Finite Group Databasebeta

← #8750076

Subgroups — #8750076

Order 512.

4319 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C211yesmaximal, characteristic, complemented
2#59583C212yesmaximal, complemented
3#56775C214yesmaximal, complemented
4#54914C214yesmaximal, complemented
5#54913C214yesmaximal, complemented
6#54229C214yesmaximal, complemented
7#53492C212yesmaximal, complemented
8#53155C212yesmaximal, complemented
9#53031C211yesmaximal, characteristic, complemented
10#53008C212yesmaximal, complemented
11#52437C214yesmaximal, complemented
12#47541C212yesmaximal, complemented
13#45364C211yesmaximal, characteristic, complemented
14#45075C212yesmaximal, complemented
15#45029C212yesmaximal, complemented
16#44894C212yesmaximal, complemented
17#44879C212yesmaximal, complemented
18#42965C212yesmaximal, complemented
19#42735C214yesmaximal, complemented
20#42725C212yesmaximal, complemented
21#42607C212yesmaximal, complemented
22#42574C212yesmaximal, complemented
23#42481C211yesmaximal, characteristic, complemented
24#42211C212yesmaximal, complemented
25#40050C212yesmaximal, complemented
26#39168C211yesmaximal, characteristic, complemented
27#36697C211yesmaximal, characteristic, complemented
28#36051C211yesmaximal, characteristic
29#35871C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×Q82C2211yescharacteristic
32C2×#555C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#544C2212yes—
35#2858C2211yescharacteristic
36#2843C2211yescharacteristic
37#2843C2212yes—
38#2843C2212yes—
39#2839C2212yes—
40#2838C2214yes—
41#2838C2214yes—
42#2838C2212yes—
43#2838C2214yes—
44#2837C2212yes—
45#2836C2212yes—
46#2836C2214yes—
47#2834C2214yes—
48#2833C2211yescharacteristic
49#2832C2211yescharacteristic
50#2831C2212yes—
51#2831C2214yes—
52#2829C2214yes—
53#2823C2211yescharacteristic
54#2821C2212yes—
55#2820C2214yes—
56#2817C2214yes—
57#2814C2212yes—
58#2811C2212yes—
59#2807C2214yes—
60#2806C2214yes—
61#2801C2214yes—
62#2800C2214yes—
63#2792C2212yes—
64#2792C2212yes—
65#2786C2214yes—
66#2777C2214yes—
67#2775C2214yes—
68#2773C2214yes—
69#2770C2214yes—
70#2767C2214yes—
71#2764C2214yes—
72#2764C2214yes—
73#2759C2214yes—
74#2759C2214yes—
75#2757C2214yes—
76#2757C2214yes—
77#2757C2214yes—
78#2754C2214yes—
79#2751C2214yes—
80#2747C2214yes—
81#2745C2214yes—
82#2738C2214yes—
83#2737C2214yes—
84#2734C2212yes—
85#2734C2214yes—
86#2732C2214yes—
87#2730C2214yes—
88#2729C2214yes—
89#2729C2214yes—
90#2717C2214yes—
91#2713C2214yes—
92#2710C2214yes—
93#2710C2214yes—
94#2704C2214yes—
95#2700C2214yes—
96#2700C2214yes—
97#2700C2214yes—
98#2700C2214yes—
99#2692C2214yes—
100#2691C2214yes—
101#2687C2214yes—
102#2686C2214yes—
103#2683C2214yes—
104#2681C2214yes—
105#2681C2214yes—
106#2680C2212yes—
107#2680C2212yes—
108#2680C2214yes—
109#2677C2214yes—
110#2674C2214yes—
111#2674C2214yes—
112#2665C2214yes—
113#2661C2212yes—
114#2653C2214yes—
115#2651C2214yes—
116#2651C2214yes—
117#2649C2214yes—
118#2649C2214yes—
119#2647C2212yes—
120#2640C2212yes—
121#2640C2211yescharacteristic
122#2640C2214yes—
123#2640C2211yescharacteristic
124#2638C2212yes—
125#2632C2214yes—
126#2625C2214yes—
127#2624C2212yes—
128#2621C2214yes—
129#2614C2212yes—
130#2611C2214yes—
131#2605C2214yes—
132#2602C2214yes—
133#2594C2214yes—
134#2592C2214yes—
135#2592C2211yescharacteristic
136#2589C2214yes—
137#2587C2214yes—
138#2586C2214yes—
139#2586C2212yes—
140#2586C2212yes—
141#2584C2212yes—
142#2584C2212yes—
143#2582C2212yes—
144#2567C2211yescharacteristic
145#2567C2211yescharacteristic
146#2566C2212yes—
147#2565C2212yes—
148#2557C2214yes—
149#2556C2214yes—
150#2551C2212yes—
151#2550C2212yes—
152#2550C2212yes—
153#2550C2212yes—
154#2550C2212yes—
155#2550C2212yes—
156#2549C2214yes—
157#2548C2211yescharacteristic
158#2546C2214yes—
159#2546C2211yescharacteristic
160#2545C2212yes—
161#2543C2212yes—
162#2542C2212yes—
163#2540C2211yescharacteristic
164#2532C2214yes—
165#2532C2214yes—
166#2527C2214yes—
167#2516C2214yes—
168#2514C2214yes—
169#2514C2212yes—
170#2514C2212yes—
171#2513C2214yes—
172#2513C2212yes—
173#2513C2212yes—
174#2507C2214yes—
175#2504C2212yes—
176#2498C2212yes—
177#2495C2212yes—
178#2495C2212yes—
179#2495C2214yes—
180#2492C2212yes—
181#2492C2214yes—
182#2491C2212yes—
183#2491C2214yes—
184#2490C2212yes—
185#2490C2212yes—
186#2490C2212yes—
187#2489C2212yes—
188#2486C2212yes—
189#2477C2214yes—
190#2474C2214yes—
191#2469C2214yes—
192#2465C2214yes—
193#2462C2214yes—
194#2461C2214yes—
195#2454C2212yes—
196#2454C2212yes—
197#2453C2212yes—
198#2452C2212yes—
199#2452C2212yes—
200#2452C2212yes—
201#2452C2212yes—
202#2452C2214yes—
203#2451C2214yes—
204#2451C2212yes—
205#2448C2212yes—
206#2448C2212yes—
207#2447C2214yes—
208#2447C2212yes—
209#2445C2212yes—
210#2440C2212yes—
211#2440C2212yes—
212#2439C2212yes—
213#2439C2212yes—
214#2438C2214yes—
215#2434C2214yes—
216#2429C2214yes—
217#2429C2214yes—
218#2428C2212yes—
219#2427C2212yes—
220#2426C2214yes—
221#2421C2214yes—
222#2409C2212yes—
223#2409C2214yes—
224#2402C2212yes—
225#2401C2212yes—
226#2399C2211yescharacteristic
227#2398C2211yescharacteristic
228#2396C2214yes—
229#2396C2212yes—
230#2396C2212yes—
231#2395C2212yes—
232#2395C2212yes—
233#2370C2212yes—
234#2370C2212yes—
235#2369C2212yes—
236#2369C2212yes—
237#2369C2212yes—
238#2365C2212yes—
239#2365C2212yes—
240#2363C2212yes—
241#2362C2212yes—
242#2361C2212yes—
243#2360C2212yes—
244#2357C2212yes—
245#2356C2214yes—
246#2354C2212yes—
247#2346C2212yes—
248#2331C2212yes—
249#2326C2212yes—
250#2324C2212yes—
251#2324C2214yes—
252#2323C2212yes—
253#2319C2211yescharacteristic
254C4×C4⋊Q8C2211yescharacteristic
255C4×#125C2212yes—
256C4×#126C2212yes—
257#2295C2211yescharacteristic
258#2275C2211yescharacteristic
259C23×Q8C2312yes—
260#559—44no—
261Q82—44no—
262#555—44no—
263D4×Q8—44no—
264#544—48no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2314yes—
277C2×#127C2311yescharacteristic
278C2×#126C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2314yes—
289C2×#124C2314yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2314yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2314yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2314yes—
328C22×C4⋊C4C2312yes—
329#401C2312yes—
330#401C2314yes—
331#401C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2312yes—
340#400C2312yes—
341#400C2312yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2311yescharacteristic
347#400C2312yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2311yescharacteristic
353#399C2312yes—
354#399C2314yes—
355#399C2312yes—
356#399C2314yes—
357#399C2314yes—
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2311yescharacteristic
367#398C2312yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2311yescharacteristic
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2312yes—
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2312yes—
431#396C2312yes—
432#396C2314yes—
433#396C2314yes—
434#396C2312yes—
435#396C2314yes—
436#396C2314yes—
437#395C2312yes—
438#395C2312yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2312yes—
444#395C2312yes—
445#395C2312yes—
446#395C2312yes—
447#395C2311yescharacteristic
448#395C2312yes—
449#395C2311yescharacteristic
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2311yescharacteristic
461#394C2312yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2312yes—
467#394C2311yescharacteristic
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#393C2312yes—
474#393C2312yes—
475#393C2314yes—
476#393C2312yes—
477#393C2312yes—
478#393C2312yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2312yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#392C2314yes—
489#392C2312yes—
490#391C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2312yes—
498#391C2314yes—
499#391C2314yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2314yes—
515#391C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2314yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2314yes—
523#390C2312yes—
524#390C2312yes—
525#390C2314yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2314yes—
531#390C2312yes—
532#390C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2314yes—
561#389C2312yes—
562#389C2314yes—
563#389C2312yes—
564#389C2314yes—
565#389C2314yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
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#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#384C2311yescharacteristic
650#384C2312yes—
651#384C2312yes—
652#384C2312yes—
653#383C2312yes—
654#383C2314yes—
655#383C2314yes—
656#383C2314yes—
657#383C2314yes—
658#382C2312yes—
659#382C2314yes—
660#382C2312yes—
661#382C2314yes—
662#382C2312yes—
663#381C2314yes—
664#381C2312yes—
665#381C2314yes—
666#381C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711#376C2311yescharacteristic
712#376C2312yes—
713#376C2314yes—
714#376C2311yescharacteristic
715C2×#95C2312yes—
716C43C2311yescharacteristic
717C22×Q8—44no—
718C22×Q8—84no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2414yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2411yescharacteristic
734C22×D4C2414yes—
735C22×D4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C4⋊Q8—28no—
743C4⋊Q8—28no—
744C4⋊Q8—28no—
745C4⋊Q8—42no—
746C4⋊Q8—42no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749C4⋊Q8—48no—
750C4⋊Q8—44no—
751C4⋊Q8—44no—
752C4⋊Q8—48no—
753C4⋊Q8—84no—
754#127—42no—
755#126—44no—
756#125—28no—
757#125—48no—
758#125—44no—
759#125—44no—
760#124—48no—
761#124—44no—
762#124—44no—
763#124—42no—
764#124—42no—
765#124—84no—
766#124—84no—
767#123—44no—
768#123—44no—
769#123—84no—
770#123—84no—
771C22⋊Q8—28no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—44no—
776C22⋊Q8—84no—
777C22⋊Q8—84no—
778C22⋊Q8—84no—
779C22⋊Q8—84no—
780C22⋊Q8—84no—
781C22⋊Q8—84no—
782#121—28no—
783#121—44no—
784#121—48no—
785#121—44no—
786C4×Q8—24no—
787C4×Q8—42no—
788C4×Q8—42no—
789C4×Q8—42no—
790C4×Q8—48no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—84no—
794C4×D4—24no—
795C4×D4—24no—
796C4×D4—28no—
797C4×D4—44no—
798C4×D4—42no—
799C4×D4—44no—
800C4×D4—84no—
801#117—28no—
802#117—44no—
803#117—44no—
804#117—84no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2414yes—
938C2×C42C2412yes—
939#95C2411yescharacteristic
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2411yescharacteristic
946#95C2411yescharacteristic
947#95C2414yes—
948#95C2411yescharacteristic
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012C24C2512yes—
1013C24C2512yes—
1014C24C2512yes—
1015C2×Q8—22no—
1016C2×Q8—28no—
1017C2×Q8—28no—
1018C2×Q8—24no—
1019C2×Q8—28no—
1020C2×Q8—22no—
1021C2×Q8—22no—
1022C2×Q8—41no—
1023C2×Q8—41no—
1024C2×Q8—42no—
1025C2×Q8—41no—
1026C2×Q8—41no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—41no—
1036C2×Q8—44no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—816no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—28no—
1047C2×D4—24no—
1048C2×D4—41no—
1049C2×D4—42no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—28no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—41no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—41no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4H(5,𝔽2)14yes—
1165C4⋊C42−1+418yes—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—44no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C42—28no—
1211C42—24no—
1212C42—24no—
1213C42—22no—
1214C42—22no—
1215C42—24no—
1216C42—22no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—22no—
1222C42—41no—
1223C42—44no—
1224C42—42no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—42no—
1233C42—42no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—24no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—24no—
1245C23—22no—
1246C23—24no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23C2611yescharacteristic
1252Q8—44no—
1253Q8—44no—
1254Q8—44no—
1255Q8—88no—
1256Q8—82no—
1257Q8—88no—
1258Q8—88no—
1259Q8—84no—
1260Q8—162no—
1261Q8—162no—
1262D4—44no—
1263D4—44no—
1264D4—84no—
1265D4—88no—
1266D4—82no—
1267D4—162no—
1268D4—164no—
1269C2×C4—21no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—21no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—21no—
1336C2×C4—48no—
1337C2×C4—84no—
1338C2×C4—88no—
1339C2×C4—84no—
1340C2×C4—88no—
1341C2×C4—164no—
1342C2×C4C2×H(5,𝔽2)14yes—
1343C2×C4C2×H(5,𝔽2)12yes—
1344C2×C4C2×2−1+418yes—
1345C2×C4C2×2−1+414yes—
1346C2×C4#58512yes—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
1354C22—44no—
1355C22—44no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—44no—
1361C22—42no—
1362C22—44no—
1363C22—42no—
1364C22C22×H(5,𝔽2)11yescharacteristic
1365C22C22×2−1+412yes—
1366C22C2×#58511yescharacteristic
1367C22H(7,𝔽2)12yes—
1368C222−1+611yescharacteristic
1369C4—24no—
1370C4—22no—
1371C4—28no—
1372C4—42no—
1373C4—42no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—44no—
1378C4—44no—
1379C4—41no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—41no—
1389C4—41no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—42no—
1394C4#355014yes—
1395C2—82no—
1396C2—82no—
1397C2—82no—
1398C2C2×#355011yescharacteristic
1399C2#6291911yescharacteristic
1400C2#6295112yes—
1401C2#6304111yescharacteristic
1402C2#6306112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36051C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59925C2semidirect
2. #59583C2semidirect
3. #56775C2semidirect
4. #54914C2semidirect
5. #54913C2semidirect
6. #54229C2semidirect
7. #53492C2semidirect
8. #53155C2semidirect
9. #53031C2semidirect
10. #53008C2semidirect
11. #52437C2semidirect
12. #47541C2semidirect
13. #45364C2semidirect
14. #45075C2semidirect
15. #45029C2semidirect
16. #44894C2semidirect
17. #44879C2semidirect
18. #42965C2semidirect
19. #42735C2semidirect
20. #42725C2semidirect
21. #42607C2semidirect
22. #42574C2semidirect
23. #42481C2semidirect
24. #42211C2semidirect
25. #40050C2semidirect
26. #39168C2semidirect
27. #36697C2semidirect
29. #35871C2semidirect

Maximal subgroups

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

subgroupindex
#599252
#595832
#567752
#549142
#549132
#542292
#534922
#531552
#530312
#530082
#524372
#475412
#453642
#450752
#450292
#448942
#448792
#429652
#427352
#427252
#426072
#425742
#424812
#422112
#400502
#391682
#366972
#360512
#358712