Finite Group Databasebeta

← #8402614

Subgroups — #8402614

Order 512.

4929 conjugacy classes of subgroups.

The subgroup lattice has 1546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59417C212yesmaximal, complemented
2#59093C212yesmaximal, complemented
3#54901C214yesmaximal, complemented
4#54390C214yesmaximal, complemented
5#49259C214yesmaximal, complemented
6#48551C214yesmaximal, complemented
7#48496C214yesmaximal, complemented
8#47894C214yesmaximal, complemented
9#46072C212yesmaximal, complemented
10#45625C212yesmaximal, complemented
11#45425C211yesmaximal, characteristic, complemented
12#45271C211yesmaximal, characteristic, complemented
13#45268C211yesmaximal, characteristic, complemented
14#45137C211yesmaximal, characteristic, complemented
15#43647C214yesmaximal, complemented
16#43369C214yesmaximal, complemented
17#42645C211yesmaximal, characteristic, complemented
18#42424C211yesmaximal, characteristic, complemented
19#39853C212yesmaximal, complemented
20#39752C212yesmaximal, complemented
21#39248C212yesmaximal, complemented
22#39008C212yesmaximal, complemented
23#37396C211yesmaximal, characteristic, complemented
24#36566C211yesmaximal, characteristic, complemented
25#36534C211yesmaximal, characteristic, complemented
26#36303C211yesmaximal, characteristic, complemented
27#36149C211yesmaximal, characteristic, complemented
28#36031C211yesmaximal, characteristic, complemented
29#35737C211yesmaximal, characteristic, complemented
30#35534C211yesmaximal, characteristic, complemented
31#34968C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#556C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2212yes—
37C2×#547C2211yescharacteristic
38C2×#540C2211yescharacteristic
39C2×#532C2212yes—
40C2×#520C2211yescharacteristic
41#2864C2212yes—
42#2862C2211yescharacteristic
43#2862C2211yescharacteristic
44#2861C2212yes—
45#2857C2212yes—
46#2850C2212yes—
47#2836C2214yes—
48#2831C2214yes—
49#2814C2212yes—
50#2814C2212yes—
51#2809C2214yes—
52#2808C2214yes—
53#2806C2214yes—
54#2799C2214yes—
55#2799C2214yes—
56#2799C2214yes—
57#2778C2214yes—
58#2770C2214yes—
59#2763C2214yes—
60#2762C2214yes—
61#2759C2214yes—
62#2756C2214yes—
63#2754C2214yes—
64#2754C2214yes—
65#2751C2214yes—
66#2750C2214yes—
67#2750C2214yes—
68#2746C2214yes—
69#2744C2214yes—
70#2744C2214yes—
71#2743C2214yes—
72#2743C2214yes—
73#2742C2214yes—
74#2741C2214yes—
75#2740C2214yes—
76#2732C2214yes—
77#2728C2214yes—
78#2717C2214yes—
79#2717C2214yes—
80#2716C2214yes—
81#2712C2214yes—
82#2712C2214yes—
83#2706C2214yes—
84#2703C2214yes—
85#2700C2214yes—
86#2700C2214yes—
87#2696C2214yes—
88#2696C2214yes—
89#2695C2214yes—
90#2693C2214yes—
91#2692C2214yes—
92#2691C2214yes—
93#2687C2214yes—
94#2686C2214yes—
95#2676C2214yes—
96#2672C2214yes—
97#2671C2214yes—
98#2671C2214yes—
99#2659C2214yes—
100#2653C2214yes—
101#2652C2214yes—
102#2639C2212yes—
103#2639C2212yes—
104#2630C2214yes—
105#2628C2211yescharacteristic
106#2627C2212yes—
107#2624C2212yes—
108#2621C2211yescharacteristic
109#2621C2212yes—
110#2615C2212yes—
111#2589C2214yes—
112#2589C2214yes—
113#2581C2212yes—
114#2581C2212yes—
115#2581C2211yescharacteristic
116#2580C2212yes—
117#2580C2211yescharacteristic
118#2574C2214yes—
119#2572C2214yes—
120#2571C2212yes—
121#2569C2214yes—
122#2569C2214yes—
123#2568C2211yescharacteristic
124#2566C2211yescharacteristic
125#2565C2212yes—
126#2565C2211yescharacteristic
127#2564C2212yes—
128#2563C2211yescharacteristic
129#2560C2214yes—
130#2560C2214yes—
131#2559C2214yes—
132#2557C2214yes—
133#2555C2214yes—
134#2548C2211yescharacteristic
135#2547C2211yescharacteristic
136#2547C2211yescharacteristic
137#2547C2212yes—
138#2544C2212yes—
139#2544C2212yes—
140#2543C2214yes—
141#2541C2211yescharacteristic
142#2536C2214yes—
143#2535C2212yes—
144#2535C2212yes—
145#2535C2211yescharacteristic
146#2535C2211yescharacteristic
147#2525C2212yes—
148#2521C2212yes—
149#2520C2212yes—
150#2515C2212yes—
151#2514C2212yes—
152#2505C2214yes—
153#2504C2211yescharacteristic
154#2503C2212yes—
155#2501C2211yescharacteristic
156#2498C2212yes—
157#2493C2214yes—
158#2492C2212yes—
159#2492C2214yes—
160#2490C2212yes—
161#2488C2214yes—
162#2488C2214yes—
163#2488C2214yes—
164#2487C2212yes—
165#2477C2214yes—
166#2471C2214yes—
167#2468C2212yes—
168#2467C2214yes—
169#2466C2214yes—
170#2465C2212yes—
171#2465C2214yes—
172#2464C2214yes—
173#2461C2212yes—
174#2459C2214yes—
175#2459C2214yes—
176#2458C2212yes—
177#2457C2214yes—
178#2456C2214yes—
179#2453C2212yes—
180#2453C2212yes—
181#2452C2212yes—
182#2451C2212yes—
183#2451C2212yes—
184#2450C2214yes—
185#2450C2214yes—
186#2447C2214yes—
187#2447C2212yes—
188#2447C2212yes—
189#2444C2214yes—
190#2443C2214yes—
191#2443C2214yes—
192#2442C2212yes—
193#2442C2212yes—
194#2442C2212yes—
195#2438C2214yes—
196#2436C2212yes—
197#2436C2212yes—
198#2431C2211yescharacteristic
199#2431C2211yescharacteristic
200#2430C2214yes—
201#2430C2214yes—
202#2430C2212yes—
203#2428C2212yes—
204#2428C2212yes—
205#2427C2214yes—
206#2427C2212yes—
207#2427C2214yes—
208#2427C2212yes—
209#2426C2212yes—
210#2426C2212yes—
211#2423C2212yes—
212#2421C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2419C2214yes—
216#2419C2214yes—
217#2417C2212yes—
218#2417C2214yes—
219#2416C2212yes—
220#2407C2214yes—
221#2407C2214yes—
222#2407C2214yes—
223#2399C2211yescharacteristic
224#2398C2211yescharacteristic
225#2396C2211yescharacteristic
226C2×#400C2212yes—
227#2392C2212yes—
228#2392C2211yescharacteristic
229#2377C2214yes—
230#2376C2214yes—
231#2368C2214yes—
232#2367C2212yes—
233#2364C2214yes—
234#2361C2212yes—
235#2352C2214yes—
236#2351C2211yescharacteristic
237#2349C2211yescharacteristic
238#2349C2211yescharacteristic
239#2349C2211yescharacteristic
240#2349C2212yes—
241Q8×C22⋊C4C2212yes—
242Q8×C22⋊C4C2212yes—
243#2339C2214yes—
244#2339C2212yes—
245#2339C2214yes—
246#2339C2214yes—
247#2333C2214yes—
248#2331C2211yescharacteristic
249#2329C2214yes—
250#2328C2211yescharacteristic
251#2327C2211yescharacteristic
252#2326C2211yescharacteristic
253#2325C2214yes—
254#2318C2214yes—
255C4×#127C2211yescharacteristic
256C4×#126C2212yes—
257C4×#124C2212yes—
258C4×#124C2212yes—
259C4×#124C2212yes—
260C4×#124C2211yescharacteristic
261C4×C22⋊Q8C2212yes—
262C4×#123C2212yes—
263#2298C2211yescharacteristic
264C2×#391C2212yes—
265C42×Q8C2211yescharacteristic
266C42×D4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269C22×#41C2314yes—
270C23×Q8C2312yes—
271#559—48no—
272#556—44no—
273#554—44no—
274D4×Q8—44no—
275#548—48no—
276#547—44no—
277#540—44no—
278#532—48no—
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2312yes—
283C2×#127C2311yescharacteristic
284C2×#127C2311yescharacteristic
285C2×#127C2311yescharacteristic
286C2×#126C2312yes—
287C2×#126C2314yes—
288C2×#125C2311yescharacteristic
289C2×#125C2312yes—
290C2×#124C2311yescharacteristic
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2312yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2312yes—
304C2×#123C2312yes—
305C2×#123C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2314yes—
326C2×#121C2311yescharacteristic
327C2×#121C2312yes—
328C2×#121C2311yescharacteristic
329C2×#121C2314yes—
330#520—44no—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2314yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2314yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×#117C2311yescharacteristic
359C2×#117C2312yes—
360C2×#117C2312yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2312yes—
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2311yescharacteristic
365C22×C42C2312yes—
366#401C2314yes—
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2312yes—
380#400C2312yes—
381#400C2314yes—
382#400C2311yescharacteristic
383#400C2314yes—
384#400C2314yes—
385#400C2312yes—
386#400C2314yes—
387#399C2312yes—
388#399C2312yes—
389#399C2314yes—
390#399C2314yes—
391#399C2311yescharacteristic
392#399C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2312yes—
402#398C2312yes—
403#398C2311yescharacteristic
404#398C2312yes—
405#398C2314yes—
406#398C2312yes—
407#398C2314yes—
408#398C2312yes—
409#398C2314yes—
410#398C2314yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2312yes—
420#397C2314yes—
421#397C2312yes—
422#397C2312yes—
423#397C2312yes—
424#397C2311yescharacteristic
425#397C2312yes—
426#397C2312yes—
427#397C2314yes—
428#397C2314yes—
429#397C2312yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2312yes—
439#396C2314yes—
440#396C2312yes—
441#395C2312yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2311yescharacteristic
446#395C2312yes—
447#395C2312yes—
448#395C2312yes—
449#395C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2311yescharacteristic
460#394C2314yes—
461#394C2312yes—
462#394C2314yes—
463#394C2312yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#393C2312yes—
469#393C2312yes—
470#393C2311yescharacteristic
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2312yes—
476#393C2312yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#393C2314yes—
481#392C2311yescharacteristic
482#392C2312yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2312yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#391C2314yes—
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2312yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2314yes—
515#391C2314yes—
516#391C2312yes—
517#390C2314yes—
518#390C2311yescharacteristic
519#390C2311yescharacteristic
520#390C2312yes—
521#390C2311yescharacteristic
522#390C2311yescharacteristic
523#390C2312yes—
524#390C2311yescharacteristic
525#390C2314yes—
526#390C2314yes—
527#390C2311yescharacteristic
528#390C2314yes—
529#390C2312yes—
530#390C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2312yes—
545#388C2312yes—
546#388C2312yes—
547#388C2312yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
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#388C2312yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
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#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2312yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2312yes—
660#384C2311yescharacteristic
661#384C2311yescharacteristic
662#383C2312yes—
663#383C2314yes—
664#382C2312yes—
665#382C2311yescharacteristic
666#382C2311yescharacteristic
667#382C2312yes—
668#382C2314yes—
669#382C2312yes—
670#382C2311yescharacteristic
671#382C2311yescharacteristic
672#382C2314yes—
673#382C2312yes—
674#382C2312yes—
675#381C2314yes—
676#381C2314yes—
677#381C2314yes—
678#381C2312yes—
679#381C2314yes—
680#381C2314yes—
681#381C2314yes—
682#381C2314yes—
683#380C2314yes—
684#380C2314yes—
685#380C2314yes—
686#380C2314yes—
687#380C2314yes—
688#380C2314yes—
689#380C2314yes—
690#380C2312yes—
691#380C2314yes—
692#380C2312yes—
693#380C2312yes—
694#380C2314yes—
695#380C2314yes—
696#380C2312yes—
697#380C2312yes—
698#380C2312yes—
699#380C2312yes—
700#380C2314yes—
701#380C2314yes—
702#380C2314yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2311yescharacteristic
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2311yescharacteristic
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2311yescharacteristic
733#376C2311yescharacteristic
734C2×#95C2312yes—
735C2×#95C2314yes—
736C2×#95C2314yes—
737C2×#95C2314yes—
738C2×#95C2312yes—
739C2×#95C2314yes—
740C2×#95C2312yes—
741C43C2312yes—
742C43C2311yescharacteristic
743C2×#41—24no—
744C2×#41—24no—
745C2×#41—48no—
746C2×#41—48no—
747C2×#41—48no—
748C2×#41—42no—
749C2×#41—44no—
750C2×#41—48no—
751C22×Q8—28no—
752C22×Q8—44no—
753C22×Q8—44no—
754C22×Q8C2412yes—
755C22×Q8C2411yescharacteristic
756C22×Q8C2411yescharacteristic
757C22×Q8C2412yes—
758C22×Q8C2414yes—
759C22×Q8C2414yes—
760C22×Q8C2412yes—
761C22×D4C2411yescharacteristic
762C22×D4C2411yescharacteristic
763C22×D4C2411yescharacteristic
764C22×D4C2414yes—
765C22×D4C2412yes—
766C22×D4C2414yes—
767C22×D4C2411yescharacteristic
768C22×D4C2412yes—
769C22×D4C2414yes—
770C22×D4C2414yes—
771C22×D4C2414yes—
772C22×D4C2412yes—
773C22×D4C2412yes—
774C22×D4C2412yes—
775C22×D4C2412yes—
776C23×C4C2411yescharacteristic
777C23×C4C2412yes—
778C23×C4C2412yes—
779C23×C4C2412yes—
780C23×C4C2412yes—
781C23×C4C2414yes—
782C23×C4C2412yes—
783C23×C4C2414yes—
784C23×C4C2414yes—
785C23×C4C2412yes—
786C23×C4C2412yes—
787C23×C4C2412yes—
788C23×C4C2414yes—
789C23×C4C2412yes—
790C23×C4C2414yes—
791C23×C4C2414yes—
792C4⋊Q8—24no—
793C4⋊Q8—24no—
794C4⋊Q8—44no—
795C4⋊Q8—44no—
796#127—24no—
797#127—24no—
798#127—42no—
799#126—44no—
800#126—48no—
801#125—42no—
802#125—44no—
803#124—24no—
804#124—24no—
805#124—28no—
806#124—44no—
807#124—44no—
808#124—44no—
809#124—48no—
810#124—48no—
811#124—48no—
812#123—48no—
813#123—48no—
814#123—48no—
815#123—44no—
816#123—44no—
817#123—44no—
818#123—48no—
819C22⋊Q8—48no—
820C22⋊Q8—48no—
821C22⋊Q8—48no—
822C22⋊Q8—48no—
823C22⋊Q8—44no—
824C22⋊Q8—48no—
825C22⋊Q8—44no—
826C22⋊Q8—44no—
827C22⋊Q8—44no—
828C22⋊Q8—44no—
829C22⋊Q8—44no—
830#121—28no—
831#121—44no—
832#121—44no—
833#121—48no—
834#121—48no—
835#121—48no—
836#121—48no—
837#121—48no—
838#121—44no—
839#121—42no—
840#121—42no—
841#121—44no—
842#121—48no—
843C4×Q8—24no—
844C4×Q8—24no—
845C4×Q8—44no—
846C4×Q8—44no—
847C4×Q8—42no—
848C4×Q8—44no—
849C4×Q8—44no—
850C4×Q8—44no—
851C4×D4—28no—
852C4×D4—24no—
853C4×D4—24no—
854C4×D4—24no—
855C4×D4—24no—
856C4×D4—44no—
857C4×D4—48no—
858C4×D4—42no—
859C4×D4—44no—
860C4×D4—44no—
861C4×D4—44no—
862C4×D4—44no—
863C4×D4—44no—
864C4×D4—44no—
865C4×D4—48no—
866C4×D4—44no—
867C4×D4—48no—
868C4×D4—48no—
869C4×D4—48no—
870#117—24no—
871#117—44no—
872#117—44no—
873C2×C4⋊C4—44no—
874C2×C4⋊C4—42no—
875C2×C4⋊C4—44no—
876C2×C4⋊C4—44no—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C22⋊C4C2411yescharacteristic
931C2×C22⋊C4C2411yescharacteristic
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C42—44no—
984C2×C42C2412yes—
985C2×C42C2411yescharacteristic
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2414yes—
996C2×C42C2412yes—
997C2×C42C2414yes—
998C2×C42C2414yes—
999C2×C42C2412yes—
1000C2×C42C2414yes—
1001C2×C42C2412yes—
1002C2×C42C2412yes—
1003C2×C42C2412yes—
1004C2×C42C2412yes—
1005C2×C42C2412yes—
1006C2×C42C2411yescharacteristic
1007#95C2411yescharacteristic
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2411yescharacteristic
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2411yescharacteristic
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2411yescharacteristic
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2414yes—
1063#95C2412yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075C24C2511yescharacteristic
1076C24C2512yes—
1077C24C2512yes—
1078C24C2512yes—
1079C24C2512yes—
1080#41—416no—
1081#41—832no—
1082#41—816no—
1083C2×Q8—22no—
1084C2×Q8—22no—
1085C2×Q8—22no—
1086C2×Q8—24no—
1087C2×Q8—24no—
1088C2×Q8—24no—
1089C2×Q8—24no—
1090C2×Q8—28no—
1091C2×Q8—28no—
1092C2×Q8—42no—
1093C2×Q8—42no—
1094C2×Q8—44no—
1095C2×Q8—44no—
1096C2×Q8—42no—
1097C2×Q8—44no—
1098C2×Q8—42no—
1099C2×Q8—44no—
1100C2×Q8—44no—
1101C2×Q8—816no—
1102C2×Q82−1+414yes—
1103C2×D4—24no—
1104C2×D4—28no—
1105C2×D4—28no—
1106C2×D4—24no—
1107C2×D4—28no—
1108C2×D4—28no—
1109C2×D4—24no—
1110C2×D4—28no—
1111C2×D4—28no—
1112C2×D4—22no—
1113C2×D4—22no—
1114C2×D4—22no—
1115C2×D4—22no—
1116C2×D4—22no—
1117C2×D4—22no—
1118C2×D4—22no—
1119C2×D4—22no—
1120C2×D4—22no—
1121C2×D4—24no—
1122C2×D4—28no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—42no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—42no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—42no—
1135C2×D4—42no—
1136C2×D4—42no—
1137C2×D4—42no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4H(5,𝔽2)14yes—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—28no—
1146C22×C4—28no—
1147C22×C4—24no—
1148C22×C4—22no—
1149C22×C4—24no—
1150C22×C4—22no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—22no—
1154C22×C4—24no—
1155C22×C4—24no—
1156C22×C4—24no—
1157C22×C4—24no—
1158C22×C4—28no—
1159C22×C4—24no—
1160C22×C4—42no—
1161C22×C4—42no—
1162C22×C4—42no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—42no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—44no—
1176C22×C4—42no—
1177C22×C4—42no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4—44no—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2514yes—
1190C22×C4C2514yes—
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2514yes—
1196C22×C4C2514yes—
1197C22×C4C2511yescharacteristic
1198C22×C4C2512yes—
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2511yescharacteristic
1202C22×C4C2512yes—
1203C22×C4C2512yes—
1204C22×C4C2512yes—
1205C22×C4C2512yes—
1206C22×C4C2512yes—
1207C22×C4C2511yescharacteristic
1208C22×C4C2511yescharacteristic
1209C22×C4C2512yes—
1210C22×C4C2512yes—
1211C22×C4C2511yescharacteristic
1212C4⋊C4—22no—
1213C4⋊C4—22no—
1214C4⋊C4—22no—
1215C4⋊C4—22no—
1216C4⋊C4—24no—
1217C4⋊C4—22no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—22no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—24no—
1228C4⋊C4—28no—
1229C4⋊C4—24no—
1230C4⋊C4—24no—
1231C4⋊C4—24no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—42no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4—42no—
1253C4⋊C4—42no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—42no—
1265C22⋊C4—28no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—24no—
1272C22⋊C4—24no—
1273C22⋊C4—22no—
1274C22⋊C4—22no—
1275C22⋊C4—24no—
1276C22⋊C4—24no—
1277C22⋊C4—24no—
1278C22⋊C4—24no—
1279C22⋊C4—28no—
1280C22⋊C4—28no—
1281C22⋊C4—28no—
1282C22⋊C4—24no—
1283C22⋊C4—42no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—42no—
1305C22⋊C4—42no—
1306C22⋊C4—42no—
1307C22⋊C4—44no—
1308C22⋊C4—42no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—42no—
1313C22⋊C4—42no—
1314C22⋊C4—44no—
1315C22⋊C4—44no—
1316C22⋊C4—42no—
1317C22⋊C4—42no—
1318C42—22no—
1319C42—24no—
1320C42—22no—
1321C42—24no—
1322C42—24no—
1323C42—24no—
1324C42—22no—
1325C42—22no—
1326C42—22no—
1327C42—24no—
1328C42—42no—
1329C42—42no—
1330C42—42no—
1331C42—44no—
1332C42—42no—
1333C42—44no—
1334C42—44no—
1335C42—44no—
1336C42—42no—
1337C42—42no—
1338C42—42no—
1339C42—42no—
1340C42H(5,𝔽2)14yes—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—24no—
1349C23—24no—
1350C23—22no—
1351C23—21no—
1352C23—22no—
1353C23—22no—
1354C23—21no—
1355C23—22no—
1356C23—22no—
1357C23—22no—
1358C23—22no—
1359C23—21no—
1360C23—24no—
1361C23—22no—
1362C23—22no—
1363C23—24no—
1364C23—24no—
1365C23—24no—
1366C23C2×H(5,𝔽2)14yes—
1367C23#58514yes—
1368C23C2611yescharacteristic
1369Q8—28no—
1370Q8—44no—
1371Q8—48no—
1372Q8—88no—
1373Q8—88no—
1374Q8—84no—
1375Q8—84no—
1376D4—28no—
1377D4—28no—
1378D4—48no—
1379D4—416no—
1380D4—416no—
1381D4—44no—
1382D4—44no—
1383D4—88no—
1384D4—84no—
1385D4—88no—
1386D4—88no—
1387D4—162no—
1388D4—162no—
1389D4—162no—
1390D4—162no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—21no—
1417C2×C4—24no—
1418C2×C4—21no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—21no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—24no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—24no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—24no—
1449C2×C4—24no—
1450C2×C4—24no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—48no—
1455C2×C4—48no—
1456C2×C4—48no—
1457C2×C4—44no—
1458C2×C4—84no—
1459C2×C4—84no—
1460C2×C4—84no—
1461C2×C4—88no—
1462C2×C4—84no—
1463C2×C4—88no—
1464C2×C4—88no—
1465C2×C4—88no—
1466C2×C4—164no—
1467C2×C4—164no—
1468C2×C4—162no—
1469C2×C4—162no—
1470C2×C4C2×H(5,𝔽2)12yes—
1471C2×C4C2×H(5,𝔽2)12yes—
1472C2×C4C2×H(5,𝔽2)12yes—
1473C2×C4C2×H(5,𝔽2)12yes—
1474C2×C4C2×2−1+414yes—
1475C2×C4C2×2−1+412yes—
1476C2×C4#58514yes—
1477C22—24no—
1478C22—24no—
1479C22—28no—
1480C22—24no—
1481C22—24no—
1482C22—42no—
1483C22—42no—
1484C22—42no—
1485C22—44no—
1486C22—42no—
1487C22—42no—
1488C22—42no—
1489C22—41no—
1490C22—42no—
1491C22—42no—
1492C22—44no—
1493C22—44no—
1494C22—42no—
1495C22—44no—
1496C22—44no—
1497C22—42no—
1498C22—42no—
1499C22—41no—
1500C22—42no—
1501C22—42no—
1502C22—41no—
1503C22—42no—
1504C22C22×H(5,𝔽2)11yescharacteristic
1505C22C22×H(5,𝔽2)11yescharacteristic
1506C22C22×2−1+411yescharacteristic
1507C22C2×#58512yes—
1508C22C2×#58512yes—
1509C4—24no—
1510C4—24no—
1511C4—22no—
1512C4—22no—
1513C4—41no—
1514C4—42no—
1515C4—44no—
1516C4—42no—
1517C4—44no—
1518C4—44no—
1519C4—42no—
1520C4—42no—
1521C4—42no—
1522C4—42no—
1523C4—42no—
1524C4—42no—
1525C4—42no—
1526C4—44no—
1527C4—42no—
1528C4—41no—
1529C4—42no—
1530C4—42no—
1531C4—42no—
1532C4—41no—
1533C4—42no—
1534C4#353614yes—
1535C2—44no—
1536C2—44no—
1537C2—81no—
1538C2—82no—
1539C2—82no—
1540C2C2×#353611yescharacteristic
1541C2#6282411yescharacteristic
1542C2#6283611yescharacteristic
1543C2#6301712yes—
1544C2#6303312yes—
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. #59417C2semidirect
2. #59093C2semidirect
3. #54901C2semidirect
4. #54390C2semidirect
5. #49259C2semidirect
6. #48551C2semidirect
7. #48496C2semidirect
8. #47894C2semidirect
9. #46072C2semidirect
10. #45625C2semidirect
11. #45425C2semidirect
12. #45271C2semidirect
13. #45268C2semidirect
14. #45137C2semidirect
15. #43647C2semidirect
16. #43369C2semidirect
17. #42645C2semidirect
18. #42424C2semidirect
19. #39853C2semidirect
20. #39752C2semidirect
21. #39248C2semidirect
22. #39008C2semidirect
23. #37396C2semidirect
24. #36566C2semidirect
25. #36534C2semidirect
26. #36303C2semidirect
27. #36149C2semidirect
28. #36031C2semidirect
29. #35737C2semidirect
30. #35534C2semidirect
31. #34968C2semidirect

Maximal subgroups

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

subgroupindex
#594172
#590932
#549012
#543902
#492592
#485512
#484962
#478942
#460722
#456252
#454252
#452712
#452682
#451372
#436472
#433692
#426452
#424242
#398532
#397522
#392482
#390082
#373962
#365662
#365342
#363032
#361492
#360312
#357372
#355342
#349682