Finite Group Databasebeta

← #7644204

Subgroups — #7644204

Order 512.

4500 conjugacy classes of subgroups.

The subgroup lattice has 1479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42905C212yesmaximal, complemented
2#42866C212yesmaximal, complemented
3#42852C212yesmaximal, complemented
4#42832C212yesmaximal, complemented
5#42818C211yesmaximal, characteristic, complemented
6#42807C211yesmaximal, characteristic, complemented
7#42786C212yesmaximal, complemented
8#42697C211yesmaximal, characteristic, complemented
9#42686C211yesmaximal, characteristic, complemented
10#42653C212yesmaximal, complemented
11#42380C214yesmaximal, complemented
12#42285C212yesmaximal, complemented
13#42275C212yesmaximal, complemented
14#41732C214yesmaximal, complemented
15#41679C212yesmaximal, complemented
16#41660C212yesmaximal, complemented
17#37535C212yesmaximal, complemented
18#37490C212yesmaximal, complemented
19#37467C214yesmaximal, complemented
20#37266C212yesmaximal, complemented
21#37261C212yesmaximal, complemented
22#37213C214yesmaximal, complemented
23#35665C212yesmaximal, complemented
24#35663C212yesmaximal, complemented
25#35657C212yesmaximal, complemented
26#35645C212yesmaximal, complemented
27#35163C212yesmaximal, complemented
28#34636C211yesmaximal, characteristic
29#34627C211yesmaximal, characteristic, complemented
30#34291C212yesmaximal, complemented
31C4×#536C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2212yes—
33C2×#536C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C2×#519C2212yes—
37C2×C4×#41C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2866C2214yes—
40#2864C2214yes—
41#2841C2212yes—
42#2839C2214yes—
43#2837C2214yes—
44#2835C2212yes—
45#2831C2214yes—
46#2831C2214yes—
47#2826C2214yes—
48#2824C2212yes—
49#2817C2212yes—
50#2814C2214yes—
51#2809C2212yes—
52#2808C2214yes—
53#2806C2214yes—
54#2805C2214yes—
55#2805C2214yes—
56#2803C2214yes—
57#2800C2214yes—
58#2799C2212yes—
59#2798C2214yes—
60#2795C2212yes—
61#2794C2212yes—
62#2794C2212yes—
63#2792C2212yes—
64#2786C2214yes—
65#2785C2214yes—
66#2783C2214yes—
67#2783C2214yes—
68#2781C2214yes—
69#2779C2214yes—
70#2777C2214yes—
71#2775C2214yes—
72#2775C2214yes—
73#2775C2214yes—
74#2774C2214yes—
75#2774C2214yes—
76#2768C2214yes—
77#2767C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2734C2214yes—
81#2734C2212yes—
82#2731C2214yes—
83#2730C2214yes—
84#2729C2214yes—
85#2729C2214yes—
86#2728C2212yes—
87#2667C2214yes—
88#2666C2214yes—
89#2666C2214yes—
90#2663C2214yes—
91#2654C2214yes—
92#2652C2214yes—
93#2652C2214yes—
94#2652C2214yes—
95#2650C2214yes—
96#2650C2214yes—
97#2650C2214yes—
98#2649C2214yes—
99#2649C2214yes—
100#2649C2214yes—
101#2648C2214yes—
102#2648C2214yes—
103#2638C2214yes—
104#2638C2211yescharacteristic
105#2638C2212yes—
106#2638C2212yes—
107#2638C2211yescharacteristic
108#2637C2212yes—
109#2636C2212yes—
110#2635C2211yescharacteristic
111#2635C2211yescharacteristic
112#2634C2212yes—
113#2634C2211yescharacteristic
114#2633C2212yes—
115#2633C2211yescharacteristic
116#2632C2211yescharacteristic
117#2631C2211yescharacteristic
118#2630C2214yes—
119#2630C2212yes—
120#2630C2212yes—
121#2628C2211yescharacteristic
122#2628C2211yescharacteristic
123#2625C2212yes—
124#2621C2211yescharacteristic
125#2621C2211yescharacteristic
126#2616C2212yes—
127#2609C2214yes—
128#2607C2212yes—
129#2602C2214yes—
130#2600C2212yes—
131#2599C2214yes—
132#2599C2214yes—
133#2597C2214yes—
134#2596C2214yes—
135#2595C2214yes—
136#2590C2214yes—
137#2587C2214yes—
138#2587C2214yes—
139#2582C2212yes—
140#2581C2212yes—
141#2581C2214yes—
142#2575C2214yes—
143#2573C2214yes—
144#2571C2212yes—
145#2565C2212yes—
146#2562C2212yes—
147#2538C2212yes—
148#2538C2212yes—
149#2536C2212yes—
150#2533C2214yes—
151#2533C2214yes—
152#2533C2214yes—
153#2533C2214yes—
154#2530C2214yes—
155#2529C2214yes—
156#2529C2214yes—
157#2526C2214yes—
158#2525C2214yes—
159#2524C2214yes—
160#2524C2214yes—
161#2523C2212yes—
162#2522C2214yes—
163#2518C2214yes—
164#2518C2214yes—
165#2517C2214yes—
166#2517C2212yes—
167#2515C2214yes—
168#2511C2212yes—
169#2511C2212yes—
170#2509C2212yes—
171#2508C2214yes—
172#2508C2212yes—
173#2499C2212yes—
174#2497C2212yes—
175#2497C2212yes—
176#2495C2212yes—
177#2495C2212yes—
178#2489C2212yes—
179#2489C2212yes—
180#2485C2212yes—
181#2485C2212yes—
182#2485C2212yes—
183#2478C2214yes—
184#2477C2214yes—
185#2476C2214yes—
186#2475C2214yes—
187#2474C2214yes—
188#2470C2214yes—
189#2469C2214yes—
190#2465C2214yes—
191#2465C2214yes—
192#2462C2214yes—
193#2462C2214yes—
194#2458C2214yes—
195#2453C2212yes—
196#2451C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2441C2212yes—
200#2439C2212yes—
201#2434C2212yes—
202#2429C2212yes—
203#2429C2212yes—
204#2423C2212yes—
205#2421C2212yes—
206#2421C2212yes—
207#2421C2212yes—
208#2415C2212yes—
209#2415C2212yes—
210#2409C2212yes—
211#2409C2212yes—
212#2409C2212yes—
213#2399C2212yes—
214#2398C2212yes—
215#2396C2211yescharacteristic
216#2396C2211yescharacteristic
217#2395C2212yes—
218#2395C2212yes—
219#2395C2212yes—
220#2392C2211yescharacteristic
221#2392C2211yescharacteristic
222#2388C2212yes—
223#2365C2214yes—
224#2365C2212yes—
225#2362C2214yes—
226#2362C2212yes—
227#2360C2214yes—
228#2360C2212yes—
229#2352C2214yes—
230#2352C2212yes—
231#2351C2212yes—
232Q8×C22⋊C4C2212yes—
233Q8×C22⋊C4C2212yes—
234#2330C2212yes—
235#2327C2212yes—
236#2327C2212yes—
237#2327C2214yes—
238#2326C2212yes—
239#2323C2212yes—
240#2323C2212yes—
241#2323C2212yes—
242#2323C2212yes—
243#2323C2214yes—
244#2322C2212yes—
245#2322C2212yes—
246#2320C2212yes—
247#2317C2211yescharacteristic
248#2314C2212yes—
249#2311C2211yescharacteristic
250#2310C2211yescharacteristic
251C4×C4⋊Q8C2212yes—
252C4×#124C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×C22⋊Q8C2212yes—
257C4×C22⋊Q8C2214yes—
258C4×#123C2212yes—
259C4×#123C2212yes—
260#2290C2212yes—
261#2290C2212yes—
262#2290C2214yes—
263#2283C2211yescharacteristic
264#2283C2211yescharacteristic
265#2276C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C23×Q8C2312yes—
269C23×Q8C2311yescharacteristic
270D4×Q8—216no—
271#536—28no—
272#533—44no—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278#529—44no—
279C2×#126C2312yes—
280C2×#125C2312yes—
281C2×#125C2311yescharacteristic
282C2×#125C2312yes—
283C2×#124C2312yes—
284C2×#124C2311yescharacteristic
285C2×#123C2312yes—
286C2×#123C2312yes—
287C2×#123C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2312yes—
299C2×#121C2311yescharacteristic
300#519—48no—
301C4×#41—44no—
302C2×C4×Q8—44no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2314yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2312yes—
341C22×C42C2311yescharacteristic
342C22×C42C2311yescharacteristic
343C22×C42C2311yescharacteristic
344C22×C42C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
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#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2312yes—
371#400C2311yescharacteristic
372#400C2311yescharacteristic
373#400C2312yes—
374#399C2314yes—
375#399C2314yes—
376#399C2312yes—
377#399C2311yescharacteristic
378#399C2312yes—
379#399C2312yes—
380#399C2311yescharacteristic
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2311yescharacteristic
400#398C2311yescharacteristic
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#397C2311yescharacteristic
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2312yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#397C2312yes—
422#397C2314yes—
423#397C2314yes—
424#397C2312yes—
425#397C2314yes—
426#397C2312yes—
427#397C2311yescharacteristic
428#397C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2312yes—
441#396C2312yes—
442#396C2312yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#395C2312yes—
451#395C2312yes—
452#395C2311yescharacteristic
453#395C2311yescharacteristic
454#395C2312yes—
455#395C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2312yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2312yes—
472#394C2311yescharacteristic
473#394C2311yescharacteristic
474#394C2312yes—
475#393C2312yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2311yescharacteristic
480#393C2314yes—
481#393C2312yes—
482#393C2311yescharacteristic
483#393C2312yes—
484#392C2311yescharacteristic
485#392C2312yes—
486#392C2312yes—
487#392C2312yes—
488#392C2311yescharacteristic
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2312yes—
505#391C2314yes—
506#391C2312yes—
507#391C2314yes—
508#391C2312yes—
509#390C2312yes—
510#390C2314yes—
511#390C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2312yes—
580#388C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#386C2312yes—
638#386C2312yes—
639#386C2314yes—
640#386C2314yes—
641#386C2312yes—
642#386C2314yes—
643#386C2314yes—
644#386C2312yes—
645#386C2312yes—
646#386C2312yes—
647#385C2312yes—
648#385C2314yes—
649#385C2312yes—
650#385C2314yes—
651#385C2314yes—
652#385C2312yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2312yes—
659#385C2312yes—
660#385C2312yes—
661#385C2314yes—
662#385C2314yes—
663#384C2312yes—
664#384C2312yes—
665#384C2312yes—
666#383C2314yes—
667#383C2311yescharacteristic
668#383C2311yescharacteristic
669#383C2312yes—
670#383C2314yes—
671#383C2314yes—
672#382C2311yescharacteristic
673#382C2312yes—
674#382C2311yescharacteristic
675#382C2314yes—
676#382C2312yes—
677#382C2314yes—
678#382C2312yes—
679#382C2314yes—
680#382C2314yes—
681#382C2314yes—
682#382C2312yes—
683#382C2314yes—
684#381C2312yes—
685#381C2312yes—
686#381C2311yescharacteristic
687#381C2311yescharacteristic
688#381C2312yes—
689#380C2312yes—
690#380C2312yes—
691#380C2312yes—
692#380C2312yes—
693#380C2312yes—
694#380C2312yes—
695#380C2314yes—
696#380C2312yes—
697#380C2314yes—
698#380C2312yes—
699#380C2312yes—
700#380C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2311yescharacteristic
718C4×C4⋊C4C2311yescharacteristic
719C4×C4⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2314yes—
735C4×C22⋊C4C2314yes—
736#376C2312yes—
737#376C2312yes—
738#376C2314yes—
739#376C2312yes—
740C43C2312yes—
741C2×#41—24no—
742C2×#41—42no—
743C2×#41—42no—
744C22×Q8—28no—
745C22×Q8—42no—
746C22×Q8—44no—
747C22×Q8—42no—
748C22×Q8—44no—
749C22×Q8#4118yes—
750C22×Q8C2412yes—
751C22×Q8C2412yes—
752C22×Q8C2414yes—
753C22×Q8C2411yescharacteristic
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2412yes—
757C22×D4C2412yes—
758C22×D4C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2411yescharacteristic
761C22×D4C2412yes—
762C22×D4C2411yescharacteristic
763C22×D4C2412yes—
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2411yescharacteristic
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C23×C4C2414yes—
771C23×C4C2411yescharacteristic
772C23×C4C2411yescharacteristic
773C23×C4C2411yescharacteristic
774C23×C4C2411yescharacteristic
775C23×C4C2412yes—
776C23×C4C2412yes—
777C4⋊Q8—28no—
778C4⋊Q8—28no—
779C4⋊Q8—216no—
780C4⋊Q8—42no—
781C4⋊Q8—42no—
782#126—44no—
783#125—44no—
784#125—42no—
785#125—44no—
786#124—28no—
787#124—42no—
788#123—28no—
789#123—28no—
790#123—44no—
791C22⋊Q8—28no—
792C22⋊Q8—28no—
793C22⋊Q8—28no—
794C22⋊Q8—216no—
795C22⋊Q8—28no—
796C22⋊Q8—216no—
797C22⋊Q8—42no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800C22⋊Q8—44no—
801C22⋊Q8—44no—
802#121—42no—
803C4×Q8—28no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—44no—
807C4×Q8—42no—
808C4×Q8—42no—
809C4×Q8—42no—
810C4×Q8—44no—
811C4×Q8—44no—
812C4×Q8—48no—
813C4×Q8—48no—
814C4×Q8—44no—
815C4×Q8—44no—
816C4×Q8—44no—
817C4×Q8—44no—
818C4×D4—28no—
819C4×D4—216no—
820C4×D4—44no—
821C4×D4—42no—
822C4×D4—42no—
823C4×D4—42no—
824C4×D4—42no—
825C4×D4—42no—
826C4×D4—42no—
827C4×D4—42no—
828C4×D4—44no—
829#117—24no—
830#117—28no—
831#117—42no—
832#117—42no—
833#117—42no—
834#117—44no—
835#117—48no—
836#117—48no—
837#117—42no—
838#117—44no—
839C2×C4⋊C4—42no—
840C2×C4⋊C4—44no—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2411yescharacteristic
915C2×C22⋊C4C2411yescharacteristic
916C2×C22⋊C4C2411yescharacteristic
917C2×C22⋊C4C2411yescharacteristic
918C2×C22⋊C4C2411yescharacteristic
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C42—24no—
948C2×C42—24no—
949C2×C42—24no—
950C2×C42—44no—
951C2×C42C2411yescharacteristic
952C2×C42C2414yes—
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2411yescharacteristic
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2411yescharacteristic
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2411yescharacteristic
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053C24C2511yescharacteristic
1054C24C2511yescharacteristic
1055C24C2512yes—
1056C24C2511yescharacteristic
1057#41—416no—
1058C2×Q8—28no—
1059C2×Q8—24no—
1060C2×Q8—22no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—42no—
1066C2×Q8—44no—
1067C2×Q8—41no—
1068C2×Q8—42no—
1069C2×Q8—44no—
1070C2×Q8—41no—
1071C2×Q8—41no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×Q8—42no—
1075C2×Q8—416no—
1076C2×Q8—432no—
1077C2×Q8C2×#4118yes—
1078C2×Q8C2×#4118yes—
1079C2×D4—24no—
1080C2×D4—22no—
1081C2×D4—22no—
1082C2×D4—22no—
1083C2×D4—41no—
1084C2×D4—41no—
1085C2×D4—41no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D4—41no—
1089C2×D4—41no—
1090C2×D4—41no—
1091C2×D4—42no—
1092C2×D4—41no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—28no—
1102C22×C4—24no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—22no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—24no—
1110C22×C4—22no—
1111C22×C4—24no—
1112C22×C4—22no—
1113C22×C4—22no—
1114C22×C4—22no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—42no—
1118C22×C4—44no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4C2×#4114yes—
1130C22×C4C2×#4118yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2511yescharacteristic
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2514yes—
1140C22×C4C2514yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2514yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2514yes—
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2514yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2511yescharacteristic
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—28no—
1164C4⋊C4—28no—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—28no—
1168C4⋊C4—28no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—28no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—41no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—41no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—41no—
1213C4⋊C4—44no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—44no—
1250C22⋊C4—41no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C42—24no—
1265C42—28no—
1266C42—24no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—22no—
1273C42—22no—
1274C42—22no—
1275C42—22no—
1276C42—28no—
1277C42—24no—
1278C42—28no—
1279C42—24no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—42no—
1287C42—44no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42H(5,𝔽2)14yes—
1292C23—21no—
1293C23—21no—
1294C23—22no—
1295C23—22no—
1296C23—21no—
1297C23—21no—
1298C23—22no—
1299C23—22no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—22no—
1304C23—21no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23C22×#4112yes—
1314C23C2611yescharacteristic
1315Q8—216no—
1316Q8—48no—
1317Q8—416no—
1318Q8—44no—
1319Q8—48no—
1320Q8—82no—
1321Q8—84no—
1322D4—44no—
1323D4—48no—
1324D4—44no—
1325D4—44no—
1326D4—82no—
1327D4—84no—
1328D4—84no—
1329C2×C4—21no—
1330C2×C4—24no—
1331C2×C4—21no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—28no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—21no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—48no—
1397C2×C4—44no—
1398C2×C4—44no—
1399C2×C4—416no—
1400C2×C4—48no—
1401C2×C4—44no—
1402C2×C4—44no—
1403C2×C4—82no—
1404C2×C4—82no—
1405C2×C4—82no—
1406C2×C4—82no—
1407C2×C4—84no—
1408C2×C4C22×#4112yes—
1409C2×C4C22×#4118yes—
1410C2×C4C22×#4112yes—
1411C2×C4C2×H(5,𝔽2)12yes—
1412C2×C4C2×H(5,𝔽2)12yes—
1413C2×C4C2×H(5,𝔽2)12yes—
1414C2×C4#58512yes—
1415C22—24no—
1416C22—22no—
1417C22—41no—
1418C22—41no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—41no—
1436C22—41no—
1437C22C23×#4111yescharacteristic
1438C22C22×H(5,𝔽2)11yescharacteristic
1439C22C2×#58511yescharacteristic
1440C222−1+612yes—
1441C222−1+612yes—
1442C4—22no—
1443C4—22no—
1444C4—22no—
1445C4—28no—
1446C4—44no—
1447C4—42no—
1448C4—44no—
1449C4—42no—
1450C4—41no—
1451C4—41no—
1452C4—41no—
1453C4—41no—
1454C4—44no—
1455C4—41no—
1456C4—41no—
1457C4—42no—
1458C4—42no—
1459C4—44no—
1460C4—42no—
1461C4—44no—
1462C4—44no—
1463C4—42no—
1464C4—41no—
1465C4—41no—
1466C4—44no—
1467C4—42no—
1468C4#345914yes—
1469C2—42no—
1470C2—82no—
1471C2—81no—
1472C2—81no—
1473C2C2×#345911yescharacteristic
1474C2#6285012yes—
1475C2#6288611yescharacteristic
1476C2#6288611yescharacteristic
1477C2#6289012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34636C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42905C2semidirect
2. #42866C2semidirect
3. #42852C2semidirect
4. #42832C2semidirect
5. #42818C2semidirect
6. #42807C2semidirect
7. #42786C2semidirect
8. #42697C2semidirect
9. #42686C2semidirect
10. #42653C2semidirect
11. #42380C2semidirect
12. #42285C2semidirect
13. #42275C2semidirect
14. #41732C2semidirect
15. #41679C2semidirect
16. #41660C2semidirect
17. #37535C2semidirect
18. #37490C2semidirect
19. #37467C2semidirect
20. #37266C2semidirect
21. #37261C2semidirect
22. #37213C2semidirect
23. #35665C2semidirect
24. #35663C2semidirect
25. #35657C2semidirect
26. #35645C2semidirect
27. #35163C2semidirect
29. #34627C2semidirect
30. #34291C2semidirect
31. C4×#536C2semidirect

Maximal subgroups

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

subgroupindex
#429052
#428662
#428522
#428322
#428182
#428072
#427862
#426972
#426862
#426532
#423802
#422852
#422752
#417322
#416792
#416602
#375352
#374902
#374672
#372662
#372612
#372132
#356652
#356632
#356572
#356452
#351632
#346362
#346272
#342912
C4×#5362