Finite Group Databasebeta

← #7689613

Subgroups — #7689613

Order 512.

5242 conjugacy classes of subgroups.

The subgroup lattice has 1746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59754C214yesmaximal, complemented
2#59710C212yesmaximal, complemented
3#59701C212yesmaximal, complemented
4#59673C211yesmaximal, characteristic, complemented
5#59118C212yesmaximal, complemented
6#59056C211yesmaximal, characteristic, complemented
7#59050C211yesmaximal, characteristic, complemented
8#59049C212yesmaximal, complemented
9#45399C212yesmaximal, complemented
10#45048C212yesmaximal, complemented
11#44107C214yesmaximal, complemented
12#43195C214yesmaximal, complemented
13#39793C212yesmaximal, complemented
14#39735C211yesmaximal, characteristic, complemented
15#39237C212yesmaximal, complemented
16#39202C211yesmaximal, characteristic, complemented
17#38660C214yesmaximal, complemented
18#38216C212yesmaximal, complemented
19#36507C212yesmaximal, complemented
20#36495C212yesmaximal, complemented
21#36473C211yesmaximal, characteristic, complemented
22#36449C211yesmaximal, characteristic, complemented
23#36393C212yesmaximal, complemented
24#36150C211yesmaximal, characteristic, complemented
25#36126C211yesmaximal, characteristic, complemented
26#36115C211yesmaximal, characteristic, complemented
27#35798C212yesmaximal, complemented
28#35768C212yesmaximal, complemented
29#34889C212yesmaximal, complemented
30#34797C211yesmaximal, characteristic, complemented
31#34321C211yesmaximal, characteristic, complemented
32#34316C212yesmaximal, complemented
33#34213C211yesmaximal, characteristic, complemented
34C4×#553C211yesmaximal, characteristic, complemented
35#34155C211yesmaximal, characteristic, complemented
36C2×#556C2212yes—
37C2×#555C2211yescharacteristic
38C2×#553C2211yescharacteristic
39C2×#547C2212yes—
40C2×#533C2211yescharacteristic
41C2×#532C2211yescharacteristic
42C2×#532C2212yes—
43C2×#529C2212yes—
44#2863C2212yes—
45#2860C2212yes—
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2854C2212yes—
50#2853C2214yes—
51#2850C2212yes—
52#2803C2214yes—
53#2800C2214yes—
54#2799C2214yes—
55#2797C2214yes—
56#2797C2214yes—
57#2795C2214yes—
58#2777C2214yes—
59#2753C2214yes—
60#2753C2214yes—
61#2753C2214yes—
62#2753C2214yes—
63#2752C2214yes—
64#2749C2214yes—
65#2733C2214yes—
66#2730C2214yes—
67#2718C2214yes—
68#2714C2214yes—
69#2714C2214yes—
70#2710C2214yes—
71#2709C2214yes—
72#2703C2214yes—
73#2661C2214yes—
74#2648C2214yes—
75#2624C2212yes—
76#2619C2212yes—
77#2604C2214yes—
78#2602C2214yes—
79#2601C2214yes—
80#2598C2214yes—
81#2597C2214yes—
82#2596C2214yes—
83#2595C2214yes—
84#2581C2214yes—
85#2578C2214yes—
86#2578C2214yes—
87#2577C2214yes—
88#2571C2211yescharacteristic
89#2560C2214yes—
90#2559C2214yes—
91#2559C2214yes—
92#2557C2214yes—
93#2554C2214yes—
94#2551C2211yescharacteristic
95#2550C2212yes—
96#2550C2212yes—
97#2548C2212yes—
98#2548C2214yes—
99#2547C2211yescharacteristic
100#2544C2212yes—
101#2542C2211yescharacteristic
102#2541C2211yescharacteristic
103#2541C2211yescharacteristic
104#2541C2212yes—
105#2541C2212yes—
106#2540C2212yes—
107#2540C2212yes—
108#2535C2212yes—
109#2531C2212yes—
110#2530C2214yes—
111#2529C2212yes—
112#2523C2214yes—
113#2521C2214yes—
114#2521C2214yes—
115#2518C2214yes—
116#2518C2214yes—
117#2518C2212yes—
118#2516C2214yes—
119#2515C2214yes—
120#2513C2212yes—
121#2513C2214yes—
122#2512C2212yes—
123#2512C2211yescharacteristic
124#2512C2214yes—
125#2509C2212yes—
126#2509C2212yes—
127#2508C2212yes—
128#2508C2212yes—
129#2507C2211yescharacteristic
130#2500C2212yes—
131#2500C2214yes—
132#2500C2211yescharacteristic
133#2496C2212yes—
134#2495C2211yescharacteristic
135#2495C2212yes—
136#2492C2212yes—
137#2491C2212yes—
138#2491C2212yes—
139#2490C2212yes—
140#2490C2212yes—
141#2490C2211yescharacteristic
142#2490C2212yes—
143#2485C2212yes—
144#2485C2211yescharacteristic
145#2479C2214yes—
146#2471C2214yes—
147#2469C2214yes—
148#2467C2212yes—
149#2467C2214yes—
150#2467C2214yes—
151#2467C2214yes—
152#2466C2214yes—
153#2464C2214yes—
154#2461C2214yes—
155#2461C2214yes—
156#2458C2214yes—
157#2457C2214yes—
158#2454C2212yes—
159#2452C2212yes—
160#2448C2212yes—
161#2448C2212yes—
162#2448C2214yes—
163#2448C2214yes—
164#2447C2212yes—
165#2445C2212yes—
166#2445C2212yes—
167#2445C2212yes—
168#2445C2214yes—
169#2441C2212yes—
170#2441C2211yescharacteristic
171#2431C2214yes—
172#2431C2214yes—
173#2430C2214yes—
174#2428C2212yes—
175#2428C2212yes—
176#2427C2212yes—
177#2427C2212yes—
178#2427C2212yes—
179#2426C2212yes—
180#2426C2212yes—
181#2426C2212yes—
182#2426C2212yes—
183#2422C2212yes—
184#2421C2212yes—
185#2420C2212yes—
186#2416C2212yes—
187#2415C2212yes—
188#2415C2212yes—
189#2414C2212yes—
190#2414C2212yes—
191#2414C2212yes—
192#2414C2212yes—
193#2414C2212yes—
194#2414C2211yescharacteristic
195#2407C2212yes—
196#2395C2214yes—
197#2395C2212yes—
198#2392C2212yes—
199#2388C2214yes—
200#2374C2214yes—
201#2374C2214yes—
202#2374C2212yes—
203#2373C2212yes—
204#2372C2214yes—
205#2370C2211yescharacteristic
206#2370C2212yes—
207#2370C2212yes—
208#2369C2211yescharacteristic
209#2369C2211yescharacteristic
210#2369C2211yescharacteristic
211#2367C2214yes—
212#2367C2212yes—
213#2366C2211yescharacteristic
214#2366C2212yes—
215#2366C2211yescharacteristic
216#2365C2212yes—
217#2365C2211yescharacteristic
218#2365C2212yes—
219#2365C2211yescharacteristic
220#2364C2212yes—
221#2363C2212yes—
222#2363C2212yes—
223#2363C2212yes—
224#2363C2212yes—
225#2363C2212yes—
226#2363C2212yes—
227#2363C2212yes—
228#2363C2212yes—
229#2363C2211yescharacteristic
230#2362C2214yes—
231#2362C2212yes—
232#2362C2212yes—
233#2361C2212yes—
234#2361C2212yes—
235#2361C2211yescharacteristic
236#2357C2211yescharacteristic
237#2355C2212yes—
238#2355C2214yes—
239#2354C2212yes—
240#2354C2212yes—
241#2354C2211yescharacteristic
242#2353C2212yes—
243#2352C2211yescharacteristic
244#2352C2212yes—
245Q8×C4⋊C4C2212yes—
246D4×C4⋊C4C2211yescharacteristic
247#2347C2212yes—
248#2347C2212yes—
249#2347C2214yes—
250#2347C2211yescharacteristic
251#2345C2211yescharacteristic
252#2345C2212yes—
253#2341C2214yes—
254#2341C2212yes—
255#2337C2214yes—
256#2335C2214yes—
257#2335C2214yes—
258#2329C2214yes—
259#2324C2212yes—
260#2324C2212yes—
261#2324C2212yes—
262#2317C2212yes—
263C4×C4⋊Q8C2212yes—
264C4×C4⋊Q8C2211yescharacteristic
265C4×#125C2211yescharacteristic
266C4×#125C2211yescharacteristic
267C4×#126C2212yes—
268C4×#126C2212yes—
269C4×#124C2212yes—
270C4×C22⋊Q8C2214yes—
271C4×C22⋊Q8C2212yes—
272C4×C22⋊Q8C2212yes—
273C4×#123C2212yes—
274C4×#121C2212yes—
275C4×#121C2211yescharacteristic
276C4×#121C2211yescharacteristic
277C4×#121C2214yes—
278C4×#121C2211yescharacteristic
279C4×#121C2212yes—
280C4×#121C2211yescharacteristic
281#2297C2214yes—
282#2297C2214yes—
283#2296C2212yes—
284#2293C2212yes—
285#2293C2211yescharacteristic
286#2293C2212yes—
287#2293C2212yes—
288#2285C2211yescharacteristic
289#2274C2212yes—
290#2274C2212yes—
291C42×D4C2212yes—
292C42×D4C2211yescharacteristic
293C42×D4C2212yes—
294C42×D4C2211yescharacteristic
295C42×D4C2212yes—
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2314yes—
300C22×#41C2312yes—
301#556—48no—
302#555—28no—
303#553—28no—
304#547—216no—
305#533—28no—
306#532—28no—
307#532—48no—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2311yescharacteristic
312C2×#127C2311yescharacteristic
313C2×#127C2312yes—
314C2×#127C2312yes—
315C2×#127C2314yes—
316#529—48no—
317C2×#126C2312yes—
318C2×#126C2312yes—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#125C2311yescharacteristic
323C2×#125C2311yescharacteristic
324C2×#125C2312yes—
325C2×#124C2314yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2314yes—
330C2×#124C2312yes—
331C2×#124C2314yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×#123C2312yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2312yes—
346C2×#121C2311yescharacteristic
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2311yescharacteristic
351C2×#121C2312yes—
352C2×#121C2311yescharacteristic
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2311yescharacteristic
358C2×#121C2314yes—
359C2×#121C2314yes—
360C2×#121C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2314yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2314yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2314yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2314yes—
391C2×#117C2312yes—
392C2×#117C2311yescharacteristic
393C2×#117C2312yes—
394C2×#117C2312yes—
395C2×#117C2311yescharacteristic
396C2×#117C2312yes—
397C2×#117C2312yes—
398C2×#117C2314yes—
399C2×#117C2311yescharacteristic
400C2×#117C2312yes—
401C2×#117C2314yes—
402C2×#117C2311yescharacteristic
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2311yescharacteristic
405C22×C4⋊C4C2311yescharacteristic
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2312yes—
409C22×C42C2312yes—
410C22×C42C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2312yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2312yes—
422#399C2314yes—
423#398C2312yes—
424#398C2312yes—
425#398C2314yes—
426#398C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2312yes—
435#397C2314yes—
436#397C2314yes—
437#397C2312yes—
438#397C2312yes—
439#397C2314yes—
440#397C2312yes—
441#397C2314yes—
442#397C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2312yes—
446#396C2312yes—
447#396C2314yes—
448#396C2314yes—
449#395C2314yes—
450#395C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2312yes—
461#394C2314yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2314yes—
466#394C2314yes—
467#394C2312yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#393C2314yes—
477#393C2314yes—
478#392C2314yes—
479#392C2314yes—
480#392C2314yes—
481#392C2314yes—
482#392C2312yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2314yes—
487#392C2314yes—
488#392C2314yes—
489#391C2314yes—
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#390C2314yes—
501#390C2314yes—
502#390C2314yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2314yes—
508#390C2314yes—
509#390C2312yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2314yes—
514#390C2314yes—
515#390C2314yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2311yescharacteristic
523#390C2312yes—
524#390C2311yescharacteristic
525#390C2314yes—
526#390C2311yescharacteristic
527#390C2314yes—
528#390C2312yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2314yes—
534#390C2314yes—
535#390C2311yescharacteristic
536#390C2311yescharacteristic
537#390C2314yes—
538#390C2312yes—
539#390C2311yescharacteristic
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2311yescharacteristic
544#389C2311yescharacteristic
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2311yescharacteristic
564#389C2311yescharacteristic
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2311yescharacteristic
569#389C2311yescharacteristic
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2311yescharacteristic
575#389C2312yes—
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2312yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2312yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2312yes—
619#388C2312yes—
620#388C2314yes—
621#388C2312yes—
622#388C2312yes—
623#388C2314yes—
624#388C2314yes—
625#388C2312yes—
626#388C2312yes—
627#388C2312yes—
628#388C2312yes—
629#388C2312yes—
630#388C2314yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2314yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2312yes—
658#387C2314yes—
659#386C2314yes—
660#386C2312yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2312yes—
679#386C2312yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2312yes—
684#386C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2312yes—
695#384C2311yescharacteristic
696#384C2312yes—
697#384C2314yes—
698#384C2311yescharacteristic
699#384C2311yescharacteristic
700#383C2312yes—
701#383C2312yes—
702#383C2314yes—
703#383C2314yes—
704#382C2311yescharacteristic
705#382C2311yescharacteristic
706#382C2312yes—
707#382C2312yes—
708#382C2314yes—
709#382C2314yes—
710#382C2312yes—
711#381C2314yes—
712#381C2312yes—
713#380C2314yes—
714#380C2312yes—
715#380C2314yes—
716#380C2311yescharacteristic
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2314yes—
722#380C2311yescharacteristic
723#380C2312yes—
724#380C2311yescharacteristic
725#380C2312yes—
726#380C2312yes—
727#380C2311yescharacteristic
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730C4×C4⋊C4C2311yescharacteristic
731C4×C4⋊C4C2311yescharacteristic
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2311yescharacteristic
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2314yes—
811C4×C22⋊C4C2312yes—
812#376C2312yes—
813#376C2312yes—
814C2×#95C2312yes—
815C43C2312yes—
816C43C2312yes—
817C43C2311yescharacteristic
818C2×#41—28no—
819C2×#41—216no—
820C2×#41—44no—
821C2×#41—48no—
822C2×#41—82no—
823C2×#41—84no—
824C22×Q8C2412yes—
825C22×Q8C2414yes—
826C22×Q8C2412yes—
827C22×D4C2411yescharacteristic
828C22×D4C2412yes—
829C22×D4C2411yescharacteristic
830C22×D4C2412yes—
831C22×D4C2412yes—
832C22×D4C2412yes—
833C22×D4C2411yescharacteristic
834C22×D4C2414yes—
835C22×D4C2412yes—
836C22×D4C2414yes—
837C22×D4C2414yes—
838C22×D4C2414yes—
839C22×D4C2412yes—
840C22×D4C2414yes—
841C22×D4C2414yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C23×C4C2412yes—
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2414yes—
850C23×C4C2414yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2414yes—
854C23×C4C2412yes—
855C23×C4C2411yescharacteristic
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2414yes—
859C23×C4C2412yes—
860C4⋊Q8—28no—
861C4⋊Q8—28no—
862C4⋊Q8—24no—
863C4⋊Q8#4118yescomplemented
864#127—24no—
865#127—44no—
866#127—44no—
867#127—84no—
868#126—28no—
869#126—44no—
870#126—48no—
871#126—48no—
872#126—48no—
873#125—28no—
874#125—24no—
875#125—24no—
876#124—28no—
877#124—216no—
878#124—44no—
879#124—44no—
880#124—44no—
881#124—48no—
882#124—48no—
883#123—216no—
884#123—216no—
885#123—28no—
886#123—48no—
887#123—84no—
888C22⋊Q8—28no—
889C22⋊Q8—28no—
890C22⋊Q8—216no—
891C22⋊Q8—28no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894#121—28no—
895#121—28no—
896#121—24no—
897#121—28no—
898#121—28no—
899#121—28no—
900#121—24no—
901#121—28no—
902#121—28no—
903#121—24no—
904#121—48no—
905#121—48no—
906#121—44no—
907#121—42no—
908#121—44no—
909#121—44no—
910#121—44no—
911#121—82no—
912C4×Q8—28no—
913C4×Q8—28no—
914C4×Q8—44no—
915C4×Q8—44no—
916C4×Q8—48no—
917C4×Q8—84no—
918C4×Q8—82no—
919C4×D4—28no—
920C4×D4—28no—
921C4×D4—24no—
922C4×D4—28no—
923C4×D4—28no—
924C4×D4—28no—
925C4×D4—24no—
926C4×D4—28no—
927C4×D4—24no—
928C4×D4—24no—
929C4×D4—44no—
930C4×D4—42no—
931C4×D4—44no—
932C4×D4—44no—
933C4×D4—44no—
934C4×D4—44no—
935C4×D4—44no—
936C4×D4—42no—
937C4×D4—44no—
938C4×D4—42no—
939C4×D4—48no—
940C4×D4—48no—
941C4×D4—84no—
942#117—28no—
943#117—24no—
944#117—28no—
945#117—28no—
946#117—24no—
947#117—44no—
948#117—48no—
949#117—44no—
950#117—42no—
951#117—42no—
952#117—48no—
953#117—44no—
954C2×C4⋊C4—28no—
955C2×C4⋊C4—42no—
956C2×C4⋊C4#4118yescomplemented
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2411yescharacteristic
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C42—24no—
1083C2×C42—24no—
1084C2×C42—44no—
1085C2×C42—44no—
1086C2×C42—84no—
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2411yescharacteristic
1090C2×C42C2414yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2414yes—
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2412yes—
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2411yescharacteristic
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2414yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2411yescharacteristic
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2412yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2411yescharacteristic
1144#95C2412yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2411yescharacteristic
1148#95C2412yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2411yescharacteristic
1152#95C2411yescharacteristic
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189C24C2512yes—
1190C24C2514yes—
1191C24C2512yes—
1192C24C2511yescharacteristic
1193C24C2511yescharacteristic
1194#41—816no—
1195#41—832no—
1196C2×Q8—24no—
1197C2×Q8—28no—
1198C2×Q8—24no—
1199C2×Q8—28no—
1200C2×Q8—24no—
1201C2×Q8—42no—
1202C2×Q8—44no—
1203C2×Q8—42no—
1204C2×Q8C2×#4118yes—
1205C2×D4—24no—
1206C2×D4—22no—
1207C2×D4—24no—
1208C2×D4—28no—
1209C2×D4—24no—
1210C2×D4—22no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—24no—
1214C2×D4—24no—
1215C2×D4—24no—
1216C2×D4—28no—
1217C2×D4—28no—
1218C2×D4—28no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—22no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—42no—
1228C2×D4—41no—
1229C2×D4—42no—
1230C2×D4—41no—
1231C2×D4—42no—
1232C2×D4—44no—
1233C2×D4—44no—
1234C2×D4—42no—
1235C2×D4—42no—
1236C2×D4—44no—
1237C2×D4—44no—
1238C2×D4—44no—
1239C2×D4—44no—
1240C2×D4—44no—
1241C2×D4—42no—
1242C2×D4—44no—
1243C2×D4—42no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—44no—
1250C2×D4—44no—
1251C2×D4—42no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—28no—
1267C22×C4—28no—
1268C22×C4—22no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—28no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—28no—
1276C22×C4—22no—
1277C22×C4—24no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—28no—
1281C22×C4—24no—
1282C22×C4—42no—
1283C22×C4—44no—
1284C22×C4—44no—
1285C22×C4—41no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—44no—
1291C22×C4—42no—
1292C22×C4—44no—
1293C22×C4—41no—
1294C22×C4—44no—
1295C22×C4—42no—
1296C22×C4—44no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—44no—
1301C22×C4—41no—
1302C22×C4C2×#4114yes—
1303C22×C4C2×#4118yes—
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2512yes—
1309C22×C4C2511yescharacteristic
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2512yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2511yescharacteristic
1317C22×C4C2514yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C22×C4C2514yes—
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2512yes—
1327C22×C4C2514yes—
1328C22×C4C2512yes—
1329C22×C4C2511yescharacteristic
1330C22×C4C2512yes—
1331C22×C4C2511yescharacteristic
1332C22×C4C2511yescharacteristic
1333C22×C4C2511yescharacteristic
1334C4⋊C4—24no—
1335C4⋊C4—28no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—22no—
1343C4⋊C4—28no—
1344C4⋊C4—28no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—28no—
1348C4⋊C4—22no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—28no—
1352C4⋊C4—24no—
1353C4⋊C4—28no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—22no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—41no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4C2×#4114yes—
1388C4⋊C4C2×#4114yes—
1389C4⋊C4C2×#4118yes—
1390C4⋊C4C2×#4118yes—
1391C4⋊C4C2×#4118yes—
1392C4⋊C4H(5,𝔽2)14yes—
1393C22⋊C4—22no—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—28no—
1397C22⋊C4—28no—
1398C22⋊C4—28no—
1399C22⋊C4—28no—
1400C22⋊C4—28no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—24no—
1405C22⋊C4—22no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—28no—
1413C22⋊C4—24no—
1414C22⋊C4—28no—
1415C22⋊C4—22no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—44no—
1429C22⋊C4—41no—
1430C22⋊C4—41no—
1431C22⋊C4—44no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—41no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—42no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—42no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—22no—
1463C42—22no—
1464C42—22no—
1465C42—28no—
1466C42—24no—
1467C42—28no—
1468C42—22no—
1469C42—24no—
1470C42—24no—
1471C42—22no—
1472C42—24no—
1473C42—24no—
1474C42—24no—
1475C42—22no—
1476C42—24no—
1477C42—24no—
1478C42—24no—
1479C42—24no—
1480C42—22no—
1481C42—42no—
1482C42—42no—
1483C42—42no—
1484C42—42no—
1485C42—42no—
1486C42—42no—
1487C42—44no—
1488C42—44no—
1489C42—42no—
1490C42—42no—
1491C42—44no—
1492C42—44no—
1493C42—41no—
1494C42—44no—
1495C42—44no—
1496C42—41no—
1497C42—44no—
1498C42C2×#4114yes—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—24no—
1506C23—22no—
1507C23—21no—
1508C23—22no—
1509C23—22no—
1510C23—24no—
1511C23—22no—
1512C23—21no—
1513C23—21no—
1514C23—22no—
1515C23—24no—
1516C23—22no—
1517C23—22no—
1518C23—22no—
1519C23—22no—
1520C23—21no—
1521C23—24no—
1522C23—22no—
1523C23—21no—
1524C23—22no—
1525C23—24no—
1526C23—24no—
1527C23—21no—
1528C23—22no—
1529C23—22no—
1530C23—24no—
1531C23—22no—
1532C23—21no—
1533C23C22×#4112yes—
1534C23C2611yescharacteristic
1535Q8—48no—
1536Q8—416no—
1537Q8—48no—
1538D4—48no—
1539D4—48no—
1540D4—44no—
1541D4—44no—
1542D4—48no—
1543D4—44no—
1544D4—48no—
1545D4—84no—
1546D4—88no—
1547D4—88no—
1548D4—84no—
1549D4—88no—
1550D4—88no—
1551D4—88no—
1552D4—88no—
1553D4—84no—
1554D4—164no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—24no—
1563C2×C4—24no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—28no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—24no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—21no—
1591C2×C4—22no—
1592C2×C4—24no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—21no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—24no—
1620C2×C4—21no—
1621C2×C4—22no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—24no—
1632C2×C4—21no—
1633C2×C4—48no—
1634C2×C4—416no—
1635C2×C4—416no—
1636C2×C4—44no—
1637C2×C4—44no—
1638C2×C4—48no—
1639C2×C4—44no—
1640C2×C4—44no—
1641C2×C4—48no—
1642C2×C4—84no—
1643C2×C4—82no—
1644C2×C4—88no—
1645C2×C4—84no—
1646C2×C4—84no—
1647C2×C4—88no—
1648C2×C4C22×#4112yes—
1649C2×C4C22×#4118yes—
1650C2×C4C22×#4114yes—
1651C2×C4C22×#4112yes—
1652C2×C4C22×#4114yes—
1653C2×C4C22×#4112yes—
1654C2×C4C22×#4112yes—
1655C2×C4C22×#4112yes—
1656C2×C4C2×H(5,𝔽2)14yes—
1657C2×C4C2×H(5,𝔽2)12yes—
1658C2×C4#58512yes—
1659C2×C4#58512yes—
1660C2×C4#58512yes—
1661C22—22no—
1662C22—22no—
1663C22—22no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—41no—
1668C22—44no—
1669C22—42no—
1670C22—42no—
1671C22—41no—
1672C22—41no—
1673C22—44no—
1674C22—42no—
1675C22—42no—
1676C22—42no—
1677C22—44no—
1678C22—42no—
1679C22—41no—
1680C22—42no—
1681C22—41no—
1682C22—42no—
1683C22—44no—
1684C22—42no—
1685C22—41no—
1686C22—44no—
1687C22—42no—
1688C22—44no—
1689C22—41no—
1690C22—42no—
1691C22—42no—
1692C22—42no—
1693C22—41no—
1694C22—42no—
1695C22—44no—
1696C22C23×#4111yescharacteristic
1697C22C23×#4111yescharacteristic
1698C22C22×H(5,𝔽2)11yescharacteristic
1699C22C2×#58511yescharacteristic
1700C22C2×#58511yescharacteristic
1701C22C2×#58511yescharacteristic
1702C22H(7,𝔽2)11yescharacteristic
1703C4—24no—
1704C4—24no—
1705C4—24no—
1706C4—22no—
1707C4—22no—
1708C4—28no—
1709C4—22no—
1710C4—41no—
1711C4—44no—
1712C4—41no—
1713C4—42no—
1714C4—42no—
1715C4—41no—
1716C4—42no—
1717C4—42no—
1718C4—41no—
1719C4—42no—
1720C4—41no—
1721C4—44no—
1722C4—42no—
1723C4—42no—
1724C4—41no—
1725C4—41no—
1726C4—42no—
1727C4—42no—
1728C4—42no—
1729C4—41no—
1730C4—42no—
1731C4#348014yes—
1732C4#351714yes—
1733C2—42no—
1734C2—84no—
1735C2—82no—
1736C2—82no—
1737C2—81no—
1738C2C2×#348011yescharacteristic
1739C2C2×#351711yescharacteristic
1740C2#6279311yescharacteristic
1741C2#6293811yescharacteristic
1742C2#6298311yescharacteristic
1743C2#6299011yescharacteristic
1744C2#6302211yescharacteristic
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. #59754C2semidirect
2. #59710C2semidirect
3. #59701C2semidirect
4. #59673C2semidirect
5. #59118C2semidirect
6. #59056C2semidirect
7. #59050C2semidirect
8. #59049C2semidirect
9. #45399C2semidirect
10. #45048C2semidirect
11. #44107C2semidirect
12. #43195C2semidirect
13. #39793C2semidirect
14. #39735C2semidirect
15. #39237C2semidirect
16. #39202C2semidirect
17. #38660C2semidirect
18. #38216C2semidirect
19. #36507C2semidirect
20. #36495C2semidirect
21. #36473C2semidirect
22. #36449C2semidirect
23. #36393C2semidirect
24. #36150C2semidirect
25. #36126C2semidirect
26. #36115C2semidirect
27. #35798C2semidirect
28. #35768C2semidirect
29. #34889C2semidirect
30. #34797C2semidirect
31. #34321C2semidirect
32. #34316C2semidirect
33. #34213C2semidirect
34. C4×#553C2semidirect
35. #34155C2semidirect
863. C4⋊Q8#41semidirect
956. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#597542
#597102
#597012
#596732
#591182
#590562
#590502
#590492
#453992
#450482
#441072
#431952
#397932
#397352
#392372
#392022
#386602
#382162
#365072
#364952
#364732
#364492
#363932
#361502
#361262
#361152
#357982
#357682
#348892
#347972
#343212
#343162
#342132
C4×#5532
#341552