Finite Group Databasebeta

← #7680745

Subgroups — #7680745

Order 512.

5298 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C212yesmaximal, complemented
2#59823C212yesmaximal, complemented
3#59666C212yesmaximal, complemented
4#59457C212yesmaximal, complemented
5#59455C214yesmaximal, complemented
6#59155C214yesmaximal, complemented
7#45434C214yesmaximal, complemented
8#44966C214yesmaximal, complemented
9#43555C218yesmaximal, complemented
10#38966C212yesmaximal, complemented
11#38965C212yesmaximal, complemented
12#38104C214yesmaximal, complemented
13#38099C214yesmaximal, complemented
14#36407C212yesmaximal, complemented
15#36261C212yesmaximal, complemented
16#35532C212yesmaximal, complemented
17#35519C212yesmaximal, complemented
18#35286C211yesmaximal, characteristic, complemented
19#35280C212yesmaximal, complemented
20#34938C211yesmaximal, characteristic, complemented
21C2×#2552C211yesmaximal, characteristic, complemented
22#34250C212yesmaximal, complemented
23#34207C211yesmaximal, characteristic
24#34206C211yesmaximal, characteristic
25#34141C211yesmaximal, characteristic
26C4×#544C211yesmaximal, characteristic, complemented
27C2×#554C2214yes—
28C2×#544C2211yescharacteristic
29C2×#533C2212yes—
30C2×#532C2211yescharacteristic
31C22×#125C2212yes—
32C2×#520C2212yes—
33C2×#520C2212yes—
34C2×C4×#41C2212yes—
35#2859C2212yes—
36#2859C2212yes—
37#2857C2214yes—
38#2857C2214yes—
39#2806C2218yes—
40#2802C2218yes—
41#2790C2218yes—
42#2788C2218yes—
43#2780C2218yes—
44#2768C2218yes—
45#2768C2218yes—
46#2768C2218yes—
47#2732C2218yes—
48#2720C2218yes—
49#2704C2218yes—
50#2704C2218yes—
51#2647C2214yes—
52#2629C2214yes—
53#2629C2214yes—
54#2587C2218yes—
55#2584C2214yes—
56#2584C2214yes—
57#2583C2218yes—
58#2582C2214yes—
59#2582C2214yes—
60#2582C2214yes—
61#2581C2214yes—
62#2580C2214yes—
63#2574C2218yes—
64#2571C2212yes—
65#2571C2212yes—
66#2567C2214yes—
67#2566C2214yes—
68#2566C2214yes—
69#2565C2214yes—
70#2556C2218yes—
71#2556C2218yes—
72#2552C2212yes—
73#2552C2214yes—
74#2552C2211yescharacteristic
75#2552C2212yes—
76#2552C2211yescharacteristic
77#2552C2212yes—
78#2552C2212yes—
79#2552C2214yes—
80#2552C2214yes—
81#2552C2212yes—
82#2552C2212yes—
83#2551C2211yescharacteristic
84#2551C2211yescharacteristic
85#2550C2214yes—
86#2550C2212yes—
87#2550C2212yes—
88#2549C2214yes—
89#2549C2218yes—
90#2549C2218yes—
91#2542C2214yes—
92#2538C2214yes—
93#2538C2214yes—
94#2538C2214yes—
95#2538C2214yes—
96#2520C2218yes—
97#2508C2214yes—
98#2507C2214yes—
99#2507C2218yes—
100#2473C2218yes—
101#2454C2214yes—
102#2454C2214yes—
103#2454C2214yes—
104#2452C2214yes—
105#2450C2218yes—
106#2450C2218yes—
107#2449C2218yes—
108#2449C2218yes—
109#2449C2218yes—
110#2442C2214yes—
111#2442C2214yes—
112#2442C2214yes—
113#2441C2214yes—
114#2441C2214yes—
115#2441C2214yes—
116#2440C2212yes—
117#2440C2214yes—
118#2440C2212yes—
119#2440C2214yes—
120#2440C2214yes—
121#2439C2214yes—
122#2417C2218yes—
123#2417C2218yes—
124#2417C2218yes—
125#2399C2214yes—
126C2×#398C2214yes—
127#2370C2214yes—
128#2369C2214yes—
129#2367C2212yes—
130#2367C2212yes—
131#2367C2214yes—
132#2366C2211yescharacteristic
133#2366C2212yes—
134#2366C2211yescharacteristic
135#2365C2211yescharacteristic
136#2365C2212yes—
137#2365C2211yescharacteristic
138#2364C2214yes—
139#2361C2212yes—
140#2361C2214yes—
141#2361C2214yes—
142#2361C2212yes—
143#2354C2212yes—
144#2354C2212yes—
145#2354C2212yes—
146#2352C2214yes—
147#2351C2214yes—
148Q8×C4⋊C4C2214yes—
149#2349C2218yes—
150#2349C2214yes—
151#2349C2214yes—
152D4×C4⋊C4C2218yes—
153D4×C4⋊C4C2212yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2214yes—
157#2331C2212yes—
158#2331C2212yes—
159#2330C2212yes—
160#2330C2212yes—
161#2329C2214yes—
162#2326C2214yes—
163#2325C2214yes—
164#2317C2211yescharacteristic
165#2317C2211yescharacteristic
166#2317C2214yes—
167#2317C2212yes—
168#2316C2211yescharacteristic
169#2316C2214yes—
170#2316C2212yes—
171#2311C2212yes—
172#2311C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×#127C2212yes—
179C4×#125C2212yes—
180C4×#125C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×#121C2214yes—
183#2297C2212yes—
184#2296C2214yes—
185#2296C2212yes—
186#2293C2212yes—
187C2×#389C2212yes—
188C2×#389C2212yes—
189C2×#389C2214yes—
190#2290C2214yes—
191#2285C2211yescharacteristic
192C2×#384C2211yescharacteristic
193C2×#384C2212yes—
194C42×D4C2212yes—
195C4×#117C2211yescharacteristic
196C4×#117C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2312yes—
200#554—416no—
201#544—28no—
202#533—48no—
203#532Q8116yescomplemented
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#125—48no—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2318yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233#520—216no—
234#520—48no—
235C4×#41—48no—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×#117C2311yescharacteristic
259C2×#117C2312yes—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2314yes—
263C2×#117C2314yes—
264C2×#117C2314yes—
265C2×#117C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2318yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2314yes—
279C22×C42C2312yes—
280C22×C42C2314yes—
281C22×C42C2312yes—
282C22×C42C2311yescharacteristic
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2314yes—
318#395C2318yes—
319#395C2314yes—
320#395C2314yes—
321#395C2314yes—
322#393C2318yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2318yes—
332#391C2318yes—
333#391C2318yes—
334#391C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2312yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2318yes—
389#389C2314yes—
390#389C2318yes—
391#389C2312yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2314yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2314yes—
429#385C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2314yes—
448#384C2314yes—
449#384C2314yes—
450#384C2312yes—
451#384C2318yes—
452#384C2314yes—
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2311yescharacteristic
456#384C2312yes—
457#384C2314yes—
458#382C2312yes—
459#382C2312yes—
460#382C2314yes—
461#382C2314yes—
462#382C2314yes—
463#382C2318yes—
464#382C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2312yes—
475#380C2318yes—
476#380C2318yes—
477#380C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2318yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519#376C2312yes—
520#376C2312yes—
521C2×#95C2312yes—
522C2×#95C2318yes—
523C2×#95C2314yes—
524C2×#95C2312yes—
525C43C2312yes—
526C43C2312yes—
527C2×#41—28no—
528C2×#41—28no—
529C2×#41C2×Q8116yes—
530C22×Q8C2412yes—
531C22×Q8C2414yes—
532C22×Q8C2414yes—
533C22×Q8C2414yes—
534C22×D4C2412yes—
535C22×D4C2414yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2418yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2418yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C4⋊Q8—28no—
552C4⋊Q8—28no—
553C4⋊Q8—28no—
554C4⋊Q8—28no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557C4⋊Q8C2×Q818yes—
558#127C2×Q818yes—
559#125—28no—
560#125—216no—
561#125—28no—
562#125—48no—
563#125—44no—
564#125—44no—
565#125—48no—
566#125—416no—
567#125—84no—
568#124C2×Q8116yes—
569C22⋊Q8—216no—
570C22⋊Q8—48no—
571C22⋊Q8—48no—
572C22⋊Q8—416no—
573C22⋊Q8—416no—
574C22⋊Q8—416no—
575C22⋊Q8—88no—
576C22⋊Q8—88no—
577#121C2×Q8116yes—
578#121C2×Q8116yes—
579C4×Q8—216no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×Q8—48no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—232no—
589C4×D4—216no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—48no—
595C4×D4—48no—
596C4×D4—48no—
597C4×D4—416no—
598C4×D4—84no—
599C4×D4C2×Q8116yes—
600C4×D4C2×Q8116yes—
601#117—24no—
602#117—24no—
603#117—28no—
604#117—24no—
605#117—216no—
606#117—48no—
607#117—48no—
608#117#4118yes—
609C2×C4⋊C4—28no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—216no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—48no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4—416no—
620C2×C4⋊C4—82no—
621C2×C4⋊C4—84no—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C42—28no—
707C2×C42—48no—
708C2×C42—44no—
709C2×C42C2×Q818yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2418yes—
725C2×C42C2412yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2412yes—
729C2×C42C2414yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2418yes—
747#95C2418yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2418yes—
777C24C2514yes—
778C24C2511yescharacteristic
779#41—264no—
780C2×Q8—24no—
781C2×Q8—28no—
782C2×Q8—24no—
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8C22×Q818yes—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C22×Q818yes—
801C2×D4C22×Q8116yes—
802C2×D4C22×Q818yes—
803C2×D4C22×Q818yes—
804C22×C4—28no—
805C22×C4—22no—
806C22×C4—28no—
807C22×C4—22no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—28no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—216no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—41no—
819C22×C4—42no—
820C22×C4—41no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—42no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—42no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4C22×Q814yes—
838C22×C4C22×Q8116yes—
839C22×C4C22×Q814yes—
840C22×C4C22×Q814yes—
841C22×C4C2×#4114yes—
842C22×C4H(5,𝔽2)14yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2518yes—
855C22×C4C2512yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C4⋊C4—28no—
868C4⋊C4—216no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—216no—
884C4⋊C4—28no—
885C4⋊C4—216no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—42no—
926C4⋊C4C22×Q818yes—
927C4⋊C4C22×Q818yes—
928C4⋊C4C2×#4114yes—
929C4⋊C4C2×#4114yes—
930C4⋊C4H(5,𝔽2)14yes—
931C4⋊C42−1+414yes—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—24no—
936C22⋊C4—216no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4C22×Q8116yes—
949C22⋊C4C22×Q8116yes—
950C22⋊C4C2×#4118yes—
951C42—216no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—28no—
959C42—28no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—44no—
966C42—44no—
967C42—44no—
968C42—42no—
969C42—42no—
970C42—48no—
971C42—42no—
972C42—42no—
973C42C22×Q814yes—
974C42C22×Q814yes—
975C42C22×Q814yes—
976C42C22×Q814yes—
977C42C2×#4118yes—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23C23×Q818yes—
989C23C23×Q812yes—
990C23C22×#4112yes—
991C23C2×H(5,𝔽2)12yes—
992C23C2611yescharacteristic
993Q8—216no—
994Q8—88no—
995Q8—88no—
996Q8—88no—
997D4—232no—
998D4—216no—
999D4—216no—
1000D4—48no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—232no—
1018C2×C4—28no—
1019C2×C4—22no—
1020C2×C4—28no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—28no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—28no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—816no—
1062C2×C4—88no—
1063C2×C4—88no—
1064C2×C4—88no—
1065C2×C4—84no—
1066C2×C4—84no—
1067C2×C4—168no—
1068C2×C4#554116yescomplemented
1069C2×C4C23×Q812yes—
1070C2×C4C23×Q812yes—
1071C2×C4C23×Q812yes—
1072C2×C4C23×Q818yes—
1073C2×C4C23×Q812yes—
1074C2×C4C23×Q812yes—
1075C2×C4C23×Q812yes—
1076C2×C4C22×#4114yes—
1077C2×C4C22×#4114yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C2×H(5,𝔽2)14yes—
1081C2×C4C2×H(5,𝔽2)12yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×2−1+414yes—
1085C2×C4C2×2−1+412yes—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—28no—
1093C22—28no—
1094C22—28no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22C2×#55414yes—
1100C22C24×Q811yescharacteristic
1101C22C23×#4111yescharacteristic
1102C22C22×H(5,𝔽2)11yescharacteristic
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C22×2−1+411yescharacteristic
1105C22H(7,𝔽2)11yescharacteristic
1106C222−1+611yescharacteristic
1107C4—24no—
1108C4—24no—
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—24no—
1113C4—24no—
1114C4—28no—
1115C4—48no—
1116C4—44no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—44no—
1122C4—44no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—44no—
1127C4—42no—
1128C4C2×#55414yes—
1129C4C2×#55414yes—
1130C4#350314yes—
1131C2—24no—
1132C2—48no—
1133C2C22×#55411yescharacteristic
1134C2C2×#350311yescharacteristic
1135C2#6285411yescharacteristic
1136C2#6291411yescharacteristic
1137C2#6294411yescharacteristic
1138C2#6298611yescharacteristic
1139C2#6300111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59823C2semidirect
3. #59666C2semidirect
4. #59457C2semidirect
5. #59455C2semidirect
6. #59155C2semidirect
7. #45434C2semidirect
8. #44966C2semidirect
9. #43555C2semidirect
10. #38966C2semidirect
11. #38965C2semidirect
12. #38104C2semidirect
13. #38099C2semidirect
14. #36407C2semidirect
15. #36261C2semidirect
16. #35532C2semidirect
17. #35519C2semidirect
18. #35286C2semidirect
19. #35280C2semidirect
20. #34938C2semidirect
21. C2×#2552C2semidirect
22. #34250C2semidirect
26. C4×#544C2semidirect
203. #532Q8semidirect
1068. C2×C4#554semidirect

Maximal subgroups

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

subgroupindex
#598712
#598232
#596662
#594572
#594552
#591552
#454342
#449662
#435552
#389662
#389652
#381042
#380992
#364072
#362612
#355322
#355192
#352862
#352802
#349382
C2×#25522
#342502
#342072
#342062
#341412
C4×#5442