Finite Group Databasebeta

← #7626943

Subgroups — #7626943

Order 512.

6446 conjugacy classes of subgroups.

The subgroup lattice has 1437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic
2#34507C214yesmaximal, complemented
3#34505C214yesmaximal, complemented
4#34500C212yesmaximal, complemented
5#34499C212yesmaximal, complemented
6#34488C212yesmaximal, complemented
7#34486C214yesmaximal, complemented
8#34444C214yesmaximal, complemented
9#34443C214yesmaximal, complemented
10#34439C212yesmaximal, complemented
11#34439C212yesmaximal, complemented
12#34405C212yesmaximal, complemented
13#34402C211yesmaximal, characteristic
14#34400C212yesmaximal, complemented
15#34375C211yesmaximal, characteristic, complemented
16#34329C212yesmaximal, complemented
17#34328C212yesmaximal, complemented
18#34326C212yesmaximal, complemented
19#34322C212yesmaximal, complemented
20#34297C214yesmaximal, complemented
21#34263C212yesmaximal, complemented
22#34260C212yesmaximal, complemented
23#34244C212yesmaximal, complemented
24#34232C211yesmaximal, characteristic
25#34192C211yesmaximal, characteristic, complemented
26C4×#556C212yesmaximal, complemented
27#34128C211yesmaximal, characteristic, complemented
28#34085C211yesmaximal, characteristic, complemented
29#34081C212yesmaximal, complemented
30#3507C4132yescomplemented
31C2×#559C2211yescharacteristic
32C2×#559C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#556C2212yes—
36C2×#556C2212yes—
37C2×#556C2212yes—
38C2×#554C2212yes—
39C2×#552C2214yes—
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#2381C2212yes—
53#2379C2214yes—
54#2378C2214yes—
55#2378C2214yes—
56#2378C2214yes—
57#2377C2212yes—
58#2377C2212yes—
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#2371C2214yes—
74#2371C2214yes—
75#2371C2214yes—
76#2370C2214yes—
77#2370C2214yes—
78#2368C2214yes—
79#2368C2214yes—
80#2368C2214yes—
81#2367C2212yes—
82#2367C2212yes—
83#2367C2212yes—
84#2367C2212yes—
85#2367C2212yes—
86#2367C2212yes—
87#2366C2212yes—
88#2365C2212yes—
89#2365C2212yes—
90#2365C2212yes—
91#2365C2212yes—
92#2365C2212yes—
93#2363C2214yes—
94#2362C2214yes—
95#2360C2214yes—
96#2359C2214yes—
97#2359C2214yes—
98#2357C2212yes—
99#2357C2214yes—
100#2356C2212yes—
101#2356C2212yes—
102#2356C2214yes—
103#2356C2212yes—
104#2356C2214yes—
105#2356C2214yes—
106#2355C2212yes—
107#2355C2212yes—
108#2355C2212yes—
109#2355C2212yes—
110#2355C2212yes—
111#2355C2214yes—
112#2354C2212yes—
113#2354C2214yes—
114#2353C2214yes—
115#2353C2214yes—
116#2353C2214yes—
117#2353C2214yes—
118#2352C2214yes—
119#2352C2214yes—
120#2351C2212yes—
121#2351C2212yes—
122#2351C2212yes—
123Q8×C4⋊C4C2212yes—
124#2349C2212yes—
125D4×C4⋊C4C2212yes—
126#2347C2214yes—
127#2346C2214yes—
128#2345C2212yes—
129#2345C2212yes—
130#2345C2211yescharacteristic
131#2345C2211yescharacteristic
132#2345C2214yes—
133#2344C2214yes—
134#2344C2212yes—
135#2344C2214yes—
136#2343C2214yes—
137#2343C2214yes—
138#2343C2214yes—
139#2343C2214yes—
140#2341C2212yes—
141#2341C2212yes—
142Q8×C22⋊C4C2212yes—
143Q8×C22⋊C4C2211yescharacteristic
144Q8×C22⋊C4C2211yescharacteristic
145#2339C2212yes—
146#2339C2212yes—
147#2337C2214yes—
148#2337C2214yes—
149#2336C2214yes—
150#2336C2214yes—
151#2336C2214yes—
152#2336C2212yes—
153#2336C2212yes—
154#2336C2214yes—
155#2335C2214yes—
156#2335C2214yes—
157#2335C2214yes—
158#2335C2214yes—
159#2335C2214yes—
160#2335C2214yes—
161#2334C2214yes—
162#2334C2214yes—
163#2334C2214yes—
164#2334C2214yes—
165#2334C2214yes—
166#2333C2212yes—
167#2333C2212yes—
168#2333C2212yes—
169#2333C2212yes—
170#2332C2214yes—
171#2332C2211yescharacteristic
172#2332C2212yes—
173#2332C2211yescharacteristic
174#2332C2211yescharacteristic
175#2332C2211yescharacteristic
176#2332C2212yes—
177#2332C2214yes—
178#2332C2214yes—
179#2332C2214yes—
180#2331C2212yes—
181#2330C2214yes—
182#2329C2214yes—
183#2329C2214yes—
184#2329C2214yes—
185#2328C2212yes—
186#2327C2212yes—
187#2327C2212yes—
188#2327C2212yes—
189#2327C2212yes—
190#2326C2212yes—
191#2326C2212yes—
192#2323C2214yes—
193#2323C2212yes—
194#2323C2212yes—
195#2322C2214yes—
196#2320C2214yes—
197#2320C2214yes—
198#2320C2212yes—
199#2320C2212yes—
200#2319C2214yes—
201#2319C2212yes—
202#2319C2212yes—
203#2318C2214yes—
204#2318C2214yes—
205#2318C2214yes—
206#2314C2212yes—
207#2314C2212yes—
208#2314C2214yes—
209#2314C2214yes—
210#2313C2214yes—
211C4×C4⋊Q8C2212yes—
212C4×C4⋊Q8C2212yes—
213C4×#125C2214yes—
214C4×#126C2214yes—
215C4×#126C2214yes—
216C4×#126C2214yes—
217C4×#124C2212yes—
218C4×#124C2212yes—
219C4×#124C2212yes—
220C4×#124C2212yes—
221C4×C22⋊Q8C2214yes—
222C4×#123C2214yes—
223#2298C2214yes—
224#2298C2212yes—
225#2298C2212yes—
226#2298C2214yes—
227#2295C2211yescharacteristic
228#2295C2212yes—
229#2295C2212yes—
230#2295C2214yes—
231#2295C2212yes—
232#2295C2212yes—
233#2295C2211yescharacteristic
234#2295C2212yes—
235#2295C2212yes—
236#2293C2212yes—
237#2293C2214yes—
238#2290C2214yes—
239#2290C2214yes—
240C2×#387C2214yes—
241#2283C2212yes—
242#2283C2211yescharacteristic
243#2283C2211yescharacteristic
244#2283C2211yescharacteristic
245#2283C2212yes—
246#2283C2212yes—
247#2276C2212yes—
248#2276C2212yes—
249#2275C2212yes—
250#2275C2212yes—
251#2274C2214yes—
252C42×Q8C2212yes—
253C42×Q8C2211yescharacteristic
254C42×Q8C2212yes—
255C42×Q8C2211yescharacteristic
256C42×D4C2212yes—
257C4×#117C2212yes—
258C4×#117C2214yes—
259C4×#117C2211yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2311yescharacteristic
262#559C2×C4116yes—
263#559C2×C4116yes—
264#557C2×C4116yescomplemented
265#557C2×C4116yescomplemented
266#556C2×C4132yescomplemented
267#556C2×C4132yescomplemented
268#556C2×C4132yescomplemented
269#554C2×C4132yescomplemented
270#552C2×C4164yescomplemented
271#539C2×C4164yescomplemented
272#536C2×C4132yescomplemented
273#533C2×C4116yescomplemented
274#532C2×C4116yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×#127C2311yescharacteristic
281#529C2×C4132yescomplemented
282#529C2×C4132yescomplemented
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2311yescharacteristic
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310#520C2×C4132yescomplemented
311C2×C4×Q8C2×C4116yescomplemented
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2314yes—
351C2×#117C2314yes—
352C2×#117C2312yes—
353C2×#117C2314yes—
354C2×#117C2314yes—
355C2×#117C2314yes—
356C22×C4⋊C4C2314yes—
357C22×C4⋊C4C2314yes—
358C22×C4⋊C4C2311yescharacteristic
359C22×C4⋊C4C2312yes—
360C22×C42C2314yes—
361C22×C42C2312yes—
362C22×C42C2311yescharacteristic
363#391C2312yes—
364#391C2312yes—
365#391C2312yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2312yes—
374#391C2312yes—
375#391C2314yes—
376#391C2312yes—
377#391C2312yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2314yes—
385#390C2312yes—
386#390C2312yes—
387#390C2314yes—
388#390C2314yes—
389#390C2314yes—
390#390C2312yes—
391#390C2314yes—
392#390C2314yes—
393#390C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2312yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2312yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2312yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2312yes—
448#388C2312yes—
449#388C2312yes—
450#388C2312yes—
451#388C2312yes—
452#388C2312yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#387C2312yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2312yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2312yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2312yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2312yes—
512#387C2314yes—
513#387C2314yes—
514#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2312yes—
518#387C2312yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2312yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#384C2312yes—
564#384C2312yes—
565#384C2314yes—
566#383C2314yes—
567#383C2314yes—
568#383C2312yes—
569#383C2314yes—
570#383C2314yes—
571#383C2312yes—
572#383C2312yes—
573#383C2314yes—
574#382C2314yes—
575#382C2314yes—
576#382C2314yes—
577#382C2312yes—
578#382C2312yes—
579#382C2312yes—
580#382C2314yes—
581#382C2314yes—
582#382C2312yes—
583#382C2314yes—
584#382C2312yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2314yes—
589#381C2314yes—
590#381C2311yescharacteristic
591#381C2311yescharacteristic
592#381C2312yes—
593#381C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2311yescharacteristic
597#380C2312yes—
598#380C2311yescharacteristic
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⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2311yescharacteristic
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C22⋊C4C2314yes—
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⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2311yescharacteristic
686C4×C22⋊C4C2311yescharacteristic
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
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⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705#376C2312yes—
706#376C2314yes—
707#376C2312yes—
708#376C2312yes—
709#376C2312yes—
710#376C2314yes—
711#376C2314yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2312yes—
716#376C2312yes—
717#376C2314yes—
718#376C2314yes—
719C2×#95C2314yes—
720C2×#95C2314yes—
721C2×#95C2314yes—
722C2×#95C2314yes—
723C43C2312yes—
724C43C2312yes—
725C43C2314yes—
726C43C2312yes—
727C43C2312yes—
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×Q8C2411yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2412yes—
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2414yes—
746C23×C4C2411yescharacteristic
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C23×C4C2411yescharacteristic
758C4⋊Q8C22×C418yes—
759C4⋊Q8C22×C418yes—
760C4⋊Q8C22×C418yes—
761C4⋊Q8C22×C4116yes—
762C4⋊Q8C22×C4116yes—
763#127C22×C418yes—
764#126C22×C4132yes—
765#126C22×C4132yes—
766#126C22×C4132yes—
767#126C22×C4132yes—
768#125C22×C4116yes—
769#125C22×C4116yes—
770#125C22×C4116yes—
771#125C22×C4132yes—
772#125C22×C4132yes—
773#124C22×C4116yes—
774#124C22×C4116yes—
775#124C22×C4116yes—
776#124C22×C4116yes—
777#124C22×C4116yes—
778#123C22×C4132yes—
779#123C22×C4132yes—
780#123C22×C4132yes—
781#123C22×C4132yes—
782C22⋊Q8C22×C418yes—
783C22⋊Q8C22×C418yes—
784C22⋊Q8C22×C4116yes—
785C22⋊Q8C22×C4132yes—
786C22⋊Q8C22×C4132yes—
787C22⋊Q8C22×C4132yes—
788C22⋊Q8C22×C4132yes—
789#121C22×C4116yes—
790#121C22×C4116yes—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8C22×C4116yes—
802C4×Q8C22×C4116yes—
803C4×Q8C22×C418yes—
804C4×Q8C22×C418yes—
805C4×Q8C22×C418yes—
806C4×Q8C22×C418yes—
807C4×Q8C22×C4116yes—
808C4×Q8C22×C4116yes—
809C4×Q8C22×C4116yes—
810C4×Q8C22×C4116yes—
811C4×Q8C22×C4116yes—
812C4×Q8C22×C418yes—
813C4×Q8C22×C418yes—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—48no—
819C4×D4C22×C4132yes—
820C4×D4C22×C4132yes—
821C4×D4C22×C4116yes—
822C4×D4C22×C4116yes—
823C4×D4C22×C4116yes—
824C4×D4C22×C4116yes—
825C4×D4C22×C4116yes—
826C4×D4C22×C4116yes—
827#117—48no—
828#117—48no—
829#117—48no—
830#117—44no—
831#117C22×C4116yes—
832#117C22×C4132yes—
833#117C22×C4132yes—
834#117C22×C4132yes—
835C2×C4⋊C4—48no—
836C2×C4⋊C4C22×C418yes—
837C2×C4⋊C4C22×C4116yes—
838C2×C4⋊C4C22×C4132yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C42—48no—
927C2×C42C22×C4116yes—
928C2×C42C22×C418yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2411yescharacteristic
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
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#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048C24C2511yescharacteristic
1049C24C2514yes—
1050#41—432no—
1051C2×Q8—24no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—44no—
1058C2×Q8—41no—
1059C2×Q8—41no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—416no—
1063C2×Q8C23×C414yes—
1064C2×Q8C23×C414yes—
1065C2×Q8C23×C418yes—
1066C2×Q8C23×C414yes—
1067C2×Q8C23×C414yes—
1068C2×Q8C23×C418yes—
1069C2×Q8C23×C418yes—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—44no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4C23×C418yes—
1078C2×D4C23×C418yes—
1079C2×D4C23×C4116yes—
1080C2×D4C23×C418yes—
1081C22×C4—24no—
1082C22×C4—28no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4C23×C414yes—
1106C22×C4C23×C414yes—
1107C22×C4C23×C418yes—
1108C22×C4C23×C414yes—
1109C22×C4C23×C418yes—
1110C22×C4C23×C4116yes—
1111C22×C4C23×C4116yes—
1112C22×C4C23×C4116yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2511yescharacteristic
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2511yescharacteristic
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4C23×C418yes—
1173C4⋊C4C23×C418yes—
1174C4⋊C4C23×C414yes—
1175C4⋊C4C23×C414yes—
1176C4⋊C4C23×C4116yes—
1177C4⋊C4C23×C4116yes—
1178C4⋊C4C23×C418yes—
1179C4⋊C4C23×C418yes—
1180C4⋊C4C23×C418yes—
1181C4⋊C4C23×C418yes—
1182C4⋊C4C23×C418yes—
1183C4⋊C4C23×C418yes—
1184C4⋊C4C23×C418yes—
1185C4⋊C4C23×C4116yes—
1186C4⋊C4C23×C4116yes—
1187C4⋊C4C23×C414yes—
1188C4⋊C4C23×C414yes—
1189C4⋊C4C23×C418yes—
1190C4⋊C4C23×C418yes—
1191C4⋊C4C23×C418yes—
1192C4⋊C4C23×C418yes—
1193C4⋊C4C23×C4116yes—
1194C4⋊C4C23×C4116yes—
1195C4⋊C4C23×C418yes—
1196C22⋊C4—24no—
1197C22⋊C4—28no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—41no—
1202C22⋊C4—42no—
1203C22⋊C4—41no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—41no—
1207C22⋊C4—41no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4C23×C4116yes—
1218C22⋊C4C23×C418yes—
1219C22⋊C4C23×C418yes—
1220C22⋊C4C23×C4116yes—
1221C22⋊C4C23×C4116yes—
1222C22⋊C4C23×C4116yes—
1223C22⋊C4C23×C4116yes—
1224C22⋊C4C23×C4116yes—
1225C22⋊C4C23×C4116yes—
1226C22⋊C4C23×C4116yes—
1227C42—24no—
1228C42—28no—
1229C42—24no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—24no—
1234C42—24no—
1235C42—44no—
1236C42—44no—
1237C42—41no—
1238C42—41no—
1239C42—42no—
1240C42—42no—
1241C42—41no—
1242C42—41no—
1243C42—42no—
1244C42—42no—
1245C42—44no—
1246C42—44no—
1247C42—42no—
1248C42—42no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—42no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—42no—
1263C42—42no—
1264C42C23×C418yes—
1265C42C23×C418yes—
1266C42C23×C414yes—
1267C42C23×C414yes—
1268C42C23×C418yes—
1269C42C23×C418yes—
1270C42C23×C414yes—
1271C42C23×C414yes—
1272C42C23×C4116yes—
1273C42C23×C4116yes—
1274C42C23×C418yes—
1275C42C23×C418yes—
1276C23—22no—
1277C23—24no—
1278C23—24no—
1279C23—24no—
1280C23—24no—
1281C23—22no—
1282C23—21no—
1283C23—21no—
1284C23—24no—
1285C23—24no—
1286C23C24×C418yes—
1287C23C24×C412yes—
1288C23C2611yescharacteristic
1289Q8—28no—
1290Q8—28no—
1291Q8—216no—
1292Q8—48no—
1293Q8—48no—
1294Q8—44no—
1295Q8—44no—
1296D4—216no—
1297D4—48no—
1298D4—48no—
1299D4—416no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—28no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—48no—
1358C2×C4—416no—
1359C2×C4—416no—
1360C2×C4—44no—
1361C2×C4—44no—
1362C2×C4—48no—
1363C2×C4—416no—
1364C2×C4—88no—
1365C2×C4—88no—
1366C2×C4—164no—
1367C2×C4—164no—
1368C2×C4C24×C412yes—
1369C2×C4C24×C412yes—
1370C2×C4C24×C414yes—
1371C2×C4C24×C414yes—
1372C2×C4C24×C414yes—
1373C2×C4C24×C414yes—
1374C2×C4C24×C414yes—
1375C2×C4C24×C414yes—
1376C2×C4C24×C412yes—
1377C2×C4C24×C418yes—
1378C2×C4C24×C412yes—
1379C2×C4C24×C412yes—
1380C2×C4C24×C414yes—
1381C2×C4C24×C414yes—
1382C2×C4C24×C412yes—
1383C2×C4#58514yes—
1384C2×C4#58514yes—
1385C22—22no—
1386C22—28no—
1387C22—22no—
1388C22—28no—
1389C22—22no—
1390C22—28no—
1391C22—44no—
1392C22—44no—
1393C22—42no—
1394C22—44no—
1395C22—42no—
1396C22—44no—
1397C22C25×C411yescharacteristic
1398C22C2×#58512yes—
1399C22C2×#58512yes—
1400C222−1+611yescharacteristic
1401C222−1+611yescharacteristic
1402C4—22no—
1403C4—28no—
1404C4—24no—
1405C4—24no—
1406C4—24no—
1407C4—24no—
1408C4—24no—
1409C4—24no—
1410C4—22no—
1411C4—22no—
1412C4—22no—
1413C4—22no—
1414C4—24no—
1415C4—24no—
1416C4—24no—
1417C4—42no—
1418C4—44no—
1419C4—44no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—44no—
1427C4—42no—
1428C4#342814yes—
1429C2—42no—
1430C2—48no—
1431C2C2×#342811yescharacteristic
1432C2C4×#58511yescharacteristic
1433C2#6265311yescharacteristic
1434C2#6296412yes—
1435C2#6296712yes—
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. #34507C2semidirect
3. #34505C2semidirect
4. #34500C2semidirect
5. #34499C2semidirect
6. #34488C2semidirect
7. #34486C2semidirect
8. #34444C2semidirect
9. #34443C2semidirect
10. #34439C2semidirect
11. #34439C2semidirect
12. #34405C2semidirect
14. #34400C2semidirect
15. #34375C2semidirect
16. #34329C2semidirect
17. #34328C2semidirect
18. #34326C2semidirect
19. #34322C2semidirect
20. #34297C2semidirect
21. #34263C2semidirect
22. #34260C2semidirect
23. #34244C2semidirect
25. #34192C2semidirect
26. C4×#556C2semidirect
27. #34128C2semidirect
28. #34085C2semidirect
29. #34081C2semidirect
30. #3507C4semidirect
264. #557C2×C4semidirect
265. #557C2×C4semidirect
266. #556C2×C4semidirect
267. #556C2×C4semidirect
268. #556C2×C4semidirect
269. #554C2×C4semidirect
270. #552C2×C4semidirect
271. #539C2×C4semidirect
272. #536C2×C4semidirect
273. #533C2×C4semidirect
281. #529C2×C4semidirect
282. #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
#345072
#345052
#345002
#344992
#344882
#344862
#344442
#344432
#344392
#344052
#344022
#344002
#343752
#343292
#343282
#343262
#343222
#342972
#342632
#342602
#342442
#342322
#341922
C4×#5562
#341282
#340852
#340812