Finite Group Databasebeta

← #8726244

Subgroups — #8726244

Order 512.

5422 conjugacy classes of subgroups.

The subgroup lattice has 1540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59809C212yesmaximal, complemented
2#59379C211yesmaximal, characteristic, complemented
3#59127C212yesmaximal, complemented
4#59096C212yesmaximal, complemented
5#59042C212yesmaximal, complemented
6#58956C212yesmaximal, complemented
7#58007C214yesmaximal, complemented
8#56675C214yesmaximal, complemented
9#55134C214yesmaximal, complemented
10#53006C212yesmaximal, complemented
11#52958C211yesmaximal, characteristic, complemented
12#52299C211yesmaximal, characteristic, complemented
13#47725C214yesmaximal, complemented
14#47122C212yesmaximal, complemented
15#45418C211yesmaximal, characteristic, complemented
16#45305C212yesmaximal, complemented
17#44325C212yesmaximal, complemented
18#44281C214yesmaximal, complemented
19#42857C212yesmaximal, complemented
20#42810C211yesmaximal, characteristic, complemented
21#41180C214yesmaximal, complemented
22#41174C212yesmaximal, complemented
23#40218C212yesmaximal, complemented
24#39854C212yesmaximal, complemented
25#39721C211yesmaximal, characteristic, complemented
26#39222C212yesmaximal, complemented
27#39166C212yesmaximal, complemented
28#35687C211yesmaximal, characteristic, complemented
29#35687C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×#548C2211yescharacteristic
37C2×#548C2212yes—
38C2×#533C2212yes—
39C22×C4⋊Q8C2211yescharacteristic
40#2854C2211yescharacteristic
41#2850C2212yes—
42#2843C2214yes—
43#2837C2214yes—
44#2837C2214yes—
45#2835C2212yes—
46#2832C2214yes—
47#2832C2212yes—
48#2830C2214yes—
49#2826C2214yes—
50#2820C2212yes—
51#2811C2212yes—
52#2808C2214yes—
53#2808C2214yes—
54#2801C2212yes—
55#2800C2214yes—
56#2799C2214yes—
57#2797C2214yes—
58#2795C2214yes—
59#2788C2214yes—
60#2788C2214yes—
61#2787C2214yes—
62#2770C2214yes—
63#2764C2212yes—
64#2762C2214yes—
65#2760C2211yescharacteristic
66#2758C2214yes—
67#2756C2214yes—
68#2756C2214yes—
69#2752C2212yes—
70#2752C2211yescharacteristic
71#2750C2214yes—
72#2747C2214yes—
73#2742C2214yes—
74#2742C2211yescharacteristic
75#2742C2212yes—
76#2731C2214yes—
77#2731C2214yes—
78#2730C2214yes—
79#2729C2214yes—
80#2729C2214yes—
81#2728C2214yes—
82#2720C2214yes—
83#2717C2212yes—
84#2713C2214yes—
85#2713C2214yes—
86#2712C2212yes—
87#2712C2214yes—
88#2711C2214yes—
89#2710C2214yes—
90#2710C2214yes—
91#2708C2214yes—
92#2704C2214yes—
93#2703C2212yes—
94#2703C2212yes—
95#2703C2212yes—
96#2692C2214yes—
97#2692C2214yes—
98#2692C2214yes—
99#2690C2214yes—
100#2690C2214yes—
101#2677C2212yes—
102#2677C2212yes—
103#2677C2214yes—
104#2677C2214yes—
105#2677C2214yes—
106#2676C2214yes—
107#2676C2214yes—
108#2675C2211yescharacteristic
109#2652C2214yes—
110#2651C2214yes—
111#2651C2214yes—
112#2648C2214yes—
113#2640C2211yescharacteristic
114#2639C2214yes—
115#2633C2212yes—
116#2632C2214yes—
117#2631C2212yes—
118#2618C2212yes—
119#2616C2211yescharacteristic
120#2616C2212yes—
121#2616C2214yes—
122#2616C2212yes—
123#2610C2214yes—
124#2605C2214yes—
125#2605C2214yes—
126#2598C2214yes—
127#2593C2214yes—
128#2591C2212yes—
129#2589C2214yes—
130#2589C2214yes—
131#2579C2212yes—
132#2578C2214yes—
133#2577C2214yes—
134#2574C2214yes—
135#2568C2212yes—
136#2564C2214yes—
137#2556C2214yes—
138#2555C2214yes—
139#2551C2214yes—
140#2549C2214yes—
141#2549C2214yes—
142#2547C2212yes—
143#2547C2211yescharacteristic
144#2546C2212yes—
145#2545C2212yes—
146#2543C2214yes—
147#2542C2212yes—
148#2540C2211yescharacteristic
149#2536C2212yes—
150#2536C2212yes—
151#2536C2212yes—
152#2535C2212yes—
153#2530C2214yes—
154#2523C2212yes—
155#2523C2214yes—
156#2513C2212yes—
157#2495C2212yes—
158#2495C2212yes—
159#2492C2212yes—
160#2492C2212yes—
161#2492C2214yes—
162#2492C2214yes—
163#2492C2212yes—
164#2491C2212yes—
165#2487C2212yes—
166#2477C2214yes—
167#2477C2214yes—
168#2465C2214yes—
169#2463C2212yes—
170#2463C2214yes—
171#2463C2212yes—
172#2452C2214yes—
173#2451C2212yes—
174#2451C2214yes—
175#2451C2212yes—
176#2451C2214yes—
177#2450C2214yes—
178#2450C2214yes—
179#2450C2214yes—
180#2449C2214yes—
181#2449C2214yes—
182#2448C2212yes—
183#2446C2212yes—
184#2446C2212yes—
185#2440C2214yes—
186#2438C2214yes—
187#2436C2211yescharacteristic
188#2434C2214yes—
189#2434C2212yes—
190#2434C2211yescharacteristic
191#2434C2212yes—
192#2434C2212yes—
193#2432C2212yes—
194#2432C2214yes—
195#2432C2214yes—
196#2432C2214yes—
197#2432C2212yes—
198#2432C2212yes—
199#2429C2212yes—
200#2429C2212yes—
201#2429C2212yes—
202#2427C2214yes—
203#2421C2212yes—
204#2421C2212yes—
205#2421C2212yes—
206#2417C2212yes—
207#2417C2212yes—
208#2416C2212yes—
209#2409C2212yes—
210#2409C2214yes—
211#2409C2211yescharacteristic
212#2409C2212yes—
213#2409C2211yescharacteristic
214#2409C2212yes—
215#2409C2212yes—
216#2409C2212yes—
217#2407C2212yes—
218#2407C2214yes—
219#2407C2212yes—
220#2407C2212yes—
221#2407C2214yes—
222#2407C2214yes—
223#2401C2212yes—
224#2397C2211yescharacteristic
225#2388C2212yes—
226#2388C2212yes—
227#2388C2211yescharacteristic
228#2388C2214yes—
229#2372C2212yes—
230#2367C2214yes—
231#2365C2212yes—
232#2365C2212yes—
233#2364C2214yes—
234#2361C2214yes—
235#2360C2212yes—
236#2359C2214yes—
237#2356C2212yes—
238#2341C2211yescharacteristic
239#2341C2212yes—
240Q8×C22⋊C4C2211yescharacteristic
241Q8×C22⋊C4C2212yes—
242Q8×C22⋊C4C2212yes—
243Q8×C22⋊C4C2212yes—
244#2337C2214yes—
245#2337C2214yes—
246#2327C2212yes—
247#2326C2214yes—
248#2325C2214yes—
249#2322C2212yes—
250#2320C2211yescharacteristic
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#123C2212yes—
254C4×#123C2211yescharacteristic
255C4×#121C2212yes—
256C4×#121C2212yes—
257C4×#121C2212yes—
258C2×#391C2212yes—
259C2×2−1+4—48no—
260C2×2−1+4—44no—
261C22×#41C2311yescharacteristic
262C22×#41C2312yes—
263C22×#41C2311yescharacteristic
264C22×#41C2314yes—
265C22×#41C2312yes—
266C23×Q8C2312yes—
267C23×Q8C2311yescharacteristic
268C23×Q8C2311yescharacteristic
269C23×Q8C2312yes—
270C23×Q8C2312yes—
271C23×Q8C2311yescharacteristic
272#554—44no—
273D4×Q8—48no—
274D4×Q8—48no—
275D4×Q8—48no—
276D4×Q8—48no—
277#548—48no—
278#548—44no—
279#533—48no—
280C2×C4⋊Q8—44no—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2312yes—
285C2×C4⋊Q8C2311yescharacteristic
286C2×C4⋊Q8C2314yes—
287C2×C4⋊Q8C2312yes—
288C2×C4⋊Q8C2314yes—
289C2×C4⋊Q8C2314yes—
290C2×C4⋊Q8C2314yes—
291C2×C4⋊Q8C2314yes—
292C2×#125C2312yes—
293C2×#125C2314yes—
294C2×#124C2314yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#124C2312yes—
300C2×#124C2311yescharacteristic
301C2×#123C2312yes—
302C2×#123C2312yes—
303C2×#123C2311yescharacteristic
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2312yes—
330C2×#121C2312yes—
331C2×#121C2311yescharacteristic
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2314yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2311yescharacteristic
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×#117C2314yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C42C2312yes—
361C22×C42C2311yescharacteristic
362#401C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2312yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2312yes—
379#399C2314yes—
380#399C2311yescharacteristic
381#399C2312yes—
382#399C2314yes—
383#399C2314yes—
384#399C2314yes—
385#399C2311yescharacteristic
386#399C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2314yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2312yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2312yes—
432#395C2314yes—
433#395C2312yes—
434#395C2312yes—
435#395C2312yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2312yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2312yes—
444#395C2311yescharacteristic
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2311yescharacteristic
453#394C2312yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2312yes—
468#394C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2312yes—
475#393C2314yes—
476#393C2311yescharacteristic
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2312yes—
481#393C2314yes—
482#393C2312yes—
483#392C2312yes—
484#392C2312yes—
485#392C2314yes—
486#392C2311yescharacteristic
487#392C2314yes—
488#392C2311yescharacteristic
489#392C2312yes—
490#392C2312yes—
491#392C2312yes—
492#392C2314yes—
493#392C2311yescharacteristic
494#392C2312yes—
495#391C2314yes—
496#391C2312yes—
497#391C2314yes—
498#391C2312yes—
499#391C2314yes—
500#391C2312yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2312yes—
520#391C2312yes—
521#391C2312yes—
522#391C2314yes—
523#391C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2314yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2314yes—
531#390C2314yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2312yes—
582#388C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
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#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2312yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2312yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2314yes—
622#386C2311yescharacteristic
623#386C2312yes—
624#386C2314yes—
625#386C2314yes—
626#386C2312yes—
627#386C2314yes—
628#386C2312yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2312yes—
634#386C2312yes—
635#386C2312yes—
636#386C2312yes—
637#386C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2312yes—
643#385C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2311yescharacteristic
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2312yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#384C2314yes—
665#383C2312yes—
666#383C2314yes—
667#383C2314yes—
668#383C2314yes—
669#382C2312yes—
670#382C2312yes—
671#382C2312yes—
672#381C2311yescharacteristic
673#381C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679#380C2312yes—
680#380C2311yescharacteristic
681#380C2312yes—
682#380C2312yes—
683#380C2314yes—
684#380C2312yes—
685#380C2312yes—
686#380C2314yes—
687#380C2312yes—
688#380C2311yescharacteristic
689#380C2312yes—
690#380C2312yes—
691#380C2314yes—
692#380C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2311yescharacteristic
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2311yescharacteristic
718C4×C22⋊C4C2312yes—
719#376C2311yescharacteristic
720#376C2314yes—
721C2×#95C2314yes—
722C2×#95C2314yes—
7232−1+4—464no—
724C2×#41—28no—
725C2×#41—24no—
726C2×#41—44no—
727C2×#41—42no—
728C2×#41—48no—
729C2×#41—44no—
730C2×#41—44no—
731C2×#41—44no—
732C2×#41—44no—
733C2×#41—48no—
734C2×#41—48no—
735C2×#41—48no—
736C22×Q8—28no—
737C22×Q8—28no—
738C22×Q8—28no—
739C22×Q8—24no—
740C22×Q8—28no—
741C22×Q8—44no—
742C22×Q8—42no—
743C22×Q8—48no—
744C22×Q8—44no—
745C22×Q8—42no—
746C22×Q8—44no—
747C22×Q8—44no—
748C22×Q8—44no—
749C22×Q8—44no—
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2412yes—
753C22×Q8C2414yes—
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2414yes—
757C22×Q8C2414yes—
758C22×Q8C2412yes—
759C22×Q8C2412yes—
760C22×Q8C2412yes—
761C22×Q8C2411yescharacteristic
762C22×D4C2411yescharacteristic
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2411yescharacteristic
766C22×D4C2412yes—
767C22×D4C2412yes—
768C22×D4C2412yes—
769C22×D4C2412yes—
770C22×D4C2414yes—
771C22×D4C2411yescharacteristic
772C22×D4C2412yes—
773C22×D4C2414yes—
774C22×D4C2412yes—
775C22×D4C2411yescharacteristic
776C23×C4C2412yes—
777C23×C4C2411yescharacteristic
778C23×C4C2411yescharacteristic
779C23×C4C2412yes—
780C23×C4C2411yescharacteristic
781C23×C4C2412yes—
782C23×C4C2414yes—
783C23×C4C2412yes—
784C23×C4C2411yescharacteristic
785C23×C4C2412yes—
786C23×C4C2414yes—
787C23×C4C2414yes—
788C23×C4C2412yes—
789C23×C4C2412yes—
790C23×C4C2412yes—
791C23×C4C2414yes—
792C4⋊Q8—28no—
793C4⋊Q8—28no—
794C4⋊Q8—28no—
795C4⋊Q8—44no—
796C4⋊Q8—42no—
797C4⋊Q8—44no—
798C4⋊Q8—48no—
799C4⋊Q8—48no—
800C4⋊Q8—48no—
801C4⋊Q8—48no—
802C4⋊Q8—48no—
803#125—44no—
804#125—48no—
805#124—216no—
806#124—44no—
807#124—48no—
808#124—44no—
809#124—42no—
810#124—44no—
811#124—48no—
812#123—28no—
813#123—42no—
814#123—44no—
815C22⋊Q8—28no—
816C22⋊Q8—28no—
817C22⋊Q8—28no—
818C22⋊Q8—48no—
819C22⋊Q8—48no—
820C22⋊Q8—48no—
821C22⋊Q8—48no—
822C22⋊Q8—48no—
823C22⋊Q8—48no—
824C22⋊Q8—48no—
825C22⋊Q8—48no—
826C22⋊Q8—48no—
827C22⋊Q8—48no—
828C22⋊Q8—44no—
829C22⋊Q8—42no—
830C22⋊Q8—44no—
831C22⋊Q8—48no—
832C22⋊Q8—44no—
833C22⋊Q8—44no—
834C22⋊Q8—44no—
835C22⋊Q8—44no—
836C22⋊Q8—44no—
837#121—28no—
838#121—28no—
839#121—44no—
840#121—48no—
841#121—42no—
842#121—44no—
843#121—48no—
844#121—44no—
845C4×Q8—28no—
846C4×Q8—24no—
847C4×Q8—48no—
848C4×Q8—44no—
849C4×Q8—44no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×Q8—44no—
853C4×D4—44no—
854C4×D4—44no—
855C4×D4—48no—
856C4×D4—44no—
857C4×D4—42no—
858C4×D4—44no—
859C4×D4—44no—
860C4×D4—44no—
861C4×D4—44no—
862C4×D4—42no—
863C4×D4—48no—
864C4×D4—48no—
865C4×D4—48no—
866C4×D4—48no—
867#117—48no—
868C2×C4⋊C4—44no—
869C2×C4⋊C4—44no—
870C2×C4⋊C4—44no—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2411yescharacteristic
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2411yescharacteristic
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2411yescharacteristic
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2411yescharacteristic
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C42—42no—
978C2×C42—44no—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2411yescharacteristic
1009#95C2414yes—
1010#95C2411yescharacteristic
1011#95C2412yes—
1012#95C2412yes—
1013#95C2411yescharacteristic
1014#95C2414yes—
1015#95C2411yescharacteristic
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060C24C2511yescharacteristic
1061C24C2512yes—
1062C24C2512yes—
1063C24C2512yes—
1064C24C2511yescharacteristic
1065#41—432no—
1066#41—416no—
1067#41—464no—
1068#41—432no—
1069#41—416no—
1070C2×Q8—24no—
1071C2×Q8—24no—
1072C2×Q8—24no—
1073C2×Q8—24no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—22no—
1077C2×Q8—24no—
1078C2×Q8—28no—
1079C2×Q8—28no—
1080C2×Q8—28no—
1081C2×Q8—28no—
1082C2×Q8—24no—
1083C2×Q8—28no—
1084C2×Q8—44no—
1085C2×Q8—42no—
1086C2×Q8—42no—
1087C2×Q8—41no—
1088C2×Q8—44no—
1089C2×Q8—44no—
1090C2×Q8—44no—
1091C2×Q8—44no—
1092C2×Q8—44no—
1093C2×Q8—44no—
1094C2×Q8—42no—
1095C2×Q8—42no—
1096C2×Q8—42no—
1097C2×Q8—42no—
1098C2×Q8—416no—
1099C2×Q8—432no—
1100C2×Q8—432no—
1101C2×Q8—816no—
1102C2×Q8—88no—
1103C2×Q8—88no—
1104C2×Q8H(5,𝔽2)18yes—
1105C2×Q8H(5,𝔽2)14yes—
1106C2×D4—24no—
1107C2×D4—24no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4—24no—
1111C2×D4—24no—
1112C2×D4—24no—
1113C2×D4—28no—
1114C2×D4—24no—
1115C2×D4—22no—
1116C2×D4—28no—
1117C2×D4—24no—
1118C2×D4—24no—
1119C2×D4—22no—
1120C2×D4—24no—
1121C2×D4—24no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—41no—
1125C2×D4—42no—
1126C2×D4—42no—
1127C2×D4—42no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—42no—
1132C2×D4—41no—
1133C2×D4—42no—
1134C2×D4—42no—
1135C2×D4—42no—
1136C2×D4—42no—
1137C2×D4—41no—
1138C2×D4—44no—
1139C2×D4—42no—
1140C2×D4—44no—
1141C2×D4—42no—
1142C2×D4—42no—
1143C2×D4—41no—
1144C22×C4—24no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—24no—
1151C22×C4—28no—
1152C22×C4—28no—
1153C22×C4—28no—
1154C22×C4—24no—
1155C22×C4—24no—
1156C22×C4—24no—
1157C22×C4—28no—
1158C22×C4—24no—
1159C22×C4—24no—
1160C22×C4—22no—
1161C22×C4—24no—
1162C22×C4—24no—
1163C22×C4—28no—
1164C22×C4—24no—
1165C22×C4—41no—
1166C22×C4—41no—
1167C22×C4—42no—
1168C22×C4—42no—
1169C22×C4—41no—
1170C22×C4—44no—
1171C22×C4—42no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—42no—
1176C22×C4—42no—
1177C22×C4—44no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—42no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4C2511yescharacteristic
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2514yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2512yes—
1191C22×C4C2512yes—
1192C22×C4C2512yes—
1193C22×C4C2514yes—
1194C22×C4C2514yes—
1195C22×C4C2512yes—
1196C22×C4C2514yes—
1197C22×C4C2512yes—
1198C22×C4C2511yescharacteristic
1199C22×C4C2512yes—
1200C22×C4C2511yescharacteristic
1201C22×C4C2514yes—
1202C22×C4C2512yes—
1203C22×C4C2512yes—
1204C22×C4C2514yes—
1205C22×C4C2512yes—
1206C22×C4C2512yes—
1207C22×C4C2512yes—
1208C22×C4C2511yescharacteristic
1209C4⋊C4—22no—
1210C4⋊C4—28no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—28no—
1215C4⋊C4—28no—
1216C4⋊C4—28no—
1217C4⋊C4—24no—
1218C4⋊C4—28no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—28no—
1223C4⋊C4—28no—
1224C4⋊C4—28no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—24no—
1228C4⋊C4—24no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—42no—
1236C4⋊C4—41no—
1237C4⋊C4—44no—
1238C4⋊C4—42no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C22⋊C4—28no—
1260C22⋊C4—22no—
1261C22⋊C4—28no—
1262C22⋊C4—24no—
1263C22⋊C4—28no—
1264C22⋊C4—28no—
1265C22⋊C4—28no—
1266C22⋊C4—24no—
1267C22⋊C4—24no—
1268C22⋊C4—24no—
1269C22⋊C4—24no—
1270C22⋊C4—28no—
1271C22⋊C4—28no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—44no—
1278C22⋊C4—42no—
1279C22⋊C4—44no—
1280C22⋊C4—41no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—41no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—42no—
1299C22⋊C4—41no—
1300C22⋊C4—42no—
1301C22⋊C4—44no—
1302C22⋊C4—42no—
1303C22⋊C4—44no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C22⋊C4—44no—
1310C22⋊C4—42no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C42−1+418yescomplemented
1315C42—24no—
1316C42—24no—
1317C42—24no—
1318C42—28no—
1319C42—24no—
1320C42—22no—
1321C42—24no—
1322C42—28no—
1323C42—42no—
1324C42—42no—
1325C42—42no—
1326C42—44no—
1327C42—44no—
1328C42—44no—
1329C42—44no—
1330C42—44no—
1331C42—44no—
1332C42—42no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—21no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—21no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—22no—
1348C23—21no—
1349C23—22no—
1350C23—24no—
1351C23—22no—
1352C23—22no—
1353C23—22no—
1354C23—21no—
1355C23—22no—
1356C23—22no—
1357C23—22no—
1358C23—22no—
1359C23—21no—
1360C23C2×2−1+414yes—
1361C23#58512yes—
1362C23C2611yescharacteristic
1363Q8—216no—
1364Q8—28no—
1365Q8—416no—
1366Q8—48no—
1367Q8—44no—
1368Q8—44no—
1369Q8—48no—
1370Q8—88no—
1371Q8—88no—
1372Q8—84no—
1373Q8—84no—
1374Q8—162no—
1375D4—48no—
1376D4—48no—
1377D4—48no—
1378D4—416no—
1379D4—48no—
1380D4—44no—
1381D4—48no—
1382D4—48no—
1383D4—44no—
1384D4—44no—
1385D4—84no—
1386D4—88no—
1387D4—84no—
1388D4—82no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—21no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—21no—
1434C2×C4—24no—
1435C2×C4—24no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—21no—
1448C2×C4—24no—
1449C2×C4—44no—
1450C2×C4—416no—
1451C2×C4—48no—
1452C2×C4—48no—
1453C2×C4—416no—
1454C2×C4—48no—
1455C2×C4—44no—
1456C2×C4—48no—
1457C2×C4—44no—
1458C2×C4—48no—
1459C2×C4—44no—
1460C2×C4—84no—
1461C2×C4—88no—
1462C2×C4—84no—
1463C2×C4—84no—
1464C2×C4—164no—
1465C2×C4C2×H(5,𝔽2)18yes—
1466C2×C4C2×H(5,𝔽2)14yes—
1467C2×C4C2×H(5,𝔽2)14yes—
1468C2×C4C2×H(5,𝔽2)12yes—
1469C2×C4C2×2−1+414yes—
1470C2×C4C2×2−1+414yes—
1471C22—24no—
1472C22—24no—
1473C22—24no—
1474C22—24no—
1475C22—22no—
1476C22—42no—
1477C22—41no—
1478C22—42no—
1479C22—42no—
1480C22—42no—
1481C22—41no—
1482C22—42no—
1483C22—42no—
1484C22—44no—
1485C22—42no—
1486C22—42no—
1487C22—42no—
1488C22—42no—
1489C22—41no—
1490C22—42no—
1491C22—42no—
1492C22—44no—
1493C22—42no—
1494C22—41no—
1495C22—42no—
1496C22—42no—
1497C22—42no—
1498C22—41no—
1499C22—42no—
1500C22C22×H(5,𝔽2)12yes—
1501C22C22×H(5,𝔽2)11yescharacteristic
1502C22C22×2−1+412yes—
1503C22C2×#58511yescharacteristic
1504C222−1+611yescharacteristic
1505C4—24no—
1506C4—24no—
1507C4—24no—
1508C4—28no—
1509C4—42no—
1510C4—42no—
1511C4—44no—
1512C4—44no—
1513C4—41no—
1514C4—44no—
1515C4—42no—
1516C4—42no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—44no—
1521C4—41no—
1522C4—42no—
1523C4—41no—
1524C4—42no—
1525C4—41no—
1526C4—44no—
1527C4—42no—
1528C4#353214yes—
1529C2—42no—
1530C2—44no—
1531C2—82no—
1532C2—82no—
1533C2—81no—
1534C2C2×#353211yescharacteristic
1535C2#6291312yes—
1536C2#6291911yescharacteristic
1537C2#6301512yes—
1538C2#6301611yescharacteristic
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. #59809C2semidirect
2. #59379C2semidirect
3. #59127C2semidirect
4. #59096C2semidirect
5. #59042C2semidirect
6. #58956C2semidirect
7. #58007C2semidirect
8. #56675C2semidirect
9. #55134C2semidirect
10. #53006C2semidirect
11. #52958C2semidirect
12. #52299C2semidirect
13. #47725C2semidirect
14. #47122C2semidirect
15. #45418C2semidirect
16. #45305C2semidirect
17. #44325C2semidirect
18. #44281C2semidirect
19. #42857C2semidirect
20. #42810C2semidirect
21. #41180C2semidirect
22. #41174C2semidirect
23. #40218C2semidirect
24. #39854C2semidirect
25. #39721C2semidirect
26. #39222C2semidirect
27. #39166C2semidirect
28. #35687C2semidirect
29. #35687C2semidirect
1314. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#598092
#593792
#591272
#590962
#590422
#589562
#580072
#566752
#551342
#530062
#529582
#522992
#477252
#471222
#454182
#453052
#443252
#442812
#428572
#428102
#411802
#411742
#402182
#398542
#397212
#392222
#391662
#356872