22⋊C4—26no—
1041C22⋊C42−1+414yes—
1042C42—26no—
1043C42—26no—
1044C42—26no—
1045C42—26no—
1046C42—26no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—22no—
1057C42—22no—
1058C42—46no—
1059C42—46no—
1060C42—46no—
1061C42—46no—
1062C42—43no—
1063C42—43no—
1064C42—46no—
1065C42—43no—
1066C42—43no—
1067C42—43no—
1068C42—43no—
1069C42—46no—
1070C42C22×Q8112yes—
1071C42C22×Q8112yes—
1072C42C22×Q8112yes—
1073C42C22×Q8112yes—
1074C42C2×#41112yes—
1075C42C2×#41112yes—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23C23×Q812yes—
1081C23C2×2−1+412yes—
1082C23#58512yes—
1083C23C2611yescharacteristic
1084Q8—224no—
1085Q8—44no—
1086Q8—412no—
1087Q8—86no—
1088Q8—86no—
1089Q8—812no—
1090Q8#533116yes—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—23no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—28no—
1114C2×C4—224no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—412no—
1170C2×C4—44no—
1171C2×C4—412no—
1172C2×C4—44no—
1173C2×C4—412no—
1174C2×C4C23×Q812yes—
1175C2×C4C23×Q812yes—
1176C2×C4C23×Q816yes—
1177C2×C4C23×Q816yes—
1178C2×C4C23×Q816yes—
1179C2×C4C23×Q816yes—
1180C2×C4C22×#4112yes—
1181C2×C4C22×#4112yes—
1182C2×C4C22×#4116yes—
1183C2×C4C22×#4116yes—
1184C2×C4C22×#4116yes—
1185C2×C4C22×#4116yes—
1186C2×C4C2×2−1+412yes—
1187C2×C4C2×2−1+412yes—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—22no—
1193C22—22no—
1194C22#350214yes—
1195C22C24×Q811yescharacteristic
1196C22C23×#4111yescharacteristic
1197C22C23×#4111yescharacteristic
1198C22C22×2−1+411yescharacteristic
1199C22C2×#58511yescharacteristic
1200C22H(7,𝔽2)11yescharacteristic
1201C222−1+611yescharacteristic
1202C4—22no—
1203C4—22no—
1204C4—26no—
1205C4—22no—
1206C4—22no—
1207C4—26no—
1208C4—22no—
1209C4—22no—
1210C4—26no—
1211C4—26no—
1212C4—26no—
1213C4—41no—
1214C4—43no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—43no—
1220C4—43no—
1221C4—41no—
1222C4—43no—
1223C4—41no—
1224C4—43no—
1225C4—43no—
1226C4—43no—
1227C4—43no—
1228C4—43no—
1229C4—43no—
1230C4—41no—
1231C4C2×#533112yes—
1232C2—24no—
1233C2C22×#53311yescharacteristic
1234C2C2×#350211yescharacteristic
1235C2#6285411yescharacteristic
1236C2#6299811yescharacteristic
1237C2#6300011yescharacteristic
1238C2#6300511yescharacteristic
1239C2#6300811yescharacteristic
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
9. #35972C2semidirect
10. #35971C2semidirect
11. #35958C2semidirect
12. #35957C2semidirect
13. #35937C2semidirect
14. #35936C2semidirect
15. #35868C2semidirect
16. #35867C2semidirect
17. #35643C2semidirect
18. #35642C2semidirect
19. #35583C2semidirect
20. #35582C2semidirect
25. #34337C2semidirect
26. #34336C2semidirect
27. #34336C2semidirect
28. #34335C2semidirect
264. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#365992
#365772
#365642
Q8×C22⋊Q82
#365192
#364352
#359722
#359712
#359582
#359572
#359372
#359362
#358682
#358672
#356432
#356422
#355832
#355822
#353042
#352392
#349662
#348782
#343372
#343362
#343352
#341922
Q8×#1172
C2×#22762