Finite Group Databasebeta

← #8107697

Subgroups — #8107697

Order 512.

4259 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53021C212yesmaximal
2#53013C212yesmaximal, complemented
3#52831C214yesmaximal, complemented
4#52572C214yesmaximal, complemented
5#45436C211yesmaximal, characteristic, complemented
6#45434C211yesmaximal, characteristic, complemented
7#45394C211yesmaximal, characteristic, complemented
8#45389C211yesmaximal, characteristic, complemented
9#44853C214yesmaximal, complemented
10#44804C214yesmaximal, complemented
11#42879C211yesmaximal, characteristic, complemented
12#42823C212yesmaximal, complemented
13#42791C211yesmaximal, characteristic, complemented
14#42789C211yesmaximal, characteristic
15#42702C212yesmaximal, complemented
16#42649C211yesmaximal, characteristic
17#42273C214yesmaximal, complemented
18#42194C214yesmaximal, complemented
19#42062C214yesmaximal, complemented
20#42006C214yesmaximal, complemented
21#36508C211yesmaximal, characteristic, complemented
22#36481C212yesmaximal, complemented
23#36474C211yesmaximal, characteristic, complemented
24#36394C211yesmaximal, characteristic, complemented
25#36385C212yesmaximal
26#36383C211yesmaximal, characteristic, complemented
27#35318C211yesmaximal, characteristic
28#35314C211yesmaximal, characteristic, complemented
29#35199C212yesmaximal, complemented
30#35184C212yesmaximal, complemented
31#34552C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#556C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#541C2211yescharacteristic
38#2864C2211yescharacteristic
39#2863C2212yes—
40#2863C2212yes—
41#2863C2212yes—
42#2862C2212yes—
43#2862C2211yescharacteristic
44#2862C2211yescharacteristic
45#2861C2212yes—
46#2861C2211yescharacteristic
47#2857C2211yescharacteristic
48#2850C2211yescharacteristic
49#2845C2214yes—
50#2843C2214yes—
51#2841C2214yes—
52#2839C2214yes—
53#2837C2214yes—
54#2836C2214yes—
55#2836C2214yes—
56#2836C2214yes—
57#2831C2214yes—
58#2822C2212yes—
59#2821C2212yes—
60#2821C2212yes—
61#2820C2214yes—
62#2814C2212yes—
63#2802C2214yes—
64#2792C2214yes—
65#2783C2214yes—
66#2783C2214yes—
67#2779C2214yes—
68#2777C2214yes—
69#2774C2214yes—
70#2773C2214yes—
71#2769C2214yes—
72#2769C2214yes—
73#2768C2214yes—
74#2768C2214yes—
75#2755C2214yes—
76#2754C2214yes—
77#2738C2214yes—
78#2734C2214yes—
79#2726C2214yes—
80#2726C2214yes—
81#2725C2214yes—
82#2722C2214yes—
83#2721C2214yes—
84#2721C2214yes—
85#2720C2214yes—
86#2719C2214yes—
87#2715C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2704C2214yes—
91#2704C2214yes—
92#2700C2214yes—
93#2677C2214yes—
94#2674C2214yes—
95#2667C2214yes—
96#2666C2214yes—
97#2666C2214yes—
98#2666C2214yes—
99#2664C2212yes—
100#2660C2212yes—
101#2660C2214yes—
102#2660C2211yescharacteristic
103#2659C2212yes—
104#2658C2212yes—
105#2658C2211yescharacteristic
106#2654C2214yes—
107#2654C2214yes—
108#2654C2214yes—
109#2637C2212yes—
110#2634C2212yes—
111#2632C2212yes—
112#2628C2211yescharacteristic
113#2625C2212yes—
114#2625C2212yes—
115#2621C2211yescharacteristic
116#2621C2211yescharacteristic
117#2620C2211yescharacteristic
118#2612C2214yes—
119#2612C2214yes—
120#2609C2214yes—
121#2606C2214yes—
122#2606C2214yes—
123#2606C2214yes—
124#2604C2212yes—
125#2604C2212yes—
126#2599C2214yes—
127#2584C2212yes—
128#2582C2212yes—
129#2581C2211yescharacteristic
130#2581C2211yescharacteristic
131#2581C2211yescharacteristic
132#2580C2211yescharacteristic
133#2577C2214yes—
134#2575C2214yes—
135#2574C2214yes—
136#2568C2212yes—
137#2568C2212yes—
138#2567C2212yes—
139#2567C2211yescharacteristic
140#2565C2212yes—
141#2556C2214yes—
142#2556C2214yes—
143#2553C2214yes—
144#2552C2212yes—
145#2552C2212yes—
146#2551C2212yes—
147#2550C2214yes—
148#2550C2212yes—
149#2550C2214yes—
150#2550C2214yes—
151#2549C2214yes—
152#2547C2212yes—
153#2546C2212yes—
154#2546C2211yescharacteristic
155#2546C2212yes—
156#2546C2211yescharacteristic
157#2546C2212yes—
158#2545C2212yes—
159#2545C2212yes—
160#2542C2211yescharacteristic
161#2538C2212yes—
162#2533C2214yes—
163#2532C2214yes—
164#2529C2214yes—
165#2525C2214yes—
166#2525C2214yes—
167#2524C2214yes—
168#2524C2214yes—
169#2523C2214yes—
170#2522C2214yes—
171#2522C2214yes—
172#2522C2214yes—
173#2521C2214yes—
174#2520C2214yes—
175#2520C2214yes—
176#2520C2214yes—
177#2519C2214yes—
178#2519C2214yes—
179#2519C2214yes—
180#2518C2214yes—
181#2517C2214yes—
182#2508C2212yes—
183#2508C2214yes—
184#2507C2214yes—
185#2506C2212yes—
186#2498C2212yes—
187#2495C2214yes—
188#2491C2212yes—
189#2489C2212yes—
190#2475C2214yes—
191#2474C2214yes—
192#2469C2214yes—
193#2462C2214yes—
194#2462C2214yes—
195#2453C2212yes—
196#2453C2212yes—
197#2451C2214yes—
198#2451C2212yes—
199#2451C2212yes—
200#2448C2212yes—
201#2448C2212yes—
202#2447C2212yes—
203#2446C2214yes—
204#2446C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2441C2214yes—
208#2429C2212yes—
209#2429C2212yes—
210#2429C2214yes—
211#2429C2212yes—
212#2427C2212yes—
213#2423C2212yes—
214#2423C2214yes—
215#2423C2212yes—
216#2402C2212yes—
217#2402C2212yes—
218#2402C2212yes—
219#2399C2212yes—
220#2399C2212yes—
221#2399C2211yescharacteristic
222#2399C2211yescharacteristic
223#2396C2212yes—
224#2396C2212yes—
225#2396C2211yescharacteristic
226#2396C2212yes—
227#2396C2212yes—
228#2396C2211yescharacteristic
229#2396C2212yes—
230#2372C2214yes—
231#2371C2214yes—
232#2370C2214yes—
233#2367C2212yes—
234#2365C2212yes—
235#2362C2214yes—
236#2356C2211yescharacteristic
237#2356C2212yes—
238#2356C2211yescharacteristic
239#2351C2211yescharacteristic
240#2351C2214yes—
241Q8×C4⋊C4C2212yes—
242#2349C2211yescharacteristic
243#2347C2214yes—
244#2346C2214yes—
245#2343C2214yes—
246#2331C2214yes—
247#2331C2211yescharacteristic
248#2327C2211yescharacteristic
249#2327C2211yescharacteristic
250#2326C2211yescharacteristic
251#2323C2214yes—
252#2320C2214yes—
253#2320C2212yes—
254#2314C2214yes—
255C4×C4⋊Q8C2211yescharacteristic
256C4×C4⋊Q8C2212yes—
257C4×C4⋊Q8C2212yes—
258C4×#124C2211yescharacteristic
259C4×C22⋊Q8C2212yes—
260#2295C2212yes—
261#2293C2212yes—
262C42×Q8C2211yescharacteristic
263C42×Q8C2211yescharacteristic
264C42×Q8C2212yes—
265C4×#117C2212yes—
266C4×#117C2211yescharacteristic
267Q82—44no—
268#557—44no—
269#557—44no—
270#556—44no—
271#542—44no—
272#541—44no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2311yescharacteristic
285C2×C4⋊Q8C2312yes—
286C2×C4⋊Q8C2314yes—
287C2×#126C2312yes—
288C2×#126C2312yes—
289C2×#126C2312yes—
290C2×#126C2314yes—
291C2×#125C2314yes—
292C2×#125C2312yes—
293C2×#125C2312yes—
294C2×#125C2312yes—
295C2×#125C2311yescharacteristic
296C2×#125C2314yes—
297C2×#125C2312yes—
298C2×#125C2314yes—
299C2×#125C2314yes—
300C2×#124C2311yescharacteristic
301C2×#124C2314yes—
302C2×#124C2311yescharacteristic
303C2×#124C2312yes—
304C2×#124C2311yescharacteristic
305C2×#124C2312yes—
306C2×#123C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2311yescharacteristic
309C2×C22⋊Q8C2311yescharacteristic
310C2×C22⋊Q8C2311yescharacteristic
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×#121C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2311yescharacteristic
340C2×#117C2312yes—
341C2×#117C2311yescharacteristic
342C2×#117C2312yes—
343C22×C42C2311yescharacteristic
344#400C2311yescharacteristic
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#399C2314yes—
369#399C2314yes—
370#399C2312yes—
371#399C2312yes—
372#399C2312yes—
373#399C2314yes—
374#399C2314yes—
375#399C2311yescharacteristic
376#399C2312yes—
377#399C2312yes—
378#399C2311yescharacteristic
379#399C2314yes—
380#399C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2312yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2312yes—
415#398C2312yes—
416#398C2312yes—
417#398C2314yes—
418#398C2314yes—
419#398C2312yes—
420#398C2312yes—
421#398C2312yes—
422#398C2312yes—
423#398C2312yes—
424#398C2312yes—
425#398C2312yes—
426#398C2312yes—
427#398C2312yes—
428#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2312yes—
442#397C2312yes—
443#397C2314yes—
444#396C2312yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2312yes—
457#396C2312yes—
458#395C2314yes—
459#395C2314yes—
460#395C2312yes—
461#395C2312yes—
462#395C2314yes—
463#395C2314yes—
464#395C2312yes—
465#395C2314yes—
466#395C2312yes—
467#395C2312yes—
468#395C2311yescharacteristic
469#395C2312yes—
470#395C2312yes—
471#395C2312yes—
472#395C2314yes—
473#395C2311yescharacteristic
474#395C2312yes—
475#395C2312yes—
476#395C2312yes—
477#395C2314yes—
478#395C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#393C2311yescharacteristic
483#393C2314yes—
484#393C2312yes—
485#393C2312yes—
486#393C2311yescharacteristic
487#393C2312yes—
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2312yes—
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2311yescharacteristic
497#391C2311yescharacteristic
498#391C2312yes—
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2312yes—
510#391C2311yescharacteristic
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#390C2312yes—
518#390C2311yescharacteristic
519#390C2311yescharacteristic
520#390C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2314yes—
561#389C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#386C2314yes—
637#386C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#384C2312yes—
645#384C2311yescharacteristic
646#384C2312yes—
647#384C2314yes—
648#384C2311yescharacteristic
649#384C2314yes—
650#383C2312yes—
651#383C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#383C2314yes—
656#383C2314yes—
657#382C2314yes—
658#382C2311yescharacteristic
659#382C2312yes—
660#382C2314yes—
661#382C2314yes—
662#382C2314yes—
663#382C2314yes—
664#382C2314yes—
665#382C2314yes—
666#382C2311yescharacteristic
667#382C2311yescharacteristic
668#382C2311yescharacteristic
669#382C2314yes—
670#382C2314yes—
671#381C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727#376C2311yescharacteristic
728#376C2314yes—
729#376C2311yescharacteristic
730#376C2312yes—
731#376C2312yes—
732#376C2314yes—
733#376C2312yes—
734#376C2312yes—
735C2×#95C2312yes—
736C43C2312yes—
737C43C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2411yescharacteristic
742C22×Q8C2411yescharacteristic
743C22×Q8C2411yescharacteristic
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2412yes—
748C22×Q8C2412yes—
749C22×Q8C2414yes—
750C22×D4C2411yescharacteristic
751C22×D4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C4⋊Q8—24no—
757C4⋊Q8—24no—
758C4⋊Q8—24no—
759C4⋊Q8—48no—
760C4⋊Q8—42no—
761C4⋊Q8—44no—
762C4⋊Q8—44no—
763C4⋊Q8—42no—
764C4⋊Q8—44no—
765C4⋊Q8—44no—
766C4⋊Q8—42no—
767C4⋊Q8—44no—
768C4⋊Q8—44no—
769C4⋊Q8—48no—
770#126—44no—
771#126—44no—
772#126—44no—
773#126—48no—
774#125—48no—
775#125—42no—
776#125—44no—
777#125—44no—
778#125—44no—
779#125—44no—
780#125—48no—
781#125—48no—
782#125—48no—
783#124—24no—
784#124—48no—
785#124—44no—
786#124—42no—
787#124—42no—
788#124—44no—
789#123—44no—
790C22⋊Q8—48no—
791C22⋊Q8—48no—
792C22⋊Q8—44no—
793C22⋊Q8—44no—
794C22⋊Q8—42no—
795C22⋊Q8—42no—
796C22⋊Q8—42no—
797C22⋊Q8—44no—
798#121—42no—
799C4×Q8—24no—
800C4×Q8—24no—
801C4×Q8—24no—
802C4×Q8—24no—
803C4×Q8—24no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—28no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×Q8—44no—
812C4×Q8—44no—
813C4×Q8—44no—
814C4×Q8—44no—
815C4×Q8—44no—
816C4×Q8—44no—
817C4×Q8—44no—
818C4×D4—24no—
819C4×D4—44no—
820#117—24no—
821#117—28no—
822#117—216no—
823#117—42no—
824#117—44no—
825#117—44no—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C42—24no—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2411yescharacteristic
968C2×C42C2412yes—
969C2×C42C2411yescharacteristic
970#95C2411yescharacteristic
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2411yescharacteristic
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2411yescharacteristic
1003#95C2414yes—
1004#95C2412yes—
1005#95C2411yescharacteristic
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
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—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046C24C2511yescharacteristic
1047C24C2512yes—
1048C2×Q8—22no—
1049C2×Q8—22no—
1050C2×Q8—22no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—24no—
1058C2×Q8—22no—
1059C2×Q8—22no—
1060C2×Q8—22no—
1061C2×Q8—22no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—42no—
1067C2×Q8—42no—
1068C2×Q8—44no—
1069C2×Q8—42no—
1070C2×Q8—44no—
1071C2×Q8—44no—
1072C2×Q8—44no—
1073C2×Q8—44no—
1074C2×D4—22no—
1075C2×D4—22no—
1076C2×D4—22no—
1077C2×D4—42no—
1078C2×D4—44no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—24no—
1083C22×C4—22no—
1084C22×C4—24no—
1085C22×C4—28no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—28no—
1155C4⋊C4—28no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
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—44no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C22⋊C4—22no—
1201C22⋊C4—22no—
1202C22⋊C4—24no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C42—22no—
1228C42—24no—
1229C42—24no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—22no—
1234C42—24no—
1235C42—24no—
1236C42—28no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—24no—
1241C42—28no—
1242C42—24no—
1243C42—22no—
1244C42—22no—
1245C42—24no—
1246C42—24no—
1247C42—28no—
1248C42—42no—
1249C42—44no—
1250C42—42no—
1251C42—42no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42H(5,𝔽2)14yes—
1260C422−1+414yes—
1261C422−1+418yes—
1262C23—21no—
1263C23—22no—
1264C23—24no—
1265C23—22no—
1266C23—22no—
1267C23—21no—
1268C23—24no—
1269C23—22no—
1270C23—21no—
1271C23—22no—
1272C23C2611yescharacteristic
1273Q8—28no—
1274Q8—48no—
1275Q8—44no—
1276Q8—44no—
1277Q8—44no—
1278Q8—44no—
1279Q8—48no—
1280Q8—84no—
1281Q8—162no—
1282Q8—164no—
1283D4—44no—
1284D4—162no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—48no—
1355C2×C4—44no—
1356C2×C4—88no—
1357C2×C4—84no—
1358C2×C4C2×H(5,𝔽2)12yes—
1359C2×C4C2×H(5,𝔽2)12yes—
1360C2×C4C2×H(5,𝔽2)12yes—
1361C2×C4C2×2−1+414yes—
1362C2×C4C2×2−1+414yes—
1363C2×C4C2×2−1+414yes—
1364C2×C4C2×2−1+414yes—
1365C2×C4C2×2−1+412yes—
1366C2×C4#58514yes—
1367C2×C4#58512yes—
1368C22—41no—
1369C22—42no—
1370C22—44no—
1371C22—42no—
1372C22—41no—
1373C22—42no—
1374C22—42no—
1375C22—41no—
1376C22—42no—
1377C22—44no—
1378C22C22×H(5,𝔽2)11yescharacteristic
1379C22C22×2−1+411yescharacteristic
1380C22C22×2−1+412yes—
1381C22C2×#58511yescharacteristic
1382C22C2×#58512yes—
1383C4—24no—
1384C4—24no—
1385C4—22no—
1386C4—24no—
1387C4—22no—
1388C4—24no—
1389C4—24no—
1390C4—41no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—44no—
1399C4—42no—
1400C4—42no—
1401C4—41no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—41no—
1409C4—42no—
1410C4—44no—
1411C4#354714yes—
1412C2—81no—
1413C2—82no—
1414C2C2×#354711yescharacteristic
1415C2#6275212yes—
1416C2#6283311yescharacteristic
1417C2#6283611yescharacteristic
1418C2#6283712yes—
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. #53013C2semidirect
3. #52831C2semidirect
4. #52572C2semidirect
5. #45436C2semidirect
6. #45434C2semidirect
7. #45394C2semidirect
8. #45389C2semidirect
9. #44853C2semidirect
10. #44804C2semidirect
11. #42879C2semidirect
12. #42823C2semidirect
13. #42791C2semidirect
15. #42702C2semidirect
17. #42273C2semidirect
18. #42194C2semidirect
19. #42062C2semidirect
20. #42006C2semidirect
21. #36508C2semidirect
22. #36481C2semidirect
23. #36474C2semidirect
24. #36394C2semidirect
26. #36383C2semidirect
28. #35314C2semidirect
29. #35199C2semidirect
30. #35184C2semidirect
31. #34552C2semidirect

Maximal subgroups

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

subgroupindex
#530212
#530132
#528312
#525722
#454362
#454342
#453942
#453892
#448532
#448042
#428792
#428232
#427912
#427892
#427022
#426492
#422732
#421942
#420622
#420062
#365082
#364812
#364742
#363942
#363852
#363832
#353182
#353142
#351992
#351842
#345522