Finite Group Databasebeta

← #8096263

Subgroups — #8096263

Order 512.

5009 conjugacy classes of subgroups.

The subgroup lattice has 1539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53110C212yesmaximal, complemented
2#53059C212yesmaximal, complemented
3#52973C212yesmaximal, complemented
4#52683C214yesmaximal, complemented
5#52333C214yesmaximal, complemented
6#52329C214yesmaximal, complemented
7#52306C211yesmaximal, characteristic, complemented
8#52167C212yesmaximal, complemented
9#46346C211yesmaximal, characteristic, complemented
10#46329C211yesmaximal, characteristic, complemented
11#46310C212yesmaximal, complemented
12#46275C212yesmaximal, complemented
13#46228C212yesmaximal, complemented
14#46084C211yesmaximal, characteristic, complemented
15#46050C212yesmaximal, complemented
16#46044C212yesmaximal, complemented
17#46010C212yesmaximal, complemented
18#45914C214yesmaximal, complemented
19#45865C214yesmaximal, complemented
20#45814C214yesmaximal, complemented
21#36527C212yesmaximal, complemented
22#36495C212yesmaximal, complemented
23#36452C212yesmaximal, complemented
24#36419C211yesmaximal, characteristic, complemented
25#36128C211yesmaximal, characteristic, complemented
26#36125C211yesmaximal, characteristic, complemented
27#35787C212yesmaximal, complemented
28#35715C212yesmaximal, complemented
29#35704C212yesmaximal, complemented
30C2×#563C2212yes—
31C2×#556C2211yescharacteristic
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#532C2212yes—
36C2×#532C2212yes—
37C2×#520C2212yes—
38#2867C2211yescharacteristic
39#2863C2212yes—
40#2861C2212yes—
41#2860C2212yes—
42#2858C2211yescharacteristic
43#2858C2211yescharacteristic
44#2856C2212yes—
45#2853C2214yes—
46#2852C2214yes—
47#2851C2214yes—
48#2850C2212yes—
49#2850C2212yes—
50#2833C2212yes—
51#2829C2214yes—
52#2829C2214yes—
53#2829C2214yes—
54#2828C2212yes—
55#2828C2214yes—
56#2827C2214yes—
57#2826C2214yes—
58#2826C2214yes—
59#2825C2214yes—
60#2825C2214yes—
61#2823C2212yes—
62#2820C2214yes—
63#2818C2214yes—
64#2818C2214yes—
65#2813C2214yes—
66#2813C2214yes—
67#2813C2214yes—
68#2809C2211yescharacteristic
69#2797C2214yes—
70#2794C2212yes—
71#2782C2212yes—
72#2775C2212yes—
73#2775C2212yes—
74#2769C2212yes—
75#2766C2214yes—
76#2761C2214yes—
77#2758C2214yes—
78#2753C2214yes—
79#2753C2214yes—
80#2749C2214yes—
81#2749C2214yes—
82#2743C2214yes—
83#2734C2212yes—
84#2734C2211yescharacteristic
85#2733C2212yes—
86#2731C2211yescharacteristic
87#2731C2211yescharacteristic
88#2731C2212yes—
89#2730C2214yes—
90#2728C2212yes—
91#2727C2212yes—
92#2721C2212yes—
93#2721C2212yes—
94#2714C2214yes—
95#2714C2214yes—
96#2711C2214yes—
97#2711C2214yes—
98#2710C2214yes—
99#2709C2214yes—
100#2709C2214yes—
101#2709C2214yes—
102#2708C2214yes—
103#2707C2214yes—
104#2706C2214yes—
105#2702C2214yes—
106#2699C2214yes—
107#2691C2214yes—
108#2691C2214yes—
109#2688C2214yes—
110#2686C2214yes—
111#2686C2214yes—
112#2682C2214yes—
113#2676C2214yes—
114#2673C2214yes—
115#2673C2214yes—
116#2673C2214yes—
117#2673C2214yes—
118#2672C2214yes—
119#2672C2214yes—
120#2636C2214yes—
121#2635C2214yes—
122#2630C2214yes—
123#2624C2212yes—
124#2620C2212yes—
125#2619C2212yes—
126#2609C2214yes—
127#2602C2214yes—
128#2601C2214yes—
129#2595C2214yes—
130#2591C2214yes—
131#2581C2212yes—
132#2578C2214yes—
133#2578C2214yes—
134#2577C2214yes—
135#2576C2214yes—
136#2576C2214yes—
137#2573C2214yes—
138#2568C2211yescharacteristic
139#2566C2212yes—
140#2559C2214yes—
141#2559C2214yes—
142#2559C2214yes—
143#2558C2214yes—
144#2553C2214yes—
145#2548C2211yescharacteristic
146#2548C2211yescharacteristic
147#2548C2211yescharacteristic
148#2548C2212yes—
149#2546C2211yescharacteristic
150#2544C2212yes—
151#2544C2212yes—
152#2544C2212yes—
153#2544C2212yes—
154#2541C2211yescharacteristic
155#2541C2212yes—
156#2541C2212yes—
157#2538C2212yes—
158#2518C2214yes—
159#2517C2214yes—
160#2516C2214yes—
161#2514C2212yes—
162#2512C2212yes—
163#2509C2212yes—
164#2506C2212yes—
165#2500C2212yes—
166#2490C2212yes—
167#2489C2212yes—
168#2481C2214yes—
169#2477C2214yes—
170#2476C2214yes—
171#2476C2214yes—
172#2471C2214yes—
173#2467C2214yes—
174#2467C2214yes—
175#2466C2214yes—
176#2466C2214yes—
177#2464C2214yes—
178#2464C2214yes—
179#2463C2214yes—
180#2460C2214yes—
181#2457C2214yes—
182#2456C2214yes—
183#2456C2214yes—
184#2454C2212yes—
185#2454C2212yes—
186#2452C2212yes—
187#2451C2212yes—
188#2449C2214yes—
189#2449C2214yes—
190#2448C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2446C2212yes—
194#2445C2212yes—
195#2445C2212yes—
196#2445C2212yes—
197#2445C2212yes—
198#2443C2214yes—
199#2432C2212yes—
200#2432C2212yes—
201#2432C2212yes—
202#2431C2212yes—
203#2431C2212yes—
204#2431C2212yes—
205#2431C2212yes—
206#2431C2212yes—
207#2431C2212yes—
208#2431C2212yes—
209#2428C2212yes—
210#2428C2212yes—
211#2428C2214yes—
212#2428C2214yes—
213#2428C2212yes—
214#2428C2212yes—
215#2427C2212yes—
216#2426C2212yes—
217#2422C2212yes—
218#2420C2212yes—
219#2407C2212yes—
220#2407C2214yes—
221#2406C2214yes—
222#2396C2212yes—
223#2396C2212yes—
224#2395C2212yes—
225#2392C2214yes—
226#2388C2214yes—
227#2388C2214yes—
228#2381C2212yes—
229#2380C2214yes—
230#2379C2212yes—
231#2377C2214yes—
232#2377C2214yes—
233#2370C2212yes—
234#2367C2212yes—
235#2367C2212yes—
236#2367C2212yes—
237#2366C2212yes—
238#2366C2212yes—
239#2361C2212yes—
240#2361C2212yes—
241#2361C2212yes—
242#2360C2212yes—
243#2357C2212yes—
244#2355C2212yes—
245#2345C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2211yescharacteristic
248C4×#125C2212yes—
249C4×#126C2212yes—
250C4×#126C2212yes—
251C4×#124C2211yescharacteristic
252C4×#123C2214yes—
253C4×#123C2214yes—
254C4×#121C2214yes—
255#2297C2212yes—
256C42×D4C2211yescharacteristic
257C42×D4C2211yescharacteristic
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261C22×#41C2312yes—
262C22×#41C2312yes—
263#563—48no—
264#556—44no—
265#550—44no—
266#550—44no—
267#547—44no—
268#532—48no—
269#532—48no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×#127C2312yes—
276C2×#127C2314yes—
277C2×#127C2312yes—
278C2×#127C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#127C2312yes—
281C2×#127C2312yes—
282C2×#127C2311yescharacteristic
283C2×#127C2311yescharacteristic
284C2×#127C2312yes—
285C2×#127C2312yes—
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#125C2312yes—
292C2×#125C2314yes—
293C2×#125C2312yes—
294C2×#124C2312yes—
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2312yes—
302C2×#124C2312yes—
303C2×#124C2312yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×#121C2314yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332#520—48no—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×#117C2314yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2314yes—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2312yes—
362#401C2314yes—
363#400C2312yes—
364#400C2312yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2312yes—
374#400C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2312yes—
379#399C2314yes—
380#399C2312yes—
381#399C2312yes—
382#398C2314yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2312yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2312yes—
420#396C2312yes—
421#396C2312yes—
422#395C2312yes—
423#395C2314yes—
424#395C2314yes—
425#395C2312yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2312yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#393C2312yes—
469#393C2314yes—
470#393C2312yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#392C2314yes—
475#392C2314yes—
476#392C2314yes—
477#392C2314yes—
478#392C2314yes—
479#392C2314yes—
480#392C2314yes—
481#392C2314yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2314yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#391C2311yescharacteristic
492#391C2311yescharacteristic
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2311yescharacteristic
504#391C2314yes—
505#390C2312yes—
506#390C2312yes—
507#390C2311yescharacteristic
508#390C2314yes—
509#390C2312yes—
510#390C2314yes—
511#390C2314yes—
512#390C2312yes—
513#390C2312yes—
514#390C2314yes—
515#390C2314yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2314yes—
530#390C2314yes—
531#390C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2312yes—
580#388C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#384C2311yescharacteristic
662#384C2311yescharacteristic
663#384C2312yes—
664#383C2312yes—
665#383C2312yes—
666#383C2314yes—
667#383C2314yes—
668#382C2312yes—
669#382C2314yes—
670#382C2312yes—
671#382C2312yes—
672#382C2314yes—
673#382C2311yescharacteristic
674#381C2314yes—
675#381C2314yes—
676#381C2314yes—
677#381C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682#380C2314yes—
683#380C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C43C2311yescharacteristic
718C43C2311yescharacteristic
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—44no—
725C2×#41—44no—
726C2×#41—44no—
727C2×#41—44no—
728C2×#41—44no—
729C2×#41—82no—
730C2×#41—82no—
731C2×#41—82no—
732C22×Q8C2412yes—
733C22×Q8C2411yescharacteristic
734C22×Q8C2411yescharacteristic
735C22×Q8C2412yes—
736C22×Q8C2411yescharacteristic
737C22×D4C2411yescharacteristic
738C22×D4C2411yescharacteristic
739C22×D4C2411yescharacteristic
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2411yescharacteristic
744C22×D4C2412yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2412yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2414yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2414yes—
760C22×D4C2414yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2414yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C4⋊Q8—24no—
773C4⋊Q8—28no—
774C4⋊Q8—24no—
775C4⋊Q8—42no—
776C4⋊Q8—42no—
777#127—44no—
778#127—44no—
779#127—48no—
780#127—44no—
781#127—44no—
782#127—44no—
783#127—42no—
784#127—42no—
785#127—42no—
786#127—42no—
787#127—82no—
788#126—44no—
789#126—48no—
790#126—48no—
791#126—48no—
792#126—44no—
793#125—44no—
794#125—48no—
795#125—44no—
796#124—24no—
797#124—28no—
798#124—44no—
799#124—44no—
800#124—44no—
801#124—44no—
802#124—44no—
803#124—44no—
804#124—82no—
805#124—82no—
806#123—48no—
807#123—48no—
808#123—48no—
809#123—48no—
810#123—84no—
811#123—84no—
812C22⋊Q8—48no—
813C22⋊Q8—48no—
814C22⋊Q8—44no—
815C22⋊Q8—44no—
816C22⋊Q8—44no—
817#121—44no—
818#121—48no—
819#121—44no—
820#121—44no—
821#121—44no—
822#121—48no—
823#121—48no—
824#121—48no—
825#121—48no—
826#121—48no—
827#121—44no—
828#121—44no—
829#121—44no—
830#121—48no—
831#121—48no—
832#121—44no—
833#121—84no—
834C4×Q8—28no—
835C4×Q8—42no—
836C4×Q8—42no—
837C4×Q8—42no—
838C4×Q8—44no—
839C4×D4—28no—
840C4×D4—24no—
841C4×D4—24no—
842C4×D4—24no—
843C4×D4—44no—
844C4×D4—44no—
845C4×D4—44no—
846C4×D4—44no—
847C4×D4—48no—
848C4×D4—42no—
849C4×D4—48no—
850C4×D4—48no—
851C4×D4—48no—
852C4×D4—48no—
853C4×D4—48no—
854C4×D4—84no—
855#117—44no—
856#117—44no—
857#117—48no—
858C2×C4⋊C4—28no—
859C2×C4⋊C4—48no—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2411yescharacteristic
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C42—44no—
970C2×C42—44no—
971C2×C42—82no—
972C2×C42C2414yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2411yescharacteristic
982C2×C42C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052C24C2514yes—
1053C24C2512yes—
1054C24C2512yes—
1055C24C2512yes—
1056C24C2512yes—
1057#41—432no—
1058#41—816no—
1059#41—816no—
1060#41—816no—
1061C2×Q8—24no—
1062C2×Q8—22no—
1063C2×Q8—22no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—41no—
1068C2×Q8—41no—
1069C2×Q8—41no—
1070C2×Q8—41no—
1071C2×Q8—41no—
1072C2×Q8—42no—
1073C2×Q8—41no—
1074C2×Q8—42no—
1075C2×Q8H(5,𝔽2)14yes—
1076C2×D4—24no—
1077C2×D4—22no—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—22no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—24no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—28no—
1091C2×D4—28no—
1092C2×D4—44no—
1093C2×D4—41no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—41no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—42no—
1119C2×D4—42no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—42no—
1126C2×D4—42no—
1127C2×D4—42no—
1128C2×D4—42no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—28no—
1151C22×C4—28no—
1152C22×C4—28no—
1153C22×C4—42no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4C2512yes—
1175C22×C4C2511yescharacteristic
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2514yes—
1179C22×C4C2514yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2514yes—
1188C22×C4C2514yes—
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2512yes—
1192C22×C4C2511yescharacteristic
1193C22×C4C2511yescharacteristic
1194C22×C4C2512yes—
1195C22×C4C2511yescharacteristic
1196C22×C4C2512yes—
1197C22×C4C2511yescharacteristic
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—28no—
1204C4⋊C4—28no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—42no—
1218C4⋊C4—41no—
1219C4⋊C4—42no—
1220C4⋊C4—41no—
1221C4⋊C4—44no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4H(5,𝔽2)14yes—
1248C22⋊C4—28no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—24no—
1257C22⋊C4—24no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—42no—
1304C22⋊C4—42no—
1305C22⋊C4—42no—
1306C22⋊C4—42no—
1307C42—22no—
1308C42—22no—
1309C42—24no—
1310C42—24no—
1311C42—28no—
1312C42—24no—
1313C42—24no—
1314C42—22no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—24no—
1319C42—24no—
1320C42—24no—
1321C42—24no—
1322C42—44no—
1323C42—44no—
1324C42—41no—
1325C42—44no—
1326C42—42no—
1327C42—44no—
1328C42—41no—
1329C42—42no—
1330C42—42no—
1331C42—41no—
1332C23—24no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—24no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—24no—
1345C23—24no—
1346C23—24no—
1347C23—22no—
1348C23—24no—
1349C23—24no—
1350C23—24no—
1351C23—24no—
1352C23—24no—
1353C23—24no—
1354C23—24no—
1355C23—22no—
1356C23—22no—
1357C23—22no—
1358C23—22no—
1359C23—24no—
1360C23—22no—
1361C23C2611yescharacteristic
1362Q8—44no—
1363Q8—44no—
1364Q8—48no—
1365Q8—82no—
1366Q8—84no—
1367D4—44no—
1368D4—416no—
1369D4—44no—
1370D4—44no—
1371D4—44no—
1372D4—48no—
1373D4—88no—
1374D4—88no—
1375D4—84no—
1376D4—84no—
1377D4—84no—
1378D4—84no—
1379D4—88no—
1380D4—88no—
1381D4—88no—
1382D4—88no—
1383D4—88no—
1384D4—164no—
1385D4—162no—
1386D4—162no—
1387D4—162no—
1388D4—162no—
1389D4—164no—
1390D4—164no—
1391C2×C4—22no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—22no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—24no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—24no—
1451C2×C4—22no—
1452C2×C4—48no—
1453C2×C4—48no—
1454C2×C4—48no—
1455C2×C4—416no—
1456C2×C4—48no—
1457C2×C4—88no—
1458C2×C4—88no—
1459C2×C4—88no—
1460C2×C4—88no—
1461C2×C4—88no—
1462C2×C4—164no—
1463C2×C4C2×H(5,𝔽2)12yes—
1464C2×C4C2×H(5,𝔽2)12yes—
1465C2×C4C2×H(5,𝔽2)14yes—
1466C2×C4C2×H(5,𝔽2)12yes—
1467C2×C4C2×H(5,𝔽2)12yes—
1468C2×C4#58514yes—
1469C2×C4#58514yes—
1470C22—44no—
1471C22—44no—
1472C22—44no—
1473C22—42no—
1474C22—42no—
1475C22—44no—
1476C22—44no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—44no—
1481C22—42no—
1482C22—42no—
1483C22—42no—
1484C22—42no—
1485C22—42no—
1486C22—44no—
1487C22—44no—
1488C22—42no—
1489C22—42no—
1490C22—42no—
1491C22—42no—
1492C22—44no—
1493C22—42no—
1494C22—44no—
1495C22—44no—
1496C22—44no—
1497C22—42no—
1498C22—44no—
1499C22C22×H(5,𝔽2)11yescharacteristic
1500C22C22×H(5,𝔽2)11yescharacteristic
1501C22C2×#58512yes—
1502C22C2×#58512yes—
1503C22H(7,𝔽2)11yescharacteristic
1504C4—24no—
1505C4—24no—
1506C4—22no—
1507C4—22no—
1508C4—22no—
1509C4—42no—
1510C4—44no—
1511C4—42no—
1512C4—44no—
1513C4—42no—
1514C4—42no—
1515C4—41no—
1516C4—41no—
1517C4—41no—
1518C4—42no—
1519C4—44no—
1520C4—42no—
1521C4—42no—
1522C4—44no—
1523C4—42no—
1524C4—42no—
1525C4—44no—
1526C4—42no—
1527C4#352914yes—
1528C2—82no—
1529C2—82no—
1530C2—82no—
1531C2—82no—
1532C2—84no—
1533C2C2×#352911yescharacteristic
1534C2#6289211yescharacteristic
1535C2#6296912yes—
1536C2#6301912yes—
1537C2#6303511yescharacteristic
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. #53110C2semidirect
2. #53059C2semidirect
3. #52973C2semidirect
4. #52683C2semidirect
5. #52333C2semidirect
6. #52329C2semidirect
7. #52306C2semidirect
8. #52167C2semidirect
9. #46346C2semidirect
10. #46329C2semidirect
11. #46310C2semidirect
12. #46275C2semidirect
13. #46228C2semidirect
14. #46084C2semidirect
15. #46050C2semidirect
16. #46044C2semidirect
17. #46010C2semidirect
18. #45914C2semidirect
19. #45865C2semidirect
20. #45814C2semidirect
21. #36527C2semidirect
22. #36495C2semidirect
23. #36452C2semidirect
24. #36419C2semidirect
25. #36128C2semidirect
26. #36125C2semidirect
27. #35787C2semidirect
28. #35715C2semidirect
29. #35704C2semidirect

Maximal subgroups

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

subgroupindex
#531102
#530592
#529732
#526832
#523332
#523292
#523062
#521672
#463462
#463292
#463102
#462752
#462282
#460842
#460502
#460442
#460102
#459142
#458652
#458142
#365272
#364952
#364522
#364192
#361282
#361252
#357872
#357152
#357042