Finite Group Databasebeta

← #7651858

Subgroups — #7651858

Order 512.

4432 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42971C211yesmaximal, characteristic
2#42933C211yesmaximal, characteristic, complemented
3#42734C212yesmaximal, complemented
4#42686C211yesmaximal, characteristic, complemented
5#42614C212yesmaximal, complemented
6#42517C211yesmaximal, characteristic, complemented
7#41826C214yesmaximal, complemented
8#41661C214yesmaximal, complemented
9#41308C214yesmaximal, complemented
10#41139C214yesmaximal, complemented
11#40251C214yesmaximal, complemented
12#40121C212yesmaximal, complemented
13#39891C212yesmaximal, complemented
14#39571C214yesmaximal, complemented
15#39011C212yesmaximal, complemented
16#38939C212yesmaximal, complemented
17#38300C214yesmaximal, complemented
18#38284C214yesmaximal, complemented
19#35602C212yesmaximal, complemented
20#35589C212yesmaximal, complemented
21#35546C212yesmaximal, complemented
22#35296C211yesmaximal, characteristic, complemented
23#35192C212yesmaximal, complemented
24#34879C211yesmaximal, characteristic, complemented
25#34797C212yesmaximal, complemented
26#34306C212yesmaximal, complemented
27#34215C211yesmaximal, characteristic, complemented
28C2×#555C2212yes—
29C2×#533C2211yescharacteristic
30#2864C2214yes—
31#2864C2211yescharacteristic
32#2862C2214yes—
33#2858C2211yescharacteristic
34#2854C2212yes—
35#2843C2212yes—
36#2831C2214yes—
37#2829C2214yes—
38#2824C2212yes—
39#2824C2212yes—
40#2819C2212yes—
41#2807C2212yes—
42#2795C2212yes—
43#2794C2212yes—
44#2785C2212yes—
45#2785C2214yes—
46#2783C2214yes—
47#2783C2214yes—
48#2782C2212yes—
49#2781C2214yes—
50#2775C2214yes—
51#2775C2214yes—
52#2766C2214yes—
53#2762C2214yes—
54#2761C2214yes—
55#2754C2214yes—
56#2754C2214yes—
57#2744C2214yes—
58#2737C2214yes—
59#2731C2214yes—
60#2731C2214yes—
61#2729C2214yes—
62#2718C2214yes—
63#2716C2214yes—
64#2712C2214yes—
65#2712C2212yes—
66#2705C2214yes—
67#2700C2214yes—
68#2689C2214yes—
69#2689C2214yes—
70#2686C2214yes—
71#2681C2214yes—
72#2677C2212yes—
73#2676C2214yes—
74#2675C2212yes—
75#2674C2214yes—
76#2672C2214yes—
77#2666C2214yes—
78#2665C2214yes—
79#2665C2214yes—
80#2662C2214yes—
81#2654C2214yes—
82#2653C2214yes—
83#2652C2214yes—
84#2649C2214yes—
85#2644C2212yes—
86#2640C2214yes—
87#2639C2214yes—
88#2637C2214yes—
89#2636C2214yes—
90#2632C2214yes—
91#2628C2211yescharacteristic
92#2620C2214yes—
93#2619C2211yescharacteristic
94#2609C2212yes—
95#2607C2214yes—
96#2605C2214yes—
97#2605C2214yes—
98#2599C2214yes—
99#2595C2214yes—
100#2594C2214yes—
101#2589C2214yes—
102#2580C2212yes—
103#2578C2214yes—
104#2576C2214yes—
105#2574C2214yes—
106#2574C2214yes—
107#2574C2212yes—
108#2573C2212yes—
109#2572C2212yes—
110#2572C2214yes—
111#2571C2212yes—
112#2571C2212yes—
113#2569C2214yes—
114#2563C2212yes—
115#2560C2214yes—
116#2557C2214yes—
117#2553C2212yes—
118#2551C2212yes—
119#2551C2212yes—
120#2551C2212yes—
121#2550C2212yes—
122#2546C2212yes—
123#2545C2214yes—
124#2533C2214yes—
125#2531C2214yes—
126#2529C2214yes—
127#2527C2214yes—
128#2524C2212yes—
129#2523C2212yes—
130#2522C2214yes—
131#2521C2214yes—
132#2518C2214yes—
133#2518C2214yes—
134#2515C2212yes—
135#2513C2212yes—
136#2512C2212yes—
137#2512C2212yes—
138#2509C2212yes—
139#2509C2212yes—
140#2508C2212yes—
141#2507C2212yes—
142#2507C2212yes—
143#2500C2212yes—
144#2500C2212yes—
145#2495C2212yes—
146#2495C2212yes—
147#2494C2212yes—
148#2492C2214yes—
149#2491C2212yes—
150#2491C2214yes—
151#2491C2212yes—
152#2490C2212yes—
153#2488C2214yes—
154#2488C2214yes—
155#2485C2212yes—
156#2485C2212yes—
157#2476C2214yes—
158#2474C2214yes—
159#2474C2214yes—
160#2471C2214yes—
161#2469C2214yes—
162#2468C2214yes—
163#2468C2212yes—
164#2467C2214yes—
165#2459C2214yes—
166#2457C2212yes—
167#2457C2214yes—
168#2455C2212yes—
169#2454C2212yes—
170#2452C2212yes—
171#2452C2212yes—
172#2445C2212yes—
173#2444C2214yes—
174#2441C2212yes—
175#2440C2212yes—
176#2439C2214yes—
177#2439C2212yes—
178#2439C2214yes—
179#2439C2212yes—
180#2439C2214yes—
181#2439C2212yes—
182#2439C2212yes—
183#2438C2214yes—
184#2429C2214yes—
185#2428C2212yes—
186#2427C2214yes—
187#2427C2214yes—
188#2425C2214yes—
189#2420C2212yes—
190#2416C2212yes—
191#2414C2212yes—
192#2402C2211yescharacteristic
193#2398C2211yescharacteristic
194#2396C2211yescharacteristic
195#2395C2214yes—
196#2392C2211yescharacteristic
197#2392C2214yes—
198#2372C2214yes—
199#2368C2214yes—
200#2368C2214yes—
201#2367C2214yes—
202#2365C2212yes—
203#2364C2214yes—
204#2363C2212yes—
205#2361C2212yes—
206#2357C2212yes—
207#2355C2214yes—
208#2355C2214yes—
209#2352C2212yes—
210#2347C2212yes—
211#2346C2212yes—
212#2343C2214yes—
213#2337C2214yes—
214#2335C2214yes—
215#2333C2214yes—
216#2331C2212yes—
217#2331C2212yes—
218#2331C2212yes—
219#2331C2211yescharacteristic
220#2331C2212yes—
221#2328C2211yescharacteristic
222#2324C2212yes—
223#2323C2214yes—
224#2320C2214yes—
225#2319C2212yes—
226#2318C2214yes—
227#2317C2211yescharacteristic
228#2317C2211yescharacteristic
229C4×#125C2212yes—
230C4×#125C2212yes—
231C4×#126C2214yes—
232C4×#126C2212yes—
233C4×#124C2214yes—
234C4×#123C2212yes—
235C4×#121C2212yes—
236C4×#121C2212yes—
237#2298C2214yes—
238#2295C2211yescharacteristic
239#2293C2212yes—
240#2293C2214yes—
241#2290C2212yes—
242#2285C2212yes—
243#2283C2212yes—
244C2×#382C2211yescharacteristic
245#2275C2212yes—
246#2274C2211yescharacteristic
247#2274C2211yescharacteristic
248C42×D4C2211yescharacteristic
249C4×#117C2212yes—
250C4×#117C2211yescharacteristic
251#555—216no—
252#533—28no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2314yes—
258C2×C4⋊Q8C2314yes—
259C2×C4⋊Q8C2314yes—
260C2×#127C2311yescharacteristic
261C2×#126C2314yes—
262C2×#126C2312yes—
263C2×#126C2314yes—
264C2×#125C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#123C2314yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2314yes—
295C2×#117C2311yescharacteristic
296C2×#117C2314yes—
297C2×#117C2311yescharacteristic
298C2×#117C2312yes—
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2314yes—
302C2×#117C2314yes—
303C2×#117C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2312yes—
308#401C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2311yescharacteristic
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2312yes—
328#399C2314yes—
329#399C2311yescharacteristic
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2311yescharacteristic
340#398C2312yes—
341#398C2314yes—
342#398C2312yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2312yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2311yescharacteristic
358#397C2314yes—
359#396C2312yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2312yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2311yescharacteristic
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2312yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2311yescharacteristic
383#394C2312yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2312yes—
390#394C2312yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2311yescharacteristic
407#393C2314yes—
408#393C2312yes—
409#393C2314yes—
410#393C2312yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2311yescharacteristic
418#392C2312yes—
419#392C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#390C2314yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#388C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2312yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2312yes—
540#387C2314yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2312yes—
564#386C2314yes—
565#386C2312yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2312yes—
573#386C2314yes—
574#386C2314yes—
575#385C2312yes—
576#385C2312yes—
577#385C2314yes—
578#385C2314yes—
579#385C2312yes—
580#385C2312yes—
581#385C2312yes—
582#385C2312yes—
583#385C2314yes—
584#385C2314yes—
585#385C2312yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#384C2312yes—
591#384C2312yes—
592#384C2312yes—
593#384C2312yes—
594#383C2312yes—
595#383C2314yes—
596#383C2312yes—
597#383C2314yes—
598#383C2312yes—
599#383C2314yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2311yescharacteristic
604#382C2314yes—
605#382C2314yes—
606#382C2312yes—
607#382C2312yes—
608#382C2312yes—
609#382C2314yes—
610#382C2314yes—
611#382C2312yes—
612#382C2311yescharacteristic
613#382C2314yes—
614#382C2312yes—
615#382C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2312yes—
619#381C2312yes—
620#381C2312yes—
621#381C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2314yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2311yescharacteristic
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682#376C2312yes—
683#376C2314yes—
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2314yes—
687C2×#95C2314yes—
688C2×#95C2314yes—
689C43C2311yescharacteristic
690C43C2314yes—
691C43C2311yescharacteristic
692C22×Q8C2414yes—
693C22×Q8C2414yes—
694C22×Q8C2411yescharacteristic
695C22×Q8C2414yes—
696C22×Q8C2412yes—
697C22×D4C2412yes—
698C22×D4C2412yes—
699C22×D4C2414yes—
700C22×D4C2414yes—
701C22×D4C2411yescharacteristic
702C22×D4C2414yes—
703C22×D4C2412yes—
704C22×D4C2412yes—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2412yes—
713C23×C4C2412yes—
714C23×C4C2414yes—
715C4⋊Q8—28no—
716C4⋊Q8—28no—
717C4⋊Q8—42no—
718C4⋊Q8—44no—
719C4⋊Q8—84no—
720C4⋊Q8—84no—
721C4⋊Q8—84no—
722#127—42no—
723#126—48no—
724#126—44no—
725#126—84no—
726#125—28no—
727#124—216no—
728#124—216no—
729#124—84no—
730#124—84no—
731#124—84no—
732#123—44no—
733#123—48no—
734#123—84no—
735C22⋊Q8—216no—
736C22⋊Q8—48no—
737C22⋊Q8—84no—
738C22⋊Q8—84no—
739#121—28no—
740#121—28no—
741#121—216no—
742#121—44no—
743#121—84no—
744#121—84no—
745C4×Q8—216no—
746C4×Q8—42no—
747C4×Q8—48no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—28no—
751C4×D4—48no—
752C4×D4—44no—
753C4×D4—42no—
754C4×D4—48no—
755C4×D4—44no—
756C4×D4—84no—
757#117—24no—
758#117—28no—
759#117—216no—
760#117—24no—
761#117—42no—
762#117—44no—
763#117—84no—
764#117—84no—
765#117#4118yes—
766C2×C4⋊C4—42no—
767C2×C4⋊C4—42no—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C42—24no—
868C2×C42—28no—
869C2×C42C2414yes—
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2411yescharacteristic
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2411yescharacteristic
958#95C2411yescharacteristic
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970C24C2514yes—
971C24C2512yes—
972C24C2511yescharacteristic
973C2×Q8—28no—
974C2×Q8—28no—
975C2×Q8—44no—
976C2×Q8—41no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8—42no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—42no—
986C2×D4—24no—
987C2×D4—28no—
988C2×D4—24no—
989C2×D4—28no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—41no—
993C2×D4—42no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C22×C4—22no—
1008C22×C4—22no—
1009C22×C4—24no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—28no—
1016C22×C4—24no—
1017C22×C4—28no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4C2×#4114yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—41no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—41no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4C2×#4118yes—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—28no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—42no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—42no—
1140C22⋊C4—44no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4C2×#4118yes—
1158C42—24no—
1159C42—22no—
1160C42—22no—
1161C42—28no—
1162C42—24no—
1163C42—24no—
1164C42—24no—
1165C42—24no—
1166C42—24no—
1167C42—22no—
1168C42—22no—
1169C42—22no—
1170C42—28no—
1171C42—24no—
1172C42—44no—
1173C42—42no—
1174C42—44no—
1175C42—44no—
1176C42—44no—
1177C42—42no—
1178C42—44no—
1179C42—44no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—42no—
1184C42—44no—
1185C42C2×#4118yes—
1186C422−1+414yes—
1187C23—21no—
1188C23—22no—
1189C23—21no—
1190C23—22no—
1191C23—24no—
1192C23—22no—
1193C23—24no—
1194C23—22no—
1195C23—24no—
1196C23—22no—
1197C23—24no—
1198C23—22no—
1199C23—22no—
1200C23—24no—
1201C23—24no—
1202C23—22no—
1203C23—24no—
1204C23—22no—
1205C23C22×#4112yes—
1206C23C2611yescharacteristic
1207Q8—88no—
1208Q8—88no—
1209Q8—82no—
1210Q8—164no—
1211Q8—162no—
1212D4—44no—
1213D4—48no—
1214D4—88no—
1215D4—84no—
1216D4—88no—
1217D4—88no—
1218D4—162no—
1219D4—162no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—28no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—24no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—88no—
1285C2×C4—84no—
1286C2×C4—88no—
1287C2×C4—84no—
1288C2×C4—162no—
1289C2×C4—164no—
1290C2×C4—162no—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4118yes—
1293C2×C4C22×#4112yes—
1294C2×C4C2×2−1+414yes—
1295C2×C4C2×2−1+412yes—
1296C2×C4#58514yes—
1297C2×C4#58512yes—
1298C22—24no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—44no—
1304C22—42no—
1305C22—44no—
1306C22—42no—
1307C22—44no—
1308C22—42no—
1309C22—42no—
1310C22—44no—
1311C22—42no—
1312C22—44no—
1313C22—42no—
1314C22—44no—
1315C22—42no—
1316C22—44no—
1317C22C23×#4111yescharacteristic
1318C22C22×2−1+411yescharacteristic
1319C22C2×#58512yes—
1320C22C2×#58511yescharacteristic
1321C22H(7,𝔽2)12yes—
1322C4—28no—
1323C4—22no—
1324C4—24no—
1325C4—24no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—44no—
1330C4—44no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—41no—
1335C4—41no—
1336C4—44no—
1337C4—41no—
1338C4—41no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4#346114yes—
1346C2—42no—
1347C2—84no—
1348C2—82no—
1349C2C2×#346111yescharacteristic
1350C2#6284111yescharacteristic
1351C2#6288511yescharacteristic
1352C2#6295812yes—
1353C2#6299412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42971C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42933C2semidirect
3. #42734C2semidirect
4. #42686C2semidirect
5. #42614C2semidirect
6. #42517C2semidirect
7. #41826C2semidirect
8. #41661C2semidirect
9. #41308C2semidirect
10. #41139C2semidirect
11. #40251C2semidirect
12. #40121C2semidirect
13. #39891C2semidirect
14. #39571C2semidirect
15. #39011C2semidirect
16. #38939C2semidirect
17. #38300C2semidirect
18. #38284C2semidirect
19. #35602C2semidirect
20. #35589C2semidirect
21. #35546C2semidirect
22. #35296C2semidirect
23. #35192C2semidirect
24. #34879C2semidirect
25. #34797C2semidirect
26. #34306C2semidirect
27. #34215C2semidirect

Maximal subgroups

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

subgroupindex
#429712
#429332
#427342
#426862
#426142
#425172
#418262
#416612
#413082
#411392
#402512
#401212
#398912
#395712
#390112
#389392
#383002
#382842
#356022
#355892
#355462
#352962
#351922
#348792
#347972
#343062
#342152