Finite Group Databasebeta

← #7654846

Subgroups — #7654846

Order 512.

4864 conjugacy classes of subgroups.

The subgroup lattice has 1105 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42931C214yesmaximal
2#42006C218yesmaximal, complemented
3#39625C212yesmaximal, complemented
4#39369C212yesmaximal, complemented
5#39365C214yesmaximal, complemented
6#39180C212yesmaximal, complemented
7#38965C212yesmaximal, complemented
8#38960C214yesmaximal, complemented
9#38104C214yesmaximal, complemented
10#37690C214yesmaximal, complemented
11#37643C211yesmaximal, characteristic, complemented
12#37624C212yesmaximal, complemented
13#36563C212yesmaximal, complemented
14#36497C212yesmaximal, complemented
15#36407C212yesmaximal, complemented
16#36134C212yesmaximal, complemented
17#35747C214yesmaximal, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35275C211yesmaximal, characteristic, complemented
20#35202C212yesmaximal, complemented
21#35167C212yesmaximal, complemented
22#34978C211yesmaximal, characteristic, complemented
23#34938C212yesmaximal, complemented
24#34188C211yesmaximal, characteristic
25#34129C211yesmaximal, characteristic
26#34127C211yesmaximal, characteristic
27C2×#544C2212yes—
28C2×#544C2214yes—
29C2×#544C2212yes—
30C2×#533C2214yes—
31C2×C4×#41C2211yescharacteristic
32#2868C2212yes—
33#2868C2212yes—
34#2864C2214yes—
35#2859C2212yes—
36#2859C2212yes—
37#2859C2214yes—
38#2857C2214yes—
39#2857C2214yes—
40#2845C2214yes—
41#2841C2218yes—
42#2792C2218yes—
43#2780C2218yes—
44#2768C2218yes—
45#2755C2218yes—
46#2734C2218yes—
47#2732C2218yes—
48#2726C2218yes—
49#2720C2218yes—
50#2704C2218yes—
51#2692C2218yes—
52#2683C2218yes—
53#2677C2218yes—
54#2667C2218yes—
55#2666C2218yes—
56#2660C2214yes—
57#2660C2214yes—
58#2660C2214yes—
59#2659C2218yes—
60#2647C2214yes—
61#2629C2214yes—
62#2629C2214yes—
63#2629C2214yes—
64#2629C2214yes—
65#2628C2214yes—
66#2612C2214yes—
67#2606C2218yes—
68#2587C2218yes—
69#2584C2214yes—
70#2582C2214yes—
71#2574C2218yes—
72#2571C2211yescharacteristic
73#2570C2214yes—
74#2567C2214yes—
75#2556C2218yes—
76#2556C2218yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2212yes—
80#2552C2212yes—
81#2552C2212yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2214yes—
85#2552C2212yes—
86#2552C2211yescharacteristic
87#2552C2212yes—
88#2552C2211yescharacteristic
89#2552C2212yes—
90#2551C2212yes—
91#2551C2214yes—
92#2551C2212yes—
93#2551C2212yes—
94#2551C2211yescharacteristic
95#2551C2212yes—
96#2551C2214yes—
97#2550C2214yes—
98#2550C2218yes—
99#2550C2214yes—
100#2550C2214yes—
101#2550C2214yes—
102#2550C2214yes—
103#2549C2218yes—
104#2542C2214yes—
105#2538C2214yes—
106#2520C2218yes—
107#2507C2218yes—
108#2507C2214yes—
109#2506C2214yes—
110#2465C2218yes—
111#2462C2218yes—
112#2454C2214yes—
113#2453C2214yes—
114#2452C2214yes—
115#2451C2218yes—
116#2451C2214yes—
117#2441C2214yes—
118#2441C2214yes—
119#2441C2214yes—
120#2441C2214yes—
121#2441C2214yes—
122#2441C2212yes—
123#2441C2212yes—
124#2440C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2440C2214yes—
128#2440C2214yes—
129#2440C2214yes—
130#2439C2212yes—
131#2439C2214yes—
132#2439C2212yes—
133#2429C2218yes—
134#2429C2218yes—
135#2423C2218yes—
136#2399C2218yes—
137#2396C2214yes—
138#2370C2214yes—
139#2369C2214yes—
140#2365C2214yes—
141#2355C2212yes—
142#2355C2211yescharacteristic
143#2355C2211yescharacteristic
144#2355C2212yes—
145#2354C2211yescharacteristic
146#2354C2212yes—
147#2354C2212yes—
148#2354C2211yescharacteristic
149#2354C2212yes—
150#2354C2212yes—
151#2352C2212yes—
152#2352C2214yes—
153#2352C2214yes—
154#2352C2212yes—
155Q8×C4⋊C4C2211yescharacteristic
156Q8×C4⋊C4C2214yes—
157Q8×C4⋊C4C2211yescharacteristic
158D4×C4⋊C4C2211yescharacteristic
159D4×C4⋊C4C2211yescharacteristic
160#2347C2212yes—
161#2346C2214yes—
162#2346C2212yes—
163#2343C2214yes—
164#2341C2212yes—
165#2339C2212yes—
166#2330C2214yes—
167#2330C2214yes—
168#2317C2212yes—
169#2317C2212yes—
170#2316C2214yes—
171#2314C2214yes—
172#2311C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2214yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2214yes—
177C4×#125C2212yes—
178C4×#125C2212yes—
179#2296C2214yes—
180#2295C2212yes—
181#2293C2214yes—
182#2293C2212yes—
183#2290C2214yes—
184#2285C2211yescharacteristic
185#2285C2211yescharacteristic
186#2285C2211yescharacteristic
187#2285C2212yes—
188#2285C2212yes—
189#2285C2212yes—
190C2×#384C2211yescharacteristic
191#2283C2212yes—
192#2274C2212yes—
193C42×Q8C2212yes—
194C42×D4C2212yes—
195C4×#117C2211yescharacteristic
196C4×#117C2212yes—
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200#544—416no—
201#544—48no—
202#544—48no—
203#533—416no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2318yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C4×#41Q8116yescomplemented
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2318yes—
234C2×C4×Q8C2318yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C42C2314yes—
265C22×C42C2312yes—
266C22×C42C2311yescharacteristic
267#400C2318yes—
268#400C2314yes—
269#400C2318yes—
270#399C2318yes—
271#399C2314yes—
272#399C2318yes—
273#399C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2318yes—
299#396C2318yes—
300#396C2314yes—
301#396C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2314yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#393C2318yes—
314#393C2314yes—
315#391C2318yes—
316#391C2314yes—
317#391C2314yes—
318#391C2318yes—
319#391C2314yes—
320#391C2312yes—
321#391C2318yes—
322#391C2312yes—
323#391C2318yes—
324#391C2318yes—
325#390C2314yes—
326#390C2314yes—
327#390C2312yes—
328#390C2314yes—
329#390C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2318yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2318yes—
371#389C2318yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2318yes—
405#386C2318yes—
406#386C2314yes—
407#386C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2314yes—
412#385C2314yes—
413#385C2318yes—
414#384C2314yes—
415#384C2312yes—
416#384C2312yes—
417#384C2314yes—
418#384C2314yes—
419#384C2314yes—
420#384C2312yes—
421#384C2311yescharacteristic
422#384C2314yes—
423#384C2314yes—
424#384C2314yes—
425#384C2314yes—
426#384C2314yes—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2312yes—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2311yescharacteristic
437#383C2314yes—
438#382C2312yes—
439#382C2312yes—
440#382C2312yes—
441#382C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2314yes—
449#382C2314yes—
450#381C2314yes—
451#380C2314yes—
452#380C2314yes—
453#380C2318yes—
454#380C2318yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2314yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2312yes—
518#376C2314yes—
519#376C2312yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2312yes—
523C43C2314yes—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41C2×Q818yes—
527C22×Q8C2414yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2418yes—
530C22×Q8C2418yes—
531C22×D4C2411yescharacteristic
532C22×D4C2412yes—
533C23×C4C2412yes—
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2412yes—
538C23×C4C2414yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2412yes—
542C4⋊Q8—28no—
543C4⋊Q8—216no—
544C4⋊Q8—28no—
545C4⋊Q8—48no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548C4⋊Q8—48no—
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—48no—
552C4⋊Q8—416no—
553#125—216no—
554#125—28no—
555#125—28no—
556#125—48no—
557#125—48no—
558#125—48no—
559#125—48no—
560#125—48no—
561#125—48no—
562#125—416no—
563C22⋊Q8—416no—
564C22⋊Q8—416no—
565C22⋊Q8—416no—
566C22⋊Q8—416no—
567C22⋊Q8—416no—
568C22⋊Q8—416no—
569C4×Q8—48no—
570C4×Q8—416no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—416no—
574C4×Q8C2×Q818yes—
575C4×Q8C2×Q818yes—
576C4×D4—44no—
577C4×D4—44no—
578C4×D4C2×Q818yes—
579C4×D4C2×Q818yes—
580C4×D4C2×Q8116yes—
581C4×D4C2×Q8116yes—
582#117—28no—
583#117—24no—
584#117—24no—
585#117—24no—
586#117—24no—
587#117—28no—
588#117—44no—
589#117—44no—
590#117—48no—
591#117—44no—
592#117—48no—
593#117—48no—
594#117C2×Q818yes—
595#117C2×Q8116yes—
596C2×C4⋊C4—28no—
597C2×C4⋊C4—28no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4—44no—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C42—48no—
687C2×C42C2×Q818yes—
688C2×C42C2×Q8116yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2414yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2412yes—
718C2×C42C2411yescharacteristic
719#95C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2412yes—
724#95C2412yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2414yes—
731#95C2414yes—
732#95C2412yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24C2511yescharacteristic
762C24C2512yes—
763#41—416no—
764C2×Q8—28no—
765C2×Q8—216no—
766C2×Q8—28no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—44no—
770C2×Q8—48no—
771C2×Q8—48no—
772C2×Q8—48no—
773C2×Q8—48no—
774C2×Q8—48no—
775C2×Q8C22×Q814yes—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4C22×Q814yes—
781C2×D4C22×Q818yes—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—24no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4C22×Q814yes—
804C22×C4C22×Q818yes—
805C22×C4C22×Q814yes—
806C22×C4C22×Q814yes—
807C22×C4C22×Q818yes—
808C22×C4C22×Q818yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2518yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2511yescharacteristic
822C22×C4C2512yes—
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—22no—
838C4⋊C4—24no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—216no—
844C4⋊C4—216no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—216no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—44no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4C22×Q818yes—
893C4⋊C4C22×Q818yes—
894C4⋊C4C22×Q814yes—
895C4⋊C4C22×Q814yes—
896C4⋊C4H(5,𝔽2)14yes—
897C4⋊C4H(5,𝔽2)14yes—
898C4⋊C42−1+414yes—
899C4⋊C42−1+414yes—
900C22⋊C4—24no—
901C22⋊C4—28no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4C22×Q818yes—
916C22⋊C4C22×Q818yes—
917C22⋊C4C22×Q818yes—
918C42—24no—
919C42—28no—
920C42—28no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—28no—
925C42—28no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—28no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—44no—
936C42—44no—
937C42—48no—
938C42—48no—
939C42—44no—
940C42—44no—
941C42C22×Q814yes—
942C42C22×Q814yes—
943C42C22×Q818yes—
944C42C22×Q818yes—
945C42C22×Q818yes—
946C42C22×Q814yes—
947C42C22×Q814yes—
948C23—22no—
949C23—21no—
950C23—21no—
951C23—22no—
952C23—21no—
953C23—21no—
954C23—22no—
955C23—22no—
956C23—21no—
957C23—22no—
958C23—22no—
959C23—21no—
960C23C23×Q812yes—
961C23C23×Q814yes—
962C23C2611yescharacteristic
963Q8—28no—
964Q8—416no—
965Q8—816no—
966Q8—168no—
967D4—28no—
968D4—48no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—28no—
990C2×C4—216no—
991C2×C4—216no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—28no—
1006C2×C4—28no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—48no—
1028C2×C4—88no—
1029C2×C4—88no—
1030C2×C4—164no—
1031C2×C4C23×Q812yes—
1032C2×C4C23×Q814yes—
1033C2×C4C23×Q812yes—
1034C2×C4C23×Q812yes—
1035C2×C4C23×Q814yes—
1036C2×C4C23×Q814yes—
1037C2×C4C23×Q812yes—
1038C2×C4C23×Q812yes—
1039C2×C4C23×Q812yes—
1040C2×C4C2×H(5,𝔽2)14yes—
1041C2×C4C2×H(5,𝔽2)14yes—
1042C2×C4C2×H(5,𝔽2)12yes—
1043C2×C4C2×H(5,𝔽2)12yes—
1044C2×C4C2×2−1+414yes—
1045C2×C4C2×2−1+414yes—
1046C2×C4C2×2−1+412yes—
1047C2×C4C2×2−1+412yes—
1048C2×C4#58512yes—
1049C2×C4#58512yes—
1050C22—22no—
1051C22—22no—
1052C22—24no—
1053C22—24no—
1054C22—22no—
1055C22—24no—
1056C22—42no—
1057C22—41no—
1058C22—42no—
1059C22—41no—
1060C22—41no—
1061C22—42no—
1062C22—41no—
1063C22—42no—
1064C22C24×Q811yescharacteristic
1065C22C22×H(5,𝔽2)11yescharacteristic
1066C22C22×H(5,𝔽2)11yescharacteristic
1067C22C22×2−1+411yescharacteristic
1068C22C22×2−1+411yescharacteristic
1069C22C2×#58511yescharacteristic
1070C22C2×#58511yescharacteristic
1071C4—24no—
1072C4—24no—
1073C4—24no—
1074C4—24no—
1075C4—24no—
1076C4—22no—
1077C4—22no—
1078C4—24no—
1079C4—22no—
1080C4—24no—
1081C4—44no—
1082C4—44no—
1083C4—44no—
1084C4—48no—
1085C4—44no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4#345814yes—
1093C4#350314yes—
1094C4#350314yes—
1095C2—42no—
1096C2—44no—
1097C2C2×#345811yescharacteristic
1098C2C2×#350311yescharacteristic
1099C2C2×#350311yescharacteristic
1100C2#6301311yescharacteristic
1101C2#6301411yescharacteristic
1102C2#6303211yescharacteristic
1103C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42006C2semidirect
3. #39625C2semidirect
4. #39369C2semidirect
5. #39365C2semidirect
6. #39180C2semidirect
7. #38965C2semidirect
8. #38960C2semidirect
9. #38104C2semidirect
10. #37690C2semidirect
11. #37643C2semidirect
12. #37624C2semidirect
13. #36563C2semidirect
14. #36497C2semidirect
15. #36407C2semidirect
16. #36134C2semidirect
17. #35747C2semidirect
18. #35275C2semidirect
19. #35275C2semidirect
20. #35202C2semidirect
21. #35167C2semidirect
22. #34978C2semidirect
23. #34938C2semidirect
231. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#429312
#420062
#396252
#393692
#393652
#391802
#389652
#389602
#381042
#376902
#376432
#376242
#365632
#364972
#364072
#361342
#357472
#352752
#352022
#351672
#349782
#349382
#341882
#341292
#341272