Finite Group Databasebeta

← #7732365

Subgroups — #7732365

Order 512.

4740 conjugacy classes of subgroups.

The subgroup lattice has 1484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51105C214yesmaximal, complemented
2#50734C214yesmaximal, complemented
3#47759C214yesmaximal, complemented
4#47744C214yesmaximal, complemented
5#44024C214yesmaximal, complemented
6#43978C214yesmaximal, complemented
7#39797C212yesmaximal, complemented
8#39796C212yesmaximal, complemented
9#39768C212yesmaximal, complemented
10#39767C212yesmaximal, complemented
11#39694C212yesmaximal, complemented
12#39297C212yesmaximal, complemented
13#38291C212yesmaximal, complemented
14#38124C212yesmaximal, complemented
15#37796C212yesmaximal, complemented
16#37704C212yesmaximal, complemented
17#37555C211yesmaximal, characteristic, complemented
18#37408C212yesmaximal, complemented
19#37357C212yesmaximal, complemented
20#36305C212yesmaximal, complemented
21#36112C212yesmaximal, complemented
22#35643C212yesmaximal, complemented
23#35572C212yesmaximal, complemented
24#35238C211yesmaximal, characteristic
25#35180C211yesmaximal, characteristic, complemented
26C2×#2550C211yesmaximal, characteristic, complemented
27#34398C211yesmaximal, characteristic, complemented
28#34235C211yesmaximal, characteristic, complemented
29#34083C211yesmaximal, characteristic, complemented
30C2×#542C2212yes—
31C2×#533C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#529C2212yes—
36C22×#125C2211yescharacteristic
37#2861C2212yes—
38#2860C2212yes—
39#2856C2212yes—
40#2855C2212yes—
41#2851C2212yes—
42#2850C2212yes—
43#2850C2212yes—
44#2850C2212yes—
45#2822C2212yes—
46#2820C2212yes—
47#2808C2214yes—
48#2808C2214yes—
49#2804C2214yes—
50#2800C2214yes—
51#2796C2214yes—
52#2796C2214yes—
53#2788C2214yes—
54#2783C2214yes—
55#2772C2214yes—
56#2767C2214yes—
57#2765C2214yes—
58#2764C2214yes—
59#2763C2214yes—
60#2762C2214yes—
61#2761C2214yes—
62#2759C2214yes—
63#2759C2214yes—
64#2757C2214yes—
65#2757C2214yes—
66#2754C2214yes—
67#2751C2214yes—
68#2751C2214yes—
69#2748C2214yes—
70#2745C2214yes—
71#2744C2214yes—
72#2742C2214yes—
73#2740C2214yes—
74#2737C2214yes—
75#2737C2214yes—
76#2731C2214yes—
77#2729C2214yes—
78#2724C2214yes—
79#2723C2214yes—
80#2722C2214yes—
81#2717C2214yes—
82#2716C2214yes—
83#2715C2214yes—
84#2700C2214yes—
85#2689C2214yes—
86#2674C2214yes—
87#2662C2214yes—
88#2659C2212yes—
89#2644C2212yes—
90#2640C2212yes—
91#2639C2212yes—
92#2639C2212yes—
93#2639C2212yes—
94#2637C2214yes—
95#2628C2212yes—
96#2628C2212yes—
97#2625C2212yes—
98#2621C2212yes—
99#2612C2214yes—
100#2610C2214yes—
101#2605C2214yes—
102#2605C2214yes—
103#2603C2214yes—
104#2601C2214yes—
105#2592C2214yes—
106#2592C2214yes—
107#2588C2214yes—
108#2587C2214yes—
109#2586C2214yes—
110#2581C2212yes—
111#2580C2214yes—
112#2579C2214yes—
113#2577C2214yes—
114#2574C2214yes—
115#2570C2214yes—
116#2568C2212yes—
117#2567C2211yescharacteristic
118#2566C2212yes—
119#2564C2214yes—
120#2563C2212yes—
121#2563C2211yescharacteristic
122#2562C2214yes—
123#2560C2214yes—
124#2558C2214yes—
125#2554C2214yes—
126#2550C2212yes—
127#2550C2212yes—
128#2550C2214yes—
129#2550C2212yes—
130#2550C2214yes—
131#2550C2212yes—
132#2548C2212yes—
133#2548C2211yescharacteristic
134#2547C2212yes—
135#2544C2214yes—
136#2544C2212yes—
137#2541C2211yescharacteristic
138#2536C2212yes—
139#2532C2214yes—
140#2531C2214yes—
141#2526C2214yes—
142#2525C2214yes—
143#2521C2214yes—
144#2520C2214yes—
145#2519C2214yes—
146#2513C2214yes—
147#2511C2214yes—
148#2510C2214yes—
149#2509C2212yes—
150#2508C2212yes—
151#2505C2214yes—
152#2504C2214yes—
153#2498C2214yes—
154#2495C2212yes—
155#2494C2212yes—
156#2492C2212yes—
157#2491C2212yes—
158#2490C2212yes—
159#2489C2212yes—
160#2481C2214yes—
161#2481C2214yes—
162#2481C2214yes—
163#2478C2214yes—
164#2475C2214yes—
165#2469C2214yes—
166#2466C2214yes—
167#2465C2214yes—
168#2461C2214yes—
169#2460C2214yes—
170#2454C2212yes—
171#2453C2212yes—
172#2452C2212yes—
173#2451C2212yes—
174#2447C2214yes—
175#2447C2212yes—
176#2447C2212yes—
177#2445C2214yes—
178#2444C2214yes—
179#2444C2214yes—
180#2443C2214yes—
181#2443C2214yes—
182#2438C2214yes—
183#2436C2214yes—
184#2430C2214yes—
185#2426C2212yes—
186#2426C2212yes—
187#2419C2214yes—
188#2417C2212yes—
189#2417C2212yes—
190#2416C2212yes—
191#2416C2212yes—
192#2409C2214yes—
193C2×#398C2212yes—
194C2×#395C2212yes—
195#2379C2212yes—
196#2379C2212yes—
197#2365C2211yescharacteristic
198#2365C2211yescharacteristic
199#2365C2211yescharacteristic
200#2365C2211yescharacteristic
201#2361C2214yes—
202#2361C2212yes—
203#2361C2212yes—
204#2361C2214yes—
205#2360C2212yes—
206#2360C2212yes—
207#2357C2212yes—
208#2356C2212yes—
209#2353C2214yes—
210#2352C2214yes—
211#2351C2212yes—
212#2349C2212yes—
213#2343C2214yes—
214#2339C2214yes—
215#2337C2212yes—
216#2336C2212yes—
217#2336C2214yes—
218#2334C2212yes—
219#2334C2212yes—
220#2331C2212yes—
221#2331C2212yes—
222#2329C2211yescharacteristic
223#2329C2211yescharacteristic
224#2328C2212yes—
225#2325C2211yescharacteristic
226#2325C2211yescharacteristic
227#2325C2212yes—
228#2325C2212yes—
229#2324C2212yes—
230#2324C2212yes—
231#2324C2212yes—
232#2322C2212yes—
233#2322C2212yes—
234#2320C2212yes—
235#2320C2212yes—
236#2318C2214yes—
237#2311C2212yes—
238#2311C2212yes—
239C4×#125C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×#121C2212yes—
243#2298C2212yes—
244#2296C2212yes—
245#2295C2212yes—
246#2295C2212yes—
247C2×#391C2212yes—
248C2×#389C2212yes—
249C2×#389C2211yescharacteristic
250C2×#389C2211yescharacteristic
251#2290C2212yes—
252#2290C2212yes—
253#2283C2211yescharacteristic
254C2×#382C2211yescharacteristic
255#2276C2212yes—
256C42×D4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#542—48no—
262#533—28no—
263#532—28no—
264C2×C4⋊Q8—44no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273#529—28no—
274#529—48no—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125—44no—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2311yescharacteristic
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#123C2312yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2311yescharacteristic
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×#117C2312yes—
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2314yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345C22×C42C2312yes—
346C22×C42C2312yes—
347C22×C42C2311yescharacteristic
348#401C2314yes—
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#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#398C2314yes—
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#397C2314yes—
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#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#392C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2314yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
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#388C2312yes—
519#388C2312yes—
520#388C2312yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2312yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2312yes—
529#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2312yes—
593#386C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2312yes—
614#385C2312yes—
615#385C2312yes—
616#385C2312yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#384C2312yes—
631#383C2312yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2314yes—
641#382C2314yes—
642#382C2314yes—
643#382C2312yes—
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2312yes—
647#382C2312yes—
648#381C2314yes—
649#381C2312yes—
650#381C2314yes—
651#381C2314yes—
652#381C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2311yescharacteristic
664#380C2311yescharacteristic
665#380C2314yes—
666#380C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2314yes—
711C2×#95C2312yes—
712C2×#95C2311yescharacteristic
713C2×#95C2311yescharacteristic
714C2×#95C2312yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C2×#95C2312yes—
718C43C2312yes—
719C2×#41—28no—
720C2×#41—44no—
721C2×#41—44no—
722C22×Q8—44no—
723C22×Q8—44no—
724C22×Q8—82no—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2414yes—
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2411yescharacteristic
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C4⋊Q8—28no—
757C4⋊Q8—24no—
758C4⋊Q8—24no—
759C4⋊Q8—24no—
760C4⋊Q8—44no—
761C4⋊Q8—48no—
762#127—24no—
763#127—82no—
764#126—28no—
765#126—48no—
766#126—48no—
767#126—84no—
768#125—28no—
769#125—24no—
770#125—28no—
771#125—44no—
772#125—48no—
773#124—24no—
774#124—28no—
775#124—44no—
776#124—44no—
777#124—48no—
778#124—82no—
779#124—84no—
780#123—28no—
781#123—48no—
782#123—48no—
783C22⋊Q8—24no—
784C22⋊Q8—28no—
785C22⋊Q8—28no—
786C22⋊Q8—48no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—84no—
790#121—24no—
791#121—28no—
792#121—28no—
793#121—28no—
794#121—28no—
795#121—48no—
796#121—48no—
797C4×Q8—28no—
798C4×Q8—28no—
799C4×Q8—24no—
800C4×Q8—28no—
801C4×Q8—28no—
802C4×Q8—82no—
803C4×Q8—82no—
804C4×D4—28no—
805C4×D4—24no—
806C4×D4—28no—
807C4×D4—28no—
808C4×D4—44no—
809C4×D4—48no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—48no—
814C4×D4—48no—
815C4×D4—84no—
816#117—28no—
817#117—28no—
818#117—44no—
819#117—48no—
820C2×C4⋊C4—24no—
821C2×C4⋊C4—24no—
822C2×C4⋊C4—44no—
823C2×C4⋊C4—42no—
824C2×C4⋊C4—44no—
825C2×C4⋊C4—42no—
826C2×C4⋊C4—44no—
827C2×C4⋊C4—42no—
828C2×C4⋊C4—42no—
829C2×C4⋊C4—44no—
830C2×C4⋊C4—82no—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C42—42no—
934C2×C42—44no—
935C2×C42—42no—
936C2×C42—82no—
937C2×C42#4118yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
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—
1034C24C2512yes—
1035C24C2514yes—
1036C24C2511yescharacteristic
1037#41—816no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—22no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—28no—
1044C2×Q8—24no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—41no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—41no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—816no—
1057C2×D4—24no—
1058C2×D4—28no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—28no—
1062C2×D4—28no—
1063C2×D4—24no—
1064C2×D4—22no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—28no—
1069C2×D4—24no—
1070C2×D4—28no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—41no—
1077C2×D4—41no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—22no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—22no—
1090C22×C4—24no—
1091C22×C4—22no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—28no—
1099C22×C4—41no—
1100C22×C4—41no—
1101C22×C4—41no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—41no—
1114C22×C4—42no—
1115C22×C4—44no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—44no—
1119C22×C4—42no—
1120C22×C4—41no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4C2×#4114yes—
1130C22×C4C2×#4114yes—
1131C22×C4C2×#4114yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—22no—
1165C4⋊C4—24no—
1166C4⋊C4—22no—
1167C4⋊C4—28no—
1168C4⋊C4—28no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—22no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—24no—
1181C4⋊C4—22no—
1182C4⋊C4—28no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—42no—
1215C4⋊C4—44no—
1216C4⋊C4H(5,𝔽2)14yes—
1217C4⋊C42−1+414yes—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C42—24no—
1261C42—28no—
1262C42—24no—
1263C42—24no—
1264C42—24no—
1265C42—28no—
1266C42—24no—
1267C42—28no—
1268C42—42no—
1269C42—42no—
1270C42—42no—
1271C42—42no—
1272C42—42no—
1273C42—42no—
1274C42—42no—
1275C42—42no—
1276C42—42no—
1277C42—42no—
1278C42—42no—
1279C42—44no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—42no—
1284C42C2×#4114yes—
1285C42C2×#4114yes—
1286C42C2×#4114yes—
1287C42C2×#4114yes—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—22no—
1293C23—24no—
1294C23—24no—
1295C23—22no—
1296C23—24no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—24no—
1301C23—24no—
1302C23—24no—
1303C23—22no—
1304C23—22no—
1305C23—24no—
1306C23C22×#4112yes—
1307C23#58512yes—
1308C23#58512yes—
1309C23C2611yescharacteristic
1310Q8—48no—
1311Q8—48no—
1312Q8—82no—
1313Q8—88no—
1314Q8—84no—
1315Q8—88no—
1316D4—48no—
1317D4—416no—
1318D4—48no—
1319D4—82no—
1320D4—84no—
1321D4—88no—
1322D4—88no—
1323D4—84no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—28no—
1339C2×C4—28no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
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—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—44no—
1395C2×C4—48no—
1396C2×C4—48no—
1397C2×C4—44no—
1398C2×C4—44no—
1399C2×C4—48no—
1400C2×C4—88no—
1401C2×C4—82no—
1402C2×C4—82no—
1403C2×C4—84no—
1404C2×C4—84no—
1405C2×C4—84no—
1406C2×C4—84no—
1407C2×C4—88no—
1408C2×C4—164no—
1409C2×C4C22×#4112yes—
1410C2×C4C22×#4112yes—
1411C2×C4C22×#4112yes—
1412C2×C4C22×#4112yes—
1413C2×C4C22×#4112yes—
1414C2×C4C22×#4112yes—
1415C2×C4C2×H(5,𝔽2)14yes—
1416C2×C4C2×H(5,𝔽2)12yes—
1417C2×C4C2×2−1+414yes—
1418C2×C4C2×2−1+412yes—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—22no—
1424C22—22no—
1425C22—42no—
1426C22—44no—
1427C22—44no—
1428C22—42no—
1429C22—42no—
1430C22—44no—
1431C22—42no—
1432C22—44no—
1433C22—44no—
1434C22—42no—
1435C22—42no—
1436C22—44no—
1437C22—44no—
1438C22—42no—
1439C22#351014yes—
1440C22C23×#4111yescharacteristic
1441C22C22×H(5,𝔽2)11yescharacteristic
1442C22C22×2−1+411yescharacteristic
1443C22C2×#58511yescharacteristic
1444C22C2×#58511yescharacteristic
1445C22H(7,𝔽2)11yescharacteristic
1446C222−1+611yescharacteristic
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—24no—
1453C4—24no—
1454C4—42no—
1455C4—44no—
1456C4—44no—
1457C4—42no—
1458C4—44no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—42no—
1463C4—42no—
1464C4—44no—
1465C4—42no—
1466C4—42no—
1467C4—44no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—42no—
1472C4#351114yes—
1473C2—24no—
1474C2—82no—
1475C2—84no—
1476C2C2×#351111yescharacteristic
1477C2C2×#351011yescharacteristic
1478C2#6285611yescharacteristic
1479C2#6289611yescharacteristic
1480C2#6289711yescharacteristic
1481C2#6294811yescharacteristic
1482C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35238C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51105C2semidirect
2. #50734C2semidirect
3. #47759C2semidirect
4. #47744C2semidirect
5. #44024C2semidirect
6. #43978C2semidirect
7. #39797C2semidirect
8. #39796C2semidirect
9. #39768C2semidirect
10. #39767C2semidirect
11. #39694C2semidirect
12. #39297C2semidirect
13. #38291C2semidirect
14. #38124C2semidirect
15. #37796C2semidirect
16. #37704C2semidirect
17. #37555C2semidirect
18. #37408C2semidirect
19. #37357C2semidirect
20. #36305C2semidirect
21. #36112C2semidirect
22. #35643C2semidirect
23. #35572C2semidirect
25. #35180C2semidirect
26. C2×#2550C2semidirect
27. #34398C2semidirect
28. #34235C2semidirect
29. #34083C2semidirect

Maximal subgroups

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

subgroupindex
#511052
#507342
#477592
#477442
#440242
#439782
#397972
#397962
#397682
#397672
#396942
#392972
#382912
#381242
#377962
#377042
#375552
#374082
#373572
#363052
#361122
#356432
#355722
#352382
#351802
C2×#25502
#343982
#342352
#340832