Finite Group Databasebeta

← #7648478

Subgroups — #7648478

Order 512.

4346 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42237C214yesmaximal, complemented
2#42231C214yesmaximal, complemented
3#42070C214yesmaximal, complemented
4#42062C214yesmaximal, complemented
5#39676C214yesmaximal, complemented
6#39073C214yesmaximal, complemented
7#38257C214yesmaximal, complemented
8#38233C214yesmaximal
9#37617C211yesmaximal, characteristic
10#37555C211yesmaximal, characteristic
11#37504C212yesmaximal, complemented
12#37397C211yesmaximal, characteristic, complemented
13#37396C211yesmaximal, characteristic, complemented
14#37359C212yesmaximal, complemented
15#37354C212yesmaximal, complemented
16#37320C211yesmaximal, characteristic, complemented
17#37320C211yesmaximal, characteristic, complemented
18#35604C212yesmaximal, complemented
19#35583C212yesmaximal, complemented
20#35324C211yesmaximal, characteristic, complemented
21#35314C211yesmaximal, characteristic, complemented
22#35294C211yesmaximal, characteristic, complemented
23#35283C211yesmaximal, characteristic, complemented
24#35281C211yesmaximal, characteristic, complemented
25#35231C212yesmaximal, complemented
26#35132C211yesmaximal, characteristic, complemented
27#35017C212yesmaximal, complemented
28#34772C212yesmaximal, complemented
29#34221C211yesmaximal, characteristic, complemented
30#34149C211yesmaximal, characteristic
31C2×#2331C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2868C2211yescharacteristic
36#2868C2211yescharacteristic
37#2864C2211yescharacteristic
38#2864C2211yescharacteristic
39#2863C2212yes—
40#2862C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2212yes—
45#2857C2212yes—
46#2855C2212yes—
47#2852C2214yes—
48#2851C2214yes—
49#2839C2214yes—
50#2836C2214yes—
51#2822C2212yes—
52#2821C2212yes—
53#2821C2212yes—
54#2820C2212yes—
55#2799C2214yes—
56#2799C2214yes—
57#2798C2214yes—
58#2794C2214yes—
59#2794C2214yes—
60#2789C2214yes—
61#2776C2214yes—
62#2775C2214yes—
63#2773C2214yes—
64#2772C2214yes—
65#2770C2214yes—
66#2769C2214yes—
67#2767C2214yes—
68#2766C2214yes—
69#2762C2214yes—
70#2759C2214yes—
71#2758C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2754C2214yes—
75#2721C2214yes—
76#2721C2214yes—
77#2719C2214yes—
78#2716C2214yes—
79#2716C2214yes—
80#2715C2214yes—
81#2713C2214yes—
82#2713C2214yes—
83#2713C2214yes—
84#2713C2214yes—
85#2700C2214yes—
86#2698C2214yes—
87#2667C2214yes—
88#2666C2214yes—
89#2666C2214yes—
90#2664C2214yes—
91#2660C2214yes—
92#2659C2212yes—
93#2658C2212yes—
94#2655C2214yes—
95#2655C2214yes—
96#2654C2214yes—
97#2647C2212yes—
98#2646C2214yes—
99#2645C2212yes—
100#2643C2214yes—
101#2642C2212yes—
102#2639C2212yes—
103#2637C2212yes—
104#2637C2212yes—
105#2629C2212yes—
106#2628C2211yescharacteristic
107#2628C2211yescharacteristic
108#2628C2211yescharacteristic
109#2628C2211yescharacteristic
110#2628C2211yescharacteristic
111#2628C2211yescharacteristic
112#2625C2212yes—
113#2623C2212yes—
114#2623C2212yes—
115#2621C2211yescharacteristic
116#2621C2211yescharacteristic
117#2612C2214yes—
118#2612C2214yes—
119#2606C2214yes—
120#2605C2214yes—
121#2596C2214yes—
122#2588C2214yes—
123#2588C2214yes—
124#2588C2214yes—
125#2585C2214yes—
126#2585C2214yes—
127#2581C2212yes—
128#2575C2214yes—
129#2570C2212yes—
130#2570C2214yes—
131#2567C2212yes—
132#2567C2212yes—
133#2556C2214yes—
134#2550C2212yes—
135#2550C2214yes—
136#2550C2214yes—
137#2547C2212yes—
138#2546C2214yes—
139#2546C2212yes—
140#2536C2212yes—
141#2530C2214yes—
142#2529C2214yes—
143#2528C2214yes—
144#2527C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2523C2214yes—
148#2522C2214yes—
149#2521C2214yes—
150#2520C2214yes—
151#2520C2214yes—
152#2520C2214yes—
153#2519C2214yes—
154#2517C2214yes—
155#2514C2212yes—
156#2511C2212yes—
157#2511C2214yes—
158#2510C2214yes—
159#2507C2212yes—
160#2507C2212yes—
161#2506C2212yes—
162#2506C2212yes—
163#2505C2214yes—
164#2505C2214yes—
165#2502C2212yes—
166#2502C2212yes—
167#2498C2212yes—
168#2498C2212yes—
169#2497C2212yes—
170#2497C2212yes—
171#2496C2212yes—
172#2496C2212yes—
173#2492C2212yes—
174#2492C2214yes—
175#2489C2212yes—
176#2487C2212yes—
177#2487C2212yes—
178#2481C2214yes—
179#2478C2214yes—
180#2474C2214yes—
181#2473C2214yes—
182#2473C2214yes—
183#2462C2214yes—
184#2453C2212yes—
185#2451C2212yes—
186#2451C2214yes—
187#2451C2214yes—
188#2450C2214yes—
189#2449C2214yes—
190#2442C2212yes—
191#2441C2214yes—
192#2440C2212yes—
193#2439C2214yes—
194#2438C2214yes—
195#2436C2212yes—
196#2434C2214yes—
197#2434C2212yes—
198#2423C2212yes—
199#2423C2214yes—
200#2421C2212yes—
201#2417C2212yes—
202#2417C2212yes—
203#2402C2214yes—
204#2396C2214yes—
205#2373C2212yes—
206#2373C2212yes—
207#2372C2212yes—
208#2371C2214yes—
209#2371C2212yes—
210#2368C2214yes—
211#2368C2212yes—
212#2364C2212yes—
213#2359C2212yes—
214#2359C2212yes—
215#2356C2214yes—
216#2343C2214yes—
217#2331C2212yes—
218#2331C2211yescharacteristic
219#2331C2211yescharacteristic
220#2331C2214yes—
221#2331C2214yes—
222#2331C2211yescharacteristic
223#2331C2211yescharacteristic
224#2331C2212yes—
225#2331C2211yescharacteristic
226#2331C2211yescharacteristic
227#2330C2212yes—
228#2329C2214yes—
229#2329C2214yes—
230#2327C2211yescharacteristic
231#2327C2211yescharacteristic
232#2323C2212yes—
233#2320C2212yes—
234#2320C2212yes—
235#2318C2214yes—
236#2317C2214yes—
237#2314C2212yes—
238C4×C4⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2214yes—
243#2298C2211yescharacteristic
244#2298C2211yescharacteristic
245#2295C2211yescharacteristic
246#2295C2211yescharacteristic
247#2295C2212yes—
248C2×#391C2214yes—
249C2×#389C2212yes—
250#2290C2211yescharacteristic
251#2290C2214yes—
252#2290C2211yescharacteristic
253#2290C2211yescharacteristic
254#2290C2211yescharacteristic
255C2×#387C2214yes—
256#2285C2212yes—
257#2283C2211yescharacteristic
258C2×#382C2211yescharacteristic
259#2276C2212yes—
260C42×D4C2211yescharacteristic
261C42×D4C2211yescharacteristic
262C4×#117C2211yescharacteristic
263C4×#117C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2212yes—
266C2×#376C2211yescharacteristic
267C23×Q8C2312yes—
268#533—28no—
269C2×C4⋊Q8—28no—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2314yes—
281#529—28no—
282C2×#126C2311yescharacteristic
283C2×#126C2311yescharacteristic
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#125C2312yes—
287C2×#125C2311yescharacteristic
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#124C2311yescharacteristic
293C2×#124C2314yes—
294C2×#123C2311yescharacteristic
295C2×#123C2311yescharacteristic
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2311yescharacteristic
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×#121C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C2×#117C2314yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2314yes—
331C22×C42C2311yescharacteristic
332#401C2314yes—
333#401C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2312yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#399C2312yes—
365#399C2312yes—
366#399C2314yes—
367#399C2314yes—
368#399C2312yes—
369#399C2314yes—
370#399C2312yes—
371#399C2312yes—
372#399C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2312yes—
435#395C2312yes—
436#394C2314yes—
437#393C2312yes—
438#393C2312yes—
439#393C2312yes—
440#393C2312yes—
441#393C2312yes—
442#393C2312yes—
443#393C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
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#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
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#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2312yes—
603#386C2312yes—
604#386C2312yes—
605#386C2312yes—
606#386C2314yes—
607#386C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2312yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2312yes—
621#385C2312yes—
622#385C2314yes—
623#385C2314yes—
624#384C2312yes—
625#384C2312yes—
626#384C2312yes—
627#384C2312yes—
628#384C2314yes—
629#384C2312yes—
630#384C2314yes—
631#383C2312yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2312yes—
640#382C2314yes—
641#382C2314yes—
642#382C2314yes—
643#382C2314yes—
644#382C2314yes—
645#382C2311yescharacteristic
646#382C2311yescharacteristic
647#382C2311yescharacteristic
648#382C2311yescharacteristic
649#382C2312yes—
650#382C2314yes—
651#381C2314yes—
652#381C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2311yescharacteristic
714C4×C22⋊C4C2311yescharacteristic
715#376C2311yescharacteristic
716#376C2311yescharacteristic
717#376C2311yescharacteristic
718#376C2311yescharacteristic
719#376C2312yes—
720#376C2312yes—
721#376C2311yescharacteristic
722#376C2314yes—
723#376C2314yes—
724#376C2312yes—
725#376C2312yes—
726#376C2311yescharacteristic
727C2×#95C2314yes—
728C2×#95C2312yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2312yes—
732C2×#95C2314yes—
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C22×Q8—28no—
738C22×Q8—84no—
739C22×Q8C2412yes—
740C22×Q8C2414yes—
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×Q8C2414yes—
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×D4C2411yescharacteristic
747C22×D4C2411yescharacteristic
748C22×D4C2411yescharacteristic
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2414yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2411yescharacteristic
760C4⋊Q8—24no—
761C4⋊Q8—24no—
762C4⋊Q8—28no—
763C4⋊Q8—28no—
764C4⋊Q8—28no—
765C4⋊Q8—24no—
766C4⋊Q8—24no—
767C4⋊Q8—44no—
768C4⋊Q8—84no—
769C4⋊Q8—84no—
770C4⋊Q8—84no—
771#126—24no—
772#126—24no—
773#126—84no—
774#126—84no—
775#125—24no—
776#125—28no—
777#125—44no—
778#125—84no—
779#125—84no—
780#125—84no—
781#124—24no—
782#124—84no—
783#123—24no—
784#123—24no—
785C22⋊Q8—24no—
786C22⋊Q8—28no—
787C22⋊Q8—28no—
788C22⋊Q8—216no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C22⋊Q8—84no—
792#121—24no—
793C4×Q8—24no—
794C4×Q8—28no—
795C4×Q8—28no—
796C4×Q8—28no—
797C4×Q8—44no—
798C4×Q8—84no—
799C4×D4—24no—
800C4×D4—24no—
801C4×D4—28no—
802C4×D4—28no—
803C4×D4—24no—
804#117—28no—
805#117—28no—
806#117—24no—
807#117—24no—
808#117—24no—
809#117—42no—
810#117—84no—
811C2×C4⋊C4—28no—
812C2×C4⋊C4—28no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—84no—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2411yescharacteristic
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C42—24no—
912C2×C42—24no—
913C2×C42—42no—
914C2×C42—42no—
915C2×C42—84no—
916C2×C42#4118yes—
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2414yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928C2×C42C2414yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035C24C2511yescharacteristic
1036C24C2511yescharacteristic
1037C24C2511yescharacteristic
1038C2×Q8—24no—
1039C2×Q8—22no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—28no—
1044C2×Q8—24no—
1045C2×Q8—28no—
1046C2×Q8—24no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—42no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—816no—
1056C2×D4—22no—
1057C2×D4—22no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—42no—
1062C22×C4—24no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—28no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—28no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—24no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—42no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4C2×#4114yes—
1091C22×C4C2×#4114yes—
1092C22×C4C2×#4114yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—22no—
1129C4⋊C4—22no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—22no—
1135C4⋊C4—22no—
1136C4⋊C4—22no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C22⋊C4—28no—
1190C22⋊C4—22no—
1191C22⋊C4—22no—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—22no—
1195C22⋊C4—22no—
1196C22⋊C4—22no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—22no—
1201C22⋊C4—22no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C42−1+418yes—
1217C42—22no—
1218C42—22no—
1219C42—28no—
1220C42—22no—
1221C42—24no—
1222C42—24no—
1223C42—22no—
1224C42—24no—
1225C42—24no—
1226C42—22no—
1227C42—24no—
1228C42—24no—
1229C42—28no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—22no—
1234C42—42no—
1235C42—42no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—42no—
1243C42—44no—
1244C42—42no—
1245C42—44no—
1246C42—42no—
1247C42—42no—
1248C42C2×#4114yes—
1249C42C2×#4114yes—
1250C42C2×#4114yes—
1251C42C2×#4114yes—
1252C422−1+414yes—
1253C23—21no—
1254C23—21no—
1255C23—22no—
1256C23—21no—
1257C23—21no—
1258C23—21no—
1259C23—22no—
1260C23—22no—
1261C23—21no—
1262C23—21no—
1263C23—21no—
1264C23—22no—
1265C23—22no—
1266C23C22×#4112yes—
1267C23C2×2−1+414yes—
1268C23C2611yescharacteristic
1269Q8—48no—
1270Q8—82no—
1271Q8—84no—
1272Q8—88no—
1273Q8—88no—
1274Q8—84no—
1275Q8—84no—
1276D4—44no—
1277D4—44no—
1278D4—82no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—28no—
1292C2×C4—28no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—21no—
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—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—21no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—44no—
1347C2×C4—48no—
1348C2×C4—48no—
1349C2×C4—416no—
1350C2×C4—44no—
1351C2×C4—44no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—88no—
1355C2×C4C22×#4112yes—
1356C2×C4C22×#4112yes—
1357C2×C4C22×#4112yes—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C2×2−1+414yes—
1362C2×C4C2×2−1+414yes—
1363C2×C4C2×2−1+414yes—
1364C2×C4C2×2−1+412yes—
1365C2×C4#58512yes—
1366C22—22no—
1367C22—22no—
1368C22—24no—
1369C22—24no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22#350914yes—
1381C22C23×#4111yescharacteristic
1382C22C22×2−1+412yes—
1383C22C22×2−1+411yescharacteristic
1384C22C2×#58511yescharacteristic
1385C22H(7,𝔽2)12yes—
1386C4—22no—
1387C4—22no—
1388C4—22no—
1389C4—22no—
1390C4—22no—
1391C4—24no—
1392C4—24no—
1393C4—24no—
1394C4—41no—
1395C4—41no—
1396C4—44no—
1397C4—44no—
1398C4—41no—
1399C4—41no—
1400C4—44no—
1401C4—41no—
1402C4—41no—
1403C4—44no—
1404C4—42no—
1405C4—44no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—42no—
1411C4—44no—
1412C4—44no—
1413C4#346114yes—
1414C2—24no—
1415C2—81no—
1416C2—81no—
1417C2C2×#346111yescharacteristic
1418C2C2×#350911yescharacteristic
1419C2#6285511yescharacteristic
1420C2#6294512yes—
1421C2#6295112yes—
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
1. #42237C2semidirect
2. #42231C2semidirect
3. #42070C2semidirect
4. #42062C2semidirect
5. #39676C2semidirect
6. #39073C2semidirect
7. #38257C2semidirect
11. #37504C2semidirect
12. #37397C2semidirect
13. #37396C2semidirect
14. #37359C2semidirect
15. #37354C2semidirect
16. #37320C2semidirect
17. #37320C2semidirect
18. #35604C2semidirect
19. #35583C2semidirect
20. #35324C2semidirect
21. #35314C2semidirect
22. #35294C2semidirect
23. #35283C2semidirect
24. #35281C2semidirect
25. #35231C2semidirect
26. #35132C2semidirect
27. #35017C2semidirect
28. #34772C2semidirect
29. #34221C2semidirect
31. C2×#2331C2semidirect

Maximal subgroups

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

subgroupindex
#422372
#422312
#420702
#420622
#396762
#390732
#382572
#382332
#376172
#375552
#375042
#373972
#373962
#373592
#373542
#373202
#356042
#355832
#353242
#353142
#352942
#352832
#352812
#352312
#351322
#350172
#347722
#342212
#341492
C2×#23312