Finite Group Databasebeta

← #8701607

Subgroups — #8701607

Order 512.

4943 conjugacy classes of subgroups.

The subgroup lattice has 1528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59904C212yesmaximal, complemented
2#59886C212yesmaximal, complemented
3#59097C212yesmaximal, complemented
4#59039C212yesmaximal, complemented
5#54875C214yesmaximal, complemented
6#54388C214yesmaximal, complemented
7#53918C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic, complemented
9#51746C214yesmaximal, complemented
10#49745C214yesmaximal, complemented
11#49202C214yesmaximal, complemented
12#46016C211yesmaximal, characteristic, complemented
13#46006C211yesmaximal, characteristic, complemented
14#45995C211yesmaximal, characteristic, complemented
15#45208C212yesmaximal, complemented
16#45003C212yesmaximal, complemented
17#44995C212yesmaximal, complemented
18#42927C212yesmaximal, complemented
19#42547C212yesmaximal, complemented
20#42457C212yesmaximal, complemented
21#40007C212yesmaximal, complemented
22#39657C212yesmaximal, complemented
23#39343C212yesmaximal, complemented
24#37217C212yesmaximal, complemented
25#37190C212yesmaximal, complemented
26#37156C212yesmaximal, complemented
27#36464C211yesmaximal, characteristic, complemented
28#36463C211yesmaximal, characteristic, complemented
29#36303C211yesmaximal, characteristic, complemented
30C2×#562C2212yes—
31C2×#550C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#536C2214yes—
35C2×#532C2212yes—
36#2862C2211yescharacteristic
37#2859C2211yescharacteristic
38#2858C2211yescharacteristic
39#2857C2212yes—
40#2854C2212yes—
41#2854C2212yes—
42#2850C2212yes—
43#2844C2212yes—
44#2838C2214yes—
45#2826C2214yes—
46#2820C2212yes—
47#2819C2212yes—
48#2813C2214yes—
49#2808C2211yescharacteristic
50#2806C2211yescharacteristic
51#2805C2212yes—
52#2804C2212yes—
53#2803C2214yes—
54#2801C2214yes—
55#2783C2212yes—
56#2781C2212yes—
57#2778C2214yes—
58#2777C2214yes—
59#2774C2214yes—
60#2755C2214yes—
61#2753C2214yes—
62#2752C2214yes—
63#2750C2214yes—
64#2745C2214yes—
65#2744C2212yes—
66#2743C2214yes—
67#2743C2214yes—
68#2742C2214yes—
69#2741C2214yes—
70#2740C2214yes—
71#2737C2214yes—
72#2737C2214yes—
73#2734C2212yes—
74#2733C2212yes—
75#2732C2211yescharacteristic
76#2732C2212yes—
77#2731C2214yes—
78#2730C2212yes—
79#2730C2214yes—
80#2730C2214yes—
81#2729C2214yes—
82#2729C2214yes—
83#2728C2214yes—
84#2713C2214yes—
85#2712C2214yes—
86#2709C2214yes—
87#2708C2214yes—
88#2706C2214yes—
89#2703C2214yes—
90#2699C2214yes—
91#2696C2214yes—
92#2696C2214yes—
93#2696C2214yes—
94#2694C2212yes—
95#2693C2214yes—
96#2692C2214yes—
97#2686C2214yes—
98#2686C2212yes—
99#2686C2214yes—
100#2686C2214yes—
101#2682C2212yes—
102#2682C2211yescharacteristic
103#2676C2214yes—
104#2674C2214yes—
105#2674C2214yes—
106#2674C2214yes—
107#2673C2214yes—
108#2673C2214yes—
109#2672C2214yes—
110#2672C2214yes—
111#2672C2214yes—
112#2671C2214yes—
113#2665C2214yes—
114#2663C2214yes—
115#2649C2214yes—
116#2639C2214yes—
117#2635C2214yes—
118#2632C2214yes—
119#2630C2214yes—
120#2620C2212yes—
121#2618C2214yes—
122#2616C2214yes—
123#2592C2212yes—
124#2589C2214yes—
125#2579C2214yes—
126#2578C2214yes—
127#2578C2214yes—
128#2576C2214yes—
129#2574C2214yes—
130#2573C2214yes—
131#2569C2214yes—
132#2568C2211yescharacteristic
133#2567C2212yes—
134#2564C2214yes—
135#2563C2211yescharacteristic
136#2563C2212yes—
137#2558C2214yes—
138#2557C2214yes—
139#2557C2214yes—
140#2555C2214yes—
141#2555C2214yes—
142#2551C2212yes—
143#2551C2212yes—
144#2547C2211yescharacteristic
145#2542C2212yes—
146#2541C2211yescharacteristic
147#2538C2212yes—
148#2538C2211yescharacteristic
149#2537C2212yes—
150#2537C2211yescharacteristic
151#2520C2214yes—
152#2518C2214yes—
153#2518C2214yes—
154#2515C2214yes—
155#2514C2212yes—
156#2513C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2511C2212yes—
160#2503C2212yes—
161#2501C2212yes—
162#2499C2212yes—
163#2498C2214yes—
164#2498C2214yes—
165#2497C2212yes—
166#2495C2212yes—
167#2493C2214yes—
168#2492C2214yes—
169#2492C2212yes—
170#2492C2212yes—
171#2492C2212yes—
172#2491C2214yes—
173#2491C2212yes—
174#2491C2212yes—
175#2491C2212yes—
176#2490C2212yes—
177#2488C2214yes—
178#2488C2214yes—
179#2477C2214yes—
180#2471C2214yes—
181#2465C2214yes—
182#2464C2214yes—
183#2459C2214yes—
184#2459C2214yes—
185#2457C2214yes—
186#2451C2212yes—
187#2450C2214yes—
188#2447C2212yes—
189#2446C2212yes—
190#2445C2214yes—
191#2445C2212yes—
192#2445C2212yes—
193#2440C2212yes—
194#2436C2212yes—
195#2432C2212yes—
196#2431C2214yes—
197#2431C2212yes—
198#2431C2212yes—
199#2430C2214yes—
200#2430C2214yes—
201#2430C2214yes—
202#2428C2212yes—
203#2428C2214yes—
204#2426C2212yes—
205#2423C2212yes—
206#2422C2212yes—
207#2422C2212yes—
208#2422C2212yes—
209#2420C2214yes—
210#2420C2212yes—
211#2417C2212yes—
212#2416C2212yes—
213#2415C2214yes—
214#2414C2212yes—
215#2409C2214yes—
216#2407C2212yes—
217#2407C2212yes—
218#2407C2212yes—
219#2396C2212yes—
220#2395C2212yes—
221#2392C2212yes—
222#2382C2212yes—
223#2379C2212yes—
224#2369C2211yescharacteristic
225#2368C2214yes—
226#2367C2212yes—
227#2366C2211yescharacteristic
228#2366C2212yes—
229#2364C2214yes—
230#2363C2212yes—
231#2357C2212yes—
232#2354C2211yescharacteristic
233#2354C2212yes—
234#2352C2212yes—
235Q8×C4⋊C4C2211yescharacteristic
236#2349C2214yes—
237#2347C2212yes—
238#2345C2212yes—
239#2339C2212yes—
240#2339C2212yes—
241#2339C2212yes—
242#2335C2214yes—
243#2335C2214yes—
244#2324C2212yes—
245#2314C2212yes—
246#2311C2212yes—
247C4×#125C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#123C2212yes—
254C4×#121C2212yes—
255C4×#121C2212yes—
256#2297C2212yes—
257C2×#391C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261C22×#41C2314yes—
262C23×Q8C2312yes—
263#562—48no—
264#550—48no—
265D4×Q8—44no—
266#547—44no—
267#536—416no—
268#532—48no—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2314yes—
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2314yes—
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#124C2311yescharacteristic
282C2×#124C2311yescharacteristic
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2314yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2314yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2314yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C42C2312yes—
350C22×C42C2312yes—
351#401C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2312yes—
373#399C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2312yes—
407#396C2312yes—
408#396C2312yes—
409#396C2314yes—
410#395C2312yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2314yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2314yes—
442#394C2312yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2312yes—
456#393C2314yes—
457#393C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2312yes—
465#392C2314yes—
466#392C2314yes—
467#392C2314yes—
468#392C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2312yes—
487#391C2314yes—
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#390C2312yes—
491#390C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2314yes—
495#390C2314yes—
496#390C2312yes—
497#390C2311yescharacteristic
498#390C2311yescharacteristic
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2312yes—
507#390C2314yes—
508#390C2312yes—
509#390C2312yes—
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
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#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2312yes—
619#386C2312yes—
620#386C2314yes—
621#386C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2312yes—
641#384C2311yescharacteristic
642#384C2312yes—
643#383C2314yes—
644#383C2314yes—
645#382C2311yescharacteristic
646#382C2312yes—
647#382C2314yes—
648#382C2312yes—
649#382C2311yescharacteristic
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2311yescharacteristic
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C43C2311yescharacteristic
718C2×#41—28no—
719C2×#41—48no—
720C2×#41—48no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—44no—
725C2×#41—44no—
726C2×#41—84no—
727C22×Q8—28no—
728C22×Q8—44no—
729C22×Q8—82no—
730C22×Q8C2412yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2414yes—
733C22×Q8C2412yes—
734C22×Q8C2412yes—
735C22×Q8C2414yes—
736C22×Q8C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2411yescharacteristic
740C22×D4C2411yescharacteristic
741C22×D4C2411yescharacteristic
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2414yes—
747C22×D4C2412yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2414yes—
751C22×D4C2412yes—
752C22×D4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C4⋊Q8—42no—
767C4⋊Q8—44no—
768C4⋊Q8—44no—
769C4⋊Q8—42no—
770C4⋊Q8—42no—
771C4⋊Q8—48no—
772C4⋊Q8—48no—
773#127—28no—
774#127—42no—
775#127—48no—
776#125—24no—
777#125—44no—
778#124—24no—
779#124—44no—
780#124—44no—
781#124—44no—
782#124—42no—
783#124—48no—
784#124—48no—
785#124—48no—
786#124—82no—
787#124—84no—
788#123—28no—
789#123—48no—
790#123—48no—
791#123—48no—
792#123—48no—
793#123—48no—
794#123—48no—
795#123—48no—
796#123—48no—
797C22⋊Q8—28no—
798C22⋊Q8—216no—
799C22⋊Q8—44no—
800C22⋊Q8—48no—
801C22⋊Q8—48no—
802C22⋊Q8—44no—
803C22⋊Q8—44no—
804C22⋊Q8—48no—
805C22⋊Q8—48no—
806C22⋊Q8—44no—
807C22⋊Q8—84no—
808#121—28no—
809#121—28no—
810#121—48no—
811#121—44no—
812#121—48no—
813#121—48no—
814#121—48no—
815#121—44no—
816#121—44no—
817#121—44no—
818#121—44no—
819#121—48no—
820#121—82no—
821#121—84no—
822#121—82no—
823C4×Q8—42no—
824C4×Q8—42no—
825C4×Q8—44no—
826C4×Q8—82no—
827C4×D4—28no—
828C4×D4—24no—
829C4×D4—44no—
830C4×D4—42no—
831C4×D4—42no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—42no—
835C4×D4—42no—
836C4×D4—44no—
837C4×D4—48no—
838C4×D4—48no—
839C4×D4—48no—
840C4×D4—82no—
841#117—44no—
842#117—44no—
843#117—48no—
844C2×C4⋊C4—44no—
845C2×C4⋊C4—44no—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C42—44no—
959C2×C42—82no—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2412yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2411yescharacteristic
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041C24C2512yes—
1042C24C2514yes—
1043C24C2512yes—
1044C24C2512yes—
1045#41—832no—
1046#41—816no—
1047#41—816no—
1048C2×Q8—24no—
1049C2×Q8—28no—
1050C2×Q8—24no—
1051C2×Q8—22no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—41no—
1055C2×Q8—41no—
1056C2×Q8—41no—
1057C2×Q8—41no—
1058C2×Q8—44no—
1059C2×Q8—42no—
1060C2×Q8—44no—
1061C2×Q8—44no—
1062C2×Q8—42no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—42no—
1066C2×Q8—42no—
1067C2×Q8—42no—
1068C2×Q8—816no—
1069C2×Q8H(5,𝔽2)14yes—
1070C2×D4—28no—
1071C2×D4—28no—
1072C2×D4—28no—
1073C2×D4—28no—
1074C2×D4—24no—
1075C2×D4—22no—
1076C2×D4—28no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—22no—
1080C2×D4—22no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—22no—
1084C2×D4—44no—
1085C2×D4—41no—
1086C2×D4—42no—
1087C2×D4—41no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—41no—
1095C2×D4—42no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—41no—
1103C2×D4—42no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—42no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—42no—
1116C2×D4—42no—
1117C2×D4H(5,𝔽2)14yes—
1118C22×C4—24no—
1119C22×C4—28no—
1120C22×C4—28no—
1121C22×C4—24no—
1122C22×C4—28no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—28no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—42no—
1144C22×C4—42no—
1145C22×C4—42no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4C2514yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2514yes—
1171C22×C4C2514yes—
1172C22×C4C2514yes—
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2512yes—
1180C22×C4C2511yescharacteristic
1181C22×C4C2511yescharacteristic
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—24no—
1185C4⋊C4—22no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—22no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—41no—
1202C4⋊C4—44no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—41no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—41no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—41no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—42no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C42−1+414yes—
1237C22⋊C4—28no—
1238C22⋊C4—24no—
1239C22⋊C4—28no—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—28no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—24no—
1250C22⋊C4—28no—
1251C22⋊C4—24no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
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—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—42no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C42—24no—
1295C42—24no—
1296C42—22no—
1297C42—22no—
1298C42—22no—
1299C42—24no—
1300C42—24no—
1301C42—22no—
1302C42—22no—
1303C42—22no—
1304C42—42no—
1305C42—42no—
1306C42—41no—
1307C42—42no—
1308C42—42no—
1309C42—42no—
1310C42—44no—
1311C42—44no—
1312C42—44no—
1313C42—44no—
1314C42—44no—
1315C42—44no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—24no—
1324C23—22no—
1325C23—22no—
1326C23—24no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—24no—
1331C23—24no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—24no—
1336C23—22no—
1337C23—22no—
1338C23—24no—
1339C23—22no—
1340C23—22no—
1341C23—24no—
1342C23—22no—
1343C23C2×H(5,𝔽2)14yes—
1344C23C2611yescharacteristic
1345Q8—44no—
1346Q8—44no—
1347Q8—48no—
1348Q8—88no—
1349Q8—84no—
1350Q8—88no—
1351Q8—162no—
1352D4—28no—
1353D4—416no—
1354D4—48no—
1355D4—84no—
1356D4—82no—
1357D4—82no—
1358D4—84no—
1359D4—88no—
1360D4—88no—
1361D4—88no—
1362D4—84no—
1363D4—88no—
1364D4—88no—
1365D4—164no—
1366D4—162no—
1367D4—164no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—22no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—48no—
1436C2×C4—416no—
1437C2×C4—48no—
1438C2×C4—48no—
1439C2×C4—48no—
1440C2×C4—84no—
1441C2×C4—84no—
1442C2×C4—84no—
1443C2×C4—88no—
1444C2×C4—88no—
1445C2×C4—88no—
1446C2×C4—164no—
1447C2×C4—164no—
1448C2×C4C2×H(5,𝔽2)12yes—
1449C2×C4C2×H(5,𝔽2)14yes—
1450C2×C4C2×H(5,𝔽2)12yes—
1451C2×C4C2×2−1+412yes—
1452C2×C4C2×2−1+414yes—
1453C2×C4#58512yes—
1454C2×C4#58512yes—
1455C2×C4#58512yes—
1456C22—24no—
1457C22—24no—
1458C22—24no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—44no—
1466C22—42no—
1467C22—44no—
1468C22—42no—
1469C22—42no—
1470C22—44no—
1471C22—42no—
1472C22—42no—
1473C22—44no—
1474C22—42no—
1475C22—42no—
1476C22—44no—
1477C22—42no—
1478C22—44no—
1479C22—42no—
1480C22—42no—
1481C22—44no—
1482C22—42no—
1483C22—42no—
1484C22C22×H(5,𝔽2)11yescharacteristic
1485C22C22×H(5,𝔽2)11yescharacteristic
1486C22C22×2−1+411yescharacteristic
1487C22C2×#58511yescharacteristic
1488C22C2×#58511yescharacteristic
1489C22C2×#58511yescharacteristic
1490C22H(7,𝔽2)11yescharacteristic
1491C4—24no—
1492C4—24no—
1493C4—22no—
1494C4—22no—
1495C4—22no—
1496C4—42no—
1497C4—42no—
1498C4—44no—
1499C4—41no—
1500C4—42no—
1501C4—44no—
1502C4—44no—
1503C4—41no—
1504C4—41no—
1505C4—42no—
1506C4—42no—
1507C4—42no—
1508C4—44no—
1509C4—42no—
1510C4—44no—
1511C4—42no—
1512C4—42no—
1513C4—42no—
1514C4—42no—
1515C4#354514yes—
1516C2—44no—
1517C2—82no—
1518C2—82no—
1519C2—84no—
1520C2C2×#354511yescharacteristic
1521C2#6289211yescharacteristic
1522C2#6290811yescharacteristic
1523C2#6296211yescharacteristic
1524C2#6301311yescharacteristic
1525C2#6303511yescharacteristic
1526C2#6303911yescharacteristic
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. #59904C2semidirect
2. #59886C2semidirect
3. #59097C2semidirect
4. #59039C2semidirect
5. #54875C2semidirect
6. #54388C2semidirect
7. #53918C2semidirect
8. #52303C2semidirect
9. #51746C2semidirect
10. #49745C2semidirect
11. #49202C2semidirect
12. #46016C2semidirect
13. #46006C2semidirect
14. #45995C2semidirect
15. #45208C2semidirect
16. #45003C2semidirect
17. #44995C2semidirect
18. #42927C2semidirect
19. #42547C2semidirect
20. #42457C2semidirect
21. #40007C2semidirect
22. #39657C2semidirect
23. #39343C2semidirect
24. #37217C2semidirect
25. #37190C2semidirect
26. #37156C2semidirect
27. #36464C2semidirect
28. #36463C2semidirect
29. #36303C2semidirect

Maximal subgroups

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

subgroupindex
#599042
#598862
#590972
#590392
#548752
#543882
#539182
#523032
#517462
#497452
#492022
#460162
#460062
#459952
#452082
#450032
#449952
#429272
#425472
#424572
#400072
#396572
#393432
#372172
#371902
#371562
#364642
#364632
#363032