Finite Group Databasebeta

← #7626975

Subgroups — #7626975

Order 512.

6456 conjugacy classes of subgroups.

The subgroup lattice has 1419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic
2#34490C212yesmaximal, complemented
3#34490C212yesmaximal, complemented
4#34488C212yesmaximal, complemented
5#34486C214yesmaximal, complemented
6#34486C214yesmaximal, complemented
7#34464C214yesmaximal, complemented
8#34434C212yesmaximal, complemented
9#34434C212yesmaximal, complemented
10#34432C214yesmaximal, complemented
11#34432C214yesmaximal, complemented
12#34389C212yesmaximal, complemented
13#34378C211yesmaximal, characteristic, complemented
14#34373C211yesmaximal, characteristic, complemented
15#34372C212yesmaximal, complemented
16#34333C212yesmaximal, complemented
17#34333C212yesmaximal, complemented
18#34332C212yesmaximal, complemented
19#34328C212yesmaximal, complemented
20#34299C214yesmaximal, complemented
21#34260C212yesmaximal
22#34260C212yesmaximal
23#34239C211yesmaximal, characteristic, complemented
24#34235C212yesmaximal, complemented
25#34195C211yesmaximal, characteristic
26C4×#554C212yesmaximal, complemented
27#34127C211yesmaximal, characteristic
28#34085C211yesmaximal, characteristic, complemented
29C2×#2336C212yesmaximal, complemented
30#3504C4132yescomplemented
31C2×#557C2212yes—
32C2×#557C2212yes—
33C2×#554C2212yes—
34C2×#554C2212yes—
35C2×#554C2214yes—
36C2×#554C2214yes—
37C2×#544C2212yes—
38C2×#544C2212yes—
39C2×#544C2211yescharacteristic
40C2×#544C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#533C2212yes—
43C22×#125C2212yes—
44C22×#125C2211yescharacteristic
45C2×#520C2211yescharacteristic
46C2×#520C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic
48#2382C2214yes—
49#2382C2214yes—
50#2382C2214yes—
51#2382C2214yes—
52#2382C2214yes—
53#2381C2214yes—
54#2381C2214yes—
55#2381C2214yes—
56#2381C2214yes—
57#2378C2214yes—
58#2378C2214yes—
59#2378C2214yes—
60#2371C2214yes—
61#2371C2214yes—
62#2371C2214yes—
63#2371C2214yes—
64#2371C2214yes—
65#2370C2212yes—
66#2370C2212yes—
67#2370C2212yes—
68#2370C2212yes—
69#2370C2212yes—
70#2370C2212yes—
71#2370C2212yes—
72#2370C2212yes—
73#2369C2212yes—
74#2369C2212yes—
75#2368C2214yes—
76#2368C2214yes—
77#2368C2214yes—
78#2368C2214yes—
79#2368C2214yes—
80#2368C2214yes—
81#2365C2212yes—
82#2365C2214yes—
83#2365C2212yes—
84#2365C2214yes—
85#2365C2214yes—
86#2365C2214yes—
87#2362C2214yes—
88#2362C2214yes—
89#2362C2214yes—
90#2360C2214yes—
91#2360C2214yes—
92#2360C2214yes—
93#2360C2214yes—
94#2360C2214yes—
95#2360C2214yes—
96#2356C2214yes—
97#2356C2212yes—
98#2356C2212yes—
99#2356C2214yes—
100#2356C2214yes—
101#2356C2212yes—
102#2355C2212yes—
103#2355C2212yes—
104#2355C2212yes—
105#2355C2212yes—
106#2355C2212yes—
107#2355C2212yes—
108#2353C2214yes—
109#2353C2214yes—
110#2353C2214yes—
111#2352C2214yes—
112#2352C2214yes—
113#2352C2214yes—
114#2351C2214yes—
115Q8×C4⋊C4C2212yes—
116#2349C2212yes—
117#2349C2212yes—
118#2349C2212yes—
119D4×C4⋊C4C2212yes—
120D4×C4⋊C4C2212yes—
121D4×C4⋊C4C2212yes—
122#2347C2212yes—
123#2347C2212yes—
124#2345C2214yes—
125#2345C2214yes—
126#2345C2214yes—
127#2345C2214yes—
128#2345C2212yes—
129#2345C2212yes—
130#2344C2212yes—
131#2344C2214yes—
132#2344C2212yes—
133#2344C2214yes—
134#2343C2214yes—
135#2343C2214yes—
136#2343C2214yes—
137#2343C2214yes—
138#2343C2214yes—
139#2343C2214yes—
140#2339C2212yes—
141#2339C2212yes—
142#2336C2214yes—
143#2336C2214yes—
144#2336C2211yescharacteristic
145#2336C2212yes—
146#2336C2212yes—
147#2336C2214yes—
148#2336C2214yes—
149#2336C2214yes—
150#2336C2214yes—
151#2336C2214yes—
152#2336C2212yes—
153#2336C2211yescharacteristic
154#2336C2211yescharacteristic
155#2336C2211yescharacteristic
156#2336C2212yes—
157#2336C2212yes—
158#2336C2214yes—
159#2336C2214yes—
160#2336C2212yes—
161#2336C2214yes—
162#2336C2214yes—
163#2336C2214yes—
164#2332C2212yes—
165#2332C2212yes—
166#2332C2214yes—
167#2332C2214yes—
168#2331C2212yes—
169#2331C2212yes—
170#2331C2212yes—
171#2331C2212yes—
172#2331C2214yes—
173#2331C2214yes—
174#2330C2212yes—
175#2330C2212yes—
176#2330C2212yes—
177#2330C2212yes—
178#2329C2214yes—
179#2329C2214yes—
180#2329C2214yes—
181#2329C2214yes—
182#2329C2214yes—
183#2329C2214yes—
184#2327C2214yes—
185#2327C2212yes—
186#2327C2212yes—
187#2327C2214yes—
188#2323C2212yes—
189#2323C2212yes—
190#2323C2214yes—
191#2323C2214yes—
192#2320C2214yes—
193#2320C2214yes—
194#2320C2211yescharacteristic
195#2320C2211yescharacteristic
196#2320C2214yes—
197#2320C2212yes—
198#2320C2212yes—
199#2318C2212yes—
200#2318C2212yes—
201#2318C2214yes—
202#2318C2214yes—
203#2316C2212yes—
204#2314C2212yes—
205#2314C2212yes—
206#2313C2214yes—
207#2313C2214yes—
208#2313C2212yes—
209#2313C2212yes—
210C4×C4⋊Q8C2212yes—
211C4×C4⋊Q8C2212yes—
212C4×#125C2212yes—
213C4×#125C2212yes—
214C4×#125C2212yes—
215C4×#125C2212yes—
216C4×C22⋊Q8C2214yes—
217C4×C22⋊Q8C2214yes—
218C4×C22⋊Q8C2214yes—
219C4×C22⋊Q8C2214yes—
220C4×C22⋊Q8C2214yes—
221C4×C22⋊Q8C2214yes—
222#2298C2212yes—
223#2298C2212yes—
224#2295C2211yescharacteristic
225#2295C2212yes—
226#2295C2212yes—
227#2295C2212yes—
228#2295C2212yes—
229#2295C2212yes—
230#2295C2211yescharacteristic
231C2×#389C2214yes—
232#2290C2212yes—
233#2290C2212yes—
234#2290C2214yes—
235#2290C2214yes—
236C2×#387C2214yes—
237C2×#387C2214yes—
238C2×#387C2214yes—
239C2×#387C2214yes—
240#2285C2211yescharacteristic
241#2283C2211yescharacteristic
242#2283C2212yes—
243#2283C2212yes—
244#2283C2211yescharacteristic
245C2×#383C2212yes—
246#2276C2214yes—
247#2275C2211yescharacteristic
248#2275C2212yes—
249#2275C2211yescharacteristic
250#2275C2212yes—
251#2274C2212yes—
252C42×Q8C2212yes—
253C42×D4C2212yes—
254C42×D4C2211yescharacteristic
255C42×D4C2212yes—
256C42×D4C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C2×C4×C4⋊C4C2214yes—
260C22×#41C2311yescharacteristic
261#557C2×C4132yescomplemented
262#557C2×C4132yescomplemented
263#554C2×C4132yes—
264#554C2×C4132yes—
265#554C2×C4164yescomplemented
266#554C2×C4164yescomplemented
267#544C2×C4132yescomplemented
268#544C2×C4132yescomplemented
269#544C2×C4116yescomplemented
270#544C2×C4116yescomplemented
271#533C2×C4116yescomplemented
272#533C2×C4132yescomplemented
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281C2×#125C2×C4132yescomplemented
282C2×#125C2×C4116yescomplemented
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2311yescharacteristic
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2311yescharacteristic
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#125C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307#520C2×C4116yes—
308#520C2×C4116yes—
309C4×#41C2×C4116yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×#117C2312yes—
338C2×#117C2314yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2311yescharacteristic
342C2×#117C2311yescharacteristic
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2311yescharacteristic
347C22×C4⋊C4C2314yes—
348C22×C4⋊C4C2314yes—
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2311yescharacteristic
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2314yes—
357C22×C4⋊C4C2314yes—
358C22×C42C2314yes—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2314yes—
362C22×C42C2312yes—
363C22×C42C2311yescharacteristic
364#391C2314yes—
365#391C2314yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2312yes—
375#391C2312yes—
376#391C2314yes—
377#391C2312yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2312yes—
387#391C2312yes—
388#391C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2312yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2312yes—
422#389C2314yes—
423#389C2312yes—
424#389C2312yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2312yes—
435#388C2312yes—
436#388C2314yes—
437#388C2314yes—
438#388C2312yes—
439#388C2312yes—
440#388C2314yes—
441#388C2314yes—
442#388C2312yes—
443#388C2312yes—
444#388C2312yes—
445#388C2312yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2312yes—
455#387C2312yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
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#387C2312yes—
483#387C2312yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2312yes—
497#387C2312yes—
498#387C2312yes—
499#387C2312yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2314yes—
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#387C2312yes—
524#387C2314yes—
525#387C2312yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#384C2312yes—
565#384C2312yes—
566#384C2312yes—
567#383C2312yes—
568#383C2312yes—
569#383C2314yes—
570#383C2314yes—
571#383C2314yes—
572#383C2314yes—
573#383C2311yescharacteristic
574#383C2312yes—
575#383C2311yescharacteristic
576#383C2314yes—
577#383C2314yes—
578#383C2314yes—
579#382C2312yes—
580#382C2312yes—
581#382C2312yes—
582#382C2314yes—
583#382C2314yes—
584#382C2312yes—
585#382C2312yes—
586#382C2314yes—
587#382C2314yes—
588#382C2314yes—
589#382C2312yes—
590#382C2312yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2314yes—
595#381C2312yes—
596#381C2312yes—
597#380C2311yescharacteristic
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2311yescharacteristic
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2311yescharacteristic
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C22⋊C4C2311yescharacteristic
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704#376C2314yes—
705#376C2311yescharacteristic
706#376C2311yescharacteristic
707#376C2312yes—
708#376C2312yes—
709#376C2314yes—
710#376C2314yes—
711#376C2312yes—
712#376C2312yes—
713#376C2314yes—
714#376C2314yes—
715#376C2312yes—
716#376C2312yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#95C2314yes—
720C2×#95C2314yes—
721C2×#95C2314yes—
722C2×#95C2314yes—
723C2×#95C2314yes—
724C2×#95C2314yes—
725C2×#95C2314yes—
726C43C2311yescharacteristic
727C43C2311yescharacteristic
728C43C2312yes—
729C43C2312yes—
730C2×#41—28no—
731C2×#41C22×C418yes—
732C22×Q8C2411yescharacteristic
733C22×Q8C2414yes—
734C22×Q8C2412yes—
735C22×Q8C2414yes—
736C22×Q8C2412yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2412yes—
753C4⋊Q8C22×C418yes—
754C4⋊Q8C22×C418yes—
755C4⋊Q8C22×C4116yes—
756C4⋊Q8C22×C4116yes—
757C4⋊Q8C22×C4116yes—
758C4⋊Q8C22×C4116yes—
759C4⋊Q8C22×C4132yes—
760C4⋊Q8C22×C4132yes—
761#125C22×C418yes—
762#125C22×C4116yes—
763#125C22×C4116yes—
764#125C22×C4116yes—
765#125C22×C4116yes—
766#125C22×C4116yes—
767#125C22×C4116yes—
768#125C22×C4132yes—
769#125C22×C4132yes—
770#125C22×C418yes—
771#125C22×C4116yes—
772#125C22×C4116yes—
773#125C22×C4132yes—
774#125C22×C4132yes—
775C22⋊Q8C22×C4132yes—
776C22⋊Q8C22×C4132yes—
777C22⋊Q8C22×C4116yes—
778C22⋊Q8C22×C4116yes—
779C22⋊Q8C22×C4132yes—
780C22⋊Q8C22×C4132yes—
781C22⋊Q8C22×C4132yes—
782C22⋊Q8C22×C4132yes—
783C22⋊Q8C22×C4132yes—
784C22⋊Q8C22×C4132yes—
785C4×Q8—44no—
786C4×Q8—48no—
787C4×Q8—44no—
788C4×Q8—48no—
789C4×Q8—84no—
790C4×Q8—84no—
791C4×Q8—84no—
792C4×Q8C22×C418yes—
793C4×Q8C22×C418yes—
794C4×Q8C22×C4116yes—
795C4×Q8C22×C4116yes—
796C4×Q8C22×C4116yes—
797C4×Q8C22×C4116yes—
798C4×Q8C22×C4132yes—
799C4×Q8C22×C4132yes—
800C4×D4—28no—
801C4×D4—28no—
802C4×D4—28no—
803C4×D4—28no—
804C4×D4C22×C418yes—
805C4×D4C22×C418yes—
806C4×D4C22×C4116yes—
807C4×D4C22×C4116yes—
808C4×D4C22×C4116yes—
809C4×D4C22×C4116yes—
810C4×D4C22×C4132yes—
811C4×D4C22×C4132yes—
812#117—48no—
813#117—44no—
814#117—82no—
815#117—84no—
816#117C22×C4116yes—
817#117C22×C418yes—
818#117C22×C418yes—
819#117C22×C418yes—
820#117C22×C4116yes—
821#117C22×C4116yes—
822C2×C4⋊C4—48no—
823C2×C4⋊C4—48no—
824C2×C4⋊C4—84no—
825C2×C4⋊C4C22×C4116yes—
826C2×C4⋊C4C22×C4116yes—
827C2×C4⋊C4C22×C418yes—
828C2×C4⋊C4C22×C418yes—
829C2×C4⋊C4C22×C4132yes—
830C2×C4⋊C4C22×C4132yes—
831C2×C4⋊C4C22×C4116yes—
832C2×C4⋊C4C22×C4116yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C42—48no—
915C2×C42—82no—
916C2×C42—84no—
917C2×C42—82no—
918C2×C42C22×C4116yes—
919C2×C42C22×C418yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2411yescharacteristic
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969#95C2412yes—
970#95C2411yescharacteristic
971#95C2411yescharacteristic
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2411yescharacteristic
1010#95C2411yescharacteristic
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047C24C2511yescharacteristic
1048C24C2512yes—
1049#41—232no—
1050C2×Q8—24no—
1051C2×Q8—42no—
1052C2×Q8—44no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—44no—
1059C2×Q8C23×C414yes—
1060C2×Q8C23×C418yes—
1061C2×Q8C23×C418yes—
1062C2×Q8C23×C4116yes—
1063C2×Q8C23×C4116yes—
1064C2×D4—28no—
1065C2×D4C23×C418yes—
1066C2×D4C23×C414yes—
1067C2×D42−1+418yes—
1068C22×C4—28no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—28no—
1072C22×C4—28no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—41no—
1084C22×C4—42no—
1085C22×C4—41no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4C23×C418yes—
1096C22×C4C23×C414yes—
1097C22×C4C23×C414yes—
1098C22×C4C23×C414yes—
1099C22×C4C23×C418yes—
1100C22×C4C23×C418yes—
1101C22×C4C23×C418yes—
1102C22×C4C23×C418yes—
1103C22×C4C23×C4116yes—
1104C22×C4C23×C4116yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2514yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4C23×C414yes—
1167C4⋊C4C23×C418yes—
1168C4⋊C4C23×C414yes—
1169C4⋊C4C23×C418yes—
1170C4⋊C4C23×C418yes—
1171C4⋊C4C23×C418yes—
1172C4⋊C4C23×C4116yes—
1173C4⋊C4C23×C4116yes—
1174C4⋊C4C23×C4116yes—
1175C4⋊C4C23×C4116yes—
1176C4⋊C4C23×C418yes—
1177C4⋊C4C23×C418yes—
1178C4⋊C4C23×C4116yes—
1179C4⋊C4C23×C4116yes—
1180C4⋊C4C23×C4116yes—
1181C4⋊C4C23×C4116yes—
1182C4⋊C4C23×C4116yes—
1183C4⋊C4C23×C4116yes—
1184C4⋊C4C23×C414yes—
1185C4⋊C4C23×C414yes—
1186C4⋊C4C23×C418yes—
1187C4⋊C4C23×C418yes—
1188C4⋊C4C23×C414yes—
1189C4⋊C4C23×C414yes—
1190C4⋊C4C23×C418yes—
1191C4⋊C4C23×C418yes—
1192C4⋊C4C23×C418yes—
1193C4⋊C4C23×C418yes—
1194C4⋊C4C23×C4116yes—
1195C4⋊C4C23×C4116yes—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4C23×C418yes—
1207C22⋊C4C23×C418yes—
1208C22⋊C4C23×C4116yes—
1209C22⋊C4C23×C4116yes—
1210C22⋊C4C23×C418yes—
1211C22⋊C4C23×C418yes—
1212C22⋊C4C23×C418yes—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—28no—
1219C42—24no—
1220C42—24no—
1221C42—44no—
1222C42—44no—
1223C42—41no—
1224C42—42no—
1225C42—41no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—41no—
1234C42—41no—
1235C42—42no—
1236C42—44no—
1237C42—42no—
1238C42—42no—
1239C42—44no—
1240C42—42no—
1241C42—44no—
1242C42—44no—
1243C42—42no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C42—42no—
1248C42—42no—
1249C42—44no—
1250C42—42no—
1251C42C23×C414yes—
1252C42C23×C414yes—
1253C42C23×C418yes—
1254C42C23×C418yes—
1255C42C23×C418yes—
1256C42C23×C414yes—
1257C42C23×C414yes—
1258C42C23×C4116yes—
1259C42C23×C4116yes—
1260C42C23×C418yes—
1261C42C23×C418yes—
1262C23—24no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—21no—
1268C23—21no—
1269C23C24×C412yes—
1270C23C24×C414yes—
1271C23C2×2−1+418yes—
1272C23C2611yescharacteristic
1273Q8—28no—
1274Q8—48no—
1275Q8—416no—
1276Q8—416no—
1277Q8—48no—
1278D4—216no—
1279D4#519116yes—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—216no—
1306C2×C4—28no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—48no—
1341C2×C4—44no—
1342C2×C4—416no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—44no—
1346C2×C4—416no—
1347C2×C4—48no—
1348C2×C4—416no—
1349C2×C4—88no—
1350C2×C4—88no—
1351C2×C4—88no—
1352C2×C4C24×C414yes—
1353C2×C4C24×C412yes—
1354C2×C4C24×C412yes—
1355C2×C4C24×C412yes—
1356C2×C4C24×C414yes—
1357C2×C4C24×C414yes—
1358C2×C4C24×C412yes—
1359C2×C4C24×C414yes—
1360C2×C4C24×C414yes—
1361C2×C4C24×C412yes—
1362C2×C4C24×C418yes—
1363C2×C4C24×C414yes—
1364C2×C4C24×C418yes—
1365C2×C4C24×C414yes—
1366C2×C4C24×C412yes—
1367C2×C4C2×2−1+414yes—
1368C2×C4#58514yes—
1369C22—24no—
1370C22—24no—
1371C22—28no—
1372C22—28no—
1373C22—22no—
1374C22—22no—
1375C22—22no—
1376C22—42no—
1377C22—42no—
1378C22C2×#51918yes—
1379C22C25×C411yescharacteristic
1380C22C22×2−1+412yes—
1381C22C2×#58512yes—
1382C22H(7,𝔽2)11yescharacteristic
1383C222−1+611yescharacteristic
1384C4—22no—
1385C4—24no—
1386C4—22no—
1387C4—24no—
1388C4—28no—
1389C4—22no—
1390C4—24no—
1391C4—24no—
1392C4—22no—
1393C4—24no—
1394C4—28no—
1395C4—24no—
1396C4—22no—
1397C4—24no—
1398C4—24no—
1399C4—42no—
1400C4—44no—
1401C4—44no—
1402C4—44no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—44no—
1409C4—42no—
1410C4C2×#51914yes—
1411C2—28no—
1412C2—42no—
1413C2C22×#51911yescharacteristic
1414C2C4×#58511yescharacteristic
1415C2#6265411yescharacteristic
1416C2#6294812yes—
1417C2#6295012yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC22×#41C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34490C2semidirect
3. #34490C2semidirect
4. #34488C2semidirect
5. #34486C2semidirect
6. #34486C2semidirect
7. #34464C2semidirect
8. #34434C2semidirect
9. #34434C2semidirect
10. #34432C2semidirect
11. #34432C2semidirect
12. #34389C2semidirect
13. #34378C2semidirect
14. #34373C2semidirect
15. #34372C2semidirect
16. #34333C2semidirect
17. #34333C2semidirect
18. #34332C2semidirect
19. #34328C2semidirect
20. #34299C2semidirect
23. #34239C2semidirect
24. #34235C2semidirect
26. C4×#554C2semidirect
28. #34085C2semidirect
29. C2×#2336C2semidirect
30. #3504C4semidirect
261. #557C2×C4semidirect
262. #557C2×C4semidirect
265. #554C2×C4semidirect
266. #554C2×C4semidirect
267. #544C2×C4semidirect
268. #544C2×C4semidirect
269. #544C2×C4semidirect
270. #544C2×C4semidirect
271. #533C2×C4semidirect
272. #533C2×C4semidirect
281. C2×#125C2×C4semidirect
282. C2×#125C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
#344902
#344882
#344862
#344642
#344342
#344322
#343892
#343782
#343732
#343722
#343332
#343322
#343282
#342992
#342602
#342392
#342352
#341952
C4×#5542
#341272
#340852
C2×#23362