Finite Group Databasebeta

← #7651851

Subgroups — #7651851

Order 512.

4752 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42941C211yesmaximal, characteristic, complemented
2#42937C211yesmaximal, characteristic, complemented
3#42709C212yesmaximal, complemented
4#42673C211yesmaximal, characteristic
5#42639C212yesmaximal, complemented
6#42487C211yesmaximal, characteristic, complemented
7#41788C214yesmaximal, complemented
8#41616C214yesmaximal, complemented
9#41367C214yesmaximal, complemented
10#41077C214yesmaximal, complemented
11#40476C214yesmaximal, complemented
12#40073C212yesmaximal, complemented
13#39939C212yesmaximal, complemented
14#39542C214yesmaximal, complemented
15#39035C212yesmaximal, complemented
16#38918C212yesmaximal, complemented
17#38329C214yesmaximal, complemented
18#38258C214yesmaximal, complemented
19#35665C212yesmaximal, complemented
20#35632C212yesmaximal, complemented
21#35547C212yesmaximal, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35200C212yesmaximal, complemented
24#34879C211yesmaximal, characteristic, complemented
25#34720C212yesmaximal, complemented
26#34292C212yesmaximal, complemented
27#34211C211yesmaximal, characteristic, complemented
28C2×#546C2212yes—
29C2×#533C2212yescomplemented
30C22×#124C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#518C2211yescharacteristic
33C2×C4×#41C2212yes—
34#2864C2211yescharacteristic, complemented
35#2862C2211yescharacteristic, complemented
36#2855C2212yes—
37#2851C2214yescomplemented
38#2851C2214yescomplemented
39#2840C2212yes—
40#2835C2214yescomplemented
41#2833C2212yescomplemented
42#2832C2212yescomplemented
43#2826C2214yescomplemented
44#2812C2212yes—
45#2804C2212yes—
46#2787C2214yescomplemented
47#2786C2214yescomplemented
48#2784C2212yes—
49#2781C2214yescomplemented
50#2779C2214yescomplemented
51#2771C2212yes—
52#2771C2212yes—
53#2771C2214yescomplemented
54#2765C2214yes—
55#2765C2214yescomplemented
56#2764C2212yes—
57#2764C2214yescomplemented
58#2753C2214yescomplemented
59#2752C2212yes—
60#2751C2214yes—
61#2751C2214yescomplemented
62#2747C2214yescomplemented
63#2745C2214yes—
64#2745C2214yescomplemented
65#2745C2214yescomplemented
66#2739C2214yes—
67#2739C2214yescomplemented
68#2737C2214yes—
69#2737C2214yescomplemented
70#2724C2212yes—
71#2717C2214yes—
72#2717C2214yes—
73#2707C2214yes—
74#2702C2214yescomplemented
75#2701C2214yes—
76#2699C2212yes—
77#2692C2214yes—
78#2690C2214yescomplemented
79#2686C2214yes—
80#2686C2214yes—
81#2666C2214yescomplemented
82#2653C2214yescomplemented
83#2653C2214yescomplemented
84#2653C2214yescomplemented
85#2652C2214yescomplemented
86#2650C2214yescomplemented
87#2650C2214yescomplemented
88#2645C2212yescomplemented
89#2643C2214yescomplemented
90#2638C2214yescomplemented
91#2638C2214yescomplemented
92#2628C2211yescharacteristic
93#2627C2214yescomplemented
94#2626C2214yes—
95#2622C2214yes—
96#2622C2214yes—
97#2621C2211yescharacteristic
98#2609C2214yes—
99#2599C2214yes—
100#2599C2214yescomplemented
101#2599C2214yescomplemented
102#2599C2214yescomplemented
103#2594C2214yescomplemented
104#2588C2214yescomplemented
105#2588C2214yescomplemented
106#2586C2212yescomplemented
107#2586C2212yescomplemented
108#2581C2214yescomplemented
109#2580C2212yes—
110#2577C2214yescomplemented
111#2576C2214yescomplemented
112#2575C2214yes—
113#2575C2214yescomplemented
114#2574C2212yescomplemented
115#2573C2212yescomplemented
116#2572C2212yes—
117#2572C2214yescomplemented
118#2570C2212yescomplemented
119#2568C2212yescomplemented
120#2567C2212yescomplemented
121#2563C2212yes—
122#2553C2212yes—
123#2547C2212yes—
124#2547C2212yes—
125#2546C2212yescomplemented
126#2530C2214yescomplemented
127#2528C2214yescomplemented
128#2527C2214yes—
129#2527C2214yescomplemented
130#2524C2212yescomplemented
131#2523C2214yescomplemented
132#2523C2214yescomplemented
133#2523C2214yescomplemented
134#2518C2214yescomplemented
135#2517C2214yescomplemented
136#2515C2212yes—
137#2515C2214yescomplemented
138#2514C2212yescomplemented
139#2514C2212yescomplemented
140#2511C2212yescomplemented
141#2506C2212yescomplemented
142#2505C2214yescomplemented
143#2505C2214yescomplemented
144#2505C2214yescomplemented
145#2499C2212yescomplemented
146#2499C2212yescomplemented
147#2497C2212yescomplemented
148#2493C2214yescomplemented
149#2493C2214yescomplemented
150#2492C2212yescomplemented
151#2489C2214yescomplemented
152#2485C2214yescomplemented
153#2485C2214yescomplemented
154#2483C2214yes—
155#2483C2212yes—
156#2481C2214yescomplemented
157#2477C2214yes—
158#2477C2214yescomplemented
159#2475C2214yes—
160#2475C2214yescomplemented
161#2473C2214yescomplemented
162#2468C2212yescomplemented
163#2465C2214yescomplemented
164#2463C2214yescomplemented
165#2462C2214yescomplemented
166#2460C2214yescomplemented
167#2460C2214yescomplemented
168#2457C2212yes—
169#2452C2212yes—
170#2452C2212yes—
171#2451C2212yescomplemented
172#2450C2214yescomplemented
173#2447C2212yes—
174#2447C2212yes—
175#2447C2212yes—
176#2446C2212yescomplemented
177#2446C2212yescomplemented
178#2439C2212yes—
179#2439C2212yescomplemented
180#2437C2212yes—
181#2434C2212yes—
182#2432C2212yes—
183#2432C2212yes—
184#2432C2212yes—
185#2429C2212yescomplemented
186#2427C2212yes—
187#2427C2212yes—
188#2421C2212yescomplemented
189#2421C2212yescomplemented
190#2420C2212yes—
191#2415C2212yes—
192#2415C2212yescomplemented
193#2412C2214yes—
194#2409C2212yes—
195#2407C2212yes—
196#2402C2211yescharacteristic, complemented
197#2398C2214yescomplemented
198#2398C2211yescharacteristic, complemented
199#2396C2211yescharacteristic
200#2392C2211yescharacteristic
201#2392C2214yescomplemented
202#2367C2214yes—
203#2367C2214yes—
204#2367C2212yes—
205#2363C2212yes—
206#2362C2212yes—
207#2361C2214yes—
208#2359C2214yes—
209#2358C2214yes—
210#2354C2212yes—
211D4×C4⋊C4C2212yes—
212#2342C2214yes—
213#2342C2214yes—
214#2342C2214yes—
215#2339C2212yes—
216D4×C22⋊C4C2212yes—
217#2336C2214yescomplemented
218#2331C2211yescharacteristic, complemented
219#2329C2214yescomplemented
220#2327C2212yescomplemented
221#2327C2211yescharacteristic, complemented
222#2326C2212yes—
223#2326C2212yes—
224#2326C2212yes—
225#2325C2214yes—
226#2323C2212yes—
227#2321C2214yes—
228#2320C2212yescomplemented
229#2315C2214yes—
230#2313C2214yescomplemented
231#2310C2211yescharacteristic
232#2309C2211yescharacteristic
233C4×#126C2212yescomplemented
234C4×#124C2212yes—
235C4×#124C2212yes—
236C4×C22⋊Q8C2214yescomplemented
237C4×C22⋊Q8C2212yescomplemented
238C4×#123C2212yes—
239C4×#123C2214yes—
240C4×#121C2212yes—
241#2295C2211yescharacteristic, complemented
242#2295C2212yescomplemented
243#2290C2212yes—
244#2290C2214yescomplemented
245C2×#388C2214yes—
246#2285C2211yescharacteristic
247#2283C2212yescomplemented
248#2275C2212yes—
249C42×D4C2211yescharacteristic, complemented
250C4×#117C2211yescharacteristic
251C22×#41C2312yes—
252C23×Q8C2311yescharacteristic
253C23×D4C2311yescharacteristic
254#546—216no—
255#533—48no—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×#126C2312yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#124—28no—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#124C2312yes—
269C2×#123C2314yes—
270C2×#123C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#120C2314yes—
281#519—44no—
282#518—44no—
283C4×#41—48no—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2314yes—
308C2×#117C2314yes—
309C2×#117C2314yes—
310C2×#117C2312yes—
311C22×C4⋊C4C2314yes—
312C22×C22⋊C4C2314yes—
313C22×C22⋊C4C2314yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2314yes—
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2314yes—
319#401C2314yes—
320#401C2314yes—
321#401C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2311yescharacteristic
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#399C2314yes—
345#399C2312yes—
346#399C2311yescharacteristic
347#398C2314yes—
348#398C2312yes—
349#398C2312yes—
350#398C2314yes—
351#398C2311yescharacteristic
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2312yes—
361#397C2314yes—
362#397C2314yes—
363#397C2312yes—
364#397C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2311yescharacteristic
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2312yes—
389#396C2314yes—
390#396C2314yes—
391#396C2312yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2311yescharacteristic
397#395C2312yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#394C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2312yes—
407#394C2314yes—
408#394C2311yescharacteristic
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2311yescharacteristic
420#393C2312yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2312yes—
428#393C2314yes—
429#392C2314yes—
430#392C2311yescharacteristic
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
485#388C2312yes—
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#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#387C2312yes—
513#387C2312yes—
514#387C2312yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2312yes—
536#387C2314yes—
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#386C2314yes—
561#386C2314yes—
562#386C2312yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2312yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#385C2314yes—
575#385C2312yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
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#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#384C2312yes—
606#384C2312yes—
607#383C2312yes—
608#383C2312yes—
609#383C2314yes—
610#383C2314yes—
611#383C2312yes—
612#383C2314yes—
613#382C2311yescharacteristic
614#382C2312yes—
615#382C2314yes—
616#382C2312yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2311yescharacteristic
621#382C2312yes—
622#381C2312yes—
623#381C2312yes—
624#381C2314yes—
625#381C2314yes—
626#381C2312yes—
627#381C2312yes—
628#381C2314yes—
629#381C2312yes—
630#381C2314yes—
631#381C2314yes—
632#381C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2312yes—
640#380C2314yes—
641#380C2312yes—
642#380C2314yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#379C2312yes—
649#379C2312yes—
650#379C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2312yes—
688#376C2312yes—
689#376C2311yescharacteristic
690#376C2311yescharacteristic
691#376C2314yes—
692C2×#95C2314yes—
693C2×#95C2314yes—
694C43C2311yescharacteristic
695C43C2311yescharacteristic
696C25C2412yes—
697C2×#41—28no—
698C2×#41—44no—
699C2×#41—44no—
700C22×Q8—24no—
701C22×Q8—42no—
702C22×Q8—42no—
703C22×Q8C2412yes—
704C22×Q8C2412yes—
705C22×Q8C2412yes—
706C22×Q8C2414yes—
707C22×Q8C2411yescharacteristic
708C22×Q8C2412yes—
709C22×D4—42no—
710C22×D4—42no—
711C22×D4#4118yes—
712C22×D4C2412yes—
713C22×D4C2414yes—
714C22×D4C2412yes—
715C22×D4C2414yes—
716C22×D4C2411yescharacteristic
717C22×D4C2412yes—
718C23×C4C2412yes—
719C23×C4C2412yes—
720C23×C4C2411yescharacteristic
721C23×C4C2412yes—
722C23×C4C2412yes—
723C23×C4C2414yes—
724C23×C4C2414yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C23×C4C2412yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C4⋊Q8—42no—
731C4⋊Q8—44no—
732C4⋊Q8—42no—
733C4⋊Q8—44no—
734C4⋊Q8—44no—
735#126—44no—
736#125—48no—
737#125—48no—
738#124—28no—
739#124—28no—
740#124—216no—
741#124—28no—
742#123—216no—
743#123—44no—
744C22⋊Q8—28no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—48no—
748C22⋊Q8—44no—
749C22⋊Q8—44no—
750C22⋊Q8—44no—
751#121—28no—
752#121—216no—
753#120—216no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—42no—
757C4×Q8—48no—
758C4×Q8—48no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—44no—
765C4×D4—44no—
766C4×D4—44no—
767C4×D4—42no—
768C4×D4—48no—
769C4×D4—48no—
770C4×D4—44no—
771C4×D4—48no—
772C4×D4—48no—
773#117—24no—
774#117—42no—
775#117—48no—
776#117—48no—
777#117—48no—
778#117—44no—
779#117—42no—
780#117—42no—
781C2×C4⋊C4—48no—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C22⋊C4—216no—
833C2×C22⋊C4—216no—
834C2×C22⋊C4—48no—
835C2×C22⋊C4—48no—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2411yescharacteristic
862C2×C22⋊C4C2411yescharacteristic
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C42—24no—
883C2×C42—28no—
884C2×C42—48no—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2414yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2411yescharacteristic
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2411yescharacteristic
936#95C2412yes—
937#95C2411yescharacteristic
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2411yescharacteristic
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987C24—42no—
988C24—44no—
989C24—42no—
990C24—44no—
991C24C2×#4118yes—
992C24C2512yes—
993C24C2511yescharacteristic
994C24C2514yes—
995#41—432no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—42no—
1004C2×Q8—42no—
1005C2×Q8—44no—
1006C2×Q8—41no—
1007C2×Q8—44no—
1008C2×Q8—42no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—42no—
1012C2×Q8—416no—
1013C2×D4—28no—
1014C2×D4—24no—
1015C2×D4—28no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—416no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—41no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—42no—
1027C2×D4—44no—
1028C2×D4—42no—
1029C2×D4C2×#4118yes—
1030C2×D4C2×#4118yes—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—28no—
1035C22×C4—24no—
1036C22×C4—28no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4C2×#4114yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2514yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C22⋊C4—24no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—24no—
1157C22⋊C4—42no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—42no—
1164C22⋊C4—44no—
1165C22⋊C4—42no—
1166C22⋊C4—44no—
1167C22⋊C4—42no—
1168C22⋊C4—44no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C42—24no—
1188C42—22no—
1189C42—22no—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—28no—
1195C42—22no—
1196C42—28no—
1197C42—22no—
1198C42—22no—
1199C42—24no—
1200C42—44no—
1201C42—44no—
1202C42—42no—
1203C42—44no—
1204C42—42no—
1205C42—42no—
1206C42—42no—
1207C42—44no—
1208C42—42no—
1209C42—44no—
1210C42—44no—
1211C42—42no—
1212C42H(5,𝔽2)14yes—
1213C23—21no—
1214C23—24no—
1215C23—24no—
1216C23—22no—
1217C23—24no—
1218C23—21no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—48no—
1231C23—416no—
1232C23—162no—
1233C23—162no—
1234C23—164no—
1235C23C22×#4118yes—
1236C23C22×#4112yes—
1237C23C2611yescharacteristic
1238Q8—48no—
1239Q8—48no—
1240Q8—48no—
1241Q8—82no—
1242Q8—88no—
1243Q8—162no—
1244D4—216no—
1245D4—48no—
1246D4—416no—
1247D4—44no—
1248D4—88no—
1249D4—84no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—28no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—48no—
1314C2×C4—48no—
1315C2×C4—416no—
1316C2×C4—48no—
1317C2×C4—88no—
1318C2×C4—84no—
1319C2×C4—88no—
1320C2×C4—84no—
1321C2×C4—88no—
1322C2×C4—164no—
1323C2×C4—164no—
1324C2×C4C22×#4112yes—
1325C2×C4C22×#4112yes—
1326C2×C4C2×H(5,𝔽2)14yes—
1327C2×C4C2×H(5,𝔽2)12yes—
1328C2×C4#58514yes—
1329C2×C4#58512yes—
1330C22—24no—
1331C22—28no—
1332C22—28no—
1333C22—22no—
1334C22—28no—
1335C22—44no—
1336C22—41no—
1337C22—44no—
1338C22—41no—
1339C22—44no—
1340C22—44no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—168no—
1350C22C23×#4111yescharacteristic
1351C22C22×H(5,𝔽2)11yescharacteristic
1352C22C2×#58512yes—
1353C22C2×#58511yescharacteristic
1354C222−1+612yes—
1355C4—22no—
1356C4—24no—
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—42no—
1371C4—44no—
1372C4—44no—
1373C4—44no—
1374C4—44no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4#345914yes—
1379C2—48no—
1380C2—42no—
1381C2—82no—
1382C2C2×#345911yescharacteristic
1383C2#6284111yescharacteristic
1384C2#6289111yescharacteristic
1385C2#6295412yes—
1386C2#6299112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42673C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42941C2semidirect
2. #42937C2semidirect
3. #42709C2semidirect
5. #42639C2semidirect
6. #42487C2semidirect
7. #41788C2semidirect
8. #41616C2semidirect
9. #41367C2semidirect
10. #41077C2semidirect
11. #40476C2semidirect
12. #40073C2semidirect
13. #39939C2semidirect
14. #39542C2semidirect
15. #39035C2semidirect
16. #38918C2semidirect
17. #38329C2semidirect
18. #38258C2semidirect
19. #35665C2semidirect
20. #35632C2semidirect
21. #35547C2semidirect
22. #35324C2semidirect
23. #35200C2semidirect
24. #34879C2semidirect
25. #34720C2semidirect
26. #34292C2semidirect
27. #34211C2semidirect
29. C2×#533C22semidirect
34. #2864C22semidirect
35. #2862C22semidirect
37. #2851C22semidirect
38. #2851C22semidirect
40. #2835C22semidirect
41. #2833C22semidirect
42. #2832C22semidirect
43. #2826C22semidirect
46. #2787C22semidirect
47. #2786C22semidirect
49. #2781C22semidirect
50. #2779C22semidirect
53. #2771C22semidirect
55. #2765C22semidirect
57. #2764C22semidirect
58. #2753C22semidirect
61. #2751C22semidirect
62. #2747C22semidirect
64. #2745C22semidirect
65. #2745C22semidirect
67. #2739C22semidirect
69. #2737C22semidirect
74. #2702C22semidirect
78. #2690C22semidirect
81. #2666C22semidirect
82. #2653C22semidirect
83. #2653C22semidirect
84. #2653C22semidirect
85. #2652C22semidirect
86. #2650C22semidirect
87. #2650C22semidirect
88. #2645C22semidirect
89. #2643C22semidirect
90. #2638C22semidirect
91. #2638C22semidirect
93. #2627C22semidirect
100. #2599C22semidirect
101. #2599C22semidirect
102. #2599C22semidirect
103. #2594C22semidirect
104. #2588C22semidirect
105. #2588C22semidirect
106. #2586C22semidirect
107. #2586C22semidirect
108. #2581C22semidirect
110. #2577C22semidirect
111. #2576C22semidirect
113. #2575C22semidirect
114. #2574C22semidirect
115. #2573C22semidirect
117. #2572C22semidirect
118. #2570C22semidirect
119. #2568C22semidirect
120. #2567C22semidirect
125. #2546C22semidirect
126. #2530C22semidirect
127. #2528C22semidirect
129. #2527C22semidirect
130. #2524C22semidirect
131. #2523C22semidirect
132. #2523C22semidirect
133. #2523C22semidirect
134. #2518C22semidirect
135. #2517C22semidirect
137. #2515C22semidirect
138. #2514C22semidirect
139. #2514C22semidirect
140. #2511C22semidirect
141. #2506C22semidirect
142. #2505C22semidirect
143. #2505C22semidirect
144. #2505C22semidirect
145. #2499C22semidirect
146. #2499C22semidirect
147. #2497C22semidirect
148. #2493C22semidirect
149. #2493C22semidirect
150. #2492C22semidirect
151. #2489C22semidirect
152. #2485C22semidirect
153. #2485C22semidirect
156. #2481C22semidirect
158. #2477C22semidirect
160. #2475C22semidirect
161. #2473C22semidirect
162. #2468C22semidirect
163. #2465C22semidirect
164. #2463C22semidirect
165. #2462C22semidirect
166. #2460C22semidirect
167. #2460C22semidirect
171. #2451C22semidirect
172. #2450C22semidirect
176. #2446C22semidirect
177. #2446C22semidirect
179. #2439C22semidirect
185. #2429C22semidirect
188. #2421C22semidirect
189. #2421C22semidirect
192. #2415C22semidirect
196. #2402C22semidirect
197. #2398C22semidirect
198. #2398C22semidirect
201. #2392C22semidirect
217. #2336C22semidirect
218. #2331C22semidirect
219. #2329C22semidirect
220. #2327C22semidirect
221. #2327C22semidirect
228. #2320C22semidirect
230. #2313C22semidirect
233. C4×#126C22semidirect
236. C4×C22⋊Q8C22semidirect
237. C4×C22⋊Q8C22semidirect
241. #2295C22semidirect
242. #2295C22semidirect
244. #2290C22semidirect
247. #2283C22semidirect
249. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#429412
#429372
#427092
#426732
#426392
#424872
#417882
#416162
#413672
#410772
#404762
#400732
#399392
#395422
#390352
#389182
#383292
#382582
#356652
#356322
#355472
#353242
#352002
#348792
#347202
#342922
#342112