Finite Group Databasebeta

← #7677591

Subgroups — #7677591

Order 512.

5120 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59681C212yesmaximal, complemented
2#59679C212yesmaximal, complemented
3#59646C212yesmaximal, complemented
4#59434C212yesmaximal, complemented
5#59219C212yesmaximal, complemented
6#59218C212yesmaximal, complemented
7#59214C212yesmaximal, complemented
8#59211C212yesmaximal, complemented
9#45262C214yesmaximal, complemented
10#45156C214yesmaximal, complemented
11#44969C214yesmaximal, complemented
12#44926C214yesmaximal, complemented
13#39815C218yesmaximal, complemented
14#39732C214yesmaximal, complemented
15#36588C214yesmaximal, complemented
16#35545C212yesmaximal, complemented
17#35517C212yesmaximal, complemented
18#35178C212yesmaximal, complemented
19#35178C211yesmaximal, characteristic, complemented
20#34948C211yesmaximal, characteristic, complemented
21#34937C211yesmaximal, characteristic
22#34266C212yesmaximal, complemented
23#34207C211yesmaximal, characteristic, complemented
24#34188C211yesmaximal, characteristic, complemented
25C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
26C4×#536C211yesmaximal, characteristic, complemented
27C2×#536C2211yescharacteristic
28C2×#536C2212yes—
29C2×#532C2211yescharacteristic
30C2×#532C2212yes—
31C2×#520C2212yes—
32C2×C4×#41C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×Q8C2212yes—
35#2854C2214yes—
36#2854C2218yes—
37#2803C2218yes—
38#2802C2218yes—
39#2800C2218yes—
40#2795C2218yes—
41#2793C2218yes—
42#2790C2218yes—
43#2783C2218yes—
44#2780C2218yes—
45#2779C2218yes—
46#2777C2218yes—
47#2765C2218yes—
48#2718C2218yes—
49#2618C2218yes—
50#2618C2214yes—
51#2602C2218yes—
52#2601C2218yes—
53#2595C2218yes—
54#2594C2218yes—
55#2594C2218yes—
56#2593C2218yes—
57#2590C2218yes—
58#2587C2218yes—
59#2573C2218yes—
60#2571C2211yescharacteristic
61#2571C2211yescharacteristic
62#2570C2214yes—
63#2570C2212yes—
64#2570C2212yes—
65#2569C2214yes—
66#2566C2214yes—
67#2552C2211yescharacteristic
68#2552C2211yescharacteristic
69#2548C2211yescharacteristic
70#2548C2212yes—
71#2548C2214yes—
72#2547C2211yescharacteristic
73#2546C2211yescharacteristic
74#2546C2212yes—
75#2546C2214yes—
76#2545C2214yes—
77#2545C2214yes—
78#2545C2212yes—
79#2545C2214yes—
80#2544C2212yes—
81#2543C2214yes—
82#2541C2211yescharacteristic
83#2538C2212yes—
84#2538C2214yes—
85#2538C2212yes—
86#2538C2214yes—
87#2536C2214yes—
88#2536C2214yes—
89#2536C2214yes—
90#2525C2218yes—
91#2514C2214yes—
92#2513C2214yes—
93#2513C2214yes—
94#2512C2214yes—
95#2512C2214yes—
96#2511C2214yes—
97#2510C2218yes—
98#2509C2214yes—
99#2507C2214yes—
100#2500C2214yes—
101#2497C2214yes—
102#2497C2214yes—
103#2496C2214yes—
104#2495C2214yes—
105#2494C2214yes—
106#2494C2214yes—
107#2490C2214yes—
108#2487C2214yes—
109#2486C2214yes—
110#2485C2214yes—
111#2485C2214yes—
112#2481C2218yes—
113#2470C2218yes—
114#2466C2218yes—
115#2448C2214yes—
116#2447C2214yes—
117#2446C2214yes—
118#2445C2214yes—
119#2444C2218yes—
120#2443C2218yes—
121#2442C2212yes—
122#2442C2212yes—
123#2441C2214yes—
124#2422C2214yes—
125#2416C2212yes—
126#2416C2212yes—
127#2402C2214yes—
128#2392C2214yes—
129#2370C2214yes—
130#2367C2214yes—
131#2367C2214yes—
132#2365C2214yes—
133#2365C2214yes—
134#2363C2214yes—
135#2362C2214yes—
136#2362C2214yes—
137#2361C2214yes—
138#2361C2214yes—
139#2360C2214yes—
140#2360C2214yes—
141#2357C2214yes—
142#2355C2212yes—
143#2355C2212yes—
144#2354C2212yes—
145#2354C2212yes—
146#2354C2212yes—
147#2354C2212yes—
148#2352C2214yes—
149#2352C2214yes—
150Q8×C4⋊C4C2212yes—
151Q8×C4⋊C4C2212yes—
152Q8×C4⋊C4C2212yes—
153Q8×C4⋊C4C2212yes—
154Q8×C4⋊C4C2214yes—
155Q8×C4⋊C4C2214yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158#2347C2214yes—
159#2327C2212yes—
160#2326C2212yes—
161#2326C2214yes—
162#2323C2212yes—
163#2323C2212yes—
164#2322C2214yes—
165#2322C2218yes—
166#2317C2211yescharacteristic
167#2314C2214yes—
168#2311C2211yescharacteristic
169#2311C2212yes—
170#2311C2212yes—
171#2311C2212yes—
172#2310C2211yescharacteristic
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×#127C2212yes—
176C4×#125C2212yes—
177C4×#125C2212yes—
178C4×#124C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×#123C2214yes—
182C4×#123C2218yes—
183C4×#121C2212yes—
184C4×#121C2212yes—
185#2297C2212yes—
186#2296C2212yes—
187C2×#389C2214yes—
188C2×#389C2212yes—
189#2285C2212yes—
190#2285C2212yes—
191#2285C2211yescharacteristic
192#2285C2212yes—
193C2×#384C2212yes—
194C2×#384C2211yescharacteristic
195#2274C2212yes—
196C4×#117C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C23×Q8C2311yescharacteristic
202#536—28no—
203#536—216no—
204#532—28no—
205#532—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×#127C2311yescharacteristic
211C2×#127C2312yes—
212C2×#126C2318yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2314yes—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#123C2314yes—
221C2×#123C2318yes—
222C2×#123C2318yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2312yes—
233#520—48no—
234C4×#41—28no—
235C2×C4×Q8—28no—
236C2×C4×Q8—48no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2318yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2314yes—
282C22×C42C2311yescharacteristic
283#401C2318yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#399C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#398C2314yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2314yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2314yes—
324#394C2314yes—
325#394C2318yes—
326#392C2314yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2314yes—
342#390C2312yes—
343#390C2314yes—
344#390C2314yes—
345#390C2318yes—
346#390C2318yes—
347#390C2314yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2318yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#386C2314yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2314yes—
430#386C2318yes—
431#386C2314yes—
432#386C2314yes—
433#386C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#385C2318yes—
443#385C2318yes—
444#384C2312yes—
445#384C2312yes—
446#384C2314yes—
447#384C2312yes—
448#384C2314yes—
449#384C2312yes—
450#384C2312yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2312yes—
454#384C2312yes—
455#384C2318yes—
456#383C2318yes—
457#382C2312yes—
458#382C2312yes—
459#382C2314yes—
460#382C2312yes—
461#382C2312yes—
462#382C2312yes—
463#382C2312yes—
464#382C2314yes—
465#381C2314yes—
466#381C2318yes—
467#380C2314yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2314yes—
482#380C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2318yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2318yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2314yes—
523#376C2312yes—
524C2×#95C2312yes—
525C2×#95C2314yes—
526C43C2312yes—
527C2×#41—24no—
528C2×#41—28no—
529C2×#41—24no—
530C2×#41—28no—
531C2×#41—28no—
532C2×#41—24no—
533C22×Q8—24no—
534C22×Q8—24no—
535C22×Q8#4118yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2414yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2412yes—
546C22×D4C2414yes—
547C22×D4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2411yescharacteristic
553C23×C4C2412yes—
554C23×C4C2414yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2418yes—
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C4⋊Q8—28no—
562C4⋊Q8—216no—
563C4⋊Q8—24no—
564C4⋊Q8—44no—
565#127—24no—
566#127—44no—
567#126—88no—
568#125—28no—
569#125—44no—
570#124—28no—
571#124—216no—
572#124—28no—
573#124—44no—
574#124—44no—
575#123—216no—
576#123—232no—
577#123—88no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—216no—
581C22⋊Q8—216no—
582#121—28no—
583#121—28no—
584#121—28no—
585#121—44no—
586#121—48no—
587#121—48no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8—24no—
593C4×Q8—24no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×Q8—48no—
598C4×Q8—48no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—28no—
604C4×D4—28no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—416no—
610C4×D4—84no—
611#117—24no—
612#117—24no—
613#117—28no—
614#117—24no—
615#117—28no—
616#117—48no—
617#117—48no—
618#117—84no—
619C2×C4⋊C4—28no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—28no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—42no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4—48no—
627C2×C4⋊C4—82no—
628C2×C4⋊C4—84no—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C42—28no—
712C2×C42—28no—
713C2×C42—28no—
714C2×C42—48no—
715C2×C42#4118yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2412yes—
730C2×C42C2418yes—
731C2×C42C2418yes—
732C2×C42C2418yes—
733C2×C42C2412yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736C2×C42C2412yes—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741#95C2418yes—
742#95C2412yes—
743#95C2412yes—
744#95C2418yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2418yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781C24C2512yes—
782C24C2514yes—
783C24C2511yescharacteristic
784#41—416no—
785#41—432no—
786C2×Q8—232no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—22no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—22no—
797C2×Q8C2×#4118yes—
798C2×Q8C2×#4118yes—
799C2×D4—24no—
800C2×D4—28no—
801C2×D4—24no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—24no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—22no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—28no—
815C2×D4—24no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—44no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—28no—
835C22×C4—28no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—41no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—41no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—44no—
850C22×C4—42no—
851C22×C4—44no—
852C22×C4—42no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4C2×#4114yes—
857C22×C4C2×#4118yes—
858C22×C4C2×#4114yes—
859C22×C4C2×#4114yes—
860C22×C4C2×#4114yes—
861C22×C4H(5,𝔽2)14yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2514yes—
870C22×C4C2512yes—
871C22×C4C2514yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2512yes—
875C22×C4C2518yes—
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2514yes—
881C22×C4C2512yes—
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—216no—
901C4⋊C4—28no—
902C4⋊C4—216no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—24no—
908C4⋊C4—22no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—28no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—24no—
916C4⋊C4—44no—
917C4⋊C4—42no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—42no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—42no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C42−1+414yes—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—28no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—216no—
948C22⋊C4—28no—
949C22⋊C4—216no—
950C22⋊C4—28no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—28no—
971C42—28no—
972C42—24no—
973C42—28no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—24no—
981C42—48no—
982C42—48no—
983C42—42no—
984C42—48no—
985C42—48no—
986C42—48no—
987C42—42no—
988C42C2×#4114yes—
989C42C2×#4114yes—
990C42C2×#4114yes—
991C42C2×#4114yes—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23—22no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23C22×#4112yes—
1011C23C22×#4112yes—
1012C23C2×H(5,𝔽2)12yes—
1013C23C2611yescharacteristic
1014Q8—216no—
1015Q8—216no—
1016Q8—44no—
1017Q8—48no—
1018D4—48no—
1019D4—48no—
1020D4—416no—
1021D4—44no—
1022D4—48no—
1023D4—48no—
1024D4—88no—
1025D4—88no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—216no—
1037C2×C4—28no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—28no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—44no—
1084C2×C4—48no—
1085C2×C4—48no—
1086C2×C4—48no—
1087C2×C4—48no—
1088C2×C4—416no—
1089C2×C4—48no—
1090C2×C4—84no—
1091C2×C4—88no—
1092C2×C4—168no—
1093C2×C4#553116yes—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4112yes—
1096C2×C4C22×#4112yes—
1097C2×C4C22×#4118yes—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4112yes—
1101C2×C4C22×#4112yes—
1102C2×C4C22×#4112yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4C2×2−1+414yes—
1106C2×C4C2×2−1+412yes—
1107C2×C4#58512yes—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—44no—
1115C22—42no—
1116C22—42no—
1117C22—44no—
1118C22—42no—
1119C22—44no—
1120C22—42no—
1121C22—44no—
1122C22—42no—
1123C22—44no—
1124C22—44no—
1125C22—42no—
1126C22—42no—
1127C22—44no—
1128C22C2×#55314yes—
1129C22C23×#4111yescharacteristic
1130C22C23×#4111yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C22×2−1+411yescharacteristic
1133C22C2×#58511yescharacteristic
1134C22H(7,𝔽2)11yescharacteristic
1135C222−1+611yescharacteristic
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—24no—
1140C4—28no—
1141C4—42no—
1142C4—44no—
1143C4—42no—
1144C4—44no—
1145C4—42no—
1146C4—42no—
1147C4—44no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—48no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—44no—
1156C4C2×#55314yes—
1157C4C2×#55314yes—
1158C4#350714yes—
1159C2—24no—
1160C2—82no—
1161C2—84no—
1162C2C22×#55311yescharacteristic
1163C2C2×#350711yescharacteristic
1164C2#6284511yescharacteristic
1165C2#6294211yescharacteristic
1166C2#6295511yescharacteristic
1167C2#6299911yescharacteristic
1168C2#6300711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
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. #59679C2semidirect
3. #59646C2semidirect
4. #59434C2semidirect
5. #59219C2semidirect
6. #59218C2semidirect
7. #59214C2semidirect
8. #59211C2semidirect
9. #45262C2semidirect
10. #45156C2semidirect
11. #44969C2semidirect
12. #44926C2semidirect
13. #39815C2semidirect
14. #39732C2semidirect
15. #36588C2semidirect
16. #35545C2semidirect
17. #35517C2semidirect
18. #35178C2semidirect
19. #35178C2semidirect
20. #34948C2semidirect
22. #34266C2semidirect
23. #34207C2semidirect
24. #34188C2semidirect
25. C2×Q8×C4⋊C4C2semidirect
26. C4×#536C2semidirect

Maximal subgroups

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

subgroupindex
#596812
#596792
#596462
#594342
#592192
#592182
#592142
#592112
#452622
#451562
#449692
#449262
#398152
#397322
#365882
#355452
#355172
#351782
#349482
#349372
#342662
#342072
#341882
C2×Q8×C4⋊C42
C4×#5362