Finite Group Databasebeta

← #8504931

Subgroups — #8504931

Order 512.

4457 conjugacy classes of subgroups.

The subgroup lattice has 1458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59933C211yesmaximal, characteristic, complemented
2#58538C214yesmaximal, complemented
3#57593C214yesmaximal, complemented
4#57475C214yesmaximal, complemented
5#57221C214yesmaximal, complemented
6#54891C214yesmaximal, complemented
7#53341C214yesmaximal, complemented
8#53012C212yesmaximal, complemented
9#52185C211yesmaximal, characteristic, complemented
10#50274C212yesmaximal, complemented
11#49103C212yesmaximal, complemented
12#46330C212yesmaximal, complemented
13#45683C211yesmaximal, characteristic, complemented
14#45599C211yesmaximal, characteristic
15#45203C212yesmaximal, complemented
16#44999C212yesmaximal, complemented
17#42847C212yesmaximal, complemented
18#42641C212yesmaximal, complemented
19#42441C212yesmaximal, complemented
20#39594C211yesmaximal, characteristic, complemented
21#39592C211yesmaximal, characteristic, complemented
22#38285C212yesmaximal, complemented
23#37704C212yesmaximal, complemented
24#37665C212yesmaximal, complemented
25#37409C212yesmaximal, complemented
26#37282C212yesmaximal, complemented
27#37241C212yesmaximal, complemented
28#36496C211yesmaximal, characteristic, complemented
29#35217C212yesmaximal, complemented
30C2×#559C2211yescharacteristic, complemented
31C2×#554C2211yescharacteristic
32C2×#542C2212yes—
33C22×C4⋊Q8C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2866C2214yes—
36#2863C2214yescomplemented
37#2861C2212yescomplemented
38#2858C2211yescharacteristic, complemented
39#2855C2211yescharacteristic, complemented
40#2850C2212yescomplemented
41#2848C2211yescharacteristic
42#2847C2212yes—
43#2843C2214yescomplemented
44#2838C2214yes—
45#2837C2214yes—
46#2833C2214yescomplemented
47#2831C2214yescomplemented
48#2826C2212yes—
49#2824C2212yescomplemented
50#2821C2214yes—
51#2814C2214yescomplemented
52#2803C2214yes—
53#2799C2212yescomplemented
54#2797C2214yes—
55#2793C2214yescomplemented
56#2793C2214yescomplemented
57#2793C2214yescomplemented
58#2787C2214yescomplemented
59#2786C2214yes—
60#2784C2214yes—
61#2784C2214yes—
62#2784C2214yescomplemented
63#2779C2214yes—
64#2778C2214yes—
65#2778C2214yes—
66#2760C2212yescomplemented
67#2759C2214yes—
68#2759C2214yescomplemented
69#2758C2214yescomplemented
70#2757C2214yes—
71#2752C2214yes—
72#2751C2214yes—
73#2750C2214yes—
74#2750C2214yes—
75#2749C2214yes—
76#2748C2212yes—
77#2748C2211yescharacteristic
78#2748C2214yescomplemented
79#2748C2214yescomplemented
80#2747C2212yes—
81#2747C2214yescomplemented
82#2746C2212yes—
83#2745C2212yes—
84#2745C2214yescomplemented
85#2745C2214yescomplemented
86#2744C2212yes—
87#2743C2214yes—
88#2743C2212yes—
89#2743C2214yescomplemented
90#2741C2214yes—
91#2741C2214yes—
92#2740C2214yes—
93#2739C2214yescomplemented
94#2737C2214yescomplemented
95#2735C2212yes—
96#2731C2214yes—
97#2731C2214yescomplemented
98#2729C2214yescomplemented
99#2721C2214yes—
100#2720C2214yes—
101#2717C2211yescharacteristic
102#2716C2214yescomplemented
103#2715C2214yes—
104#2715C2214yescomplemented
105#2713C2214yescomplemented
106#2713C2214yescomplemented
107#2712C2214yes—
108#2711C2214yes—
109#2709C2212yes—
110#2702C2214yes—
111#2700C2214yes—
112#2697C2211yescharacteristic
113#2695C2214yescomplemented
114#2692C2214yes—
115#2692C2214yes—
116#2690C2214yescomplemented
117#2688C2214yes—
118#2687C2214yes—
119#2686C2214yes—
120#2685C2214yes—
121#2684C2211yescharacteristic
122#2684C2214yes—
123#2677C2214yes—
124#2674C2214yes—
125#2672C2214yes—
126#2669C2212yes—
127#2668C2212yes—
128#2665C2214yescomplemented
129#2655C2214yescomplemented
130#2653C2214yes—
131#2650C2214yes—
132#2649C2214yescomplemented
133#2640C2212yescomplemented
134#2630C2214yes—
135#2629C2214yescomplemented
136#2628C2212yes—
137#2627C2212yescomplemented
138#2626C2212yes—
139#2625C2212yes—
140#2620C2212yes—
141#2620C2212yes—
142#2618C2214yes—
143#2612C2212yescomplemented
144#2610C2214yes—
145#2594C2214yes—
146#2589C2214yescomplemented
147#2588C2214yescomplemented
148#2582C2212yescomplemented
149#2578C2214yes—
150#2578C2214yescomplemented
151#2570C2212yescomplemented
152#2567C2211yescharacteristic, complemented
153#2566C2212yescomplemented
154#2551C2212yescomplemented
155#2547C2212yescomplemented
156#2545C2212yescomplemented
157#2544C2212yes—
158#2544C2212yescomplemented
159#2542C2212yes—
160#2541C2211yescharacteristic
161#2535C2212yes—
162#2533C2214yescomplemented
163#2532C2214yes—
164#2526C2214yescomplemented
165#2522C2214yes—
166#2514C2212yescomplemented
167#2514C2212yescomplemented
168#2509C2212yescomplemented
169#2506C2212yescomplemented
170#2502C2212yes—
171#2502C2211yescharacteristic, complemented
172#2497C2212yes—
173#2496C2212yes—
174#2495C2212yes—
175#2492C2212yes—
176#2492C2212yes—
177#2492C2212yes—
178#2491C2212yes—
179#2491C2214yes—
180#2487C2211yescharacteristic
181#2487C2212yes—
182#2487C2214yescomplemented
183#2484C2214yescomplemented
184#2481C2214yes—
185#2481C2214yes—
186#2481C2214yescomplemented
187#2477C2214yes—
188#2476C2214yes—
189#2474C2214yescomplemented
190#2472C2214yes—
191#2467C2214yes—
192#2461C2214yes—
193#2461C2214yescomplemented
194#2460C2214yes—
195#2452C2212yescomplemented
196#2451C2212yescomplemented
197#2451C2212yescomplemented
198#2446C2212yescomplemented
199#2443C2214yes—
200#2440C2212yes—
201#2436C2212yes—
202#2436C2214yes—
203#2434C2211yescharacteristic
204#2434C2212yescomplemented
205#2429C2212yes—
206#2428C2212yes—
207#2427C2212yes—
208#2427C2212yes—
209#2427C2212yescomplemented
210#2426C2212yes—
211#2426C2212yes—
212#2426C2212yescomplemented
213#2423C2212yes—
214#2423C2212yescomplemented
215#2421C2212yes—
216#2420C2212yes—
217#2420C2212yes—
218#2418C2214yes—
219#2417C2214yes—
220#2417C2212yes—
221#2417C2214yes—
222#2417C2214yescomplemented
223#2416C2212yes—
224#2409C2211yescharacteristic
225#2409C2212yes—
226#2409C2214yescomplemented
227#2401C2212yes—
228#2396C2212yes—
229#2395C2212yes—
230#2380C2212yes—
231#2380C2212yes—
232#2372C2212yes—
233#2367C2212yescomplemented
234#2361C2212yes—
235#2361C2212yescomplemented
236#2360C2212yescomplemented
237#2354C2212yescomplemented
238D4×C4⋊C4C2212yescomplemented
239#2345C2211yescharacteristic
240#2345C2211yescharacteristic, complemented
241Q8×C22⋊C4C2212yes—
242#2331C2212yescomplemented
243#2327C2212yescomplemented
244#2324C2212yes—
245#2323C2212yes—
246#2323C2212yes—
247#2322C2212yes—
248#2321C2212yes—
249#2319C2212yescomplemented
250C4×#127C2212yes—
251C4×#124C2211yescharacteristic
252C4×#123C2211yescharacteristic
253C4×#120C2211yescharacteristic
254#2298C2212yes—
255#2295C2212yescomplemented
256#2290C2212yes—
257#2280C2212yes—
258C42×Q8C2211yescharacteristic, complemented
259C23×Q8C2311yescharacteristic
260C23×Q8C2312yes—
261C24×C4C2311yescharacteristic
262#559—44no—
263#554—44no—
264#542—48no—
265C2×C4⋊Q8—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×#127C2312yes—
273C2×#127C2311yescharacteristic
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#124C2311yescharacteristic
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#123C2311yescharacteristic
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8—44no—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#120C2311yescharacteristic
309C2×#120C2314yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2314yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2314yes—
333C22×C22⋊C4C2312yes—
334C22×C42C2311yescharacteristic
335#401C2314yes—
336#401C2314yes—
337#401C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#399C2312yes—
361#399C2314yes—
362#399C2312yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2312yes—
404#397C2314yes—
405#397C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2312yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2312yes—
420#396C2312yes—
421#396C2314yes—
422#396C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2312yes—
431#395C2312yes—
432#395C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2312yes—
448#394C2312yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2312yes—
455#393C2314yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#393C2314yes—
460#393C2312yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#392C2312yes—
465#392C2312yes—
466#392C2314yes—
467#392C2314yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2312yes—
483#391C2311yescharacteristic
484#391C2314yes—
485#391C2312yes—
486#391C2314yes—
487#391C2314yes—
488#390C2311yescharacteristic
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2312yes—
498#390C2314yes—
499#390C2312yes—
500#390C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2312yes—
552#388C2312yes—
553#388C2314yes—
554#388C2312yes—
555#388C2314yes—
556#388C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#386C2314yes—
594#386C2314yes—
595#386C2312yes—
596#386C2314yes—
597#386C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2311yescharacteristic
612#386C2311yescharacteristic
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2311yescharacteristic
625#385C2311yescharacteristic
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2312yes—
636#385C2312yes—
637#385C2314yes—
638#385C2314yes—
639#385C2312yes—
640#385C2312yes—
641#385C2314yes—
642#385C2312yes—
643#385C2312yes—
644#385C2312yes—
645#384C2312yes—
646#384C2312yes—
647#384C2312yes—
648#384C2314yes—
649#383C2314yes—
650#383C2314yes—
651#383C2314yes—
652#382C2311yescharacteristic
653#382C2312yes—
654#382C2312yes—
655#381C2314yes—
656#381C2312yes—
657#381C2311yescharacteristic
658#381C2314yes—
659#381C2314yes—
660#381C2312yes—
661#381C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2311yescharacteristic
670#380C2314yes—
671#380C2311yescharacteristic
672#380C2312yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#380C2314yes—
681#380C2312yes—
682#380C2312yes—
683#380C2312yes—
684#379C2312yes—
685#379C2311yescharacteristic
686#379C2312yes—
687#379C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C25C2411yescharacteristic
718C22×Q8—42no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8—84no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2414yes—
732C22×D4C2414yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C23×C4—42no—
739C23×C4—44no—
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C4⋊Q8—28no—
755C4⋊Q8—44no—
756C4⋊Q8—42no—
757C4⋊Q8—44no—
758C4⋊Q8—48no—
759C4⋊Q8—84no—
760#127—28no—
761#127—42no—
762#126—48no—
763#126—84no—
764#125—44no—
765#125—84no—
766#124—24no—
767#124—44no—
768#124—44no—
769#124—44no—
770#124—44no—
771#124—48no—
772#124—84no—
773#124—84no—
774#123—24no—
775#123—48no—
776#123—48no—
777C22⋊Q8—28no—
778C22⋊Q8—48no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—48no—
785C22⋊Q8—42no—
786C22⋊Q8—42no—
787C22⋊Q8—84no—
788C22⋊Q8—84no—
789#121—44no—
790#121—44no—
791#121—44no—
792#121—44no—
793#121—84no—
794#121—84no—
795#120—24no—
796#120—84no—
797C4×Q8—24no—
798C4×Q8—42no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×D4—28no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—42no—
808C4×D4—44no—
809C4×D4—84no—
810C4×D4—84no—
811#117—44no—
812#117—44no—
813#117—84no—
814C2×C4⋊C4—24no—
815C2×C4⋊C4—24no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—42no—
818C2×C4⋊C4—44no—
819C2×C4⋊C4—84no—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C22⋊C4—44no—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2411yescharacteristic
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2411yescharacteristic
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C42—42no—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020C24—22no—
1021C24—41no—
1022C24—41no—
1023C24—42no—
1024C24—42no—
1025C24C2512yes—
1026C24C2514yes—
1027C24C2511yescharacteristic
1028C24C2511yescharacteristic
1029C2×Q8—22no—
1030C2×Q8—24no—
1031C2×Q8—28no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—41no—
1037C2×Q8—42no—
1038C2×Q8—44no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—41no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—88no—
1048C2×Q8—816no—
1049C2×D4—24no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—41no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D42−1+414yes—
1075C22×C4—22no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—28no—
1086C22×C4—41no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—41no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—88no—
1110C22×C4C2514yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2512yes—
1127C22×C4C2514yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2511yescharacteristic
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—22no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4H(5,𝔽2)14yes—
1190C22⋊C4—22no—
1191C22⋊C4—22no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—41no—
1203C22⋊C4—42no—
1204C22⋊C4—41no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—41no—
1219C22⋊C4—41no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
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—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—44no—
1246C22⋊C4—42no—
1247C42—24no—
1248C42—24no—
1249C42—24no—
1250C42—22no—
1251C42—22no—
1252C42—24no—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—42no—
1257C42—41no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—42no—
1265C42—44no—
1266C23—21no—
1267C23—21no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—21no—
1273C23—21no—
1274C23—22no—
1275C23—24no—
1276C23—22no—
1277C23—24no—
1278C23—24no—
1279C23—22no—
1280C23—24no—
1281C23—22no—
1282C23—22no—
1283C23—24no—
1284C23—24no—
1285C23—22no—
1286C23—22no—
1287C23—24no—
1288C23—44no—
1289C23—84no—
1290C23—82no—
1291C23—82no—
1292C23—84no—
1293C23C2×2−1+412yes—
1294C23C2×2−1+412yes—
1295C23C2611yescharacteristic
1296Q8—44no—
1297Q8—48no—
1298Q8—82no—
1299Q8—88no—
1300Q8—84no—
1301Q8—88no—
1302Q8—162no—
1303D4—44no—
1304D4—48no—
1305D4—84no—
1306D4—84no—
1307D4—88no—
1308D4—88no—
1309D4—164no—
1310D4—162no—
1311D4—164no—
1312C2×C4—21no—
1313C2×C4—24no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—44no—
1376C2×C4—44no—
1377C2×C4—44no—
1378C2×C4—48no—
1379C2×C4—44no—
1380C2×C4—88no—
1381C2×C4—84no—
1382C2×C4—84no—
1383C2×C4—88no—
1384C2×C4—82no—
1385C2×C4—84no—
1386C2×C4—84no—
1387C2×C4—84no—
1388C2×C4—164no—
1389C2×C4C2×H(5,𝔽2)14yes—
1390C2×C4C2×H(5,𝔽2)12yes—
1391C2×C4C2×2−1+412yes—
1392C2×C4#58514yes—
1393C22—22no—
1394C22—22no—
1395C22—24no—
1396C22—24no—
1397C22—41no—
1398C22—41no—
1399C22—41no—
1400C22—41no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—44no—
1405C22—44no—
1406C22—42no—
1407C22—44no—
1408C22—42no—
1409C22—44no—
1410C22—42no—
1411C22—44no—
1412C22—42no—
1413C22—44no—
1414C22—44no—
1415C22—42no—
1416C22—42no—
1417C22—88no—
1418C22C22×H(5,𝔽2)11yescharacteristic
1419C22C22×2−1+411yescharacteristic
1420C22C2×#58512yes—
1421C22H(7,𝔽2)12yes—
1422C222−1+611yescharacteristic
1423C4—24no—
1424C4—22no—
1425C4—41no—
1426C4—42no—
1427C4—41no—
1428C4—44no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—44no—
1433C4—42no—
1434C4—42no—
1435C4—41no—
1436C4—42no—
1437C4—44no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4#355114yes—
1448C2—42no—
1449C2—42no—
1450C2—84no—
1451C2—82no—
1452C2C2×#355111yescharacteristic
1453C2#6288212yes—
1454C2#6289311yescharacteristic
1455C2#6295112yes—
1456C2#6304111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#45599C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59933C2semidirect
2. #58538C2semidirect
3. #57593C2semidirect
4. #57475C2semidirect
5. #57221C2semidirect
6. #54891C2semidirect
7. #53341C2semidirect
8. #53012C2semidirect
9. #52185C2semidirect
10. #50274C2semidirect
11. #49103C2semidirect
12. #46330C2semidirect
13. #45683C2semidirect
15. #45203C2semidirect
16. #44999C2semidirect
17. #42847C2semidirect
18. #42641C2semidirect
19. #42441C2semidirect
20. #39594C2semidirect
21. #39592C2semidirect
22. #38285C2semidirect
23. #37704C2semidirect
24. #37665C2semidirect
25. #37409C2semidirect
26. #37282C2semidirect
27. #37241C2semidirect
28. #36496C2semidirect
29. #35217C2semidirect
30. C2×#559C22semidirect
33. C22×C4⋊Q8C22semidirect
36. #2863C22semidirect
37. #2861C22semidirect
38. #2858C22semidirect
39. #2855C22semidirect
40. #2850C22semidirect
43. #2843C22semidirect
46. #2833C22semidirect
47. #2831C22semidirect
49. #2824C22semidirect
51. #2814C22semidirect
53. #2799C22semidirect
55. #2793C22semidirect
56. #2793C22semidirect
57. #2793C22semidirect
58. #2787C22semidirect
62. #2784C22semidirect
66. #2760C22semidirect
68. #2759C22semidirect
69. #2758C22semidirect
78. #2748C22semidirect
79. #2748C22semidirect
81. #2747C22semidirect
84. #2745C22semidirect
85. #2745C22semidirect
89. #2743C22semidirect
93. #2739C22semidirect
94. #2737C22semidirect
97. #2731C22semidirect
98. #2729C22semidirect
102. #2716C22semidirect
104. #2715C22semidirect
105. #2713C22semidirect
106. #2713C22semidirect
113. #2695C22semidirect
116. #2690C22semidirect
128. #2665C22semidirect
129. #2655C22semidirect
132. #2649C22semidirect
133. #2640C22semidirect
135. #2629C22semidirect
137. #2627C22semidirect
143. #2612C22semidirect
146. #2589C22semidirect
147. #2588C22semidirect
148. #2582C22semidirect
150. #2578C22semidirect
151. #2570C22semidirect
152. #2567C22semidirect
153. #2566C22semidirect
154. #2551C22semidirect
155. #2547C22semidirect
156. #2545C22semidirect
158. #2544C22semidirect
162. #2533C22semidirect
164. #2526C22semidirect
166. #2514C22semidirect
167. #2514C22semidirect
168. #2509C22semidirect
169. #2506C22semidirect
171. #2502C22semidirect
182. #2487C22semidirect
183. #2484C22semidirect
186. #2481C22semidirect
189. #2474C22semidirect
193. #2461C22semidirect
195. #2452C22semidirect
196. #2451C22semidirect
197. #2451C22semidirect
198. #2446C22semidirect
204. #2434C22semidirect
209. #2427C22semidirect
212. #2426C22semidirect
214. #2423C22semidirect
222. #2417C22semidirect
226. #2409C22semidirect
233. #2367C22semidirect
235. #2361C22semidirect
236. #2360C22semidirect
237. #2354C22semidirect
238. D4×C4⋊C4C22semidirect
240. #2345C22semidirect
242. #2331C22semidirect
243. #2327C22semidirect
249. #2319C22semidirect
255. #2295C22semidirect
258. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#599332
#585382
#575932
#574752
#572212
#548912
#533412
#530122
#521852
#502742
#491032
#463302
#456832
#455992
#452032
#449992
#428472
#426412
#424412
#395942
#395922
#382852
#377042
#376652
#374092
#372822
#372412
#364962
#352172