Finite Group Databasebeta

← #7712049

Subgroups — #7712049

Order 512.

4912 conjugacy classes of subgroups.

The subgroup lattice has 1231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59681C212yesmaximal, complemented
2#59642C212yesmaximal, complemented
3#59459C212yesmaximal, complemented
4#59413C212yesmaximal, complemented
5#45503C214yesmaximal, complemented
6#45501C214yesmaximal, complemented
7#39663C214yesmaximal, complemented
8#39662C214yesmaximal, complemented
9#39626C212yesmaximal, complemented
10#39609C212yesmaximal, complemented
11#39606C212yesmaximal
12#39599C212yesmaximal, complemented
13#39596C212yesmaximal
14#39498C212yesmaximal, complemented
15#37878C214yesmaximal, complemented
16#37624C212yesmaximal, complemented
17#37313C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19#36645C211yesmaximal, characteristic, complemented
20#36598C211yesmaximal, characteristic, complemented
21#36593C211yesmaximal, characteristic, complemented
22#36134C211yesmaximal, characteristic, complemented
23#36134C212yesmaximal, complemented
24#36129C212yesmaximal, complemented
25D4×C4⋊Q8C211yesmaximal, characteristic, complemented
26#35283C212yesmaximal, complemented
27#35281C212yesmaximal, complemented
28#34383C212yesmaximal
29C4×#529C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×D4×Q8C2212yes—
32C2×#533C2212yes—
33C2×#533C2212yes—
34C2×#533C2212yes—
35C22×C4⋊Q8C2212yes—
36C2×#529C2211yescharacteristic
37#2868C2211yescharacteristic
38#2868C2211yescharacteristic
39#2868C2211yescharacteristic
40#2868C2211yescharacteristic
41#2868C2212yes—
42#2862C2212yes—
43#2862C2212yes—
44#2862C2212yes—
45#2859C2212yes—
46#2859C2212yes—
47#2859C2212yes—
48#2859C2212yes—
49#2857C2212yes—
50#2857C2211yescharacteristic
51#2857C2212yes—
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2857C2212yes—
57#2857C2212yes—
58#2857C2212yes—
59#2857C2212yes—
60#2841C2218yes—
61#2807C2218yes—
62#2807C2218yes—
63#2806C2218yes—
64#2802C2218yes—
65#2792C2218yes—
66#2792C2218yes—
67#2788C2218yes—
68#2774C2218yes—
69#2768C2218yes—
70#2748C2218yes—
71#2742C2218yes—
72#2726C2218yes—
73#2720C2218yes—
74#2704C2218yes—
75#2704C2218yes—
76#2692C2218yes—
77#2666C2218yes—
78#2660C2214yes—
79#2660C2214yes—
80#2647C2214yes—
81#2629C2214yes—
82#2628C2214yes—
83#2628C2214yes—
84#2590C2218yes—
85#2589C2218yes—
86#2586C2218yes—
87#2584C2214yes—
88#2582C2212yes—
89#2582C2214yes—
90#2580C2214yes—
91#2571C2212yes—
92#2570C2214yes—
93#2570C2214yes—
94#2568C2212yes—
95#2567C2214yes—
96#2567C2214yes—
97#2567C2214yes—
98#2556C2218yes—
99#2552C2214yes—
100#2552C2212yes—
101#2552C2212yes—
102#2552C2212yes—
103#2552C2214yes—
104#2552C2214yes—
105#2551C2212yes—
106#2551C2212yes—
107#2550C2214yes—
108#2550C2214yes—
109#2546C2212yes—
110#2546C2212yes—
111#2546C2214yes—
112#2546C2214yes—
113#2546C2214yes—
114#2542C2214yes—
115#2542C2212yes—
116#2538C2212yes—
117#2538C2214yes—
118#2511C2214yes—
119#2511C2214yes—
120#2511C2214yes—
121#2509C2214yes—
122#2507C2214yes—
123#2502C2214yes—
124#2502C2214yes—
125#2492C2214yes—
126#2492C2214yes—
127#2492C2214yes—
128#2454C2214yes—
129#2451C2214yes—
130#2451C2214yes—
131#2451C2214yes—
132#2451C2214yes—
133#2446C2214yes—
134#2446C2214yes—
135#2442C2214yes—
136#2441C2214yes—
137#2441C2214yes—
138#2441C2214yes—
139#2440C2214yes—
140#2440C2214yes—
141#2439C2214yes—
142#2434C2214yes—
143#2434C2214yes—
144#2434C2214yes—
145#2429C2214yes—
146#2429C2214yes—
147#2429C2214yes—
148#2429C2214yes—
149#2423C2214yes—
150#2423C2214yes—
151#2423C2214yes—
152#2423C2214yes—
153#2423C2214yes—
154#2417C2214yes—
155#2409C2214yes—
156#2376C2218yes—
157#2370C2214yes—
158#2367C2214yes—
159#2365C2214yes—
160#2365C2212yes—
161#2365C2212yes—
162#2360C2214yes—
163#2355C2212yes—
164#2355C2212yes—
165#2354C2212yes—
166#2354C2214yes—
167#2352C2214yes—
168Q8×C4⋊C4C2212yes—
169Q8×C4⋊C4C2214yes—
170Q8×C4⋊C4C2212yes—
171Q8×C4⋊C4C2212yes—
172D4×C4⋊C4C2212yes—
173D4×C4⋊C4C2212yes—
174Q8×C22⋊C4C2214yes—
175#2334C2218yes—
176#2331C2214yes—
177#2324C2214yes—
178#2323C2214yes—
179#2317C2214yes—
180#2317C2214yes—
181#2314C2214yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2212yes—
186C4×C4⋊Q8C2211yescharacteristic
187C4×C4⋊Q8C2212yes—
188C4×C4⋊Q8C2212yes—
189C4×C4⋊Q8C2212yes—
190C4×C4⋊Q8C2212yes—
191C4×C4⋊Q8C2212yes—
192C4×C4⋊Q8C2212yes—
193C4×#125C2211yescharacteristic
194C4×#125C2211yescharacteristic
195C4×#126C2212yes—
196C4×#126C2212yes—
197C4×#124C2211yescharacteristic
198C4×#124C2211yescharacteristic
199C4×C22⋊Q8C2211yescharacteristic
200C4×C22⋊Q8C2211yescharacteristic
201C4×#123C2212yes—
202C4×#123C2212yes—
203C4×#121C2211yescharacteristic
204C4×#121C2211yescharacteristic
205#2298C2212yes—
206#2295C2211yescharacteristic
207#2293C2211yescharacteristic
208#2290C2212yes—
209#2285C2212yes—
210#2285C2212yes—
211#2285C2212yes—
212#2285C2212yes—
213#2283C2211yescharacteristic
214C42×Q8C2211yescharacteristic
215C42×D4C2211yescharacteristic
216C42×D4C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C23×Q8C2314yes—
220#557—48no—
221D4×Q8—48no—
222#533—48no—
223#533—48no—
224#533—48no—
225C2×C4⋊Q8—48no—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2314yes—
245#529Q8116yescomplemented
246C2×#126C2312yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×#125C2318yes—
252C2×#125C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#123C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2318yes—
265C2×C22⋊Q8C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×#117C2312yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C2×#117C2312yes—
292C22×C4⋊C4C2314yes—
293C22×C4⋊C4C2314yes—
294C22×C42C2312yes—
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302#400C2318yes—
303#400C2318yes—
304#400C2318yes—
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#399C2318yes—
309#399C2318yes—
310#399C2318yes—
311#399C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2318yes—
320#398C2318yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2318yes—
335#395C2318yes—
336#395C2318yes—
337#395C2318yes—
338#395C2318yes—
339#395C2318yes—
340#393C2318yes—
341#393C2318yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2312yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2318yes—
356#391C2314yes—
357#391C2314yes—
358#391C2311yescharacteristic
359#391C2318yes—
360#391C2314yes—
361#391C2318yes—
362#391C2318yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2311yescharacteristic
367#390C2314yes—
368#390C2318yes—
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2314yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2318yes—
400#389C2318yes—
401#389C2318yes—
402#389C2318yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2318yes—
410#389C2318yes—
411#389C2318yes—
412#389C2314yes—
413#389C2314yes—
414#389C2318yes—
415#389C2318yes—
416#389C2318yes—
417#389C2314yes—
418#389C2314yes—
419#389C2318yes—
420#388C2312yes—
421#388C2312yes—
422#388C2312yes—
423#388C2312yes—
424#388C2312yes—
425#388C2312yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2312yes—
433#388C2312yes—
434#387C2312yes—
435#387C2312yes—
436#387C2312yes—
437#387C2312yes—
438#387C2312yes—
439#387C2312yes—
440#387C2312yes—
441#387C2312yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#386C2318yes—
455#386C2312yes—
456#386C2312yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2312yes—
465#385C2312yes—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2312yes—
469#384C2312yes—
470#384C2312yes—
471#384C2312yes—
472#384C2312yes—
473#384C2312yes—
474#384C2312yes—
475#384C2312yes—
476#384C2314yes—
477#384C2314yes—
478#384C2318yes—
479#384C2312yes—
480#384C2312yes—
481#384C2314yes—
482#384C2312yes—
483#384C2312yes—
484#384C2314yes—
485#384C2314yes—
486#384C2312yes—
487#384C2312yes—
488#384C2312yes—
489#383C2312yes—
490#382C2311yescharacteristic
491#382C2311yescharacteristic
492#382C2314yes—
493#382C2314yes—
494#382C2314yes—
495#382C2314yes—
496#382C2314yes—
497#382C2314yes—
498#382C2314yes—
499#381C2312yes—
500#380C2314yes—
501#380C2314yes—
502#380C2314yes—
503#380C2314yes—
504#380C2314yes—
505#380C2314yes—
506#380C2318yes—
507#380C2312yes—
508#380C2312yes—
509#380C2312yes—
510#380C2312yes—
511#380C2314yes—
512#380C2314yes—
513#380C2314yes—
514#380C2314yes—
515#380C2311yescharacteristic
516#380C2311yescharacteristic
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2311yescharacteristic
525C4×C4⋊C4C2311yescharacteristic
526C4×C4⋊C4C2311yescharacteristic
527C4×C4⋊C4C2311yescharacteristic
528C4×C4⋊C4C2312yes—
529C4×C4⋊C4C2312yes—
530C4×C4⋊C4C2314yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2311yescharacteristic
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2318yes—
548C4×C4⋊C4C2311yescharacteristic
549C4×C4⋊C4C2312yes—
550C4×C22⋊C4C2312yes—
551C4×C22⋊C4C2312yes—
552C4×C22⋊C4C2312yes—
553C4×C22⋊C4C2312yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2318yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2312yes—
562C4×C22⋊C4C2312yes—
563C4×C22⋊C4C2312yes—
564#376C2312yes—
565#376C2312yes—
566C43C2311yescharacteristic
567C43C2311yescharacteristic
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2312yes—
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2311yescharacteristic
575C22×Q8—48no—
576C22×Q8—48no—
577C22×Q8—48no—
578C22×Q8C2412yes—
579C22×Q8C2414yes—
580C22×Q8C2414yes—
581C22×Q8C2412yes—
582C22×Q8C2411yescharacteristic
583C22×Q8C2414yes—
584C22×Q8C2418yes—
585C22×D4C2411yescharacteristic
586C22×D4C2412yes—
587C23×C4C2412yes—
588C23×C4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2418yes—
597C23×C4C2411yescharacteristic
598C4⋊Q8—24no—
599C4⋊Q8—28no—
600C4⋊Q8—28no—
601C4⋊Q8—24no—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—48no—
606C4⋊Q8—48no—
607C4⋊Q8—44no—
608C4⋊Q8—44no—
609C4⋊Q8—48no—
610C4⋊Q8—48no—
611C4⋊Q8—44no—
612C4⋊Q8—44no—
613C4⋊Q8—44no—
614C4⋊Q8—48no—
615C4⋊Q8—44no—
616C4⋊Q8—48no—
617#126C2×Q8116yescomplemented
618#125—48no—
619#125—48no—
620#125—48no—
621#125—48no—
622#125—416no—
623#125C2×Q818yescomplemented
624#124C2×Q818yes—
625#123C2×Q8116yescomplemented
626C22⋊Q8—416no—
627C22⋊Q8—48no—
628C22⋊Q8—48no—
629C22⋊Q8—48no—
630C22⋊Q8—44no—
631C22⋊Q8—44no—
632C22⋊Q8—48no—
633C22⋊Q8—48no—
634C22⋊Q8—48no—
635C22⋊Q8—48no—
636C22⋊Q8C2×Q818yescomplemented
637#121C2×Q818yes—
638C4×Q8—28no—
639C4×Q8—28no—
640C4×Q8—24no—
641C4×Q8—24no—
642C4×Q8—48no—
643C4×Q8—48no—
644C4×Q8—48no—
645C4×Q8—48no—
646C4×Q8—48no—
647C4×Q8—48no—
648C4×Q8—48no—
649C4×Q8—48no—
650C4×Q8C2×Q818yescomplemented
651C4×D4—24no—
652C4×D4—24no—
653C4×D4—48no—
654C4×D4—44no—
655C4×D4—44no—
656C4×D4C2×Q818yes—
657C4×D4C2×Q8116yescomplemented
658#117—28no—
659#117—48no—
660#117—48no—
661#117—48no—
662#117C2×Q8116yescomplemented
663C2×C4⋊C4—48no—
664C2×C4⋊C4—48no—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2418yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2418yes—
710C2×C4⋊C4C2418yes—
711C2×C4⋊C4C2418yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2412yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2412yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2412yes—
747C2×C42—28no—
748C2×C42—24no—
749C2×C42—24no—
750C2×C42—24no—
751C2×C42—24no—
752C2×C42—42no—
753C2×C42—42no—
754C2×C42C2×Q818yescomplemented
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2412yes—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2412yes—
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2418yes—
782C2×C42C2418yes—
783C2×C42C2418yes—
784C2×C42C2418yes—
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2412yes—
791C2×C42C2411yescharacteristic
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798#95C2412yes—
799#95C2412yes—
800#95C2412yes—
801#95C2412yes—
802#95C2412yes—
803#95C2412yes—
804#95C2412yes—
805#95C2412yes—
806#95C2414yes—
807#95C2412yes—
808#95C2412yes—
809#95C2412yes—
810#95C2412yes—
811#95C2412yes—
812#95C2412yes—
813#95C2412yes—
814#95C2412yes—
815#95C2412yes—
816#95C2418yes—
817#95C2414yes—
818#95C2412yes—
819#95C2412yes—
820#95C2412yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2418yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2418yes—
840#95C2418yes—
841#95C2418yes—
842C24C2512yes—
843C24C2511yescharacteristic
844C2×Q8—22no—
845C2×Q8—24no—
846C2×Q8—24no—
847C2×Q8—24no—
848C2×Q8—28no—
849C2×Q8—28no—
850C2×Q8—28no—
851C2×Q8—24no—
852C2×Q8—22no—
853C2×Q8—28no—
854C2×Q8—28no—
855C2×Q8—28no—
856C2×Q8—24no—
857C2×Q8—28no—
858C2×Q8—24no—
859C2×Q8—44no—
860C2×Q8—48no—
861C2×Q8—48no—
862C2×Q8—44no—
863C2×Q8—48no—
864C2×Q8—832no—
865C2×Q8C22×Q814yes—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4C22×Q814yes—
871C2×D4C22×Q818yes—
872C22×C4—24no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—24no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4C22×Q814yes—
902C22×C4C22×Q814yes—
903C22×C4C22×Q818yes—
904C22×C4C22×Q814yes—
905C22×C4C2512yes—
906C22×C4C2511yescharacteristic
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2518yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2514yes—
913C22×C4C2512yes—
914C22×C4C2518yes—
915C22×C4C2511yescharacteristic
916C22×C4C2514yes—
917C22×C4C2511yescharacteristic
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—28no—
940C4⋊C4—24no—
941C4⋊C4—28no—
942C4⋊C4—24no—
943C4⋊C4—28no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—28no—
947C4⋊C4—24no—
948C4⋊C4—28no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—22no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—28no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—48no—
962C4⋊C4—48no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—48no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—48no—
974C4⋊C4—44no—
975C4⋊C4—48no—
976C4⋊C4—48no—
977C4⋊C4—48no—
978C4⋊C4—48no—
979C4⋊C4—48no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—48no—
988C4⋊C4—48no—
989C4⋊C4C22×Q818yes—
990C4⋊C4C22×Q818yes—
991C4⋊C4C22×Q814yes—
992C4⋊C4C22×Q818yes—
993C4⋊C4C22×Q814yes—
994C4⋊C4C22×Q818yes—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—24no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—48no—
1008C22⋊C4—48no—
1009C22⋊C4C22×Q818yes—
1010C22⋊C4C22×Q818yes—
1011C22⋊C4C22×Q818yes—
1012C22⋊C4C22×Q818yes—
1013C22⋊C4C22×Q818yes—
1014C42—22no—
1015C42—22no—
1016C42—22no—
1017C42—24no—
1018C42—24no—
1019C42—22no—
1020C42—22no—
1021C42—24no—
1022C42—22no—
1023C42—28no—
1024C42—28no—
1025C42—24no—
1026C42—22no—
1027C42—22no—
1028C42—22no—
1029C42—22no—
1030C42—22no—
1031C42—22no—
1032C42—24no—
1033C42—24no—
1034C42—22no—
1035C42—22no—
1036C42—22no—
1037C42—22no—
1038C42—24no—
1039C42—24no—
1040C42—41no—
1041C42—41no—
1042C42—41no—
1043C42—41no—
1044C42—48no—
1045C42—48no—
1046C42—48no—
1047C42—48no—
1048C42C22×Q814yes—
1049C42C22×Q814yes—
1050C42C22×Q814yes—
1051C42C22×Q814yes—
1052C42C22×Q818yes—
1053C42H(5,𝔽2)14yes—
1054C42H(5,𝔽2)14yes—
1055C422−1+414yes—
1056C422−1+414yes—
1057C23—22no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—21no—
1064C23—21no—
1065C23—22no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23C23×Q814yes—
1070C23C23×Q812yes—
1071C23C2611yescharacteristic
1072Q8—28no—
1073Q8—48no—
1074Q8—416no—
1075Q8—48no—
1076Q8—416no—
1077Q8—88no—
1078Q8—816no—
1079D4—28no—
1080D4—48no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—216no—
1104C2×C4—28no—
1105C2×C4—28no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—28no—
1117C2×C4—24no—
1118C2×C4—28no—
1119C2×C4—28no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—28no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—24no—
1135C2×C4—28no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—28no—
1141C2×C4—24no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—48no—
1147C2×C4—48no—
1148C2×C4—44no—
1149C2×C4—816no—
1150C2×C4C23×Q812yes—
1151C2×C4C23×Q812yes—
1152C2×C4C23×Q812yes—
1153C2×C4C23×Q812yes—
1154C2×C4C23×Q814yes—
1155C2×C4C23×Q814yes—
1156C2×C4C23×Q814yes—
1157C2×C4C23×Q812yes—
1158C2×C4C23×Q812yes—
1159C2×C4C2×H(5,𝔽2)12yes—
1160C2×C4C2×H(5,𝔽2)12yes—
1161C2×C4C2×H(5,𝔽2)12yes—
1162C2×C4C2×H(5,𝔽2)12yes—
1163C2×C4C2×H(5,𝔽2)12yes—
1164C2×C4C2×H(5,𝔽2)12yes—
1165C2×C4C2×2−1+412yes—
1166C2×C4C2×2−1+412yes—
1167C2×C4C2×2−1+412yes—
1168C2×C4C2×2−1+412yes—
1169C2×C4C2×2−1+412yes—
1170C2×C4C2×2−1+412yes—
1171C2×C4#58512yes—
1172C2×C4#58512yes—
1173C22—22no—
1174C22—22no—
1175C22—24no—
1176C22—24no—
1177C22—22no—
1178C22—24no—
1179C22—41no—
1180C22—42no—
1181C22—42no—
1182C22—41no—
1183C22—41no—
1184C22—42no—
1185C22—41no—
1186C22—42no—
1187C22C24×Q811yescharacteristic
1188C22C22×H(5,𝔽2)11yescharacteristic
1189C22C22×H(5,𝔽2)11yescharacteristic
1190C22C22×2−1+411yescharacteristic
1191C22C22×2−1+411yescharacteristic
1192C22C2×#58511yescharacteristic
1193C22C2×#58511yescharacteristic
1194C4—22no—
1195C4—24no—
1196C4—22no—
1197C4—24no—
1198C4—22no—
1199C4—22no—
1200C4—24no—
1201C4—22no—
1202C4—22no—
1203C4—22no—
1204C4—22no—
1205C4—41no—
1206C4—42no—
1207C4—48no—
1208C4—41no—
1209C4—42no—
1210C4—44no—
1211C4—48no—
1212C4—44no—
1213C4—42no—
1214C4—44no—
1215C4—44no—
1216C4—42no—
1217C4#350314yes—
1218C4#350314yes—
1219C4#354614yes—
1220C4#355414yes—
1221C2—42no—
1222C2—44no—
1223C2C2×#355411yescharacteristic
1224C2C2×#354611yescharacteristic
1225C2C2×#350311yescharacteristic
1226C2C2×#350311yescharacteristic
1227C2#6281311yescharacteristic
1228C2#6283511yescharacteristic
1229C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59681C2semidirect
2. #59642C2semidirect
3. #59459C2semidirect
4. #59413C2semidirect
5. #45503C2semidirect
6. #45501C2semidirect
7. #39663C2semidirect
8. #39662C2semidirect
9. #39626C2semidirect
10. #39609C2semidirect
12. #39599C2semidirect
14. #39498C2semidirect
15. #37878C2semidirect
16. #37624C2semidirect
17. #37313C2semidirect
18. #36645C2semidirect
19. #36645C2semidirect
20. #36598C2semidirect
21. #36593C2semidirect
22. #36134C2semidirect
23. #36134C2semidirect
24. #36129C2semidirect
25. D4×C4⋊Q8C2semidirect
26. #35283C2semidirect
27. #35281C2semidirect
245. #529Q8semidirect
617. #126C2×Q8semidirect
623. #125C2×Q8semidirect
625. #123C2×Q8semidirect
636. C22⋊Q8C2×Q8semidirect
650. C4×Q8C2×Q8semidirect
657. C4×D4C2×Q8semidirect
662. #117C2×Q8semidirect
754. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#596812
#596422
#594592
#594132
#455032
#455012
#396632
#396622
#396262
#396092
#396062
#395992
#395962
#394982
#378782
#376242
#373132
#366452
#365982
#365932
#361342
#361292
D4×C4⋊Q82
#352832
#352812
#343832
C4×#5292