Finite Group Databasebeta

← #8751619

Subgroups — #8751619

Order 512.

5393 conjugacy classes of subgroups.

The subgroup lattice has 1559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59477C212yesmaximal, complemented
3#58944C212yesmaximal, complemented
4#58898C214yesmaximal, complemented
5#58021C214yesmaximal, complemented
6#55580C214yesmaximal, complemented
7#55126C214yesmaximal, complemented
8#53044C212yesmaximal, complemented
9#52958C211yesmaximal, characteristic, complemented
10#52421C212yesmaximal, complemented
11#52334C214yesmaximal, complemented
12#47725C212yesmaximal, complemented
13#45351C211yesmaximal, characteristic, complemented
14#45303C212yesmaximal, complemented
15#45291C212yesmaximal, complemented
16#45289C212yesmaximal, complemented
17#45248C212yesmaximal, complemented
18#42913C211yesmaximal, characteristic, complemented
19#42894C212yesmaximal, complemented
20#42835C212yesmaximal, complemented
21#42806C212yesmaximal, complemented
22#42805C212yesmaximal, complemented
23#42043C212yesmaximal, complemented
24#41009C214yesmaximal, complemented
25#39790C212yesmaximal, complemented
26#39747C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#35757C211yesmaximal, characteristic, complemented
29#35687C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#550C2211yescharacteristic
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×#548C2212yes—
37C2×#548C2212yes—
38C2×#542C2212yes—
39C2×#536C2211yescharacteristic
40#2858C2211yescharacteristic
41#2843C2211yescharacteristic
42#2835C2212yes—
43#2832C2212yes—
44#2832C2214yes—
45#2830C2212yes—
46#2830C2214yes—
47#2830C2211yescharacteristic
48#2830C2214yes—
49#2829C2214yes—
50#2829C2212yes—
51#2829C2212yes—
52#2829C2212yes—
53#2829C2214yes—
54#2828C2212yes—
55#2828C2214yes—
56#2828C2211yescharacteristic
57#2823C2211yescharacteristic
58#2819C2214yes—
59#2818C2212yes—
60#2816C2214yes—
61#2816C2212yes—
62#2813C2214yes—
63#2811C2212yes—
64#2803C2214yes—
65#2803C2214yes—
66#2803C2214yes—
67#2800C2214yes—
68#2799C2212yes—
69#2788C2214yes—
70#2786C2214yes—
71#2780C2214yes—
72#2755C2214yes—
73#2754C2214yes—
74#2742C2214yes—
75#2742C2214yes—
76#2733C2214yes—
77#2732C2214yes—
78#2731C2214yes—
79#2730C2214yes—
80#2729C2214yes—
81#2727C2214yes—
82#2722C2212yes—
83#2716C2214yes—
84#2716C2214yes—
85#2715C2214yes—
86#2715C2214yes—
87#2715C2214yes—
88#2715C2214yes—
89#2714C2214yes—
90#2714C2214yes—
91#2714C2214yes—
92#2712C2212yes—
93#2712C2214yes—
94#2710C2214yes—
95#2710C2214yes—
96#2709C2214yes—
97#2708C2214yes—
98#2705C2214yes—
99#2702C2214yes—
100#2700C2214yes—
101#2700C2214yes—
102#2700C2214yes—
103#2696C2214yes—
104#2692C2214yes—
105#2692C2214yes—
106#2689C2214yes—
107#2687C2214yes—
108#2683C2214yes—
109#2683C2212yes—
110#2683C2212yes—
111#2681C2214yes—
112#2677C2214yes—
113#2676C2214yes—
114#2674C2214yes—
115#2673C2214yes—
116#2672C2214yes—
117#2662C2214yes—
118#2662C2214yes—
119#2662C2214yes—
120#2662C2214yes—
121#2657C2212yes—
122#2649C2214yes—
123#2648C2214yes—
124#2639C2212yes—
125#2638C2214yes—
126#2638C2212yes—
127#2636C2214yes—
128#2635C2214yes—
129#2624C2211yescharacteristic
130#2620C2212yes—
131#2616C2212yes—
132#2616C2214yes—
133#2615C2212yes—
134#2615C2211yescharacteristic
135#2605C2214yes—
136#2600C2214yes—
137#2597C2214yes—
138#2589C2214yes—
139#2588C2214yes—
140#2587C2214yes—
141#2586C2212yes—
142#2586C2214yes—
143#2574C2214yes—
144#2567C2212yes—
145#2564C2212yes—
146#2560C2214yes—
147#2555C2214yes—
148#2554C2214yes—
149#2551C2212yes—
150#2549C2214yes—
151#2548C2212yes—
152#2547C2211yescharacteristic
153#2547C2212yes—
154#2545C2212yes—
155#2544C2214yes—
156#2544C2212yes—
157#2544C2212yes—
158#2541C2211yescharacteristic
159#2540C2212yes—
160#2538C2212yes—
161#2538C2212yes—
162#2537C2212yes—
163#2522C2214yes—
164#2521C2214yes—
165#2517C2212yes—
166#2512C2212yes—
167#2497C2212yes—
168#2496C2212yes—
169#2492C2214yes—
170#2492C2212yes—
171#2492C2212yes—
172#2492C2212yes—
173#2491C2212yes—
174#2485C2212yes—
175#2468C2214yes—
176#2466C2214yes—
177#2465C2214yes—
178#2463C2214yes—
179#2461C2214yes—
180#2459C2214yes—
181#2459C2214yes—
182#2457C2214yes—
183#2456C2214yes—
184#2452C2214yes—
185#2452C2214yes—
186#2452C2214yes—
187#2451C2212yes—
188#2451C2212yes—
189#2451C2214yes—
190#2448C2212yes—
191#2446C2212yes—
192#2446C2212yes—
193#2436C2212yes—
194#2436C2212yes—
195#2436C2211yescharacteristic
196#2436C2211yescharacteristic
197#2434C2214yes—
198#2434C2212yes—
199#2432C2214yes—
200#2432C2212yes—
201#2432C2212yes—
202#2432C2214yes—
203#2431C2214yes—
204#2431C2212yes—
205#2429C2212yes—
206#2427C2212yes—
207#2426C2212yes—
208#2425C2214yes—
209#2423C2212yes—
210#2423C2212yes—
211#2422C2212yes—
212#2415C2212yes—
213#2414C2212yes—
214#2414C2212yes—
215#2409C2214yes—
216#2409C2211yescharacteristic
217#2409C2212yes—
218#2409C2212yes—
219#2409C2212yes—
220#2409C2212yes—
221#2409C2211yescharacteristic
222#2407C2214yes—
223#2407C2214yes—
224#2407C2212yes—
225#2407C2212yes—
226#2407C2212yes—
227#2407C2212yes—
228#2407C2214yes—
229#2395C2211yescharacteristic
230#2395C2212yes—
231#2392C2212yes—
232#2392C2212yes—
233#2392C2212yes—
234#2388C2214yes—
235#2388C2212yes—
236#2388C2212yes—
237#2388C2211yescharacteristic
238#2373C2214yes—
239#2367C2212yes—
240#2366C2212yes—
241#2365C2212yes—
242#2362C2212yes—
243#2355C2212yes—
244#2341C2211yescharacteristic
245#2341C2212yes—
246Q8×C22⋊C4C2212yes—
247Q8×C22⋊C4C2212yes—
248Q8×C22⋊C4C2212yes—
249#2339C2211yescharacteristic
250#2337C2214yes—
251#2326C2212yes—
252#2323C2212yes—
253#2323C2212yes—
254#2310C2212yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#126C2212yes—
258#2295C2211yescharacteristic
259C2×2−1+4—48no—
260C2×2−1+4—44no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2311yescharacteristic
265C22×#41C2312yes—
266C22×#41C2314yes—
267C23×Q8C2312yes—
268C23×Q8C2311yescharacteristic
269C23×Q8C2312yes—
270C23×Q8C2312yes—
271C23×Q8C2311yescharacteristic
272#556—44no—
273#550—44no—
274D4×Q8—48no—
275D4×Q8—48no—
276D4×Q8—48no—
277#548—48no—
278#548—48no—
279#542—48no—
280#536—44no—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2311yescharacteristic
285C2×C4⋊Q8C2314yes—
286C2×C4⋊Q8C2314yes—
287C2×C4⋊Q8C2314yes—
288C2×#127C2311yescharacteristic
289C2×#127C2311yescharacteristic
290C2×#127C2312yes—
291C2×#127C2312yes—
292C2×#126C2312yes—
293C2×#126C2314yes—
294C2×#126C2314yes—
295C2×#126C2314yes—
296C2×#126C2314yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2314yes—
300C2×#124C2314yes—
301C2×#124C2312yes—
302C2×#124C2312yes—
303C2×#124C2314yes—
304C2×#124C2312yes—
305C2×#124C2312yes—
306C2×#124C2312yes—
307C2×#124C2314yes—
308C2×#124C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×#121C2314yes—
331C2×#121C2312yes—
332C2×#121C2311yescharacteristic
333C2×#121C2314yes—
334C2×#121C2312yes—
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2311yescharacteristic
338C2×#121C2312yes—
339C2×#121C2314yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2312yes—
350C2×C4×D4C2311yescharacteristic
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2314yes—
361C2×#117C2312yes—
362C2×#117C2312yes—
363C2×#117C2311yescharacteristic
364#400C2311yescharacteristic
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#399C2311yescharacteristic
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2312yes—
378#399C2314yes—
379#399C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2311yescharacteristic
385#398C2312yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2311yescharacteristic
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2312yes—
411#397C2312yes—
412#396C2312yes—
413#396C2312yes—
414#396C2312yes—
415#396C2314yes—
416#396C2312yes—
417#396C2312yes—
418#396C2312yes—
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#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2311yescharacteristic
435#395C2312yes—
436#395C2314yes—
437#395C2314yes—
438#395C2312yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#394C2314yes—
445#394C2312yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2314yes—
461#394C2314yes—
462#394C2311yescharacteristic
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2312yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2312yes—
473#394C2312yes—
474#394C2312yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#393C2314yes—
488#393C2312yes—
489#393C2312yes—
490#393C2314yes—
491#393C2312yes—
492#393C2314yes—
493#393C2314yes—
494#393C2314yes—
495#393C2312yes—
496#393C2311yescharacteristic
497#393C2312yes—
498#393C2314yes—
499#393C2314yes—
500#393C2312yes—
501#393C2312yes—
502#393C2314yes—
503#393C2312yes—
504#393C2314yes—
505#392C2312yes—
506#392C2312yes—
507#392C2312yes—
508#392C2312yes—
509#392C2312yes—
510#392C2312yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2311yescharacteristic
516#392C2312yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2312yes—
521#392C2314yes—
522#392C2314yes—
523#392C2314yes—
524#392C2314yes—
525#391C2314yes—
526#391C2312yes—
527#391C2312yes—
528#391C2312yes—
529#391C2312yes—
530#391C2312yes—
531#391C2312yes—
532#391C2314yes—
533#391C2312yes—
534#391C2312yes—
535#391C2314yes—
536#391C2312yes—
537#391C2314yes—
538#391C2312yes—
539#391C2314yes—
540#391C2314yes—
541#391C2314yes—
542#391C2314yes—
543#391C2314yes—
544#391C2314yes—
545#391C2314yes—
546#391C2314yes—
547#391C2314yes—
548#391C2312yes—
549#391C2314yes—
550#390C2314yes—
551#390C2311yescharacteristic
552#390C2312yes—
553#390C2311yescharacteristic
554#390C2312yes—
555#390C2314yes—
556#390C2314yes—
557#390C2314yes—
558#390C2314yes—
559#390C2312yes—
560#390C2312yes—
561#390C2312yes—
562#390C2312yes—
563#390C2314yes—
564#390C2314yes—
565#390C2312yes—
566#390C2314yes—
567#390C2314yes—
568#390C2314yes—
569#390C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2312yes—
576#389C2314yes—
577#389C2312yes—
578#389C2314yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2312yes—
583#389C2312yes—
584#389C2314yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
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#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
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#387C2314yes—
635#387C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2312yes—
645#386C2312yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2312yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2312yes—
671#385C2314yes—
672#384C2311yescharacteristic
673#384C2312yes—
674#384C2312yes—
675#383C2312yes—
676#382C2314yes—
677#381C2314yes—
678#381C2312yes—
679#381C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2312yes—
683#380C2312yes—
684#380C2311yescharacteristic
685#380C2312yes—
686#380C2312yes—
687#380C2314yes—
688#380C2314yes—
689#380C2312yes—
690#380C2312yes—
691#380C2311yescharacteristic
692#380C2312yes—
693#380C2314yes—
694#380C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2311yescharacteristic
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2311yescharacteristic
719C4×C22⋊C4C2312yes—
720#376C2312yes—
721C2×#95C2312yes—
722C43C2311yescharacteristic
7232−1+4—464no—
724C2×#41—28no—
725C2×#41—24no—
726C2×#41—24no—
727C2×#41—44no—
728C2×#41—48no—
729C2×#41—42no—
730C2×#41—44no—
731C2×#41—44no—
732C2×#41—48no—
733C2×#41—44no—
734C2×#41—48no—
735C2×#41—44no—
736C2×#41—48no—
737C2×#41—44no—
738C22×Q8—28no—
739C22×Q8—28no—
740C22×Q8—28no—
741C22×Q8—28no—
742C22×Q8—42no—
743C22×Q8—44no—
744C22×Q8—44no—
745C22×Q8—48no—
746C22×Q8—42no—
747C22×Q8—44no—
748C22×Q8—44no—
749C22×Q8—44no—
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2414yes—
757C22×Q8C2412yes—
758C22×Q8C2414yes—
759C22×Q8C2411yescharacteristic
760C22×D4C2411yescharacteristic
761C22×D4C2411yescharacteristic
762C22×D4C2412yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2411yescharacteristic
766C22×D4C2411yescharacteristic
767C22×D4C2412yes—
768C22×D4C2414yes—
769C22×D4C2412yes—
770C22×D4C2412yes—
771C22×D4C2412yes—
772C22×D4C2414yes—
773C22×D4C2412yes—
774C22×D4C2414yes—
775C22×D4C2414yes—
776C22×D4C2412yes—
777C22×D4C2412yes—
778C22×D4C2412yes—
779C22×D4C2411yescharacteristic
780C22×D4C2412yes—
781C23×C4C2412yes—
782C23×C4C2411yescharacteristic
783C23×C4C2412yes—
784C23×C4C2411yescharacteristic
785C23×C4C2414yes—
786C23×C4C2412yes—
787C23×C4C2414yes—
788C23×C4C2412yes—
789C23×C4C2412yes—
790C23×C4C2414yes—
791C23×C4C2412yes—
792C23×C4C2414yes—
793C4⋊Q8—28no—
794C4⋊Q8—28no—
795C4⋊Q8—44no—
796C4⋊Q8—42no—
797C4⋊Q8—48no—
798C4⋊Q8—48no—
799C4⋊Q8—48no—
800#127—24no—
801#127—42no—
802#127—44no—
803#127—82no—
804#126—28no—
805#126—48no—
806#126—48no—
807#126—84no—
808#126—84no—
809#124—28no—
810#124—28no—
811#124—48no—
812#124—44no—
813#124—44no—
814#124—44no—
815#124—48no—
816#124—48no—
817#124—82no—
818#124—84no—
819#124—84no—
820#124—82no—
821#123—48no—
822#123—48no—
823#123—84no—
824C22⋊Q8—28no—
825C22⋊Q8—28no—
826C22⋊Q8—28no—
827C22⋊Q8—48no—
828C22⋊Q8—48no—
829C22⋊Q8—48no—
830C22⋊Q8—48no—
831C22⋊Q8—48no—
832C22⋊Q8—44no—
833C22⋊Q8—44no—
834C22⋊Q8—48no—
835C22⋊Q8—48no—
836C22⋊Q8—48no—
837C22⋊Q8—44no—
838C22⋊Q8—48no—
839C22⋊Q8—44no—
840C22⋊Q8—44no—
841C22⋊Q8—44no—
842#121—48no—
843#121—44no—
844#121—44no—
845#121—48no—
846#121—44no—
847#121—42no—
848#121—42no—
849#121—44no—
850#121—44no—
851#121—84no—
852C4×Q8—28no—
853C4×Q8—24no—
854C4×Q8—44no—
855C4×Q8—44no—
856C4×Q8—44no—
857C4×Q8—44no—
858C4×Q8—44no—
859C4×D4—44no—
860C4×D4—44no—
861C4×D4—44no—
862C4×D4—48no—
863C4×D4—44no—
864C4×D4—44no—
865C4×D4—44no—
866C4×D4—42no—
867C4×D4—44no—
868C4×D4—42no—
869C4×D4—48no—
870C4×D4—48no—
871C4×D4—48no—
872C4×D4—48no—
873#117—42no—
874#117—44no—
875#117—44no—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2411yescharacteristic
944C2×C22⋊C4C2411yescharacteristic
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2414yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2414yes—
996C2×C42C2414yes—
997C2×C42C2414yes—
998C2×C42C2414yes—
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2412yes—
1005C2×C42C2412yes—
1006C2×C42C2411yescharacteristic
1007#95C2411yescharacteristic
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2411yescharacteristic
1014#95C2412yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2411yescharacteristic
1022#95C2414yes—
1023#95C2411yescharacteristic
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062C24C2512yes—
1063C24C2512yes—
1064C24C2511yescharacteristic
1065C24C2511yescharacteristic
1066C24C2512yes—
1067C24C2512yes—
1068#41—432no—
1069#41—416no—
1070#41—432no—
1071#41—464no—
1072#41—416no—
1073#41—88no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—24no—
1078C2×Q8—24no—
1079C2×Q8—24no—
1080C2×Q8—28no—
1081C2×Q8—28no—
1082C2×Q8—28no—
1083C2×Q8—28no—
1084C2×Q8—24no—
1085C2×Q8—44no—
1086C2×Q8—42no—
1087C2×Q8—41no—
1088C2×Q8—42no—
1089C2×Q8—42no—
1090C2×Q8—42no—
1091C2×Q8—44no—
1092C2×Q8—44no—
1093C2×Q8—44no—
1094C2×Q8—42no—
1095C2×Q8—44no—
1096C2×Q8—44no—
1097C2×Q8—44no—
1098C2×Q8—416no—
1099C2×Q8—432no—
1100C2×Q8—432no—
1101C2×Q8—816no—
1102C2×Q8—88no—
1103C2×Q8H(5,𝔽2)18yes—
1104C2×Q8H(5,𝔽2)14yes—
1105C2×D4—24no—
1106C2×D4—22no—
1107C2×D4—28no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4—22no—
1111C2×D4—24no—
1112C2×D4—24no—
1113C2×D4—24no—
1114C2×D4—24no—
1115C2×D4—22no—
1116C2×D4—22no—
1117C2×D4—42no—
1118C2×D4—42no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—41no—
1128C2×D4—42no—
1129C2×D4—42no—
1130C2×D4—42no—
1131C2×D4—42no—
1132C2×D4—42no—
1133C2×D4—42no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—41no—
1137C2×D4—42no—
1138C2×D4—41no—
1139C2×D4—44no—
1140C2×D4—42no—
1141C2×D4—44no—
1142C2×D4—41no—
1143C2×D4—42no—
1144C2×D4—42no—
1145C2×D4—44no—
1146C2×D4—41no—
1147C2×D4—44no—
1148C2×D4—42no—
1149C2×D4—42no—
1150C2×D4—44no—
1151C2×D4—42no—
1152C2×D4—42no—
1153C2×D4—42no—
1154C2×D4—44no—
1155C2×D4—44no—
1156C2×D4—44no—
1157C2×D4—44no—
1158C2×D4—44no—
1159C2×D4—44no—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—22no—
1163C22×C4—24no—
1164C22×C4—24no—
1165C22×C4—28no—
1166C22×C4—24no—
1167C22×C4—24no—
1168C22×C4—22no—
1169C22×C4—28no—
1170C22×C4—28no—
1171C22×C4—24no—
1172C22×C4—24no—
1173C22×C4—28no—
1174C22×C4—24no—
1175C22×C4—28no—
1176C22×C4—24no—
1177C22×C4—44no—
1178C22×C4—44no—
1179C22×C4—42no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4—44no—
1186C22×C4—42no—
1187C22×C4—44no—
1188C22×C4—44no—
1189C22×C4—44no—
1190C22×C4C2512yes—
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2512yes—
1196C22×C4C2514yes—
1197C22×C4C2512yes—
1198C22×C4C2511yescharacteristic
1199C22×C4C2512yes—
1200C22×C4C2514yes—
1201C22×C4C2514yes—
1202C22×C4C2512yes—
1203C22×C4C2514yes—
1204C22×C4C2514yes—
1205C22×C4C2511yescharacteristic
1206C22×C4C2512yes—
1207C22×C4C2512yes—
1208C22×C4C2514yes—
1209C22×C4C2512yes—
1210C22×C4C2511yescharacteristic
1211C22×C4C2512yes—
1212C22×C4C2511yescharacteristic
1213C4⋊C4—22no—
1214C4⋊C4—24no—
1215C4⋊C4—28no—
1216C4⋊C4—24no—
1217C4⋊C4—28no—
1218C4⋊C4—28no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—28no—
1222C4⋊C4—24no—
1223C4⋊C4—28no—
1224C4⋊C4—28no—
1225C4⋊C4—28no—
1226C4⋊C4—28no—
1227C4⋊C4—24no—
1228C4⋊C4—24no—
1229C4⋊C4—24no—
1230C4⋊C4—44no—
1231C4⋊C4—42no—
1232C4⋊C4—44no—
1233C4⋊C4—42no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—41no—
1237C4⋊C4—42no—
1238C4⋊C4—41no—
1239C4⋊C4—42no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—44no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—28no—
1265C22⋊C4—28no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—24no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—44no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—44no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—42no—
1303C22⋊C4—44no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—42no—
1315C22⋊C4—44no—
1316C22⋊C4—44no—
1317C22⋊C4—42no—
1318C22⋊C4—44no—
1319C22⋊C4—42no—
1320C22⋊C4—44no—
1321C22⋊C4—44no—
1322C22⋊C4—44no—
1323C22⋊C4—44no—
1324C22⋊C4—42no—
1325C22⋊C4—42no—
1326C42—24no—
1327C42—24no—
1328C42—24no—
1329C42—22no—
1330C42—24no—
1331C42—24no—
1332C42—28no—
1333C42—42no—
1334C42—44no—
1335C42—44no—
1336C42—44no—
1337C42—44no—
1338C42—44no—
1339C42—41no—
1340C42—44no—
1341C42—44no—
1342C42—42no—
1343C422−1+414yescomplemented
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23—21no—
1353C23—24no—
1354C23—22no—
1355C23—22no—
1356C23—22no—
1357C23—21no—
1358C23—22no—
1359C23—22no—
1360C23—22no—
1361C23—22no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—22no—
1367C23—22no—
1368C23—22no—
1369C23—22no—
1370C23—22no—
1371C23—24no—
1372C23—22no—
1373C23—22no—
1374C23—22no—
1375C23—22no—
1376C23—24no—
1377C23—22no—
1378C23C2611yescharacteristic
1379Q8—216no—
1380Q8—28no—
1381Q8—416no—
1382Q8—48no—
1383Q8—44no—
1384Q8—48no—
1385Q8—84no—
1386Q8—88no—
1387Q8—84no—
1388Q8—164no—
1389D4—48no—
1390D4—48no—
1391D4—48no—
1392D4—416no—
1393D4—48no—
1394D4—44no—
1395D4—48no—
1396D4—44no—
1397D4—44no—
1398D4—84no—
1399D4—82no—
1400D4—82no—
1401D4—84no—
1402D4—84no—
1403D4—88no—
1404D4—88no—
1405D4—84no—
1406D4—162no—
1407D4—162no—
1408D4—162no—
1409D4—164no—
1410C2×C4—21no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—21no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—21no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—24no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—21no—
1436C2×C4—21no—
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—22no—
1447C2×C4—22no—
1448C2×C4—24no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—24no—
1452C2×C4—24no—
1453C2×C4—24no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—22no—
1460C2×C4—24no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—24no—
1464C2×C4—24no—
1465C2×C4—22no—
1466C2×C4—24no—
1467C2×C4—416no—
1468C2×C4—48no—
1469C2×C4—48no—
1470C2×C4—416no—
1471C2×C4—48no—
1472C2×C4—44no—
1473C2×C4—48no—
1474C2×C4—44no—
1475C2×C4—88no—
1476C2×C4—84no—
1477C2×C4—84no—
1478C2×C4—164no—
1479C2×C4C2×H(5,𝔽2)18yes—
1480C2×C4C2×H(5,𝔽2)14yes—
1481C2×C4C2×H(5,𝔽2)12yes—
1482C2×C4C2×H(5,𝔽2)14yes—
1483C2×C4C2×2−1+414yes—
1484C2×C4C2×2−1+412yes—
1485C22—42no—
1486C22—42no—
1487C22—42no—
1488C22—41no—
1489C22—42no—
1490C22—41no—
1491C22—44no—
1492C22—42no—
1493C22—42no—
1494C22—42no—
1495C22—44no—
1496C22—42no—
1497C22—42no—
1498C22—42no—
1499C22—42no—
1500C22—42no—
1501C22—42no—
1502C22—42no—
1503C22—44no—
1504C22—42no—
1505C22—44no—
1506C22—42no—
1507C22—42no—
1508C22—42no—
1509C22—41no—
1510C22—42no—
1511C22—41no—
1512C22—42no—
1513C22—41no—
1514C22—42no—
1515C22—42no—
1516C22—41no—
1517C22—42no—
1518C22—42no—
1519C22C22×H(5,𝔽2)11yescharacteristic
1520C22C22×H(5,𝔽2)12yes—
1521C22C22×2−1+411yescharacteristic
1522C22H(7,𝔽2)11yescharacteristic
1523C222−1+612yes—
1524C4—24no—
1525C4—22no—
1526C4—24no—
1527C4—28no—
1528C4—42no—
1529C4—42no—
1530C4—41no—
1531C4—42no—
1532C4—42no—
1533C4—44no—
1534C4—44no—
1535C4—44no—
1536C4—42no—
1537C4—42no—
1538C4—42no—
1539C4—42no—
1540C4—44no—
1541C4—41no—
1542C4—42no—
1543C4—41no—
1544C4—42no—
1545C4—44no—
1546C4#353214yes—
1547C2—82no—
1548C2—82no—
1549C2—82no—
1550C2—81no—
1551C2—82no—
1552C2—81no—
1553C2C2×#353211yescharacteristic
1554C2#6291312yes—
1555C2#6291711yescharacteristic
1556C2#6304811yescharacteristic
1557C2#6305212yes—
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. #59817C2semidirect
2. #59477C2semidirect
3. #58944C2semidirect
4. #58898C2semidirect
5. #58021C2semidirect
6. #55580C2semidirect
7. #55126C2semidirect
8. #53044C2semidirect
9. #52958C2semidirect
10. #52421C2semidirect
11. #52334C2semidirect
12. #47725C2semidirect
13. #45351C2semidirect
14. #45303C2semidirect
15. #45291C2semidirect
16. #45289C2semidirect
17. #45248C2semidirect
18. #42913C2semidirect
19. #42894C2semidirect
20. #42835C2semidirect
21. #42806C2semidirect
22. #42805C2semidirect
23. #42043C2semidirect
24. #41009C2semidirect
25. #39790C2semidirect
26. #39747C2semidirect
27. #36696C2semidirect
28. #35757C2semidirect
29. #35687C2semidirect
1343. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
#598172
#594772
#589442
#588982
#580212
#555802
#551262
#530442
#529582
#524212
#523342
#477252
#453512
#453032
#452912
#452892
#452482
#429132
#428942
#428352
#428062
#428052
#420432
#410092
#397902
#397472
#366962
#357572
#356872