Finite Group Databasebeta

← #7712321

Subgroups — #7712321

Order 512.

4404 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59451C212yesmaximal, complemented
2#59450C212yesmaximal, complemented
3#59437C212yesmaximal, complemented
4#59434C212yesmaximal, complemented
5#46245C214yesmaximal, complemented
6#46244C214yesmaximal, complemented
7#39822C214yesmaximal, complemented
8#39820C214yesmaximal, complemented
9#39566C214yesmaximal, complemented
10#39564C214yesmaximal, complemented
11#38987C212yesmaximal, complemented
12#38986C212yesmaximal, complemented
13#38978C212yesmaximal, complemented
14#38977C212yesmaximal, complemented
15#37641C211yesmaximal, characteristic, complemented
16#37640C211yesmaximal, characteristic
17#37430C214yesmaximal, complemented
18#36640C211yesmaximal, characteristic, complemented
19#36639C211yesmaximal, characteristic
20#36591C212yesmaximal, complemented
21#36590C212yesmaximal, complemented
22#36556C212yesmaximal, complemented
23#36555C212yesmaximal, complemented
24#35340C214yesmaximal, complemented
25#34374C211yesmaximal, characteristic, complemented
26#34368C211yesmaximal, characteristic
27C4×#533C211yesmaximal, characteristic, complemented
28C2×#533C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31#2864C2214yes—
32#2864C2212yes—
33#2864C2212yes—
34#2862C2211yescharacteristic
35#2862C2211yescharacteristic
36#2861C2214yes—
37#2861C2212yes—
38#2861C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2858C2211yescharacteristic
44#2858C2211yescharacteristic
45#2851C2212yes—
46#2851C2212yes—
47#2851C2212yes—
48#2851C2212yes—
49#2850C2212yes—
50#2850C2212yes—
51#2850C2212yes—
52#2850C2212yes—
53#2822C2214yes—
54#2820C2214yes—
55#2796C2218yes—
56#2789C2218yes—
57#2787C2218yes—
58#2786C2218yes—
59#2782C2218yes—
60#2777C2218yes—
61#2777C2218yes—
62#2773C2218yes—
63#2772C2218yes—
64#2771C2218yes—
65#2765C2218yes—
66#2758C2218yes—
67#2757C2218yes—
68#2746C2218yes—
69#2740C2218yes—
70#2739C2218yes—
71#2645C2214yes—
72#2644C2214yes—
73#2625C2214yes—
74#2625C2214yes—
75#2624C2214yes—
76#2621C2214yes—
77#2620C2214yes—
78#2616C2214yes—
79#2597C2218yes—
80#2596C2218yes—
81#2595C2218yes—
82#2595C2218yes—
83#2594C2218yes—
84#2594C2218yes—
85#2588C2218yes—
86#2587C2218yes—
87#2582C2212yes—
88#2582C2212yes—
89#2578C2218yes—
90#2577C2218yes—
91#2576C2218yes—
92#2575C2218yes—
93#2571C2214yes—
94#2570C2214yes—
95#2568C2212yes—
96#2568C2212yes—
97#2567C2212yes—
98#2548C2212yes—
99#2547C2212yes—
100#2547C2214yes—
101#2546C2212yes—
102#2546C2212yes—
103#2545C2214yes—
104#2542C2212yes—
105#2538C2212yes—
106#2538C2212yes—
107#2525C2218yes—
108#2522C2218yes—
109#2520C2218yes—
110#2516C2218yes—
111#2514C2214yes—
112#2514C2214yes—
113#2514C2214yes—
114#2513C2214yes—
115#2513C2214yes—
116#2511C2214yes—
117#2509C2214yes—
118#2508C2214yes—
119#2503C2214yes—
120#2499C2214yes—
121#2497C2214yes—
122#2495C2214yes—
123#2494C2214yes—
124#2494C2214yes—
125#2489C2214yes—
126#2489C2214yes—
127#2454C2214yes—
128#2453C2214yes—
129#2448C2214yes—
130#2448C2214yes—
131#2448C2214yes—
132#2447C2214yes—
133#2447C2214yes—
134#2446C2214yes—
135#2442C2214yes—
136#2441C2214yes—
137#2423C2214yes—
138#2421C2214yes—
139#2382C2214yes—
140#2379C2214yes—
141#2369C2212yes—
142#2367C2214yes—
143#2366C2212yes—
144#2365C2214yes—
145#2365C2212yes—
146#2365C2212yes—
147#2362C2214yes—
148#2360C2214yes—
149#2357C2214yes—
150#2355C2212yes—
151#2355C2214yes—
152#2355C2212yes—
153#2354C2212yes—
154#2354C2212yes—
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159#2347C2214yes—
160#2345C2214yes—
161#2324C2214yes—
162#2324C2214yes—
163#2323C2214yes—
164#2323C2214yes—
165#2320C2214yes—
166#2319C2214yes—
167#2314C2214yes—
168#2311C2214yes—
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×#125C2214yes—
174C4×#125C2212yes—
175C4×#125C2212yes—
176C4×#125C2212yes—
177C4×#125C2212yes—
178C4×#125C2212yes—
179C4×#125C2212yes—
180C4×#124C2214yes—
181C4×#124C2212yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2297C2212yes—
190#2297C2212yes—
191#2296C2212yes—
192#2296C2212yes—
193#2296C2212yes—
194#2295C2212yes—
195#2295C2212yes—
196#2285C2211yescharacteristic
197#2285C2211yescharacteristic
198#2285C2211yescharacteristic
199C42×Q8C2212yes—
200C42×Q8C2212yes—
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203C22×#41C2312yes—
204#533—28no—
205#533—28no—
206#532—28no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2314yes—
213C2×#127C2311yescharacteristic
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2314yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C22×C4⋊C4C2314yes—
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262#401C2318yes—
263#401C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#395C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2318yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#390C2318yes—
325#390C2312yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2314yes—
337#390C2314yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2318yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2318yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2314yes—
431#386C2314yes—
432#386C2314yes—
433#386C2314yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2314yes—
447#384C2314yes—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#383C2318yes—
453#383C2318yes—
454#382C2312yes—
455#382C2312yes—
456#382C2312yes—
457#382C2312yes—
458#382C2312yes—
459#382C2312yes—
460#382C2312yes—
461#382C2312yes—
462#382C2314yes—
463#382C2314yes—
464#382C2312yes—
465#382C2312yes—
466#382C2318yes—
467#382C2312yes—
468#382C2318yes—
469#381C2318yes—
470#381C2318yes—
471#380C2312yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2318yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2318yes—
482#380C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2318yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523#376C2314yes—
524C43C2311yescharacteristic
525C43C2311yescharacteristic
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2314yes—
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C2×#41—28no—
534C2×#41—44no—
535C2×#41—44no—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2418yes—
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—48no—
560#127—24no—
561#125—28no—
562#125—28no—
563#125—28no—
564#125—44no—
565#125—44no—
566#125—44no—
567#124—28no—
568#124—28no—
569#124—44no—
570#124—44no—
571#124—44no—
572#124—48no—
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579#121—28no—
580#121—28no—
581C4×Q8—28no—
582C4×Q8—28no—
583C4×Q8—28no—
584C4×Q8—28no—
585C4×Q8—44no—
586C4×Q8—44no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—48no—
594C4×D4—48no—
595#117—28no—
596#117—28no—
597#117—44no—
598#117—44no—
599#117—44no—
600#117—48no—
601C2×C4⋊C4—48no—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C42—24no—
676C2×C42—42no—
677C2×C42—42no—
678C2×C42—42no—
679C2×C42—42no—
680C2×C42—42no—
681C2×C42#4118yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2418yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2418yes—
706C2×C42C2418yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766C24C2514yes—
767C24C2511yescharacteristic
768#41—816no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×D4—28no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—44no—
795C2×D4—44no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—28no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4C2×#4114yes—
821C22×C4C2×#4114yes—
822C22×C4C2×#4114yes—
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—48no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C42—28no—
922C42—28no—
923C42—22no—
924C42—22no—
925C42—22no—
926C42—22no—
927C42—22no—
928C42—22no—
929C42—22no—
930C42—22no—
931C42—22no—
932C42—22no—
933C42—22no—
934C42—22no—
935C42—22no—
936C42—28no—
937C42—28no—
938C42—28no—
939C42—41no—
940C42—41no—
941C42—41no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—41no—
949C42—48no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—44no—
954C42—48no—
955C42—48no—
956C42C2×#4114yes—
957C42C2×#4114yes—
958C42C2×#4114yes—
959C42C2×#4114yes—
960C422−1+414yes—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23C22×#4112yes—
975C23C2611yescharacteristic
976Q8—48no—
977Q8—48no—
978Q8—48no—
979Q8—48no—
980Q8—84no—
981D4—48no—
982D4—48no—
983D4—84no—
984D4—88no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—44no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—416no—
1054C2×C4—168no—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C2×2−1+412yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4C2×2−1+412yes—
1064C2×C4#58512yes—
1065C2×C4#58512yes—
1066C2×C4#58512yes—
1067C2×C4#58512yes—
1068C2×C4#58512yes—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22C23×#4111yescharacteristic
1084C22C22×2−1+411yescharacteristic
1085C22C2×#58511yescharacteristic
1086C22C2×#58511yescharacteristic
1087C22C2×#58511yescharacteristic
1088C22C2×#58511yescharacteristic
1089C22C2×#58511yescharacteristic
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—22no—
1094C4—22no—
1095C4—44no—
1096C4—44no—
1097C4—41no—
1098C4—41no—
1099C4—44no—
1100C4—44no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—44no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—44no—
1111C4—44no—
1112C4#350714yes—
1113C4#351014yes—
1114C4#351214yes—
1115C2—42no—
1116C2—84no—
1117C2#6276111yescharacteristic
1118C2#6276111yescharacteristic
1119C2C2×#350711yescharacteristic
1120C2C2×#351011yescharacteristic
1121C2C2×#351211yescharacteristic
1122C2#6284011yescharacteristic
1123C2#6284111yescharacteristic
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. #59451C2semidirect
2. #59450C2semidirect
3. #59437C2semidirect
4. #59434C2semidirect
5. #46245C2semidirect
6. #46244C2semidirect
7. #39822C2semidirect
8. #39820C2semidirect
9. #39566C2semidirect
10. #39564C2semidirect
11. #38987C2semidirect
12. #38986C2semidirect
13. #38978C2semidirect
14. #38977C2semidirect
15. #37641C2semidirect
17. #37430C2semidirect
18. #36640C2semidirect
20. #36591C2semidirect
21. #36590C2semidirect
22. #36556C2semidirect
23. #36555C2semidirect
24. #35340C2semidirect
25. #34374C2semidirect
27. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#594512
#594502
#594372
#594342
#462452
#462442
#398222
#398202
#395662
#395642
#389872
#389862
#389782
#389772
#376412
#376402
#374302
#366402
#366392
#365912
#365902
#365562
#365552
#353402
#343742
#343682
C4×#5332