Finite Group Databasebeta

← #7681882

Subgroups — #7681882

Order 512.

4925 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60016C214yesmaximal, complemented
2#59537C214yesmaximal, complemented
3#59516C214yesmaximal, complemented
4#59509C214yesmaximal, complemented
5#43832C214yesmaximal, complemented
6#43823C214yesmaximal, complemented
7#43454C214yesmaximal, complemented
8#43373C214yesmaximal, complemented
9#39740C211yesmaximal, characteristic, complemented
10#39622C211yesmaximal, characteristic, complemented
11#38943C212yesmaximal, complemented
12#38937C212yesmaximal, complemented
13#38936C212yesmaximal, complemented
14#37952C212yesmaximal, complemented
15#37774C212yesmaximal, complemented
16#36504C212yesmaximal, complemented
17#36209C211yesmaximal, characteristic, complemented
18#36136C211yesmaximal, characteristic, complemented
19#35637C212yesmaximal, complemented
20#35570C212yesmaximal, complemented
21#35332C211yesmaximal, characteristic, complemented
22#35326C212yesmaximal, complemented
23#34919C212yesmaximal, complemented
24#34326C212yesmaximal, complemented
25#34220C212yesmaximal, complemented
26#34123C211yesmaximal, characteristic, complemented
27C4×#541C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#541C2211yescharacteristic
30C2×#541C2211yescharacteristic
31C2×#540C2211yescharacteristic
32C2×#533C2212yes—
33C2×#529C2212yes—
34C2×#529C2212yes—
35C2×C4×#41C2211yescharacteristic
36#2859C2211yescharacteristic
37#2858C2211yescharacteristic
38#2857C2212yes—
39#2857C2212yes—
40#2850C2212yes—
41#2850C2212yes—
42#2850C2212yes—
43#2806C2214yes—
44#2792C2214yes—
45#2785C2214yes—
46#2785C2214yes—
47#2784C2214yes—
48#2781C2214yes—
49#2781C2214yes—
50#2781C2214yes—
51#2775C2214yes—
52#2769C2214yes—
53#2769C2214yes—
54#2756C2214yes—
55#2744C2214yes—
56#2744C2214yes—
57#2744C2214yes—
58#2744C2214yes—
59#2732C2214yes—
60#2727C2214yes—
61#2727C2214yes—
62#2721C2214yes—
63#2705C2214yes—
64#2694C2214yes—
65#2686C2214yes—
66#2686C2214yes—
67#2660C2212yes—
68#2658C2212yes—
69#2642C2211yescharacteristic
70#2642C2212yes—
71#2641C2211yescharacteristic
72#2640C2212yes—
73#2620C2212yes—
74#2611C2214yes—
75#2611C2214yes—
76#2611C2214yes—
77#2604C2214yes—
78#2604C2214yes—
79#2604C2214yes—
80#2602C2214yes—
81#2601C2214yes—
82#2593C2214yes—
83#2586C2214yes—
84#2574C2214yes—
85#2572C2214yes—
86#2572C2214yes—
87#2571C2214yes—
88#2565C2214yes—
89#2564C2214yes—
90#2564C2214yes—
91#2560C2214yes—
92#2560C2214yes—
93#2559C2214yes—
94#2559C2214yes—
95#2559C2214yes—
96#2558C2214yes—
97#2558C2214yes—
98#2558C2214yes—
99#2556C2214yes—
100#2554C2214yes—
101#2553C2214yes—
102#2552C2212yes—
103#2550C2212yes—
104#2550C2212yes—
105#2546C2212yes—
106#2545C2212yes—
107#2544C2212yes—
108#2543C2214yes—
109#2542C2212yes—
110#2540C2212yes—
111#2540C2212yes—
112#2537C2212yes—
113#2536C2212yes—
114#2536C2212yes—
115#2532C2214yes—
116#2526C2214yes—
117#2519C2214yes—
118#2519C2214yes—
119#2518C2214yes—
120#2508C2214yes—
121#2508C2214yes—
122#2507C2214yes—
123#2506C2214yes—
124#2500C2214yes—
125#2498C2214yes—
126#2498C2214yes—
127#2498C2214yes—
128#2497C2214yes—
129#2495C2214yes—
130#2495C2214yes—
131#2495C2214yes—
132#2492C2212yes—
133#2491C2212yes—
134#2490C2212yes—
135#2489C2212yes—
136#2489C2212yes—
137#2489C2212yes—
138#2485C2214yes—
139#2479C2214yes—
140#2479C2214yes—
141#2479C2214yes—
142#2479C2214yes—
143#2479C2214yes—
144#2479C2214yes—
145#2476C2214yes—
146#2474C2214yes—
147#2467C2214yes—
148#2467C2214yes—
149#2467C2214yes—
150#2464C2214yes—
151#2461C2214yes—
152#2459C2214yes—
153#2456C2214yes—
154#2454C2214yes—
155#2441C2214yes—
156#2429C2212yes—
157#2429C2212yes—
158#2429C2212yes—
159#2428C2212yes—
160#2427C2212yes—
161#2426C2212yes—
162#2423C2214yes—
163#2422C2214yes—
164#2420C2214yes—
165#2407C2214yes—
166#2396C2214yes—
167#2392C2214yes—
168#2373C2214yes—
169#2373C2214yes—
170#2373C2214yes—
171#2373C2214yes—
172#2368C2214yes—
173#2367C2212yes—
174#2367C2212yes—
175#2365C2212yes—
176#2363C2214yes—
177#2363C2214yes—
178#2359C2214yes—
179#2359C2214yes—
180#2357C2212yes—
181#2356C2212yes—
182#2356C2212yes—
183#2355C2212yes—
184#2355C2212yes—
185#2354C2214yes—
186#2353C2212yes—
187#2353C2212yes—
188#2353C2214yes—
189#2349C2212yes—
190#2349C2214yes—
191#2346C2212yes—
192#2346C2214yes—
193#2346C2214yes—
194#2343C2214yes—
195#2343C2214yes—
196#2343C2212yes—
197#2343C2212yes—
198#2339C2212yes—
199#2336C2214yes—
200#2334C2214yes—
201#2334C2214yes—
202#2332C2214yes—
203#2330C2211yescharacteristic
204#2330C2212yes—
205#2327C2212yes—
206#2327C2211yescharacteristic
207#2326C2212yes—
208#2326C2212yes—
209#2326C2212yes—
210#2323C2212yes—
211#2320C2212yes—
212#2320C2212yes—
213#2319C2212yes—
214#2314C2211yescharacteristic
215C4×C4⋊Q8C2211yescharacteristic
216C4×#125C2211yescharacteristic
217C4×#125C2214yes—
218C4×#126C2214yes—
219C4×#126C2214yes—
220C4×#124C2212yes—
221C4×#124C2214yes—
222C4×C22⋊Q8C2212yes—
223C4×C22⋊Q8C2212yes—
224C4×C22⋊Q8C2212yes—
225C4×#121C2212yes—
226C4×#121C2212yes—
227#2298C2214yes—
228#2295C2211yescharacteristic
229#2295C2211yescharacteristic
230#2293C2214yes—
231#2290C2212yes—
232#2290C2212yes—
233#2285C2212yes—
234#2283C2212yes—
235#2283C2211yescharacteristic
236#2276C2212yes—
237#2275C2212yes—
238C42×Q8C2212yes—
239C42×D4C2211yescharacteristic
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×#376C2212yes—
243C22×#41C2311yescharacteristic
244#556—216no—
245#541—28no—
246#541—44no—
247#540—44no—
248#533—48no—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×#127C2311yescharacteristic
255#529—216no—
256#529—48no—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2311yescharacteristic
266C2×#125C2311yescharacteristic
267C2×#125C2314yes—
268C2×#125C2312yes—
269C2×#125C2311yescharacteristic
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C4×#41—28no—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317C2×#117C2312yes—
318C2×#117C2314yes—
319C2×#117C2314yes—
320C2×#117C2311yescharacteristic
321C2×#117C2314yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C22×C42C2311yescharacteristic
325C22×C42C2312yes—
326C22×C42C2312yes—
327C22×C42C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#392C2314yes—
398#392C2314yes—
399#392C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2312yes—
403#391C2314yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#390C2314yes—
415#390C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#389C2312yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2312yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2312yes—
489#388C2312yes—
490#388C2312yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#387C2312yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2312yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2312yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2314yes—
534#387C2314yes—
535#386C2312yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2312yes—
547#386C2312yes—
548#386C2312yes—
549#386C2314yes—
550#386C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2312yes—
561#385C2312yes—
562#385C2312yes—
563#385C2312yes—
564#385C2314yes—
565#385C2314yes—
566#384C2311yescharacteristic
567#384C2314yes—
568#384C2314yes—
569#384C2312yes—
570#384C2312yes—
571#383C2314yes—
572#383C2314yes—
573#383C2312yes—
574#383C2314yes—
575#383C2311yescharacteristic
576#383C2311yescharacteristic
577#383C2312yes—
578#382C2311yescharacteristic
579#382C2314yes—
580#382C2314yes—
581#382C2312yes—
582#382C2314yes—
583#382C2314yes—
584#382C2314yes—
585#382C2312yes—
586#382C2312yes—
587#382C2314yes—
588#382C2312yes—
589#382C2314yes—
590#382C2312yes—
591#381C2311yescharacteristic
592#381C2314yes—
593#381C2314yes—
594#381C2312yes—
595#381C2312yes—
596#381C2311yescharacteristic
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2312yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2314yes—
607#380C2312yes—
608#380C2314yes—
609#380C2312yes—
610#380C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2311yescharacteristic
639C4×C4⋊C4C2311yescharacteristic
640C4×C4⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663#376C2312yes—
664#376C2311yescharacteristic
665#376C2311yescharacteristic
666#376C2312yes—
667#376C2312yes—
668#376C2312yes—
669#376C2312yes—
670#376C2312yes—
671#376C2314yes—
672#376C2314yes—
673#376C2312yes—
674C2×#95C2312yes—
675C2×#95C2312yes—
676C2×#95C2312yes—
677C2×#95C2314yes—
678C2×#95C2312yes—
679C43C2314yes—
680C43C2311yescharacteristic
681C43C2311yescharacteristic
682C2×#41—24no—
683C2×#41—44no—
684C22×Q8C2412yes—
685C22×Q8C2412yes—
686C22×Q8C2414yes—
687C22×Q8C2411yescharacteristic
688C22×D4C2411yescharacteristic
689C22×D4C2412yes—
690C22×D4C2414yes—
691C22×D4C2412yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C23×C4C2411yescharacteristic
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2411yescharacteristic
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C4⋊Q8—24no—
709C4⋊Q8—28no—
710C4⋊Q8—44no—
711C4⋊Q8—44no—
712C4⋊Q8—42no—
713#127—42no—
714#126—216no—
715#126—216no—
716#126—216no—
717#126—216no—
718#126—48no—
719#126—48no—
720#125—216no—
721#125—44no—
722#125—48no—
723#125—42no—
724#125—42no—
725#125—48no—
726#125#4118yescomplemented
727#124—28no—
728#124—28no—
729#124—28no—
730#124—44no—
731#124—48no—
732#123—216no—
733#123—48no—
734#123—48no—
735C22⋊Q8—216no—
736C22⋊Q8—28no—
737C22⋊Q8—28no—
738C22⋊Q8—48no—
739C22⋊Q8—44no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C22⋊Q8—44no—
743#121—28no—
744#121—48no—
745#121—48no—
746#121—48no—
747#121—44no—
748#121—44no—
749C4×Q8—24no—
750C4×Q8—28no—
751C4×Q8—28no—
752C4×Q8—28no—
753C4×Q8—28no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—48no—
757C4×Q8#4118yes—
758C4×D4—28no—
759C4×D4—24no—
760C4×D4—28no—
761C4×D4—216no—
762C4×D4—28no—
763C4×D4—24no—
764C4×D4—28no—
765C4×D4—28no—
766C4×D4—48no—
767C4×D4—48no—
768C4×D4—48no—
769C4×D4—44no—
770C4×D4—44no—
771#117—28no—
772#117—24no—
773#117—216no—
774#117—216no—
775#117—24no—
776#117—24no—
777#117—48no—
778#117—48no—
779#117—48no—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C42—28no—
873C2×C42—24no—
874C2×C42—28no—
875C2×C42—28no—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2411yescharacteristic
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2411yescharacteristic
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2411yescharacteristic
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2411yescharacteristic
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2411yescharacteristic
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975C24C2511yescharacteristic
976C24C2514yes—
977C24C2512yes—
978#41—416no—
979C2×Q8—24no—
980C2×Q8—24no—
981C2×Q8—24no—
982C2×Q8—24no—
983C2×Q8—24no—
984C2×Q8—24no—
985C2×Q8—42no—
986C2×Q8—44no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8C2×#4114yes—
990C2×D4—24no—
991C2×D4—28no—
992C2×D4—24no—
993C2×D4—28no—
994C2×D4—22no—
995C2×D4—24no—
996C2×D4—28no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—44no—
1001C2×D4—42no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—22no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—22no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—24no—
1029C22×C4—28no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4C2511yescharacteristic
1048C22×C4C2512yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4C2×#4118yes—
1118C4⋊C4C2×#4114yes—
1119C4⋊C4C2×#41116yes—
1120C4⋊C4C2×#4118yes—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—24no—
1141C22⋊C4—28no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C42—22no—
1164C42—22no—
1165C42—24no—
1166C42—24no—
1167C42—22no—
1168C42—24no—
1169C42—24no—
1170C42—24no—
1171C42—28no—
1172C42—22no—
1173C42—28no—
1174C42—28no—
1175C42—28no—
1176C42—24no—
1177C42—24no—
1178C42—24no—
1179C42—22no—
1180C42—28no—
1181C42—28no—
1182C42—44no—
1183C42—42no—
1184C42—42no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—42no—
1190C42—44no—
1191C42—42no—
1192C42—44no—
1193C42C2×#4114yes—
1194C42C2×#4118yes—
1195C42C2×#4114yes—
1196C42H(5,𝔽2)14yes—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—21no—
1204C23—24no—
1205C23—24no—
1206C23—21no—
1207C23—21no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—22no—
1212C23—24no—
1213C23—22no—
1214C23—24no—
1215C23#58514yes—
1216C23C2611yescharacteristic
1217Q8—44no—
1218Q8—48no—
1219Q8—48no—
1220Q8—88no—
1221D4—28no—
1222D4—416no—
1223D4—48no—
1224D4—48no—
1225D4—88no—
1226D4—164no—
1227D4—164no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—48no—
1287C2×C4—48no—
1288C2×C4—48no—
1289C2×C4—44no—
1290C2×C4—48no—
1291C2×C4—44no—
1292C2×C4—84no—
1293C2×C4—88no—
1294C2×C4—88no—
1295C2×C4—84no—
1296C2×C4—82no—
1297C2×C4—88no—
1298C2×C4—84no—
1299C2×C4C22×#4112yes—
1300C2×C4C22×#4114yes—
1301C2×C4C22×#4114yes—
1302C2×C4C22×#4118yes—
1303C2×C4C22×#4112yes—
1304C2×C4C22×#4114yes—
1305C2×C4C22×#4112yes—
1306C2×C4C22×#4112yes—
1307C2×C4C2×H(5,𝔽2)14yes—
1308C2×C4C2×H(5,𝔽2)12yes—
1309C22—24no—
1310C22—24no—
1311C22—24no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—44no—
1317C22—44no—
1318C22—42no—
1319C22—41no—
1320C22—44no—
1321C22—41no—
1322C22—44no—
1323C22—44no—
1324C22—44no—
1325C22—42no—
1326C22—41no—
1327C22—44no—
1328C22C23×#4111yescharacteristic
1329C22C23×#4111yescharacteristic
1330C22C22×H(5,𝔽2)11yescharacteristic
1331C22C2×#58512yes—
1332C222−1+612yes—
1333C4—24no—
1334C4—28no—
1335C4—24no—
1336C4—22no—
1337C4—22no—
1338C4—24no—
1339C4—24no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—41no—
1344C4—44no—
1345C4—41no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—41no—
1354C4—44no—
1355C4—44no—
1356C4#348314yes—
1357C2—44no—
1358C2—84no—
1359C2—81no—
1360C2C2×#348311yescharacteristic
1361C2#6281411yescharacteristic
1362C2#6286111yescharacteristic
1363C2#6295412yes—
1364C2#6299312yes—
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. #60016C2semidirect
2. #59537C2semidirect
3. #59516C2semidirect
4. #59509C2semidirect
5. #43832C2semidirect
6. #43823C2semidirect
7. #43454C2semidirect
8. #43373C2semidirect
9. #39740C2semidirect
10. #39622C2semidirect
11. #38943C2semidirect
12. #38937C2semidirect
13. #38936C2semidirect
14. #37952C2semidirect
15. #37774C2semidirect
16. #36504C2semidirect
17. #36209C2semidirect
18. #36136C2semidirect
19. #35637C2semidirect
20. #35570C2semidirect
21. #35332C2semidirect
22. #35326C2semidirect
23. #34919C2semidirect
24. #34326C2semidirect
25. #34220C2semidirect
26. #34123C2semidirect
27. C4×#541C2semidirect
726. #125#41semidirect

Maximal subgroups

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

subgroupindex
#600162
#595372
#595162
#595092
#438322
#438232
#434542
#433732
#397402
#396222
#389432
#389372
#389362
#379522
#377742
#365042
#362092
#361362
#356372
#355702
#353322
#353262
#349192
#343262
#342202
#341232
C4×#5412