Finite Group Databasebeta

← #7648463

Subgroups — #7648463

Order 512.

4464 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41752C214yesmaximal, complemented
2#41631C214yesmaximal, complemented
3#41121C214yesmaximal, complemented
4#40952C214yesmaximal, complemented
5#40295C214yesmaximal, complemented
6#40277C214yesmaximal, complemented
7#38695C214yesmaximal, complemented
8#38661C214yesmaximal, complemented
9#37571C212yesmaximal, complemented
10#37560C211yesmaximal, characteristic, complemented
11#37554C211yesmaximal, characteristic
12#37434C211yesmaximal, characteristic, complemented
13#37360C212yesmaximal, complemented
14#37339C212yesmaximal, complemented
15#37322C211yesmaximal, characteristic, complemented
16#37321C211yesmaximal, characteristic, complemented
17#37320C211yesmaximal, characteristic, complemented
18#35603C212yesmaximal, complemented
19#35597C212yesmaximal, complemented
20#35337C211yesmaximal, characteristic, complemented
21#35298C211yesmaximal, characteristic, complemented
22#35296C211yesmaximal, characteristic, complemented
23#35296C211yesmaximal, characteristic, complemented
24#35283C211yesmaximal, characteristic, complemented
25#35218C212yesmaximal, complemented
26#35132C211yesmaximal, characteristic, complemented
27#35107C212yesmaximal, complemented
28#34893C212yesmaximal, complemented
29#34215C211yesmaximal, characteristic, complemented
30#34151C211yesmaximal, characteristic, complemented
31#34086C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2868C2211yescharacteristic
36#2864C2211yescharacteristic
37#2864C2211yescharacteristic
38#2862C2211yescharacteristic
39#2862C2211yescharacteristic
40#2859C2211yescharacteristic
41#2858C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2212yes—
44#2854C2212yes—
45#2854C2212yes—
46#2853C2214yes—
47#2852C2214yes—
48#2851C2212yes—
49#2836C2214yes—
50#2831C2214yes—
51#2820C2212yes—
52#2819C2212yes—
53#2817C2212yes—
54#2816C2212yes—
55#2798C2214yes—
56#2798C2214yes—
57#2796C2214yes—
58#2796C2214yes—
59#2794C2214yes—
60#2793C2214yes—
61#2790C2214yes—
62#2782C2214yes—
63#2781C2214yes—
64#2775C2214yes—
65#2758C2214yes—
66#2758C2214yes—
67#2757C2214yes—
68#2751C2214yes—
69#2750C2214yes—
70#2744C2214yes—
71#2730C2214yes—
72#2728C2214yes—
73#2721C2214yes—
74#2718C2214yes—
75#2716C2214yes—
76#2715C2214yes—
77#2713C2214yes—
78#2712C2214yes—
79#2710C2214yes—
80#2708C2214yes—
81#2708C2214yes—
82#2705C2214yes—
83#2700C2214yes—
84#2691C2214yes—
85#2681C2214yes—
86#2680C2214yes—
87#2666C2214yes—
88#2664C2214yes—
89#2663C2212yes—
90#2663C2212yes—
91#2656C2212yes—
92#2652C2214yes—
93#2652C2214yes—
94#2652C2214yes—
95#2650C2214yes—
96#2650C2214yes—
97#2648C2214yes—
98#2647C2212yes—
99#2647C2212yes—
100#2644C2212yes—
101#2644C2212yes—
102#2639C2212yes—
103#2636C2212yes—
104#2636C2212yes—
105#2634C2212yes—
106#2632C2212yes—
107#2630C2214yes—
108#2628C2211yescharacteristic
109#2628C2211yescharacteristic
110#2628C2211yescharacteristic
111#2628C2211yescharacteristic
112#2628C2211yescharacteristic
113#2628C2211yescharacteristic
114#2620C2214yes—
115#2619C2211yescharacteristic
116#2619C2211yescharacteristic
117#2612C2214yes—
118#2604C2212yes—
119#2604C2212yes—
120#2597C2214yes—
121#2597C2214yes—
122#2595C2214yes—
123#2595C2214yes—
124#2595C2214yes—
125#2595C2214yes—
126#2595C2214yes—
127#2593C2214yes—
128#2593C2214yes—
129#2589C2214yes—
130#2589C2214yes—
131#2589C2214yes—
132#2588C2214yes—
133#2588C2214yes—
134#2587C2214yes—
135#2587C2214yes—
136#2584C2212yes—
137#2580C2212yes—
138#2578C2214yes—
139#2573C2214yes—
140#2570C2212yes—
141#2566C2212yes—
142#2566C2212yes—
143#2562C2212yes—
144#2559C2214yes—
145#2557C2214yes—
146#2557C2214yes—
147#2554C2214yes—
148#2550C2212yes—
149#2545C2214yes—
150#2535C2212yes—
151#2525C2214yes—
152#2525C2214yes—
153#2522C2214yes—
154#2513C2212yes—
155#2512C2212yes—
156#2511C2214yes—
157#2509C2212yes—
158#2509C2212yes—
159#2507C2212yes—
160#2506C2212yes—
161#2500C2212yes—
162#2500C2212yes—
163#2497C2212yes—
164#2496C2212yes—
165#2495C2212yes—
166#2495C2212yes—
167#2492C2214yes—
168#2491C2212yes—
169#2490C2214yes—
170#2490C2212yes—
171#2485C2212yes—
172#2485C2212yes—
173#2478C2214yes—
174#2477C2214yes—
175#2477C2214yes—
176#2476C2214yes—
177#2475C2214yes—
178#2475C2214yes—
179#2474C2214yes—
180#2474C2214yes—
181#2474C2214yes—
182#2471C2214yes—
183#2471C2214yes—
184#2470C2214yes—
185#2469C2214yes—
186#2465C2214yes—
187#2461C2214yes—
188#2454C2212yes—
189#2452C2212yes—
190#2451C2214yes—
191#2442C2212yes—
192#2440C2212yes—
193#2438C2214yes—
194#2432C2214yes—
195#2430C2212yes—
196#2430C2212yes—
197#2426C2214yes—
198#2423C2214yes—
199#2422C2212yes—
200#2420C2212yes—
201#2416C2212yes—
202#2416C2212yes—
203#2396C2214yes—
204#2396C2214yes—
205#2374C2212yes—
206#2374C2212yes—
207#2373C2212yes—
208#2373C2212yes—
209#2370C2212yes—
210#2368C2214yes—
211#2368C2214yes—
212#2367C2212yes—
213#2363C2212yes—
214#2362C2212yes—
215#2355C2214yes—
216#2355C2214yes—
217#2337C2214yes—
218#2337C2214yes—
219#2335C2214yes—
220#2333C2214yes—
221#2331C2211yescharacteristic
222#2331C2211yescharacteristic
223#2331C2211yescharacteristic
224#2331C2211yescharacteristic
225#2331C2211yescharacteristic
226#2331C2211yescharacteristic
227#2329C2214yes—
228#2328C2211yescharacteristic
229#2328C2211yescharacteristic
230#2326C2214yes—
231#2324C2212yes—
232#2324C2212yes—
233#2324C2212yes—
234#2324C2212yes—
235#2317C2212yes—
236#2314C2212yes—
237#2314C2212yes—
238C4×C4⋊Q8C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#125C2212yes—
242C4×C22⋊Q8C2214yes—
243#2298C2211yescharacteristic
244#2298C2211yescharacteristic
245#2297C2214yes—
246#2296C2214yes—
247#2295C2211yescharacteristic
248#2293C2211yescharacteristic
249#2293C2212yes—
250#2293C2211yescharacteristic
251#2293C2212yes—
252#2293C2212yes—
253#2293C2211yescharacteristic
254#2290C2214yes—
255#2290C2211yescharacteristic
256#2290C2211yescharacteristic
257#2283C2211yescharacteristic
258C2×#382C2211yescharacteristic
259#2274C2212yes—
260C42×Q8C2211yescharacteristic
261C42×D4C2211yescharacteristic
262C42×D4C2212yes—
263C4×#117C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268#533—28no—
269#532—28no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2314yes—
275C2×#127C2311yescharacteristic
276#529—28no—
277C2×#126C2311yescharacteristic
278C2×#126C2311yescharacteristic
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2311yescharacteristic
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#124C2314yes—
290C2×#123C2311yescharacteristic
291C2×#123C2311yescharacteristic
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×#121C2311yescharacteristic
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×#117C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2312yes—
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C22×C4⋊C4C2312yes—
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2314yes—
336C22×C42C2311yescharacteristic
337#400C2314yes—
338#400C2312yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#399C2312yes—
360#399C2312yes—
361#399C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2314yes—
365#399C2312yes—
366#399C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#395C2314yes—
410#395C2312yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2314yes—
415#395C2312yes—
416#395C2312yes—
417#395C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2312yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2314yes—
435#393C2312yes—
436#393C2312yes—
437#393C2314yes—
438#393C2312yes—
439#393C2312yes—
440#393C2314yes—
441#393C2312yes—
442#393C2312yes—
443#393C2314yes—
444#392C2312yes—
445#392C2312yes—
446#392C2314yes—
447#392C2312yes—
448#392C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2314yes—
477#390C2314yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2312yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#384C2312yes—
636#384C2312yes—
637#384C2312yes—
638#384C2314yes—
639#384C2314yes—
640#383C2314yes—
641#383C2314yes—
642#383C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2311yescharacteristic
650#382C2311yescharacteristic
651#382C2311yescharacteristic
652#382C2311yescharacteristic
653#382C2312yes—
654#381C2312yes—
655#381C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2311yescharacteristic
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2311yescharacteristic
718C4×C22⋊C4C2311yescharacteristic
719C4×C22⋊C4C2311yescharacteristic
720C4×C22⋊C4C2311yescharacteristic
721C4×C22⋊C4C2311yescharacteristic
722C4×C22⋊C4C2311yescharacteristic
723#376C2312yes—
724#376C2311yescharacteristic
725#376C2311yescharacteristic
726#376C2312yes—
727#376C2311yescharacteristic
728#376C2311yescharacteristic
729C2×#95C2312yes—
730C2×#95C2312yes—
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C2×#41—28no—
738C2×#41—84no—
739C22×Q8C2411yescharacteristic
740C22×Q8C2414yes—
741C22×Q8C2412yes—
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C22×D4C2412yes—
745C22×D4C2411yescharacteristic
746C22×D4C2411yescharacteristic
747C22×D4C2411yescharacteristic
748C22×D4C2412yes—
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2411yescharacteristic
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C4⋊Q8—24no—
765C4⋊Q8—24no—
766C4⋊Q8—24no—
767C4⋊Q8—44no—
768C4⋊Q8—84no—
769#127—24no—
770#126—24no—
771#126—24no—
772#126—84no—
773#126—84no—
774#125—24no—
775#125—28no—
776#125—44no—
777#125—84no—
778#124—24no—
779#124—28no—
780#124—48no—
781#124—48no—
782#124—84no—
783#123—24no—
784#123—24no—
785#123—48no—
786#123—84no—
787#123—84no—
788C22⋊Q8—24no—
789C22⋊Q8—28no—
790C22⋊Q8—28no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—84no—
794#121—24no—
795#121—28no—
796#121—28no—
797#121—44no—
798#121—44no—
799#121—84no—
800#121—84no—
801C4×Q8—24no—
802C4×Q8—28no—
803C4×Q8—28no—
804C4×Q8—44no—
805C4×Q8—84no—
806C4×D4—24no—
807C4×D4—24no—
808C4×D4—24no—
809C4×D4—28no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—44no—
813C4×D4—44no—
814#117—28no—
815#117—24no—
816#117—24no—
817#117—24no—
818#117—24no—
819#117—24no—
820#117—42no—
821#117—48no—
822#117—44no—
823#117—84no—
824#117—84no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2411yescharacteristic
899C2×C22⋊C4C2411yescharacteristic
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2411yescharacteristic
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
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×C42—42no—
935C2×C42—42no—
936C2×C42—84no—
937C2×C42#4118yes—
938C2×C42C2412yes—
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040C24C2511yescharacteristic
1041C24C2511yescharacteristic
1042C24C2514yes—
1043C24C2511yescharacteristic
1044#41—816no—
1045C2×Q8—22no—
1046C2×Q8—24no—
1047C2×Q8—24no—
1048C2×Q8—24no—
1049C2×Q8—28no—
1050C2×Q8—42no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×D4—22no—
1057C2×D4—22no—
1058C2×D4—28no—
1059C2×D4—22no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—24no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—22no—
1082C22×C4—28no—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—28no—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4C2×#4114yes—
1107C22×C4C2×#4114yes—
1108C22×C4C2×#4114yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2514yes—
1121C22×C4C2514yes—
1122C22×C4C2514yes—
1123C22×C4C2514yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C4⋊C4—22no—
1137C4⋊C4—22no—
1138C4⋊C4—22no—
1139C4⋊C4—22no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—22no—
1145C4⋊C4—22no—
1146C4⋊C4—22no—
1147C4⋊C4—22no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C22⋊C4—28no—
1195C22⋊C4—22no—
1196C22⋊C4—22no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—22no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—22no—
1204C22⋊C4—22no—
1205C22⋊C4—22no—
1206C22⋊C4—22no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—42no—
1244C42—22no—
1245C42—22no—
1246C42—28no—
1247C42—22no—
1248C42—22no—
1249C42—22no—
1250C42—22no—
1251C42—22no—
1252C42—22no—
1253C42—24no—
1254C42—22no—
1255C42—24no—
1256C42—42no—
1257C42—42no—
1258C42—42no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C42—42no—
1264C42—42no—
1265C42—42no—
1266C42—44no—
1267C42—42no—
1268C42—42no—
1269C42—42no—
1270C42—42no—
1271C42—44no—
1272C42—42no—
1273C42—44no—
1274C42—42no—
1275C42C2×#4114yes—
1276C42C2×#4114yes—
1277C42C2×#4114yes—
1278C42C2×#4114yes—
1279C422−1+414yes—
1280C23—21no—
1281C23—22no—
1282C23—21no—
1283C23—22no—
1284C23—21no—
1285C23—21no—
1286C23—24no—
1287C23—21no—
1288C23—21no—
1289C23—24no—
1290C23—24no—
1291C23—24no—
1292C23—22no—
1293C23—22no—
1294C23—24no—
1295C23—21no—
1296C23—21no—
1297C23—24no—
1298C23—22no—
1299C23—22no—
1300C23—24no—
1301C23C22×#4112yes—
1302C23C2611yescharacteristic
1303Q8—44no—
1304Q8—84no—
1305Q8—84no—
1306Q8—88no—
1307Q8—84no—
1308D4—44no—
1309D4—48no—
1310D4—84no—
1311D4—84no—
1312D4—82no—
1313D4—82no—
1314D4—88no—
1315D4—164no—
1316D4—164no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—28no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—44no—
1382C2×C4—44no—
1383C2×C4—416no—
1384C2×C4—416no—
1385C2×C4—44no—
1386C2×C4—44no—
1387C2×C4—84no—
1388C2×C4—84no—
1389C2×C4—88no—
1390C2×C4—164no—
1391C2×C4C22×#4112yes—
1392C2×C4C22×#4112yes—
1393C2×C4C22×#4112yes—
1394C2×C4C22×#4112yes—
1395C2×C4C22×#4112yes—
1396C2×C4C22×#4112yes—
1397C2×C4C2×2−1+414yes—
1398C2×C4C2×2−1+412yes—
1399C2×C4#58514yes—
1400C2×C4#58512yes—
1401C22—22no—
1402C22—22no—
1403C22—22no—
1404C22—42no—
1405C22—42no—
1406C22—41no—
1407C22—41no—
1408C22—44no—
1409C22—44no—
1410C22—41no—
1411C22—41no—
1412C22—44no—
1413C22—42no—
1414C22—42no—
1415C22—44no—
1416C22—41no—
1417C22—41no—
1418C22—44no—
1419C22—42no—
1420C22—42no—
1421C22—44no—
1422C22—44no—
1423C22C23×#4111yescharacteristic
1424C22C22×2−1+411yescharacteristic
1425C22C2×#58512yes—
1426C22C2×#58511yescharacteristic
1427C22H(7,𝔽2)12yes—
1428C4—22no—
1429C4—22no—
1430C4—22no—
1431C4—22no—
1432C4—24no—
1433C4—22no—
1434C4—24no—
1435C4—41no—
1436C4—41no—
1437C4—44no—
1438C4—44no—
1439C4—41no—
1440C4—41no—
1441C4—44no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—44no—
1446C4—41no—
1447C4—41no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—44no—
1452C4—44no—
1453C4—44no—
1454C4#346114yes—
1455C2—42no—
1456C2—81no—
1457C2—81no—
1458C2—84no—
1459C2C2×#346111yescharacteristic
1460C2#6281511yescharacteristic
1461C2#6285511yescharacteristic
1462C2#6292612yes—
1463C2#6297012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37554C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41752C2semidirect
2. #41631C2semidirect
3. #41121C2semidirect
4. #40952C2semidirect
5. #40295C2semidirect
6. #40277C2semidirect
7. #38695C2semidirect
8. #38661C2semidirect
9. #37571C2semidirect
10. #37560C2semidirect
12. #37434C2semidirect
13. #37360C2semidirect
14. #37339C2semidirect
15. #37322C2semidirect
16. #37321C2semidirect
17. #37320C2semidirect
18. #35603C2semidirect
19. #35597C2semidirect
20. #35337C2semidirect
21. #35298C2semidirect
22. #35296C2semidirect
23. #35296C2semidirect
24. #35283C2semidirect
25. #35218C2semidirect
26. #35132C2semidirect
27. #35107C2semidirect
28. #34893C2semidirect
29. #34215C2semidirect
30. #34151C2semidirect
31. #34086C2semidirect

Maximal subgroups

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

subgroupindex
#417522
#416312
#411212
#409522
#402952
#402772
#386952
#386612
#375712
#375602
#375542
#374342
#373602
#373392
#373222
#373212
#373202
#356032
#355972
#353372
#352982
#352962
#352832
#352182
#351322
#351072
#348932
#342152
#341512
#340862