Finite Group Databasebeta

← #8174529

Subgroups — #8174529

Order 512.

5095 conjugacy classes of subgroups.

The subgroup lattice has 1790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59322C211yesmaximal, characteristic, complemented
2#59314C211yesmaximal, characteristic, complemented
3#59078C211yesmaximal, characteristic, complemented
4#59033C211yesmaximal, characteristic, complemented
5#58602C214yesmaximal, complemented
6#56618C214yesmaximal, complemented
7#53624C214yesmaximal, complemented
8#53509C214yesmaximal, complemented
9#53021C212yesmaximal, complemented
10#52972C212yesmaximal, complemented
11#52964C212yesmaximal, complemented
12#52963C212yesmaximal, complemented
13#45417C212yesmaximal, complemented
14#45303C212yesmaximal, complemented
15#42931C212yesmaximal, complemented
16#42931C212yesmaximal, complemented
17#42904C212yesmaximal, complemented
18#42855C212yesmaximal, complemented
19#42794C212yesmaximal, complemented
20#42520C212yesmaximal, complemented
21#39609C211yesmaximal, characteristic, complemented
22#39433C212yesmaximal, complemented
23#39432C212yesmaximal, complemented
24#39351C211yesmaximal, characteristic, complemented
25#39351C211yesmaximal, characteristic, complemented
26#39350C211yesmaximal, characteristic, complemented
27#39127C211yesmaximal, characteristic, complemented
28#38909C211yesmaximal, characteristic, complemented
29#37524C212yesmaximal, complemented
30#37299C212yesmaximal, complemented
31#36577C211yesmaximal, characteristic, complemented
32#36576C211yesmaximal, characteristic, complemented
33#35273C211yesmaximal, characteristic, complemented
34#34952C211yesmaximal, characteristic, complemented
35#34614C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic
37C2×#554C2212yes—
38C2×#550C2211yescharacteristic
39C2×#548C2212yes—
40C2×#542C2212yes—
41C2×#542C2212yes—
42C2×#542C2212yes—
43C2×#537C2212yes—
44C2×#532C2211yescharacteristic
45C2×#529C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C22×C4×Q8C2211yescharacteristic
48#2857C2212yes—
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2856C2212yes—
52#2856C2211yescharacteristic
53#2856C2211yescharacteristic
54#2841C2214yes—
55#2841C2214yes—
56#2837C2214yes—
57#2837C2214yes—
58#2831C2214yes—
59#2829C2214yes—
60#2827C2214yes—
61#2827C2214yes—
62#2827C2214yes—
63#2826C2214yes—
64#2820C2214yes—
65#2816C2214yes—
66#2792C2214yes—
67#2783C2214yes—
68#2781C2214yes—
69#2780C2214yes—
70#2780C2214yes—
71#2779C2214yes—
72#2774C2214yes—
73#2750C2214yes—
74#2742C2214yes—
75#2732C2214yes—
76#2732C2214yes—
77#2727C2214yes—
78#2727C2214yes—
79#2725C2214yes—
80#2723C2214yes—
81#2723C2214yes—
82#2720C2214yes—
83#2717C2214yes—
84#2715C2214yes—
85#2714C2214yes—
86#2711C2214yes—
87#2710C2214yes—
88#2708C2214yes—
89#2707C2214yes—
90#2704C2214yes—
91#2700C2214yes—
92#2700C2214yes—
93#2698C2214yes—
94#2692C2214yes—
95#2692C2214yes—
96#2691C2214yes—
97#2689C2214yes—
98#2688C2214yes—
99#2686C2214yes—
100#2683C2214yes—
101#2683C2214yes—
102#2683C2214yes—
103#2681C2214yes—
104#2681C2214yes—
105#2676C2214yes—
106#2672C2214yes—
107#2672C2214yes—
108#2672C2214yes—
109#2672C2214yes—
110#2672C2214yes—
111#2672C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2667C2214yes—
115#2667C2214yes—
116#2664C2214yes—
117#2659C2214yes—
118#2654C2214yes—
119#2652C2214yes—
120#2648C2214yes—
121#2637C2212yes—
122#2636C2214yes—
123#2636C2212yes—
124#2630C2212yes—
125#2630C2212yes—
126#2629C2211yescharacteristic
127#2629C2211yescharacteristic
128#2629C2212yes—
129#2628C2212yes—
130#2625C2212yes—
131#2625C2211yescharacteristic
132#2624C2212yes—
133#2624C2211yescharacteristic
134#2624C2212yes—
135#2624C2212yes—
136#2620C2211yescharacteristic
137#2620C2212yes—
138#2620C2211yescharacteristic
139#2620C2212yes—
140#2616C2211yescharacteristic
141#2615C2211yescharacteristic
142#2583C2214yes—
143#2582C2211yescharacteristic
144#2582C2211yescharacteristic
145#2582C2212yes—
146#2582C2211yescharacteristic
147#2581C2212yes—
148#2580C2212yes—
149#2579C2212yes—
150#2579C2212yes—
151#2568C2212yes—
152#2568C2211yescharacteristic
153#2567C2212yes—
154#2567C2212yes—
155#2567C2212yes—
156#2562C2212yes—
157#2560C2214yes—
158#2559C2214yes—
159#2555C2214yes—
160#2551C2211yescharacteristic
161#2551C2211yescharacteristic
162#2549C2214yes—
163#2549C2214yes—
164#2548C2212yes—
165#2548C2211yescharacteristic
166#2548C2211yescharacteristic
167#2547C2211yescharacteristic
168#2547C2212yes—
169#2545C2212yes—
170#2545C2212yes—
171#2544C2212yes—
172#2544C2212yes—
173#2542C2212yes—
174#2542C2212yes—
175#2542C2212yes—
176#2540C2214yes—
177#2538C2212yes—
178#2538C2211yescharacteristic
179#2538C2212yes—
180#2538C2211yescharacteristic
181#2538C2212yes—
182#2538C2211yescharacteristic
183#2538C2212yes—
184#2537C2212yes—
185#2537C2212yes—
186#2535C2212yes—
187#2512C2212yes—
188#2512C2212yes—
189#2511C2212yes—
190#2509C2212yes—
191#2507C2212yes—
192#2507C2212yes—
193#2506C2212yes—
194#2496C2212yes—
195#2492C2212yes—
196#2491C2212yes—
197#2491C2212yes—
198#2490C2212yes—
199#2487C2212yes—
200#2487C2211yescharacteristic
201#2487C2211yescharacteristic
202#2486C2212yes—
203#2466C2214yes—
204#2464C2214yes—
205#2460C2214yes—
206#2460C2214yes—
207#2459C2214yes—
208#2454C2212yes—
209#2454C2212yes—
210#2453C2214yes—
211#2453C2212yes—
212#2453C2212yes—
213#2452C2212yes—
214#2452C2212yes—
215#2451C2212yes—
216#2451C2212yes—
217#2449C2214yes—
218#2448C2212yes—
219#2448C2212yes—
220#2448C2212yes—
221#2447C2212yes—
222#2447C2212yes—
223#2444C2214yes—
224#2442C2214yes—
225#2442C2212yes—
226#2440C2212yes—
227#2440C2212yes—
228#2440C2212yes—
229#2440C2212yes—
230#2440C2212yes—
231#2432C2212yes—
232#2431C2212yes—
233#2429C2212yes—
234#2428C2212yes—
235#2427C2212yes—
236#2427C2214yes—
237#2426C2212yes—
238#2426C2212yes—
239#2426C2212yes—
240#2426C2214yes—
241#2425C2214yes—
242#2423C2212yes—
243#2423C2212yes—
244#2422C2212yes—
245#2422C2212yes—
246#2420C2212yes—
247#2416C2214yes—
248#2416C2212yes—
249#2416C2212yes—
250#2416C2212yes—
251#2416C2212yes—
252#2416C2212yes—
253#2416C2212yes—
254#2409C2211yescharacteristic
255#2409C2211yescharacteristic
256#2407C2212yes—
257#2407C2212yes—
258#2396C2212yes—
259#2396C2212yes—
260#2396C2212yes—
261#2392C2212yes—
262#2392C2212yes—
263#2392C2212yes—
264#2367C2212yes—
265#2366C2211yescharacteristic
266#2365C2211yescharacteristic
267#2361C2212yes—
268#2360C2212yes—
269#2360C2212yes—
270#2351C2212yes—
271Q8×C4⋊C4C2211yescharacteristic
272Q8×C4⋊C4C2211yescharacteristic
273Q8×C4⋊C4C2211yescharacteristic
274D4×C4⋊C4C2211yescharacteristic
275#2341C2212yes—
276#2341C2212yes—
277Q8×C22⋊C4C2212yes—
278#2339C2212yes—
279#2339C2212yes—
280#2323C2212yes—
281#2323C2212yes—
282#2311C2212yes—
283#2311C2212yes—
284C4×C22⋊Q8C2212yes—
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×C22⋊Q8C2211yescharacteristic
289C4×C22⋊Q8C2211yescharacteristic
290C4×C22⋊Q8C2211yescharacteristic
291C4×#121C2212yes—
292C4×#121C2211yescharacteristic
293C4×#121C2211yescharacteristic
294#2297C2212yes—
295#2296C2212yes—
296#2285C2211yescharacteristic
297#2285C2211yescharacteristic
298C2×#384C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×Q8C2311yescharacteristic
303#557—44no—
304#554—48no—
305#550—44no—
306#548—48no—
307#542—48no—
308#542—48no—
309#542—48no—
310#537—48no—
311#532—44no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×#127C2311yescharacteristic
319C2×#127C2312yes—
320#529—44no—
321C2×#126C2314yes—
322C2×#126C2312yes—
323C2×#126C2314yes—
324C2×#126C2314yes—
325C2×#125C2312yes—
326C2×#125C2314yes—
327C2×#125C2311yescharacteristic
328C2×#125C2314yes—
329C2×#124C2312yes—
330C2×#124C2314yes—
331C2×#124C2311yescharacteristic
332C2×#124C2312yes—
333C2×#124C2314yes—
334C2×#124C2314yes—
335C2×#124C2312yes—
336C2×#124C2314yes—
337C2×#124C2312yes—
338C2×#123C2312yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2311yescharacteristic
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2314yes—
355C2×C22⋊Q8C2314yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2314yes—
359C2×C22⋊Q8C2314yes—
360C2×C22⋊Q8C2314yes—
361C2×C22⋊Q8C2314yes—
362C2×C22⋊Q8C2314yes—
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2311yescharacteristic
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2314yes—
374C2×#121C2314yes—
375C2×#121C2312yes—
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2314yes—
379C2×#121C2312yes—
380C2×#121C2314yes—
381C2×#121C2312yes—
382C4×#41—44no—
383C2×C4×Q8—44no—
384C2×C4×Q8C2311yescharacteristic
385C2×C4×Q8C2311yescharacteristic
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2311yescharacteristic
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2312yes—
391C2×C4×Q8C2312yes—
392C2×C4×Q8C2312yes—
393C2×C4×Q8C2312yes—
394C2×C4×Q8C2311yescharacteristic
395C2×C4×Q8C2311yescharacteristic
396C2×C4×Q8C2311yescharacteristic
397C2×C4×Q8C2312yes—
398C2×C4×Q8C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2314yes—
410C2×C4×D4C2311yescharacteristic
411C2×C4×D4C2311yescharacteristic
412C2×C4×D4C2311yescharacteristic
413C2×C4×D4C2312yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2314yes—
416C2×C4×D4C2312yes—
417C2×#117C2312yes—
418C2×#117C2311yescharacteristic
419C2×#117C2312yes—
420C2×#117C2312yes—
421C2×#117C2311yescharacteristic
422C2×#117C2311yescharacteristic
423C22×C4⋊C4C2312yes—
424C22×C4⋊C4C2312yes—
425C22×C4⋊C4C2312yes—
426C22×C4⋊C4C2312yes—
427C22×C4⋊C4C2311yescharacteristic
428C22×C4⋊C4C2312yes—
429C22×C42C2311yescharacteristic
430C22×C42C2311yescharacteristic
431C22×C42C2311yescharacteristic
432C22×C42C2312yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2314yes—
438#400C2312yes—
439#400C2314yes—
440#400C2314yes—
441#400C2314yes—
442#400C2312yes—
443#400C2312yes—
444#400C2314yes—
445#399C2312yes—
446#399C2314yes—
447#399C2314yes—
448#399C2314yes—
449#399C2312yes—
450#399C2314yes—
451#399C2314yes—
452#399C2312yes—
453#399C2314yes—
454#399C2314yes—
455#399C2314yes—
456#399C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2312yes—
465#398C2314yes—
466#398C2312yes—
467#398C2312yes—
468#398C2312yes—
469#398C2312yes—
470#398C2314yes—
471#398C2314yes—
472#398C2312yes—
473#398C2314yes—
474#398C2314yes—
475#398C2312yes—
476#398C2312yes—
477#398C2312yes—
478#398C2314yes—
479#397C2314yes—
480#397C2312yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#397C2312yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2314yes—
490#397C2314yes—
491#397C2314yes—
492#397C2312yes—
493#397C2314yes—
494#397C2314yes—
495#396C2312yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2312yes—
502#396C2312yes—
503#396C2314yes—
504#396C2314yes—
505#396C2314yes—
506#396C2312yes—
507#396C2314yes—
508#396C2314yes—
509#396C2312yes—
510#396C2312yes—
511#396C2314yes—
512#396C2314yes—
513#396C2312yes—
514#396C2312yes—
515#396C2312yes—
516#396C2312yes—
517#396C2314yes—
518#396C2314yes—
519#396C2312yes—
520#396C2312yes—
521#396C2314yes—
522#396C2314yes—
523#395C2314yes—
524#395C2314yes—
525#395C2314yes—
526#395C2314yes—
527#395C2314yes—
528#395C2314yes—
529#395C2312yes—
530#395C2312yes—
531#395C2314yes—
532#395C2314yes—
533#395C2312yes—
534#395C2314yes—
535#394C2314yes—
536#394C2312yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2314yes—
542#394C2314yes—
543#394C2314yes—
544#394C2312yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2314yes—
549#394C2314yes—
550#394C2314yes—
551#394C2312yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2312yes—
556#394C2312yes—
557#394C2312yes—
558#394C2312yes—
559#394C2312yes—
560#394C2312yes—
561#394C2314yes—
562#394C2314yes—
563#394C2314yes—
564#394C2314yes—
565#393C2312yes—
566#393C2314yes—
567#393C2314yes—
568#393C2314yes—
569#393C2312yes—
570#393C2312yes—
571#392C2314yes—
572#392C2314yes—
573#392C2312yes—
574#392C2312yes—
575#392C2312yes—
576#392C2314yes—
577#391C2312yes—
578#391C2311yescharacteristic
579#391C2312yes—
580#391C2312yes—
581#391C2312yes—
582#391C2311yescharacteristic
583#391C2311yescharacteristic
584#391C2312yes—
585#391C2312yes—
586#391C2311yescharacteristic
587#391C2312yes—
588#391C2312yes—
589#391C2314yes—
590#391C2314yes—
591#391C2311yescharacteristic
592#391C2312yes—
593#391C2314yes—
594#391C2311yescharacteristic
595#391C2312yes—
596#391C2312yes—
597#391C2314yes—
598#390C2314yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2312yes—
603#390C2314yes—
604#390C2312yes—
605#390C2312yes—
606#390C2312yes—
607#390C2314yes—
608#390C2312yes—
609#390C2312yes—
610#390C2312yes—
611#390C2314yes—
612#390C2314yes—
613#390C2312yes—
614#390C2312yes—
615#390C2312yes—
616#390C2311yescharacteristic
617#390C2311yescharacteristic
618#390C2312yes—
619#390C2312yes—
620#390C2312yes—
621#390C2312yes—
622#390C2314yes—
623#389C2314yes—
624#389C2314yes—
625#389C2314yes—
626#389C2314yes—
627#389C2314yes—
628#389C2314yes—
629#389C2312yes—
630#389C2312yes—
631#389C2314yes—
632#389C2312yes—
633#389C2312yes—
634#389C2312yes—
635#389C2312yes—
636#389C2314yes—
637#389C2311yescharacteristic
638#389C2312yes—
639#389C2312yes—
640#389C2311yescharacteristic
641#389C2311yescharacteristic
642#389C2311yescharacteristic
643#389C2311yescharacteristic
644#389C2314yes—
645#389C2314yes—
646#389C2312yes—
647#389C2314yes—
648#389C2312yes—
649#389C2312yes—
650#389C2314yes—
651#389C2312yes—
652#389C2312yes—
653#389C2312yes—
654#389C2312yes—
655#389C2314yes—
656#389C2312yes—
657#389C2312yes—
658#389C2312yes—
659#389C2312yes—
660#389C2311yescharacteristic
661#389C2311yescharacteristic
662#389C2311yescharacteristic
663#389C2314yes—
664#389C2312yes—
665#388C2314yes—
666#388C2314yes—
667#388C2314yes—
668#388C2314yes—
669#388C2314yes—
670#388C2314yes—
671#388C2314yes—
672#388C2314yes—
673#388C2314yes—
674#388C2314yes—
675#388C2314yes—
676#388C2314yes—
677#388C2312yes—
678#388C2312yes—
679#388C2314yes—
680#388C2314yes—
681#388C2314yes—
682#388C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2312yes—
688#387C2312yes—
689#387C2312yes—
690#387C2312yes—
691#387C2314yes—
692#387C2314yes—
693#387C2312yes—
694#387C2312yes—
695#387C2314yes—
696#387C2314yes—
697#387C2314yes—
698#387C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2312yes—
708#386C2312yes—
709#386C2312yes—
710#386C2312yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#386C2314yes—
715#386C2314yes—
716#386C2312yes—
717#386C2312yes—
718#386C2314yes—
719#386C2314yes—
720#385C2314yes—
721#385C2312yes—
722#385C2312yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2312yes—
727#385C2312yes—
728#385C2312yes—
729#385C2312yes—
730#385C2312yes—
731#385C2312yes—
732#385C2312yes—
733#385C2314yes—
734#385C2314yes—
735#385C2314yes—
736#385C2314yes—
737#385C2312yes—
738#385C2314yes—
739#385C2314yes—
740#385C2314yes—
741#385C2314yes—
742#385C2314yes—
743#384C2312yes—
744#384C2311yescharacteristic
745#384C2312yes—
746#384C2312yes—
747#384C2312yes—
748#384C2311yescharacteristic
749#384C2312yes—
750#384C2311yescharacteristic
751#384C2311yescharacteristic
752#384C2311yescharacteristic
753#384C2311yescharacteristic
754#384C2312yes—
755#382C2314yes—
756#382C2312yes—
757#382C2312yes—
758#382C2312yes—
759#381C2314yes—
760#381C2314yes—
761#381C2314yes—
762#380C2311yescharacteristic
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2314yes—
767#380C2314yes—
768#380C2314yes—
769#380C2314yes—
770#380C2312yes—
771#380C2314yes—
772#380C2314yes—
773#380C2311yescharacteristic
774#380C2312yes—
775#380C2312yes—
776#380C2314yes—
777#380C2311yescharacteristic
778#380C2312yes—
779#380C2312yes—
780#380C2314yes—
781#380C2312yes—
782#380C2311yescharacteristic
783#380C2311yescharacteristic
784#380C2311yescharacteristic
785#380C2311yescharacteristic
786#380C2311yescharacteristic
787#380C2312yes—
788#380C2311yescharacteristic
789#380C2311yescharacteristic
790#380C2311yescharacteristic
791#380C2311yescharacteristic
792C4×C4⋊C4C2314yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2311yescharacteristic
801C4×C4⋊C4C2312yes—
802C4×C4⋊C4C2311yescharacteristic
803C4×C4⋊C4C2311yescharacteristic
804C4×C4⋊C4C2312yes—
805C4×C4⋊C4C2312yes—
806C4×C4⋊C4C2312yes—
807C4×C4⋊C4C2312yes—
808C4×C4⋊C4C2312yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2314yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2314yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2314yes—
818C4×C22⋊C4C2312yes—
819C4×C22⋊C4C2312yes—
820C4×C22⋊C4C2312yes—
821C2×#95C2314yes—
822C2×#41—28no—
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—28no—
826C2×#41—42no—
827C2×#41—44no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—44no—
831C22×Q8—24no—
832C22×Q8—24no—
833C22×Q8—42no—
834C22×Q8C2411yescharacteristic
835C22×Q8C2412yes—
836C22×Q8C2411yescharacteristic
837C22×Q8C2412yes—
838C22×Q8C2411yescharacteristic
839C22×Q8C2411yescharacteristic
840C22×Q8C2414yes—
841C22×Q8C2414yes—
842C22×D4C2411yescharacteristic
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2411yescharacteristic
846C22×D4C2411yescharacteristic
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2412yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C23×C4C2411yescharacteristic
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2411yescharacteristic
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2411yescharacteristic
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2414yes—
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2414yes—
874C4⋊Q8—24no—
875C4⋊Q8—44no—
876C4⋊Q8—44no—
877C4⋊Q8—44no—
878C4⋊Q8—44no—
879C4⋊Q8—44no—
880#127—24no—
881#127—44no—
882#126—44no—
883#126—48no—
884#126—48no—
885#126—48no—
886#125—42no—
887#125—48no—
888#125—44no—
889#125—48no—
890#124—28no—
891#124—48no—
892#124—42no—
893#124—44no—
894#124—44no—
895#124—44no—
896#124—48no—
897#124—48no—
898#124—48no—
899#123—48no—
900#123—48no—
901#123—48no—
902#123—44no—
903C22⋊Q8—24no—
904C22⋊Q8—28no—
905C22⋊Q8—24no—
906C22⋊Q8—24no—
907C22⋊Q8—24no—
908C22⋊Q8—28no—
909C22⋊Q8—24no—
910C22⋊Q8—24no—
911C22⋊Q8—48no—
912C22⋊Q8—48no—
913C22⋊Q8—48no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—48no—
917C22⋊Q8—48no—
918C22⋊Q8—42no—
919C22⋊Q8—44no—
920C22⋊Q8—84no—
921C22⋊Q8—84no—
922C22⋊Q8—84no—
923C22⋊Q8—84no—
924#121—28no—
925#121—24no—
926#121—24no—
927#121—48no—
928#121—48no—
929#121—48no—
930#121—48no—
931#121—48no—
932#121—42no—
933#121—44no—
934#121—44no—
935#121—44no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—84no—
940#121—82no—
941#121—82no—
942#121—84no—
943C4×Q8—28no—
944C4×Q8—24no—
945C4×Q8—24no—
946C4×Q8—24no—
947C4×Q8—44no—
948C4×Q8—42no—
949C4×Q8—42no—
950C4×Q8—44no—
951C4×Q8—42no—
952C4×Q8—42no—
953C4×Q8—44no—
954C4×Q8—44no—
955C4×Q8—44no—
956C4×Q8—44no—
957C4×Q8—44no—
958C4×D4—24no—
959C4×D4—48no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—42no—
967C4×D4—42no—
968C4×D4—42no—
969C4×D4—42no—
970C4×D4—42no—
971C4×D4—42no—
972C4×D4—44no—
973C4×D4—44no—
974C4×D4—44no—
975C4×D4—48no—
976#117—28no—
977#117—42no—
978#117—42no—
979#117—42no—
980#117—44no—
981#117—44no—
982C2×C4⋊C4—42no—
983C2×C4⋊C4—44no—
984C2×C4⋊C4—44no—
985C2×C4⋊C4—44no—
986C2×C4⋊C4—44no—
987C2×C4⋊C4—82no—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2411yescharacteristic
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C4⋊C4C2411yescharacteristic
1034C2×C4⋊C4C2411yescharacteristic
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2414yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2412yes—
1065C2×C4⋊C4C2412yes—
1066C2×C4⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2411yescharacteristic
1084C2×C22⋊C4C2411yescharacteristic
1085C2×C22⋊C4C2411yescharacteristic
1086C2×C22⋊C4C2411yescharacteristic
1087C2×C22⋊C4C2411yescharacteristic
1088C2×C22⋊C4C2411yescharacteristic
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2412yes—
1123C2×C22⋊C4C2412yes—
1124C2×C22⋊C4C2412yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C42—24no—
1130C2×C42—24no—
1131C2×C42—24no—
1132C2×C42—44no—
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2412yes—
1147C2×C42C2414yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2412yes—
1150C2×C42C2414yes—
1151C2×C42C2414yes—
1152C2×C42C2412yes—
1153C2×C42C2412yes—
1154C2×C42C2414yes—
1155C2×C42C2414yes—
1156C2×C42C2411yescharacteristic
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2414yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215C24C2511yescharacteristic
1216C24C2514yes—
1217C24C2512yes—
1218C24C2511yescharacteristic
1219C24C2511yescharacteristic
1220#41—416no—
1221#41—816no—
1222#41—816no—
1223C2×Q8—22no—
1224C2×Q8—22no—
1225C2×Q8—22no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—24no—
1229C2×Q8—24no—
1230C2×Q8—22no—
1231C2×Q8—24no—
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—24no—
1235C2×Q8—22no—
1236C2×Q8—24no—
1237C2×Q8—42no—
1238C2×Q8—41no—
1239C2×Q8—44no—
1240C2×Q8—44no—
1241C2×Q8—44no—
1242C2×Q8—44no—
1243C2×Q8—44no—
1244C2×Q8—44no—
1245C2×Q8—416no—
1246C2×Q8H(5,𝔽2)14yes—
1247C2×Q82−1+414yes—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—24no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—28no—
1254C2×D4—24no—
1255C2×D4—28no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—22no—
1263C2×D4—24no—
1264C2×D4—22no—
1265C2×D4—22no—
1266C2×D4—24no—
1267C2×D4—24no—
1268C2×D4—28no—
1269C2×D4—42no—
1270C2×D4—41no—
1271C2×D4—41no—
1272C2×D4—41no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—44no—
1276C2×D4—42no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—44no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—24no—
1304C22×C4—22no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—24no—
1312C22×C4—22no—
1313C22×C4—24no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—28no—
1318C22×C4—28no—
1319C22×C4—42no—
1320C22×C4—41no—
1321C22×C4—41no—
1322C22×C4—42no—
1323C22×C4—44no—
1324C22×C4—44no—
1325C22×C4—44no—
1326C22×C4—44no—
1327C22×C4—41no—
1328C22×C4—41no—
1329C22×C4—42no—
1330C22×C4—41no—
1331C22×C4—41no—
1332C22×C4—42no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4—44no—
1336C22×C4—44no—
1337C22×C4—44no—
1338C22×C4—44no—
1339C22×C4—44no—
1340C22×C4—44no—
1341C22×C4—44no—
1342C22×C4H(5,𝔽2)14yes—
1343C22×C42−1+414yes—
1344C22×C4C2512yes—
1345C22×C4C2512yes—
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2511yescharacteristic
1349C22×C4C2511yescharacteristic
1350C22×C4C2514yes—
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2512yes—
1355C22×C4C2511yescharacteristic
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2511yescharacteristic
1360C22×C4C2512yes—
1361C22×C4C2512yes—
1362C22×C4C2512yes—
1363C22×C4C2512yes—
1364C22×C4C2514yes—
1365C22×C4C2512yes—
1366C22×C4C2514yes—
1367C22×C4C2511yescharacteristic
1368C22×C4C2512yes—
1369C22×C4C2511yescharacteristic
1370C22×C4C2512yes—
1371C22×C4C2511yescharacteristic
1372C22×C4C2511yescharacteristic
1373C22×C4C2511yescharacteristic
1374C4⋊C4—24no—
1375C4⋊C4—22no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—22no—
1379C4⋊C4—24no—
1380C4⋊C4—22no—
1381C4⋊C4—24no—
1382C4⋊C4—24no—
1383C4⋊C4—24no—
1384C4⋊C4—24no—
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—22no—
1388C4⋊C4—24no—
1389C4⋊C4—24no—
1390C4⋊C4—28no—
1391C4⋊C4—22no—
1392C4⋊C4—28no—
1393C4⋊C4—24no—
1394C4⋊C4—22no—
1395C4⋊C4—28no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—22no—
1400C4⋊C4—22no—
1401C4⋊C4—22no—
1402C4⋊C4—22no—
1403C4⋊C4—24no—
1404C4⋊C4—24no—
1405C4⋊C4—24no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—44no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—44no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—41no—
1421C4⋊C4—41no—
1422C4⋊C4—41no—
1423C4⋊C4—41no—
1424C4⋊C4—41no—
1425C4⋊C4—41no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—42no—
1430C4⋊C4—42no—
1431C4⋊C4—42no—
1432C4⋊C4—42no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—42no—
1443C4⋊C4—42no—
1444C4⋊C4—42no—
1445C4⋊C4—42no—
1446C4⋊C4—42no—
1447C4⋊C4—44no—
1448C4⋊C4—44no—
1449C4⋊C4—44no—
1450C4⋊C4—44no—
1451C4⋊C4—44no—
1452C4⋊C4—44no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—28no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—24no—
1459C22⋊C4—24no—
1460C22⋊C4—28no—
1461C22⋊C4—28no—
1462C22⋊C4—28no—
1463C22⋊C4—24no—
1464C22⋊C4—28no—
1465C22⋊C4—24no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—41no—
1477C22⋊C4—41no—
1478C22⋊C4—41no—
1479C22⋊C4—41no—
1480C22⋊C4—41no—
1481C22⋊C4—41no—
1482C22⋊C4—42no—
1483C22⋊C4—42no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—42no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—44no—
1495C22⋊C4—42no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—42no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C22⋊C4—42no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—22no—
1519C42—22no—
1520C42—22no—
1521C42—22no—
1522C42—22no—
1523C42—22no—
1524C42—24no—
1525C42—24no—
1526C42—24no—
1527C42—24no—
1528C42—24no—
1529C42—24no—
1530C42—24no—
1531C42—28no—
1532C42—42no—
1533C42—42no—
1534C42—44no—
1535C42—44no—
1536C42—44no—
1537C42—44no—
1538C42H(5,𝔽2)14yes—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—24no—
1553C23—22no—
1554C23—22no—
1555C23—24no—
1556C23—22no—
1557C23—21no—
1558C23—21no—
1559C23—24no—
1560C23—21no—
1561C23—22no—
1562C23—21no—
1563C23—22no—
1564C23—24no—
1565C23—24no—
1566C23—24no—
1567C23—22no—
1568C23—21no—
1569C23—24no—
1570C23—21no—
1571C23—22no—
1572C23C2×H(5,𝔽2)12yes—
1573C23C2×2−1+412yes—
1574C23C2611yescharacteristic
1575Q8—28no—
1576Q8—28no—
1577Q8—48no—
1578Q8—44no—
1579Q8—44no—
1580Q8—48no—
1581Q8—164no—
1582Q8—164no—
1583D4—44no—
1584D4—44no—
1585D4—44no—
1586D4—48no—
1587D4—44no—
1588D4—48no—
1589D4—48no—
1590D4—84no—
1591D4—88no—
1592D4—88no—
1593D4—84no—
1594D4—88no—
1595D4—84no—
1596D4—164no—
1597D4—164no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—28no—
1609C2×C4—28no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—24no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—24no—
1633C2×C4—24no—
1634C2×C4—24no—
1635C2×C4—24no—
1636C2×C4—22no—
1637C2×C4—24no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—22no—
1654C2×C4—21no—
1655C2×C4—24no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—21no—
1664C2×C4—22no—
1665C2×C4—24no—
1666C2×C4—24no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—22no—
1673C2×C4—22no—
1674C2×C4—22no—
1675C2×C4—21no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—48no—
1680C2×C4—44no—
1681C2×C4—44no—
1682C2×C4—44no—
1683C2×C4—44no—
1684C2×C4—44no—
1685C2×C4—48no—
1686C2×C4—82no—
1687C2×C4—82no—
1688C2×C4—88no—
1689C2×C4—88no—
1690C2×C4—84no—
1691C2×C4—164no—
1692C2×C4—164no—
1693C2×C4—164no—
1694C2×C4C2×H(5,𝔽2)12yes—
1695C2×C4C2×H(5,𝔽2)14yes—
1696C2×C4C2×H(5,𝔽2)12yes—
1697C2×C4C2×H(5,𝔽2)12yes—
1698C2×C4C2×H(5,𝔽2)12yes—
1699C2×C4C2×H(5,𝔽2)12yes—
1700C2×C4C2×H(5,𝔽2)12yes—
1701C2×C4C2×2−1+412yes—
1702C2×C4C2×2−1+414yes—
1703C2×C4C2×2−1+412yes—
1704C2×C4C2×2−1+412yes—
1705C22—22no—
1706C22—22no—
1707C22—22no—
1708C22—22no—
1709C22—22no—
1710C22—22no—
1711C22—41no—
1712C22—41no—
1713C22—41no—
1714C22—41no—
1715C22—41no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—42no—
1721C22—41no—
1722C22—44no—
1723C22—44no—
1724C22—42no—
1725C22—41no—
1726C22—42no—
1727C22—44no—
1728C22—42no—
1729C22—41no—
1730C22—44no—
1731C22—42no—
1732C22—44no—
1733C22—41no—
1734C22—41no—
1735C22—42no—
1736C22—44no—
1737C22—42no—
1738C22—44no—
1739C22—41no—
1740C22C22×H(5,𝔽2)11yescharacteristic
1741C22C22×H(5,𝔽2)11yescharacteristic
1742C22C22×H(5,𝔽2)11yescharacteristic
1743C22C22×2−1+411yescharacteristic
1744C22C22×2−1+411yescharacteristic
1745C22H(7,𝔽2)11yescharacteristic
1746C222−1+611yescharacteristic
1747C4—22no—
1748C4—22no—
1749C4—24no—
1750C4—24no—
1751C4—22no—
1752C4—41no—
1753C4—41no—
1754C4—42no—
1755C4—41no—
1756C4—41no—
1757C4—44no—
1758C4—42no—
1759C4—41no—
1760C4—41no—
1761C4—41no—
1762C4—42no—
1763C4—42no—
1764C4—42no—
1765C4—42no—
1766C4—42no—
1767C4—44no—
1768C4—42no—
1769C4—42no—
1770C4—42no—
1771C4—44no—
1772C4—42no—
1773C4—42no—
1774C4—42no—
1775C4#353614yes—
1776C4#353614yes—
1777C2—42no—
1778C2—42no—
1779C2—81no—
1780C2—82no—
1781C2—84no—
1782C2C2×#353611yescharacteristic
1783C2C2×#353611yescharacteristic
1784C2#6287511yescharacteristic
1785C2#6291311yescharacteristic
1786C2#6291611yescharacteristic
1787C2#6294311yescharacteristic
1788C2#6294611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59322C2semidirect
2. #59314C2semidirect
3. #59078C2semidirect
4. #59033C2semidirect
5. #58602C2semidirect
6. #56618C2semidirect
7. #53624C2semidirect
8. #53509C2semidirect
9. #53021C2semidirect
10. #52972C2semidirect
11. #52964C2semidirect
12. #52963C2semidirect
13. #45417C2semidirect
14. #45303C2semidirect
15. #42931C2semidirect
16. #42931C2semidirect
17. #42904C2semidirect
18. #42855C2semidirect
19. #42794C2semidirect
20. #42520C2semidirect
21. #39609C2semidirect
22. #39433C2semidirect
23. #39432C2semidirect
24. #39351C2semidirect
25. #39351C2semidirect
26. #39350C2semidirect
27. #39127C2semidirect
28. #38909C2semidirect
29. #37524C2semidirect
30. #37299C2semidirect
31. #36577C2semidirect
32. #36576C2semidirect
33. #35273C2semidirect
34. #34952C2semidirect
35. #34614C2semidirect

Maximal subgroups

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

subgroupindex
#593222
#593142
#590782
#590332
#586022
#566182
#536242
#535092
#530212
#529722
#529642
#529632
#454172
#453032
#429312
#429042
#428552
#427942
#425202
#396092
#394332
#394322
#393512
#393502
#391272
#389092
#375242
#372992
#365772
#365762
#352732
#349522
#346142