Finite Group Databasebeta

← #8466878

Subgroups — #8466878

Order 512.

4662 conjugacy classes of subgroups.

The subgroup lattice has 1737 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59640C211yesmaximal, characteristic, complemented
2#59084C211yesmaximal, characteristic, complemented
3#59049C211yesmaximal, characteristic, complemented
4#56409C214yesmaximal, complemented
5#56055C214yesmaximal, complemented
6#55560C214yesmaximal, complemented
7#53116C212yesmaximal, complemented
8#53061C212yesmaximal, complemented
9#49173C214yesmaximal, complemented
10#46061C212yesmaximal, complemented
11#45508C212yesmaximal, complemented
12#45209C212yesmaximal, complemented
13#45204C212yesmaximal, complemented
14#42858C212yesmaximal, complemented
15#42757C212yesmaximal, complemented
16#42749C212yesmaximal, complemented
17#42664C212yesmaximal, complemented
18#39934C212yesmaximal, complemented
19#39766C212yesmaximal, complemented
20#39515C211yesmaximal, characteristic, complemented
21#39224C212yesmaximal, complemented
22#39172C211yesmaximal, characteristic, complemented
23#39125C211yesmaximal, characteristic, complemented
24#38943C211yesmaximal, characteristic, complemented
25#37858C212yesmaximal, complemented
26#37625C211yesmaximal, characteristic, complemented
27#37357C212yesmaximal, complemented
28#37282C212yesmaximal, complemented
29#36459C211yesmaximal, characteristic, complemented
30#36161C211yesmaximal, characteristic, complemented
31#36149C211yesmaximal, characteristic, complemented
32#35237C211yesmaximal, characteristic, complemented
33#35191C211yesmaximal, characteristic, complemented
34#34803C211yesmaximal, characteristic, complemented
35#34700C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic, complemented
37C2×#556C2211yescharacteristic
38C2×#532C2211yescharacteristic
39C2×#532C2211yescharacteristic, complemented
40C2×#529C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42#2862C2211yescharacteristic, complemented
43#2861C2212yescomplemented
44#2860C2212yes—
45#2858C2212yes—
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic, complemented
48#2848C2212yes—
49#2847C2212yes—
50#2847C2212yes—
51#2830C2214yescomplemented
52#2829C2214yes—
53#2829C2214yescomplemented
54#2828C2214yes—
55#2826C2214yescomplemented
56#2824C2214yes—
57#2819C2214yes—
58#2812C2214yes—
59#2803C2214yes—
60#2803C2214yescomplemented
61#2800C2214yescomplemented
62#2798C2214yescomplemented
63#2797C2214yes—
64#2796C2214yescomplemented
65#2796C2214yescomplemented
66#2796C2214yescomplemented
67#2784C2214yes—
68#2779C2214yes—
69#2778C2214yescomplemented
70#2770C2214yescomplemented
71#2769C2214yescomplemented
72#2761C2214yescomplemented
73#2759C2214yescomplemented
74#2757C2214yescomplemented
75#2756C2214yes—
76#2754C2214yescomplemented
77#2753C2214yes—
78#2753C2214yescomplemented
79#2751C2214yescomplemented
80#2751C2214yescomplemented
81#2751C2214yescomplemented
82#2750C2214yescomplemented
83#2749C2214yescomplemented
84#2749C2214yescomplemented
85#2746C2214yes—
86#2745C2214yescomplemented
87#2744C2214yes—
88#2743C2214yescomplemented
89#2743C2214yescomplemented
90#2737C2214yescomplemented
91#2731C2214yescomplemented
92#2730C2214yescomplemented
93#2723C2214yescomplemented
94#2716C2214yescomplemented
95#2716C2214yescomplemented
96#2716C2214yescomplemented
97#2715C2214yescomplemented
98#2714C2214yescomplemented
99#2705C2214yes—
100#2700C2214yescomplemented
101#2697C2214yes—
102#2685C2214yes—
103#2685C2214yes—
104#2684C2214yes—
105#2684C2214yes—
106#2674C2214yescomplemented
107#2670C2214yes—
108#2661C2214yescomplemented
109#2654C2214yescomplemented
110#2652C2214yescomplemented
111#2648C2214yes—
112#2648C2214yescomplemented
113#2644C2212yescomplemented
114#2643C2214yescomplemented
115#2642C2212yescomplemented
116#2641C2212yes—
117#2640C2212yes—
118#2631C2214yes—
119#2630C2214yescomplemented
120#2628C2212yescomplemented
121#2628C2212yescomplemented
122#2624C2212yescomplemented
123#2620C2212yescomplemented
124#2603C2214yescomplemented
125#2595C2214yescomplemented
126#2595C2214yescomplemented
127#2592C2212yes—
128#2592C2212yescomplemented
129#2581C2212yescomplemented
130#2578C2214yes—
131#2572C2214yescomplemented
132#2571C2212yescomplemented
133#2568C2212yescomplemented
134#2563C2211yescharacteristic
135#2563C2211yescharacteristic
136#2560C2214yescomplemented
137#2557C2214yescomplemented
138#2552C2211yescharacteristic, complemented
139#2550C2212yescomplemented
140#2548C2212yes—
141#2548C2212yes—
142#2548C2211yescharacteristic, complemented
143#2548C2211yescharacteristic, complemented
144#2547C2211yescharacteristic
145#2547C2212yescomplemented
146#2546C2211yescharacteristic, complemented
147#2545C2212yes—
148#2544C2212yes—
149#2541C2211yescharacteristic
150#2541C2211yescharacteristic
151#2540C2212yescomplemented
152#2538C2211yescharacteristic
153#2536C2212yescomplemented
154#2535C2212yes—
155#2535C2212yes—
156#2535C2212yes—
157#2533C2212yescomplemented
158#2532C2214yescomplemented
159#2527C2212yes—
160#2523C2212yescomplemented
161#2521C2214yes—
162#2516C2214yescomplemented
163#2516C2214yescomplemented
164#2514C2212yescomplemented
165#2514C2211yescharacteristic, complemented
166#2510C2214yescomplemented
167#2510C2214yescomplemented
168#2509C2211yescharacteristic, complemented
169#2508C2212yescomplemented
170#2504C2212yes—
171#2500C2212yescomplemented
172#2499C2211yescharacteristic, complemented
173#2497C2212yes—
174#2496C2211yescharacteristic
175#2496C2212yescomplemented
176#2495C2212yes—
177#2495C2214yescomplemented
178#2495C2212yescomplemented
179#2495C2212yescomplemented
180#2494C2212yescomplemented
181#2492C2211yescharacteristic
182#2491C2212yes—
183#2491C2212yes—
184#2491C2212yes—
185#2491C2212yescomplemented
186#2490C2212yes—
187#2489C2212yes—
188#2488C2214yescomplemented
189#2485C2212yes—
190#2485C2211yescharacteristic
191#2485C2212yescomplemented
192#2480C2212yes—
193#2480C2214yes—
194#2468C2212yes—
195#2467C2214yescomplemented
196#2466C2214yes—
197#2466C2212yes—
198#2459C2214yescomplemented
199#2457C2212yes—
200#2454C2211yescharacteristic
201#2454C2212yescomplemented
202#2452C2212yescomplemented
203#2452C2212yescomplemented
204#2448C2212yes—
205#2448C2212yes—
206#2448C2212yescomplemented
207#2447C2212yes—
208#2447C2211yescharacteristic
209#2447C2212yescomplemented
210#2447C2212yescomplemented
211#2445C2212yes—
212#2442C2211yescharacteristic
213#2439C2212yescomplemented
214#2439C2212yescomplemented
215#2439C2211yescharacteristic, complemented
216#2435C2212yes—
217#2435C2211yescharacteristic
218#2433C2212yes—
219#2432C2214yes—
220#2432C2212yescomplemented
221#2431C2212yes—
222#2431C2212yes—
223#2429C2212yes—
224#2427C2212yes—
225#2427C2211yescharacteristic
226#2427C2212yescomplemented
227#2427C2212yescomplemented
228#2427C2212yescomplemented
229#2426C2212yes—
230#2426C2212yes—
231#2422C2212yescomplemented
232#2421C2212yescomplemented
233#2421C2212yescomplemented
234#2421C2212yescomplemented
235#2420C2212yes—
236#2420C2211yescharacteristic
237#2420C2212yescomplemented
238#2420C2212yescomplemented
239#2418C2212yes—
240#2417C2211yescharacteristic
241#2415C2212yes—
242#2415C2211yescharacteristic
243#2414C2212yescomplemented
244#2414C2212yescomplemented
245#2414C2212yescomplemented
246#2408C2211yescharacteristic
247#2407C2212yes—
248#2407C2212yes—
249#2404C2214yes—
250#2401C2212yescomplemented
251#2398C2212yes—
252#2395C2212yes—
253#2392C2212yes—
254#2375C2214yes—
255#2369C2211yescharacteristic, complemented
256#2367C2212yes—
257#2367C2212yescomplemented
258#2367C2212yescomplemented
259#2365C2211yescharacteristic, complemented
260#2363C2212yescomplemented
261#2363C2212yescomplemented
262#2360C2212yes—
263#2357C2212yescomplemented
264#2355C2211yescharacteristic, complemented
265#2354C2211yescharacteristic
266#2354C2212yescomplemented
267#2349C2212yescomplemented
268#2347C2212yescomplemented
269#2341C2212yescomplemented
270#2339C2212yes—
271#2339C2212yescomplemented
272#2337C2214yes—
273#2328C2212yes—
274#2328C2212yes—
275#2327C2212yescomplemented
276#2324C2212yescomplemented
277#2324C2212yescomplemented
278#2323C2212yescomplemented
279#2320C2212yescomplemented
280#2314C2212yescomplemented
281C4×C4⋊Q8C2211yescharacteristic, complemented
282C4×#127C2211yescharacteristic, complemented
283C4×#125C2212yescomplemented
284C4×#126C2212yes—
285C4×#124C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×C22⋊Q8C2211yescharacteristic, complemented
289C4×#121C2211yescharacteristic
290C4×#120C2212yes—
291#2295C2211yescharacteristic, complemented
292#2295C2212yescomplemented
293#2293C2211yescharacteristic
294#2283C2211yescharacteristic
295#2280C2212yes—
296#2280C2212yes—
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C22×#41C2312yes—
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303Q82—44no—
304#556—44no—
305#532—44no—
306#532—44no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2314yes—
314C2×#127C2311yescharacteristic
315C2×#127C2312yes—
316C2×#127C2312yes—
317#529—44no—
318C2×#126C2312yes—
319C2×#126C2312yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#125C2312yes—
323C2×#125C2311yescharacteristic
324C2×#124C2312yes—
325C2×#124C2312yes—
326C2×#124C2314yes—
327C2×#124C2311yescharacteristic
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2311yescharacteristic
333C2×#124C2314yes—
334C2×#124C2314yes—
335C2×#123C2312yes—
336C2×#123C2314yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2314yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2311yescharacteristic
354C2×#121C2311yescharacteristic
355C2×#121C2312yes—
356C2×#120C2314yes—
357C2×#120C2312yes—
358C2×#120C2314yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×D4—44no—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2311yescharacteristic
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C22⋊C4C2312yes—
393C22×C42C2311yescharacteristic
394C22×C42C2311yescharacteristic
395#401C2314yes—
396#401C2312yes—
397#400C2314yes—
398#400C2314yes—
399#400C2312yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2312yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2312yes—
410#400C2312yes—
411#400C2314yes—
412#400C2312yes—
413#400C2312yes—
414#399C2314yes—
415#399C2314yes—
416#399C2314yes—
417#399C2312yes—
418#399C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2312yes—
423#398C2312yes—
424#398C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2312yes—
439#397C2314yes—
440#397C2312yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2312yes—
447#397C2312yes—
448#397C2312yes—
449#397C2314yes—
450#397C2312yes—
451#397C2312yes—
452#397C2312yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#396C2312yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2312yes—
462#396C2314yes—
463#396C2314yes—
464#396C2312yes—
465#396C2314yes—
466#396C2314yes—
467#395C2314yes—
468#395C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2312yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2312yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2312yes—
492#394C2312yes—
493#394C2314yes—
494#394C2314yes—
495#394C2312yes—
496#394C2312yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2312yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#393C2314yes—
508#393C2314yes—
509#393C2314yes—
510#393C2312yes—
511#392C2312yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#391C2314yes—
522#391C2312yes—
523#391C2314yes—
524#391C2312yes—
525#391C2314yes—
526#391C2312yes—
527#391C2312yes—
528#391C2311yescharacteristic
529#391C2312yes—
530#391C2312yes—
531#391C2311yescharacteristic
532#391C2312yes—
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2311yescharacteristic
539#391C2311yescharacteristic
540#391C2311yescharacteristic
541#391C2311yescharacteristic
542#391C2312yes—
543#391C2312yes—
544#390C2314yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2314yes—
551#390C2314yes—
552#390C2314yes—
553#390C2314yes—
554#390C2312yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2311yescharacteristic
559#390C2314yes—
560#390C2312yes—
561#390C2314yes—
562#390C2311yescharacteristic
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2314yes—
567#390C2314yes—
568#390C2312yes—
569#390C2312yes—
570#390C2314yes—
571#390C2314yes—
572#390C2311yescharacteristic
573#390C2311yescharacteristic
574#389C2311yescharacteristic
575#389C2312yes—
576#389C2311yescharacteristic
577#389C2311yescharacteristic
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2314yes—
586#389C2312yes—
587#389C2311yescharacteristic
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2314yes—
593#389C2311yescharacteristic
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2312yes—
597#389C2312yes—
598#389C2311yescharacteristic
599#389C2311yescharacteristic
600#389C2311yescharacteristic
601#389C2312yes—
602#388C2312yes—
603#388C2312yes—
604#388C2312yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2312yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2312yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2312yes—
642#388C2312yes—
643#388C2312yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2314yes—
664#387C2314yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#386C2312yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2312yes—
693#386C2312yes—
694#386C2312yes—
695#386C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2312yes—
704#385C2314yes—
705#385C2312yes—
706#385C2314yes—
707#385C2314yes—
708#385C2312yes—
709#385C2312yes—
710#385C2312yes—
711#385C2312yes—
712#384C2311yescharacteristic
713#384C2311yescharacteristic
714#384C2312yes—
715#383C2312yes—
716#383C2314yes—
717#383C2314yes—
718#383C2314yes—
719#383C2312yes—
720#382C2312yes—
721#382C2312yes—
722#382C2314yes—
723#382C2311yescharacteristic
724#382C2312yes—
725#382C2311yescharacteristic
726#382C2314yes—
727#382C2312yes—
728#382C2312yes—
729#382C2311yescharacteristic
730#381C2312yes—
731#381C2314yes—
732#381C2314yes—
733#381C2314yes—
734#381C2312yes—
735#381C2312yes—
736#381C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2311yescharacteristic
751#380C2314yes—
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2314yes—
756#380C2311yescharacteristic
757#380C2311yescharacteristic
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2311yescharacteristic
762#379C2314yes—
763#379C2312yes—
764#379C2312yes—
765#379C2314yes—
766#379C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C22⋊C4C2311yescharacteristic
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810#376C2312yes—
811#376C2312yes—
812#376C2312yes—
813C2×#95C2314yes—
814C43C2312yes—
815C43C2311yescharacteristic
816C25C2412yes—
817C2×#41—44no—
818C2×#41—44no—
819C2×#41—44no—
820C2×#41—44no—
821C2×#41—44no—
822C2×#41—82no—
823C22×Q8C2411yescharacteristic
824C22×Q8C2411yescharacteristic
825C22×Q8C2412yes—
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2414yes—
829C22×D4—42no—
830C22×D4—42no—
831C22×D4—42no—
832C22×D4C2412yes—
833C22×D4C2411yescharacteristic
834C22×D4C2411yescharacteristic
835C22×D4C2412yes—
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2414yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C23×C4—44no—
848C23×C4—44no—
849C23×C4—44no—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2412yes—
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2414yes—
864C4⋊Q8—24no—
865C4⋊Q8—24no—
866C4⋊Q8—42no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870C4⋊Q8—48no—
871#127—24no—
872#127—44no—
873#127—44no—
874#126—44no—
875#126—44no—
876#126—48no—
877#126—84no—
878#125—44no—
879#125—42no—
880#124—44no—
881#124—42no—
882#124—44no—
883#124—44no—
884#124—42no—
885#124—44no—
886#124—44no—
887#124—44no—
888#124—48no—
889#124—84no—
890#124—84no—
891#123—44no—
892#123—84no—
893C22⋊Q8—44no—
894C22⋊Q8—42no—
895C22⋊Q8—44no—
896C22⋊Q8—42no—
897C22⋊Q8—42no—
898C22⋊Q8—42no—
899C22⋊Q8—44no—
900C22⋊Q8—84no—
901C22⋊Q8—82no—
902#121—44no—
903#121—44no—
904#121—44no—
905#121—44no—
906#121—42no—
907#121—42no—
908#121—44no—
909#121—44no—
910#121—44no—
911#121—44no—
912#120—48no—
913#120—44no—
914#120—84no—
915C4×Q8—24no—
916C4×Q8—24no—
917C4×Q8—44no—
918C4×Q8—44no—
919C4×Q8—44no—
920C4×Q8—44no—
921C4×Q8—44no—
922C4×D4—24no—
923C4×D4—24no—
924C4×D4—44no—
925C4×D4—42no—
926C4×D4—42no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—44no—
932C4×D4—44no—
933C4×D4—44no—
934C4×D4—44no—
935C4×D4—42no—
936C4×D4—42no—
937C4×D4—44no—
938C4×D4—42no—
939C4×D4—82no—
940#117—44no—
941#117—44no—
942#117—44no—
943#117—42no—
944#117—42no—
945#117—44no—
946C2×C4⋊C4—42no—
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C22⋊C4—44no—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2411yescharacteristic
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2411yescharacteristic
1029C2×C22⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
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×C42—24no—
1075C2×C42—24no—
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2412yes—
1079C2×C42C2412yes—
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2411yescharacteristic
1091C2×C42C2412yes—
1092C2×C42C2414yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2414yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2414yes—
1099C2×C42C2414yes—
1100C2×C42C2414yes—
1101C2×C42C2414yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2411yescharacteristic
1105#95C2411yescharacteristic
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2411yescharacteristic
1125#95C2411yescharacteristic
1126#95C2411yescharacteristic
1127#95C2412yes—
1128#95C2411yescharacteristic
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2411yescharacteristic
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2414yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177C24—24no—
1178C24—42no—
1179C24—42no—
1180C24—42no—
1181C24—42no—
1182C24—42no—
1183C24—42no—
1184C24C2512yes—
1185C24C2512yes—
1186C24C2514yes—
1187C24C2511yescharacteristic
1188C24C2511yescharacteristic
1189#41—816no—
1190#41—816no—
1191C2×Q8—22no—
1192C2×Q8—22no—
1193C2×Q8—24no—
1194C2×Q8—24no—
1195C2×Q8—24no—
1196C2×Q8—22no—
1197C2×Q8—22no—
1198C2×Q8—22no—
1199C2×Q8—24no—
1200C2×Q8—22no—
1201C2×Q8—42no—
1202C2×Q8—42no—
1203C2×Q8—42no—
1204C2×Q8—42no—
1205C2×Q8—42no—
1206C2×Q8—44no—
1207C2×Q8—44no—
1208C2×Q8—44no—
1209C2×D4—22no—
1210C2×D4—28no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—24no—
1214C2×D4—24no—
1215C2×D4—24no—
1216C2×D4—24no—
1217C2×D4—24no—
1218C2×D4—24no—
1219C2×D4—22no—
1220C2×D4—22no—
1221C2×D4—24no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—42no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—42no—
1228C2×D4—42no—
1229C2×D4—42no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—42no—
1234C2×D4—42no—
1235C2×D4—44no—
1236C2×D4—44no—
1237C2×D4—44no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—44no—
1248C2×D4—44no—
1249C2×D4—44no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—416no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—24no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—24no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—41no—
1277C22×C4—42no—
1278C22×C4—42no—
1279C22×C4—42no—
1280C22×C4—44no—
1281C22×C4—44no—
1282C22×C4—41no—
1283C22×C4—41no—
1284C22×C4—44no—
1285C22×C4—42no—
1286C22×C4—42no—
1287C22×C4—42no—
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—44no—
1297C22×C4—816no—
1298C22×C4C2511yescharacteristic
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2511yescharacteristic
1305C22×C4C2512yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2511yescharacteristic
1308C22×C4C2512yes—
1309C22×C4C2512yes—
1310C22×C4C2514yes—
1311C22×C4C2514yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2514yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C4⋊C4—22no—
1329C4⋊C4—22no—
1330C4⋊C4—22no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—22no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—22no—
1339C4⋊C4—24no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—42no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—41no—
1354C4⋊C4—42no—
1355C4⋊C4—41no—
1356C4⋊C4—41no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—44no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C22⋊C4—22no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—42no—
1392C22⋊C4—42no—
1393C22⋊C4—42no—
1394C22⋊C4—42no—
1395C22⋊C4—44no—
1396C22⋊C4—42no—
1397C22⋊C4—42no—
1398C22⋊C4—42no—
1399C22⋊C4—42no—
1400C22⋊C4—44no—
1401C22⋊C4—44no—
1402C22⋊C4—42no—
1403C22⋊C4—42no—
1404C22⋊C4—44no—
1405C22⋊C4—41no—
1406C22⋊C4—41no—
1407C22⋊C4—41no—
1408C22⋊C4—41no—
1409C22⋊C4—41no—
1410C22⋊C4—44no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—42no—
1415C22⋊C4—42no—
1416C22⋊C4—44no—
1417C22⋊C4—42no—
1418C22⋊C4—44no—
1419C22⋊C4—42no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—44no—
1440C22⋊C4—42no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—44no—
1453C22⋊C4—42no—
1454C42—22no—
1455C42—22no—
1456C42—22no—
1457C42—22no—
1458C42—22no—
1459C42—22no—
1460C42—24no—
1461C42—24no—
1462C42—22no—
1463C42—24no—
1464C42—22no—
1465C42—22no—
1466C42—22no—
1467C42—24no—
1468C42—24no—
1469C42—24no—
1470C42—44no—
1471C42—42no—
1472C42—42no—
1473C42—44no—
1474C42—41no—
1475C42—41no—
1476C42—44no—
1477C42—44no—
1478C42—44no—
1479C42—44no—
1480C42—42no—
1481C42—42no—
1482C42H(5,𝔽2)14yes—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—22no—
1490C23—22no—
1491C23—24no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—24no—
1496C23—22no—
1497C23—24no—
1498C23—22no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—22no—
1503C23—22no—
1504C23—24no—
1505C23—24no—
1506C23—22no—
1507C23—21no—
1508C23—24no—
1509C23—21no—
1510C23—21no—
1511C23—22no—
1512C23—22no—
1513C23—21no—
1514C23—22no—
1515C23—22no—
1516C23—24no—
1517C23—48no—
1518C23—84no—
1519C23—84no—
1520C23—84no—
1521C23—84no—
1522C23—84no—
1523C23—84no—
1524C23#58512yes—
1525C23C2611yescharacteristic
1526Q8—44no—
1527Q8—48no—
1528Q8—44no—
1529Q8—84no—
1530Q8—84no—
1531Q8—164no—
1532D4—48no—
1533D4—44no—
1534D4—48no—
1535D4—44no—
1536D4—44no—
1537D4—48no—
1538D4—48no—
1539D4—88no—
1540D4—84no—
1541D4—84no—
1542D4—88no—
1543D4—164no—
1544D4—164no—
1545D4—164no—
1546D4—164no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—24no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—24no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—24no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—24no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—24no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—24no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—21no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—21no—
1630C2×C4—44no—
1631C2×C4—44no—
1632C2×C4—44no—
1633C2×C4—44no—
1634C2×C4—48no—
1635C2×C4—48no—
1636C2×C4—44no—
1637C2×C4—82no—
1638C2×C4—84no—
1639C2×C4—84no—
1640C2×C4—84no—
1641C2×C4—88no—
1642C2×C4—88no—
1643C2×C4—164no—
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—
1650C2×C4#58512yes—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—41no—
1658C22—41no—
1659C22—44no—
1660C22—42no—
1661C22—42no—
1662C22—42no—
1663C22—42no—
1664C22—41no—
1665C22—44no—
1666C22—41no—
1667C22—42no—
1668C22—42no—
1669C22—44no—
1670C22—41no—
1671C22—42no—
1672C22—44no—
1673C22—42no—
1674C22—44no—
1675C22—41no—
1676C22—42no—
1677C22—42no—
1678C22—42no—
1679C22—44no—
1680C22—41no—
1681C22—42no—
1682C22—44no—
1683C22—42no—
1684C22—41no—
1685C22—42no—
1686C22—816no—
1687C22C22×H(5,𝔽2)11yescharacteristic
1688C22C2×#58511yescharacteristic
1689C22C2×#58511yescharacteristic
1690C22C2×#58511yescharacteristic
1691C22C2×#58511yescharacteristic
1692C22C2×#58511yescharacteristic
1693C22H(7,𝔽2)11yescharacteristic
1694C4—22no—
1695C4—41no—
1696C4—41no—
1697C4—44no—
1698C4—42no—
1699C4—41no—
1700C4—42no—
1701C4—42no—
1702C4—41no—
1703C4—42no—
1704C4—41no—
1705C4—42no—
1706C4—42no—
1707C4—42no—
1708C4—41no—
1709C4—42no—
1710C4—41no—
1711C4—41no—
1712C4—44no—
1713C4—42no—
1714C4—42no—
1715C4—42no—
1716C4—42no—
1717C4—42no—
1718C4—41no—
1719C4—44no—
1720C4—41no—
1721C4—42no—
1722C4#354014yes—
1723C4#356214yes—
1724C2—42no—
1725C2—81no—
1726C2—84no—
1727C2—82no—
1728C2—82no—
1729C2C2×#354011yescharacteristic
1730C2C2×#356211yescharacteristic
1731C2#6282711yescharacteristic
1732C2#6292411yescharacteristic
1733C2#6293711yescharacteristic
1734C2#6296611yescharacteristic
1735C2#6302911yescharacteristic
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. #59640C2semidirect
2. #59084C2semidirect
3. #59049C2semidirect
4. #56409C2semidirect
5. #56055C2semidirect
6. #55560C2semidirect
7. #53116C2semidirect
8. #53061C2semidirect
9. #49173C2semidirect
10. #46061C2semidirect
11. #45508C2semidirect
12. #45209C2semidirect
13. #45204C2semidirect
14. #42858C2semidirect
15. #42757C2semidirect
16. #42749C2semidirect
17. #42664C2semidirect
18. #39934C2semidirect
19. #39766C2semidirect
20. #39515C2semidirect
21. #39224C2semidirect
22. #39172C2semidirect
23. #39125C2semidirect
24. #38943C2semidirect
25. #37858C2semidirect
26. #37625C2semidirect
27. #37357C2semidirect
28. #37282C2semidirect
29. #36459C2semidirect
30. #36161C2semidirect
31. #36149C2semidirect
32. #35237C2semidirect
33. #35191C2semidirect
34. #34803C2semidirect
35. #34700C2semidirect
36. C2×Q82C22semidirect
39. C2×#532C22semidirect
42. #2862C22semidirect
43. #2861C22semidirect
47. #2857C22semidirect
51. #2830C22semidirect
53. #2829C22semidirect
55. #2826C22semidirect
60. #2803C22semidirect
61. #2800C22semidirect
62. #2798C22semidirect
64. #2796C22semidirect
65. #2796C22semidirect
66. #2796C22semidirect
69. #2778C22semidirect
70. #2770C22semidirect
71. #2769C22semidirect
72. #2761C22semidirect
73. #2759C22semidirect
74. #2757C22semidirect
76. #2754C22semidirect
78. #2753C22semidirect
79. #2751C22semidirect
80. #2751C22semidirect
81. #2751C22semidirect
82. #2750C22semidirect
83. #2749C22semidirect
84. #2749C22semidirect
86. #2745C22semidirect
88. #2743C22semidirect
89. #2743C22semidirect
90. #2737C22semidirect
91. #2731C22semidirect
92. #2730C22semidirect
93. #2723C22semidirect
94. #2716C22semidirect
95. #2716C22semidirect
96. #2716C22semidirect
97. #2715C22semidirect
98. #2714C22semidirect
100. #2700C22semidirect
106. #2674C22semidirect
108. #2661C22semidirect
109. #2654C22semidirect
110. #2652C22semidirect
112. #2648C22semidirect
113. #2644C22semidirect
114. #2643C22semidirect
115. #2642C22semidirect
119. #2630C22semidirect
120. #2628C22semidirect
121. #2628C22semidirect
122. #2624C22semidirect
123. #2620C22semidirect
124. #2603C22semidirect
125. #2595C22semidirect
126. #2595C22semidirect
128. #2592C22semidirect
129. #2581C22semidirect
131. #2572C22semidirect
132. #2571C22semidirect
133. #2568C22semidirect
136. #2560C22semidirect
137. #2557C22semidirect
138. #2552C22semidirect
139. #2550C22semidirect
142. #2548C22semidirect
143. #2548C22semidirect
145. #2547C22semidirect
146. #2546C22semidirect
151. #2540C22semidirect
153. #2536C22semidirect
157. #2533C22semidirect
158. #2532C22semidirect
160. #2523C22semidirect
162. #2516C22semidirect
163. #2516C22semidirect
164. #2514C22semidirect
165. #2514C22semidirect
166. #2510C22semidirect
167. #2510C22semidirect
168. #2509C22semidirect
169. #2508C22semidirect
171. #2500C22semidirect
172. #2499C22semidirect
175. #2496C22semidirect
177. #2495C22semidirect
178. #2495C22semidirect
179. #2495C22semidirect
180. #2494C22semidirect
185. #2491C22semidirect
188. #2488C22semidirect
191. #2485C22semidirect
195. #2467C22semidirect
198. #2459C22semidirect
201. #2454C22semidirect
202. #2452C22semidirect
203. #2452C22semidirect
206. #2448C22semidirect
209. #2447C22semidirect
210. #2447C22semidirect
213. #2439C22semidirect
214. #2439C22semidirect
215. #2439C22semidirect
220. #2432C22semidirect
226. #2427C22semidirect
227. #2427C22semidirect
228. #2427C22semidirect
231. #2422C22semidirect
232. #2421C22semidirect
233. #2421C22semidirect
234. #2421C22semidirect
237. #2420C22semidirect
238. #2420C22semidirect
243. #2414C22semidirect
244. #2414C22semidirect
245. #2414C22semidirect
250. #2401C22semidirect
255. #2369C22semidirect
257. #2367C22semidirect
258. #2367C22semidirect
259. #2365C22semidirect
260. #2363C22semidirect
261. #2363C22semidirect
263. #2357C22semidirect
264. #2355C22semidirect
266. #2354C22semidirect
267. #2349C22semidirect
268. #2347C22semidirect
269. #2341C22semidirect
271. #2339C22semidirect
275. #2327C22semidirect
276. #2324C22semidirect
277. #2324C22semidirect
278. #2323C22semidirect
279. #2320C22semidirect
280. #2314C22semidirect
281. C4×C4⋊Q8C22semidirect
282. C4×#127C22semidirect
283. C4×#125C22semidirect
288. C4×C22⋊Q8C22semidirect
291. #2295C22semidirect
292. #2295C22semidirect
298. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#596402
#590842
#590492
#564092
#560552
#555602
#531162
#530612
#491732
#460612
#455082
#452092
#452042
#428582
#427572
#427492
#426642
#399342
#397662
#395152
#392242
#391722
#391252
#389432
#378582
#376252
#373572
#372822
#364592
#361612
#361492
#352372
#351912
#348032
#347002