Finite Group Databasebeta

← #7632165

Subgroups — #7632165

Order 512.

4925 conjugacy classes of subgroups.

The subgroup lattice has 1483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36535C212yesmaximal, complemented
2#36525C214yesmaximal, complemented
3#36484C212yesmaximal, complemented
4#36418C212yesmaximal, complemented
5#36388C214yesmaximal, complemented
6#36270C212yesmaximal, complemented
7#36088C212yesmaximal, complemented
8#36081C212yesmaximal, complemented
9#36026C212yesmaximal, complemented
10#36008C212yesmaximal, complemented
11#35980C212yesmaximal, complemented
12#35832C212yesmaximal, complemented
13#35832C212yesmaximal, complemented
14#35734C212yesmaximal, complemented
15#35657C212yesmaximal, complemented
16#35609C212yesmaximal, complemented
17#35506C212yesmaximal, complemented
18#35496C212yesmaximal, complemented
19#35440C212yesmaximal, complemented
20#35430C212yesmaximal
21#35345C211yesmaximal, characteristic, complemented
22#35245C211yesmaximal, characteristic, complemented
23#35113C214yesmaximal, complemented
24#34971C211yesmaximal, characteristic, complemented
25#34910C211yesmaximal, characteristic
26#34866C214yesmaximal, complemented
27#34304C212yesmaximal, complemented
28#34300C212yesmaximal, complemented
29#34244C211yesmaximal, characteristic, complemented
30#34121C211yesmaximal, characteristic, complemented
31C4×#519C211yesmaximal, characteristic, complemented
32C2×#552C2212yes—
33C2×#552C2212yes—
34C2×#529C2211yescharacteristic
35C2×#519C2212yes—
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2866C2214yes—
39#2865C2214yes—
40#2864C2212yes—
41#2864C2214yes—
42#2860C2214yes—
43#2859C2212yes—
44#2853C2214yes—
45#2655C2214yes—
46#2651C2214yes—
47#2637C2214yes—
48#2637C2214yes—
49#2634C2212yes—
50#2632C2212yes—
51#2629C2212yes—
52#2629C2212yes—
53#2609C2214yes—
54#2609C2214yes—
55#2608C2214yes—
56#2608C2212yes—
57#2608C2212yes—
58#2606C2214yes—
59#2606C2212yes—
60#2606C2212yes—
61#2604C2214yes—
62#2602C2212yes—
63#2602C2212yes—
64#2601C2212yes—
65#2601C2212yes—
66#2601C2214yes—
67#2601C2214yes—
68#2601C2214yes—
69#2601C2214yes—
70#2599C2212yes—
71#2599C2212yes—
72#2597C2214yes—
73#2596C2214yes—
74#2595C2214yes—
75#2594C2214yes—
76#2594C2214yes—
77#2591C2212yes—
78#2590C2214yes—
79#2590C2214yes—
80#2590C2214yes—
81#2588C2214yes—
82#2588C2214yes—
83#2588C2214yes—
84#2587C2214yes—
85#2583C2212yes—
86#2581C2212yes—
87#2581C2212yes—
88#2577C2214yes—
89#2576C2214yes—
90#2575C2214yes—
91#2573C2214yes—
92#2571C2212yes—
93#2570C2214yes—
94#2566C2211yescharacteristic
95#2565C2212yes—
96#2565C2212yes—
97#2565C2211yescharacteristic
98#2562C2212yes—
99#2562C2212yes—
100#2558C2214yes—
101#2558C2214yes—
102#2558C2214yes—
103#2554C2214yes—
104#2552C2212yes—
105#2550C2214yes—
106#2545C2211yescharacteristic
107#2544C2211yescharacteristic
108#2538C2212yes—
109#2538C2212yes—
110#2536C2212yes—
111#2536C2212yes—
112#2533C2214yes—
113#2533C2214yes—
114#2531C2214yes—
115#2529C2214yes—
116#2528C2214yes—
117#2528C2214yes—
118#2526C2214yes—
119#2526C2214yes—
120#2525C2214yes—
121#2525C2214yes—
122#2524C2214yes—
123#2522C2214yes—
124#2522C2214yes—
125#2521C2214yes—
126#2520C2214yes—
127#2519C2214yes—
128#2519C2214yes—
129#2516C2214yes—
130#2515C2214yes—
131#2515C2214yes—
132#2515C2214yes—
133#2506C2214yes—
134#2500C2211yescharacteristic
135#2499C2211yescharacteristic
136#2497C2212yes—
137#2496C2212yes—
138#2495C2212yes—
139#2494C2212yes—
140#2487C2212yes—
141#2486C2211yescharacteristic
142#2486C2211yescharacteristic
143#2484C2212yes—
144#2479C2214yes—
145#2475C2214yes—
146#2475C2214yes—
147#2475C2214yes—
148#2474C2214yes—
149#2471C2214yes—
150#2471C2214yes—
151#2470C2214yes—
152#2462C2214yes—
153#2462C2214yes—
154#2458C2214yes—
155#2458C2214yes—
156#2457C2214yes—
157#2445C2214yes—
158#2432C2211yescharacteristic
159#2431C2211yescharacteristic
160#2423C2212yes—
161#2423C2212yes—
162#2421C2212yes—
163#2421C2212yes—
164#2409C2211yescharacteristic
165#2409C2211yescharacteristic
166#2409C2212yes—
167#2406C2212yes—
168#2402C2214yes—
169#2399C2212yes—
170#2398C2212yes—
171#2396C2214yes—
172#2396C2214yes—
173#2395C2214yes—
174#2392C2212yes—
175#2392C2212yes—
176#2374C2214yes—
177#2374C2214yes—
178#2373C2214yes—
179#2373C2214yes—
180#2372C2212yes—
181#2371C2214yes—
182#2371C2212yes—
183#2370C2214yes—
184#2370C2212yes—
185#2370C2212yes—
186#2362C2212yes—
187#2362C2212yes—
188#2360C2212yes—
189#2360C2212yes—
190#2359C2214yes—
191#2357C2212yes—
192#2356C2212yes—
193#2355C2212yes—
194#2355C2212yes—
195#2355C2212yes—
196#2355C2212yes—
197#2354C2212yes—
198#2354C2212yes—
199#2354C2212yes—
200#2353C2212yes—
201#2353C2212yes—
202#2352C2212yes—
203#2352C2212yes—
204#2352C2212yes—
205#2352C2212yes—
206D4×C4⋊C4C2212yes—
207#2347C2212yes—
208#2346C2214yes—
209#2346C2212yes—
210#2345C2212yes—
211#2344C2212yes—
212#2343C2214yes—
213#2336C2214yes—
214#2335C2214yes—
215#2334C2214yes—
216#2334C2214yes—
217#2333C2212yes—
218#2332C2212yes—
219#2330C2212yes—
220#2330C2212yes—
221#2323C2212yes—
222#2323C2212yes—
223#2314C2212yes—
224C4×C4⋊Q8C2211yescharacteristic
225C4×#127C2211yescharacteristic
226C4×#125C2214yes—
227C4×#125C2214yes—
228C4×#126C2214yes—
229C4×#126C2214yes—
230C4×#124C2211yescharacteristic
231C4×#124C2211yescharacteristic
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×#123C2214yes—
235C4×#123C2212yes—
236C4×#123C2212yes—
237#2298C2214yes—
238#2298C2212yes—
239#2298C2214yes—
240#2298C2212yes—
241#2297C2212yes—
242#2296C2214yes—
243#2293C2214yes—
244#2290C2212yes—
245#2290C2212yes—
246#2285C2211yescharacteristic
247#2283C2211yescharacteristic
248#2283C2211yescharacteristic
249#2283C2211yescharacteristic
250#2276C2212yes—
251#2276C2212yes—
252#2276C2212yes—
253#2276C2212yes—
254#2274C2212yes—
255#2274C2212yes—
256#2274C2212yes—
257#2274C2212yes—
258C42×Q8C2214yes—
259C42×Q8C2212yes—
260C42×Q8C2212yes—
261C4×#117C2211yescharacteristic
262C4×#117C2214yes—
263C4×#117C2212yes—
264C4×#117C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C23×Q8C2311yescharacteristic
269#552—216no—
270#552—216no—
271C2×C4⋊Q8C2311yescharacteristic
272C2×#127C2311yescharacteristic
273#529—28no—
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2311yescharacteristic
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×#121C2311yescharacteristic
298#519—216no—
299C4×#41—28no—
300C2×C4×Q8—28no—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2314yes—
325C2×#117C2312yes—
326C2×#117C2314yes—
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2311yescharacteristic
336C2×#117C2314yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2311yescharacteristic
343C22×C42C2312yes—
344C22×C42C2311yescharacteristic
345C22×C42C2311yescharacteristic
346C22×C42C2312yes—
347C22×C42C2311yescharacteristic
348#401C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2312yes—
390#397C2312yes—
391#396C2312yes—
392#396C2312yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2312yes—
412#394C2314yes—
413#394C2312yes—
414#394C2312yes—
415#394C2312yes—
416#394C2314yes—
417#394C2312yes—
418#394C2312yes—
419#393C2312yes—
420#393C2312yes—
421#393C2314yes—
422#392C2312yes—
423#392C2312yes—
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2311yescharacteristic
431#391C2314yes—
432#391C2314yes—
433#391C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2312yes—
437#390C2312yes—
438#390C2311yescharacteristic
439#390C2314yes—
440#390C2314yes—
441#390C2311yescharacteristic
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#388C2312yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#388C2314yes—
489#388C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2312yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2312yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2312yes—
582#386C2314yes—
583#386C2312yes—
584#386C2314yes—
585#386C2312yes—
586#386C2312yes—
587#386C2312yes—
588#386C2314yes—
589#386C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2312yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2312yes—
602#385C2312yes—
603#385C2312yes—
604#384C2311yescharacteristic
605#384C2311yescharacteristic
606#384C2312yes—
607#384C2312yes—
608#384C2312yes—
609#384C2312yes—
610#383C2312yes—
611#383C2314yes—
612#383C2314yes—
613#383C2312yes—
614#383C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2312yes—
618#382C2312yes—
619#382C2311yescharacteristic
620#382C2311yescharacteristic
621#382C2314yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#382C2312yes—
626#381C2312yes—
627#381C2314yes—
628#381C2312yes—
629#381C2312yes—
630#381C2312yes—
631#381C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2311yescharacteristic
642#380C2312yes—
643#380C2312yes—
644#380C2311yescharacteristic
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2311yescharacteristic
720C4×C22⋊C4C2311yescharacteristic
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724#376C2312yes—
725#376C2314yes—
726#376C2312yes—
727#376C2314yes—
728#376C2312yes—
729#376C2312yes—
730#376C2312yes—
731#376C2314yes—
732#376C2312yes—
733C2×#95C2312yes—
734C43C2312yes—
735C43C2314yes—
736C43C2312yes—
737C43C2314yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—24no—
741C2×#41—42no—
742C2×#41—42no—
743C22×Q8—28no—
744C22×Q8—24no—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2412yes—
748C22×Q8C2411yescharacteristic
749C22×D4C2412yes—
750C22×D4C2411yescharacteristic
751C22×D4C2411yescharacteristic
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2411yescharacteristic
755C22×D4C2412yes—
756C23×C4C2411yescharacteristic
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2411yescharacteristic
760C23×C4C2411yescharacteristic
761C23×C4C2414yes—
762C23×C4C2411yescharacteristic
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2411yescharacteristic
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C4⋊Q8—42no—
771#127—42no—
772#126—28no—
773#126—216no—
774#126—216no—
775#126—48no—
776#125—216no—
777#125—216no—
778#125—24no—
779#125—28no—
780#125—28no—
781#125—48no—
782#124—24no—
783#124—42no—
784#124—42no—
785#123—28no—
786#123—216no—
787#123—216no—
788#123—44no—
789#123—44no—
790C22⋊Q8—28no—
791C22⋊Q8—28no—
792C22⋊Q8—28no—
793C22⋊Q8—28no—
794C22⋊Q8—24no—
795#121—24no—
796C4×Q8—28no—
797C4×Q8—28no—
798C4×Q8—216no—
799C4×Q8—28no—
800C4×Q8—28no—
801C4×Q8—28no—
802C4×Q8—28no—
803C4×Q8—24no—
804C4×Q8—24no—
805C4×Q8—216no—
806C4×Q8—28no—
807C4×Q8—24no—
808C4×Q8#41116yescomplemented
809C4×D4—24no—
810C4×D4—24no—
811C4×D4—24no—
812C4×D4—24no—
813C4×D4—28no—
814C4×D4—24no—
815C4×D4—24no—
816C4×D4—24no—
817C4×D4—28no—
818C4×D4—28no—
819C4×D4—48no—
820#117—24no—
821#117—28no—
822#117—216no—
823#117—28no—
824#117—28no—
825#117—24no—
826#117—24no—
827#117—216no—
828#117—28no—
829#117—28no—
830#117—216no—
831#117—216no—
832#117—48no—
833#117—44no—
834C2×C4⋊C4—28no—
835C2×C4⋊C4—24no—
836C2×C4⋊C4—28no—
837C2×C4⋊C4—28no—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2411yescharacteristic
905C2×C22⋊C4C2411yescharacteristic
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C42—28no—
942C2×C42—24no—
943C2×C42—24no—
944C2×C42—44no—
945C2×C42#4118yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2412yes—
979C2×C42C2414yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2414yes—
1053C24C2511yescharacteristic
1054C24C2512yes—
1055C24C2511yescharacteristic
1056C24C2511yescharacteristic
1057#41—416no—
1058C2×Q8—232no—
1059C2×Q8—28no—
1060C2×Q8—24no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—22no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—41no—
1067C2×Q8—41no—
1068C2×Q8—41no—
1069C2×Q8C2×#4118yes—
1070C2×D4—22no—
1071C2×D4—22no—
1072C2×D4—24no—
1073C2×D4—22no—
1074C2×D4—22no—
1075C2×D4—24no—
1076C2×D4—22no—
1077C2×D4—24no—
1078C2×D4—22no—
1079C2×D4—24no—
1080C2×D4—22no—
1081C2×D4—42no—
1082C2×D4—41no—
1083C2×D4—41no—
1084C2×D4—41no—
1085C2×D4—41no—
1086C2×D4—42no—
1087C2×D4—41no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C22×C4—24no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—28no—
1095C22×C4—24no—
1096C22×C4—22no—
1097C22×C4—28no—
1098C22×C4—24no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—28no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—22no—
1109C22×C4—22no—
1110C22×C4—28no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—41no—
1114C22×C4—41no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—42no—
1120C22×C4—44no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4C2×#4114yes—
1124C22×C4C2×#4114yes—
1125C22×C4C2×#4114yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2514yes—
1137C22×C4C2514yes—
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2514yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C4⋊C4—28no—
1154C4⋊C4—28no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—28no—
1161C4⋊C4—22no—
1162C4⋊C4—22no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—24no—
1171C4⋊C4—28no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—28no—
1180C4⋊C4—28no—
1181C4⋊C4—22no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—22no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—28no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4C2×#4118yes—
1212C4⋊C4C2×#41116yes—
1213C22⋊C4—22no—
1214C22⋊C4—22no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—22no—
1224C22⋊C4—22no—
1225C22⋊C4—22no—
1226C22⋊C4—22no—
1227C22⋊C4—24no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—24no—
1231C22⋊C4—28no—
1232C22⋊C4—28no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—24no—
1237C22⋊C4—28no—
1238C22⋊C4—28no—
1239C22⋊C4—24no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C42—22no—
1257C42—22no—
1258C42—22no—
1259C42—22no—
1260C42—22no—
1261C42—22no—
1262C42—28no—
1263C42—28no—
1264C42—28no—
1265C42—28no—
1266C42—24no—
1267C42—28no—
1268C42—28no—
1269C42—28no—
1270C42—28no—
1271C42—24no—
1272C42—42no—
1273C42—44no—
1274C42—42no—
1275C42—44no—
1276C42—42no—
1277C42—42no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—42no—
1284C42—42no—
1285C42—44no—
1286C42—41no—
1287C42—41no—
1288C42—44no—
1289C42—44no—
1290C42—41no—
1291C42—41no—
1292C42C2×#4114yes—
1293C42C2×#4114yes—
1294C42C2×#4114yes—
1295C42C2×#4114yes—
1296C42C2×#41116yes—
1297C42C2×#4118yes—
1298C23—22no—
1299C23—22no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—21no—
1311C23—22no—
1312C23—21no—
1313C23—22no—
1314C23—21no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23C22×#4112yes—
1319C23#58512yes—
1320C23C2611yescharacteristic
1321Q8—216no—
1322Q8—216no—
1323Q8—44no—
1324Q8—82no—
1325D4—48no—
1326D4—44no—
1327D4—44no—
1328D4—44no—
1329D4—84no—
1330D4—82no—
1331D4—84no—
1332C2×C4—216no—
1333C2×C4—28no—
1334C2×C4—21no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—28no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—44no—
1397C2×C4—44no—
1398C2×C4—416no—
1399C2×C4—44no—
1400C2×C4—44no—
1401C2×C4—44no—
1402C2×C4—48no—
1403C2×C4—88no—
1404C2×C4—82no—
1405C2×C4—82no—
1406C2×C4—84no—
1407C2×C4C22×#4112yes—
1408C2×C4C22×#4112yes—
1409C2×C4C22×#4118yes—
1410C2×C4C22×#4112yes—
1411C2×C4C22×#4114yes—
1412C2×C4C22×#4118yes—
1413C2×C4C22×#4114yes—
1414C2×C4C22×#4112yes—
1415C2×C4C22×#4112yes—
1416C2×C4C22×#4112yes—
1417C2×C4C22×#4114yes—
1418C2×C4#58512yes—
1419C22—24no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—22no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—41no—
1428C22—41no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—41no—
1436C22—42no—
1437C22—41no—
1438C22—42no—
1439C22—41no—
1440C22—42no—
1441C22C23×#4112yes—
1442C22C23×#4111yescharacteristic
1443C22C2×#58511yescharacteristic
1444C22C2×#58511yescharacteristic
1445C222−1+612yes—
1446C4—28no—
1447C4—24no—
1448C4—24no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—28no—
1455C4—22no—
1456C4—42no—
1457C4—44no—
1458C4—44no—
1459C4—42no—
1460C4—44no—
1461C4—44no—
1462C4—44no—
1463C4—41no—
1464C4—44no—
1465C4—42no—
1466C4—41no—
1467C4—41no—
1468C4—42no—
1469C4—41no—
1470C4—41no—
1471C4—42no—
1472C4#344414yes—
1473C2—42no—
1474C2—42no—
1475C2—82no—
1476C2—81no—
1477C2C2×#344411yescharacteristic
1478C2#6281411yescharacteristic
1479C2#6286011yescharacteristic
1480C2#6299312yes—
1481C2#6300712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2431C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36535C2semidirect
2. #36525C2semidirect
3. #36484C2semidirect
4. #36418C2semidirect
5. #36388C2semidirect
6. #36270C2semidirect
7. #36088C2semidirect
8. #36081C2semidirect
9. #36026C2semidirect
10. #36008C2semidirect
11. #35980C2semidirect
12. #35832C2semidirect
13. #35832C2semidirect
14. #35734C2semidirect
15. #35657C2semidirect
16. #35609C2semidirect
17. #35506C2semidirect
18. #35496C2semidirect
19. #35440C2semidirect
21. #35345C2semidirect
22. #35245C2semidirect
23. #35113C2semidirect
24. #34971C2semidirect
26. #34866C2semidirect
27. #34304C2semidirect
28. #34300C2semidirect
29. #34244C2semidirect
30. #34121C2semidirect
31. C4×#519C2semidirect
808. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#365352
#365252
#364842
#364182
#363882
#362702
#360882
#360812
#360262
#360082
#359802
#358322
#357342
#356572
#356092
#355062
#354962
#354402
#354302
#353452
#352452
#351132
#349712
#349102
#348662
#343042
#343002
#342442
#341212
C4×#5192