Finite Group Databasebeta

← #7687974

Subgroups — #7687974

Order 512.

5053 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59902C214yesmaximal, complemented
2#59870C212yesmaximal, complemented
3#59821C211yesmaximal, characteristic, complemented
4#59768C214yesmaximal, complemented
5#59678C212yesmaximal, complemented
6#59227C212yesmaximal, complemented
7#45155C214yesmaximal, complemented
8#43302C218yesmaximal, complemented
9#40034C214yesmaximal, complemented
10#39771C212yesmaximal, complemented
11#39244C214yesmaximal, complemented
12#39167C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36594C211yesmaximal, characteristic, complemented
15#36579C212yesmaximal, complemented
16#36454C212yesmaximal, complemented
17#36419C212yesmaximal
18#36405C212yesmaximal, complemented
19#36188C211yesmaximal, characteristic, complemented
20#35869C214yesmaximal, complemented
21#34952C212yesmaximal, complemented
22#34951C211yesmaximal, characteristic, complemented
23#34324C212yesmaximal, complemented
24#34324C212yesmaximal, complemented
25C4×D4×Q8C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic
27C2×#556C2212yes—
28C2×#556C2212yes—
29C2×#556C2212yes—
30C2×#550C2211yescharacteristic
31C2×D4×Q8C2211yescharacteristic
32C2×C4×#41C2212yes—
33C22×C4×Q8C2212yes—
34#2868C2211yescharacteristic
35#2862C2212yes—
36#2858C2212yes—
37#2857C2212yes—
38#2855C2214yes—
39#2850C2214yes—
40#2805C2218yes—
41#2796C2218yes—
42#2796C2218yes—
43#2786C2218yes—
44#2782C2218yes—
45#2781C2218yes—
46#2751C2218yes—
47#2750C2218yes—
48#2727C2214yes—
49#2723C2218yes—
50#2723C2218yes—
51#2650C2218yes—
52#2640C2214yes—
53#2597C2218yes—
54#2596C2218yes—
55#2595C2218yes—
56#2592C2214yes—
57#2585C2214yes—
58#2582C2212yes—
59#2582C2211yescharacteristic
60#2581C2214yes—
61#2581C2214yes—
62#2580C2214yes—
63#2579C2218yes—
64#2575C2218yes—
65#2574C2218yes—
66#2571C2214yes—
67#2571C2212yes—
68#2570C2214yes—
69#2568C2212yes—
70#2568C2212yes—
71#2568C2211yescharacteristic
72#2567C2214yes—
73#2562C2214yes—
74#2559C2218yes—
75#2559C2218yes—
76#2552C2211yescharacteristic
77#2548C2212yes—
78#2547C2212yes—
79#2547C2212yes—
80#2547C2212yes—
81#2546C2211yescharacteristic
82#2545C2214yes—
83#2544C2214yes—
84#2544C2214yes—
85#2542C2212yes—
86#2538C2212yes—
87#2538C2212yes—
88#2538C2212yes—
89#2530C2218yes—
90#2529C2218yes—
91#2517C2218yes—
92#2513C2214yes—
93#2512C2214yes—
94#2512C2214yes—
95#2512C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2511C2212yes—
99#2511C2214yes—
100#2509C2218yes—
101#2509C2212yes—
102#2500C2214yes—
103#2499C2214yes—
104#2496C2214yes—
105#2496C2214yes—
106#2489C2214yes—
107#2487C2214yes—
108#2485C2214yes—
109#2481C2218yes—
110#2478C2218yes—
111#2469C2218yes—
112#2468C2218yes—
113#2453C2212yes—
114#2448C2214yes—
115#2448C2214yes—
116#2447C2214yes—
117#2447C2214yes—
118#2446C2214yes—
119#2446C2212yes—
120#2432C2214yes—
121#2421C2214yes—
122#2415C2214yes—
123#2415C2214yes—
124#2415C2214yes—
125#2409C2214yes—
126#2409C2214yes—
127#2402C2214yes—
128#2396C2218yes—
129#2373C2218yes—
130#2373C2218yes—
131#2367C2214yes—
132#2367C2214yes—
133#2367C2214yes—
134#2366C2211yescharacteristic
135#2366C2212yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2212yes—
139#2365C2212yes—
140#2365C2214yes—
141#2365C2211yescharacteristic
142#2363C2214yes—
143#2363C2212yes—
144#2362C2214yes—
145#2362C2214yes—
146#2360C2214yes—
147#2360C2212yes—
148#2355C2214yes—
149#2355C2214yes—
150#2355C2212yes—
151#2355C2212yes—
152#2354C2211yescharacteristic
153#2354C2212yes—
154#2354C2212yes—
155#2354C2212yes—
156#2354C2212yes—
157#2352C2214yes—
158Q8×C4⋊C4C2211yescharacteristic
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162D4×C4⋊C4C2212yes—
163#2346C2214yes—
164#2346C2214yes—
165#2341C2212yes—
166Q8×C22⋊C4C2212yes—
167#2334C2218yes—
168#2334C2218yes—
169#2326C2214yes—
170#2326C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×#127C2212yes—
178C4×#127C2211yescharacteristic
179C4×#125C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2214yes—
185C4×#121C2214yes—
186C4×#121C2212yes—
187#2297C2214yes—
188#2296C2214yes—
189#2296C2214yes—
190#2295C2212yes—
191#2295C2212yes—
192#2285C2212yes—
193#2276C2214yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2212yes—
198C42×D4C2211yescharacteristic
199C22×#41C2312yes—
200C23×Q8C2312yes—
201#556—216no—
202#556—216no—
203#556—48no—
204#550—28no—
205D4×Q8—28no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×#127C2311yescharacteristic
214C2×#127C2312yes—
215C2×#126C2318yes—
216C2×#126C2318yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#124C2314yes—
220C2×#124C2314yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C4×#41—48no—
232C2×C4×Q8—48no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2312yes—
271C22×C42C2312yes—
272C22×C42C2314yes—
273C22×C42C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#399C2318yes—
286#399C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#395C2318yes—
305#395C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#393C2318yes—
312#393C2318yes—
313#391C2312yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2312yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2318yes—
366#389C2318yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2312yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#385C2314yes—
438#385C2318yes—
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2312yes—
444#384C2311yescharacteristic
445#384C2314yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#384C2312yes—
450#382C2312yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2318yes—
456#382C2318yes—
457#381C2318yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2318yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2318yes—
521#376C2314yes—
522#376C2318yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—44no—
529C22×Q8—28no—
530C22×Q8—44no—
531C22×Q8—44no—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×Q8C2412yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×Q8C2414yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2411yescharacteristic
542C22×D4C2414yes—
543C22×D4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2414yes—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—28no—
557C4⋊Q8—24no—
558C4⋊Q8—44no—
559#127—28no—
560#127—24no—
561#126—232no—
562#126—232no—
563#126—416no—
564#125—44no—
565#124—216no—
566#124—216no—
567#124—48no—
568#124—48no—
569C22⋊Q8—216no—
570C22⋊Q8—216no—
571C22⋊Q8—28no—
572C22⋊Q8—216no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575#121—28no—
576#121—216no—
577C4×Q8—24no—
578C4×Q8—216no—
579C4×Q8—24no—
580C4×Q8—216no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—42no—
590C4×Q8—48no—
591C4×Q8—44no—
592C4×Q8—48no—
593C4×Q8#4118yescomplemented
594C4×D4—28no—
595C4×D4—24no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—28no—
599C4×D4—44no—
600C4×D4—44no—
601C4×D4—42no—
602C4×D4—44no—
603C4×D4—44no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4#4118yes—
608#117—216no—
609#117—216no—
610#117—48no—
611#117—44no—
612#117—48no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2412yes—
693C2×C42—28no—
694C2×C42—48no—
695C2×C42—48no—
696C2×C42C2412yes—
697C2×C42C2418yes—
698C2×C42C2418yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2412yes—
709C2×C42C2414yes—
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2418yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2418yes—
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2412yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770C24C2514yes—
771C24C2512yes—
772#41—432no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—28no—
776C2×Q8—28no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—432no—
790C2×Q8C2×#4114yes—
791C2×Q82−1+414yes—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—22no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—28no—
801C2×D4—24no—
802C2×D4—22no—
803C2×D4—24no—
804C2×D4—44no—
805C2×D4—42no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—44no—
809C2×D4C2×#4114yes—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—42no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4C2×#4118yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2511yescharacteristic
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2518yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2512yes—
851C22×C4C2511yescharacteristic
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2512yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—216no—
867C4⋊C4—216no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—22no—
889C4⋊C4—24no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—42no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—42no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4C2×#4114yes—
910C4⋊C4C2×#4114yes—
911C4⋊C4C2×#4118yes—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—216no—
920C22⋊C4—28no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—42no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4C2×#4118yes—
936C42—216no—
937C42—216no—
938C42—24no—
939C42—28no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—28no—
946C42—24no—
947C42—22no—
948C42—24no—
949C42—22no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—22no—
954C42—44no—
955C42—44no—
956C42—44no—
957C42—44no—
958C42—41no—
959C42—42no—
960C42—42no—
961C42—48no—
962C42—42no—
963C42—48no—
964C42C2×#4114yes—
965C42C2×#4118yes—
966C42C2×#4114yes—
967C42H(5,𝔽2)14yes—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23C22×#4114yes—
982C23C2611yescharacteristic
983Q8—28no—
984Q8—28no—
985Q8—416no—
986Q8—416no—
987Q8—48no—
988Q8—48no—
989D4—28no—
990D4—416no—
991D4—48no—
992D4—48no—
993D4—84no—
994D4—88no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—216no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—28no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—416no—
1053C2×C4—416no—
1054C2×C4—416no—
1055C2×C4—48no—
1056C2×C4—84no—
1057C2×C4—88no—
1058C2×C4—88no—
1059C2×C4C22×#4114yes—
1060C2×C4C22×#4114yes—
1061C2×C4C22×#4112yes—
1062C2×C4C22×#4114yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×2−1+414yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4#58512yes—
1074C2×C4#58512yes—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22C23×#4111yescharacteristic
1090C22C23×#4111yescharacteristic
1091C22C22×H(5,𝔽2)11yescharacteristic
1092C22C22×2−1+411yescharacteristic
1093C22C2×#58511yescharacteristic
1094C22C2×#58511yescharacteristic
1095C222−1+611yescharacteristic
1096C4—22no—
1097C4—22no—
1098C4—24no—
1099C4—24no—
1100C4—24no—
1101C4—24no—
1102C4—22no—
1103C4—44no—
1104C4—42no—
1105C4—44no—
1106C4—42no—
1107C4—44no—
1108C4—44no—
1109C4—42no—
1110C4—42no—
1111C4—41no—
1112C4—44no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—48no—
1117C4#348014yes—
1118C4#350614yes—
1119C4#352014yes—
1120C2—44no—
1121C2—84no—
1122C2C2×#348011yescharacteristic
1123C2C2×#350611yescharacteristic
1124C2C2×#352011yescharacteristic
1125C2#6296011yescharacteristic
1126C2#6299511yescharacteristic
1127C2#6300111yescharacteristic
1128C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59902C2semidirect
2. #59870C2semidirect
3. #59821C2semidirect
4. #59768C2semidirect
5. #59678C2semidirect
6. #59227C2semidirect
7. #45155C2semidirect
8. #43302C2semidirect
9. #40034C2semidirect
10. #39771C2semidirect
11. #39244C2semidirect
12. #39167C2semidirect
13. #36598C2semidirect
14. #36594C2semidirect
15. #36579C2semidirect
16. #36454C2semidirect
18. #36405C2semidirect
19. #36188C2semidirect
20. #35869C2semidirect
21. #34952C2semidirect
22. #34951C2semidirect
23. #34324C2semidirect
24. #34324C2semidirect
25. C4×D4×Q8C2semidirect
593. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599022
#598702
#598212
#597682
#596782
#592272
#451552
#433022
#400342
#397712
#392442
#391672
#365982
#365942
#365792
#364542
#364192
#364052
#361882
#358692
#349522
#349512
#343242
C4×D4×Q82
C4×#5502