Finite Group Databasebeta

← #7690099

Subgroups — #7690099

Order 512.

5192 conjugacy classes of subgroups.

The subgroup lattice has 1745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59970C214yesmaximal, complemented
2#59550C212yesmaximal, complemented
3#59546C212yesmaximal, complemented
4#59428C211yesmaximal, characteristic, complemented
5#59410C212yesmaximal, complemented
6#59312C211yesmaximal, characteristic, complemented
7#59291C212yesmaximal, complemented
8#59217C211yesmaximal, characteristic, complemented
9#44975C212yesmaximal, complemented
10#44900C212yesmaximal, complemented
11#44800C214yesmaximal, complemented
12#44527C214yesmaximal, complemented
13#39527C212yesmaximal, complemented
14#39471C211yesmaximal, characteristic, complemented
15#39006C212yesmaximal, complemented
16#38965C211yesmaximal, characteristic, complemented
17#38718C214yesmaximal, complemented
18#37970C212yesmaximal, complemented
19#36481C211yesmaximal, characteristic, complemented
20#36464C211yesmaximal, characteristic, complemented
21#36414C212yesmaximal, complemented
22#36366C212yesmaximal, complemented
23#36315C211yesmaximal, characteristic, complemented
24#36268C212yesmaximal, complemented
25#36259C211yesmaximal, characteristic, complemented
26#36189C211yesmaximal, characteristic, complemented
27#36087C212yesmaximal, complemented
28#36026C212yesmaximal, complemented
29#34916C212yesmaximal, complemented
30#34715C211yesmaximal, characteristic, complemented
31#34316C211yesmaximal, characteristic, complemented
32#34253C212yesmaximal, complemented
33#34207C211yesmaximal, characteristic, complemented
34C4×#555C211yesmaximal, characteristic, complemented
35#34129C211yesmaximal, characteristic, complemented
36C2×#556C2212yes—
37C2×#555C2211yescharacteristic
38C2×#552C2212yes—
39C2×#547C2211yescharacteristic
40C2×#547C2212yes—
41C2×#532C2211yescharacteristic
42C2×#520C2212yes—
43C2×C4×#41C2211yescharacteristic
44#2863C2212yes—
45#2861C2212yes—
46#2860C2214yes—
47#2859C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2854C2212yes—
51#2854C2212yes—
52#2800C2214yes—
53#2798C2214yes—
54#2786C2214yes—
55#2781C2214yes—
56#2774C2214yes—
57#2768C2214yes—
58#2768C2214yes—
59#2754C2214yes—
60#2752C2214yes—
61#2743C2214yes—
62#2721C2214yes—
63#2710C2214yes—
64#2706C2214yes—
65#2705C2214yes—
66#2705C2214yes—
67#2704C2214yes—
68#2703C2214yes—
69#2701C2214yes—
70#2693C2214yes—
71#2691C2214yes—
72#2689C2214yes—
73#2651C2214yes—
74#2632C2214yes—
75#2629C2212yes—
76#2615C2212yes—
77#2606C2214yes—
78#2601C2214yes—
79#2601C2214yes—
80#2598C2214yes—
81#2590C2214yes—
82#2589C2214yes—
83#2588C2214yes—
84#2587C2214yes—
85#2584C2212yes—
86#2581C2212yes—
87#2570C2212yes—
88#2562C2212yes—
89#2558C2214yes—
90#2558C2214yes—
91#2556C2214yes—
92#2554C2214yes—
93#2554C2214yes—
94#2554C2214yes—
95#2553C2214yes—
96#2552C2211yescharacteristic
97#2552C2211yescharacteristic
98#2552C2212yes—
99#2547C2211yescharacteristic
100#2546C2211yescharacteristic
101#2540C2214yes—
102#2540C2212yes—
103#2538C2212yes—
104#2538C2211yescharacteristic
105#2537C2212yes—
106#2537C2211yescharacteristic
107#2531C2214yes—
108#2531C2214yes—
109#2529C2214yes—
110#2529C2214yes—
111#2526C2214yes—
112#2526C2214yes—
113#2525C2214yes—
114#2522C2214yes—
115#2519C2214yes—
116#2518C2214yes—
117#2516C2214yes—
118#2515C2214yes—
119#2512C2212yes—
120#2511C2212yes—
121#2507C2212yes—
122#2507C2212yes—
123#2507C2212yes—
124#2501C2212yes—
125#2497C2212yes—
126#2497C2212yes—
127#2497C2212yes—
128#2497C2212yes—
129#2496C2212yes—
130#2496C2212yes—
131#2495C2212yes—
132#2492C2212yes—
133#2490C2212yes—
134#2489C2212yes—
135#2487C2212yes—
136#2487C2212yes—
137#2486C2212yes—
138#2486C2212yes—
139#2485C2212yes—
140#2485C2212yes—
141#2478C2214yes—
142#2476C2214yes—
143#2476C2212yes—
144#2474C2212yes—
145#2473C2214yes—
146#2471C2214yes—
147#2471C2214yes—
148#2471C2214yes—
149#2471C2214yes—
150#2464C2214yes—
151#2464C2214yes—
152#2461C2214yes—
153#2461C2214yes—
154#2459C2212yes—
155#2457C2214yes—
156#2456C2212yes—
157#2454C2212yes—
158#2451C2211yescharacteristic
159#2447C2212yes—
160#2446C2212yes—
161#2445C2211yescharacteristic
162#2442C2212yes—
163#2441C2212yes—
164#2441C2212yes—
165#2441C2212yes—
166#2441C2212yes—
167#2440C2212yes—
168#2440C2212yes—
169#2439C2211yescharacteristic
170#2438C2214yes—
171#2431C2212yes—
172#2431C2211yescharacteristic
173#2429C2212yes—
174#2429C2212yes—
175#2426C2212yes—
176#2426C2212yes—
177#2426C2211yescharacteristic
178#2425C2214yes—
179#2423C2212yes—
180#2423C2212yes—
181#2423C2212yes—
182#2422C2212yes—
183#2420C2211yescharacteristic
184#2417C2214yes—
185#2417C2212yes—
186#2416C2212yes—
187#2416C2212yes—
188#2415C2212yes—
189#2414C2214yes—
190#2414C2212yes—
191#2414C2211yescharacteristic
192#2413C2214yes—
193#2413C2214yes—
194#2407C2212yes—
195#2407C2211yescharacteristic
196#2402C2214yes—
197#2396C2214yes—
198#2392C2212yes—
199#2388C2212yes—
200#2374C2214yes—
201#2372C2212yes—
202#2372C2212yes—
203#2370C2212yes—
204#2369C2211yescharacteristic
205#2365C2211yescharacteristic
206#2363C2212yes—
207#2363C2212yes—
208#2363C2212yes—
209#2363C2212yes—
210#2363C2211yescharacteristic
211#2363C2211yescharacteristic
212#2362C2212yes—
213#2361C2214yes—
214#2361C2212yes—
215#2361C2212yes—
216#2360C2212yes—
217#2359C2214yes—
218#2354C2211yescharacteristic
219#2354C2211yescharacteristic
220#2354C2211yescharacteristic
221#2354C2211yescharacteristic
222#2354C2212yes—
223#2354C2212yes—
224#2354C2212yes—
225#2354C2211yescharacteristic
226#2354C2211yescharacteristic
227#2354C2212yes—
228#2353C2214yes—
229#2353C2214yes—
230#2352C2214yes—
231#2352C2212yes—
232#2352C2214yes—
233Q8×C4⋊C4C2211yescharacteristic
234Q8×C4⋊C4C2211yescharacteristic
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2211yescharacteristic
237D4×C4⋊C4C2212yes—
238#2347C2212yes—
239#2347C2212yes—
240#2346C2212yes—
241#2346C2214yes—
242#2346C2212yes—
243#2346C2212yes—
244#2346C2211yescharacteristic
245#2346C2211yescharacteristic
246#2345C2212yes—
247#2345C2212yes—
248#2345C2212yes—
249#2344C2212yes—
250#2344C2212yes—
251#2341C2212yes—
252#2341C2212yes—
253#2339C2212yes—
254#2335C2214yes—
255#2326C2214yes—
256#2324C2212yes—
257#2320C2214yes—
258#2319C2214yes—
259#2316C2212yes—
260#2311C2212yes—
261#2311C2212yes—
262C4×C4⋊Q8C2211yescharacteristic
263C4×C4⋊Q8C2212yes—
264C4×C4⋊Q8C2211yescharacteristic
265C4×C4⋊Q8C2212yes—
266C4×#127C2212yes—
267C4×#124C2212yes—
268C4×#124C2211yescharacteristic
269C4×#124C2212yes—
270C4×C22⋊Q8C2212yes—
271C4×C22⋊Q8C2212yes—
272C4×C22⋊Q8C2211yescharacteristic
273C4×#123C2212yes—
274C4×#121C2211yescharacteristic
275C4×#121C2211yescharacteristic
276C4×#121C2211yescharacteristic
277C4×#121C2212yes—
278#2298C2214yes—
279#2297C2212yes—
280#2297C2212yes—
281#2295C2214yes—
282#2295C2212yes—
283#2293C2211yescharacteristic
284#2293C2212yes—
285#2293C2214yes—
286#2293C2214yes—
287C2×#389C2212yes—
288#2285C2211yescharacteristic
289#2285C2212yes—
290C2×#384C2211yescharacteristic
291#2274C2212yes—
292C42×Q8C2212yes—
293C42×D4C2211yescharacteristic
294C42×D4C2211yescharacteristic
295C4×#117C2212yes—
296C4×#117C2212yes—
297C4×#117C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C22×#41C2312yes—
302#556—48no—
303#555—28no—
304#552—48no—
305#547—28no—
306#547—48no—
307#532—28no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×#127C2311yescharacteristic
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#126C2314yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2314yes—
319C2×#125C2312yes—
320C2×#124C2312yes—
321C2×#124C2312yes—
322C2×#124C2312yes—
323C2×#124C2311yescharacteristic
324C2×#124C2312yes—
325C2×#123C2314yes—
326C2×#123C2312yes—
327C2×#123C2314yes—
328C2×#123C2314yes—
329C2×#123C2314yes—
330C2×#123C2314yes—
331C2×#123C2314yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2311yescharacteristic
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339C2×#121C2312yes—
340C2×#121C2311yescharacteristic
341C2×#121C2311yescharacteristic
342C2×#121C2311yescharacteristic
343C2×#121C2312yes—
344C2×#121C2311yescharacteristic
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2314yes—
349C2×#121C2311yescharacteristic
350C2×#121C2314yes—
351#520—216no—
352C4×#41—28no—
353C2×C4×Q8C2314yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2312yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2314yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2314yes—
381C2×C4×D4C2311yescharacteristic
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2311yescharacteristic
385C2×#117C2312yes—
386C2×#117C2311yescharacteristic
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2311yescharacteristic
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2314yes—
393C2×#117C2314yes—
394C2×#117C2311yescharacteristic
395C2×#117C2312yes—
396C2×#117C2312yes—
397C2×#117C2314yes—
398C2×#117C2311yescharacteristic
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2312yes—
406C22×C42C2312yes—
407C22×C42C2311yescharacteristic
408C22×C42C2311yescharacteristic
409C22×C42C2312yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2312yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#397C2312yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2312yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2312yes—
464#394C2314yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#393C2314yes—
479#393C2312yes—
480#392C2314yes—
481#392C2314yes—
482#392C2314yes—
483#392C2312yes—
484#392C2312yes—
485#392C2312yes—
486#392C2312yes—
487#392C2314yes—
488#391C2311yescharacteristic
489#391C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2311yescharacteristic
503#390C2314yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2314yes—
508#390C2312yes—
509#390C2314yes—
510#390C2312yes—
511#390C2314yes—
512#390C2311yescharacteristic
513#390C2312yes—
514#390C2314yes—
515#390C2314yes—
516#390C2311yescharacteristic
517#390C2311yescharacteristic
518#390C2312yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2311yescharacteristic
523#390C2311yescharacteristic
524#390C2312yes—
525#390C2314yes—
526#390C2312yes—
527#390C2312yes—
528#390C2311yescharacteristic
529#390C2312yes—
530#389C2311yescharacteristic
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2312yes—
549#389C2312yes—
550#389C2311yescharacteristic
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2311yescharacteristic
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2312yes—
566#389C2311yescharacteristic
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2311yescharacteristic
571#389C2314yes—
572#389C2311yescharacteristic
573#389C2311yescharacteristic
574#389C2312yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
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#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2312yes—
598#388C2314yes—
599#388C2312yes—
600#388C2314yes—
601#388C2312yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2312yes—
611#388C2314yes—
612#388C2314yes—
613#388C2312yes—
614#388C2312yes—
615#388C2314yes—
616#388C2314yes—
617#388C2312yes—
618#388C2312yes—
619#388C2314yes—
620#388C2314yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2312yes—
625#388C2312yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2312yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2312yes—
663#386C2312yes—
664#386C2314yes—
665#386C2312yes—
666#386C2312yes—
667#386C2314yes—
668#386C2312yes—
669#386C2312yes—
670#386C2312yes—
671#386C2312yes—
672#386C2312yes—
673#386C2312yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2312yes—
685#385C2312yes—
686#384C2312yes—
687#384C2311yescharacteristic
688#384C2311yescharacteristic
689#384C2312yes—
690#384C2312yes—
691#384C2311yescharacteristic
692#384C2311yescharacteristic
693#384C2312yes—
694#384C2312yes—
695#384C2312yes—
696#384C2312yes—
697#383C2314yes—
698#383C2314yes—
699#382C2312yes—
700#382C2312yes—
701#382C2312yes—
702#382C2314yes—
703#382C2311yescharacteristic
704#382C2314yes—
705#382C2312yes—
706#381C2314yes—
707#381C2314yes—
708#381C2314yes—
709#381C2312yes—
710#380C2311yescharacteristic
711#380C2312yes—
712#380C2312yes—
713#380C2312yes—
714#380C2311yescharacteristic
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2314yes—
724#380C2314yes—
725#380C2312yes—
726#380C2312yes—
727#380C2314yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2311yescharacteristic
736#380C2312yes—
737#380C2311yescharacteristic
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2314yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2311yescharacteristic
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807#376C2314yes—
808#376C2312yes—
809#376C2312yes—
810#376C2312yes—
811#376C2314yes—
812#376C2312yes—
813C2×#95C2314yes—
814C43C2312yes—
815C43C2311yescharacteristic
816C43C2314yes—
817C43C2312yes—
818C2×#41—24no—
819C2×#41—24no—
820C2×#41—28no—
821C2×#41—28no—
822C2×#41—28no—
823C2×#41—44no—
824C2×#41—42no—
825C2×#41—44no—
826C2×#41—44no—
827C22×Q8C2412yes—
828C22×Q8C2412yes—
829C22×Q8C2411yescharacteristic
830C22×Q8C2412yes—
831C22×D4C2411yescharacteristic
832C22×D4C2411yescharacteristic
833C22×D4C2411yescharacteristic
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2411yescharacteristic
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2412yes—
844C22×D4C2414yes—
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2414yes—
858C23×C4C2414yes—
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2412yes—
862C4⋊Q8—28no—
863C4⋊Q8—24no—
864C4⋊Q8—24no—
865C4⋊Q8—24no—
866#127—24no—
867#126—48no—
868#126—48no—
869#126—48no—
870#125—44no—
871#125—44no—
872#125—48no—
873#125—82no—
874#124—24no—
875#124—28no—
876#124—28no—
877#124—28no—
878#124—44no—
879#123—28no—
880#123—216no—
881#123—48no—
882#123—48no—
883#123—48no—
884#123—84no—
885#123—84no—
886C22⋊Q8—28no—
887C22⋊Q8—24no—
888C22⋊Q8—28no—
889C22⋊Q8—48no—
890C22⋊Q8—44no—
891C22⋊Q8—44no—
892C22⋊Q8—84no—
893#121—24no—
894#121—28no—
895#121—24no—
896#121—24no—
897#121—24no—
898#121—28no—
899#121—28no—
900#121—48no—
901#121—44no—
902#121—42no—
903#121—44no—
904#121—84no—
905C4×Q8—28no—
906C4×Q8—24no—
907C4×Q8—24no—
908C4×Q8—216no—
909C4×Q8—44no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×D4—24no—
914C4×D4—28no—
915C4×D4—28no—
916C4×D4—24no—
917C4×D4—24no—
918C4×D4—24no—
919C4×D4—28no—
920C4×D4—216no—
921C4×D4—216no—
922C4×D4—216no—
923C4×D4—24no—
924C4×D4—24no—
925C4×D4—42no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—42no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—44no—
932C4×D4—84no—
933C4×D4#4118yes—
934#117—24no—
935#117—28no—
936#117—28no—
937#117—24no—
938#117—28no—
939#117—28no—
940#117—28no—
941#117—44no—
942#117—48no—
943#117—48no—
944#117—42no—
945#117—44no—
946#117—42no—
947#117—44no—
948#117—84no—
949#117—82no—
950#117#4118yescomplemented
951C2×C4⋊C4—28no—
952C2×C4⋊C4—28no—
953C2×C4⋊C4—28no—
954C2×C4⋊C4—28no—
955C2×C4⋊C4—48no—
956C2×C4⋊C4—44no—
957C2×C4⋊C4—82no—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2411yescharacteristic
1068C2×C22⋊C4C2411yescharacteristic
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C42—28no—
1086C2×C42—24no—
1087C2×C42—24no—
1088C2×C42—44no—
1089C2×C42C2411yescharacteristic
1090C2×C42C2414yes—
1091C2×C42C2412yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2412yes—
1094C2×C42C2414yes—
1095C2×C42C2414yes—
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2414yes—
1114C2×C42C2414yes—
1115C2×C42C2412yes—
1116C2×C42C2414yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2414yes—
1120C2×C42C2412yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2412yes—
1127C2×C42C2411yescharacteristic
1128#95C2412yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2412yes—
1133#95C2411yescharacteristic
1134#95C2412yes—
1135#95C2411yescharacteristic
1136#95C2412yes—
1137#95C2414yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2411yescharacteristic
1157#95C2411yescharacteristic
1158#95C2411yescharacteristic
1159#95C2414yes—
1160#95C2411yescharacteristic
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2414yes—
1190C24C2512yes—
1191C24C2511yescharacteristic
1192C24C2512yes—
1193C24C2512yes—
1194C24C2511yescharacteristic
1195#41—432no—
1196#41—416no—
1197#41—816no—
1198C2×Q8—22no—
1199C2×Q8—24no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—22no—
1205C2×Q8—24no—
1206C2×Q8—42no—
1207C2×Q8—42no—
1208C2×Q8—42no—
1209C2×Q8H(5,𝔽2)14yes—
1210C2×D4—24no—
1211C2×D4—24no—
1212C2×D4—24no—
1213C2×D4—22no—
1214C2×D4—24no—
1215C2×D4—24no—
1216C2×D4—24no—
1217C2×D4—24no—
1218C2×D4—28no—
1219C2×D4—24no—
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—22no—
1229C2×D4—24no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—22no—
1233C2×D4—41no—
1234C2×D4—42no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—44no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—44no—
1248C2×D4—44no—
1249C2×D4—44no—
1250C2×D4—44no—
1251C2×D4C2×#4114yes—
1252C22×C4—22no—
1253C22×C4—24no—
1254C22×C4—24no—
1255C22×C4—22no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—28no—
1259C22×C4—28no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—24no—
1272C22×C4—24no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—24no—
1278C22×C4—24no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—28no—
1284C22×C4—28no—
1285C22×C4—42no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—42no—
1291C22×C4—44no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4—42no—
1297C22×C4—44no—
1298C22×C4—44no—
1299C22×C4—42no—
1300C22×C4—44no—
1301C22×C4C2×#4118yes—
1302C22×C4C2×#4114yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2511yescharacteristic
1307C22×C4C2511yescharacteristic
1308C22×C4C2512yes—
1309C22×C4C2514yes—
1310C22×C4C2512yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2512yes—
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2514yes—
1317C22×C4C2514yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2511yescharacteristic
1321C22×C4C2514yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2512yes—
1327C22×C4C2512yes—
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2511yescharacteristic
1332C22×C4C2511yescharacteristic
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—22no—
1336C4⋊C4—28no—
1337C4⋊C4—28no—
1338C4⋊C4—28no—
1339C4⋊C4—24no—
1340C4⋊C4—28no—
1341C4⋊C4—22no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—22no—
1345C4⋊C4—24no—
1346C4⋊C4—22no—
1347C4⋊C4—24no—
1348C4⋊C4—22no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—28no—
1352C4⋊C4—28no—
1353C4⋊C4—24no—
1354C4⋊C4—22no—
1355C4⋊C4—28no—
1356C4⋊C4—24no—
1357C4⋊C4—28no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—24no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—42no—
1379C4⋊C4—41no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4C2×#4114yes—
1396C4⋊C4C2×#4114yes—
1397C4⋊C4C2×#4114yes—
1398C4⋊C42−1+414yes—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—22no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—28no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—22no—
1413C22⋊C4—28no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—28no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—24no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—41no—
1437C22⋊C4—41no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—42no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—44no—
1458C22⋊C4C2×#4118yes—
1459C22⋊C4C2×#4118yes—
1460C42—22no—
1461C42—22no—
1462C42—24no—
1463C42—22no—
1464C42—24no—
1465C42—22no—
1466C42—24no—
1467C42—22no—
1468C42—22no—
1469C42—24no—
1470C42—28no—
1471C42—28no—
1472C42—22no—
1473C42—28no—
1474C42—24no—
1475C42—24no—
1476C42—22no—
1477C42—24no—
1478C42—24no—
1479C42—22no—
1480C42—22no—
1481C42—24no—
1482C42—22no—
1483C42—24no—
1484C42—42no—
1485C42—42no—
1486C42—44no—
1487C42—42no—
1488C42—42no—
1489C42—44no—
1490C42—44no—
1491C42—42no—
1492C42—44no—
1493C42—42no—
1494C42—44no—
1495C42—44no—
1496C42—41no—
1497C42C2×#4114yes—
1498C42C2×#4118yes—
1499C23—22no—
1500C23—21no—
1501C23—21no—
1502C23—22no—
1503C23—22no—
1504C23—21no—
1505C23—21no—
1506C23—22no—
1507C23—21no—
1508C23—22no—
1509C23—22no—
1510C23—21no—
1511C23—22no—
1512C23—21no—
1513C23—22no—
1514C23—22no—
1515C23—21no—
1516C23—22no—
1517C23—22no—
1518C23—22no—
1519C23—21no—
1520C23—22no—
1521C23—22no—
1522C23—21no—
1523C23—21no—
1524C23—22no—
1525C23—22no—
1526C23—22no—
1527C23—21no—
1528C23—22no—
1529C23—21no—
1530C23—22no—
1531C23—22no—
1532C23C22×#4114yes—
1533C23C22×#4112yes—
1534C23C2611yescharacteristic
1535Q8—28no—
1536Q8—48no—
1537Q8—48no—
1538Q8—84no—
1539D4—28no—
1540D4—48no—
1541D4—44no—
1542D4—48no—
1543D4—48no—
1544D4—48no—
1545D4—48no—
1546D4—44no—
1547D4—44no—
1548D4—84no—
1549D4—84no—
1550D4—88no—
1551D4—84no—
1552D4—164no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—21no—
1562C2×C4—22no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—216no—
1572C2×C4—28no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—24no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—24no—
1586C2×C4—22no—
1587C2×C4—21no—
1588C2×C4—24no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—24no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—24no—
1615C2×C4—24no—
1616C2×C4—22no—
1617C2×C4—24no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—22no—
1622C2×C4—24no—
1623C2×C4—24no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—24no—
1630C2×C4—44no—
1631C2×C4—44no—
1632C2×C4—48no—
1633C2×C4—48no—
1634C2×C4—48no—
1635C2×C4—44no—
1636C2×C4—48no—
1637C2×C4—44no—
1638C2×C4—44no—
1639C2×C4—48no—
1640C2×C4—88no—
1641C2×C4—88no—
1642C2×C4—88no—
1643C2×C4—88no—
1644C2×C4—84no—
1645C2×C4C22×#4114yes—
1646C2×C4C22×#4112yes—
1647C2×C4C22×#4114yes—
1648C2×C4C22×#4112yes—
1649C2×C4C22×#4114yes—
1650C2×C4C22×#4112yes—
1651C2×C4C22×#4112yes—
1652C2×C4C22×#4112yes—
1653C2×C4C2×H(5,𝔽2)14yes—
1654C2×C4C2×H(5,𝔽2)12yes—
1655C2×C4C2×2−1+412yes—
1656C2×C4C2×2−1+412yes—
1657C2×C4C2×2−1+412yes—
1658C2×C4#58512yes—
1659C2×C4#58512yes—
1660C22—22no—
1661C22—24no—
1662C22—24no—
1663C22—22no—
1664C22—22no—
1665C22—24no—
1666C22—42no—
1667C22—41no—
1668C22—41no—
1669C22—42no—
1670C22—41no—
1671C22—42no—
1672C22—41no—
1673C22—42no—
1674C22—42no—
1675C22—41no—
1676C22—42no—
1677C22—41no—
1678C22—42no—
1679C22—42no—
1680C22—42no—
1681C22—42no—
1682C22—41no—
1683C22—41no—
1684C22—42no—
1685C22—42no—
1686C22—42no—
1687C22—41no—
1688C22—42no—
1689C22—42no—
1690C22—41no—
1691C22—42no—
1692C22—42no—
1693C22—41no—
1694C22—42no—
1695C22C23×#4111yescharacteristic
1696C22C23×#4111yescharacteristic
1697C22C22×H(5,𝔽2)11yescharacteristic
1698C22C22×2−1+411yescharacteristic
1699C22C2×#58511yescharacteristic
1700C22C2×#58511yescharacteristic
1701C22H(7,𝔽2)11yescharacteristic
1702C4—24no—
1703C4—22no—
1704C4—22no—
1705C4—22no—
1706C4—24no—
1707C4—22no—
1708C4—24no—
1709C4—22no—
1710C4—24no—
1711C4—44no—
1712C4—44no—
1713C4—42no—
1714C4—41no—
1715C4—42no—
1716C4—42no—
1717C4—41no—
1718C4—42no—
1719C4—42no—
1720C4—41no—
1721C4—41no—
1722C4—42no—
1723C4—44no—
1724C4—42no—
1725C4—41no—
1726C4—42no—
1727C4—44no—
1728C4—41no—
1729C4—42no—
1730C4#347514yes—
1731C4#349414yes—
1732C2—42no—
1733C2—44no—
1734C2—82no—
1735C2—81no—
1736C2—82no—
1737C2C2×#347511yescharacteristic
1738C2C2×#349411yescharacteristic
1739C2#6280511yescharacteristic
1740C2#6293711yescharacteristic
1741C2#6298611yescharacteristic
1742C2#6300011yescharacteristic
1743C2#6303911yescharacteristic
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. #59970C2semidirect
2. #59550C2semidirect
3. #59546C2semidirect
4. #59428C2semidirect
5. #59410C2semidirect
6. #59312C2semidirect
7. #59291C2semidirect
8. #59217C2semidirect
9. #44975C2semidirect
10. #44900C2semidirect
11. #44800C2semidirect
12. #44527C2semidirect
13. #39527C2semidirect
14. #39471C2semidirect
15. #39006C2semidirect
16. #38965C2semidirect
17. #38718C2semidirect
18. #37970C2semidirect
19. #36481C2semidirect
20. #36464C2semidirect
21. #36414C2semidirect
22. #36366C2semidirect
23. #36315C2semidirect
24. #36268C2semidirect
25. #36259C2semidirect
26. #36189C2semidirect
27. #36087C2semidirect
28. #36026C2semidirect
29. #34916C2semidirect
30. #34715C2semidirect
31. #34316C2semidirect
32. #34253C2semidirect
33. #34207C2semidirect
34. C4×#555C2semidirect
35. #34129C2semidirect
950. #117#41semidirect

Maximal subgroups

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

subgroupindex
#599702
#595502
#595462
#594282
#594102
#593122
#592912
#592172
#449752
#449002
#448002
#445272
#395272
#394712
#390062
#389652
#387182
#379702
#364812
#364642
#364142
#363662
#363152
#362682
#362592
#361892
#360872
#360262
#349162
#347152
#343162
#342532
#342072
C4×#5552
#341292