Finite Group Databasebeta

← #7979709

Subgroups — #7979709

Order 512.

5065 conjugacy classes of subgroups.

The subgroup lattice has 1761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59593C212yesmaximal, complemented
2#59450C211yesmaximal, characteristic, complemented
3#59307C212yesmaximal, complemented
4#59134C211yesmaximal, characteristic, complemented
5#59050C211yesmaximal, characteristic, complemented
6#51173C214yesmaximal, complemented
7#50918C214yesmaximal, complemented
8#46011C212yesmaximal, complemented
9#45625C212yesmaximal, complemented
10#45114C212yesmaximal, complemented
11#45112C212yesmaximal, complemented
12#44344C214yesmaximal, complemented
13#42910C212yesmaximal, complemented
14#42726C212yesmaximal, complemented
15#41673C214yesmaximal, complemented
16#40217C212yesmaximal, complemented
17#40007C212yesmaximal, complemented
18#39938C212yesmaximal, complemented
19#39789C212yesmaximal, complemented
20#39469C211yesmaximal, characteristic, complemented
21#39439C212yesmaximal, complemented
22#39203C211yesmaximal, characteristic, complemented
23#36561C211yesmaximal, characteristic, complemented
24#36504C211yesmaximal, characteristic, complemented
25#36480C211yesmaximal, characteristic, complemented
26#36194C212yesmaximal, complemented
27#36185C211yesmaximal, characteristic, complemented
28#36129C211yesmaximal, characteristic, complemented
29#35317C211yesmaximal, characteristic, complemented
30#35170C211yesmaximal, characteristic, complemented
31#35044C212yesmaximal, complemented
32#34947C211yesmaximal, characteristic, complemented
33#34715C211yesmaximal, characteristic, complemented
34#34413C212yesmaximal, complemented
35C4×#553C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×#555C2211yescharacteristic
38C2×#554C2212yes—
39C2×#553C2211yescharacteristic
40C2×#542C2212yes—
41C2×#536C2212yes—
42C2×#536C2212yes—
43C2×#533C2211yescharacteristic
44C2×#532C2211yescharacteristic
45C22×C4⋊Q8C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47#2868C2212yes—
48#2863C2212yes—
49#2862C2211yescharacteristic
50#2858C2212yes—
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2857C2212yes—
55#2854C2212yes—
56#2850C2212yes—
57#2850C2212yes—
58#2836C2214yes—
59#2821C2214yes—
60#2800C2214yes—
61#2798C2214yes—
62#2794C2214yes—
63#2793C2214yes—
64#2791C2214yes—
65#2771C2214yes—
66#2754C2214yes—
67#2754C2214yes—
68#2743C2214yes—
69#2743C2214yes—
70#2741C2214yes—
71#2741C2214yes—
72#2732C2214yes—
73#2730C2214yes—
74#2730C2214yes—
75#2721C2214yes—
76#2716C2214yes—
77#2716C2214yes—
78#2713C2214yes—
79#2712C2214yes—
80#2712C2214yes—
81#2706C2214yes—
82#2706C2214yes—
83#2703C2214yes—
84#2703C2214yes—
85#2701C2214yes—
86#2700C2214yes—
87#2696C2214yes—
88#2696C2214yes—
89#2694C2214yes—
90#2693C2214yes—
91#2687C2214yes—
92#2676C2214yes—
93#2663C2214yes—
94#2662C2214yes—
95#2658C2214yes—
96#2654C2214yes—
97#2649C2214yes—
98#2648C2214yes—
99#2631C2214yes—
100#2625C2212yes—
101#2615C2212yes—
102#2605C2214yes—
103#2597C2214yes—
104#2596C2214yes—
105#2589C2214yes—
106#2575C2214yes—
107#2575C2214yes—
108#2571C2212yes—
109#2571C2212yes—
110#2570C2212yes—
111#2568C2211yescharacteristic
112#2567C2211yescharacteristic
113#2566C2212yes—
114#2565C2212yes—
115#2564C2214yes—
116#2564C2214yes—
117#2563C2211yescharacteristic
118#2563C2214yes—
119#2558C2214yes—
120#2557C2214yes—
121#2557C2214yes—
122#2556C2214yes—
123#2554C2214yes—
124#2551C2211yescharacteristic
125#2550C2212yes—
126#2547C2211yescharacteristic
127#2545C2212yes—
128#2542C2212yes—
129#2542C2211yescharacteristic
130#2542C2212yes—
131#2542C2211yescharacteristic
132#2542C2211yescharacteristic
133#2542C2211yescharacteristic
134#2540C2212yes—
135#2540C2212yes—
136#2538C2214yes—
137#2537C2211yescharacteristic
138#2536C2212yes—
139#2535C2212yes—
140#2521C2214yes—
141#2521C2214yes—
142#2521C2214yes—
143#2516C2214yes—
144#2513C2212yes—
145#2513C2212yes—
146#2511C2212yes—
147#2509C2212yes—
148#2506C2212yes—
149#2503C2212yes—
150#2501C2212yes—
151#2501C2214yes—
152#2501C2212yes—
153#2500C2212yes—
154#2499C2212yes—
155#2497C2212yes—
156#2497C2214yes—
157#2497C2214yes—
158#2496C2212yes—
159#2492C2214yes—
160#2492C2212yes—
161#2492C2212yes—
162#2492C2212yes—
163#2492C2212yes—
164#2492C2214yes—
165#2492C2212yes—
166#2491C2212yes—
167#2490C2212yes—
168#2489C2212yes—
169#2489C2212yes—
170#2485C2212yes—
171#2481C2214yes—
172#2479C2214yes—
173#2476C2212yes—
174#2474C2212yes—
175#2467C2214yes—
176#2467C2214yes—
177#2465C2214yes—
178#2459C2214yes—
179#2459C2212yes—
180#2458C2214yes—
181#2457C2214yes—
182#2456C2214yes—
183#2456C2212yes—
184#2452C2212yes—
185#2451C2212yes—
186#2451C2211yescharacteristic
187#2448C2214yes—
188#2447C2212yes—
189#2446C2212yes—
190#2446C2212yes—
191#2445C2211yescharacteristic
192#2442C2212yes—
193#2441C2212yes—
194#2439C2212yes—
195#2439C2212yes—
196#2439C2212yes—
197#2439C2211yescharacteristic
198#2439C2212yes—
199#2436C2212yes—
200#2431C2211yescharacteristic
201#2429C2212yes—
202#2428C2212yes—
203#2427C2212yes—
204#2427C2212yes—
205#2427C2212yes—
206#2426C2212yes—
207#2426C2214yes—
208#2426C2211yescharacteristic
209#2423C2212yes—
210#2421C2212yes—
211#2421C2212yes—
212#2420C2211yescharacteristic
213#2417C2212yes—
214#2417C2212yes—
215#2417C2212yes—
216#2417C2212yes—
217#2417C2212yes—
218#2416C2212yes—
219#2415C2212yes—
220#2414C2212yes—
221#2414C2211yescharacteristic
222#2414C2212yes—
223#2409C2212yes—
224#2407C2211yescharacteristic
225#2407C2212yes—
226#2396C2214yes—
227#2392C2212yes—
228#2388C2212yes—
229#2381C2214yes—
230#2376C2214yes—
231#2374C2212yes—
232#2374C2214yes—
233#2373C2212yes—
234#2370C2211yescharacteristic
235#2369C2211yescharacteristic
236#2369C2214yes—
237#2365C2211yescharacteristic
238#2365C2212yes—
239#2364C2212yes—
240#2363C2212yes—
241#2363C2211yescharacteristic
242#2362C2212yes—
243#2362C2212yes—
244#2362C2212yes—
245#2361C2211yescharacteristic
246#2360C2212yes—
247#2360C2212yes—
248#2360C2212yes—
249#2357C2211yescharacteristic
250#2357C2212yes—
251#2355C2214yes—
252#2355C2211yescharacteristic
253#2354C2212yes—
254#2354C2212yes—
255#2353C2212yes—
256#2352C2212yes—
257#2352C2212yes—
258#2352C2211yescharacteristic
259D4×C4⋊C4C2211yescharacteristic
260#2347C2211yescharacteristic
261#2347C2212yes—
262#2345C2211yescharacteristic
263Q8×C22⋊C4C2212yes—
264Q8×C22⋊C4C2212yes—
265#2337C2214yes—
266#2337C2214yes—
267#2335C2214yes—
268#2335C2214yes—
269#2333C2214yes—
270#2323C2212yes—
271#2323C2212yes—
272#2311C2212yes—
273C4×C4⋊Q8C2211yescharacteristic
274C4×C4⋊Q8C2212yes—
275C4×#125C2211yescharacteristic
276C4×#126C2212yes—
277C4×#124C2211yescharacteristic
278C4×C22⋊Q8C2212yes—
279C4×C22⋊Q8C2212yes—
280C4×C22⋊Q8C2212yes—
281C4×C22⋊Q8C2211yescharacteristic
282C4×#123C2212yes—
283C4×#123C2212yes—
284C4×#121C2211yescharacteristic
285C4×#121C2212yes—
286C4×#121C2211yescharacteristic
287C4×#121C2211yescharacteristic
288C4×#121C2212yes—
289#2297C2212yes—
290#2297C2212yes—
291#2293C2211yescharacteristic
292#2285C2212yes—
293#2285C2212yes—
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C23×Q8C2312yes—
302#556—44no—
303#555—44no—
304#554—48no—
305#553—28no—
306#542—48no—
307#536—216no—
308#536—48no—
309#533—44no—
310#532—44no—
311C2×C4⋊Q8—44no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2314yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2311yescharacteristic
320C2×C4⋊Q8C2314yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2312yes—
323C2×#127C2311yescharacteristic
324C2×#126C2312yes—
325C2×#126C2314yes—
326C2×#126C2314yes—
327C2×#125C2311yescharacteristic
328C2×#125C2312yes—
329C2×#125C2314yes—
330C2×#124C2314yes—
331C2×#124C2311yescharacteristic
332C2×#124C2312yes—
333C2×#124C2314yes—
334C2×#124C2312yes—
335C2×#124C2314yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2312yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×#123C2314yes—
344C2×#123C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2311yescharacteristic
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2314yes—
362C2×#121C2311yescharacteristic
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2311yescharacteristic
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2311yescharacteristic
372C2×#121C2311yescharacteristic
373C2×#121C2312yes—
374C4×#41—44no—
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2314yes—
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2312yes—
380C2×C4×Q8C2312yes—
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2312yes—
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2314yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×#117C2311yescharacteristic
403C2×#117C2312yes—
404C2×#117C2312yes—
405C2×#117C2312yes—
406C2×#117C2312yes—
407C2×#117C2311yescharacteristic
408C2×#117C2312yes—
409C2×#117C2312yes—
410C2×#117C2311yescharacteristic
411C22×C4⋊C4C2311yescharacteristic
412C22×C4⋊C4C2311yescharacteristic
413C22×C4⋊C4C2312yes—
414C22×C4⋊C4C2312yes—
415C22×C4⋊C4C2312yes—
416C22×C42C2311yescharacteristic
417C22×C42C2311yescharacteristic
418C22×C42C2312yes—
419C22×C42C2312yes—
420C22×C42C2312yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#399C2314yes—
436#399C2314yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2314yes—
441#399C2314yes—
442#399C2314yes—
443#399C2314yes—
444#399C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2312yes—
453#398C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2312yes—
470#396C2314yes—
471#396C2312yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#395C2314yes—
479#395C2314yes—
480#395C2312yes—
481#395C2314yes—
482#394C2314yes—
483#394C2312yes—
484#394C2312yes—
485#394C2312yes—
486#394C2312yes—
487#394C2312yes—
488#394C2312yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#393C2312yes—
498#393C2314yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2312yes—
510#392C2314yes—
511#392C2314yes—
512#392C2312yes—
513#392C2312yes—
514#392C2312yes—
515#391C2314yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#391C2314yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2314yes—
525#391C2314yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2312yes—
531#391C2312yes—
532#391C2314yes—
533#391C2314yes—
534#391C2312yes—
535#391C2312yes—
536#391C2312yes—
537#391C2311yescharacteristic
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2312yes—
542#391C2311yescharacteristic
543#390C2312yes—
544#390C2314yes—
545#390C2314yes—
546#390C2312yes—
547#390C2314yes—
548#390C2314yes—
549#390C2314yes—
550#390C2311yescharacteristic
551#390C2312yes—
552#390C2314yes—
553#390C2311yescharacteristic
554#390C2312yes—
555#390C2312yes—
556#390C2311yescharacteristic
557#390C2311yescharacteristic
558#390C2312yes—
559#390C2314yes—
560#390C2312yes—
561#390C2312yes—
562#390C2314yes—
563#390C2311yescharacteristic
564#390C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2311yescharacteristic
567#389C2311yescharacteristic
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2314yes—
572#389C2312yes—
573#389C2312yes—
574#389C2311yescharacteristic
575#389C2312yes—
576#389C2311yescharacteristic
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2312yes—
583#389C2312yes—
584#389C2314yes—
585#389C2312yes—
586#389C2311yescharacteristic
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2311yescharacteristic
591#389C2314yes—
592#389C2312yes—
593#389C2314yes—
594#389C2311yescharacteristic
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2312yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2312yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2312yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2312yes—
625#388C2314yes—
626#388C2314yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2312yes—
632#388C2314yes—
633#388C2312yes—
634#388C2312yes—
635#388C2312yes—
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2312yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2312yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2312yes—
666#387C2314yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#386C2312yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2312yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2312yes—
683#386C2312yes—
684#386C2312yes—
685#386C2312yes—
686#386C2314yes—
687#386C2314yes—
688#386C2312yes—
689#386C2314yes—
690#386C2314yes—
691#386C2312yes—
692#386C2312yes—
693#386C2312yes—
694#386C2312yes—
695#386C2314yes—
696#386C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2312yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2312yes—
706#385C2312yes—
707#384C2312yes—
708#384C2311yescharacteristic
709#384C2312yes—
710#384C2312yes—
711#384C2312yes—
712#384C2312yes—
713#384C2314yes—
714#384C2314yes—
715#383C2312yes—
716#383C2314yes—
717#382C2311yescharacteristic
718#382C2312yes—
719#382C2314yes—
720#382C2314yes—
721#382C2312yes—
722#382C2312yes—
723#382C2311yescharacteristic
724#382C2312yes—
725#382C2312yes—
726#381C2312yes—
727#381C2314yes—
728#381C2312yes—
729#381C2314yes—
730#380C2314yes—
731#380C2314yes—
732#380C2312yes—
733#380C2314yes—
734#380C2312yes—
735#380C2314yes—
736#380C2312yes—
737#380C2314yes—
738#380C2311yescharacteristic
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2314yes—
743#380C2312yes—
744#380C2311yescharacteristic
745#380C2312yes—
746#380C2312yes—
747#380C2311yescharacteristic
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2311yescharacteristic
753#380C2314yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2312yes—
817#376C2312yes—
818C2×#95C2312yes—
819C43C2312yes—
820C43C2311yescharacteristic
821C2×#41—28no—
822C2×#41—24no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—42no—
826C2×#41—42no—
827C22×Q8—28no—
828C22×Q8—44no—
829C22×Q8—44no—
830C22×Q8C2412yes—
831C22×Q8C2412yes—
832C22×Q8C2411yescharacteristic
833C22×Q8C2414yes—
834C22×Q8C2412yes—
835C22×Q8C2414yes—
836C22×Q8C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2411yescharacteristic
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2414yes—
867C23×C4C2412yes—
868C4⋊Q8—28no—
869C4⋊Q8—216no—
870C4⋊Q8—24no—
871C4⋊Q8—24no—
872C4⋊Q8—24no—
873C4⋊Q8—44no—
874C4⋊Q8—44no—
875C4⋊Q8—44no—
876C4⋊Q8—42no—
877C4⋊Q8—48no—
878C4⋊Q8—44no—
879#127—42no—
880#126—28no—
881#126—48no—
882#126—48no—
883#125—24no—
884#125—44no—
885#125—48no—
886#124—216no—
887#124—44no—
888#124—48no—
889#124—42no—
890#124—44no—
891#124—44no—
892#124—48no—
893#124—48no—
894#123—216no—
895#123—216no—
896#123—28no—
897#123—48no—
898#123—48no—
899#123—48no—
900#123—44no—
901C22⋊Q8—28no—
902C22⋊Q8—28no—
903C22⋊Q8—28no—
904C22⋊Q8—28no—
905C22⋊Q8—28no—
906C22⋊Q8—28no—
907C22⋊Q8—48no—
908C22⋊Q8—44no—
909C22⋊Q8—42no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—48no—
915C22⋊Q8—44no—
916C22⋊Q8—48no—
917C22⋊Q8—44no—
918#121—24no—
919#121—24no—
920#121—24no—
921#121—28no—
922#121—44no—
923#121—48no—
924#121—44no—
925#121—42no—
926#121—42no—
927#121—44no—
928#121—44no—
929#121—44no—
930C4×Q8—24no—
931C4×Q8—48no—
932C4×Q8—42no—
933C4×Q8—44no—
934C4×Q8—44no—
935C4×Q8—44no—
936C4×Q8—44no—
937C4×Q8—44no—
938C4×D4—24no—
939C4×D4—24no—
940C4×D4—28no—
941C4×D4—24no—
942C4×D4—24no—
943C4×D4—28no—
944C4×D4—24no—
945C4×D4—24no—
946C4×D4—24no—
947C4×D4—44no—
948C4×D4—44no—
949C4×D4—42no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—42no—
955C4×D4—44no—
956C4×D4—48no—
957#117—24no—
958#117—44no—
959#117—44no—
960#117—42no—
961#117—44no—
962#117—44no—
963#117—44no—
964#117—44no—
965#117#4118yescomplemented
966C2×C4⋊C4—24no—
967C2×C4⋊C4—24no—
968C2×C4⋊C4—44no—
969C2×C4⋊C4—44no—
970C2×C4⋊C4—44no—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C4⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2411yescharacteristic
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2412yes—
1095C2×C42—24no—
1096C2×C42—24no—
1097C2×C42—44no—
1098C2×C42—44no—
1099C2×C42—44no—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2412yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2414yes—
1118C2×C42C2412yes—
1119C2×C42C2414yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2412yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2414yes—
1125C2×C42C2414yes—
1126C2×C42C2414yes—
1127C2×C42C2411yescharacteristic
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2412yes—
1134C2×C42C2411yescharacteristic
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2411yescharacteristic
1143#95C2411yescharacteristic
1144#95C2412yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2411yescharacteristic
1150#95C2412yes—
1151#95C2411yescharacteristic
1152#95C2412yes—
1153#95C2411yescharacteristic
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2411yescharacteristic
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201C24C2512yes—
1202C24C2512yes—
1203C24C2512yes—
1204C24C2511yescharacteristic
1205C24C2511yescharacteristic
1206#41—416no—
1207#41—816no—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—28no—
1211C2×Q8—24no—
1212C2×Q8—22no—
1213C2×Q8—24no—
1214C2×Q8—24no—
1215C2×Q8—24no—
1216C2×Q8—24no—
1217C2×Q8—24no—
1218C2×Q8—28no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—44no—
1222C2×Q8—42no—
1223C2×Q8—44no—
1224C2×Q8—42no—
1225C2×Q8—44no—
1226C2×Q8—42no—
1227C2×Q8—44no—
1228C2×Q8—42no—
1229C2×Q8—816no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—22no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—22no—
1240C2×D4—24no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—24no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—41no—
1254C2×D4—42no—
1255C2×D4—42no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—42no—
1260C2×D4—42no—
1261C2×D4—42no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—44no—
1270C2×D4—44no—
1271C2×D4—44no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—28no—
1277C22×C4—22no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—24no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—22no—
1290C22×C4—24no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—24no—
1296C22×C4—24no—
1297C22×C4—22no—
1298C22×C4—24no—
1299C22×C4—24no—
1300C22×C4—42no—
1301C22×C4—41no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—42no—
1307C22×C4—42no—
1308C22×C4—44no—
1309C22×C4—42no—
1310C22×C4—42no—
1311C22×C4—41no—
1312C22×C4—44no—
1313C22×C4—42no—
1314C22×C4—42no—
1315C22×C4—42no—
1316C22×C4—41no—
1317C22×C4—42no—
1318C22×C4—44no—
1319C22×C4—44no—
1320C22×C4—44no—
1321C22×C4C2×#4114yes—
1322C22×C42−1+414yes—
1323C22×C4C2511yescharacteristic
1324C22×C4C2511yescharacteristic
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2511yescharacteristic
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2514yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2514yes—
1336C22×C4C2512yes—
1337C22×C4C2511yescharacteristic
1338C22×C4C2512yes—
1339C22×C4C2514yes—
1340C22×C4C2514yes—
1341C22×C4C2512yes—
1342C22×C4C2512yes—
1343C22×C4C2511yescharacteristic
1344C22×C4C2511yescharacteristic
1345C22×C4C2512yes—
1346C22×C4C2512yes—
1347C22×C4C2511yescharacteristic
1348C22×C4C2512yes—
1349C22×C4C2511yescharacteristic
1350C22×C4C2511yescharacteristic
1351C22×C4C2511yescharacteristic
1352C22×C4C2511yescharacteristic
1353C4⋊C4—22no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—22no—
1357C4⋊C4—24no—
1358C4⋊C4—28no—
1359C4⋊C4—28no—
1360C4⋊C4—28no—
1361C4⋊C4—28no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—24no—
1374C4⋊C4—22no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—28no—
1378C4⋊C4—28no—
1379C4⋊C4—28no—
1380C4⋊C4—24no—
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—24no—
1384C4⋊C4—22no—
1385C4⋊C4—24no—
1386C4⋊C4—28no—
1387C4⋊C4—22no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—44no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4C2×#4114yes—
1414C4⋊C4C2×#4114yes—
1415C4⋊C4H(5,𝔽2)14yes—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—24no—
1419C22⋊C4—22no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—24no—
1423C22⋊C4—28no—
1424C22⋊C4—28no—
1425C22⋊C4—28no—
1426C22⋊C4—28no—
1427C22⋊C4—24no—
1428C22⋊C4—24no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—28no—
1433C22⋊C4—28no—
1434C22⋊C4—22no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—22no—
1438C22⋊C4—24no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C22⋊C4—42no—
1445C22⋊C4—42no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—42no—
1454C22⋊C4—42no—
1455C22⋊C4—41no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—42no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4C2×#4118yes—
1477C42—22no—
1478C42—22no—
1479C42—22no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—22no—
1484C42—24no—
1485C42—24no—
1486C42—22no—
1487C42—24no—
1488C42—24no—
1489C42—22no—
1490C42—22no—
1491C42—24no—
1492C42—24no—
1493C42—24no—
1494C42—42no—
1495C42—42no—
1496C42—42no—
1497C42—42no—
1498C42—42no—
1499C42—42no—
1500C42—42no—
1501C42—41no—
1502C42—44no—
1503C42—44no—
1504C42—44no—
1505C42—41no—
1506C42—44no—
1507C42—44no—
1508C42—44no—
1509C42—44no—
1510C42C2×#4118yes—
1511C42H(5,𝔽2)14yes—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—21no—
1519C23—21no—
1520C23—21no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—22no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—22no—
1529C23—22no—
1530C23—22no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—22no—
1535C23—22no—
1536C23—22no—
1537C23—22no—
1538C23—22no—
1539C23—22no—
1540C23—22no—
1541C23—22no—
1542C23—22no—
1543C23—22no—
1544C23—22no—
1545C23C22×#4112yes—
1546C23C2×2−1+412yes—
1547C23C2611yescharacteristic
1548Q8—48no—
1549Q8—48no—
1550Q8—44no—
1551Q8—88no—
1552Q8—84no—
1553Q8—88no—
1554Q8—84no—
1555D4—48no—
1556D4—44no—
1557D4—48no—
1558D4—48no—
1559D4—44no—
1560D4—44no—
1561D4—44no—
1562D4—84no—
1563D4—84no—
1564D4—84no—
1565D4—84no—
1566D4—84no—
1567D4—164no—
1568D4—164no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—28no—
1584C2×C4—28no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—24no—
1589C2×C4—24no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—24no—
1607C2×C4—22no—
1608C2×C4—24no—
1609C2×C4—24no—
1610C2×C4—24no—
1611C2×C4—24no—
1612C2×C4—24no—
1613C2×C4—21no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—24no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—24no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—24no—
1648C2×C4—44no—
1649C2×C4—48no—
1650C2×C4—44no—
1651C2×C4—48no—
1652C2×C4—48no—
1653C2×C4—44no—
1654C2×C4—48no—
1655C2×C4—84no—
1656C2×C4—84no—
1657C2×C4—84no—
1658C2×C4—84no—
1659C2×C4—82no—
1660C2×C4—88no—
1661C2×C4—84no—
1662C2×C4—164no—
1663C2×C4C22×#4112yes—
1664C2×C4C22×#4114yes—
1665C2×C4C22×#4114yes—
1666C2×C4C22×#4112yes—
1667C2×C4C2×H(5,𝔽2)12yes—
1668C2×C4C2×H(5,𝔽2)14yes—
1669C2×C4C2×H(5,𝔽2)12yes—
1670C2×C4C2×H(5,𝔽2)12yes—
1671C2×C4C2×H(5,𝔽2)12yes—
1672C2×C4C2×2−1+412yes—
1673C2×C4C2×2−1+412yes—
1674C2×C4#58512yes—
1675C2×C4#58512yes—
1676C22—22no—
1677C22—22no—
1678C22—22no—
1679C22—22no—
1680C22—22no—
1681C22—22no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—41no—
1687C22—41no—
1688C22—41no—
1689C22—41no—
1690C22—42no—
1691C22—42no—
1692C22—42no—
1693C22—42no—
1694C22—42no—
1695C22—42no—
1696C22—42no—
1697C22—42no—
1698C22—42no—
1699C22—42no—
1700C22—42no—
1701C22—42no—
1702C22—42no—
1703C22—42no—
1704C22—42no—
1705C22—42no—
1706C22—42no—
1707C22—42no—
1708C22—42no—
1709C22—42no—
1710C22—42no—
1711C22C23×#4111yescharacteristic
1712C22C22×H(5,𝔽2)11yescharacteristic
1713C22C22×H(5,𝔽2)11yescharacteristic
1714C22C22×2−1+411yescharacteristic
1715C22C2×#58511yescharacteristic
1716C22C2×#58511yescharacteristic
1717C222−1+611yescharacteristic
1718C4—22no—
1719C4—24no—
1720C4—24no—
1721C4—22no—
1722C4—24no—
1723C4—22no—
1724C4—22no—
1725C4—41no—
1726C4—42no—
1727C4—42no—
1728C4—41no—
1729C4—42no—
1730C4—41no—
1731C4—42no—
1732C4—44no—
1733C4—42no—
1734C4—41no—
1735C4—42no—
1736C4—42no—
1737C4—44no—
1738C4—44no—
1739C4—41no—
1740C4—41no—
1741C4—42no—
1742C4—42no—
1743C4—42no—
1744C4—41no—
1745C4—44no—
1746C4#350814yes—
1747C4#354114yes—
1748C2—42no—
1749C2—42no—
1750C2—82no—
1751C2—82no—
1752C2—82no—
1753C2C2×#354111yescharacteristic
1754C2C2×#350811yescharacteristic
1755C2#6280511yescharacteristic
1756C2#6291311yescharacteristic
1757C2#6295411yescharacteristic
1758C2#6299511yescharacteristic
1759C2#6302411yescharacteristic
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. #59593C2semidirect
2. #59450C2semidirect
3. #59307C2semidirect
4. #59134C2semidirect
5. #59050C2semidirect
6. #51173C2semidirect
7. #50918C2semidirect
8. #46011C2semidirect
9. #45625C2semidirect
10. #45114C2semidirect
11. #45112C2semidirect
12. #44344C2semidirect
13. #42910C2semidirect
14. #42726C2semidirect
15. #41673C2semidirect
16. #40217C2semidirect
17. #40007C2semidirect
18. #39938C2semidirect
19. #39789C2semidirect
20. #39469C2semidirect
21. #39439C2semidirect
22. #39203C2semidirect
23. #36561C2semidirect
24. #36504C2semidirect
25. #36480C2semidirect
26. #36194C2semidirect
27. #36185C2semidirect
28. #36129C2semidirect
29. #35317C2semidirect
30. #35170C2semidirect
31. #35044C2semidirect
32. #34947C2semidirect
33. #34715C2semidirect
34. #34413C2semidirect
35. C4×#553C2semidirect
965. #117#41semidirect

Maximal subgroups

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

subgroupindex
#595932
#594502
#593072
#591342
#590502
#511732
#509182
#460112
#456252
#451142
#451122
#443442
#429102
#427262
#416732
#402172
#400072
#399382
#397892
#394692
#394392
#392032
#365612
#365042
#364802
#361942
#361852
#361292
#353172
#351702
#350442
#349472
#347152
#344132
C4×#5532