Finite Group Databasebeta

← #7680323

Subgroups — #7680323

Order 512.

4716 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C212yesmaximal, complemented
2#59867C214yesmaximal
3#59828C212yesmaximal, complemented
4#59681C212yesmaximal, complemented
5#59681C212yesmaximal, complemented
6#59144C214yesmaximal
7#45426C214yesmaximal, complemented
8#44949C214yesmaximal, complemented
9#43552C218yesmaximal
10#39682C214yesmaximal, complemented
11#39680C214yesmaximal, complemented
12#39643C212yesmaximal, complemented
13#39641C212yesmaximal, complemented
14#36560C212yesmaximal, complemented
15#36556C212yesmaximal, complemented
16#35585C212yesmaximal
17#35543C212yesmaximal
18#35281C211yesmaximal, characteristic
19#35265C212yesmaximal
20#34953C211yesmaximal, characteristic
21C2×#2546C211yesmaximal, characteristic
22#34272C212yesmaximal
23#34216C211yesmaximal, characteristic
24#34213C211yesmaximal, characteristic
25Q8×#117C211yesmaximal, characteristic
26C4×#544C211yesmaximal, characteristic
27C2×#557C2214yes—
28C2×#544C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×C4⋊Q8C2212yes—
32C22×C4×Q8C2211yescharacteristic
33#2868C2212yes—
34#2864C2214yes—
35#2862C2212yes—
36#2859C2214yes—
37#2809C2218yes—
38#2802C2218yes—
39#2802C2218yes—
40#2799C2218yes—
41#2799C2218yes—
42#2791C2218yes—
43#2791C2218yes—
44#2755C2218yes—
45#2755C2218yes—
46#2726C2218yes—
47#2713C2218yes—
48#2713C2218yes—
49#2660C2214yes—
50#2647C2214yes—
51#2647C2214yes—
52#2590C2218yes—
53#2590C2218yes—
54#2588C2218yes—
55#2588C2218yes—
56#2584C2212yes—
57#2584C2212yes—
58#2583C2214yes—
59#2582C2214yes—
60#2571C2214yes—
61#2570C2214yes—
62#2570C2214yes—
63#2569C2218yes—
64#2568C2214yes—
65#2568C2214yes—
66#2567C2212yes—
67#2567C2211yescharacteristic
68#2567C2211yescharacteristic
69#2567C2212yes—
70#2565C2218yes—
71#2552C2214yes—
72#2550C2218yes—
73#2546C2214yes—
74#2546C2214yes—
75#2546C2214yes—
76#2546C2214yes—
77#2546C2212yes—
78#2546C2212yes—
79#2546C2212yes—
80#2546C2214yes—
81#2546C2212yes—
82#2546C2212yes—
83#2546C2211yescharacteristic
84#2546C2211yescharacteristic
85#2546C2212yes—
86#2520C2218yes—
87#2520C2218yes—
88#2511C2214yes—
89#2511C2214yes—
90#2509C2214yes—
91#2509C2214yes—
92#2509C2214yes—
93#2509C2214yes—
94#2508C2214yes—
95#2508C2214yes—
96#2508C2218yes—
97#2508C2214yes—
98#2508C2214yes—
99#2507C2214yes—
100#2507C2214yes—
101#2507C2214yes—
102#2507C2214yes—
103#2506C2214yes—
104#2506C2214yes—
105#2506C2214yes—
106#2506C2218yes—
107#2506C2214yes—
108#2505C2218yes—
109#2505C2218yes—
110#2502C2214yes—
111#2502C2212yes—
112#2473C2218yes—
113#2473C2218yes—
114#2453C2218yes—
115#2451C2218yes—
116#2446C2214yes—
117#2446C2214yes—
118#2446C2214yes—
119#2446C2214yes—
120#2442C2218yes—
121#2434C2212yes—
122#2434C2214yes—
123#2399C2214yes—
124C2×#398C2214yes—
125#2370C2214yes—
126#2370C2214yes—
127#2370C2214yes—
128#2369C2212yes—
129#2369C2212yes—
130#2369C2214yes—
131#2369C2212yes—
132#2368C2218yes—
133#2365C2214yes—
134#2365C2214yes—
135#2365C2214yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2212yes—
139#2360C2218yes—
140#2355C2211yescharacteristic
141#2355C2212yes—
142#2355C2212yes—
143#2355C2212yes—
144#2355C2211yescharacteristic
145#2355C2214yes—
146#2355C2214yes—
147Q8×C4⋊C4C2211yescharacteristic
148Q8×C4⋊C4C2212yes—
149Q8×C4⋊C4C2211yescharacteristic
150#2345C2214yes—
151#2345C2214yes—
152#2345C2212yes—
153Q8×C22⋊C4C2212yes—
154Q8×C22⋊C4C2214yes—
155#2331C2212yes—
156#2331C2214yes—
157#2331C2212yes—
158#2331C2214yes—
159#2330C2212yes—
160#2330C2214yes—
161#2330C2212yes—
162#2329C2214yes—
163#2329C2214yes—
164#2317C2212yes—
165#2317C2211yescharacteristic
166#2317C2211yescharacteristic
167#2317C2212yes—
168#2317C2212yes—
169#2316C2211yescharacteristic
170#2316C2212yes—
171C4×C4⋊Q8C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×#125C2214yes—
179C4×#125C2212yes—
180C4×#125C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2214yes—
183#2296C2212yes—
184#2296C2212yes—
185#2295C2214yes—
186#2295C2212yes—
187C2×#391C2212yes—
188C2×#389C2212yes—
189C2×#389C2212yes—
190#2285C2212yes—
191#2285C2211yescharacteristic
192#2274C2212yes—
193#2274C2212yes—
194C42×Q8C2212yes—
195C4×#117C2211yescharacteristic
196C4×#117C2211yescharacteristic
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2211yescharacteristic
199C23×Q8C2311yescharacteristic
200C23×Q8C2312yes—
201#557—416no—
202#544Q8116yescomplemented
203#533—28no—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×#125C2312yes—
222C2×#125C2318yes—
223C2×#125C2318yes—
224C2×#125C2318yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C4×Q8—28no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2318yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C42C2312yes—
261C22×C42C2312yes—
262C22×C42C2311yescharacteristic
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#395C2314yes—
298#395C2314yes—
299#395C2318yes—
300#395C2318yes—
301#395C2314yes—
302#395C2314yes—
303#391C2314yes—
304#391C2318yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2312yes—
309#391C2314yes—
310#391C2314yes—
311#391C2312yes—
312#391C2314yes—
313#391C2314yes—
314#391C2312yes—
315#391C2314yes—
316#391C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2318yes—
320#391C2314yes—
321#391C2318yes—
322#391C2314yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#389C2312yes—
331#389C2314yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2318yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2318yes—
376#389C2318yes—
377#389C2318yes—
378#389C2314yes—
379#389C2318yes—
380#389C2318yes—
381#389C2312yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#385C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2314yes—
427#385C2314yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#385C2314yes—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2314yes—
440#384C2314yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#384C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2318yes—
449#382C2318yes—
450#382C2312yes—
451#382C2314yes—
452#382C2312yes—
453#382C2318yes—
454#382C2314yes—
455#382C2312yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2312yes—
460#380C2312yes—
461#380C2314yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2318yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516#376C2312yes—
517#376C2314yes—
518#376C2312yes—
519C2×#95C2314yes—
520C2×#95C2312yes—
521C2×#95C2314yes—
522C43C2312yes—
523C43C2314yes—
524C43C2312yes—
525C22×Q8—24no—
526C22×Q8—24no—
527C22×Q8—28no—
528C22×Q8—42no—
529C22×Q8—44no—
530C22×Q8—44no—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2414yes—
534C22×Q8C2412yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2414yes—
539C23×C4C2412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C4⋊Q8—216no—
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—24no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558C4⋊Q8—48no—
559C4⋊Q8—416no—
560C4⋊Q8C2×Q8116yescomplemented
561C4⋊Q8C2×Q8116yescomplemented
562#125—28no—
563#125—416no—
564#125—416no—
565#125—416no—
566#125C2×Q8116yescomplemented
567#125C2×Q8116yescomplemented
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8C2×Q8132yes—
571C4×Q8—28no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—48no—
581C4×Q8—416no—
582C4×Q8—48no—
583C4×Q8—44no—
584C4×Q8—48no—
585C4×Q8—48no—
586#117—28no—
587#117—24no—
588#117—24no—
589#117—28no—
590#117C2×Q818yes—
591#117C2×Q818yes—
592C2×C4⋊C4—28no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—28no—
595C2×C4⋊C4—28no—
596C2×C4⋊C4—24no—
597C2×C4⋊C4—48no—
598C2×C4⋊C4—48no—
599C2×C4⋊C4C2×Q818yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C42—28no—
675C2×C42—44no—
676C2×C42#4118yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2418yes—
692C2×C42C2418yes—
693C2×C42C2414yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2418yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#95C2414yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2412yes—
716#95C2412yes—
717#95C2414yes—
718#95C2412yes—
719#95C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2414yes—
726#95C2412yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759C24C2511yescharacteristic
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—22no—
763C2×Q8—24no—
764C2×Q8—28no—
765C2×Q8—24no—
766C2×Q8—28no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—28no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—44no—
776C2×Q8—42no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—416no—
783C2×Q8—816no—
784C2×Q8C22×Q8116yes—
785C2×Q8H(5,𝔽2)14yes—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—28no—
792C22×C4—24no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—44no—
804C22×C4C22×Q818yes—
805C22×C4C22×Q814yes—
806C22×C4C2×#4114yes—
807C22×C4C2×#4114yes—
808C22×C4C2×#4114yes—
809C22×C42−1+414yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2518yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—216no—
853C4⋊C4—216no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4C22×Q818yes—
895C4⋊C4C22×Q818yes—
896C4⋊C4C22×Q814yes—
897C4⋊C4C22×Q814yes—
898C4⋊C4C22×Q814yes—
899C4⋊C4C22×Q814yes—
900C4⋊C4C22×Q8116yes—
901C4⋊C4C22×Q8116yes—
902C4⋊C4C22×Q8116yes—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4C22×Q818yes—
908C22⋊C4C22×Q818yes—
909C42—24no—
910C42—24no—
911C42—24no—
912C42—24no—
913C42—28no—
914C42—28no—
915C42—28no—
916C42—24no—
917C42—24no—
918C42—28no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—24no—
923C42—44no—
924C42—42no—
925C42—44no—
926C42—42no—
927C42—44no—
928C42—42no—
929C42—42no—
930C42—48no—
931C42—48no—
932C42—44no—
933C42—48no—
934C42—48no—
935C42C22×Q818yes—
936C42C22×Q818yes—
937C42C2×#4114yes—
938C42C2×#4114yes—
939C42C2×#4114yes—
940C42C2×#4114yes—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23C23×Q812yes—
946C23C22×#4112yes—
947C23C2×2−1+412yes—
948C23C2611yescharacteristic
949Q8—28no—
950Q8—416no—
951Q8—48no—
952Q8—48no—
953Q8—44no—
954Q8—416no—
955Q8—84no—
956Q8—88no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—24no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—28no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—48no—
1016C2×C4—44no—
1017C2×C4—48no—
1018C2×C4—48no—
1019C2×C4—84no—
1020C2×C4—88no—
1021C2×C4#557116yescomplemented
1022C2×C4C23×Q814yes—
1023C2×C4C23×Q814yes—
1024C2×C4C23×Q814yes—
1025C2×C4C23×Q814yes—
1026C2×C4C23×Q818yes—
1027C2×C4C23×Q812yes—
1028C2×C4C23×Q812yes—
1029C2×C4C22×#4112yes—
1030C2×C4C22×#4112yes—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4112yes—
1034C2×C4C22×#4112yes—
1035C2×C4C2×H(5,𝔽2)14yes—
1036C2×C4C2×H(5,𝔽2)12yes—
1037C2×C4C2×2−1+412yes—
1038C2×C4C2×2−1+412yes—
1039C2×C4#58512yes—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22C2×#55714yes—
1047C22C24×Q811yescharacteristic
1048C22C23×#4111yescharacteristic
1049C22C22×H(5,𝔽2)11yescharacteristic
1050C22C22×2−1+411yescharacteristic
1051C22C2×#58511yescharacteristic
1052C222−1+611yescharacteristic
1053C222−1+611yescharacteristic
1054C4—28no—
1055C4—24no—
1056C4—24no—
1057C4—24no—
1058C4—24no—
1059C4—22no—
1060C4—24no—
1061C4—22no—
1062C4—22no—
1063C4—42no—
1064C4—48no—
1065C4—44no—
1066C4—42no—
1067C4—42no—
1068C4—44no—
1069C4—44no—
1070C4—42no—
1071C4—42no—
1072C4—44no—
1073C4—42no—
1074C4—42no—
1075C4—44no—
1076C4C2×#55714yes—
1077C4C2×#55714yes—
1078C4#349414yes—
1079C2—24no—
1080C2C22×#55711yescharacteristic
1081C2C2×#349411yescharacteristic
1082C2#6286011yescharacteristic
1083C2#6291311yescharacteristic
1084C2#6295611yescharacteristic
1085C2Q8×H(5,𝔽2)11yescharacteristic
1086C2#6300411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59869C2semidirect
3. #59828C2semidirect
4. #59681C2semidirect
5. #59681C2semidirect
7. #45426C2semidirect
8. #44949C2semidirect
10. #39682C2semidirect
11. #39680C2semidirect
12. #39643C2semidirect
13. #39641C2semidirect
14. #36560C2semidirect
15. #36556C2semidirect
202. #544Q8semidirect
560. C4⋊Q8C2×Q8semidirect
561. C4⋊Q8C2×Q8semidirect
566. #125C2×Q8semidirect
567. #125C2×Q8semidirect
1021. C2×C4#557semidirect

Maximal subgroups

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

subgroupindex
#598692
#598672
#598282
#596812
#591442
#454262
#449492
#435522
#396822
#396802
#396432
#396412
#365602
#365562
#355852
#355432
#352812
#352652
#349532
C2×#25462
#342722
#342162
#342132
Q8×#1172
C4×#5442