Finite Group Databasebeta

← #7643479

Subgroups — #7643479

Order 512.

5028 conjugacy classes of subgroups.

The subgroup lattice has 1456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40388C214yesmaximal, complemented
2#40356C214yesmaximal, complemented
3#39318C214yesmaximal, complemented
4#39101C214yesmaximal, complemented
5#38890C214yesmaximal, complemented
6#38857C214yesmaximal, complemented
7#38355C214yesmaximal, complemented
8#38320C214yesmaximal, complemented
9#37430C212yesmaximal, complemented
10#37426C211yesmaximal, characteristic, complemented
11#37418C211yesmaximal, characteristic, complemented
12#37381C211yesmaximal, characteristic, complemented
13#37284C211yesmaximal, characteristic, complemented
14#37268C212yesmaximal, complemented
15#36621C212yesmaximal, complemented
16#35654C212yesmaximal, complemented
17#35648C212yesmaximal, complemented
18#35590C212yesmaximal, complemented
19#35525C212yesmaximal, complemented
20#35314C211yesmaximal, characteristic, complemented
21#35268C211yesmaximal, characteristic, complemented
22#35046C212yesmaximal, complemented
23#35044C212yesmaximal, complemented
24#35029C212yesmaximal, complemented
25#35026C212yesmaximal, complemented
26#34267C212yesmaximal, complemented
27C4×#525C211yesmaximal, characteristic, complemented
28C2×#537C2212yes—
29C2×#529C2212yes—
30C2×#525C2211yescharacteristic
31C2×#520C2212yescomplemented
32C2×C4×#41C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2864C2211yescharacteristic, complemented
35#2864C2211yescharacteristic, complemented
36#2863C2212yescomplemented
37#2862C2211yescharacteristic, complemented
38#2860C2212yescomplemented
39#2858C2211yescharacteristic, complemented
40#2855C2212yes—
41#2854C2212yes—
42#2853C2214yes—
43#2852C2214yes—
44#2852C2214yes—
45#2851C2212yes—
46#2851C2212yes—
47#2850C2212yes—
48#2850C2212yes—
49#2849C2214yes—
50#2848C2212yes—
51#2847C2212yes—
52#2804C2214yes—
53#2799C2212yescomplemented
54#2799C2212yescomplemented
55#2796C2214yes—
56#2788C2214yes—
57#2787C2214yescomplemented
58#2784C2212yescomplemented
59#2784C2212yescomplemented
60#2782C2214yes—
61#2778C2214yes—
62#2777C2214yescomplemented
63#2773C2214yescomplemented
64#2771C2212yes—
65#2771C2214yescomplemented
66#2770C2214yes—
67#2764C2212yes—
68#2760C2212yes—
69#2757C2214yes—
70#2752C2212yes—
71#2748C2214yes—
72#2746C2214yes—
73#2736C2212yes—
74#2735C2212yes—
75#2732C2214yes—
76#2728C2214yes—
77#2728C2212yescomplemented
78#2728C2212yescomplemented
79#2708C2214yes—
80#2701C2214yes—
81#2699C2212yescomplemented
82#2699C2212yescomplemented
83#2688C2214yes—
84#2688C2214yes—
85#2688C2214yes—
86#2686C2214yes—
87#2678C2214yes—
88#2671C2214yes—
89#2670C2212yes—
90#2668C2214yes—
91#2668C2212yes—
92#2655C2214yescomplemented
93#2654C2214yescomplemented
94#2653C2214yescomplemented
95#2652C2214yes—
96#2649C2214yes—
97#2648C2214yescomplemented
98#2636C2214yes—
99#2631C2214yes—
100#2628C2211yescharacteristic
101#2628C2211yescharacteristic
102#2625C2212yes—
103#2624C2212yes—
104#2621C2211yescharacteristic
105#2619C2211yescharacteristic
106#2609C2214yescomplemented
107#2600C2214yes—
108#2598C2214yes—
109#2598C2214yescomplemented
110#2597C2214yes—
111#2597C2214yescomplemented
112#2589C2214yes—
113#2589C2214yescomplemented
114#2585C2214yescomplemented
115#2579C2214yes—
116#2577C2214yescomplemented
117#2576C2214yes—
118#2576C2214yes—
119#2575C2214yes—
120#2573C2214yes—
121#2573C2214yescomplemented
122#2572C2214yes—
123#2572C2214yescomplemented
124#2557C2214yes—
125#2557C2214yes—
126#2553C2214yes—
127#2535C2214yes—
128#2533C2214yescomplemented
129#2532C2214yescomplemented
130#2527C2214yescomplemented
131#2526C2214yescomplemented
132#2524C2214yescomplemented
133#2523C2214yes—
134#2521C2214yescomplemented
135#2520C2214yescomplemented
136#2518C2214yescomplemented
137#2517C2214yes—
138#2516C2214yescomplemented
139#2515C2214yescomplemented
140#2514C2212yescomplemented
141#2514C2214yescomplemented
142#2513C2212yescomplemented
143#2509C2212yescomplemented
144#2508C2212yescomplemented
145#2504C2212yescomplemented
146#2503C2212yescomplemented
147#2495C2212yes—
148#2494C2212yes—
149#2493C2214yescomplemented
150#2492C2212yes—
151#2491C2212yes—
152#2487C2212yes—
153#2486C2212yes—
154#2485C2214yescomplemented
155#2484C2214yescomplemented
156#2481C2214yescomplemented
157#2481C2214yescomplemented
158#2478C2214yescomplemented
159#2470C2214yes—
160#2468C2214yescomplemented
161#2467C2214yes—
162#2467C2214yescomplemented
163#2459C2214yes—
164#2459C2214yes—
165#2459C2214yescomplemented
166#2457C2214yes—
167#2457C2214yes—
168#2456C2214yes—
169#2456C2214yes—
170#2454C2212yescomplemented
171#2453C2212yescomplemented
172#2448C2212yescomplemented
173#2447C2214yes—
174#2447C2212yescomplemented
175#2443C2214yes—
176#2443C2214yes—
177#2442C2212yescomplemented
178#2442C2212yescomplemented
179#2439C2212yescomplemented
180#2439C2212yescomplemented
181#2432C2212yescomplemented
182#2431C2212yescomplemented
183#2429C2212yes—
184#2428C2212yes—
185#2421C2212yes—
186#2420C2212yes—
187#2419C2214yes—
188#2417C2212yes—
189#2416C2212yes—
190#2415C2212yes—
191#2414C2212yes—
192#2407C2212yes—
193#2407C2212yes—
194#2364C2214yes—
195#2364C2214yescomplemented
196#2363C2214yes—
197#2362C2214yescomplemented
198#2361C2214yes—
199#2361C2214yes—
200#2361C2214yescomplemented
201#2360C2214yescomplemented
202#2337C2214yes—
203#2337C2214yescomplemented
204#2334C2214yescomplemented
205#2333C2214yes—
206#2331C2211yescharacteristic, complemented
207#2331C2211yescharacteristic, complemented
208#2328C2211yescharacteristic, complemented
209#2327C2211yescharacteristic, complemented
210#2325C2214yes—
211#2324C2212yes—
212#2324C2212yescomplemented
213#2323C2212yes—
214#2323C2212yescomplemented
215#2322C2214yes—
216#2320C2212yescomplemented
217#2319C2212yescomplemented
218#2318C2214yescomplemented
219#2313C2214yescomplemented
220#2311C2212yes—
221C4×C22⋊Q8C2212yes—
222C4×C22⋊Q8C2212yes—
223C4×C22⋊Q8C2212yes—
224C4×C22⋊Q8C2212yes—
225C4×C22⋊Q8C2212yescomplemented
226C4×#123C2214yes—
227C4×#123C2212yes—
228C4×#123C2212yes—
229C4×#121C2212yes—
230C4×#121C2212yes—
231C4×#121C2212yes—
232C4×#121C2212yes—
233C4×#121C2212yescomplemented
234C4×#120C2214yes—
235C4×#120C2212yes—
236C4×#120C2212yes—
237#2297C2211yescharacteristic
238#2297C2212yescomplemented
239#2296C2211yescharacteristic
240C2×#389C2212yescomplemented
241#2290C2212yes—
242#2290C2214yes—
243#2290C2214yes—
244#2290C2212yes—
245#2283C2212yes—
246#2280C2211yescharacteristic
247#2274C2212yescomplemented
248C42×D4C2212yes—
249C42×D4C2212yes—
250C4×#117C2211yescharacteristic
251C22×#41C2312yes—
252C22×#41C2311yescharacteristic
253C24×C4C2311yescharacteristic
254C24×C4C2312yes—
255#537—216no—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×#127C2311yescharacteristic
260#529—48no—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#125C2312yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#124C2312yes—
267#525—28no—
268C2×#123C2312yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#120C2312yes—
289C2×#120C2314yes—
290#520—48no—
291C4×#41—44no—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×#117C2312yes—
313C2×#117C2311yescharacteristic
314C2×#117C2312yes—
315C2×#117C2311yescharacteristic
316C2×#117C2314yes—
317C2×#117C2314yes—
318C2×#117C2311yescharacteristic
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2314yes—
323C22×C42—44no—
324C22×C42C2311yescharacteristic
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327C22×C42C2312yes—
328C22×C42C2312yes—
329C22×C42C2312yes—
330C22×C42C2312yes—
331C22×C42C2312yes—
332#401C2314yes—
333#401C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2312yes—
355#399C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2312yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#395C2312yes—
391#395C2312yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2312yes—
401#394C2312yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2312yes—
411#393C2312yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2312yes—
416#392C2312yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#390C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2314yes—
443#390C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#388C2314yes—
471#388C2314yes—
472#388C2312yes—
473#388C2314yes—
474#388C2314yes—
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#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
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#388C2312yes—
504#388C2312yes—
505#388C2312yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#386C2314yes—
543#386C2314yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2312yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2312yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2312yes—
576#386C2312yes—
577#386C2312yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2312yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2312yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2312yes—
604#385C2312yes—
605#385C2312yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#382C2314yes—
612#382C2314yes—
613#382C2314yes—
614#382C2311yescharacteristic
615#382C2311yescharacteristic
616#382C2311yescharacteristic
617#382C2311yescharacteristic
618#382C2312yes—
619#382C2312yes—
620#381C2314yes—
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#381C2311yescharacteristic
629#381C2311yescharacteristic
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#379C2314yes—
646#379C2311yescharacteristic
647#379C2311yescharacteristic
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2312yes—
690#376C2311yescharacteristic
691#376C2311yescharacteristic
692#376C2314yes—
693C2×#95C2314yes—
694C43C2311yescharacteristic
695C43C2311yescharacteristic
696C25C2411yescharacteristic
697C2×#41—28no—
698C2×#41—42no—
699C2×#41—42no—
700C2×#41—44no—
701C2×#41—44no—
702C2×#41#4118yes—
703C22×Q8C2412yes—
704C22×Q8C2412yes—
705C22×Q8C2412yes—
706C22×Q8C2411yescharacteristic
707C22×D4C2412yes—
708C22×D4C2412yes—
709C22×D4C2412yes—
710C22×D4C2414yes—
711C22×D4C2414yes—
712C22×D4C2414yes—
713C22×D4C2414yes—
714C22×D4C2414yes—
715C22×D4C2412yes—
716C22×D4C2412yes—
717C22×D4C2412yes—
718C22×D4C2411yescharacteristic
719C23×C4—24no—
720C23×C4—42no—
721C23×C4—44no—
722C23×C4—42no—
723C23×C4—44no—
724C23×C4—44no—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C4⋊Q8—42no—
744C4⋊Q8—42no—
745C4⋊Q8—42no—
746#127—42no—
747#126—48no—
748#126—48no—
749#125—44no—
750#124—48no—
751#124—44no—
752#124—48no—
753#123—28no—
754#123—48no—
755#123—48no—
756#123—48no—
757C22⋊Q8—28no—
758C22⋊Q8—216no—
759C22⋊Q8—28no—
760C22⋊Q8—28no—
761C22⋊Q8—44no—
762C22⋊Q8—44no—
763#121—28no—
764#121—216no—
765#121—216no—
766#121—216no—
767#121—28no—
768#121—28no—
769#121—48no—
770#121—48no—
771#121—44no—
772#121—44no—
773#120—28no—
774#120—48no—
775C4×Q8—28no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×D4—28no—
779C4×D4—28no—
780C4×D4—28no—
781C4×D4—44no—
782C4×D4—48no—
783C4×D4—44no—
784C4×D4—44no—
785C4×D4—44no—
786C4×D4—48no—
787C4×D4—48no—
788C4×D4—48no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—48no—
792C4×D4—44no—
793C4×D4—48no—
794C4×D4—44no—
795#117—24no—
796#117—28no—
797#117—42no—
798#117—42no—
799#117—48no—
800#117—48no—
801#117—44no—
802C2×C4⋊C4—28no—
803C2×C4⋊C4—48no—
804C2×C4⋊C4—48no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2411yescharacteristic
869C2×C22⋊C4C2411yescharacteristic
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C42—24no—
903C2×C42—28no—
904C2×C42—44no—
905C2×C42—44no—
906C2×C42—44no—
907C2×C42—44no—
908C2×C42—44no—
909C2×C42—42no—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002C24—22no—
1003C24—24no—
1004C24—41no—
1005C24—42no—
1006C24—41no—
1007C24C2514yes—
1008C24C2511yescharacteristic
1009C24C2512yes—
1010C24C2512yes—
1011#41—416no—
1012#41—432no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—41no—
1017C2×Q8—41no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×Q8C2×#4114yes—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—28no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—28no—
1029C2×D4—28no—
1030C2×D4—28no—
1031C2×D4—28no—
1032C2×D4—24no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—41no—
1036C2×D4—42no—
1037C2×D4—44no—
1038C2×D4—42no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—41no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4C2×#4118yes—
1056C2×D4C2×#4114yes—
1057C22×C4—22no—
1058C22×C4—24no—
1059C22×C4—22no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—28no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—28no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—41no—
1083C22×C4—42no—
1084C22×C4—44no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—41no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—416no—
1110C22×C4—432no—
1111C22×C4C2×#4118yes—
1112C22×C4C2×#4114yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2514yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2514yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—24no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—41no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—41no—
1199C22⋊C4—41no—
1200C22⋊C4—44no—
1201C22⋊C4—41no—
1202C22⋊C4—44no—
1203C22⋊C4—41no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C42—22no—
1233C42—22no—
1234C42—22no—
1235C42—24no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—28no—
1241C42—22no—
1242C42—22no—
1243C42—24no—
1244C42—24no—
1245C42—42no—
1246C42—42no—
1247C42—41no—
1248C42—41no—
1249C42—42no—
1250C42—42no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—42no—
1256C42—42no—
1257C42—44no—
1258C42—44no—
1259C42H(5,𝔽2)14yes—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—21no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—21no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—24no—
1277C23—24no—
1278C23—24no—
1279C23—24no—
1280C23—24no—
1281C23—24no—
1282C23—24no—
1283C23—48no—
1284C23—44no—
1285C23—48no—
1286C23—44no—
1287C23—44no—
1288C23C22×#4112yes—
1289C23C22×#4114yes—
1290C23#58514yes—
1291C23C2611yescharacteristic
1292Q8—44no—
1293Q8—48no—
1294Q8—162no—
1295Q8—162no—
1296D4—48no—
1297D4—44no—
1298D4—48no—
1299D4—48no—
1300D4—416no—
1301D4—48no—
1302D4—88no—
1303D4—88no—
1304D4—88no—
1305D4—88no—
1306D4—162no—
1307D4—162no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—28no—
1317C2×C4—216no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—48no—
1369C2×C4—48no—
1370C2×C4—48no—
1371C2×C4—48no—
1372C2×C4—48no—
1373C2×C4—48no—
1374C2×C4—416no—
1375C2×C4—44no—
1376C2×C4—48no—
1377C2×C4—48no—
1378C2×C4—88no—
1379C2×C4—84no—
1380C2×C4—84no—
1381C2×C4—88no—
1382C2×C4—164no—
1383C2×C4—164no—
1384C2×C4C22×#4114yes—
1385C2×C4C22×#4112yes—
1386C2×C4C22×#4112yes—
1387C2×C4C2×H(5,𝔽2)14yes—
1388C2×C4C2×H(5,𝔽2)12yes—
1389C2×C4#58514yes—
1390C2×C4#58512yes—
1391C22—24no—
1392C22—24no—
1393C22—24no—
1394C22—24no—
1395C22—24no—
1396C22—24no—
1397C22—22no—
1398C22—24no—
1399C22—416no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—41no—
1407C22—42no—
1408C22—42no—
1409C22—41no—
1410C22—42no—
1411C22—44no—
1412C22—44no—
1413C22—44no—
1414C22—44no—
1415C22—44no—
1416C22—44no—
1417C22—44no—
1418C22C23×#4111yescharacteristic
1419C22C22×H(5,𝔽2)11yescharacteristic
1420C22C2×#58512yes—
1421C22C2×#58512yes—
1422C22C2×#58511yescharacteristic
1423C4—24no—
1424C4—24no—
1425C4—22no—
1426C4—24no—
1427C4—44no—
1428C4—44no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—42no—
1436C4—44no—
1437C4—44no—
1438C4—41no—
1439C4—41no—
1440C4—41no—
1441C4—41no—
1442C4—44no—
1443C4—42no—
1444C4—44no—
1445C4#345914yes—
1446C2—44no—
1447C2—44no—
1448C2—42no—
1449C2—84no—
1450C2C2×#345911yescharacteristic
1451C2#6281012yes—
1452C2#6282112yes—
1453C2#6282911yescharacteristic
1454C2#6283911yescharacteristic
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. #40388C2semidirect
2. #40356C2semidirect
3. #39318C2semidirect
4. #39101C2semidirect
5. #38890C2semidirect
6. #38857C2semidirect
7. #38355C2semidirect
8. #38320C2semidirect
9. #37430C2semidirect
10. #37426C2semidirect
11. #37418C2semidirect
12. #37381C2semidirect
13. #37284C2semidirect
14. #37268C2semidirect
15. #36621C2semidirect
16. #35654C2semidirect
17. #35648C2semidirect
18. #35590C2semidirect
19. #35525C2semidirect
20. #35314C2semidirect
21. #35268C2semidirect
22. #35046C2semidirect
23. #35044C2semidirect
24. #35029C2semidirect
25. #35026C2semidirect
26. #34267C2semidirect
27. C4×#525C2semidirect
31. C2×#520C22semidirect
34. #2864C22semidirect
35. #2864C22semidirect
36. #2863C22semidirect
37. #2862C22semidirect
38. #2860C22semidirect
39. #2858C22semidirect
53. #2799C22semidirect
54. #2799C22semidirect
57. #2787C22semidirect
58. #2784C22semidirect
59. #2784C22semidirect
62. #2777C22semidirect
63. #2773C22semidirect
65. #2771C22semidirect
77. #2728C22semidirect
78. #2728C22semidirect
81. #2699C22semidirect
82. #2699C22semidirect
92. #2655C22semidirect
93. #2654C22semidirect
94. #2653C22semidirect
97. #2648C22semidirect
106. #2609C22semidirect
109. #2598C22semidirect
111. #2597C22semidirect
113. #2589C22semidirect
114. #2585C22semidirect
116. #2577C22semidirect
121. #2573C22semidirect
123. #2572C22semidirect
128. #2533C22semidirect
129. #2532C22semidirect
130. #2527C22semidirect
131. #2526C22semidirect
132. #2524C22semidirect
134. #2521C22semidirect
135. #2520C22semidirect
136. #2518C22semidirect
138. #2516C22semidirect
139. #2515C22semidirect
140. #2514C22semidirect
141. #2514C22semidirect
142. #2513C22semidirect
143. #2509C22semidirect
144. #2508C22semidirect
145. #2504C22semidirect
146. #2503C22semidirect
149. #2493C22semidirect
154. #2485C22semidirect
155. #2484C22semidirect
156. #2481C22semidirect
157. #2481C22semidirect
158. #2478C22semidirect
160. #2468C22semidirect
162. #2467C22semidirect
165. #2459C22semidirect
170. #2454C22semidirect
171. #2453C22semidirect
172. #2448C22semidirect
174. #2447C22semidirect
177. #2442C22semidirect
178. #2442C22semidirect
179. #2439C22semidirect
180. #2439C22semidirect
181. #2432C22semidirect
182. #2431C22semidirect
195. #2364C22semidirect
197. #2362C22semidirect
200. #2361C22semidirect
201. #2360C22semidirect
203. #2337C22semidirect
204. #2334C22semidirect
206. #2331C22semidirect
207. #2331C22semidirect
208. #2328C22semidirect
209. #2327C22semidirect
212. #2324C22semidirect
214. #2323C22semidirect
216. #2320C22semidirect
217. #2319C22semidirect
218. #2318C22semidirect
219. #2313C22semidirect
225. C4×C22⋊Q8C22semidirect
233. C4×#121C22semidirect
238. #2297C22semidirect
240. C2×#389C22semidirect
247. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#403882
#403562
#393182
#391012
#388902
#388572
#383552
#383202
#374302
#374262
#374182
#373812
#372842
#372682
#366212
#356542
#356482
#355902
#355252
#353142
#352682
#350462
#350442
#350292
#350262
#342672
C4×#5252