Finite Group Databasebeta

← #7626966

Subgroups — #7626966

Order 512.

6454 conjugacy classes of subgroups.

The subgroup lattice has 1464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic
2#34510C214yesmaximal, complemented
3#34505C214yesmaximal, complemented
4#34490C214yesmaximal, complemented
5#34482C212yesmaximal, complemented
6#34464C212yesmaximal, complemented
7#34463C212yesmaximal, complemented
8#34452C214yesmaximal, complemented
9#34449C214yesmaximal, complemented
10#34413C212yesmaximal, complemented
11#34412C212yesmaximal, complemented
12#34405C212yesmaximal, complemented
13#34403C211yesmaximal, characteristic, complemented
14#34400C212yesmaximal, complemented
15#34369C211yesmaximal, characteristic
16#34318C212yesmaximal, complemented
17#34314C212yesmaximal, complemented
18#34307C212yesmaximal, complemented
19#34307C214yesmaximal, complemented
20#34299C212yesmaximal, complemented
21#34253C212yesmaximal, complemented
22#34252C212yesmaximal, complemented
23#34244C212yesmaximal, complemented
24#34231C211yesmaximal, characteristic, complemented
25#34192C211yesmaximal, characteristic, complemented
26C4×#552C212yesmaximal, complemented
27#34128C211yesmaximal, characteristic, complemented
28#34086C211yesmaximal, characteristic
29#34081C212yesmaximal, complemented
30#3507C4132yescomplemented
31C2×#559C2212yes—
32C2×#557C2212yes—
33C2×#556C2211yescharacteristic
34C2×#556C2214yes—
35C2×#556C2211yescharacteristic
36C2×#554C2211yescharacteristic
37C2×#554C2211yescharacteristic
38C2×#552C2212yes—
39C2×#552C2212yes—
40C2×#539C2214yes—
41C2×#536C2212yes—
42C2×#533C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C2×#529C2212yes—
45C2×#529C2212yes—
46C2×#520C2212yes—
47C22×C4×Q8C2211yescharacteristic
48#2383C2214yes—
49#2382C2214yes—
50#2382C2214yes—
51#2381C2212yes—
52#2381C2214yes—
53#2380C2212yes—
54#2379C2214yes—
55#2379C2214yes—
56#2378C2212yes—
57#2378C2212yes—
58#2378C2214yes—
59#2376C2214yes—
60#2376C2214yes—
61#2376C2214yes—
62#2374C2214yes—
63#2374C2214yes—
64#2374C2214yes—
65#2373C2214yes—
66#2373C2214yes—
67#2373C2214yes—
68#2373C2214yes—
69#2373C2214yes—
70#2373C2214yes—
71#2373C2214yes—
72#2372C2214yes—
73#2372C2214yes—
74#2372C2214yes—
75#2371C2214yes—
76#2371C2214yes—
77#2370C2212yes—
78#2370C2214yes—
79#2370C2214yes—
80#2370C2212yes—
81#2369C2214yes—
82#2369C2212yes—
83#2368C2214yes—
84#2365C2212yes—
85#2362C2212yes—
86#2362C2214yes—
87#2362C2212yes—
88#2362C2212yes—
89#2362C2212yes—
90#2362C2214yes—
91#2360C2212yes—
92#2360C2214yes—
93#2360C2212yes—
94#2360C2212yes—
95#2360C2212yes—
96#2359C2214yes—
97#2359C2214yes—
98#2357C2214yes—
99#2356C2212yes—
100#2356C2214yes—
101#2356C2214yes—
102#2356C2214yes—
103#2356C2214yes—
104#2356C2212yes—
105#2356C2214yes—
106#2356C2214yes—
107#2355C2214yes—
108#2355C2214yes—
109#2354C2214yes—
110#2353C2214yes—
111#2353C2214yes—
112#2353C2214yes—
113#2352C2212yes—
114#2352C2214yes—
115#2352C2212yes—
116#2352C2212yes—
117#2352C2212yes—
118#2352C2214yes—
119#2352C2214yes—
120#2351C2212yes—
121#2351C2212yes—
122#2347C2214yes—
123#2347C2212yes—
124#2347C2212yes—
125#2347C2212yes—
126#2347C2212yes—
127#2346C2214yes—
128#2346C2212yes—
129#2346C2212yes—
130#2346C2212yes—
131#2346C2212yes—
132#2345C2212yes—
133#2345C2212yes—
134#2345C2212yes—
135#2345C2211yescharacteristic
136#2345C2211yescharacteristic
137#2345C2212yes—
138#2344C2212yes—
139#2344C2214yes—
140#2344C2212yes—
141#2344C2212yes—
142#2343C2214yes—
143#2343C2214yes—
144Q8×C22⋊C4C2212yes—
145Q8×C22⋊C4C2211yescharacteristic
146Q8×C22⋊C4C2211yescharacteristic
147#2337C2212yes—
148#2337C2214yes—
149#2337C2214yes—
150#2337C2214yes—
151#2337C2212yes—
152#2337C2214yes—
153#2336C2214yes—
154#2336C2214yes—
155#2336C2214yes—
156#2336C2214yes—
157#2335C2214yes—
158#2335C2214yes—
159#2335C2214yes—
160#2335C2214yes—
161#2335C2214yes—
162#2335C2214yes—
163#2334C2214yes—
164#2334C2214yes—
165#2334C2214yes—
166#2334C2214yes—
167#2334C2214yes—
168#2333C2211yescharacteristic
169#2333C2212yes—
170#2333C2211yescharacteristic
171#2333C2211yescharacteristic
172#2333C2211yescharacteristic
173#2333C2212yes—
174#2333C2214yes—
175#2332C2212yes—
176#2332C2212yes—
177#2332C2212yes—
178#2332C2212yes—
179#2332C2214yes—
180#2331C2212yes—
181#2331C2214yes—
182#2331C2212yes—
183#2331C2212yes—
184#2331C2214yes—
185#2330C2214yes—
186#2329C2214yes—
187#2328C2212yes—
188#2324C2212yes—
189#2324C2212yes—
190#2323C2212yes—
191#2323C2214yes—
192#2323C2212yes—
193#2323C2212yes—
194#2323C2212yes—
195#2322C2214yes—
196#2320C2214yes—
197#2320C2214yes—
198#2320C2212yes—
199#2320C2214yes—
200#2320C2212yes—
201#2320C2214yes—
202#2319C2214yes—
203#2318C2214yes—
204#2318C2214yes—
205#2318C2214yes—
206#2317C2212yes—
207#2316C2212yes—
208#2314C2214yes—
209#2311C2212yes—
210#2311C2212yes—
211C4×#125C2212yes—
212C4×#125C2212yes—
213C4×#125C2214yes—
214C4×#126C2214yes—
215C4×#126C2214yes—
216C4×#126C2214yes—
217C4×C22⋊Q8C2212yes—
218C4×C22⋊Q8C2214yes—
219C4×C22⋊Q8C2212yes—
220C4×C22⋊Q8C2212yes—
221C4×C22⋊Q8C2212yes—
222C4×#123C2214yes—
223#2298C2214yes—
224#2297C2212yes—
225#2297C2212yes—
226#2296C2212yes—
227#2295C2212yes—
228#2295C2214yes—
229#2295C2214yes—
230#2295C2211yescharacteristic
231#2295C2211yescharacteristic
232#2295C2212yes—
233#2293C2212yes—
234#2293C2214yes—
235C2×#389C2212yes—
236#2290C2212yes—
237#2290C2214yes—
238#2290C2214yes—
239#2290C2214yes—
240#2290C2212yes—
241#2283C2212yes—
242#2283C2211yescharacteristic
243#2283C2211yescharacteristic
244#2283C2211yescharacteristic
245#2283C2212yes—
246#2283C2212yes—
247#2276C2212yes—
248#2276C2212yes—
249#2274C2214yes—
250#2274C2212yes—
251#2274C2212yes—
252C42×Q8C2211yescharacteristic
253C42×Q8C2211yescharacteristic
254C42×D4C2212yes—
255C4×#117C2214yes—
256C4×#117C2212yes—
257C4×#117C2212yes—
258C4×#117C2211yescharacteristic
259C2×C4×C4⋊C4C2212yes—
260C22×#41C2312yes—
261C23×Q8C2311yescharacteristic
262#559C2×C4132yes—
263#557C2×C4132yescomplemented
264#556C2×C4116yescomplemented
265#556C2×C4116yescomplemented
266#556C2×C4164yescomplemented
267#554C2×C4116yescomplemented
268#554C2×C4116yescomplemented
269#552C2×C4132yescomplemented
270#552C2×C4132yescomplemented
271#539C2×C4164yescomplemented
272#536C2×C4132yescomplemented
273#533C2×C4116yescomplemented
274#532C2×C4116yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×#127C2311yescharacteristic
280#529C2×C4132yescomplemented
281#529C2×C4132yescomplemented
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#125C2312yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×#121C2312yes—
308C2×#121C2311yescharacteristic
309C2×#121C2311yescharacteristic
310#520C2×C4132yescomplemented
311C2×C4×Q8C2×C4116yescomplemented
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2314yes—
346C2×#117C2314yes—
347C2×#117C2312yes—
348C2×#117C2314yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C42C2314yes—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2312yes—
362C22×C42C2311yescharacteristic
363#391C2314yes—
364#391C2314yes—
365#391C2312yes—
366#391C2314yes—
367#391C2312yes—
368#391C2312yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2312yes—
375#391C2314yes—
376#391C2312yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2312yes—
381#391C2312yes—
382#391C2314yes—
383#391C2312yes—
384#390C2314yes—
385#390C2314yes—
386#390C2312yes—
387#390C2312yes—
388#390C2312yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2314yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#388C2312yes—
426#388C2312yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2312yes—
451#388C2312yes—
452#388C2312yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2312yes—
459#388C2314yes—
460#388C2312yes—
461#388C2312yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2312yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2312yes—
509#387C2312yes—
510#387C2312yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2312yes—
532#386C2312yes—
533#386C2312yes—
534#386C2314yes—
535#386C2314yes—
536#386C2312yes—
537#386C2312yes—
538#386C2312yes—
539#386C2312yes—
540#386C2312yes—
541#386C2312yes—
542#386C2312yes—
543#386C2312yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2312yes—
556#385C2312yes—
557#385C2312yes—
558#385C2312yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#384C2314yes—
564#383C2314yes—
565#383C2314yes—
566#383C2314yes—
567#383C2314yes—
568#383C2314yes—
569#383C2314yes—
570#383C2312yes—
571#383C2312yes—
572#383C2314yes—
573#383C2312yes—
574#382C2312yes—
575#382C2314yes—
576#382C2314yes—
577#382C2314yes—
578#382C2314yes—
579#382C2314yes—
580#382C2312yes—
581#382C2314yes—
582#382C2314yes—
583#382C2312yes—
584#382C2314yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2311yescharacteristic
589#381C2311yescharacteristic
590#381C2312yes—
591#381C2312yes—
592#380C2312yes—
593#380C2311yescharacteristic
594#380C2311yescharacteristic
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2311yescharacteristic
606#380C2311yescharacteristic
607#380C2314yes—
608#380C2312yes—
609#380C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2311yescharacteristic
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2311yescharacteristic
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709#376C2314yes—
710#376C2314yes—
711#376C2312yes—
712#376C2314yes—
713#376C2314yes—
714#376C2312yes—
715#376C2312yes—
716#376C2314yes—
717#376C2312yes—
718#376C2312yes—
719#376C2314yes—
720#376C2314yes—
721#376C2312yes—
722#376C2314yes—
723C2×#95C2314yes—
724C2×#95C2314yes—
725C43C2312yes—
726C43C2312yes—
727C43C2314yes—
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C2×#41—44no—
731C2×#41—44no—
732C2×#41C22×C4116yes—
733C22×Q8—44no—
734C22×Q8C22×C418yes—
735C22×Q8C2411yescharacteristic
736C22×Q8C2411yescharacteristic
737C22×Q8C2412yes—
738C22×Q8C2412yes—
739C22×Q8C2412yes—
740C22×Q8C2412yes—
741C22×D4C2412yes—
742C22×D4C2411yescharacteristic
743C22×D4C2411yescharacteristic
744C22×D4C2412yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2411yescharacteristic
759C23×C4C2414yes—
760C23×C4C2412yes—
761C23×C4C2411yescharacteristic
762C4⋊Q8C22×C418yes—
763C4⋊Q8C22×C418yes—
764C4⋊Q8C22×C418yes—
765C4⋊Q8C22×C4132yes—
766#127C22×C418yes—
767#126C22×C4132yes—
768#126C22×C4132yes—
769#126C22×C4132yes—
770#126C22×C4132yes—
771#125C22×C4116yes—
772#125C22×C4116yes—
773#125C22×C4116yes—
774#125C22×C4132yes—
775#125C22×C4132yes—
776#124C22×C4116yes—
777#124C22×C4116yes—
778#124C22×C4116yes—
779#124C22×C4132yes—
780#123C22×C4132yes—
781#123C22×C4132yes—
782#123C22×C4132yes—
783#123C22×C4132yes—
784C22⋊Q8C22×C4116yes—
785C22⋊Q8C22×C4116yes—
786C22⋊Q8C22×C4116yes—
787C22⋊Q8C22×C4116yes—
788C22⋊Q8C22×C4116yes—
789C22⋊Q8C22×C4116yes—
790C22⋊Q8C22×C4132yes—
791C22⋊Q8C22×C4132yes—
792#121C22×C418yes—
793#121C22×C418yes—
794#121C22×C4116yes—
795C4×Q8—48no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8C22×C418yes—
801C4×Q8C22×C418yes—
802C4×Q8C22×C418yes—
803C4×Q8C22×C418yes—
804C4×Q8C22×C4116yes—
805C4×Q8C22×C4116yes—
806C4×Q8C22×C4132yes—
807C4×Q8C22×C4116yes—
808C4×Q8C22×C4116yes—
809C4×Q8C22×C4116yes—
810C4×Q8C22×C4116yes—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4C22×C4132yes—
814C4×D4C22×C4132yes—
815C4×D4C22×C4132yes—
816C4×D4C22×C4116yes—
817C4×D4C22×C4116yes—
818C4×D4C22×C4116yes—
819C4×D4C22×C418yes—
820C4×D4C22×C418yes—
821#117—44no—
822#117—44no—
823#117—48no—
824#117—48no—
825#117—48no—
826#117—44no—
827#117—44no—
828#117—44no—
829#117C22×C4116yes—
830#117C22×C4116yes—
831#117C22×C4116yes—
832#117C22×C4132yes—
833#117C22×C4132yes—
834C2×C4⋊C4—48no—
835C2×C4⋊C4—44no—
836C2×C4⋊C4—44no—
837C2×C4⋊C4C22×C418yes—
838C2×C4⋊C4C22×C4116yes—
839C2×C4⋊C4C22×C4116yes—
840C2×C4⋊C4C22×C4116yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C42—44no—
932C2×C42—44no—
933C2×C42—48no—
934C2×C42C22×C4116yes—
935C2×C42C22×C418yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2411yescharacteristic
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2414yes—
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048C24C2511yescharacteristic
1049C24C2512yes—
1050C24C2512yes—
1051#41—432no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8—416no—
1061C2×Q8C23×C414yes—
1062C2×Q8C23×C414yes—
1063C2×Q8C23×C418yes—
1064C2×Q8C23×C418yes—
1065C2×Q8C23×C418yes—
1066C2×Q8C23×C418yes—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—41no—
1070C2×D4—41no—
1071C2×D4—41no—
1072C2×D4—41no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4C23×C414yes—
1080C2×D4C23×C414yes—
1081C2×D4C23×C418yes—
1082C2×D4C23×C418yes—
1083C2×D4C23×C418yes—
1084C2×D4C23×C418yes—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—41no—
1100C22×C4—41no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—42no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4C23×C414yes—
1118C22×C4C23×C418yes—
1119C22×C4C23×C418yes—
1120C22×C4C23×C414yes—
1121C22×C4C23×C418yes—
1122C22×C4C23×C414yes—
1123C22×C4C23×C418yes—
1124C22×C4C23×C4116yes—
1125C22×C4C23×C4116yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2512yes—
1141C22×C4C2514yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2514yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C4⋊C4—28no—
1153C4⋊C4—28no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4C23×C414yes—
1183C4⋊C4C23×C414yes—
1184C4⋊C4C23×C418yes—
1185C4⋊C4C23×C418yes—
1186C4⋊C4C23×C4116yes—
1187C4⋊C4C23×C4116yes—
1188C4⋊C4C23×C418yes—
1189C4⋊C4C23×C418yes—
1190C4⋊C4C23×C418yes—
1191C4⋊C4C23×C418yes—
1192C4⋊C4C23×C418yes—
1193C4⋊C4C23×C4116yes—
1194C4⋊C4C23×C4116yes—
1195C4⋊C4C23×C4116yes—
1196C4⋊C4C23×C418yes—
1197C4⋊C4C23×C414yes—
1198C4⋊C4C23×C414yes—
1199C4⋊C4C23×C418yes—
1200C4⋊C4C23×C4116yes—
1201C4⋊C4C23×C4116yes—
1202C4⋊C4C23×C4116yes—
1203C4⋊C4C23×C418yes—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—41no—
1210C22⋊C4—42no—
1211C22⋊C4—41no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—41no—
1217C22⋊C4—42no—
1218C22⋊C4—41no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4C23×C418yes—
1232C22⋊C4C23×C418yes—
1233C22⋊C4C23×C4116yes—
1234C22⋊C4C23×C4116yes—
1235C22⋊C4C23×C4116yes—
1236C22⋊C4C23×C4116yes—
1237C22⋊C4C23×C4116yes—
1238C22⋊C4C23×C418yes—
1239C22⋊C4C23×C418yes—
1240C22⋊C4C23×C4116yes—
1241C22⋊C4C23×C4116yes—
1242C42—24no—
1243C42—28no—
1244C42—28no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—42no—
1250C42—42no—
1251C42—44no—
1252C42—44no—
1253C42—42no—
1254C42—42no—
1255C42—41no—
1256C42—41no—
1257C42—42no—
1258C42—42no—
1259C42—41no—
1260C42—41no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—42no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42C23×C418yes—
1278C42C23×C418yes—
1279C42C23×C414yes—
1280C42C23×C414yes—
1281C42C23×C418yes—
1282C42C23×C418yes—
1283C42C23×C414yes—
1284C42C23×C414yes—
1285C42C23×C4116yes—
1286C42C23×C4116yes—
1287C42C23×C4116yes—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—21no—
1299C23—21no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23C24×C414yes—
1305C23C24×C414yes—
1306C23C24×C412yes—
1307C23C2611yescharacteristic
1308Q8—28no—
1309Q8—28no—
1310Q8—48no—
1311Q8—48no—
1312Q8—48no—
1313Q8—48no—
1314D4—48no—
1315D4—44no—
1316D4—44no—
1317D4—48no—
1318D4—48no—
1319D4—48no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—28no—
1342C2×C4—216no—
1343C2×C4—216no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—48no—
1378C2×C4—416no—
1379C2×C4—416no—
1380C2×C4—44no—
1381C2×C4—44no—
1382C2×C4—48no—
1383C2×C4—48no—
1384C2×C4—84no—
1385C2×C4—88no—
1386C2×C4—84no—
1387C2×C4—84no—
1388C2×C4—164no—
1389C2×C4C24×C412yes—
1390C2×C4C24×C412yes—
1391C2×C4C24×C412yes—
1392C2×C4C24×C414yes—
1393C2×C4C24×C414yes—
1394C2×C4C24×C418yes—
1395C2×C4C24×C414yes—
1396C2×C4C24×C414yes—
1397C2×C4C24×C412yes—
1398C2×C4C24×C414yes—
1399C2×C4C24×C414yes—
1400C2×C4C24×C412yes—
1401C2×C4C24×C418yes—
1402C2×C4C24×C412yes—
1403C2×C4#58514yes—
1404C2×C4#58514yes—
1405C22—22no—
1406C22—24no—
1407C22—24no—
1408C22—22no—
1409C22—24no—
1410C22—24no—
1411C22—22no—
1412C22—24no—
1413C22—24no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22C25×C411yescharacteristic
1425C22C2×#58512yes—
1426C22C2×#58512yes—
1427C222−1+611yescharacteristic
1428C222−1+611yescharacteristic
1429C4—22no—
1430C4—24no—
1431C4—24no—
1432C4—24no—
1433C4—24no—
1434C4—24no—
1435C4—24no—
1436C4—28no—
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—28no—
1442C4—24no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—44no—
1452C4—42no—
1453C4—42no—
1454C4#342814yes—
1455C2—42no—
1456C2—44no—
1457C2—44no—
1458C2C2×#342811yescharacteristic
1459C2C4×#58511yescharacteristic
1460C2#6265311yescharacteristic
1461C2#6293412yes—
1462C2#6293612yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#532C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34510C2semidirect
3. #34505C2semidirect
4. #34490C2semidirect
5. #34482C2semidirect
6. #34464C2semidirect
7. #34463C2semidirect
8. #34452C2semidirect
9. #34449C2semidirect
10. #34413C2semidirect
11. #34412C2semidirect
12. #34405C2semidirect
13. #34403C2semidirect
14. #34400C2semidirect
16. #34318C2semidirect
17. #34314C2semidirect
18. #34307C2semidirect
19. #34307C2semidirect
20. #34299C2semidirect
21. #34253C2semidirect
22. #34252C2semidirect
23. #34244C2semidirect
24. #34231C2semidirect
25. #34192C2semidirect
26. C4×#552C2semidirect
27. #34128C2semidirect
29. #34081C2semidirect
30. #3507C4semidirect
263. #557C2×C4semidirect
264. #556C2×C4semidirect
265. #556C2×C4semidirect
266. #556C2×C4semidirect
267. #554C2×C4semidirect
268. #554C2×C4semidirect
269. #552C2×C4semidirect
270. #552C2×C4semidirect
271. #539C2×C4semidirect
272. #536C2×C4semidirect
273. #533C2×C4semidirect
280. #529C2×C4semidirect
281. #529C2×C4semidirect
310. #520C2×C4semidirect
311. C2×C4×Q8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
#345102
#345052
#344902
#344822
#344642
#344632
#344522
#344492
#344132
#344122
#344052
#344032
#344002
#343692
#343182
#343142
#343072
#342992
#342532
#342522
#342442
#342312
#341922
C4×#5522
#341282
#340862
#340812