Finite Group Databasebeta

← #8094625

Subgroups — #8094625

Order 512.

4306 conjugacy classes of subgroups.

The subgroup lattice has 1479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53136C212yesmaximal, complemented
2#53097C212yesmaximal, complemented
3#53054C212yesmaximal, complemented
4#53011C212yesmaximal, complemented
5#52908C212yesmaximal, complemented
6#52901C212yesmaximal, complemented
7#52870C214yesmaximal, complemented
8#52763C212yesmaximal, complemented
9#52760C212yesmaximal, complemented
10#52755C214yesmaximal, complemented
11#46346C211yesmaximal, characteristic, complemented
12#46342C212yesmaximal, complemented
13#46331C211yesmaximal, characteristic, complemented
14#46316C212yesmaximal, complemented
15#46313C212yesmaximal, complemented
16#46275C212yesmaximal
17#46269C212yesmaximal, complemented
18#46196C211yesmaximal, characteristic, complemented
19#46055C212yesmaximal, complemented
20#46004C211yesmaximal, characteristic, complemented
21#45909C214yesmaximal, complemented
22#45775C214yesmaximal, complemented
23#35665C212yesmaximal, complemented
24#35665C212yesmaximal, complemented
25#35663C212yesmaximal, complemented
26#35314C212yesmaximal, complemented
27#35228C212yesmaximal, complemented
28#35162C212yesmaximal, complemented
29#34979C211yesmaximal, characteristic, complemented
30#34947C211yesmaximal, characteristic, complemented
31#34910C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#519C2212yes—
36C2×C4×#41C2211yescharacteristic
37#2865C2214yes—
38#2864C2212yes—
39#2863C2212yes—
40#2863C2212yes—
41#2863C2214yes—
42#2862C2212yes—
43#2855C2214yes—
44#2853C2214yes—
45#2844C2212yes—
46#2843C2214yes—
47#2843C2212yes—
48#2841C2214yes—
49#2838C2214yes—
50#2838C2214yes—
51#2838C2214yes—
52#2836C2214yes—
53#2833C2212yes—
54#2832C2214yes—
55#2832C2214yes—
56#2831C2214yes—
57#2831C2214yes—
58#2831C2214yes—
59#2830C2214yes—
60#2830C2214yes—
61#2830C2214yes—
62#2830C2212yes—
63#2829C2214yes—
64#2827C2214yes—
65#2827C2214yes—
66#2814C2214yes—
67#2811C2212yes—
68#2809C2212yes—
69#2808C2214yes—
70#2806C2214yes—
71#2804C2212yes—
72#2799C2212yes—
73#2798C2214yes—
74#2797C2214yes—
75#2796C2214yes—
76#2794C2212yes—
77#2793C2214yes—
78#2792C2214yes—
79#2792C2214yes—
80#2791C2214yes—
81#2790C2214yes—
82#2790C2214yes—
83#2789C2212yes—
84#2783C2214yes—
85#2774C2214yes—
86#2772C2214yes—
87#2766C2214yes—
88#2763C2214yes—
89#2763C2214yes—
90#2761C2214yes—
91#2759C2214yes—
92#2758C2214yes—
93#2757C2214yes—
94#2757C2214yes—
95#2755C2214yes—
96#2755C2214yes—
97#2755C2214yes—
98#2749C2214yes—
99#2746C2214yes—
100#2744C2214yes—
101#2739C2214yes—
102#2737C2214yes—
103#2737C2214yes—
104#2737C2214yes—
105#2734C2212yes—
106#2731C2212yes—
107#2710C2214yes—
108#2709C2214yes—
109#2700C2214yes—
110#2700C2214yes—
111#2655C2214yes—
112#2653C2214yes—
113#2652C2214yes—
114#2650C2214yes—
115#2628C2212yes—
116#2625C2212yes—
117#2625C2212yes—
118#2621C2212yes—
119#2611C2212yes—
120#2611C2212yes—
121#2609C2214yes—
122#2609C2214yes—
123#2602C2212yes—
124#2602C2212yes—
125#2601C2212yes—
126#2601C2212yes—
127#2599C2214yes—
128#2599C2214yes—
129#2599C2214yes—
130#2599C2214yes—
131#2582C2212yes—
132#2581C2212yes—
133#2581C2214yes—
134#2581C2214yes—
135#2568C2211yescharacteristic
136#2568C2211yescharacteristic
137#2567C2211yescharacteristic
138#2566C2212yes—
139#2566C2211yescharacteristic
140#2565C2211yescharacteristic
141#2565C2212yes—
142#2564C2212yes—
143#2564C2212yes—
144#2563C2211yescharacteristic
145#2547C2211yescharacteristic
146#2546C2211yescharacteristic
147#2545C2211yescharacteristic
148#2544C2211yescharacteristic
149#2542C2211yescharacteristic
150#2542C2211yescharacteristic
151#2538C2212yes—
152#2536C2212yes—
153#2532C2214yes—
154#2528C2214yes—
155#2525C2214yes—
156#2524C2214yes—
157#2524C2214yes—
158#2523C2214yes—
159#2523C2214yes—
160#2523C2214yes—
161#2520C2214yes—
162#2520C2214yes—
163#2520C2214yes—
164#2518C2214yes—
165#2517C2214yes—
166#2517C2214yes—
167#2514C2212yes—
168#2511C2212yes—
169#2509C2212yes—
170#2507C2212yes—
171#2503C2212yes—
172#2500C2211yescharacteristic
173#2499C2212yes—
174#2499C2211yescharacteristic
175#2499C2212yes—
176#2495C2212yes—
177#2494C2212yes—
178#2493C2214yes—
179#2492C2212yes—
180#2492C2212yes—
181#2488C2214yes—
182#2486C2212yes—
183#2485C2212yes—
184#2485C2212yes—
185#2485C2212yes—
186#2478C2214yes—
187#2477C2214yes—
188#2477C2214yes—
189#2476C2214yes—
190#2475C2214yes—
191#2475C2214yes—
192#2474C2214yes—
193#2470C2214yes—
194#2469C2214yes—
195#2465C2214yes—
196#2465C2214yes—
197#2465C2214yes—
198#2462C2214yes—
199#2462C2214yes—
200#2462C2214yes—
201#2458C2214yes—
202#2451C2212yes—
203#2451C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2440C2212yes—
207#2439C2212yes—
208#2439C2212yes—
209#2439C2212yes—
210#2434C2212yes—
211#2434C2212yes—
212#2432C2211yescharacteristic
213#2432C2212yes—
214#2431C2211yescharacteristic
215#2429C2212yes—
216#2429C2212yes—
217#2421C2212yes—
218#2421C2212yes—
219#2417C2212yes—
220#2417C2212yes—
221#2417C2212yes—
222#2415C2212yes—
223#2415C2212yes—
224#2415C2212yes—
225#2415C2212yes—
226#2415C2212yes—
227#2409C2212yes—
228#2409C2212yes—
229#2409C2212yes—
230#2409C2212yes—
231#2396C2212yes—
232#2396C2212yes—
233#2395C2212yes—
234#2395C2212yes—
235#2392C2212yes—
236#2392C2212yes—
237#2381C2212yes—
238#2381C2212yes—
239#2381C2212yes—
240#2379C2212yes—
241#2378C2214yes—
242#2376C2214yes—
243#2331C2212yes—
244#2327C2212yes—
245#2323C2212yes—
246#2323C2212yes—
247#2320C2212yes—
248#2320C2212yes—
249#2314C2212yes—
250C4×C4⋊Q8C2211yescharacteristic
251C4×C4⋊Q8C2212yes—
252C4×#127C2211yescharacteristic
253C4×#124C2212yes—
254C4×#124C2211yescharacteristic
255C4×#124C2211yescharacteristic
256C4×C22⋊Q8C2212yes—
257C4×C22⋊Q8C2212yes—
258C4×C22⋊Q8C2212yes—
259C4×C22⋊Q8C2212yes—
260#2297C2212yes—
261#2290C2212yes—
262#2290C2212yes—
263#2285C2212yes—
264C4×#117C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C23×Q8C2312yes—
269#533—44no—
270#533—44no—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×#127C2311yescharacteristic
280#529—44no—
281C2×#126C2312yes—
282C2×#125C2311yescharacteristic
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#124C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#124C2311yescharacteristic
288C2×#124C2312yes—
289C2×#123C2314yes—
290C2×#123C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2311yescharacteristic
302C2×C22⋊Q8C2312yes—
303C2×#121C2311yescharacteristic
304#519—48no—
305C4×#41—44no—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342C22×C42C2312yes—
343#401C2314yes—
344#401C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#399C2312yes—
368#399C2312yes—
369#399C2312yes—
370#399C2314yes—
371#399C2312yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#396C2314yes—
422#396C2314yes—
423#396C2312yes—
424#396C2312yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2312yes—
433#396C2314yes—
434#396C2312yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#394C2312yes—
451#394C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2312yes—
459#394C2314yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#393C2312yes—
466#393C2312yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#392C2312yes—
478#392C2312yes—
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2312yes—
482#391C2311yescharacteristic
483#391C2312yes—
484#391C2312yes—
485#391C2311yescharacteristic
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2311yescharacteristic
511#391C2312yes—
512#390C2311yescharacteristic
513#390C2312yes—
514#390C2312yes—
515#390C2311yescharacteristic
516#390C2312yes—
517#390C2312yes—
518#390C2311yescharacteristic
519#390C2311yescharacteristic
520#390C2314yes—
521#390C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
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#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2312yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2312yes—
642#386C2314yes—
643#386C2312yes—
644#386C2312yes—
645#386C2312yes—
646#386C2314yes—
647#386C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2312yes—
651#385C2312yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2312yes—
659#385C2314yes—
660#385C2314yes—
661#385C2312yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#384C2311yescharacteristic
666#384C2311yescharacteristic
667#384C2312yes—
668#384C2312yes—
669#384C2312yes—
670#384C2312yes—
671#383C2314yes—
672#383C2314yes—
673#383C2314yes—
674#383C2314yes—
675#383C2314yes—
676#383C2314yes—
677#382C2312yes—
678#382C2311yescharacteristic
679#382C2312yes—
680#382C2311yescharacteristic
681#382C2312yes—
682#382C2312yes—
683#382C2314yes—
684#382C2314yes—
685#382C2312yes—
686#382C2312yes—
687#382C2314yes—
688#382C2314yes—
689#381C2314yes—
690#381C2314yes—
691#381C2314yes—
692#380C2312yes—
693#380C2312yes—
694#380C2314yes—
695#380C2314yes—
696#380C2312yes—
697#380C2312yes—
698#380C2312yes—
699#380C2312yes—
700#380C2314yes—
701#380C2312yes—
702#380C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2311yescharacteristic
711C4×C4⋊C4C2311yescharacteristic
712C4×C4⋊C4C2311yescharacteristic
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2314yes—
719C4×C4⋊C4C2311yescharacteristic
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2311yescharacteristic
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2311yescharacteristic
733#376C2312yes—
734#376C2312yes—
735C2×#95C2312yes—
736C43C2311yescharacteristic
737C43C2312yes—
738C43C2311yescharacteristic
739C2×#41—24no—
740C2×#41—42no—
741C2×#41—42no—
742C22×Q8—44no—
743C22×Q8—44no—
744C22×Q8—44no—
745C22×Q8C2412yes—
746C22×Q8C2412yes—
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2414yes—
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×Q8C2411yescharacteristic
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2411yescharacteristic
756C22×D4C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2414yes—
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2414yes—
772C4⋊Q8—28no—
773C4⋊Q8—24no—
774C4⋊Q8—44no—
775C4⋊Q8—42no—
776C4⋊Q8—42no—
777C4⋊Q8—44no—
778C4⋊Q8—42no—
779C4⋊Q8—42no—
780#127—42no—
781#126—44no—
782#125—42no—
783#125—44no—
784#125—44no—
785#124—24no—
786#124—42no—
787#124—42no—
788#124—44no—
789#123—44no—
790#123—48no—
791C22⋊Q8—48no—
792C22⋊Q8—42no—
793C22⋊Q8—44no—
794C22⋊Q8—44no—
795C22⋊Q8—44no—
796C22⋊Q8—44no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800C22⋊Q8—44no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803#121—42no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—42no—
807C4×Q8—42no—
808C4×Q8—42no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×Q8—48no—
812C4×Q8—48no—
813C4×Q8—44no—
814C4×Q8—44no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—42no—
818C4×D4—42no—
819C4×D4—42no—
820C4×D4—42no—
821C4×D4—42no—
822C4×D4—42no—
823C4×D4—42no—
824C4×D4—44no—
825#117—28no—
826#117—44no—
827#117—42no—
828#117—42no—
829#117—42no—
830#117—44no—
831#117—44no—
832#117—48no—
833#117—48no—
834#117—44no—
835#117—44no—
836C2×C4⋊C4—44no—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C42—24no—
943C2×C42—24no—
944C2×C42—24no—
945C2×C42—44no—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2411yescharacteristic
968C2×C42C2412yes—
969C2×C42C2411yescharacteristic
970C2×C42C2414yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2411yescharacteristic
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049C24C2512yes—
1050C24C2511yescharacteristic
1051C24C2511yescharacteristic
1052C24C2511yescharacteristic
1053#41—416no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—22no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—24no—
1061C2×Q8—24no—
1062C2×Q8—44no—
1063C2×Q8—41no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×Q8—41no—
1067C2×Q8—41no—
1068C2×Q8—42no—
1069C2×Q8—42no—
1070C2×Q8—41no—
1071C2×Q8—42no—
1072C2×Q8—44no—
1073C2×Q8—44no—
1074C2×Q8—44no—
1075C2×Q8—44no—
1076C2×Q8—432no—
1077C2×Q82−1+414yes—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—24no—
1081C2×D4—22no—
1082C2×D4—22no—
1083C2×D4—22no—
1084C2×D4—22no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—42no—
1090C2×D4—41no—
1091C2×D4—42no—
1092C2×D4—42no—
1093C2×D4—41no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—28no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—22no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—24no—
1110C22×C4—22no—
1111C22×C4—22no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—22no—
1118C22×C4—22no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—41no—
1124C22×C4—41no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2514yes—
1137C22×C4C2514yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2514yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—28no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—41no—
1183C4⋊C4—41no—
1184C4⋊C4—41no—
1185C4⋊C4—41no—
1186C4⋊C4—41no—
1187C4⋊C4—41no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—41no—
1197C4⋊C4—42no—
1198C4⋊C4—41no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C22⋊C4—24no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C42—22no—
1262C42—22no—
1263C42—22no—
1264C42—22no—
1265C42—22no—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—24no—
1271C42—28no—
1272C42—28no—
1273C42—22no—
1274C42—24no—
1275C42—22no—
1276C42—24no—
1277C42—24no—
1278C42—44no—
1279C42—42no—
1280C42—42no—
1281C42—44no—
1282C42—42no—
1283C42—42no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42—41no—
1289C42—42no—
1290C42—41no—
1291C42H(5,𝔽2)14yes—
1292C23—21no—
1293C23—21no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—21no—
1298C23—21no—
1299C23—22no—
1300C23—21no—
1301C23—21no—
1302C23—22no—
1303C23—22no—
1304C23—21no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—21no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23#58512yes—
1314C23C2611yescharacteristic
1315Q8—44no—
1316Q8—416no—
1317Q8—48no—
1318Q8—48no—
1319Q8—82no—
1320Q8—84no—
1321Q8—84no—
1322Q8—164no—
1323D4—44no—
1324D4—44no—
1325D4—44no—
1326D4—82no—
1327D4—84no—
1328D4—84no—
1329D4—84no—
1330C2×C4—28no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—44no—
1398C2×C4—44no—
1399C2×C4—44no—
1400C2×C4—416no—
1401C2×C4—44no—
1402C2×C4—44no—
1403C2×C4—44no—
1404C2×C4—48no—
1405C2×C4—82no—
1406C2×C4—82no—
1407C2×C4—88no—
1408C2×C4C2×H(5,𝔽2)12yes—
1409C2×C4C2×H(5,𝔽2)12yes—
1410C2×C4C2×H(5,𝔽2)12yes—
1411C2×C4C2×2−1+412yes—
1412C2×C4C2×2−1+412yes—
1413C2×C4C2×2−1+412yes—
1414C2×C4#58514yes—
1415C22—22no—
1416C22—24no—
1417C22—41no—
1418C22—41no—
1419C22—42no—
1420C22—41no—
1421C22—41no—
1422C22—42no—
1423C22—41no—
1424C22—41no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—41no—
1432C22—41no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22C22×H(5,𝔽2)11yescharacteristic
1438C22C22×2−1+411yescharacteristic
1439C22C2×#58511yescharacteristic
1440C22C2×#58512yes—
1441C222−1+612yes—
1442C4—22no—
1443C4—22no—
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—42no—
1448C4—44no—
1449C4—41no—
1450C4—41no—
1451C4—41no—
1452C4—42no—
1453C4—44no—
1454C4—44no—
1455C4—44no—
1456C4—42no—
1457C4—44no—
1458C4—42no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—44no—
1463C4—44no—
1464C4—42no—
1465C4—42no—
1466C4—42no—
1467C4—44no—
1468C4#352914yes—
1469C2—42no—
1470C2—81no—
1471C2—81no—
1472C2—82no—
1473C2C2×#352911yescharacteristic
1474C2#6281911yescharacteristic
1475C2#6288611yescharacteristic
1476C2#6294012yes—
1477C2#6295312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2431C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53136C2semidirect
2. #53097C2semidirect
3. #53054C2semidirect
4. #53011C2semidirect
5. #52908C2semidirect
6. #52901C2semidirect
7. #52870C2semidirect
8. #52763C2semidirect
9. #52760C2semidirect
10. #52755C2semidirect
11. #46346C2semidirect
12. #46342C2semidirect
13. #46331C2semidirect
14. #46316C2semidirect
15. #46313C2semidirect
17. #46269C2semidirect
18. #46196C2semidirect
19. #46055C2semidirect
20. #46004C2semidirect
21. #45909C2semidirect
22. #45775C2semidirect
23. #35665C2semidirect
24. #35665C2semidirect
25. #35663C2semidirect
26. #35314C2semidirect
27. #35228C2semidirect
28. #35162C2semidirect
29. #34979C2semidirect
30. #34947C2semidirect

Maximal subgroups

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

subgroupindex
#531362
#530972
#530542
#530112
#529082
#529012
#528702
#527632
#527602
#527552
#463462
#463422
#463312
#463162
#463132
#462752
#462692
#461962
#460552
#460042
#459092
#457752
#356652
#356632
#353142
#352282
#351622
#349792
#349472
#349102