Finite Group Databasebeta

← #7985304

Subgroups — #7985304

Order 512.

5051 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic, complemented
2#59230C212yesmaximal, complemented
3#59134C212yesmaximal, complemented
4#59042C212yesmaximal, complemented
5#48529C218yesmaximal, complemented
6#45669C214yesmaximal, complemented
7#45203C214yesmaximal, complemented
8#45003C214yesmaximal, complemented
9#42924C214yesmaximal, complemented
10#42640C214yesmaximal, complemented
11#40100C214yesmaximal, complemented
12#39609C212yesmaximal, complemented
13#39478C212yesmaximal, complemented
14#39124C212yesmaximal, complemented
15#38908C212yesmaximal, complemented
16#36599C212yesmaximal, complemented
17#36504C212yesmaximal, complemented
18#36188C211yesmaximal, characteristic, complemented
19#36134C211yesmaximal, characteristic, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35279C212yesmaximal, complemented
22#35241C212yesmaximal, complemented
23#34932C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic, complemented
25#34383C212yesmaximal, complemented
26C4×#547C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×D4×Q8C2212yes—
29C2×#547C2211yescharacteristic
30C2×#533C2212yes—
31C22×C4⋊Q8C2212yes—
32C2×#529C2212yes—
33C2×#529C2212yes—
34C2×C4×#41C2212yes—
35#2868C2211yescharacteristic
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2214yes—
40#2857C2214yes—
41#2850C2214yes—
42#2838C2218yes—
43#2810C2214yes—
44#2787C2218yes—
45#2784C2218yes—
46#2778C2218yes—
47#2774C2218yes—
48#2767C2218yes—
49#2757C2218yes—
50#2747C2218yes—
51#2745C2218yes—
52#2742C2218yes—
53#2737C2218yes—
54#2723C2218yes—
55#2716C2218yes—
56#2696C2218yes—
57#2695C2218yes—
58#2693C2218yes—
59#2690C2218yes—
60#2666C2218yes—
61#2664C2218yes—
62#2628C2218yes—
63#2628C2214yes—
64#2625C2214yes—
65#2585C2218yes—
66#2578C2218yes—
67#2574C2218yes—
68#2569C2218yes—
69#2568C2212yes—
70#2568C2212yes—
71#2568C2212yes—
72#2568C2212yes—
73#2567C2214yes—
74#2565C2214yes—
75#2563C2214yes—
76#2563C2214yes—
77#2553C2214yes—
78#2553C2214yes—
79#2552C2212yes—
80#2552C2211yescharacteristic
81#2552C2211yescharacteristic
82#2551C2212yes—
83#2551C2212yes—
84#2547C2212yes—
85#2547C2212yes—
86#2547C2211yescharacteristic
87#2547C2211yescharacteristic
88#2546C2212yes—
89#2545C2214yes—
90#2542C2212yes—
91#2542C2211yescharacteristic
92#2542C2211yescharacteristic
93#2540C2214yes—
94#2538C2212yes—
95#2537C2211yescharacteristic
96#2537C2211yescharacteristic
97#2536C2214yes—
98#2535C2214yes—
99#2514C2214yes—
100#2514C2214yes—
101#2514C2214yes—
102#2511C2214yes—
103#2511C2214yes—
104#2509C2214yes—
105#2508C2214yes—
106#2499C2214yes—
107#2498C2218yes—
108#2496C2214yes—
109#2496C2214yes—
110#2496C2212yes—
111#2496C2212yes—
112#2492C2214yes—
113#2492C2214yes—
114#2489C2214yes—
115#2489C2212yes—
116#2489C2212yes—
117#2487C2218yes—
118#2481C2218yes—
119#2479C2218yes—
120#2477C2218yes—
121#2467C2218yes—
122#2451C2214yes—
123#2446C2214yes—
124#2442C2214yes—
125#2441C2214yes—
126#2440C2214yes—
127#2440C2214yes—
128#2439C2214yes—
129#2436C2214yes—
130#2434C2214yes—
131#2429C2214yes—
132#2427C2212yes—
133#2427C2212yes—
134#2427C2214yes—
135#2423C2214yes—
136#2423C2214yes—
137#2422C2212yes—
138#2422C2212yes—
139#2421C2214yes—
140#2417C2214yes—
141#2417C2214yes—
142#2417C2214yes—
143#2409C2214yes—
144#2409C2214yes—
145#2407C2214yes—
146#2395C2214yes—
147#2395C2214yes—
148#2376C2218yes—
149#2370C2214yes—
150#2367C2214yes—
151#2365C2212yes—
152#2365C2212yes—
153#2365C2212yes—
154#2365C2211yescharacteristic
155#2363C2214yes—
156#2362C2212yes—
157#2361C2212yes—
158#2359C2214yes—
159#2355C2212yes—
160#2355C2212yes—
161#2355C2212yes—
162#2354C2212yes—
163#2354C2211yescharacteristic
164#2354C2214yes—
165#2352C2214yes—
166Q8×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2212yes—
169D4×C4⋊C4C2211yescharacteristic
170#2345C2214yes—
171#2344C2212yes—
172Q8×C22⋊C4C2214yes—
173#2339C2212yes—
174#2334C2218yes—
175#2324C2214yes—
176#2323C2214yes—
177#2323C2214yes—
178#2317C2214yes—
179#2314C2214yes—
180#2311C2214yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2214yes—
188C4×#123C2214yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191C4×#121C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2314yes—
201#556—48no—
202D4×Q8—48no—
203#547—28no—
204#533—48no—
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216#529—216no—
217#529—48no—
218C2×#126C2314yes—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#124C2312yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2318yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C4×#41—48no—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2314yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×#117C2314yes—
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C2×#117C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2314yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2314yes—
283#401C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2314yes—
294#400C2314yes—
295#399C2318yes—
296#399C2314yes—
297#399C2318yes—
298#399C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2314yes—
306#398C2318yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2314yes—
315#397C2314yes—
316#397C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#395C2318yes—
321#395C2318yes—
322#395C2318yes—
323#395C2318yes—
324#394C2318yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#394C2314yes—
329#393C2318yes—
330#393C2318yes—
331#393C2318yes—
332#393C2318yes—
333#392C2318yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2318yes—
348#391C2312yes—
349#391C2312yes—
350#391C2318yes—
351#391C2314yes—
352#391C2312yes—
353#390C2312yes—
354#390C2314yes—
355#390C2318yes—
356#390C2312yes—
357#390C2318yes—
358#390C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2318yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2318yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2314yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2314yes—
425#386C2318yes—
426#386C2314yes—
427#386C2314yes—
428#385C2314yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#383C2318yes—
450#382C2314yes—
451#382C2314yes—
452#382C2318yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#382C2314yes—
457#381C2314yes—
458#380C2312yes—
459#380C2312yes—
460#380C2318yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#380C2318yes—
466#380C2314yes—
467#380C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#380C2318yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2314yes—
482#380C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2318yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525C2×#95C2314yes—
526C43C2311yescharacteristic
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—44no—
530C22×Q8—48no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2418yes—
538C22×D4C2411yescharacteristic
539C22×D4C2414yes—
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2414yes—
543C22×D4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2418yes—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—28no—
559C4⋊Q8—24no—
560C4⋊Q8—28no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—48no—
564C4⋊Q8—48no—
565C4⋊Q8—44no—
566#126—216no—
567#126—48no—
568#126—416no—
569#125—28no—
570#125—44no—
571#125—48no—
572#124—28no—
573#124—44no—
574#124—48no—
575#123—216no—
576#123—216no—
577#123—48no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—28no—
581C22⋊Q8—416no—
582C22⋊Q8—44no—
583C22⋊Q8—48no—
584C22⋊Q8—44no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589#121—28no—
590#121—28no—
591#121—28no—
592#121—44no—
593#121—44no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×Q8—28no—
597C4×Q8—44no—
598C4×Q8—48no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×D4—24no—
602C4×D4—216no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—42no—
610C4×D4—44no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4#4118yes—
616#117—216no—
617#117—48no—
618#117—48no—
619#117—44no—
620#117—48no—
621#117—48no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—28no—
624C2×C4⋊C4—48no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2412yes—
709C2×C42—28no—
710C2×C42—28no—
711C2×C42—28no—
712C2×C42—48no—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2414yes—
732C2×C42C2411yescharacteristic
733C2×C42C2418yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#95C2412yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2414yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779C24C2512yes—
780C24C2512yes—
781C24C2512yes—
782#41—432no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—28no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—28no—
794C2×Q8—24no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×Q8—48no—
798C2×Q8—832no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4C2×#4114yes—
816C2×D42−1+414yes—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—44no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4C2×#4118yes—
853C22×C4C2511yescharacteristic
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2518yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2512yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—22no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—24no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—28no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—22no—
907C4⋊C4—24no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4C2×#4114yes—
928C4⋊C42−1+414yes—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—28no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—42no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4C2×#4118yes—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—28no—
970C42—28no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—44no—
975C42—44no—
976C42—41no—
977C42—48no—
978C42—48no—
979C42—48no—
980C42C2×#4114yes—
981C42H(5,𝔽2)14yes—
982C42H(5,𝔽2)14yes—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23C22×#4114yes—
1003C23C2×2−1+414yes—
1004C23C2611yescharacteristic
1005Q8—48no—
1006Q8—48no—
1007Q8—416no—
1008Q8—48no—
1009Q8—816no—
1010D4—28no—
1011D4—28no—
1012D4—416no—
1013D4—44no—
1014D4—88no—
1015D4—88no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—216no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—28no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—28no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—416no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—84no—
1081C2×C4—88no—
1082C2×C4—816no—
1083C2×C4C22×#4112yes—
1084C2×C4C22×#4114yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4112yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×2−1+414yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4#58512yes—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22C23×#4111yescharacteristic
1119C22C22×H(5,𝔽2)11yescharacteristic
1120C22C22×H(5,𝔽2)11yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58511yescharacteristic
1124C222−1+611yescharacteristic
1125C4—22no—
1126C4—24no—
1127C4—22no—
1128C4—22no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—44no—
1133C4—48no—
1134C4—42no—
1135C4—44no—
1136C4—42no—
1137C4—44no—
1138C4—41no—
1139C4—42no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4—44no—
1144C4—44no—
1145C4#351114yes—
1146C4#352014yes—
1147C4#354614yes—
1148C2—44no—
1149C2—44no—
1150C2—82no—
1151C2C2×#354611yescharacteristic
1152C2C2×#352011yescharacteristic
1153C2C2×#351111yescharacteristic
1154C2#6294211yescharacteristic
1155C2#6294211yescharacteristic
1156C2#6300911yescharacteristic
1157C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59875C2semidirect
2. #59230C2semidirect
3. #59134C2semidirect
4. #59042C2semidirect
5. #48529C2semidirect
6. #45669C2semidirect
7. #45203C2semidirect
8. #45003C2semidirect
9. #42924C2semidirect
10. #42640C2semidirect
11. #40100C2semidirect
12. #39609C2semidirect
13. #39478C2semidirect
14. #39124C2semidirect
15. #38908C2semidirect
16. #36599C2semidirect
17. #36504C2semidirect
18. #36188C2semidirect
19. #36134C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35279C2semidirect
22. #35241C2semidirect
23. #34932C2semidirect
24. #34932C2semidirect
25. #34383C2semidirect
26. C4×#547C2semidirect

Maximal subgroups

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

subgroupindex
#598752
#592302
#591342
#590422
#485292
#456692
#452032
#450032
#429242
#426402
#401002
#396092
#394782
#391242
#389082
#365992
#365042
#361882
#361342
D4×C4⋊Q82
#352792
#352412
#349322
#343832
C4×#5472