Finite Group Databasebeta

← #8688202

Subgroups — #8688202

Order 512.

4987 conjugacy classes of subgroups.

The subgroup lattice has 1541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57248C214yesmaximal, complemented
2#55353C214yesmaximal, complemented
3#55084C214yesmaximal, complemented
4#54854C212yesmaximal, complemented
5#54115C214yesmaximal, complemented
6#53492C212yesmaximal, complemented
7#53452C214yesmaximal, complemented
8#46342C211yesmaximal, characteristic, complemented
9#46264C212yesmaximal, complemented
10#46048C212yesmaximal, complemented
11#45826C214yesmaximal, complemented
12#45385C212yesmaximal, complemented
13#45345C211yesmaximal, characteristic, complemented
14#45321C211yesmaximal, characteristic, complemented
15#45248C212yesmaximal, complemented
16#45245C212yesmaximal, complemented
17#45095C212yesmaximal, complemented
18#44897C212yesmaximal, complemented
19#42995C212yesmaximal, complemented
20#42985C211yesmaximal, characteristic, complemented
21#42913C211yesmaximal, characteristic, complemented
22#42807C212yesmaximal, complemented
23#42788C212yesmaximal, complemented
24#42778C212yesmaximal, complemented
25#42741C212yesmaximal, complemented
26#37629C212yesmaximal, complemented
27#36696C211yesmaximal, characteristic, complemented
28#36465C211yesmaximal, characteristic, complemented
29#36311C212yesmaximal, complemented
30C2×#555C2212yes—
31C2×#550C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2212yes—
35C2×#548C2212yes—
36C2×#548C2212yes—
37C2×#542C2212yes—
38C2×#537C2211yescharacteristic
39C2×#536C2212yes—
40C2×#536C2211yescharacteristic
41#2865C2214yes—
42#2863C2212yes—
43#2858C2212yes—
44#2858C2211yescharacteristic
45#2843C2211yescharacteristic
46#2836C2214yes—
47#2830C2214yes—
48#2830C2212yes—
49#2830C2212yes—
50#2830C2211yescharacteristic
51#2829C2212yes—
52#2829C2212yes—
53#2829C2212yes—
54#2828C2214yes—
55#2828C2212yes—
56#2828C2211yescharacteristic
57#2823C2211yescharacteristic
58#2821C2214yes—
59#2819C2214yes—
60#2818C2212yes—
61#2817C2214yes—
62#2816C2212yes—
63#2815C2212yes—
64#2803C2214yes—
65#2798C2214yes—
66#2797C2214yes—
67#2794C2212yes—
68#2792C2212yes—
69#2786C2214yes—
70#2784C2214yes—
71#2780C2214yes—
72#2773C2214yes—
73#2771C2212yes—
74#2757C2214yes—
75#2753C2214yes—
76#2752C2214yes—
77#2749C2214yes—
78#2749C2214yes—
79#2738C2214yes—
80#2737C2214yes—
81#2737C2214yes—
82#2737C2214yes—
83#2734C2214yes—
84#2733C2214yes—
85#2730C2214yes—
86#2729C2214yes—
87#2729C2214yes—
88#2728C2214yes—
89#2714C2214yes—
90#2712C2214yes—
91#2710C2214yes—
92#2710C2214yes—
93#2709C2214yes—
94#2709C2212yes—
95#2708C2214yes—
96#2703C2214yes—
97#2703C2214yes—
98#2701C2214yes—
99#2700C2214yes—
100#2700C2214yes—
101#2699C2214yes—
102#2696C2214yes—
103#2696C2214yes—
104#2692C2214yes—
105#2692C2214yes—
106#2691C2214yes—
107#2689C2214yes—
108#2688C2214yes—
109#2686C2214yes—
110#2686C2214yes—
111#2683C2214yes—
112#2681C2214yes—
113#2681C2214yes—
114#2680C2212yes—
115#2677C2212yes—
116#2677C2214yes—
117#2677C2214yes—
118#2676C2214yes—
119#2674C2214yes—
120#2674C2214yes—
121#2673C2214yes—
122#2673C2214yes—
123#2672C2214yes—
124#2649C2214yes—
125#2648C2214yes—
126#2644C2214yes—
127#2644C2214yes—
128#2640C2214yes—
129#2640C2214yes—
130#2639C2212yes—
131#2639C2212yes—
132#2638C2214yes—
133#2638C2214yes—
134#2638C2212yes—
135#2638C2212yes—
136#2631C2214yes—
137#2628C2214yes—
138#2624C2211yescharacteristic
139#2621C2212yes—
140#2615C2211yescharacteristic
141#2610C2214yes—
142#2607C2212yes—
143#2603C2214yes—
144#2600C2214yes—
145#2582C2212yes—
146#2564C2212yes—
147#2551C2212yes—
148#2549C2214yes—
149#2548C2214yes—
150#2547C2212yes—
151#2545C2212yes—
152#2544C2212yes—
153#2543C2212yes—
154#2542C2211yescharacteristic
155#2542C2212yes—
156#2541C2211yescharacteristic
157#2541C2212yes—
158#2540C2212yes—
159#2540C2212yes—
160#2540C2214yes—
161#2540C2214yes—
162#2540C2212yes—
163#2540C2212yes—
164#2535C2212yes—
165#2533C2214yes—
166#2532C2214yes—
167#2531C2214yes—
168#2526C2214yes—
169#2525C2214yes—
170#2524C2214yes—
171#2521C2214yes—
172#2520C2214yes—
173#2509C2212yes—
174#2504C2211yescharacteristic
175#2492C2212yes—
176#2492C2212yes—
177#2492C2212yes—
178#2491C2214yes—
179#2486C2211yescharacteristic
180#2485C2212yes—
181#2479C2214yes—
182#2474C2214yes—
183#2471C2214yes—
184#2469C2214yes—
185#2464C2214yes—
186#2463C2214yes—
187#2461C2214yes—
188#2461C2214yes—
189#2458C2214yes—
190#2456C2214yes—
191#2456C2214yes—
192#2455C2212yes—
193#2452C2214yes—
194#2452C2214yes—
195#2451C2212yes—
196#2447C2212yes—
197#2447C2214yes—
198#2447C2214yes—
199#2447C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2444C2214yes—
203#2438C2214yes—
204#2436C2211yescharacteristic
205#2436C2212yes—
206#2436C2212yes—
207#2434C2212yes—
208#2434C2212yes—
209#2432C2212yes—
210#2429C2212yes—
211#2429C2212yes—
212#2428C2212yes—
213#2427C2212yes—
214#2427C2212yes—
215#2426C2214yes—
216#2426C2212yes—
217#2426C2212yes—
218#2421C2212yes—
219#2421C2212yes—
220#2419C2214yes—
221#2417C2212yes—
222#2415C2212yes—
223#2415C2212yes—
224#2415C2212yes—
225#2415C2212yes—
226#2414C2212yes—
227#2409C2211yescharacteristic
228#2409C2212yes—
229#2409C2212yes—
230#2409C2212yes—
231#2407C2212yes—
232#2395C2211yescharacteristic
233#2395C2212yes—
234#2392C2212yes—
235#2392C2212yes—
236#2392C2212yes—
237#2388C2211yescharacteristic
238#2388C2212yes—
239#2377C2214yes—
240#2376C2212yes—
241#2365C2212yes—
242#2365C2212yes—
243#2363C2212yes—
244#2362C2212yes—
245#2362C2212yes—
246#2360C2212yes—
247#2356C2212yes—
248#2346C2212yes—
249#2339C2211yescharacteristic
250#2339C2211yescharacteristic
251#2324C2212yes—
252#2323C2212yes—
253#2310C2212yes—
254C4×#127C2211yescharacteristic
255C4×#127C2212yes—
256C4×#126C2212yes—
257#2295C2214yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262C23×Q8C2312yes—
263C23×Q8C2311yescharacteristic
264C23×Q8C2312yes—
265#555—48no—
266#550—44no—
267D4×Q8—48no—
268D4×Q8—44no—
269D4×Q8—48no—
270#548—48no—
271#548—48no—
272#542—48no—
273#537—44no—
274#536—48no—
275#536—44no—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×#127C2311yescharacteristic
285C2×#127C2312yes—
286C2×#127C2312yes—
287C2×#127C2311yescharacteristic
288C2×#126C2312yes—
289C2×#126C2314yes—
290C2×#124C2314yes—
291C2×#124C2314yes—
292C2×#124C2314yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2312yes—
300C2×#123C2312yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2312yes—
329C2×#121C2311yescharacteristic
330C2×#121C2311yescharacteristic
331C2×#121C2314yes—
332C2×#121C2312yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2312yes—
338C2×#121C2314yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2314yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2312yes—
362C2×#117C2311yescharacteristic
363C2×#117C2314yes—
364C22×C4⋊C4C2311yescharacteristic
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2311yescharacteristic
370#400C2314yes—
371#400C2314yes—
372#400C2312yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#399C2311yescharacteristic
377#399C2312yes—
378#399C2314yes—
379#399C2314yes—
380#399C2312yes—
381#399C2314yes—
382#399C2312yes—
383#399C2314yes—
384#399C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2312yes—
389#398C2311yescharacteristic
390#398C2312yes—
391#398C2312yes—
392#398C2314yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2312yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2311yescharacteristic
411#397C2312yes—
412#397C2312yes—
413#397C2312yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2312yes—
425#397C2312yes—
426#397C2314yes—
427#397C2312yes—
428#397C2314yes—
429#396C2312yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2312yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2312yes—
447#395C2314yes—
448#395C2312yes—
449#395C2311yescharacteristic
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2311yescharacteristic
466#394C2312yes—
467#394C2312yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2312yes—
478#394C2312yes—
479#394C2312yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#393C2312yes—
488#393C2312yes—
489#393C2314yes—
490#393C2314yes—
491#393C2314yes—
492#393C2314yes—
493#393C2312yes—
494#393C2314yes—
495#393C2311yescharacteristic
496#393C2312yes—
497#393C2314yes—
498#393C2314yes—
499#393C2314yes—
500#393C2312yes—
501#393C2314yes—
502#393C2314yes—
503#392C2312yes—
504#392C2312yes—
505#392C2312yes—
506#392C2312yes—
507#392C2312yes—
508#392C2312yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2312yes—
513#392C2311yescharacteristic
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2312yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#391C2314yes—
528#391C2312yes—
529#391C2314yes—
530#391C2314yes—
531#391C2314yes—
532#391C2312yes—
533#391C2312yes—
534#391C2312yes—
535#391C2312yes—
536#391C2312yes—
537#391C2314yes—
538#391C2314yes—
539#390C2311yescharacteristic
540#390C2312yes—
541#390C2311yescharacteristic
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2314yes—
546#390C2314yes—
547#390C2314yes—
548#390C2312yes—
549#390C2314yes—
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2314yes—
556#390C2314yes—
557#390C2312yes—
558#390C2314yes—
559#390C2314yes—
560#390C2314yes—
561#390C2314yes—
562#390C2314yes—
563#389C2314yes—
564#389C2312yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2312yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2312yes—
672#384C2311yescharacteristic
673#384C2312yes—
674#383C2312yes—
675#383C2314yes—
676#383C2314yes—
677#382C2314yes—
678#382C2312yes—
679#381C2312yes—
680#381C2314yes—
681#381C2314yes—
682#381C2312yes—
683#381C2312yes—
684#381C2314yes—
685#381C2314yes—
686#380C2314yes—
687#380C2312yes—
688#380C2312yes—
689#380C2311yescharacteristic
690#380C2311yescharacteristic
691#380C2312yes—
692#380C2314yes—
693#380C2314yes—
694#380C2314yes—
695#380C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2314yes—
717#376C2314yes—
718#376C2314yes—
719C2×#95C2312yes—
720C2×#95C2312yes—
721C43C2311yescharacteristic
722C43C2312yes—
723C2×#41—24no—
724C2×#41—24no—
725C2×#41—44no—
726C2×#41—42no—
727C2×#41—44no—
728C2×#41—44no—
729C22×Q8—28no—
730C22×Q8—44no—
731C22×Q8—42no—
732C22×Q8—44no—
733C22×Q8—44no—
734C22×Q8—44no—
735C22×Q8—44no—
736C22×Q8—44no—
737C22×Q8C2412yes—
738C22×Q8C2412yes—
739C22×Q8C2411yescharacteristic
740C22×Q8C2414yes—
741C22×Q8C2414yes—
742C22×Q8C2412yes—
743C22×Q8C2414yes—
744C22×Q8C2411yescharacteristic
745C22×D4C2411yescharacteristic
746C22×D4C2411yescharacteristic
747C22×D4C2411yescharacteristic
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2414yes—
760C22×D4C2414yes—
761C22×D4C2411yescharacteristic
762C22×D4C2412yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2412yes—
766C23×C4C2411yescharacteristic
767C23×C4C2412yes—
768C23×C4C2411yescharacteristic
769C23×C4C2412yes—
770C23×C4C2414yes—
771C23×C4C2412yes—
772C23×C4C2412yes—
773C23×C4C2412yes—
774C23×C4C2414yes—
775C23×C4C2414yes—
776C23×C4C2412yes—
777C23×C4C2414yes—
778C4⋊Q8—28no—
779C4⋊Q8—28no—
780C4⋊Q8—48no—
781C4⋊Q8—48no—
782C4⋊Q8—44no—
783C4⋊Q8—42no—
784C4⋊Q8—44no—
785C4⋊Q8—48no—
786#127—44no—
787#127—42no—
788#127—42no—
789#127—44no—
790#126—44no—
791#126—48no—
792#124—48no—
793#124—48no—
794#124—48no—
795#124—44no—
796#124—44no—
797#124—48no—
798#124—44no—
799#124—44no—
800#124—48no—
801#124—48no—
802#123—48no—
803#123—48no—
804#123—44no—
805#123—48no—
806#123—48no—
807C22⋊Q8—28no—
808C22⋊Q8—28no—
809C22⋊Q8—28no—
810C22⋊Q8—28no—
811C22⋊Q8—48no—
812C22⋊Q8—48no—
813C22⋊Q8—48no—
814C22⋊Q8—48no—
815C22⋊Q8—48no—
816C22⋊Q8—48no—
817C22⋊Q8—44no—
818C22⋊Q8—44no—
819C22⋊Q8—44no—
820C22⋊Q8—48no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823C22⋊Q8—44no—
824C22⋊Q8—44no—
825C22⋊Q8—44no—
826C22⋊Q8—48no—
827#121—28no—
828#121—28no—
829#121—44no—
830#121—48no—
831#121—48no—
832#121—48no—
833#121—48no—
834#121—48no—
835#121—44no—
836#121—42no—
837#121—42no—
838#121—44no—
839#121—44no—
840#121—44no—
841C4×Q8—24no—
842C4×Q8—28no—
843C4×Q8—28no—
844C4×Q8—48no—
845C4×Q8—44no—
846C4×D4—48no—
847C4×D4—44no—
848C4×D4—48no—
849C4×D4—48no—
850C4×D4—44no—
851C4×D4—44no—
852C4×D4—44no—
853C4×D4—44no—
854C4×D4—44no—
855C4×D4—42no—
856C4×D4—44no—
857C4×D4—42no—
858C4×D4—44no—
859C4×D4—44no—
860C4×D4—48no—
861#117—28no—
862#117—42no—
863#117—44no—
864#117—48no—
865#117—44no—
866C2×C4⋊C4—42no—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2411yescharacteristic
933C2×C22⋊C4C2411yescharacteristic
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C42C2414yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2414yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2414yes—
995C2×C42C2411yescharacteristic
996C2×C42C2414yes—
997C2×C42C2412yes—
998#95C2411yescharacteristic
999#95C2411yescharacteristic
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2411yescharacteristic
1018#95C2411yescharacteristic
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
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#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055C24C2512yes—
1056C24C2511yescharacteristic
1057C24C2511yescharacteristic
1058C24C2512yes—
1059C24C2512yes—
1060C24C2512yes—
1061#41—88no—
1062#41—88no—
1063#41—88no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—24no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—28no—
1072C2×Q8—28no—
1073C2×Q8—44no—
1074C2×Q8—42no—
1075C2×Q8—41no—
1076C2×Q8—44no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—44no—
1080C2×Q8—44no—
1081C2×Q8—44no—
1082C2×Q8—42no—
1083C2×Q8—44no—
1084C2×Q8—816no—
1085C2×Q8—88no—
1086C2×Q8—816no—
1087C2×Q8H(5,𝔽2)14yes—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—22no—
1091C2×D4—22no—
1092C2×D4—28no—
1093C2×D4—28no—
1094C2×D4—24no—
1095C2×D4—24no—
1096C2×D4—22no—
1097C2×D4—24no—
1098C2×D4—22no—
1099C2×D4—41no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—41no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—41no—
1112C2×D4—42no—
1113C2×D4—41no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—42no—
1117C2×D4—42no—
1118C2×D4—42no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—42no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—42no—
1126C2×D4—41no—
1127C2×D4—42no—
1128C2×D4—42no—
1129C2×D4—42no—
1130C2×D4—42no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—42no—
1134C2×D4—42no—
1135C2×D4—42no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C22×C4—22no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—22no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—28no—
1154C22×C4—24no—
1155C22×C4—24no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—42no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—42no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—42no—
1172C22×C4—44no—
1173C22×C4—42no—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2514yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2514yes—
1189C22×C4C2514yes—
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2514yes—
1195C22×C4C2511yescharacteristic
1196C22×C4C2511yescharacteristic
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—28no—
1203C4⋊C4—28no—
1204C4⋊C4—28no—
1205C4⋊C4—24no—
1206C4⋊C4—22no—
1207C4⋊C4—28no—
1208C4⋊C4—28no—
1209C4⋊C4—28no—
1210C4⋊C4—28no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—42no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—41no—
1223C4⋊C4—42no—
1224C4⋊C4—41no—
1225C4⋊C4—42no—
1226C4⋊C4—41no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—41no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4H(5,𝔽2)18yes—
1246C22⋊C4—28no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—24no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—42no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—41no—
1278C22⋊C4—42no—
1279C22⋊C4—41no—
1280C22⋊C4—42no—
1281C22⋊C4—42no—
1282C22⋊C4—44no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
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—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—42no—
1307C22⋊C4—44no—
1308C22⋊C4—42no—
1309C22⋊C4—42no—
1310C42—28no—
1311C42—24no—
1312C42—24no—
1313C42—24no—
1314C42—28no—
1315C42—24no—
1316C42—24no—
1317C42—22no—
1318C42—28no—
1319C42—24no—
1320C42—22no—
1321C42—44no—
1322C42—41no—
1323C42—42no—
1324C42—44no—
1325C42—44no—
1326C42—44no—
1327C42—44no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—24no—
1334C23—24no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—22no—
1339C23—21no—
1340C23—22no—
1341C23—21no—
1342C23—22no—
1343C23—21no—
1344C23—21no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—21no—
1352C23—21no—
1353C23—22no—
1354C23—22no—
1355C23—24no—
1356C23—22no—
1357C23—22no—
1358C23—22no—
1359C23—22no—
1360C23—24no—
1361C23—22no—
1362C23C2611yescharacteristic
1363Q8—28no—
1364Q8—48no—
1365Q8—48no—
1366Q8—88no—
1367Q8—88no—
1368Q8—84no—
1369Q8—88no—
1370Q8—82no—
1371D4—44no—
1372D4—48no—
1373D4—48no—
1374D4—44no—
1375D4—44no—
1376D4—82no—
1377D4—84no—
1378D4—88no—
1379D4—88no—
1380D4—84no—
1381D4—84no—
1382D4—84no—
1383D4—84no—
1384D4—84no—
1385D4—82no—
1386D4—84no—
1387D4—162no—
1388D4—162no—
1389D4—162no—
1390D4—164no—
1391D4—164no—
1392C2×C4—21no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—24no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—48no—
1451C2×C4—44no—
1452C2×C4—48no—
1453C2×C4—44no—
1454C2×C4—88no—
1455C2×C4—84no—
1456C2×C4—84no—
1457C2×C4—88no—
1458C2×C4—84no—
1459C2×C4—88no—
1460C2×C4—162no—
1461C2×C4—164no—
1462C2×C4C2×H(5,𝔽2)18yes—
1463C2×C4C2×H(5,𝔽2)14yes—
1464C2×C4C2×H(5,𝔽2)12yes—
1465C2×C4C2×H(5,𝔽2)14yes—
1466C2×C4#58512yes—
1467C22—41no—
1468C22—42no—
1469C22—42no—
1470C22—41no—
1471C22—42no—
1472C22—42no—
1473C22—44no—
1474C22—42no—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—44no—
1480C22—42no—
1481C22—42no—
1482C22—42no—
1483C22—42no—
1484C22—41no—
1485C22—42no—
1486C22—41no—
1487C22—41no—
1488C22—42no—
1489C22—42no—
1490C22—42no—
1491C22—41no—
1492C22—42no—
1493C22—44no—
1494C22—42no—
1495C22—42no—
1496C22—44no—
1497C22—42no—
1498C22—42no—
1499C22—42no—
1500C22—42no—
1501C22C22×H(5,𝔽2)12yes—
1502C22C22×H(5,𝔽2)11yescharacteristic
1503C22C2×#58511yescharacteristic
1504C222−1+611yescharacteristic
1505C222−1+612yes—
1506C4—24no—
1507C4—22no—
1508C4—28no—
1509C4—41no—
1510C4—41no—
1511C4—42no—
1512C4—42no—
1513C4—44no—
1514C4—44no—
1515C4—42no—
1516C4—44no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—42no—
1521C4—41no—
1522C4—42no—
1523C4—44no—
1524C4—42no—
1525C4—44no—
1526C4—42no—
1527C4—42no—
1528C4#354314yes—
1529C2—81no—
1530C2—82no—
1531C2—82no—
1532C2—81no—
1533C2—82no—
1534C2—82no—
1535C2C2×#354311yescharacteristic
1536C2#6291911yescharacteristic
1537C2#6292112yes—
1538C2#6304412yes—
1539C2#6304811yescharacteristic
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. #57248C2semidirect
2. #55353C2semidirect
3. #55084C2semidirect
4. #54854C2semidirect
5. #54115C2semidirect
6. #53492C2semidirect
7. #53452C2semidirect
8. #46342C2semidirect
9. #46264C2semidirect
10. #46048C2semidirect
11. #45826C2semidirect
12. #45385C2semidirect
13. #45345C2semidirect
14. #45321C2semidirect
15. #45248C2semidirect
16. #45245C2semidirect
17. #45095C2semidirect
18. #44897C2semidirect
19. #42995C2semidirect
20. #42985C2semidirect
21. #42913C2semidirect
22. #42807C2semidirect
23. #42788C2semidirect
24. #42778C2semidirect
25. #42741C2semidirect
26. #37629C2semidirect
27. #36696C2semidirect
28. #36465C2semidirect
29. #36311C2semidirect

Maximal subgroups

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

subgroupindex
#572482
#553532
#550842
#548542
#541152
#534922
#534522
#463422
#462642
#460482
#458262
#453852
#453452
#453212
#452482
#452452
#450952
#448972
#429952
#429852
#429132
#428072
#427882
#427782
#427412
#376292
#366962
#364652
#363112