Finite Group Databasebeta

← #7646244

Subgroups — #7646244

Order 512.

4438 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42492C212yesmaximal, complemented
2#42489C212yesmaximal, complemented
3#42486C212yesmaximal
4#42486C212yesmaximal
5#40626C214yesmaximal, complemented
6#40622C214yesmaximal, complemented
7#39976C212yesmaximal, complemented
8#39976C212yesmaximal, complemented
9#39973C212yesmaximal, complemented
10#39972C212yesmaximal, complemented
11#38452C214yesmaximal, complemented
12#38450C214yesmaximal, complemented
13#37481C212yesmaximal, complemented
14#37479C212yesmaximal, complemented
15#36756C214yesmaximal, complemented
16#36753C214yesmaximal, complemented
17#35612C212yesmaximal, complemented
18#35580C212yesmaximal, complemented
19#35345C211yesmaximal, characteristic, complemented
20#35213C211yesmaximal, characteristic, complemented
21#35176C212yesmaximal, complemented
22#35175C212yesmaximal, complemented
23#35065C212yesmaximal, complemented
24#35033C212yesmaximal, complemented
25#34912C211yesmaximal, characteristic, complemented
26#34912C211yesmaximal, characteristic, complemented
27#34190C211yesmaximal, characteristic
28#34126C211yesmaximal, characteristic
29#34058C211yesmaximal, characteristic
30C22×C4×D4C2211yescharacteristic
31#2864C2212yescomplemented
32#2863C2214yescomplemented
33#2859C2212yescomplemented
34#2857C2214yescomplemented
35#2855C2214yescomplemented
36#2855C2214yescomplemented
37#2851C2214yescomplemented
38#2842C2214yes—
39#2842C2214yes—
40#2841C2214yes—
41#2841C2214yes—
42#2807C2214yescomplemented
43#2807C2214yescomplemented
44#2806C2214yescomplemented
45#2802C2214yescomplemented
46#2792C2214yescomplemented
47#2791C2214yescomplemented
48#2791C2214yescomplemented
49#2790C2214yescomplemented
50#2790C2214yescomplemented
51#2788C2214yescomplemented
52#2780C2214yes—
53#2780C2214yes—
54#2768C2214yescomplemented
55#2768C2214yescomplemented
56#2768C2214yescomplemented
57#2755C2214yescomplemented
58#2748C2214yes—
59#2748C2214yes—
60#2742C2214yescomplemented
61#2732C2214yes—
62#2732C2214yes—
63#2729C2214yescomplemented
64#2726C2214yescomplemented
65#2720C2214yescomplemented
66#2720C2214yescomplemented
67#2720C2214yescomplemented
68#2713C2214yescomplemented
69#2704C2214yescomplemented
70#2704C2214yescomplemented
71#2692C2214yes—
72#2692C2214yes—
73#2677C2214yescomplemented
74#2667C2212yes—
75#2667C2214yes—
76#2667C2214yescomplemented
77#2667C2214yescomplemented
78#2667C2214yescomplemented
79#2667C2214yescomplemented
80#2667C2214yescomplemented
81#2667C2214yescomplemented
82#2665C2212yes—
83#2665C2214yes—
84#2665C2214yescomplemented
85#2665C2214yescomplemented
86#2629C2212yes—
87#2629C2212yes—
88#2629C2214yes—
89#2629C2214yes—
90#2626C2214yes—
91#2626C2214yes—
92#2626C2214yes—
93#2626C2214yes—
94#2612C2214yescomplemented
95#2608C2212yes—
96#2608C2212yes—
97#2608C2214yes—
98#2608C2212yes—
99#2608C2211yescharacteristic
100#2608C2211yescharacteristic
101#2608C2212yes—
102#2608C2214yescomplemented
103#2607C2211yescharacteristic
104#2607C2211yescharacteristic
105#2607C2212yes—
106#2607C2212yes—
107#2607C2214yescomplemented
108#2606C2212yescomplemented
109#2606C2212yescomplemented
110#2606C2214yescomplemented
111#2606C2212yescomplemented
112#2606C2212yescomplemented
113#2605C2212yescomplemented
114#2605C2212yescomplemented
115#2589C2214yescomplemented
116#2589C2214yescomplemented
117#2587C2214yescomplemented
118#2587C2214yescomplemented
119#2584C2212yescomplemented
120#2584C2212yescomplemented
121#2580C2212yes—
122#2580C2212yes—
123#2574C2214yescomplemented
124#2570C2212yescomplemented
125#2570C2212yescomplemented
126#2570C2212yescomplemented
127#2569C2214yescomplemented
128#2567C2212yescomplemented
129#2566C2212yes—
130#2566C2212yes—
131#2556C2214yescomplemented
132#2556C2214yescomplemented
133#2556C2214yescomplemented
134#2552C2212yescomplemented
135#2552C2212yescomplemented
136#2550C2212yescomplemented
137#2550C2212yescomplemented
138#2550C2212yescomplemented
139#2550C2212yescomplemented
140#2550C2212yescomplemented
141#2549C2214yescomplemented
142#2546C2212yescomplemented
143#2542C2212yes—
144#2542C2212yes—
145#2538C2212yes—
146#2538C2212yes—
147#2522C2214yescomplemented
148#2522C2214yescomplemented
149#2522C2214yescomplemented
150#2509C2212yescomplemented
151#2508C2212yescomplemented
152#2507C2212yescomplemented
153#2507C2212yescomplemented
154#2507C2212yescomplemented
155#2506C2212yescomplemented
156#2506C2212yescomplemented
157#2506C2212yescomplemented
158#2497C2214yescomplemented
159#2465C2214yescomplemented
160#2454C2212yes—
161#2454C2212yes—
162#2454C2212yes—
163#2454C2212yes—
164#2454C2212yes—
165#2454C2212yes—
166#2452C2212yes—
167#2452C2212yes—
168#2441C2212yes—
169#2441C2212yes—
170#2441C2212yes—
171#2441C2214yes—
172#2441C2214yescomplemented
173#2441C2214yescomplemented
174#2441C2214yescomplemented
175#2441C2214yescomplemented
176#2441C2214yescomplemented
177#2439C2212yes—
178#2439C2212yes—
179#2439C2212yes—
180#2439C2214yes—
181#2439C2214yescomplemented
182#2438C2214yescomplemented
183#2438C2214yescomplemented
184#2438C2214yescomplemented
185#2438C2214yescomplemented
186#2438C2214yescomplemented
187#2438C2214yescomplemented
188#2437C2214yes—
189#2437C2214yes—
190#2429C2214yescomplemented
191#2423C2214yescomplemented
192#2423C2214yescomplemented
193#2396C2214yes—
194#2396C2212yes—
195#2396C2212yes—
196#2357C2212yes—
197#2357C2212yes—
198#2353C2214yes—
199#2353C2214yes—
200#2349C2212yes—
201#2349C2212yes—
202#2345C2212yes—
203#2344C2211yescharacteristic
204#2344C2211yescharacteristic
205#2342C2214yes—
206#2342C2212yes—
207#2342C2212yes—
208D4×C22⋊C4C2212yes—
209D4×C22⋊C4C2211yescharacteristic
210D4×C22⋊C4C2211yescharacteristic
211#2331C2212yescomplemented
212#2330C2212yescomplemented
213#2330C2212yescomplemented
214#2330C2212yescomplemented
215#2329C2214yescomplemented
216#2329C2214yescomplemented
217#2329C2214yescomplemented
218#2329C2214yescomplemented
219#2319C2212yes—
220#2319C2212yes—
221#2319C2214yes—
222#2319C2212yes—
223#2318C2214yes—
224#2316C2212yes—
225#2312C2214yes—
226#2309C2212yes—
227C4×C4⋊Q8C2212yescomplemented
228C4×C4⋊Q8C2212yescomplemented
229C4×#125C2212yescomplemented
230C4×#125C2212yescomplemented
231#2295C2212yescomplemented
232#2295C2214yescomplemented
233#2295C2212yescomplemented
234#2293C2211yescharacteristic
235#2293C2211yescharacteristic
236#2293C2211yescharacteristic
237#2293C2211yescharacteristic
238#2293C2212yes—
239#2293C2212yes—
240#2293C2211yescharacteristic
241#2293C2211yescharacteristic
242#2290C2212yes—
243#2290C2212yes—
244#2283C2211yescharacteristic
245#2283C2211yescharacteristic
246#2283C2211yescharacteristic
247#2280C2212yes—
248#2280C2212yes—
249#2280C2212yes—
250#2280C2212yes—
251C2×#381C2212yes—
252#2275C2212yes—
253C42×D4C2211yescharacteristic
254C42×D4C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×C4×C22⋊C4C2212yes—
259C23×D4C2311yescharacteristic
260C24×C4C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2314yes—
284C2×C4×D4Q8116yescomplemented
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C22⋊C4C2314yes—
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2312yes—
311C22×C42C2312yes—
312C22×C42C2312yes—
313C22×C42C2311yescharacteristic
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2312yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2312yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2312yes—
381#396C2312yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2312yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2314yes—
409#395C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#391C2312yes—
419#391C2314yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
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#388C2314yes—
520#387C2314yes—
521#387C2312yes—
522#387C2312yes—
523#387C2314yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2312yes—
533#387C2312yes—
534#387C2314yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
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#387C2312yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#384C2312yes—
591#384C2312yes—
592#384C2312yes—
593#384C2312yes—
594#384C2314yes—
595#384C2312yes—
596#384C2314yes—
597#384C2314yes—
598#383C2312yes—
599#383C2312yes—
600#383C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2312yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2314yes—
608#381C2314yes—
609#381C2314yes—
610#381C2314yes—
611#381C2312yes—
612#381C2312yes—
613#381C2312yes—
614#381C2311yescharacteristic
615#381C2312yes—
616#381C2311yescharacteristic
617#381C2314yes—
618#381C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2311yescharacteristic
631#380C2311yescharacteristic
632#380C2312yes—
633#380C2311yescharacteristic
634#380C2311yescharacteristic
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#379C2314yes—
641#379C2314yes—
642#379C2312yes—
643#379C2312yes—
644#379C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2311yescharacteristic
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2311yescharacteristic
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2311yescharacteristic
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699#376C2312yes—
700#376C2312yes—
701#376C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2312yes—
705C2×#95C2314yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C43C2311yescharacteristic
709C43C2311yescharacteristic
710C43C2311yescharacteristic
711C43C2311yescharacteristic
712C43C2312yes—
713C25C2412yes—
714C22×Q8C2414yes—
715C22×Q8C2412yes—
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×D4—44no—
719C22×D4C2×Q818yes—
720C22×D4C2411yescharacteristic
721C22×D4C2411yescharacteristic
722C22×D4C2412yes—
723C23×C4—82no—
724C23×C4—82no—
725C23×C4C2×Q8116yes—
726C23×C4C2411yescharacteristic
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—84no—
742#125—44no—
743#125—44no—
744#125—44no—
745#125—44no—
746#125—44no—
747#125—84no—
748#125—84no—
749#125—84no—
750C22⋊Q8—48no—
751C22⋊Q8—48no—
752C22⋊Q8—48no—
753C22⋊Q8—48no—
754C22⋊Q8—84no—
755C22⋊Q8—84no—
756C22⋊Q8—84no—
757C22⋊Q8—84no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×Q8—48no—
761C4×D4—44no—
762C4×D4—44no—
763C4×D4—44no—
764C4×D4—44no—
765C4×D4C2×Q818yes—
766C4×D4C2×Q818yes—
767C4×D4C2×Q818yes—
768C4×D4C2×Q818yes—
769C4×D4C2×Q8116yes—
770C4×D4C2×Q8116yes—
771#117—44no—
772#117—44no—
773#117—44no—
774#117—82no—
775#117—82no—
776#117—82no—
777#117—82no—
778#117—82no—
779#117—82no—
780#117—82no—
781#117—82no—
782C2×C4⋊C4C2×Q818yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C22⋊C4—48no—
855C2×C22⋊C4—82no—
856C2×C22⋊C4—82no—
857C2×C22⋊C4C2×Q8116yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2411yescharacteristic
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2411yescharacteristic
869C2×C22⋊C4C2411yescharacteristic
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C42—82no—
895C2×C42—82no—
896C2×C42C2×Q818yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999C24—44no—
1000C24—42no—
1001C24—42no—
1002C24—44no—
1003C24C22×Q818yes—
1004C24C2511yescharacteristic
1005C24C2512yes—
1006C24C2512yes—
1007C2×Q8—28no—
1008C2×Q8—24no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×Q8—44no—
1017C2×Q8—44no—
1018C2×Q8—44no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—416no—
1022C2×D4—44no—
1023C2×D4C22×Q814yes—
1024C2×D4C22×Q814yes—
1025C2×D4C22×Q818yes—
1026C22×C4—24no—
1027C22×C4—28no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—816no—
1053C22×C4C22×Q814yes—
1054C22×C4C22×Q814yes—
1055C22×C4C22×Q814yes—
1056C22×C4C22×Q818yes—
1057C22×C4C22×Q818yes—
1058C22×C4C22×Q818yes—
1059C22×C4C22×Q818yes—
1060C22×C4C22×Q818yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4C22×Q818yes—
1156C4⋊C4C22×Q814yes—
1157C4⋊C4C22×Q814yes—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
1164C22⋊C4—42no—
1165C22⋊C4—42no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—41no—
1173C22⋊C4—41no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4C22×Q818yes—
1191C22⋊C4C22×Q818yes—
1192C22⋊C4C22×Q818yes—
1193C22⋊C4C22×Q818yes—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—41no—
1202C42—41no—
1203C42—42no—
1204C42—42no—
1205C42—44no—
1206C42—44no—
1207C42—42no—
1208C42—44no—
1209C42—41no—
1210C42—41no—
1211C42—41no—
1212C42—41no—
1213C42—41no—
1214C42—42no—
1215C42—42no—
1216C42—41no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—42no—
1222C42—42no—
1223C42C22×Q814yes—
1224C42C22×Q814yes—
1225C42C22×Q814yes—
1226C42C22×Q814yes—
1227C23—24no—
1228C23—22no—
1229C23—24no—
1230C23—22no—
1231C23—24no—
1232C23—24no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—21no—
1238C23—21no—
1239C23—48no—
1240C23—48no—
1241C23—48no—
1242C23—88no—
1243C23—88no—
1244C23C23×Q814yes—
1245C23C23×Q814yes—
1246C23C23×Q812yes—
1247C23C2611yescharacteristic
1248Q8—88no—
1249Q8—84no—
1250Q8—84no—
1251Q8—164no—
1252D4—28no—
1253D4—28no—
1254D4—48no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—28no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—44no—
1321C2×C4—48no—
1322C2×C4—48no—
1323C2×C4—48no—
1324C2×C4—48no—
1325C2×C4—48no—
1326C2×C4—44no—
1327C2×C4—88no—
1328C2×C4—88no—
1329C2×C4—164no—
1330C2×C4—164no—
1331C2×C4C23×Q812yes—
1332C2×C4C23×Q812yes—
1333C2×C4C23×Q812yes—
1334C2×C4C23×Q812yes—
1335C2×C4C23×Q812yes—
1336C2×C4C23×Q814yes—
1337C2×C4C23×Q814yes—
1338C2×C4C23×Q812yes—
1339C2×C4#58514yes—
1340C2×C4#58514yes—
1341C22—22no—
1342C22—24no—
1343C22—24no—
1344C22—22no—
1345C22—24no—
1346C22—24no—
1347C22—22no—
1348C22—24no—
1349C22—24no—
1350C22—44no—
1351C22—44no—
1352C22—42no—
1353C22—44no—
1354C22—44no—
1355C22—42no—
1356C22—816no—
1357C22C24×Q811yescharacteristic
1358C22C2×#58512yes—
1359C22C2×#58512yes—
1360C22H(7,𝔽2)11yescharacteristic
1361C22H(7,𝔽2)11yescharacteristic
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—22no—
1366C4—24no—
1367C4—24no—
1368C4—22no—
1369C4—24no—
1370C4—42no—
1371C4—44no—
1372C4—42no—
1373C4—44no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—44no—
1384C4—44no—
1385C4—42no—
1386C4—44no—
1387C4#345814yes—
1388C2—44no—
1389C2—44no—
1390C2—42no—
1391C2C2×#345811yescharacteristic
1392C2#6281311yescharacteristic
1393C2#6284311yescharacteristic
1394C2#6294112yes—
1395C2#6296912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42492C2semidirect
2. #42489C2semidirect
5. #40626C2semidirect
6. #40622C2semidirect
7. #39976C2semidirect
8. #39976C2semidirect
9. #39973C2semidirect
10. #39972C2semidirect
11. #38452C2semidirect
12. #38450C2semidirect
13. #37481C2semidirect
14. #37479C2semidirect
15. #36756C2semidirect
16. #36753C2semidirect
17. #35612C2semidirect
18. #35580C2semidirect
19. #35345C2semidirect
20. #35213C2semidirect
21. #35176C2semidirect
22. #35175C2semidirect
23. #35065C2semidirect
24. #35033C2semidirect
25. #34912C2semidirect
26. #34912C2semidirect
31. #2864C22semidirect
32. #2863C22semidirect
33. #2859C22semidirect
34. #2857C22semidirect
35. #2855C22semidirect
36. #2855C22semidirect
37. #2851C22semidirect
42. #2807C22semidirect
43. #2807C22semidirect
44. #2806C22semidirect
45. #2802C22semidirect
46. #2792C22semidirect
47. #2791C22semidirect
48. #2791C22semidirect
49. #2790C22semidirect
50. #2790C22semidirect
51. #2788C22semidirect
54. #2768C22semidirect
55. #2768C22semidirect
56. #2768C22semidirect
57. #2755C22semidirect
60. #2742C22semidirect
63. #2729C22semidirect
64. #2726C22semidirect
65. #2720C22semidirect
66. #2720C22semidirect
67. #2720C22semidirect
68. #2713C22semidirect
69. #2704C22semidirect
70. #2704C22semidirect
73. #2677C22semidirect
76. #2667C22semidirect
77. #2667C22semidirect
78. #2667C22semidirect
79. #2667C22semidirect
80. #2667C22semidirect
81. #2667C22semidirect
84. #2665C22semidirect
85. #2665C22semidirect
94. #2612C22semidirect
102. #2608C22semidirect
107. #2607C22semidirect
108. #2606C22semidirect
109. #2606C22semidirect
110. #2606C22semidirect
111. #2606C22semidirect
112. #2606C22semidirect
113. #2605C22semidirect
114. #2605C22semidirect
115. #2589C22semidirect
116. #2589C22semidirect
117. #2587C22semidirect
118. #2587C22semidirect
119. #2584C22semidirect
120. #2584C22semidirect
123. #2574C22semidirect
124. #2570C22semidirect
125. #2570C22semidirect
126. #2570C22semidirect
127. #2569C22semidirect
128. #2567C22semidirect
131. #2556C22semidirect
132. #2556C22semidirect
133. #2556C22semidirect
134. #2552C22semidirect
135. #2552C22semidirect
136. #2550C22semidirect
137. #2550C22semidirect
138. #2550C22semidirect
139. #2550C22semidirect
140. #2550C22semidirect
141. #2549C22semidirect
142. #2546C22semidirect
147. #2522C22semidirect
148. #2522C22semidirect
149. #2522C22semidirect
150. #2509C22semidirect
151. #2508C22semidirect
152. #2507C22semidirect
153. #2507C22semidirect
154. #2507C22semidirect
155. #2506C22semidirect
156. #2506C22semidirect
157. #2506C22semidirect
158. #2497C22semidirect
159. #2465C22semidirect
172. #2441C22semidirect
173. #2441C22semidirect
174. #2441C22semidirect
175. #2441C22semidirect
176. #2441C22semidirect
181. #2439C22semidirect
182. #2438C22semidirect
183. #2438C22semidirect
184. #2438C22semidirect
185. #2438C22semidirect
186. #2438C22semidirect
187. #2438C22semidirect
190. #2429C22semidirect
191. #2423C22semidirect
192. #2423C22semidirect
211. #2331C22semidirect
212. #2330C22semidirect
213. #2330C22semidirect
214. #2330C22semidirect
215. #2329C22semidirect
216. #2329C22semidirect
217. #2329C22semidirect
218. #2329C22semidirect
227. C4×C4⋊Q8C22semidirect
228. C4×C4⋊Q8C22semidirect
229. C4×#125C22semidirect
230. C4×#125C22semidirect
231. #2295C22semidirect
232. #2295C22semidirect
233. #2295C22semidirect
284. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#424922
#424892
#424862
#406262
#406222
#399762
#399732
#399722
#384522
#384502
#374812
#374792
#367562
#367532
#356122
#355802
#353452
#352132
#351762
#351752
#350652
#350332
#349122
#341902
#341262
#340582