Finite Group Databasebeta

← #8345837

Subgroups — #8345837

Order 512.

4922 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59810C212yesmaximal, complemented
2#59770C212yesmaximal, complemented
3#59135C212yesmaximal, complemented
4#57583C214yesmaximal, complemented
5#54970C214yesmaximal, complemented
6#53832C212yesmaximal, complemented
7#53666C214yesmaximal, complemented
8#53521C212yesmaximal, complemented
9#53106C212yesmaximal, complemented
10#52960C212yesmaximal, complemented
11#52168C211yesmaximal, characteristic, complemented
12#50740C214yesmaximal, complemented
13#48464C214yesmaximal, complemented
14#45641C212yesmaximal, complemented
15#45415C212yesmaximal, complemented
16#44717C212yesmaximal, complemented
17#42971C212yesmaximal, complemented
18#42952C211yesmaximal, characteristic, complemented
19#42839C212yesmaximal, complemented
20#42684C211yesmaximal, characteristic, complemented
21#40950C214yesmaximal, complemented
22#39984C212yesmaximal, complemented
23#39221C212yesmaximal, complemented
24#38914C212yesmaximal, complemented
25#38033C212yesmaximal, complemented
26#37523C211yesmaximal, characteristic, complemented
27#36029C211yesmaximal, characteristic, complemented
28#36011C211yesmaximal, characteristic, complemented
29#35574C211yesmaximal, characteristic, complemented
30C2×#555C2212yes—
31C2×#555C2211yescharacteristic
32C2×#553C2212yes—
33C2×#550C2212yes—
34C2×#550C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×#529C2212yes—
37C2×#520C2211yescharacteristic
38#2854C2212yes—
39#2851C2212yes—
40#2830C2214yes—
41#2826C2212yes—
42#2826C2212yes—
43#2824C2214yes—
44#2824C2214yes—
45#2824C2212yes—
46#2823C2212yes—
47#2819C2214yes—
48#2819C2214yes—
49#2816C2214yes—
50#2813C2214yes—
51#2804C2214yes—
52#2803C2214yes—
53#2801C2214yes—
54#2793C2214yes—
55#2792C2214yes—
56#2789C2212yes—
57#2788C2214yes—
58#2785C2212yes—
59#2784C2214yes—
60#2780C2214yes—
61#2772C2214yes—
62#2768C2214yes—
63#2763C2214yes—
64#2761C2214yes—
65#2755C2214yes—
66#2751C2214yes—
67#2731C2214yes—
68#2731C2214yes—
69#2725C2212yes—
70#2723C2214yes—
71#2722C2211yescharacteristic
72#2721C2214yes—
73#2712C2211yescharacteristic
74#2712C2214yes—
75#2710C2214yes—
76#2710C2214yes—
77#2709C2214yes—
78#2709C2214yes—
79#2706C2214yes—
80#2705C2212yes—
81#2704C2212yes—
82#2703C2214yes—
83#2701C2214yes—
84#2700C2214yes—
85#2696C2214yes—
86#2693C2212yes—
87#2693C2211yescharacteristic
88#2692C2214yes—
89#2691C2212yes—
90#2688C2214yes—
91#2687C2214yes—
92#2686C2214yes—
93#2686C2214yes—
94#2686C2214yes—
95#2686C2214yes—
96#2682C2214yes—
97#2681C2212yes—
98#2676C2214yes—
99#2676C2214yes—
100#2676C2214yes—
101#2675C2211yescharacteristic
102#2675C2214yes—
103#2675C2212yes—
104#2673C2214yes—
105#2673C2214yes—
106#2672C2212yes—
107#2672C2214yes—
108#2671C2214yes—
109#2671C2214yes—
110#2671C2214yes—
111#2665C2214yes—
112#2663C2214yes—
113#2661C2214yes—
114#2653C2214yes—
115#2653C2214yes—
116#2653C2214yes—
117#2649C2214yes—
118#2636C2214yes—
119#2635C2212yes—
120#2628C2211yescharacteristic
121#2624C2212yes—
122#2624C2212yes—
123#2620C2214yes—
124#2620C2214yes—
125#2619C2212yes—
126#2619C2211yescharacteristic
127#2619C2212yes—
128#2609C2214yes—
129#2607C2214yes—
130#2591C2212yes—
131#2587C2214yes—
132#2584C2212yes—
133#2581C2212yes—
134#2580C2212yes—
135#2579C2212yes—
136#2579C2212yes—
137#2576C2214yes—
138#2569C2214yes—
139#2568C2211yescharacteristic
140#2563C2212yes—
141#2563C2212yes—
142#2559C2214yes—
143#2559C2214yes—
144#2555C2214yes—
145#2555C2214yes—
146#2553C2214yes—
147#2548C2212yes—
148#2544C2214yes—
149#2543C2214yes—
150#2541C2212yes—
151#2541C2211yescharacteristic
152#2537C2212yes—
153#2536C2211yescharacteristic
154#2535C2212yes—
155#2535C2211yescharacteristic
156#2522C2214yes—
157#2517C2212yes—
158#2513C2212yes—
159#2511C2214yes—
160#2509C2212yes—
161#2508C2212yes—
162#2508C2214yes—
163#2494C2212yes—
164#2491C2214yes—
165#2491C2212yes—
166#2491C2212yes—
167#2490C2212yes—
168#2486C2212yes—
169#2485C2212yes—
170#2485C2212yes—
171#2484C2212yes—
172#2476C2214yes—
173#2474C2214yes—
174#2467C2214yes—
175#2466C2214yes—
176#2466C2214yes—
177#2464C2214yes—
178#2463C2212yes—
179#2461C2214yes—
180#2460C2214yes—
181#2459C2214yes—
182#2459C2214yes—
183#2455C2214yes—
184#2455C2212yes—
185#2454C2212yes—
186#2453C2212yes—
187#2452C2212yes—
188#2452C2212yes—
189#2452C2212yes—
190#2451C2212yes—
191#2451C2212yes—
192#2445C2212yes—
193#2445C2212yes—
194#2442C2212yes—
195#2440C2214yes—
196#2439C2212yes—
197#2439C2212yes—
198#2439C2212yes—
199#2439C2214yes—
200#2439C2214yes—
201#2436C2214yes—
202#2436C2214yes—
203#2428C2214yes—
204#2428C2212yes—
205#2428C2214yes—
206#2428C2212yes—
207#2428C2212yes—
208#2427C2214yes—
209#2425C2214yes—
210#2422C2214yes—
211#2420C2212yes—
212#2416C2212yes—
213#2416C2214yes—
214#2416C2214yes—
215#2416C2212yes—
216#2416C2212yes—
217#2416C2212yes—
218#2414C2212yes—
219#2414C2212yes—
220#2409C2212yes—
221#2409C2212yes—
222#2407C2212yes—
223#2407C2212yes—
224#2407C2212yes—
225#2396C2212yes—
226#2395C2212yes—
227#2392C2212yes—
228#2392C2211yescharacteristic
229#2392C2211yescharacteristic
230#2392C2212yes—
231#2377C2214yes—
232#2369C2212yes—
233#2364C2214yes—
234#2362C2212yes—
235#2360C2212yes—
236#2359C2214yes—
237#2357C2211yescharacteristic
238#2352C2212yes—
239#2352C2214yes—
240#2352C2212yes—
241#2351C2211yescharacteristic
242#2341C2212yes—
243#2339C2212yes—
244#2335C2214yes—
245#2329C2214yes—
246#2323C2212yes—
247#2317C2212yes—
248#2317C2211yescharacteristic
249#2316C2211yescharacteristic
250#2311C2211yescharacteristic
251C4×C22⋊Q8C2212yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255C4×#121C2212yes—
256#2297C2212yes—
257#2297C2211yescharacteristic
258#2296C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2312yes—
262#555—44no—
263#555—48no—
264#553—48no—
265#550—48no—
266#550—44no—
267C2×C4⋊Q8—44no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×#127C2312yes—
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#127C2314yes—
276#529—48no—
277C2×#126C2314yes—
278C2×#126C2312yes—
279C2×#126C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2312yes—
293C2×#123C2312yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325#520—44no—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2314yes—
347C2×#117C2311yescharacteristic
348C2×#117C2311yescharacteristic
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2311yescharacteristic
352C2×#117C2314yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C22×C4⋊C4C2311yescharacteristic
357C22×C4⋊C4C2311yescharacteristic
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2312yes—
361C22×C42C2312yes—
362C22×C42C2311yescharacteristic
363#401C2314yes—
364#400C2312yes—
365#400C2312yes—
366#400C2312yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2312yes—
373#400C2314yes—
374#399C2314yes—
375#399C2314yes—
376#399C2312yes—
377#399C2314yes—
378#399C2314yes—
379#399C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2311yescharacteristic
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2311yescharacteristic
391#398C2312yes—
392#398C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2311yescharacteristic
401#397C2312yes—
402#397C2311yescharacteristic
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2312yes—
414#396C2314yes—
415#396C2314yes—
416#396C2312yes—
417#396C2314yes—
418#396C2314yes—
419#396C2312yes—
420#396C2314yes—
421#396C2312yes—
422#396C2312yes—
423#396C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2312yes—
428#395C2312yes—
429#395C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2312yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2311yescharacteristic
455#394C2312yes—
456#394C2312yes—
457#394C2311yescharacteristic
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2312yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2312yes—
483#393C2314yes—
484#393C2314yes—
485#392C2312yes—
486#392C2314yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#392C2312yes—
493#392C2312yes—
494#392C2312yes—
495#392C2311yescharacteristic
496#392C2312yes—
497#392C2314yes—
498#392C2311yescharacteristic
499#392C2314yes—
500#392C2312yes—
501#392C2314yes—
502#392C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2314yes—
506#391C2314yes—
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2312yes—
515#390C2312yes—
516#390C2314yes—
517#390C2312yes—
518#390C2312yes—
519#390C2314yes—
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2314yes—
524#390C2312yes—
525#390C2314yes—
526#390C2314yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2312yes—
531#390C2314yes—
532#390C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2312yes—
581#388C2312yes—
582#388C2314yes—
583#388C2314yes—
584#388C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#386C2312yes—
608#386C2312yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#386C2314yes—
631#386C2314yes—
632#386C2312yes—
633#386C2314yes—
634#386C2314yes—
635#386C2312yes—
636#386C2312yes—
637#386C2314yes—
638#385C2311yescharacteristic
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2311yescharacteristic
644#385C2312yes—
645#385C2312yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2311yescharacteristic
650#385C2311yescharacteristic
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2312yes—
660#385C2312yes—
661#384C2312yes—
662#384C2314yes—
663#382C2312yes—
664#382C2314yes—
665#382C2312yes—
666#382C2314yes—
667#382C2314yes—
668#382C2312yes—
669#382C2311yescharacteristic
670#382C2312yes—
671#382C2311yescharacteristic
672#381C2314yes—
673#381C2314yes—
674#381C2314yes—
675#381C2312yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#380C2312yes—
680#380C2312yes—
681#380C2312yes—
682#380C2314yes—
683#380C2314yes—
684#380C2314yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2314yes—
691#380C2312yes—
692#380C2312yes—
693#380C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C2×#95C2314yes—
720C2×#41—24no—
721C2×#41—28no—
722C2×#41—24no—
723C2×#41—42no—
724C2×#41—44no—
725C2×#41—44no—
726C22×Q8—44no—
727C22×Q8—84no—
728C22×Q8C2411yescharacteristic
729C22×Q8C2414yes—
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2414yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2412yes—
746C22×D4C2411yescharacteristic
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2414yes—
750C22×D4C2414yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C23×C4C2412yes—
757C23×C4C2411yescharacteristic
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2411yescharacteristic
769C4⋊Q8—28no—
770C4⋊Q8—44no—
771C4⋊Q8—42no—
772C4⋊Q8—48no—
773#127—44no—
774#127—42no—
775#127—44no—
776#127—48no—
777#126—48no—
778#126—44no—
779#126—44no—
780#125—44no—
781#125—44no—
782#124—48no—
783#124—48no—
784#124—44no—
785#124—48no—
786#124—84no—
787#124—84no—
788#124—84no—
789#123—48no—
790#123—44no—
791#123—44no—
792#123—48no—
793#123—48no—
794#123—84no—
795#123—84no—
796C22⋊Q8—28no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—48no—
800C22⋊Q8—84no—
801C22⋊Q8—84no—
802#121—28no—
803#121—28no—
804#121—44no—
805#121—48no—
806#121—48no—
807#121—44no—
808#121—44no—
809#121—48no—
810#121—48no—
811#121—48no—
812#121—44no—
813#121—48no—
814#121—48no—
815#121—44no—
816#121—44no—
817#121—44no—
818#121—44no—
819#121—84no—
820#121—84no—
821#121—84no—
822#121—84no—
823#121—84no—
824#121—84no—
825C4×Q8—24no—
826C4×Q8—44no—
827C4×Q8—42no—
828C4×Q8—44no—
829C4×D4—28no—
830C4×D4—28no—
831C4×D4—24no—
832C4×D4—44no—
833C4×D4—48no—
834C4×D4—42no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—42no—
840C4×D4—44no—
841C4×D4—42no—
842C4×D4—48no—
843C4×D4—44no—
844C4×D4—48no—
845C4×D4—84no—
846#117—24no—
847#117—24no—
848#117—28no—
849#117—42no—
850#117—44no—
851#117—44no—
852#117—44no—
853#117—48no—
854#117—44no—
855C2×C4⋊C4—24no—
856C2×C4⋊C4—44no—
857C2×C4⋊C4—42no—
858C2×C4⋊C4—44no—
859C2×C4⋊C4—44no—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2411yescharacteristic
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2411yescharacteristic
918C2×C22⋊C4C2411yescharacteristic
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2411yescharacteristic
930C2×C22⋊C4C2411yescharacteristic
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2414yes—
976C2×C42—44no—
977C2×C42—42no—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2414yes—
988C2×C42C2412yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2411yescharacteristic
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2411yescharacteristic
1024#95C2414yes—
1025#95C2412yes—
1026#95C2411yescharacteristic
1027#95C2414yes—
1028#95C2411yescharacteristic
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050C24C2512yes—
1051C24C2512yes—
1052C24C2514yes—
1053C24C2512yes—
1054C24C2511yescharacteristic
1055#41—416no—
1056#41—816no—
1057C2×Q8—22no—
1058C2×Q8—22no—
1059C2×Q8—28no—
1060C2×Q8—42no—
1061C2×Q8—42no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—42no—
1065C2×Q8—44no—
1066C2×Q8—44no—
1067C2×Q8—44no—
1068C2×Q8—44no—
1069C2×Q8—42no—
1070C2×Q8—816no—
1071C2×Q82−1+414yes—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—24no—
1075C2×D4—28no—
1076C2×D4—22no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—22no—
1080C2×D4—28no—
1081C2×D4—24no—
1082C2×D4—22no—
1083C2×D4—24no—
1084C2×D4—28no—
1085C2×D4—24no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D4—44no—
1089C2×D4—41no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—41no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—44no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—42no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—42no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C22×C4—22no—
1129C22×C4—22no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—24no—
1136C22×C4—24no—
1137C22×C4—24no—
1138C22×C4—24no—
1139C22×C4—24no—
1140C22×C4—24no—
1141C22×C4—28no—
1142C22×C4—28no—
1143C22×C4—41no—
1144C22×C4—41no—
1145C22×C4—42no—
1146C22×C4—42no—
1147C22×C4—42no—
1148C22×C4—42no—
1149C22×C4—42no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—42no—
1155C22×C4—42no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—42no—
1160C22×C4—42no—
1161C22×C4—42no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4H(5,𝔽2)14yes—
1170C22×C4C2512yes—
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2512yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2514yes—
1181C22×C4C2514yes—
1182C22×C4C2512yes—
1183C22×C4C2514yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2511yescharacteristic
1189C22×C4C2512yes—
1190C22×C4C2511yescharacteristic
1191C22×C4C2512yes—
1192C22×C4C2512yes—
1193C22×C4C2511yescharacteristic
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—28no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—41no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—41no—
1217C4⋊C4—42no—
1218C4⋊C4—41no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—41no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4H(5,𝔽2)14yes—
1247C22⋊C4—24no—
1248C22⋊C4—22no—
1249C22⋊C4—22no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—28no—
1253C22⋊C4—24no—
1254C22⋊C4—28no—
1255C22⋊C4—24no—
1256C22⋊C4—24no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—28no—
1263C22⋊C4—41no—
1264C22⋊C4—42no—
1265C22⋊C4—41no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—42no—
1285C22⋊C4—44no—
1286C22⋊C4—42no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—42no—
1309C22⋊C4—42no—
1310C42—24no—
1311C42—24no—
1312C42—24no—
1313C42—28no—
1314C42—24no—
1315C42—22no—
1316C42—24no—
1317C42—24no—
1318C42—22no—
1319C42—42no—
1320C42—42no—
1321C42—42no—
1322C42—44no—
1323C42—42no—
1324C42—44no—
1325C42—44no—
1326C42—44no—
1327C42—44no—
1328C23—21no—
1329C23—21no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—24no—
1336C23—24no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—24no—
1344C23—24no—
1345C23—22no—
1346C23—24no—
1347C23—22no—
1348C23—24no—
1349C23—22no—
1350C23—22no—
1351C23—24no—
1352C23—22no—
1353C23—22no—
1354C23—24no—
1355C23—22no—
1356C23—24no—
1357C23—22no—
1358C23C2×H(5,𝔽2)12yes—
1359C23C2611yescharacteristic
1360Q8—28no—
1361Q8—88no—
1362Q8—84no—
1363Q8—88no—
1364Q8—162no—
1365D4—48no—
1366D4—44no—
1367D4—48no—
1368D4—84no—
1369D4—88no—
1370D4—88no—
1371D4—84no—
1372D4—88no—
1373D4—84no—
1374D4—84no—
1375D4—82no—
1376D4—82no—
1377D4—84no—
1378D4—88no—
1379D4—88no—
1380D4—164no—
1381D4—164no—
1382D4—162no—
1383D4—164no—
1384D4—164no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—28no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—21no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—24no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—44no—
1446C2×C4—48no—
1447C2×C4—44no—
1448C2×C4—48no—
1449C2×C4—48no—
1450C2×C4—88no—
1451C2×C4—84no—
1452C2×C4—84no—
1453C2×C4—88no—
1454C2×C4—84no—
1455C2×C4—84no—
1456C2×C4—84no—
1457C2×C4—162no—
1458C2×C4—164no—
1459C2×C4—164no—
1460C2×C4C2×H(5,𝔽2)14yes—
1461C2×C4C2×H(5,𝔽2)12yes—
1462C2×C4C2×H(5,𝔽2)12yes—
1463C2×C4C2×H(5,𝔽2)12yes—
1464C2×C4C2×2−1+414yes—
1465C2×C4C2×2−1+412yes—
1466C2×C4#58514yes—
1467C22—22no—
1468C22—24no—
1469C22—41no—
1470C22—41no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22—44no—
1476C22—44no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—42no—
1481C22—42no—
1482C22—44no—
1483C22—42no—
1484C22—42no—
1485C22—42no—
1486C22—42no—
1487C22—44no—
1488C22—42no—
1489C22—44no—
1490C22—44no—
1491C22—42no—
1492C22—42no—
1493C22—44no—
1494C22—42no—
1495C22—44no—
1496C22—44no—
1497C22—42no—
1498C22C22×H(5,𝔽2)11yescharacteristic
1499C22C22×H(5,𝔽2)11yescharacteristic
1500C22C22×2−1+411yescharacteristic
1501C22C2×#58512yes—
1502C22H(7,𝔽2)12yes—
1503C4—22no—
1504C4—24no—
1505C4—24no—
1506C4—24no—
1507C4—42no—
1508C4—42no—
1509C4—44no—
1510C4—41no—
1511C4—41no—
1512C4—42no—
1513C4—41no—
1514C4—42no—
1515C4—44no—
1516C4—41no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—42no—
1521C4—44no—
1522C4—44no—
1523C4—42no—
1524C4—42no—
1525C4—44no—
1526C4#353614yes—
1527C2—42no—
1528C2—82no—
1529C2—82no—
1530C2—82no—
1531C2—84no—
1532C2C2×#353611yescharacteristic
1533C2#6293012yes—
1534C2#6295212yes—
1535C2#6302011yescharacteristic
1536C2#6304111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59810C2semidirect
2. #59770C2semidirect
3. #59135C2semidirect
4. #57583C2semidirect
5. #54970C2semidirect
6. #53832C2semidirect
7. #53666C2semidirect
8. #53521C2semidirect
9. #53106C2semidirect
10. #52960C2semidirect
11. #52168C2semidirect
12. #50740C2semidirect
13. #48464C2semidirect
14. #45641C2semidirect
15. #45415C2semidirect
16. #44717C2semidirect
17. #42971C2semidirect
18. #42952C2semidirect
19. #42839C2semidirect
20. #42684C2semidirect
21. #40950C2semidirect
22. #39984C2semidirect
23. #39221C2semidirect
24. #38914C2semidirect
25. #38033C2semidirect
26. #37523C2semidirect
27. #36029C2semidirect
28. #36011C2semidirect
29. #35574C2semidirect

Maximal subgroups

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

subgroupindex
#598102
#597702
#591352
#575832
#549702
#538322
#536662
#535212
#531062
#529602
#521682
#507402
#484642
#456412
#454152
#447172
#429712
#429522
#428392
#426842
#409502
#399842
#392212
#389142
#380332
#375232
#360292
#360112
#355742