Finite Group Databasebeta

← #7986783

Subgroups — #7986783

Order 512.

4939 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59668C212yesmaximal, complemented
3#59305C212yesmaximal, complemented
4#59136C212yesmaximal, complemented
5#51605C218yesmaximal, complemented
6#46005C214yesmaximal, complemented
7#45359C214yesmaximal, complemented
8#44879C214yesmaximal, complemented
9#42972C214yesmaximal, complemented
10#42972C214yesmaximal, complemented
11#39633C214yesmaximal, complemented
12#39606C212yesmaximal, complemented
13#39598C212yesmaximal, complemented
14#39370C212yesmaximal, complemented
15#38966C212yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17#36288C212yesmaximal, complemented
18#36287C212yesmaximal, complemented
19#36180C211yesmaximal, characteristic, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35281C212yesmaximal, complemented
22#35275C212yesmaximal, complemented
23#34941C211yesmaximal, characteristic, complemented
24#34929C211yesmaximal, characteristic, complemented
25#34485C212yesmaximal
26C4×#555C211yesmaximal, characteristic
27C2×#555C2211yescharacteristic
28C2×#554C2212yes—
29C2×D4×Q8C2212yes—
30C2×#544C2214yes—
31C2×#533C2212yes—
32C22×C4⋊Q8C2212yes—
33#2868C2211yescharacteristic
34#2868C2214yes—
35#2862C2214yes—
36#2859C2212yes—
37#2859C2214yes—
38#2857C2212yes—
39#2857C2212yes—
40#2845C2218yes—
41#2806C2218yes—
42#2806C2214yes—
43#2790C2218yes—
44#2790C2218yes—
45#2790C2218yes—
46#2768C2218yes—
47#2768C2218yes—
48#2768C2218yes—
49#2748C2218yes—
50#2732C2218yes—
51#2729C2218yes—
52#2729C2218yes—
53#2729C2218yes—
54#2704C2218yes—
55#2704C2218yes—
56#2704C2218yes—
57#2683C2218yes—
58#2660C2218yes—
59#2660C2218yes—
60#2647C2218yes—
61#2629C2214yes—
62#2629C2214yes—
63#2612C2218yes—
64#2612C2218yes—
65#2584C2214yes—
66#2584C2214yes—
67#2582C2212yes—
68#2582C2214yes—
69#2579C2218yes—
70#2574C2218yes—
71#2574C2214yes—
72#2567C2212yes—
73#2567C2212yes—
74#2567C2211yescharacteristic
75#2567C2212yes—
76#2566C2214yes—
77#2563C2211yescharacteristic
78#2556C2218yes—
79#2556C2214yes—
80#2552C2212yes—
81#2552C2212yes—
82#2552C2214yes—
83#2552C2212yes—
84#2552C2211yescharacteristic
85#2552C2212yes—
86#2552C2212yes—
87#2551C2212yes—
88#2551C2214yes—
89#2551C2212yes—
90#2551C2211yescharacteristic
91#2550C2214yes—
92#2550C2214yes—
93#2546C2214yes—
94#2546C2212yes—
95#2546C2211yescharacteristic
96#2546C2214yes—
97#2542C2211yescharacteristic
98#2538C2214yes—
99#2538C2211yescharacteristic
100#2538C2211yescharacteristic
101#2538C2214yes—
102#2508C2214yes—
103#2508C2212yes—
104#2507C2214yes—
105#2507C2214yes—
106#2507C2214yes—
107#2507C2214yes—
108#2506C2212yes—
109#2506C2214yes—
110#2502C2214yes—
111#2502C2214yes—
112#2502C2214yes—
113#2497C2212yes—
114#2497C2214yes—
115#2492C2214yes—
116#2492C2212yes—
117#2454C2212yes—
118#2454C2214yes—
119#2452C2214yes—
120#2452C2218yes—
121#2452C2212yes—
122#2451C2218yes—
123#2451C2214yes—
124#2442C2214yes—
125#2442C2214yes—
126#2441C2214yes—
127#2440C2214yes—
128#2440C2214yes—
129#2440C2214yes—
130#2440C2218yes—
131#2440C2214yes—
132#2440C2214yes—
133#2440C2214yes—
134#2439C2214yes—
135#2434C2214yes—
136#2434C2218yes—
137#2429C2212yes—
138#2429C2214yes—
139#2423C2212yes—
140#2423C2214yes—
141#2417C2214yes—
142#2417C2214yes—
143#2409C2218yes—
144#2396C2214yes—
145#2396C2214yes—
146#2379C2218yes—
147#2372C2214yes—
148#2370C2214yes—
149#2369C2212yes—
150#2369C2211yescharacteristic
151#2369C2214yes—
152#2369C2212yes—
153#2365C2212yes—
154#2363C2212yes—
155#2363C2212yes—
156#2361C2214yes—
157#2361C2214yes—
158#2355C2212yes—
159#2354C2211yescharacteristic
160#2354C2211yescharacteristic
161Q8×C4⋊C4C2212yes—
162Q8×C4⋊C4C2212yes—
163D4×C4⋊C4C2214yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168#2346C2212yes—
169#2346C2212yes—
170#2346C2214yes—
171#2346C2214yes—
172#2326C2218yes—
173#2324C2214yes—
174#2324C2214yes—
175#2317C2214yes—
176#2317C2214yes—
177#2317C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#125C2212yes—
184C4×#124C2214yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2295C2214yes—
190#2293C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193C2×#384C2212yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199C23×Q8C2314yes—
200#555Q8116yescomplemented
201#554—48no—
202D4×Q8—48no—
203#544—416no—
204#533—48no—
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2318yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2318yes—
220C2×C4⋊Q8C2311yescharacteristic
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#125C2314yes—
227C2×#124C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2318yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273#400C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#399C2314yes—
278#399C2314yes—
279#399C2318yes—
280#398C2314yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2314yes—
305#396C2318yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#396C2314yes—
312#395C2314yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2314yes—
319#395C2318yes—
320#395C2318yes—
321#393C2314yes—
322#393C2318yes—
323#393C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2318yes—
334#391C2318yes—
335#391C2314yes—
336#391C2318yes—
337#391C2318yes—
338#391C2318yes—
339#391C2314yes—
340#391C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2318yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2314yes—
352#389C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2314yes—
380#389C2318yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2314yes—
389#389C2318yes—
390#389C2314yes—
391#389C2318yes—
392#389C2314yes—
393#389C2318yes—
394#389C2318yes—
395#389C2312yes—
396#388C2318yes—
397#388C2314yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2318yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#386C2314yes—
421#386C2318yes—
422#386C2318yes—
423#386C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2312yes—
442#384C2311yescharacteristic
443#384C2314yes—
444#384C2314yes—
445#384C2314yes—
446#384C2314yes—
447#384C2312yes—
448#384C2318yes—
449#384C2318yes—
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2314yes—
455#384C2314yes—
456#382C2312yes—
457#382C2314yes—
458#382C2318yes—
459#382C2318yes—
460#382C2318yes—
461#382C2314yes—
462#382C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2318yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2318yes—
475#380C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519#376C2318yes—
520#376C2314yes—
521#376C2314yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C43C2314yes—
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8—84no—
528C22×Q8C2412yes—
529C22×Q8C2411yescharacteristic
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×Q8C2414yes—
533C22×Q8C2418yes—
534C22×Q8C2412yes—
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2414yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2418yes—
545C23×C4C2418yes—
546C4⋊Q8—28no—
547C4⋊Q8—216no—
548C4⋊Q8—24no—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—48no—
552C4⋊Q8—48no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557C4⋊Q8—416no—
558C4⋊Q8—82no—
559C4⋊Q8—88no—
560C4⋊Q8C2×Q818yescomplemented
561#125—28no—
562#125—48no—
563#125—416no—
564#125—48no—
565#125—48no—
566#125—48no—
567#124C2×Q8132yescomplemented
568C22⋊Q8—416no—
569C22⋊Q8—416no—
570C22⋊Q8—416no—
571C22⋊Q8—416no—
572C22⋊Q8—48no—
573C22⋊Q8—48no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—48no—
579#121C2×Q8116yes—
580#121C2×Q8116yescomplemented
581C4×Q8—24no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—44no—
585C4×Q8—48no—
586C4×Q8—44no—
587C4×Q8—48no—
588C4×Q8—42no—
589C4×Q8—84no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—48no—
595C4×D4—48no—
596C4×D4—48no—
597C4×D4—88no—
598C4×D4C2×Q818yes—
599C4×D4C2×Q818yescomplemented
600#117—28no—
601#117—28no—
602#117—48no—
603#117—48no—
604#117C2×Q8116yescomplemented
605#117C2×Q8116yescomplemented
606C2×C4⋊C4—48no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—48no—
609C2×C4⋊C4—48no—
610C2×C4⋊C4—84no—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C42—28no—
698C2×C42—28no—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2418yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2418yes—
721C2×C42C2411yescharacteristic
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#95C2412yes—
728#95C2412yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2412yes—
746#95C2412yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767C24C2512yes—
768C24C2512yes—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—28no—
773C2×Q8—216no—
774C2×Q8—28no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—22no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—48no—
786C2×Q8—44no—
787C2×Q8—48no—
788C2×Q8—44no—
789C2×Q8—832no—
790C2×Q8C22×Q818yes—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4C22×Q814yes—
798C2×D4C22×Q814yes—
799C2×D4C22×Q8116yes—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4C22×Q818yes—
823C22×C4C22×Q818yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2518yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2511yescharacteristic
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2512yes—
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—216no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—22no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—42no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—42no—
888C4⋊C4—48no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4C22×Q814yes—
907C4⋊C4C22×Q814yes—
908C4⋊C4C22×Q818yes—
909C4⋊C4C22×Q818yes—
910C4⋊C4H(5,𝔽2)14yes—
911C4⋊C42−1+414yes—
912C22⋊C4—28no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4C22×Q8116yes—
931C22⋊C4C22×Q8116yes—
932C22⋊C4C22×Q818yes—
933C22⋊C4C22×Q818yes—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—28no—
938C42—24no—
939C42—24no—
940C42—28no—
941C42—28no—
942C42—22no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—28no—
947C42—22no—
948C42—24no—
949C42—24no—
950C42—28no—
951C42—22no—
952C42—48no—
953C42—48no—
954C42—42no—
955C42—42no—
956C42—44no—
957C42—41no—
958C42C22×Q8116yes—
959C42C22×Q814yes—
960C42H(5,𝔽2)14yes—
961C422−1+414yes—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23C23×Q814yes—
975C23C23×Q814yes—
976C23C2611yescharacteristic
977Q8—48no—
978Q8—48no—
979Q8—48no—
980Q8—44no—
981Q8—88no—
982Q8—88no—
983Q8—816no—
984D4—28no—
985D4—28no—
986D4—416no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—216no—
1004C2×C4—216no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—28no—
1018C2×C4—28no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—48no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—816no—
1049C2×C4—168no—
1050C2×C4C23×Q814yes—
1051C2×C4C23×Q814yes—
1052C2×C4C23×Q812yes—
1053C2×C4C23×Q818yes—
1054C2×C4C23×Q812yes—
1055C2×C4C23×Q812yes—
1056C2×C4C2×H(5,𝔽2)12yes—
1057C2×C4C2×H(5,𝔽2)14yes—
1058C2×C4C2×H(5,𝔽2)12yes—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×2−1+412yes—
1062C2×C4C2×2−1+414yes—
1063C2×C4C2×2−1+412yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4C2×2−1+412yes—
1066C2×C4#58512yes—
1067C22—24no—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—24no—
1072C22—24no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22C24×Q811yescharacteristic
1082C22C22×H(5,𝔽2)11yescharacteristic
1083C22C22×H(5,𝔽2)11yescharacteristic
1084C22C22×2−1+411yescharacteristic
1085C22C22×2−1+411yescharacteristic
1086C22C2×#58511yescharacteristic
1087C22H(7,𝔽2)11yescharacteristic
1088C4—28no—
1089C4—22no—
1090C4—24no—
1091C4—24no—
1092C4—22no—
1093C4—24no—
1094C4—22no—
1095C4—24no—
1096C4—42no—
1097C4—42no—
1098C4—44no—
1099C4—42no—
1100C4—41no—
1101C4—44no—
1102C4—44no—
1103C4—42no—
1104C4—44no—
1105C4—48no—
1106C4—44no—
1107C4—42no—
1108C4—42no—
1109C4#350314yes—
1110C4#350314yes—
1111C4#354714yes—
1112C2—44no—
1113C2—44no—
1114C2C2×#354711yescharacteristic
1115C2C2×#350311yescharacteristic
1116C2C2×#350311yescharacteristic
1117C2#6291211yescharacteristic
1118C2#6294511yescharacteristic
1119C2#6298911yescharacteristic
1120C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
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. #59668C2semidirect
3. #59305C2semidirect
4. #59136C2semidirect
5. #51605C2semidirect
6. #46005C2semidirect
7. #45359C2semidirect
8. #44879C2semidirect
9. #42972C2semidirect
10. #42972C2semidirect
11. #39633C2semidirect
12. #39606C2semidirect
13. #39598C2semidirect
14. #39370C2semidirect
15. #38966C2semidirect
16. #36563C2semidirect
17. #36288C2semidirect
18. #36287C2semidirect
19. #36180C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35281C2semidirect
22. #35275C2semidirect
23. #34941C2semidirect
24. #34929C2semidirect
200. #555Q8semidirect
560. C4⋊Q8C2×Q8semidirect
567. #124C2×Q8semidirect
580. #121C2×Q8semidirect
599. C4×D4C2×Q8semidirect
604. #117C2×Q8semidirect
605. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#596682
#593052
#591362
#516052
#460052
#453592
#448792
#429722
#396332
#396062
#395982
#393702
#389662
#365632
#362882
#362872
#361802
D4×C4⋊Q82
#352812
#352752
#349412
#349292
#344852
C4×#5552