Finite Group Databasebeta

← #7644208

Subgroups — #7644208

Order 512.

4800 conjugacy classes of subgroups.

The subgroup lattice has 1545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42892C212yesmaximal, complemented
2#42883C211yesmaximal, characteristic, complemented
3#42871C212yesmaximal, complemented
4#42855C212yesmaximal, complemented
5#42836C212yesmaximal, complemented
6#42818C211yesmaximal, characteristic, complemented
7#42796C212yesmaximal, complemented
8#42517C211yesmaximal, characteristic, complemented
9#42502C211yesmaximal, characteristic, complemented
10#42448C212yesmaximal, complemented
11#42419C212yesmaximal, complemented
12#42417C212yesmaximal, complemented
13#42130C214yesmaximal, complemented
14#41107C214yesmaximal, complemented
15#41001C212yesmaximal, complemented
16#40974C212yesmaximal, complemented
17#37533C212yesmaximal, complemented
18#37490C212yesmaximal, complemented
19#37469C214yesmaximal, complemented
20#37263C214yesmaximal, complemented
21#37226C212yesmaximal, complemented
22#37216C212yesmaximal, complemented
23#35657C212yesmaximal, complemented
24#35600C212yesmaximal, complemented
25#35587C212yesmaximal, complemented
26#35520C212yesmaximal, complemented
27#35161C212yesmaximal, complemented
28#34636C211yesmaximal, characteristic, complemented
29#34609C211yesmaximal, characteristic, complemented
30#34294C212yesmaximal, complemented
31C4×#536C211yesmaximal, characteristic, complemented
32C2×#548C2212yes—
33C2×#536C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C2×#520C2212yes—
37C2×C4×#41C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2865C2214yes—
40#2860C2214yes—
41#2841C2212yes—
42#2839C2214yes—
43#2837C2214yes—
44#2835C2212yes—
45#2829C2214yes—
46#2829C2214yes—
47#2826C2214yes—
48#2824C2212yes—
49#2815C2212yes—
50#2813C2214yes—
51#2809C2212yes—
52#2808C2214yes—
53#2807C2214yes—
54#2806C2214yes—
55#2803C2214yes—
56#2803C2214yes—
57#2799C2212yes—
58#2792C2214yes—
59#2788C2214yes—
60#2785C2212yes—
61#2782C2212yes—
62#2782C2212yes—
63#2780C2214yes—
64#2779C2214yes—
65#2773C2214yes—
66#2769C2212yes—
67#2756C2214yes—
68#2751C2214yes—
69#2733C2214yes—
70#2733C2212yes—
71#2731C2214yes—
72#2730C2214yes—
73#2730C2214yes—
74#2729C2214yes—
75#2728C2212yes—
76#2727C2214yes—
77#2721C2214yes—
78#2720C2214yes—
79#2718C2214yes—
80#2718C2214yes—
81#2718C2214yes—
82#2714C2214yes—
83#2714C2214yes—
84#2695C2214yes—
85#2689C2214yes—
86#2682C2214yes—
87#2667C2214yes—
88#2663C2214yes—
89#2661C2214yes—
90#2661C2214yes—
91#2652C2214yes—
92#2652C2214yes—
93#2650C2214yes—
94#2650C2214yes—
95#2649C2214yes—
96#2648C2214yes—
97#2648C2214yes—
98#2648C2214yes—
99#2638C2211yescharacteristic
100#2638C2211yescharacteristic
101#2637C2212yes—
102#2636C2214yes—
103#2636C2212yes—
104#2635C2214yes—
105#2635C2212yes—
106#2635C2212yes—
107#2635C2211yescharacteristic
108#2635C2211yescharacteristic
109#2635C2214yes—
110#2634C2211yescharacteristic
111#2633C2214yes—
112#2633C2211yescharacteristic
113#2632C2212yes—
114#2632C2211yescharacteristic
115#2631C2211yescharacteristic
116#2631C2212yes—
117#2630C2214yes—
118#2630C2214yes—
119#2630C2212yes—
120#2630C2212yes—
121#2628C2211yescharacteristic
122#2628C2211yescharacteristic
123#2624C2212yes—
124#2619C2211yescharacteristic
125#2619C2211yescharacteristic
126#2615C2212yes—
127#2607C2212yes—
128#2602C2214yes—
129#2600C2212yes—
130#2600C2214yes—
131#2597C2214yes—
132#2587C2214yes—
133#2582C2212yes—
134#2580C2212yes—
135#2579C2214yes—
136#2578C2214yes—
137#2577C2214yes—
138#2575C2214yes—
139#2573C2214yes—
140#2571C2212yes—
141#2565C2212yes—
142#2562C2212yes—
143#2559C2214yes—
144#2558C2214yes—
145#2538C2212yes—
146#2537C2212yes—
147#2536C2212yes—
148#2533C2214yes—
149#2533C2214yes—
150#2530C2214yes—
151#2529C2214yes—
152#2529C2214yes—
153#2526C2214yes—
154#2526C2214yes—
155#2526C2214yes—
156#2525C2214yes—
157#2519C2214yes—
158#2516C2214yes—
159#2515C2214yes—
160#2512C2212yes—
161#2512C2212yes—
162#2509C2212yes—
163#2506C2212yes—
164#2500C2212yes—
165#2497C2212yes—
166#2497C2212yes—
167#2496C2212yes—
168#2495C2212yes—
169#2490C2212yes—
170#2490C2212yes—
171#2487C2212yes—
172#2486C2212yes—
173#2485C2212yes—
174#2479C2214yes—
175#2477C2214yes—
176#2476C2214yes—
177#2474C2214yes—
178#2473C2214yes—
179#2468C2214yes—
180#2468C2214yes—
181#2467C2214yes—
182#2466C2214yes—
183#2464C2214yes—
184#2464C2214yes—
185#2463C2212yes—
186#2461C2214yes—
187#2459C2214yes—
188#2456C2214yes—
189#2455C2212yes—
190#2455C2214yes—
191#2454C2214yes—
192#2453C2212yes—
193#2451C2212yes—
194#2448C2212yes—
195#2445C2212yes—
196#2443C2214yes—
197#2441C2212yes—
198#2440C2212yes—
199#2431C2212yes—
200#2426C2212yes—
201#2426C2212yes—
202#2423C2212yes—
203#2422C2212yes—
204#2421C2212yes—
205#2421C2212yes—
206#2416C2212yes—
207#2414C2212yes—
208#2407C2214yes—
209#2407C2212yes—
210#2407C2212yes—
211#2407C2212yes—
212#2406C2214yes—
213#2398C2212yes—
214#2397C2212yes—
215#2396C2211yescharacteristic
216#2396C2211yescharacteristic
217#2395C2212yes—
218#2392C2211yescharacteristic
219#2392C2211yescharacteristic
220#2388C2212yes—
221#2388C2212yes—
222#2388C2212yes—
223#2367C2212yes—
224#2367C2214yes—
225#2361C2212yes—
226#2361C2214yes—
227#2360C2212yes—
228#2360C2214yes—
229Q8×C4⋊C4C2212yes—
230D4×C4⋊C4C2212yes—
231D4×C4⋊C4C2214yes—
232#2341C2212yes—
233Q8×C22⋊C4C2212yes—
234#2330C2212yes—
235#2327C2212yes—
236#2326C2212yes—
237#2326C2212yes—
238#2326C2214yes—
239#2324C2212yes—
240#2323C2212yes—
241#2323C2212yes—
242#2323C2212yes—
243#2323C2214yes—
244#2322C2212yes—
245#2322C2212yes—
246#2319C2212yes—
247#2317C2211yescharacteristic
248#2314C2212yes—
249#2311C2211yescharacteristic
250#2310C2211yescharacteristic
251C4×C4⋊Q8C2212yes—
252C4×#124C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2212yes—
256C4×#123C2212yes—
257C4×#121C2212yes—
258C4×#121C2212yes—
259C4×#121C2214yes—
260#2290C2212yes—
261#2290C2212yes—
262#2290C2214yes—
263#2283C2211yescharacteristic
264#2283C2211yescharacteristic
265#2276C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269C22×#41C2312yes—
270C23×Q8C2311yescharacteristic
271#548—216no—
272#536—28no—
273#532—44no—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×#127C2311yescharacteristic
277#529—44no—
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125C2312yes—
283C2×#125C2311yescharacteristic
284C2×#125C2314yes—
285C2×#124C2312yes—
286C2×#124C2314yes—
287C2×#124C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2312yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2311yescharacteristic
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2311yescharacteristic
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311#520—48no—
312C4×#41—44no—
313C2×C4×Q8—44no—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×#117C2312yes—
345C2×#117C2311yescharacteristic
346C2×#117C2311yescharacteristic
347C2×#117C2311yescharacteristic
348C2×#117C2311yescharacteristic
349C2×#117C2311yescharacteristic
350C2×#117C2314yes—
351C22×C4⋊C4C2311yescharacteristic
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C42C2311yescharacteristic
356C22×C42C2311yescharacteristic
357C22×C42C2311yescharacteristic
358C22×C42C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2312yes—
375#400C2311yescharacteristic
376#400C2311yescharacteristic
377#400C2314yes—
378#399C2314yes—
379#399C2312yes—
380#399C2314yes—
381#399C2314yes—
382#399C2314yes—
383#399C2311yescharacteristic
384#399C2314yes—
385#399C2312yes—
386#399C2312yes—
387#399C2311yescharacteristic
388#399C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2312yes—
403#398C2311yescharacteristic
404#398C2311yescharacteristic
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2311yescharacteristic
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2312yes—
420#397C2312yes—
421#397C2312yes—
422#397C2311yescharacteristic
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2312yes—
431#396C2314yes—
432#396C2314yes—
433#396C2312yes—
434#396C2312yes—
435#396C2312yes—
436#396C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2312yes—
440#395C2312yes—
441#395C2311yescharacteristic
442#395C2311yescharacteristic
443#395C2312yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2312yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2312yes—
452#394C2312yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2314yes—
467#394C2312yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2314yes—
472#394C2312yes—
473#394C2311yescharacteristic
474#394C2311yescharacteristic
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#393C2311yescharacteristic
479#393C2314yes—
480#393C2312yes—
481#393C2314yes—
482#393C2312yes—
483#393C2311yescharacteristic
484#393C2312yes—
485#392C2312yes—
486#392C2314yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#392C2312yes—
492#392C2312yes—
493#392C2312yes—
494#392C2312yes—
495#392C2312yes—
496#392C2312yes—
497#392C2311yescharacteristic
498#392C2311yescharacteristic
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2312yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#390C2312yes—
515#390C2314yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2314yes—
523#390C2312yes—
524#390C2314yes—
525#390C2314yes—
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#390C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2312yes—
554#389C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2312yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2314yes—
596#388C2312yes—
597#388C2314yes—
598#388C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2312yes—
625#387C2312yes—
626#387C2314yes—
627#386C2312yes—
628#386C2312yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2312yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2312yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2312yes—
642#386C2312yes—
643#386C2314yes—
644#386C2314yes—
645#385C2312yes—
646#385C2314yes—
647#385C2312yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2312yes—
664#385C2314yes—
665#385C2312yes—
666#385C2314yes—
667#385C2312yes—
668#385C2312yes—
669#384C2312yes—
670#384C2312yes—
671#384C2312yes—
672#384C2312yes—
673#384C2314yes—
674#383C2311yescharacteristic
675#383C2311yescharacteristic
676#383C2314yes—
677#383C2312yes—
678#382C2311yescharacteristic
679#382C2312yes—
680#382C2311yescharacteristic
681#382C2314yes—
682#382C2312yes—
683#382C2312yes—
684#381C2312yes—
685#381C2312yes—
686#381C2314yes—
687#381C2314yes—
688#381C2312yes—
689#381C2311yescharacteristic
690#381C2311yescharacteristic
691#380C2312yes—
692#380C2312yes—
693#380C2312yes—
694#380C2312yes—
695#380C2312yes—
696#380C2312yes—
697#380C2314yes—
698#380C2314yes—
699#380C2314yes—
700#380C2312yes—
701#380C2314yes—
702#380C2312yes—
703#380C2312yes—
704#380C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2311yescharacteristic
719C4×C4⋊C4C2311yescharacteristic
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2314yes—
735C4×C22⋊C4C2314yes—
736#376C2312yes—
737#376C2312yes—
738#376C2314yes—
739#376C2312yes—
740C43C2312yes—
741C2×#41—28no—
742C2×#41—24no—
743C2×#41—42no—
744C2×#41—42no—
745C2×#41—44no—
746C2×#41—44no—
747C2×#41—44no—
748C2×#41—84no—
749C22×Q8—42no—
750C22×Q8—42no—
751C22×Q8#4118yescomplemented
752C22×Q8C2412yes—
753C22×Q8C2411yescharacteristic
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2412yes—
757C22×D4C2412yes—
758C22×D4C2414yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2411yescharacteristic
762C22×D4C2411yescharacteristic
763C22×D4C2411yescharacteristic
764C22×D4C2412yes—
765C22×D4C2412yes—
766C22×D4C2414yes—
767C22×D4C2411yescharacteristic
768C22×D4C2412yes—
769C22×D4C2414yes—
770C22×D4C2414yes—
771C22×D4C2412yes—
772C23×C4C2412yes—
773C23×C4C2411yescharacteristic
774C23×C4C2411yescharacteristic
775C23×C4C2411yescharacteristic
776C23×C4C2411yescharacteristic
777C23×C4C2414yes—
778C23×C4C2414yes—
779C23×C4C2411yescharacteristic
780C23×C4C2411yescharacteristic
781C23×C4C2411yescharacteristic
782C23×C4C2411yescharacteristic
783C23×C4C2411yescharacteristic
784C23×C4C2412yes—
785C23×C4C2414yes—
786C23×C4C2414yes—
787C23×C4C2412yes—
788C4⋊Q8—28no—
789C4⋊Q8—42no—
790#127—42no—
791#126—44no—
792#126—84no—
793#126—84no—
794#126—84no—
795#125—44no—
796#125—42no—
797#125—84no—
798#124—28no—
799#124—28no—
800#124—216no—
801#124—42no—
802#124—44no—
803#123—28no—
804#123—28no—
805#123—44no—
806#123—84no—
807#123—84no—
808#123—84no—
809C22⋊Q8—28no—
810C22⋊Q8—28no—
811C22⋊Q8—28no—
812C22⋊Q8—216no—
813C22⋊Q8—42no—
814C22⋊Q8—84no—
815#121—28no—
816#121—216no—
817#121—42no—
818#121—44no—
819#121—44no—
820#121—44no—
821#121—44no—
822#121—84no—
823#121—84no—
824C4×Q8—28no—
825C4×Q8—28no—
826C4×Q8—44no—
827C4×Q8—42no—
828C4×Q8—42no—
829C4×Q8—42no—
830C4×Q8—44no—
831C4×Q8—44no—
832C4×Q8—44no—
833C4×Q8—44no—
834C4×D4—28no—
835C4×D4—216no—
836C4×D4—28no—
837C4×D4—48no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—42no—
841C4×D4—42no—
842C4×D4—42no—
843C4×D4—42no—
844C4×D4—42no—
845C4×D4—42no—
846C4×D4—42no—
847C4×D4—44no—
848C4×D4—44no—
849C4×D4—48no—
850C4×D4—84no—
851C4×D4—84no—
852C4×D4—84no—
853C4×D4—84no—
854#117—24no—
855#117—28no—
856#117—42no—
857#117—42no—
858#117—42no—
859#117—48no—
860#117—42no—
861C2×C4⋊C4—42no—
862C2×C4⋊C4—44no—
863C2×C4⋊C4—48no—
864C2×C4⋊C4—44no—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2411yescharacteristic
933C2×C22⋊C4C2411yescharacteristic
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2411yescharacteristic
936C2×C22⋊C4C2411yescharacteristic
937C2×C22⋊C4C2411yescharacteristic
938C2×C22⋊C4C2411yescharacteristic
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C42—24no—
980C2×C42—24no—
981C2×C42—24no—
982C2×C42—44no—
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2412yes—
987C2×C42C2414yes—
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2414yes—
996C2×C42C2412yes—
997C2×C42C2411yescharacteristic
998C2×C42C2414yes—
999C2×C42C2412yes—
1000C2×C42C2414yes—
1001C2×C42C2414yes—
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2411yescharacteristic
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2411yescharacteristic
1050#95C2411yescharacteristic
1051#95C2411yescharacteristic
1052#95C2411yescharacteristic
1053#95C2414yes—
1054#95C2414yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068C24C2511yescharacteristic
1069C24C2511yescharacteristic
1070C24C2512yes—
1071C24C2514yes—
1072C24C2511yescharacteristic
1073#41—416no—
1074#41—432no—
1075#41—816no—
1076C2×Q8—22no—
1077C2×Q8—24no—
1078C2×Q8—24no—
1079C2×Q8—42no—
1080C2×Q8—41no—
1081C2×Q8—42no—
1082C2×Q8—41no—
1083C2×Q8—41no—
1084C2×Q8—44no—
1085C2×Q8—42no—
1086C2×Q8—42no—
1087C2×Q8—416no—
1088C2×Q8C2×#4118yes—
1089C2×Q8C2×#4118yes—
1090C2×D4—24no—
1091C2×D4—28no—
1092C2×D4—22no—
1093C2×D4—22no—
1094C2×D4—28no—
1095C2×D4—24no—
1096C2×D4—22no—
1097C2×D4—24no—
1098C2×D4—24no—
1099C2×D4—41no—
1100C2×D4—44no—
1101C2×D4—41no—
1102C2×D4—41no—
1103C2×D4—44no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—44no—
1107C2×D4—41no—
1108C2×D4—44no—
1109C2×D4—41no—
1110C2×D4—41no—
1111C2×D4—42no—
1112C2×D4—41no—
1113C2×D4—42no—
1114C2×D4—42no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—42no—
1119C2×D4—42no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—42no—
1125C2×D4—42no—
1126C2×D4—44no—
1127C2×D4—42no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—28no—
1135C22×C4—24no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—22no—
1142C22×C4—24no—
1143C22×C4—22no—
1144C22×C4—24no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—28no—
1151C22×C4—42no—
1152C22×C4—44no—
1153C22×C4—42no—
1154C22×C4—42no—
1155C22×C4—44no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—42no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—42no—
1164C22×C4—42no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4C2×#4114yes—
1172C22×C4C2×#4118yes—
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2514yes—
1181C22×C4C2514yes—
1182C22×C4C2511yescharacteristic
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2514yes—
1188C22×C4C2512yes—
1189C22×C4C2514yes—
1190C22×C4C2514yes—
1191C22×C4C2512yes—
1192C22×C4C2511yescharacteristic
1193C22×C4C2511yescharacteristic
1194C22×C4C2511yescharacteristic
1195C22×C4C2514yes—
1196C22×C4C2511yescharacteristic
1197C22×C4C2511yescharacteristic
1198C22×C4C2511yescharacteristic
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—28no—
1202C4⋊C4—28no—
1203C4⋊C4—24no—
1204C4⋊C4—28no—
1205C4⋊C4—28no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—41no—
1231C4⋊C4—42no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—41no—
1238C4⋊C4—42no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4—42no—
1253C4⋊C4—44no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—24no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—24no—
1264C22⋊C4—24no—
1265C22⋊C4—28no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—42no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—44no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—42no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
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—42no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—42no—
1313C42—24no—
1314C42—28no—
1315C42—24no—
1316C42—22no—
1317C42—22no—
1318C42—22no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—22no—
1324C42—22no—
1325C42—28no—
1326C42—24no—
1327C42—24no—
1328C42—44no—
1329C42—44no—
1330C42—42no—
1331C42—44no—
1332C42—44no—
1333C42—44no—
1334C42—44no—
1335C42—44no—
1336C42—44no—
1337C42H(5,𝔽2)14yes—
1338C23—21no—
1339C23—21no—
1340C23—22no—
1341C23—22no—
1342C23—21no—
1343C23—21no—
1344C23—24no—
1345C23—22no—
1346C23—22no—
1347C23—24no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—24no—
1352C23—22no—
1353C23—21no—
1354C23—22no—
1355C23—24no—
1356C23—22no—
1357C23—24no—
1358C23—22no—
1359C23—22no—
1360C23—24no—
1361C23—22no—
1362C23—22no—
1363C23—22no—
1364C23—24no—
1365C23—22no—
1366C23C22×#4112yes—
1367C23C2611yescharacteristic
1368Q8—216no—
1369Q8—48no—
1370Q8—44no—
1371Q8—82no—
1372Q8—84no—
1373D4—44no—
1374D4—416no—
1375D4—416no—
1376D4—48no—
1377D4—44no—
1378D4—44no—
1379D4—48no—
1380D4—84no—
1381D4—88no—
1382D4—84no—
1383D4—84no—
1384D4—82no—
1385D4—84no—
1386D4—88no—
1387D4—164no—
1388C2×C4—21no—
1389C2×C4—24no—
1390C2×C4—21no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—28no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—21no—
1420C2×C4—22no—
1421C2×C4—21no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—24no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—24no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—24no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—48no—
1453C2×C4—44no—
1454C2×C4—416no—
1455C2×C4—44no—
1456C2×C4—48no—
1457C2×C4—44no—
1458C2×C4—44no—
1459C2×C4—82no—
1460C2×C4—82no—
1461C2×C4—82no—
1462C2×C4—82no—
1463C2×C4—88no—
1464C2×C4—84no—
1465C2×C4—164no—
1466C2×C4—164no—
1467C2×C4C22×#4112yes—
1468C2×C4C22×#4118yes—
1469C2×C4C22×#4112yes—
1470C2×C4C2×H(5,𝔽2)12yes—
1471C2×C4C2×H(5,𝔽2)12yes—
1472C2×C4C2×H(5,𝔽2)12yes—
1473C2×C4#58512yes—
1474C22—24no—
1475C22—22no—
1476C22—41no—
1477C22—42no—
1478C22—41no—
1479C22—44no—
1480C22—42no—
1481C22—42no—
1482C22—42no—
1483C22—42no—
1484C22—44no—
1485C22—41no—
1486C22—44no—
1487C22—41no—
1488C22—42no—
1489C22—42no—
1490C22—42no—
1491C22—44no—
1492C22—42no—
1493C22—44no—
1494C22—42no—
1495C22—41no—
1496C22—41no—
1497C22—42no—
1498C22—44no—
1499C22—44no—
1500C22—42no—
1501C22—41no—
1502C22—41no—
1503C22C23×#4111yescharacteristic
1504C22C22×H(5,𝔽2)11yescharacteristic
1505C22C2×#58511yescharacteristic
1506C22H(7,𝔽2)12yes—
1507C222−1+612yes—
1508C4—22no—
1509C4—22no—
1510C4—22no—
1511C4—28no—
1512C4—42no—
1513C4—44no—
1514C4—44no—
1515C4—42no—
1516C4—41no—
1517C4—41no—
1518C4—41no—
1519C4—44no—
1520C4—44no—
1521C4—42no—
1522C4—42no—
1523C4—42no—
1524C4—44no—
1525C4—44no—
1526C4—41no—
1527C4—41no—
1528C4—41no—
1529C4—42no—
1530C4—42no—
1531C4—41no—
1532C4—41no—
1533C4#345914yes—
1534C2—42no—
1535C2—84no—
1536C2—82no—
1537C2—81no—
1538C2—81no—
1539C2C2×#345911yescharacteristic
1540C2#6285112yes—
1541C2#6287411yescharacteristic
1542C2#6288412yes—
1543C2#6288611yescharacteristic
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. #42892C2semidirect
2. #42883C2semidirect
3. #42871C2semidirect
4. #42855C2semidirect
5. #42836C2semidirect
6. #42818C2semidirect
7. #42796C2semidirect
8. #42517C2semidirect
9. #42502C2semidirect
10. #42448C2semidirect
11. #42419C2semidirect
12. #42417C2semidirect
13. #42130C2semidirect
14. #41107C2semidirect
15. #41001C2semidirect
16. #40974C2semidirect
17. #37533C2semidirect
18. #37490C2semidirect
19. #37469C2semidirect
20. #37263C2semidirect
21. #37226C2semidirect
22. #37216C2semidirect
23. #35657C2semidirect
24. #35600C2semidirect
25. #35587C2semidirect
26. #35520C2semidirect
27. #35161C2semidirect
28. #34636C2semidirect
29. #34609C2semidirect
30. #34294C2semidirect
31. C4×#536C2semidirect
751. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#428922
#428832
#428712
#428552
#428362
#428182
#427962
#425172
#425022
#424482
#424192
#424172
#421302
#411072
#410012
#409742
#375332
#374902
#374692
#372632
#372262
#372162
#356572
#356002
#355872
#355202
#351612
#346362
#346092
#342942
C4×#5362