Finite Group Databasebeta

← #7681205

Subgroups — #7681205

Order 512.

4895 conjugacy classes of subgroups.

The subgroup lattice has 1407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59958C214yesmaximal
2#59704C214yesmaximal, complemented
3#59661C214yesmaximal, complemented
4#59493C214yesmaximal, complemented
5#44865C214yesmaximal, complemented
6#44863C214yesmaximal, complemented
7#44841C214yesmaximal, complemented
8#44825C214yesmaximal, complemented
9#39769C211yesmaximal, characteristic, complemented
10#39629C211yesmaximal, characteristic, complemented
11#39283C212yesmaximal, complemented
12#38251C212yesmaximal, complemented
13#38027C212yesmaximal
14#37897C211yesmaximal, characteristic, complemented
15#37894C211yesmaximal, characteristic, complemented
16#37695C211yesmaximal, characteristic, complemented
17#37695C211yesmaximal, characteristic, complemented
18#36279C212yesmaximal, complemented
19#36191C211yesmaximal, characteristic, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35665C212yesmaximal, complemented
22#35656C212yesmaximal, complemented
23#35323C211yesmaximal, characteristic, complemented
24#35322C211yesmaximal, characteristic, complemented
25#35315C211yesmaximal, characteristic, complemented
26#34691C212yesmaximal, complemented
27#34291C212yesmaximal, complemented
28#34281C211yesmaximal, characteristic, complemented
29#34209C211yesmaximal, characteristic, complemented
30#34149C211yesmaximal, characteristic
31C2×#2327C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2212yes—
33C2×#541C2211yescharacteristic
34C2×#533C2212yes—
35C22×C4⋊Q8C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic
37C2×#529C2211yescharacteristic
38C2×#519C2212yes—
39C22×C4×Q8C2212yes—
40#2868C2211yescharacteristic
41#2863C2212yes—
42#2862C2211yescharacteristic
43#2862C2212yes—
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2855C2212yes—
47#2851C2211yescharacteristic
48#2851C2211yescharacteristic
49#2806C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2799C2214yes—
53#2794C2214yes—
54#2794C2214yes—
55#2789C2214yes—
56#2777C2214yes—
57#2772C2214yes—
58#2772C2214yes—
59#2766C2214yes—
60#2766C2214yes—
61#2747C2214yes—
62#2745C2214yes—
63#2744C2214yes—
64#2741C2214yes—
65#2716C2214yes—
66#2716C2214yes—
67#2716C2214yes—
68#2713C2214yes—
69#2713C2214yes—
70#2713C2214yes—
71#2700C2214yes—
72#2698C2214yes—
73#2647C2211yescharacteristic
74#2647C2211yescharacteristic
75#2645C2212yes—
76#2642C2211yescharacteristic
77#2642C2211yescharacteristic
78#2625C2212yes—
79#2621C2211yescharacteristic
80#2621C2211yescharacteristic
81#2621C2212yes—
82#2612C2214yes—
83#2609C2214yes—
84#2605C2214yes—
85#2605C2214yes—
86#2599C2214yes—
87#2599C2214yes—
88#2596C2214yes—
89#2596C2214yes—
90#2594C2214yes—
91#2590C2214yes—
92#2590C2214yes—
93#2590C2214yes—
94#2588C2214yes—
95#2586C2214yes—
96#2585C2214yes—
97#2585C2214yes—
98#2581C2214yes—
99#2581C2212yes—
100#2577C2214yes—
101#2574C2214yes—
102#2570C2214yes—
103#2570C2212yes—
104#2569C2214yes—
105#2568C2212yes—
106#2565C2214yes—
107#2565C2214yes—
108#2551C2214yes—
109#2549C2214yes—
110#2546C2212yes—
111#2533C2214yes—
112#2533C2214yes—
113#2533C2214yes—
114#2533C2214yes—
115#2530C2214yes—
116#2528C2214yes—
117#2528C2214yes—
118#2528C2214yes—
119#2527C2214yes—
120#2524C2214yes—
121#2520C2214yes—
122#2520C2214yes—
123#2520C2214yes—
124#2520C2214yes—
125#2520C2214yes—
126#2520C2214yes—
127#2515C2214yes—
128#2514C2212yes—
129#2511C2212yes—
130#2511C2214yes—
131#2510C2214yes—
132#2505C2214yes—
133#2505C2214yes—
134#2499C2214yes—
135#2499C2214yes—
136#2493C2214yes—
137#2488C2214yes—
138#2481C2214yes—
139#2481C2214yes—
140#2477C2214yes—
141#2475C2214yes—
142#2473C2214yes—
143#2473C2214yes—
144#2473C2214yes—
145#2465C2214yes—
146#2465C2214yes—
147#2462C2214yes—
148#2462C2214yes—
149#2451C2212yes—
150#2451C2212yes—
151#2450C2214yes—
152#2449C2214yes—
153#2446C2212yes—
154#2446C2212yes—
155#2446C2212yes—
156#2446C2212yes—
157#2444C2214yes—
158#2440C2214yes—
159#2440C2214yes—
160#2440C2212yes—
161#2439C2212yes—
162#2438C2214yes—
163#2434C2212yes—
164#2434C2212yes—
165#2429C2212yes—
166#2429C2212yes—
167#2423C2212yes—
168#2421C2212yes—
169#2419C2214yes—
170#2417C2212yes—
171#2415C2212yes—
172#2409C2212yes—
173#2409C2212yes—
174#2399C2214yes—
175#2396C2214yes—
176#2373C2214yes—
177#2373C2212yes—
178#2373C2214yes—
179#2373C2212yes—
180#2372C2212yes—
181#2371C2212yes—
182#2371C2214yes—
183#2370C2214yes—
184#2368C2212yes—
185#2368C2214yes—
186#2368C2214yes—
187#2365C2214yes—
188#2365C2214yes—
189#2365C2214yes—
190#2365C2212yes—
191#2364C2212yes—
192#2362C2212yes—
193#2362C2214yes—
194#2360C2212yes—
195#2360C2214yes—
196#2359C2212yes—
197#2359C2212yes—
198#2352C2214yes—
199#2352C2212yes—
200#2351C2212yes—
201D4×C4⋊C4C2214yes—
202#2344C2214yes—
203#2344C2214yes—
204#2343C2214yes—
205Q8×C22⋊C4C2212yes—
206Q8×C22⋊C4C2212yes—
207#2330C2211yescharacteristic
208#2327C2211yescharacteristic
209#2327C2211yescharacteristic
210#2327C2214yes—
211#2327C2214yes—
212#2327C2211yescharacteristic
213#2327C2212yes—
214#2327C2212yes—
215#2327C2211yescharacteristic
216#2327C2211yescharacteristic
217#2327C2214yes—
218#2327C2211yescharacteristic
219#2327C2212yes—
220#2327C2211yescharacteristic
221#2323C2214yes—
222#2323C2212yes—
223#2323C2212yes—
224#2320C2212yes—
225#2314C2211yescharacteristic
226#2310C2212yes—
227C4×C4⋊Q8C2211yescharacteristic
228C4×C4⋊Q8C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×#125C2211yescharacteristic
231C4×C22⋊Q8C2214yes—
232C4×C22⋊Q8C2214yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235#2298C2211yescharacteristic
236#2298C2211yescharacteristic
237#2295C2211yescharacteristic
238#2295C2212yes—
239#2295C2211yescharacteristic
240#2295C2212yes—
241C2×#391C2212yes—
242#2290C2211yescharacteristic
243#2290C2211yescharacteristic
244#2290C2214yes—
245#2290C2214yes—
246#2290C2211yescharacteristic
247#2290C2211yescharacteristic
248C2×#387C2214yes—
249C2×#387C2214yes—
250#2285C2211yescharacteristic
251C2×#382C2211yescharacteristic
252#2276C2212yes—
253C42×D4C2211yescharacteristic
254C42×D4C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2312yes—
261D4×Q8—216no—
262#541—28no—
263#533—48no—
264C2×C4⋊Q8—28no—
265C2×C4⋊Q8—28no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277#529—28no—
278C2×#126C2311yescharacteristic
279C2×#126C2311yescharacteristic
280C2×#126C2314yes—
281C2×#125C2311yescharacteristic
282C2×#125C2314yes—
283C2×#125C2311yescharacteristic
284C2×#125C2314yes—
285C2×#124C2311yescharacteristic
286C2×#123C2311yescharacteristic
287C2×#123C2311yescharacteristic
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2311yescharacteristic
299#519—48no—
300C2×C4×Q8—48no—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2311yescharacteristic
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2314yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C22×C4⋊C4C2314yes—
332C22×C4⋊C4C2314yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2314yes—
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2314yes—
341#401C2314yes—
342#401C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
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#399C2314yes—
366#398C2314yes—
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#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#394C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2312yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2312yes—
491#388C2314yes—
492#388C2312yes—
493#388C2312yes—
494#388C2314yes—
495#388C2312yes—
496#388C2312yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#386C2312yes—
581#386C2314yes—
582#386C2312yes—
583#386C2314yes—
584#386C2312yes—
585#386C2312yes—
586#386C2314yes—
587#386C2314yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2312yes—
602#385C2312yes—
603#385C2314yes—
604#385C2314yes—
605#384C2312yes—
606#384C2311yescharacteristic
607#384C2314yes—
608#384C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#382C2311yescharacteristic
613#382C2314yes—
614#382C2314yes—
615#382C2314yes—
616#382C2312yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2311yescharacteristic
621#382C2311yescharacteristic
622#382C2314yes—
623#381C2314yes—
624#381C2314yes—
625#381C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2312yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2314yes—
633#380C2312yes—
634#380C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2311yescharacteristic
672C4×C22⋊C4C2311yescharacteristic
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2311yescharacteristic
686C4×C22⋊C4C2311yescharacteristic
687C4×C22⋊C4C2311yescharacteristic
688C4×C22⋊C4C2311yescharacteristic
689#376C2311yescharacteristic
690#376C2311yescharacteristic
691#376C2312yes—
692#376C2312yes—
693#376C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2311yescharacteristic
696#376C2311yescharacteristic
697#376C2314yes—
698#376C2314yes—
699#376C2312yes—
700#376C2314yes—
701C2×#95C2314yes—
702C2×#95C2314yes—
703C2×#95C2312yes—
704C2×#95C2312yes—
705C2×#95C2314yes—
706C43C2311yescharacteristic
707C43C2311yescharacteristic
708C43C2311yescharacteristic
709C43C2311yescharacteristic
710C22×Q8—28no—
711C22×Q8—28no—
712C22×Q8—28no—
713C22×Q8—28no—
714C22×Q8—44no—
715C22×Q8—44no—
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×D4C2411yescharacteristic
724C22×D4C2411yescharacteristic
725C22×D4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C23×C4C2411yescharacteristic
728C23×C4C2414yes—
729C23×C4C2414yes—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2414yes—
737C23×C4C2411yescharacteristic
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—216no—
741C4⋊Q8—216no—
742C4⋊Q8—216no—
743C4⋊Q8—24no—
744C4⋊Q8—24no—
745C4⋊Q8—28no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8#4118yes—
749#126—24no—
750#126—216no—
751#126—24no—
752#125—24no—
753#125—216no—
754#125—24no—
755#125—48no—
756#124—24no—
757#123—24no—
758#123—24no—
759C22⋊Q8—28no—
760C22⋊Q8—28no—
761C22⋊Q8—28no—
762C22⋊Q8—24no—
763C22⋊Q8—216no—
764C22⋊Q8—216no—
765C22⋊Q8—216no—
766C22⋊Q8—48no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769#121—24no—
770C4×Q8—28no—
771C4×Q8—24no—
772C4×Q8—28no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8—28no—
776C4×Q8—48no—
777C4×Q8—48no—
778C4×Q8—48no—
779C4×Q8—48no—
780C4×Q8—48no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×D4—216no—
786C4×D4—24no—
787C4×D4—24no—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4#4118yes—
791#117—24no—
792#117—28no—
793#117—24no—
794#117—24no—
795#117—24no—
796#117—48no—
797#117—48no—
798#117—48no—
799#117—44no—
800C2×C4⋊C4—216no—
801C2×C4⋊C4—216no—
802C2×C4⋊C4—48no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2411yescharacteristic
868C2×C22⋊C4C2411yescharacteristic
869C2×C22⋊C4C2411yescharacteristic
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2412yes—
893C2×C42—24no—
894C2×C42—24no—
895C2×C42—24no—
896C2×C42—24no—
897C2×C42—24no—
898C2×C42—48no—
899C2×C42C2414yes—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015C24C2511yescharacteristic
1016C24C2511yescharacteristic
1017C24C2511yescharacteristic
1018C2×Q8—24no—
1019C2×Q8—28no—
1020C2×Q8—28no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—28no—
1024C2×Q8—28no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—28no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—42no—
1036C2×Q8—44no—
1037C2×Q8—432no—
1038C2×Q8—432no—
1039C2×Q8C2×#4118yes—
1040C2×D4—24no—
1041C2×D4—22no—
1042C2×D4—24no—
1043C2×D4—22no—
1044C2×D4—42no—
1045C2×D4C2×#4114yes—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—28no—
1052C22×C4—28no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—22no—
1057C22×C4—28no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—28no—
1061C22×C4—28no—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4C2×#4114yes—
1079C22×C4C2×#4114yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2514yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—28no—
1122C4⋊C4—22no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4C2×#41116yes—
1169C4⋊C4C2×#4114yes—
1170C22⋊C4—22no—
1171C22⋊C4—22no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—22no—
1175C22⋊C4—22no—
1176C22⋊C4—24no—
1177C22⋊C4—28no—
1178C22⋊C4—22no—
1179C22⋊C4—22no—
1180C22⋊C4—24no—
1181C22⋊C4—22no—
1182C22⋊C4—22no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4C2×#4114yes—
1195C22⋊C4C2×#4114yes—
1196C22⋊C42−1+418yes—
1197C42—22no—
1198C42—22no—
1199C42—22no—
1200C42—22no—
1201C42—22no—
1202C42—24no—
1203C42—24no—
1204C42—22no—
1205C42—22no—
1206C42—22no—
1207C42—28no—
1208C42—28no—
1209C42—24no—
1210C42—22no—
1211C42—24no—
1212C42—22no—
1213C42—28no—
1214C42—28no—
1215C42—22no—
1216C42—28no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—44no—
1222C42—44no—
1223C42—42no—
1224C42—44no—
1225C42—42no—
1226C42—44no—
1227C42—42no—
1228C42—42no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42C2×#4114yes—
1234C42C2×#4114yes—
1235C42H(5,𝔽2)14yes—
1236C23—21no—
1237C23—21no—
1238C23—22no—
1239C23—21no—
1240C23—21no—
1241C23—22no—
1242C23—22no—
1243C23—21no—
1244C23—21no—
1245C23—21no—
1246C23—22no—
1247C23—22no—
1248C23C22×#4112yes—
1249C23C22×#4112yes—
1250C23C2×2−1+414yes—
1251C23C2611yescharacteristic
1252Q8—216no—
1253Q8—416no—
1254Q8—416no—
1255Q8—48no—
1256Q8—48no—
1257Q8—82no—
1258Q8—88no—
1259D4—28no—
1260D4—44no—
1261D4—82no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—24no—
1269C2×C4—21no—
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—28no—
1279C2×C4—28no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—21no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—48no—
1329C2×C4—48no—
1330C2×C4—48no—
1331C2×C4—48no—
1332C2×C4—416no—
1333C2×C4—416no—
1334C2×C4—44no—
1335C2×C4—44no—
1336C2×C4—82no—
1337C2×C4—88no—
1338C2×C4C22×#4112yes—
1339C2×C4C22×#4114yes—
1340C2×C4C22×#4112yes—
1341C2×C4C22×#4118yes—
1342C2×C4C22×#4112yes—
1343C2×C4C22×#4112yes—
1344C2×C4C22×#4112yes—
1345C2×C4C22×#4112yes—
1346C2×C4C2×H(5,𝔽2)14yes—
1347C2×C4C2×H(5,𝔽2)12yes—
1348C2×C4C2×2−1+414yes—
1349C2×C4C2×2−1+414yes—
1350C22—24no—
1351C22—22no—
1352C22—24no—
1353C22—22no—
1354C22—22no—
1355C22—22no—
1356C22—22no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—41no—
1361C22—41no—
1362C22—42no—
1363C22—41no—
1364C22#350914yes—
1365C22C23×#4111yescharacteristic
1366C22C23×#4111yescharacteristic
1367C22C22×H(5,𝔽2)11yescharacteristic
1368C22C22×2−1+412yes—
1369C222−1+612yes—
1370C4—24no—
1371C4—24no—
1372C4—22no—
1373C4—22no—
1374C4—24no—
1375C4—24no—
1376C4—22no—
1377C4—22no—
1378C4—28no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—44no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—42no—
1390C4—42no—
1391C4—44no—
1392C4—44no—
1393C4—44no—
1394C4—41no—
1395C4—44no—
1396C4—44no—
1397C4#348114yes—
1398C2—24no—
1399C2—42no—
1400C2—81no—
1401C2C2×#348111yescharacteristic
1402C2C2×#350911yescharacteristic
1403C2#6286111yescharacteristic
1404C2#6294212yes—
1405C2#6299812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59704C2semidirect
3. #59661C2semidirect
4. #59493C2semidirect
5. #44865C2semidirect
6. #44863C2semidirect
7. #44841C2semidirect
8. #44825C2semidirect
9. #39769C2semidirect
10. #39629C2semidirect
11. #39283C2semidirect
12. #38251C2semidirect
14. #37897C2semidirect
15. #37894C2semidirect
16. #37695C2semidirect
17. #37695C2semidirect
18. #36279C2semidirect
19. #36191C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35665C2semidirect
22. #35656C2semidirect
23. #35323C2semidirect
24. #35322C2semidirect
25. #35315C2semidirect
26. #34691C2semidirect
27. #34291C2semidirect
28. #34281C2semidirect
29. #34209C2semidirect
31. C2×#2327C2semidirect

Maximal subgroups

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

subgroupindex
#599582
#597042
#596612
#594932
#448652
#448632
#448412
#448252
#397692
#396292
#392832
#382512
#380272
#378972
#378942
#376952
#362792
#361912
D4×C4⋊Q82
#356652
#356562
#353232
#353222
#353152
#346912
#342912
#342812
#342092
#341492
C2×#23272