Finite Group Databasebeta

← #8197056

Subgroups — #8197056

Order 512.

4485 conjugacy classes of subgroups.

The subgroup lattice has 1524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59564C212yesmaximal, complemented
2#59361C212yesmaximal, complemented
3#59221C212yesmaximal, complemented
4#59140C212yesmaximal, complemented
5#58972C212yesmaximal, complemented
6#58355C212yesmaximal, complemented
7#55973C214yesmaximal, complemented
8#53007C211yesmaximal, characteristic, complemented
9#53006C211yesmaximal, characteristic, complemented
10#52926C212yesmaximal, complemented
11#49501C214yesmaximal, complemented
12#46849C212yesmaximal, complemented
13#46548C212yesmaximal, complemented
14#46279C212yesmaximal, complemented
15#46174C212yesmaximal, complemented
16#45251C211yesmaximal, characteristic, complemented
17#44914C211yesmaximal, characteristic, complemented
18#44840C212yesmaximal, complemented
19#42919C212yesmaximal, complemented
20#42449C212yesmaximal, complemented
21#42374C214yesmaximal, complemented
22#39998C212yesmaximal, complemented
23#39878C212yesmaximal, complemented
24#39634C212yesmaximal, complemented
25#39463C212yesmaximal, complemented
26#38694C214yesmaximal, complemented
27#36384C212yesmaximal, complemented
28#36254C212yesmaximal, complemented
29#35138C211yesmaximal, characteristic, complemented
30#34977C211yesmaximal, characteristic
31#34947C211yesmaximal, characteristic, complemented
32C2×#552C2212yes—
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C22×#125C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#2864C2212yes—
38#2859C2212yes—
39#2852C2214yes—
40#2851C2212yes—
41#2851C2212yes—
42#2843C2212yes—
43#2841C2212yes—
44#2838C2214yes—
45#2837C2214yes—
46#2837C2214yes—
47#2833C2214yes—
48#2827C2214yes—
49#2826C2212yes—
50#2823C2212yes—
51#2797C2214yes—
52#2795C2212yes—
53#2792C2212yes—
54#2791C2214yes—
55#2789C2212yes—
56#2788C2214yes—
57#2786C2214yes—
58#2783C2214yes—
59#2782C2212yes—
60#2781C2214yes—
61#2780C2214yes—
62#2780C2214yes—
63#2780C2214yes—
64#2780C2214yes—
65#2778C2214yes—
66#2778C2214yes—
67#2776C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2763C2212yes—
71#2762C2214yes—
72#2760C2212yes—
73#2757C2214yes—
74#2756C2214yes—
75#2752C2212yes—
76#2751C2214yes—
77#2744C2214yes—
78#2742C2212yes—
79#2741C2214yes—
80#2740C2214yes—
81#2727C2214yes—
82#2726C2214yes—
83#2723C2214yes—
84#2723C2214yes—
85#2721C2214yes—
86#2719C2214yes—
87#2715C2214yes—
88#2713C2214yes—
89#2711C2214yes—
90#2709C2214yes—
91#2709C2214yes—
92#2708C2214yes—
93#2707C2214yes—
94#2707C2214yes—
95#2705C2214yes—
96#2704C2214yes—
97#2690C2214yes—
98#2681C2214yes—
99#2651C2214yes—
100#2651C2214yes—
101#2649C2214yes—
102#2648C2214yes—
103#2647C2214yes—
104#2637C2214yes—
105#2636C2214yes—
106#2634C2212yes—
107#2633C2212yes—
108#2616C2212yes—
109#2616C2212yes—
110#2612C2214yes—
111#2612C2212yes—
112#2611C2214yes—
113#2611C2212yes—
114#2611C2212yes—
115#2610C2211yescharacteristic
116#2610C2211yescharacteristic
117#2610C2211yescharacteristic
118#2610C2211yescharacteristic
119#2609C2214yes—
120#2609C2212yes—
121#2607C2212yes—
122#2603C2214yes—
123#2601C2214yes—
124#2596C2214yes—
125#2585C2214yes—
126#2584C2212yes—
127#2576C2214yes—
128#2575C2214yes—
129#2574C2214yes—
130#2570C2212yes—
131#2568C2211yescharacteristic
132#2567C2211yescharacteristic
133#2567C2211yescharacteristic
134#2566C2212yes—
135#2565C2212yes—
136#2565C2212yes—
137#2564C2212yes—
138#2564C2212yes—
139#2563C2211yescharacteristic
140#2563C2211yescharacteristic
141#2562C2212yes—
142#2562C2212yes—
143#2559C2214yes—
144#2559C2214yes—
145#2548C2211yescharacteristic
146#2542C2211yescharacteristic
147#2541C2211yescharacteristic
148#2538C2212yes—
149#2538C2212yes—
150#2536C2212yes—
151#2536C2212yes—
152#2536C2212yes—
153#2533C2214yes—
154#2531C2214yes—
155#2529C2214yes—
156#2529C2214yes—
157#2528C2214yes—
158#2528C2214yes—
159#2526C2214yes—
160#2526C2214yes—
161#2522C2214yes—
162#2521C2214yes—
163#2519C2214yes—
164#2517C2214yes—
165#2516C2214yes—
166#2508C2214yes—
167#2505C2214yes—
168#2500C2212yes—
169#2496C2212yes—
170#2496C2212yes—
171#2496C2212yes—
172#2495C2212yes—
173#2494C2212yes—
174#2494C2212yes—
175#2489C2212yes—
176#2489C2212yes—
177#2487C2211yescharacteristic
178#2487C2212yes—
179#2487C2212yes—
180#2487C2211yescharacteristic
181#2487C2212yes—
182#2487C2212yes—
183#2486C2211yescharacteristic
184#2486C2211yescharacteristic
185#2485C2212yes—
186#2485C2212yes—
187#2484C2212yes—
188#2481C2214yes—
189#2479C2214yes—
190#2478C2214yes—
191#2476C2214yes—
192#2475C2214yes—
193#2474C2214yes—
194#2474C2214yes—
195#2471C2214yes—
196#2467C2214yes—
197#2463C2212yes—
198#2454C2214yes—
199#2454C2214yes—
200#2444C2214yes—
201#2443C2214yes—
202#2442C2214yes—
203#2442C2212yes—
204#2441C2212yes—
205#2440C2212yes—
206#2439C2212yes—
207#2431C2212yes—
208#2429C2212yes—
209#2429C2212yes—
210#2423C2212yes—
211#2421C2212yes—
212#2417C2212yes—
213#2417C2212yes—
214#2417C2212yes—
215#2417C2212yes—
216#2417C2212yes—
217#2417C2212yes—
218#2415C2212yes—
219#2415C2212yes—
220#2414C2212yes—
221#2414C2212yes—
222#2406C2212yes—
223#2396C2212yes—
224#2396C2212yes—
225#2388C2211yescharacteristic
226#2388C2211yescharacteristic
227#2388C2211yescharacteristic
228#2388C2211yescharacteristic
229#2383C2214yes—
230#2373C2214yes—
231#2373C2214yes—
232#2371C2214yes—
233#2370C2212yes—
234#2362C2212yes—
235#2360C2212yes—
236#2352C2214yes—
237#2352C2212yes—
238#2352C2212yes—
239#2352C2212yes—
240#2351C2212yes—
241D4×C4⋊C4C2212yes—
242D4×C4⋊C4C2212yes—
243#2346C2214yes—
244#2346C2212yes—
245#2344C2212yes—
246#2335C2214yes—
247#2328C2214yes—
248#2323C2214yes—
249#2322C2212yes—
250#2322C2212yes—
251#2311C2212yes—
252#2311C2212yes—
253C4×#127C2212yes—
254C4×#124C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×C22⋊Q8C2212yes—
257C4×#121C2212yes—
258C4×#121C2212yes—
259#2297C2212yes—
260#2295C2212yes—
261#2295C2212yes—
262#2290C2214yes—
263#2285C2212yes—
264#2283C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C22×#41C2311yescharacteristic
270#552—48no—
271#533—44no—
272#532—44no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125—44no—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#124C2311yescharacteristic
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#123C2312yes—
294C2×#123C2312yes—
295C2×#123C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C4×#41—44no—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2314yes—
333C2×#117C2314yes—
334C2×#117C2312yes—
335C2×#117C2311yescharacteristic
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2311yescharacteristic
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348C22×C42C2311yescharacteristic
349C22×C42C2312yes—
350#401C2314yes—
351#401C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2312yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#399C2312yes—
372#399C2312yes—
373#399C2314yes—
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2312yes—
380#399C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2312yes—
399#398C2314yes—
400#398C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#395C2312yes—
431#395C2312yes—
432#395C2311yescharacteristic
433#395C2311yescharacteristic
434#395C2311yescharacteristic
435#395C2311yescharacteristic
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2311yescharacteristic
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2311yescharacteristic
447#394C2312yes—
448#394C2312yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2311yescharacteristic
456#394C2314yes—
457#394C2311yescharacteristic
458#394C2312yes—
459#394C2312yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#393C2312yes—
464#393C2312yes—
465#393C2311yescharacteristic
466#393C2311yescharacteristic
467#393C2311yescharacteristic
468#393C2311yescharacteristic
469#393C2314yes—
470#392C2311yescharacteristic
471#392C2312yes—
472#392C2311yescharacteristic
473#392C2311yescharacteristic
474#392C2311yescharacteristic
475#392C2312yes—
476#392C2312yes—
477#392C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2314yes—
498#390C2314yes—
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
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#387C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2312yes—
626#386C2314yes—
627#386C2312yes—
628#386C2312yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#384C2312yes—
653#384C2312yes—
654#384C2312yes—
655#384C2312yes—
656#384C2312yes—
657#383C2314yes—
658#383C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#382C2312yes—
665#382C2314yes—
666#382C2314yes—
667#382C2314yes—
668#382C2314yes—
669#382C2314yes—
670#381C2314yes—
671#381C2312yes—
672#381C2312yes—
673#381C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683#380C2312yes—
684#380C2312yes—
685#380C2312yes—
686#380C2314yes—
687#380C2314yes—
688#380C2312yes—
689#380C2312yes—
690#380C2314yes—
691#380C2314yes—
692#380C2314yes—
693#380C2312yes—
694#380C2312yes—
695#380C2314yes—
696#380C2314yes—
697#380C2311yescharacteristic
698#380C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2311yescharacteristic
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2314yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2311yescharacteristic
730C4×C22⋊C4C2311yescharacteristic
731#376C2314yes—
732#376C2314yes—
733#376C2314yes—
734#376C2311yescharacteristic
735#376C2311yescharacteristic
736#376C2312yes—
737C2×#95C2312yes—
738C43C2312yes—
739C2×#41—24no—
740C2×#41—42no—
741C2×#41—42no—
742C2×#41—42no—
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—42no—
746C22×Q8C2412yes—
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×D4C2412yes—
752C22×D4C2412yes—
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2412yes—
761C22×D4C2411yescharacteristic
762C22×D4C2411yescharacteristic
763C22×D4C2411yescharacteristic
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2412yes—
773C23×C4C2411yescharacteristic
774C23×C4C2411yescharacteristic
775C23×C4C2411yescharacteristic
776C23×C4C2412yes—
777C23×C4C2414yes—
778C23×C4C2414yes—
779C23×C4C2414yes—
780C4⋊Q8—42no—
781C4⋊Q8—42no—
782C4⋊Q8—42no—
783#127—28no—
784#127—42no—
785#126—48no—
786#126—48no—
787#126—48no—
788#126—48no—
789#125—28no—
790#125—44no—
791#125—44no—
792#125—44no—
793#125—48no—
794#125—44no—
795#125—48no—
796#124—42no—
797#124—42no—
798#124—44no—
799#123—28no—
800#123—44no—
801#123—48no—
802C22⋊Q8—48no—
803C22⋊Q8—44no—
804C22⋊Q8—44no—
805C22⋊Q8—44no—
806C22⋊Q8—44no—
807C22⋊Q8—44no—
808C22⋊Q8—44no—
809C22⋊Q8—44no—
810C22⋊Q8—44no—
811#121—44no—
812#121—44no—
813#121—44no—
814#121—44no—
815C4×Q8—28no—
816C4×Q8—42no—
817C4×Q8—42no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×D4—28no—
822C4×D4—48no—
823C4×D4—48no—
824C4×D4—44no—
825C4×D4—44no—
826C4×D4—44no—
827C4×D4—44no—
828C4×D4—42no—
829C4×D4—42no—
830C4×D4—42no—
831C4×D4—42no—
832C4×D4—42no—
833C4×D4—42no—
834C4×D4—44no—
835#117—42no—
836#117—42no—
837#117—42no—
838#117—44no—
839#117—48no—
840#117—44no—
841#117—48no—
842#117—44no—
843#117—44no—
844C2×C4⋊C4—44no—
845C2×C4⋊C4—44no—
846C2×C4⋊C4—42no—
847C2×C4⋊C4—42no—
848C2×C4⋊C4—44no—
849C2×C4⋊C4—44no—
850C2×C4⋊C4—44no—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2411yescharacteristic
920C2×C22⋊C4C2411yescharacteristic
921C2×C22⋊C4C2411yescharacteristic
922C2×C22⋊C4C2411yescharacteristic
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2411yescharacteristic
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C42—24no—
964C2×C42—24no—
965C2×C42—24no—
966C2×C42—44no—
967C2×C42C2414yes—
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2412yes—
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2411yescharacteristic
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2411yescharacteristic
1004#95C2411yescharacteristic
1005#95C2411yescharacteristic
1006#95C2411yescharacteristic
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056C24C2512yes—
1057C24C2512yes—
1058C24C2511yescharacteristic
1059C24C2511yescharacteristic
1060C24C2511yescharacteristic
1061#41—416no—
1062#41—88no—
1063#41—88no—
1064C2×Q8—24no—
1065C2×Q8—22no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—22no—
1069C2×Q8—41no—
1070C2×Q8—42no—
1071C2×Q8—44no—
1072C2×Q8—41no—
1073C2×Q8—41no—
1074C2×Q8—42no—
1075C2×Q8—42no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—22no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—41no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—41no—
1093C2×D4—41no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—42no—
1103C2×D4—41no—
1104C2×D4—41no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—42no—
1112C2×D42−1+414yes—
1113C22×C4—22no—
1114C22×C4—22no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—24no—
1118C22×C4—22no—
1119C22×C4—22no—
1120C22×C4—22no—
1121C22×C4—22no—
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—22no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—42no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—44no—
1140C22×C4—42no—
1141C22×C4—42no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—42no—
1151C22×C4—42no—
1152C22×C4—44no—
1153C22×C4—42no—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2514yes—
1158C22×C4C2514yes—
1159C22×C4C2514yes—
1160C22×C4C2514yes—
1161C22×C4C2514yes—
1162C22×C4C2511yescharacteristic
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2514yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—28no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—44no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—42no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C22⋊C4—24no—
1240C22⋊C4—28no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C42—22no—
1293C42—22no—
1294C42—22no—
1295C42—22no—
1296C42—22no—
1297C42—22no—
1298C42—22no—
1299C42—22no—
1300C42—22no—
1301C42—28no—
1302C42—24no—
1303C42—24no—
1304C42—24no—
1305C42—24no—
1306C42—24no—
1307C42—24no—
1308C42—28no—
1309C42—44no—
1310C42—44no—
1311C42—42no—
1312C42—44no—
1313C42—44no—
1314C42—44no—
1315C42—44no—
1316C42—42no—
1317C42—44no—
1318C42H(5,𝔽2)14yes—
1319C23—21no—
1320C23—21no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—21no—
1326C23—21no—
1327C23—22no—
1328C23—22no—
1329C23—21no—
1330C23—21no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—21no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23C2×2−1+412yes—
1347C23C2×2−1+412yes—
1348C23C2611yescharacteristic
1349Q8—44no—
1350Q8—48no—
1351Q8—84no—
1352Q8—82no—
1353Q8—82no—
1354D4—44no—
1355D4—48no—
1356D4—48no—
1357D4—44no—
1358D4—44no—
1359D4—84no—
1360D4—84no—
1361D4—84no—
1362D4—84no—
1363D4—82no—
1364D4—82no—
1365D4—84no—
1366D4—84no—
1367C2×C4—28no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—22no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—21no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—24no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—44no—
1432C2×C4—44no—
1433C2×C4—44no—
1434C2×C4—44no—
1435C2×C4—44no—
1436C2×C4—48no—
1437C2×C4—48no—
1438C2×C4—44no—
1439C2×C4—82no—
1440C2×C4—82no—
1441C2×C4—84no—
1442C2×C4—84no—
1443C2×C4—88no—
1444C2×C4—88no—
1445C2×C4—88no—
1446C2×C4C2×H(5,𝔽2)12yes—
1447C2×C4C2×H(5,𝔽2)12yes—
1448C2×C4C2×H(5,𝔽2)12yes—
1449C2×C4C2×2−1+412yes—
1450C2×C4#58512yes—
1451C2×C4#58514yes—
1452C2×C4#58514yes—
1453C22—24no—
1454C22—24no—
1455C22—22no—
1456C22—22no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—42no—
1462C22—42no—
1463C22—41no—
1464C22—42no—
1465C22—42no—
1466C22—41no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—41no—
1480C22—42no—
1481C22—42no—
1482C22C22×H(5,𝔽2)11yescharacteristic
1483C22C22×2−1+411yescharacteristic
1484C22C2×#58512yes—
1485C22C2×#58512yes—
1486C22C2×#58511yescharacteristic
1487C4—22no—
1488C4—24no—
1489C4—22no—
1490C4—22no—
1491C4—22no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—42no—
1496C4—42no—
1497C4—44no—
1498C4—41no—
1499C4—41no—
1500C4—44no—
1501C4—44no—
1502C4—41no—
1503C4—44no—
1504C4—42no—
1505C4—42no—
1506C4—42no—
1507C4—44no—
1508C4—44no—
1509C4—44no—
1510C4—41no—
1511C4—44no—
1512C4#355114yes—
1513C2—42no—
1514C2—42no—
1515C2—81no—
1516C2—82no—
1517C2—82no—
1518C2C2×#355111yescharacteristic
1519C2#6275911yescharacteristic
1520C2#6281911yescharacteristic
1521C2#6302312yes—
1522C2#6303112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34977C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59564C2semidirect
2. #59361C2semidirect
3. #59221C2semidirect
4. #59140C2semidirect
5. #58972C2semidirect
6. #58355C2semidirect
7. #55973C2semidirect
8. #53007C2semidirect
9. #53006C2semidirect
10. #52926C2semidirect
11. #49501C2semidirect
12. #46849C2semidirect
13. #46548C2semidirect
14. #46279C2semidirect
15. #46174C2semidirect
16. #45251C2semidirect
17. #44914C2semidirect
18. #44840C2semidirect
19. #42919C2semidirect
20. #42449C2semidirect
21. #42374C2semidirect
22. #39998C2semidirect
23. #39878C2semidirect
24. #39634C2semidirect
25. #39463C2semidirect
26. #38694C2semidirect
27. #36384C2semidirect
28. #36254C2semidirect
29. #35138C2semidirect
31. #34947C2semidirect

Maximal subgroups

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

subgroupindex
#595642
#593612
#592212
#591402
#589722
#583552
#559732
#530072
#530062
#529262
#495012
#468492
#465482
#462792
#461742
#452512
#449142
#448402
#429192
#424492
#423742
#399982
#398782
#396342
#394632
#386942
#363842
#362542
#351382
#349772
#349472