Finite Group Databasebeta

← #8107571

Subgroups — #8107571

Order 512.

4088 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53153C212yesmaximal, complemented
2#53113C212yesmaximal, complemented
3#52911C214yesmaximal, complemented
4#52651C214yesmaximal, complemented
5#45190C212yesmaximal, complemented
6#44961C212yesmaximal
7#44511C214yesmaximal, complemented
8#44048C214yesmaximal, complemented
9#42983C211yesmaximal, characteristic
10#42981C211yesmaximal, characteristic, complemented
11#42902C212yesmaximal, complemented
12#42755C212yesmaximal, complemented
13#42697C211yesmaximal, characteristic, complemented
14#42487C211yesmaximal, characteristic
15#42371C214yesmaximal, complemented
16#42355C214yesmaximal, complemented
17#41580C214yesmaximal, complemented
18#40901C214yesmaximal, complemented
19#36403C212yesmaximal, complemented
20#36380C212yesmaximal, complemented
21#36371C212yesmaximal, complemented
22#36293C212yesmaximal
23#35324C211yesmaximal, characteristic, complemented
24#35266C211yesmaximal, characteristic
25#35185C212yesmaximal, complemented
26#35117C212yesmaximal, complemented
27#34552C211yesmaximal, characteristic, complemented
28#2864C2212yescomplemented
29#2864C2211yescharacteristic, complemented
30#2863C2212yescomplemented
31#2862C2211yescharacteristic, complemented
32#2861C2212yes—
33#2860C2212yes—
34#2860C2212yes—
35#2860C2212yes—
36#2855C2212yes—
37#2844C2212yescomplemented
38#2840C2212yes—
39#2838C2214yescomplemented
40#2838C2214yescomplemented
41#2838C2214yescomplemented
42#2838C2214yescomplemented
43#2838C2214yescomplemented
44#2835C2212yes—
45#2835C2214yescomplemented
46#2831C2214yescomplemented
47#2831C2214yescomplemented
48#2831C2214yescomplemented
49#2830C2212yes—
50#2817C2214yescomplemented
51#2807C2212yes—
52#2805C2214yescomplemented
53#2804C2212yes—
54#2798C2214yescomplemented
55#2798C2214yescomplemented
56#2794C2212yescomplemented
57#2793C2214yescomplemented
58#2792C2212yescomplemented
59#2788C2214yes—
60#2788C2214yes—
61#2787C2214yescomplemented
62#2784C2212yes—
63#2775C2214yescomplemented
64#2774C2214yescomplemented
65#2773C2214yescomplemented
66#2770C2214yescomplemented
67#2767C2214yescomplemented
68#2765C2214yescomplemented
69#2761C2214yes—
70#2745C2214yescomplemented
71#2744C2214yescomplemented
72#2744C2214yescomplemented
73#2742C2214yes—
74#2742C2212yes—
75#2738C2214yescomplemented
76#2736C2212yes—
77#2735C2214yes—
78#2735C2212yes—
79#2735C2214yes—
80#2735C2214yes—
81#2725C2214yescomplemented
82#2723C2214yes—
83#2720C2214yescomplemented
84#2698C2214yescomplemented
85#2692C2214yes—
86#2690C2214yescomplemented
87#2667C2214yescomplemented
88#2654C2214yescomplemented
89#2652C2214yes—
90#2652C2214yescomplemented
91#2651C2214yes—
92#2650C2214yescomplemented
93#2650C2214yescomplemented
94#2650C2214yescomplemented
95#2650C2214yescomplemented
96#2647C2214yescomplemented
97#2645C2212yescomplemented
98#2644C2212yes—
99#2644C2212yes—
100#2637C2214yescomplemented
101#2628C2211yescharacteristic
102#2626C2214yes—
103#2621C2211yescharacteristic
104#2612C2212yescomplemented
105#2604C2214yescomplemented
106#2604C2214yescomplemented
107#2599C2214yes—
108#2597C2214yes—
109#2596C2214yescomplemented
110#2596C2214yescomplemented
111#2593C2212yes—
112#2592C2212yes—
113#2592C2212yes—
114#2588C2214yescomplemented
115#2588C2214yescomplemented
116#2584C2212yescomplemented
117#2581C2212yescomplemented
118#2581C2212yescomplemented
119#2580C2212yes—
120#2577C2214yescomplemented
121#2575C2214yes—
122#2575C2214yescomplemented
123#2575C2214yescomplemented
124#2574C2214yes—
125#2571C2212yescomplemented
126#2567C2212yescomplemented
127#2563C2212yes—
128#2561C2214yes—
129#2550C2212yescomplemented
130#2545C2212yes—
131#2538C2212yes—
132#2532C2214yescomplemented
133#2532C2214yescomplemented
134#2531C2214yes—
135#2531C2214yes—
136#2529C2214yescomplemented
137#2528C2214yescomplemented
138#2528C2214yescomplemented
139#2527C2214yes—
140#2527C2214yes—
141#2526C2214yes—
142#2526C2214yes—
143#2525C2214yescomplemented
144#2520C2214yescomplemented
145#2517C2212yes—
146#2515C2214yes—
147#2515C2214yescomplemented
148#2514C2212yescomplemented
149#2513C2212yes—
150#2513C2212yes—
151#2513C2212yes—
152#2513C2214yes—
153#2512C2212yes—
154#2512C2214yes—
155#2511C2212yescomplemented
156#2509C2212yescomplemented
157#2509C2212yescomplemented
158#2509C2212yescomplemented
159#2509C2212yescomplemented
160#2508C2212yescomplemented
161#2507C2214yescomplemented
162#2506C2212yescomplemented
163#2499C2212yes—
164#2497C2214yes—
165#2496C2214yescomplemented
166#2489C2214yescomplemented
167#2482C2214yes—
168#2480C2214yes—
169#2480C2214yes—
170#2480C2214yes—
171#2480C2214yes—
172#2479C2214yes—
173#2478C2214yescomplemented
174#2475C2214yes—
175#2469C2214yescomplemented
176#2469C2214yescomplemented
177#2469C2214yescomplemented
178#2469C2214yescomplemented
179#2465C2214yescomplemented
180#2465C2214yescomplemented
181#2454C2212yes—
182#2453C2212yescomplemented
183#2452C2212yes—
184#2452C2212yes—
185#2451C2212yescomplemented
186#2451C2212yescomplemented
187#2448C2212yes—
188#2448C2212yes—
189#2448C2212yes—
190#2447C2212yes—
191#2447C2212yes—
192#2446C2212yescomplemented
193#2442C2212yes—
194#2439C2212yes—
195#2437C2212yes—
196#2435C2212yes—
197#2421C2214yescomplemented
198#2402C2212yescomplemented
199#2402C2212yescomplemented
200#2402C2212yescomplemented
201#2399C2211yescharacteristic, complemented
202#2399C2212yescomplemented
203#2399C2211yescharacteristic, complemented
204#2399C2212yescomplemented
205#2396C2212yes—
206#2396C2212yes—
207#2396C2212yes—
208#2396C2212yes—
209#2396C2212yes—
210#2396C2211yescharacteristic
211#2396C2211yescharacteristic
212#2373C2214yescomplemented
213#2373C2214yescomplemented
214#2373C2214yescomplemented
215#2371C2214yescomplemented
216#2370C2212yescomplemented
217#2367C2212yes—
218#2362C2212yes—
219#2362C2214yescomplemented
220#2360C2212yes—
221#2357C2212yes—
222#2356C2214yescomplemented
223#2351C2212yescomplemented
224#2346C2212yes—
225#2342C2214yes—
226#2342C2214yes—
227D4×C22⋊C4C2212yes—
228#2334C2214yescomplemented
229#2332C2214yescomplemented
230#2331C2211yescharacteristic, complemented
231#2327C2211yescharacteristic, complemented
232#2323C2212yes—
233#2323C2214yescomplemented
234#2317C2211yescharacteristic
235#2316C2211yescharacteristic
236#2314C2214yescomplemented
237#2309C2211yescharacteristic
238#2309C2211yescharacteristic
239C4×C4⋊Q8C2212yescomplemented
240C4×#124C2212yes—
241#2296C2211yescharacteristic
242#2295C2212yescomplemented
243#2295C2212yescomplemented
244#2293C2212yes—
245C2×#390C2211yescharacteristic
246C42×Q8C2211yescharacteristic, complemented
247C42×Q8C2212yescomplemented
248C42×Q8C2211yescharacteristic, complemented
249C4×#117C2212yes—
250C4×#117C2211yescharacteristic
251C23×D4C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2314yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C42C2311yescharacteristic
291#401C2314yes—
292#401C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2311yescharacteristic
318#400C2312yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2311yescharacteristic
323#400C2312yes—
324#399C2312yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2311yescharacteristic
331#399C2312yes—
332#399C2311yescharacteristic
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2312yes—
347#398C2312yes—
348#398C2312yes—
349#398C2312yes—
350#398C2312yes—
351#398C2312yes—
352#398C2312yes—
353#398C2312yes—
354#398C2312yes—
355#398C2312yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2312yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2312yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2312yes—
396#396C2312yes—
397#395C2312yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2311yescharacteristic
403#395C2314yes—
404#395C2314yes—
405#395C2312yes—
406#395C2314yes—
407#395C2312yes—
408#395C2314yes—
409#395C2312yes—
410#395C2312yes—
411#395C2312yes—
412#395C2311yescharacteristic
413#394C2314yes—
414#394C2314yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2311yescharacteristic
423#393C2314yes—
424#393C2314yes—
425#393C2312yes—
426#393C2311yescharacteristic
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#387C2314yes—
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#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#386C2314yes—
582#386C2314yes—
583#385C2312yes—
584#385C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2314yes—
599#384C2312yes—
600#383C2314yes—
601#383C2314yes—
602#382C2311yescharacteristic
603#382C2312yes—
604#382C2314yes—
605#382C2311yescharacteristic
606#382C2312yes—
607#382C2312yes—
608#382C2314yes—
609#382C2314yes—
610#382C2312yes—
611#382C2314yes—
612#382C2314yes—
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2312yes—
622#380C2314yes—
623#380C2314yes—
624#379C2314yes—
625#379C2314yes—
626#379C2312yes—
627#379C2312yes—
628#379C2314yes—
629#379C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679#376C2311yescharacteristic
680#376C2314yes—
681#376C2314yes—
682#376C2314yes—
683#376C2312yes—
684#376C2311yescharacteristic
685#376C2312yes—
686C43C2312yes—
687C43C2311yescharacteristic
688C43C2311yescharacteristic
689C43C2312yes—
690C25C2412yes—
691C22×Q8C2412yes—
692C22×Q8C2412yes—
693C22×Q8C2411yescharacteristic
694C22×Q8C2411yescharacteristic
695C22×Q8C2414yes—
696C22×Q8C2412yes—
697C22×D4—24no—
698C22×D4—42no—
699C22×D4—42no—
700C22×D4C2412yes—
701C22×D4C2412yes—
702C23×C4C2412yes—
703C23×C4C2411yescharacteristic
704C23×C4C2414yes—
705C23×C4C2412yes—
706C23×C4C2414yes—
707C4⋊Q8—42no—
708C4⋊Q8—44no—
709C4⋊Q8—42no—
710#126—48no—
711#126—48no—
712#126—48no—
713#126—48no—
714#125—44no—
715#125—48no—
716#124—44no—
717#124—44no—
718C22⋊Q8—28no—
719C22⋊Q8—48no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C4×Q8—44no—
723C4×Q8—42no—
724C4×Q8—44no—
725C4×Q8—42no—
726C4×Q8—44no—
727C4×Q8—48no—
728C4×Q8—44no—
729C4×Q8—44no—
730C4×Q8—44no—
731C4×Q8—44no—
732C4×Q8—44no—
733C4×D4—44no—
734C4×D4—44no—
735#117—24no—
736#117—42no—
737#117—44no—
738#117—42no—
739#117—48no—
740#117—44no—
741#117—42no—
742C2×C4⋊C4—42no—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C22⋊C4—48no—
807C2×C22⋊C4—48no—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C42—24no—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2411yescharacteristic
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2411yescharacteristic
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2411yescharacteristic
914#95C2412yes—
915#95C2411yescharacteristic
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955C24—24no—
956C24—42no—
957C24—44no—
958C24—44no—
959C24—42no—
960C24C2514yes—
961C24C2511yescharacteristic
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—41no—
969C2×Q8—42no—
970C2×Q8—41no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8—42no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—42no—
982C2×D4—42no—
983C2×D4—88no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—28no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—42no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C42−1+414yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2511yescharacteristic
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—28no—
1026C4⋊C4—24no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—42no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—41no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—41no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—44no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C42—22no—
1124C42—24no—
1125C42—22no—
1126C42—24no—
1127C42—24no—
1128C42—24no—
1129C42—24no—
1130C42—22no—
1131C42—24no—
1132C42—22no—
1133C42—22no—
1134C42—22no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—42no—
1143C42—44no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C23—22no—
1157C23—21no—
1158C23—21no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—84no—
1168C23—88no—
1169C23—88no—
1170C23—162no—
1171C23—162no—
1172C23C2×2−1+412yes—
1173C23C2611yescharacteristic
1174Q8—48no—
1175Q8—44no—
1176Q8—44no—
1177Q8—48no—
1178Q8—88no—
1179Q8—162no—
1180D4—48no—
1181D4—84no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—28no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—48no—
1249C2×C4—88no—
1250C2×C4—162no—
1251C2×C4—164no—
1252C2×C4C2×2−1+412yes—
1253C2×C4C2×2−1+412yes—
1254C2×C4#58514yes—
1255C2×C4#58514yes—
1256C2×C4#58512yes—
1257C2×C4#58512yes—
1258C22—22no—
1259C22—24no—
1260C22—42no—
1261C22—41no—
1262C22—41no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—168no—
1271C22C22×2−1+411yescharacteristic
1272C22C2×#58511yescharacteristic
1273C22C2×#58511yescharacteristic
1274C22C2×#58512yes—
1275C22C2×#58512yes—
1276C4—22no—
1277C4—24no—
1278C4—24no—
1279C4—44no—
1280C4—42no—
1281C4—42no—
1282C4—44no—
1283C4—42no—
1284C4—42no—
1285C4—44no—
1286C4—42no—
1287C4—44no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—41no—
1292C4—44no—
1293C4—42no—
1294C4—41no—
1295C4—42no—
1296C4—44no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4#356414yes—
1301C2—42no—
1302C2—84no—
1303C2C2×#356411yescharacteristic
1304C2#6274312yes—
1305C2#6283112yes—
1306C2#6283911yescharacteristic
1307C2#6284111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53153C2semidirect
2. #53113C2semidirect
3. #52911C2semidirect
4. #52651C2semidirect
5. #45190C2semidirect
7. #44511C2semidirect
8. #44048C2semidirect
10. #42981C2semidirect
11. #42902C2semidirect
12. #42755C2semidirect
13. #42697C2semidirect
15. #42371C2semidirect
16. #42355C2semidirect
17. #41580C2semidirect
18. #40901C2semidirect
19. #36403C2semidirect
20. #36380C2semidirect
21. #36371C2semidirect
23. #35324C2semidirect
25. #35185C2semidirect
26. #35117C2semidirect
27. #34552C2semidirect
28. #2864C22semidirect
29. #2864C22semidirect
30. #2863C22semidirect
31. #2862C22semidirect
37. #2844C22semidirect
39. #2838C22semidirect
40. #2838C22semidirect
41. #2838C22semidirect
42. #2838C22semidirect
43. #2838C22semidirect
45. #2835C22semidirect
46. #2831C22semidirect
47. #2831C22semidirect
48. #2831C22semidirect
50. #2817C22semidirect
52. #2805C22semidirect
54. #2798C22semidirect
55. #2798C22semidirect
56. #2794C22semidirect
57. #2793C22semidirect
58. #2792C22semidirect
61. #2787C22semidirect
63. #2775C22semidirect
64. #2774C22semidirect
65. #2773C22semidirect
66. #2770C22semidirect
67. #2767C22semidirect
68. #2765C22semidirect
70. #2745C22semidirect
71. #2744C22semidirect
72. #2744C22semidirect
75. #2738C22semidirect
81. #2725C22semidirect
83. #2720C22semidirect
84. #2698C22semidirect
86. #2690C22semidirect
87. #2667C22semidirect
88. #2654C22semidirect
90. #2652C22semidirect
92. #2650C22semidirect
93. #2650C22semidirect
94. #2650C22semidirect
95. #2650C22semidirect
96. #2647C22semidirect
97. #2645C22semidirect
100. #2637C22semidirect
104. #2612C22semidirect
105. #2604C22semidirect
106. #2604C22semidirect
109. #2596C22semidirect
110. #2596C22semidirect
114. #2588C22semidirect
115. #2588C22semidirect
116. #2584C22semidirect
117. #2581C22semidirect
118. #2581C22semidirect
120. #2577C22semidirect
122. #2575C22semidirect
123. #2575C22semidirect
125. #2571C22semidirect
126. #2567C22semidirect
129. #2550C22semidirect
132. #2532C22semidirect
133. #2532C22semidirect
136. #2529C22semidirect
137. #2528C22semidirect
138. #2528C22semidirect
143. #2525C22semidirect
144. #2520C22semidirect
147. #2515C22semidirect
148. #2514C22semidirect
155. #2511C22semidirect
156. #2509C22semidirect
157. #2509C22semidirect
158. #2509C22semidirect
159. #2509C22semidirect
160. #2508C22semidirect
161. #2507C22semidirect
162. #2506C22semidirect
165. #2496C22semidirect
166. #2489C22semidirect
173. #2478C22semidirect
175. #2469C22semidirect
176. #2469C22semidirect
177. #2469C22semidirect
178. #2469C22semidirect
179. #2465C22semidirect
180. #2465C22semidirect
182. #2453C22semidirect
185. #2451C22semidirect
186. #2451C22semidirect
192. #2446C22semidirect
197. #2421C22semidirect
198. #2402C22semidirect
199. #2402C22semidirect
200. #2402C22semidirect
201. #2399C22semidirect
202. #2399C22semidirect
203. #2399C22semidirect
204. #2399C22semidirect
212. #2373C22semidirect
213. #2373C22semidirect
214. #2373C22semidirect
215. #2371C22semidirect
216. #2370C22semidirect
219. #2362C22semidirect
222. #2356C22semidirect
223. #2351C22semidirect
228. #2334C22semidirect
229. #2332C22semidirect
230. #2331C22semidirect
231. #2327C22semidirect
233. #2323C22semidirect
236. #2314C22semidirect
239. C4×C4⋊Q8C22semidirect
242. #2295C22semidirect
243. #2295C22semidirect
246. C42×Q8C22semidirect
247. C42×Q8C22semidirect
248. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#531532
#531132
#529112
#526512
#451902
#449612
#445112
#440482
#429832
#429812
#429022
#427552
#426972
#424872
#423712
#423552
#415802
#409012
#364032
#363802
#363712
#362932
#353242
#352662
#351852
#351172
#345522