Finite Group Databasebeta

← #7688359

Subgroups — #7688359

Order 512.

5106 conjugacy classes of subgroups.

The subgroup lattice has 1728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59902C212yesmaximal, complemented
2#59894C212yesmaximal, complemented
3#59811C212yesmaximal, complemented
4#59700C212yesmaximal, complemented
5#59645C212yesmaximal, complemented
6#59639C211yesmaximal, characteristic, complemented
7#59575C212yesmaximal, complemented
8#59071C211yesmaximal, characteristic, complemented
9#59066C211yesmaximal, characteristic, complemented
10#44742C214yesmaximal, complemented
11#44199C214yesmaximal, complemented
12#44190C214yesmaximal, complemented
13#40200C212yesmaximal, complemented
14#40047C212yesmaximal, complemented
15#40009C212yesmaximal, complemented
16#39954C212yesmaximal, complemented
17#39783C212yesmaximal, complemented
18#39227C212yesmaximal, complemented
19#36602C212yesmaximal, complemented
20#36583C211yesmaximal, characteristic, complemented
21#36545C211yesmaximal, characteristic, complemented
22#36410C211yesmaximal, characteristic, complemented
23#36401C212yesmaximal, complemented
24#36315C211yesmaximal, characteristic, complemented
25#36302C211yesmaximal, characteristic, complemented
26#36271C211yesmaximal, characteristic, complemented
27#36150C211yesmaximal, characteristic, complemented
28#35969C214yesmaximal, complemented
29#34979C211yesmaximal, characteristic, complemented
30#34955C211yesmaximal, characteristic, complemented
31#34951C211yesmaximal, characteristic, complemented
32#34322C212yesmaximal, complemented
33#34316C212yesmaximal, complemented
34C4×#556C211yesmaximal, characteristic, complemented
35C4×#548C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic
37C2×#556C2212yes—
38C2×#556C2211yescharacteristic
39C2×#550C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#547C2212yes—
42C2×#533C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46#2861C2212yes—
47#2861C2212yes—
48#2860C2212yes—
49#2858C2212yes—
50#2858C2211yescharacteristic
51#2857C2211yescharacteristic
52#2856C2211yescharacteristic
53#2854C2212yes—
54#2851C2212yes—
55#2803C2214yes—
56#2803C2214yes—
57#2800C2214yes—
58#2798C2214yes—
59#2798C2214yes—
60#2797C2214yes—
61#2788C2214yes—
62#2786C2214yes—
63#2779C2214yes—
64#2779C2214yes—
65#2779C2214yes—
66#2775C2214yes—
67#2753C2214yes—
68#2747C2214yes—
69#2723C2214yes—
70#2719C2214yes—
71#2714C2214yes—
72#2695C2214yes—
73#2692C2214yes—
74#2676C2214yes—
75#2671C2214yes—
76#2662C2214yes—
77#2650C2214yes—
78#2648C2214yes—
79#2611C2214yes—
80#2610C2214yes—
81#2603C2214yes—
82#2602C2214yes—
83#2601C2214yes—
84#2597C2214yes—
85#2597C2214yes—
86#2597C2214yes—
87#2596C2214yes—
88#2595C2214yes—
89#2595C2214yes—
90#2595C2214yes—
91#2595C2214yes—
92#2593C2214yes—
93#2593C2214yes—
94#2592C2212yes—
95#2592C2212yes—
96#2592C2212yes—
97#2592C2212yes—
98#2591C2214yes—
99#2585C2214yes—
100#2584C2212yes—
101#2582C2211yescharacteristic
102#2581C2212yes—
103#2578C2214yes—
104#2577C2214yes—
105#2574C2214yes—
106#2568C2211yescharacteristic
107#2568C2211yescharacteristic
108#2560C2214yes—
109#2559C2214yes—
110#2557C2214yes—
111#2554C2214yes—
112#2552C2211yescharacteristic
113#2548C2212yes—
114#2548C2211yescharacteristic
115#2548C2211yescharacteristic
116#2547C2212yes—
117#2547C2211yescharacteristic
118#2546C2211yescharacteristic
119#2546C2211yescharacteristic
120#2545C2212yes—
121#2542C2211yescharacteristic
122#2540C2212yes—
123#2531C2214yes—
124#2531C2214yes—
125#2531C2214yes—
126#2530C2214yes—
127#2529C2214yes—
128#2518C2214yes—
129#2517C2214yes—
130#2513C2212yes—
131#2513C2212yes—
132#2513C2214yes—
133#2512C2212yes—
134#2511C2212yes—
135#2511C2212yes—
136#2509C2212yes—
137#2504C2212yes—
138#2500C2212yes—
139#2499C2212yes—
140#2499C2212yes—
141#2497C2212yes—
142#2492C2212yes—
143#2490C2212yes—
144#2490C2212yes—
145#2490C2212yes—
146#2490C2212yes—
147#2490C2214yes—
148#2490C2214yes—
149#2489C2212yes—
150#2489C2212yes—
151#2485C2212yes—
152#2481C2214yes—
153#2476C2214yes—
154#2476C2214yes—
155#2475C2214yes—
156#2473C2214yes—
157#2470C2214yes—
158#2464C2214yes—
159#2462C2214yes—
160#2458C2214yes—
161#2458C2214yes—
162#2454C2212yes—
163#2453C2212yes—
164#2453C2212yes—
165#2452C2212yes—
166#2448C2212yes—
167#2446C2212yes—
168#2446C2212yes—
169#2446C2212yes—
170#2445C2212yes—
171#2445C2212yes—
172#2443C2214yes—
173#2436C2212yes—
174#2434C2212yes—
175#2432C2212yes—
176#2432C2212yes—
177#2431C2212yes—
178#2429C2212yes—
179#2429C2212yes—
180#2428C2212yes—
181#2427C2212yes—
182#2427C2212yes—
183#2427C2212yes—
184#2426C2212yes—
185#2426C2212yes—
186#2426C2212yes—
187#2422C2212yes—
188#2421C2212yes—
189#2421C2212yes—
190#2415C2212yes—
191#2415C2212yes—
192#2414C2212yes—
193#2414C2212yes—
194#2407C2212yes—
195#2407C2212yes—
196#2407C2212yes—
197#2402C2214yes—
198#2398C2214yes—
199#2395C2214yes—
200#2374C2214yes—
201#2374C2214yes—
202#2374C2214yes—
203#2373C2214yes—
204#2373C2214yes—
205#2373C2212yes—
206#2373C2212yes—
207#2367C2212yes—
208#2367C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2211yescharacteristic
212#2367C2212yes—
213#2366C2211yescharacteristic
214#2365C2212yes—
215#2365C2212yes—
216#2365C2211yescharacteristic
217#2365C2211yescharacteristic
218#2363C2214yes—
219#2363C2212yes—
220#2363C2212yes—
221#2363C2212yes—
222#2362C2211yescharacteristic
223#2362C2212yes—
224#2362C2211yescharacteristic
225#2362C2212yes—
226#2362C2211yescharacteristic
227#2361C2211yescharacteristic
228#2361C2212yes—
229#2360C2214yes—
230#2360C2212yes—
231#2356C2212yes—
232#2355C2212yes—
233#2355C2211yescharacteristic
234#2355C2211yescharacteristic
235#2354C2212yes—
236#2354C2212yes—
237#2354C2211yescharacteristic
238#2354C2211yescharacteristic
239#2352C2212yes—
240#2352C2211yescharacteristic
241#2351C2211yescharacteristic
242#2351C2212yes—
243D4×C4⋊C4C2212yes—
244#2347C2211yescharacteristic
245#2347C2211yescharacteristic
246#2346C2214yes—
247#2346C2212yes—
248#2345C2214yes—
249#2341C2212yes—
250#2341C2212yes—
251#2341C2211yescharacteristic
252#2341C2212yes—
253Q8×C22⋊C4C2211yescharacteristic
254#2335C2214yes—
255#2335C2214yes—
256#2334C2214yes—
257#2334C2214yes—
258#2324C2214yes—
259#2323C2214yes—
260C4×C4⋊Q8C2212yes—
261C4×C4⋊Q8C2212yes—
262C4×C4⋊Q8C2211yescharacteristic
263C4×C4⋊Q8C2211yescharacteristic
264C4×#125C2212yes—
265C4×#126C2212yes—
266C4×#126C2212yes—
267C4×#124C2212yes—
268C4×#124C2212yes—
269C4×#124C2212yes—
270C4×#124C2212yes—
271C4×#124C2212yes—
272C4×#124C2211yescharacteristic
273C4×#124C2212yes—
274C4×C22⋊Q8C2212yes—
275C4×C22⋊Q8C2212yes—
276C4×C22⋊Q8C2212yes—
277C4×C22⋊Q8C2211yescharacteristic
278C4×C22⋊Q8C2212yes—
279C4×C22⋊Q8C2211yescharacteristic
280C4×C22⋊Q8C2211yescharacteristic
281C4×#121C2212yes—
282C4×#121C2211yescharacteristic
283#2297C2212yes—
284#2297C2212yes—
285#2297C2212yes—
286#2295C2212yes—
287#2295C2212yes—
288#2295C2212yes—
289#2293C2212yes—
290#2293C2212yes—
291#2274C2214yes—
292C42×Q8C2212yes—
293C42×Q8C2211yescharacteristic
294C42×Q8C2211yescharacteristic
295C42×D4C2212yes—
296C42×D4C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C22×#41C2312yes—
302C23×Q8C2311yescharacteristic
303#557—44no—
304#556—28no—
305#556—216no—
306#550—44no—
307#548—28no—
308#547—216no—
309#533—44no—
310#532—44no—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×#127C2311yescharacteristic
318C2×#127C2312yes—
319C2×#126C2312yes—
320C2×#126C2312yes—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#125C2312yes—
324C2×#125C2312yes—
325C2×#125C2312yes—
326C2×#125C2314yes—
327C2×#124C2311yescharacteristic
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×#123C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2311yescharacteristic
349C2×#121C2314yes—
350C2×#121C2312yes—
351C2×#121C2311yescharacteristic
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2314yes—
358C2×#121C2312yes—
359C4×#41—44no—
360C2×C4×Q8—44no—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2311yescharacteristic
369C2×C4×Q8C2311yescharacteristic
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2312yes—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2312yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×#117C2314yes—
398C2×#117C2311yescharacteristic
399C2×#117C2311yescharacteristic
400C2×#117C2314yes—
401C2×#117C2312yes—
402C2×#117C2312yes—
403C2×#117C2311yescharacteristic
404C2×#117C2311yescharacteristic
405C2×#117C2311yescharacteristic
406C2×#117C2312yes—
407C22×C4⋊C4C2314yes—
408C22×C4⋊C4C2312yes—
409C22×C4⋊C4C2311yescharacteristic
410C22×C42C2311yescharacteristic
411C22×C42C2311yescharacteristic
412C22×C42C2312yes—
413C22×C42C2312yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#399C2314yes—
426#399C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#395C2314yes—
458#395C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#392C2314yes—
481#392C2314yes—
482#392C2314yes—
483#392C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2314yes—
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2311yescharacteristic
502#391C2311yescharacteristic
503#391C2312yes—
504#391C2312yes—
505#391C2311yescharacteristic
506#391C2312yes—
507#391C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2314yes—
511#390C2314yes—
512#390C2314yes—
513#390C2314yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2312yes—
527#390C2314yes—
528#390C2312yes—
529#390C2312yes—
530#390C2311yescharacteristic
531#390C2311yescharacteristic
532#390C2312yes—
533#390C2312yes—
534#390C2314yes—
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2314yes—
541#390C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2311yescharacteristic
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2311yescharacteristic
561#389C2314yes—
562#389C2312yes—
563#389C2312yes—
564#389C2314yes—
565#389C2311yescharacteristic
566#389C2312yes—
567#389C2312yes—
568#389C2311yescharacteristic
569#389C2312yes—
570#389C2312yes—
571#389C2311yescharacteristic
572#389C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
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#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2312yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2312yes—
615#388C2312yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2312yes—
622#388C2314yes—
623#388C2314yes—
624#388C2312yes—
625#388C2312yes—
626#388C2314yes—
627#388C2312yes—
628#388C2312yes—
629#388C2312yes—
630#388C2312yes—
631#388C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2312yes—
679#386C2312yes—
680#386C2312yes—
681#386C2314yes—
682#386C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2314yes—
693#385C2314yes—
694#385C2312yes—
695#385C2314yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#384C2311yescharacteristic
700#384C2312yes—
701#384C2312yes—
702#384C2311yescharacteristic
703#383C2312yes—
704#383C2312yes—
705#382C2312yes—
706#382C2312yes—
707#382C2314yes—
708#382C2312yes—
709#382C2312yes—
710#382C2314yes—
711#382C2311yescharacteristic
712#382C2312yes—
713#380C2314yes—
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2314yes—
718#380C2311yescharacteristic
719#380C2312yes—
720#380C2311yescharacteristic
721#380C2312yes—
722#380C2312yes—
723#380C2311yescharacteristic
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2311yescharacteristic
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2311yescharacteristic
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2314yes—
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2314yes—
740C4×C4⋊C4C2314yes—
741C4×C4⋊C4C2314yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2314yes—
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C22⋊C4C2311yescharacteristic
778C4×C22⋊C4C2311yescharacteristic
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811#376C2314yes—
812#376C2314yes—
813#376C2312yes—
814#376C2312yes—
815C43C2312yes—
816C43C2312yes—
817C43C2312yes—
818C43C2311yescharacteristic
819C43C2312yes—
820C2×#41—24no—
821C2×#41—28no—
822C2×#41—28no—
823C2×#41—42no—
824C2×#41—42no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—44no—
829C22×Q8—24no—
830C22×Q8—42no—
831C22×Q8—42no—
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2412yes—
836C22×Q8C2411yescharacteristic
837C22×Q8C2411yescharacteristic
838C22×Q8C2412yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2411yescharacteristic
854C23×C4C2414yes—
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2414yes—
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C4⋊Q8—28no—
865C4⋊Q8—28no—
866C4⋊Q8—24no—
867C4⋊Q8—24no—
868C4⋊Q8—24no—
869C4⋊Q8—44no—
870#127—24no—
871#127—44no—
872#126—28no—
873#126—216no—
874#126—28no—
875#126—216no—
876#125—44no—
877#125—44no—
878#125—44no—
879#125—48no—
880#124—28no—
881#124—28no—
882#124—28no—
883#124—24no—
884#124—28no—
885#124—44no—
886#124—44no—
887#124—44no—
888#124—44no—
889#123—216no—
890#123—216no—
891#123—48no—
892C22⋊Q8—24no—
893C22⋊Q8—28no—
894C22⋊Q8—24no—
895C22⋊Q8—28no—
896C22⋊Q8—216no—
897C22⋊Q8—44no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900C22⋊Q8—44no—
901C22⋊Q8#4118yescomplemented
902#121—24no—
903#121—28no—
904#121—216no—
905#121—44no—
906#121—48no—
907#121—44no—
908#121—44no—
909#121—44no—
910#121—44no—
911#121—44no—
912C4×Q8—24no—
913C4×Q8—28no—
914C4×Q8—28no—
915C4×Q8—28no—
916C4×Q8—24no—
917C4×Q8—24no—
918C4×Q8—24no—
919C4×Q8—44no—
920C4×Q8—44no—
921C4×Q8—44no—
922C4×Q8—42no—
923C4×Q8—42no—
924C4×Q8—42no—
925C4×Q8—44no—
926C4×Q8—42no—
927C4×Q8—42no—
928C4×Q8—44no—
929C4×Q8—44no—
930C4×Q8—44no—
931C4×Q8—44no—
932C4×Q8#4118yescomplemented
933C4×D4—28no—
934C4×D4—24no—
935C4×D4—28no—
936C4×D4—28no—
937C4×D4—28no—
938C4×D4—24no—
939C4×D4—24no—
940C4×D4—42no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—42no—
947C4×D4—44no—
948#117—24no—
949#117—24no—
950#117—216no—
951#117—48no—
952#117—44no—
953#117—42no—
954#117—44no—
955#117—42no—
956#117—42no—
957#117—44no—
958C2×C4⋊C4—216no—
959C2×C4⋊C4—42no—
960C2×C4⋊C4—44no—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2411yescharacteristic
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C42—24no—
1081C2×C42—24no—
1082C2×C42—44no—
1083C2×C42—44no—
1084C2×C42C2412yes—
1085C2×C42C2411yescharacteristic
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2414yes—
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2412yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2411yescharacteristic
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2414yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2414yes—
1110C2×C42C2414yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2411yescharacteristic
1114C2×C42C2414yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2414yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2411yescharacteristic
1127C2×C42C2412yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130#95C2412yes—
1131#95C2412yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2411yescharacteristic
1145#95C2411yescharacteristic
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2411yescharacteristic
1152#95C2412yes—
1153#95C2411yescharacteristic
1154#95C2412yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2411yescharacteristic
1159#95C2412yes—
1160#95C2411yescharacteristic
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196C24C2511yescharacteristic
1197C24C2514yes—
1198C24C2512yes—
1199C24C2511yescharacteristic
1200#41—416no—
1201#41—816no—
1202#41—816no—
1203C2×Q8—24no—
1204C2×Q8—24no—
1205C2×Q8—24no—
1206C2×Q8—24no—
1207C2×Q8—22no—
1208C2×Q8—24no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—24no—
1214C2×Q8—22no—
1215C2×Q8—22no—
1216C2×Q8—24no—
1217C2×Q8—24no—
1218C2×Q8—22no—
1219C2×Q8—42no—
1220C2×Q8—42no—
1221C2×Q8—42no—
1222C2×Q8—416no—
1223C2×Q8C2×#4114yes—
1224C2×Q8C2×#4114yes—
1225C2×D4—24no—
1226C2×D4—22no—
1227C2×D4—28no—
1228C2×D4—24no—
1229C2×D4—22no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—28no—
1235C2×D4—22no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—22no—
1242C2×D4—42no—
1243C2×D4—41no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—44no—
1247C2×D4—44no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—28no—
1261C22×C4—28no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—24no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—24no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—28no—
1279C22×C4—28no—
1280C22×C4—22no—
1281C22×C4—24no—
1282C22×C4—42no—
1283C22×C4—42no—
1284C22×C4—44no—
1285C22×C4—41no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—44no—
1291C22×C4—44no—
1292C22×C4—41no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—41no—
1296C22×C4—42no—
1297C22×C4—44no—
1298C22×C4—44no—
1299C22×C4C2×#4114yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2511yescharacteristic
1304C22×C4C2512yes—
1305C22×C4C2512yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2512yes—
1308C22×C4C2512yes—
1309C22×C4C2514yes—
1310C22×C4C2512yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2512yes—
1313C22×C4C2514yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2512yes—
1316C22×C4C2511yescharacteristic
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2514yes—
1320C22×C4C2511yescharacteristic
1321C22×C4C2511yescharacteristic
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C4⋊C4—24no—
1332C4⋊C4—28no—
1333C4⋊C4—28no—
1334C4⋊C4—24no—
1335C4⋊C4—22no—
1336C4⋊C4—28no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—24no—
1340C4⋊C4—22no—
1341C4⋊C4—24no—
1342C4⋊C4—28no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—28no—
1347C4⋊C4—24no—
1348C4⋊C4—28no—
1349C4⋊C4—24no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—22no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—22no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—24no—
1367C4⋊C4—22no—
1368C4⋊C4—24no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4C2×#4118yes—
1391C4⋊C4C2×#4114yes—
1392C4⋊C4C2×#4114yes—
1393C4⋊C4C2×#4118yes—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—22no—
1397C22⋊C4—24no—
1398C22⋊C4—28no—
1399C22⋊C4—28no—
1400C22⋊C4—22no—
1401C22⋊C4—24no—
1402C22⋊C4—28no—
1403C22⋊C4—24no—
1404C22⋊C4—22no—
1405C22⋊C4—28no—
1406C22⋊C4—22no—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—28no—
1413C22⋊C4—28no—
1414C22⋊C4—24no—
1415C22⋊C4—28no—
1416C22⋊C4—22no—
1417C22⋊C4—44no—
1418C22⋊C4—42no—
1419C22⋊C4—44no—
1420C22⋊C4—42no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—44no—
1426C22⋊C4—42no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—44no—
1432C22⋊C4—42no—
1433C22⋊C4—41no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4C2×#4118yes—
1450C42—24no—
1451C42—28no—
1452C42—24no—
1453C42—24no—
1454C42—22no—
1455C42—24no—
1456C42—24no—
1457C42—24no—
1458C42—22no—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—22no—
1463C42—22no—
1464C42—24no—
1465C42—24no—
1466C42—24no—
1467C42—24no—
1468C42—22no—
1469C42—22no—
1470C42—24no—
1471C42—42no—
1472C42—42no—
1473C42—42no—
1474C42—42no—
1475C42—41no—
1476C42—42no—
1477C42—42no—
1478C42—42no—
1479C42—42no—
1480C42—44no—
1481C42—42no—
1482C42—44no—
1483C42—42no—
1484C42—44no—
1485C42—41no—
1486C42—42no—
1487C42—42no—
1488C42—44no—
1489C42—42no—
1490C42—42no—
1491C42—42no—
1492C42—44no—
1493C42C2×#4118yes—
1494C42C2×#4114yes—
1495C42H(5,𝔽2)14yes—
1496C23—21no—
1497C23—21no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—24no—
1503C23—21no—
1504C23—22no—
1505C23—21no—
1506C23—22no—
1507C23—24no—
1508C23—22no—
1509C23—21no—
1510C23—24no—
1511C23—24no—
1512C23—24no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—21no—
1517C23—21no—
1518C23—24no—
1519C23—21no—
1520C23—21no—
1521C23—24no—
1522C23—22no—
1523C23C22×#4112yes—
1524C23C2611yescharacteristic
1525Q8—28no—
1526Q8—28no—
1527Q8—48no—
1528Q8—48no—
1529Q8—48no—
1530Q8—44no—
1531Q8—48no—
1532D4—48no—
1533D4—44no—
1534D4—48no—
1535D4—48no—
1536D4—44no—
1537D4—48no—
1538D4—84no—
1539D4—88no—
1540D4—88no—
1541D4—164no—
1542D4—164no—
1543C2×C4—21no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—28no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—24no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—24no—
1586C2×C4—24no—
1587C2×C4—21no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—24no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—24no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—24no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—44no—
1623C2×C4—416no—
1624C2×C4—48no—
1625C2×C4—48no—
1626C2×C4—44no—
1627C2×C4—44no—
1628C2×C4—44no—
1629C2×C4—48no—
1630C2×C4—84no—
1631C2×C4—82no—
1632C2×C4—88no—
1633C2×C4—88no—
1634C2×C4—84no—
1635C2×C4C22×#4114yes—
1636C2×C4C22×#4112yes—
1637C2×C4C22×#4114yes—
1638C2×C4C22×#4114yes—
1639C2×C4C22×#4112yes—
1640C2×C4C22×#4112yes—
1641C2×C4C22×#4114yes—
1642C2×C4C22×#4112yes—
1643C2×C4C22×#4112yes—
1644C2×C4C2×H(5,𝔽2)12yes—
1645C2×C4C2×H(5,𝔽2)12yes—
1646C2×C4C2×H(5,𝔽2)12yes—
1647C2×C4#58512yes—
1648C2×C4#58512yes—
1649C2×C4#58512yes—
1650C22—22no—
1651C22—22no—
1652C22—22no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—44no—
1658C22—42no—
1659C22—41no—
1660C22—41no—
1661C22—42no—
1662C22—44no—
1663C22—42no—
1664C22—41no—
1665C22—44no—
1666C22—42no—
1667C22—41no—
1668C22—44no—
1669C22—41no—
1670C22—44no—
1671C22—42no—
1672C22—41no—
1673C22—42no—
1674C22—44no—
1675C22—44no—
1676C22—41no—
1677C22—42no—
1678C22C23×#4111yescharacteristic
1679C22C23×#4111yescharacteristic
1680C22C22×H(5,𝔽2)11yescharacteristic
1681C22C2×#58511yescharacteristic
1682C22C2×#58511yescharacteristic
1683C22C2×#58511yescharacteristic
1684C222−1+611yescharacteristic
1685C4—22no—
1686C4—24no—
1687C4—22no—
1688C4—24no—
1689C4—22no—
1690C4—22no—
1691C4—24no—
1692C4—24no—
1693C4—22no—
1694C4—42no—
1695C4—42no—
1696C4—42no—
1697C4—42no—
1698C4—41no—
1699C4—41no—
1700C4—41no—
1701C4—42no—
1702C4—44no—
1703C4—41no—
1704C4—42no—
1705C4—44no—
1706C4—41no—
1707C4—42no—
1708C4—44no—
1709C4—41no—
1710C4—42no—
1711C4—42no—
1712C4—42no—
1713C4—42no—
1714C4#350614yes—
1715C4#351414yes—
1716C2—42no—
1717C2—82no—
1718C2—81no—
1719C2—84no—
1720C2#41211yescharacteristic
1721C2C2×#350611yescharacteristic
1722C2C2×#351411yescharacteristic
1723C2#6295411yescharacteristic
1724C2#6300711yescharacteristic
1725C2#6300711yescharacteristic
1726C2#6303611yescharacteristic
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. #59902C2semidirect
2. #59894C2semidirect
3. #59811C2semidirect
4. #59700C2semidirect
5. #59645C2semidirect
6. #59639C2semidirect
7. #59575C2semidirect
8. #59071C2semidirect
9. #59066C2semidirect
10. #44742C2semidirect
11. #44199C2semidirect
12. #44190C2semidirect
13. #40200C2semidirect
14. #40047C2semidirect
15. #40009C2semidirect
16. #39954C2semidirect
17. #39783C2semidirect
18. #39227C2semidirect
19. #36602C2semidirect
20. #36583C2semidirect
21. #36545C2semidirect
22. #36410C2semidirect
23. #36401C2semidirect
24. #36315C2semidirect
25. #36302C2semidirect
26. #36271C2semidirect
27. #36150C2semidirect
28. #35969C2semidirect
29. #34979C2semidirect
30. #34955C2semidirect
31. #34951C2semidirect
32. #34322C2semidirect
33. #34316C2semidirect
34. C4×#556C2semidirect
35. C4×#548C2semidirect
901. C22⋊Q8#41semidirect
932. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599022
#598942
#598112
#597002
#596452
#596392
#595752
#590712
#590662
#447422
#441992
#441902
#402002
#400472
#400092
#399542
#397832
#392272
#366022
#365832
#365452
#364102
#364012
#363152
#363022
#362712
#361502
#359692
#349792
#349552
#349512
#343222
#343162
C4×#5562
C4×#5482