Finite Group Databasebeta

← #7657984

Subgroups — #7657984

Order 512.

5116 conjugacy classes of subgroups.

The subgroup lattice has 1715 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42628C212yesmaximal, complemented
2#42621C212yesmaximal, complemented
3#42574C212yesmaximal, complemented
4#42568C212yesmaximal, complemented
5#40870C214yesmaximal, complemented
6#40865C214yesmaximal, complemented
7#40761C214yesmaximal, complemented
8#40756C214yesmaximal, complemented
9#39478C211yesmaximal, characteristic, complemented
10#39350C211yesmaximal, characteristic, complemented
11#39200C211yesmaximal, characteristic, complemented
12#39193C211yesmaximal, characteristic, complemented
13#38124C212yesmaximal, complemented
14#38111C212yesmaximal, complemented
15#37853C212yesmaximal, complemented
16#37665C212yesmaximal, complemented
17#37631C211yesmaximal, characteristic, complemented
18#37627C211yesmaximal, characteristic, complemented
19#37503C212yesmaximal, complemented
20#37494C212yesmaximal, complemented
21#36303C211yesmaximal, characteristic, complemented
22#36261C211yesmaximal, characteristic, complemented
23#36153C211yesmaximal, characteristic
24D4×C22⋊Q8C211yesmaximal, characteristic, complemented
25#35976C212yesmaximal, complemented
26#35888C212yesmaximal, complemented
27#35847C212yesmaximal, complemented
28#35806C212yesmaximal, complemented
29#35291C211yesmaximal, characteristic, complemented
30#35260C212yesmaximal, complemented
31#34619C211yesmaximal, characteristic, complemented
32C2×#2625C212yesmaximal, complemented
33#34334C211yesmaximal, characteristic, complemented
34#34308C211yesmaximal, characteristic, complemented
35D4×#117C211yesmaximal, characteristic, complemented
36C2×#554C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×#547C2211yescharacteristic
39C2×#546C2212yes—
40C2×#542C2212yes—
41C22×C22⋊Q8C2212yes—
42C2×#520C2212yes—
43C22×C4×D4C2211yescharacteristic
44C22×#117C2212yes—
45#2862C2211yescharacteristic, complemented
46#2859C2211yescharacteristic, complemented
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2212yescomplemented
50#2850C2212yescomplemented
51#2848C2212yes—
52#2847C2212yes—
53#2839C2214yescomplemented
54#2838C2214yescomplemented
55#2838C2214yescomplemented
56#2837C2214yescomplemented
57#2832C2214yescomplemented
58#2831C2214yescomplemented
59#2800C2214yescomplemented
60#2799C2214yescomplemented
61#2798C2214yescomplemented
62#2779C2214yescomplemented
63#2773C2214yescomplemented
64#2772C2214yescomplemented
65#2767C2214yescomplemented
66#2765C2214yescomplemented
67#2759C2214yescomplemented
68#2757C2214yescomplemented
69#2757C2214yescomplemented
70#2755C2214yescomplemented
71#2754C2214yescomplemented
72#2747C2214yes—
73#2747C2214yescomplemented
74#2745C2214yes—
75#2742C2214yescomplemented
76#2738C2214yes—
77#2717C2214yes—
78#2702C2214yescomplemented
79#2700C2214yes—
80#2698C2214yescomplemented
81#2692C2214yescomplemented
82#2687C2214yes—
83#2666C2214yescomplemented
84#2665C2214yescomplemented
85#2654C2212yescomplemented
86#2654C2214yescomplemented
87#2653C2212yes—
88#2653C2214yescomplemented
89#2651C2214yescomplemented
90#2650C2214yescomplemented
91#2650C2212yescomplemented
92#2649C2212yes—
93#2647C2211yescharacteristic, complemented
94#2645C2212yescomplemented
95#2645C2211yescharacteristic, complemented
96#2645C2212yescomplemented
97#2644C2211yescharacteristic, complemented
98#2643C2214yescomplemented
99#2640C2212yes—
100#2640C2211yescharacteristic, complemented
101#2639C2214yes—
102#2629C2212yescomplemented
103#2628C2211yescharacteristic
104#2628C2212yescomplemented
105#2627C2214yescomplemented
106#2625C2212yes—
107#2625C2214yes—
108#2625C2211yescharacteristic
109#2625C2214yes—
110#2625C2212yes—
111#2625C2212yes—
112#2625C2212yescomplemented
113#2625C2212yescomplemented
114#2625C2214yescomplemented
115#2625C2212yescomplemented
116#2625C2214yescomplemented
117#2625C2212yescomplemented
118#2624C2211yescharacteristic
119#2624C2212yes—
120#2623C2214yes—
121#2620C2211yescharacteristic
122#2620C2212yescomplemented
123#2592C2212yes—
124#2584C2212yescomplemented
125#2583C2214yescomplemented
126#2582C2212yescomplemented
127#2579C2214yescomplemented
128#2568C2211yescharacteristic, complemented
129#2565C2212yescomplemented
130#2561C2214yes—
131#2552C2211yescharacteristic, complemented
132#2551C2211yescharacteristic, complemented
133#2550C2212yescomplemented
134#2549C2214yescomplemented
135#2547C2212yes—
136#2547C2211yescharacteristic
137#2547C2211yescharacteristic, complemented
138#2542C2211yescharacteristic
139#2538C2211yescharacteristic
140#2537C2211yescharacteristic
141#2514C2212yescomplemented
142#2511C2212yescomplemented
143#2511C2212yescomplemented
144#2511C2212yescomplemented
145#2510C2214yescomplemented
146#2509C2212yescomplemented
147#2508C2212yescomplemented
148#2508C2212yescomplemented
149#2504C2214yes—
150#2504C2212yes—
151#2503C2212yescomplemented
152#2498C2214yes—
153#2497C2212yescomplemented
154#2496C2212yescomplemented
155#2495C2212yes—
156#2495C2212yescomplemented
157#2495C2212yescomplemented
158#2494C2212yes—
159#2494C2212yescomplemented
160#2493C2214yescomplemented
161#2493C2214yescomplemented
162#2493C2214yescomplemented
163#2492C2212yescomplemented
164#2492C2212yescomplemented
165#2492C2212yescomplemented
166#2492C2212yescomplemented
167#2490C2212yes—
168#2490C2212yes—
169#2489C2212yes—
170#2489C2212yes—
171#2488C2214yes—
172#2488C2214yes—
173#2488C2214yescomplemented
174#2488C2214yescomplemented
175#2486C2212yes—
176#2486C2212yes—
177#2482C2214yes—
178#2481C2214yescomplemented
179#2481C2214yescomplemented
180#2479C2214yescomplemented
181#2477C2214yescomplemented
182#2474C2214yes—
183#2472C2214yes—
184#2472C2214yes—
185#2470C2214yes—
186#2453C2212yescomplemented
187#2452C2212yes—
188#2451C2212yescomplemented
189#2451C2212yescomplemented
190#2450C2214yescomplemented
191#2449C2214yes—
192#2449C2214yescomplemented
193#2448C2212yes—
194#2448C2212yes—
195#2447C2212yescomplemented
196#2444C2214yes—
197#2444C2214yes—
198#2442C2212yescomplemented
199#2440C2212yes—
200#2440C2212yescomplemented
201#2440C2212yescomplemented
202#2440C2212yescomplemented
203#2438C2214yescomplemented
204#2438C2214yescomplemented
205#2437C2214yes—
206#2436C2212yescomplemented
207#2427C2212yes—
208#2427C2212yescomplemented
209#2426C2212yescomplemented
210#2425C2214yes—
211#2423C2212yescomplemented
212#2423C2212yescomplemented
213#2421C2212yes—
214#2421C2212yes—
215#2418C2214yes—
216#2418C2214yes—
217#2417C2212yes—
218#2417C2212yes—
219#2417C2214yescomplemented
220#2416C2212yes—
221#2412C2214yes—
222#2409C2212yes—
223#2401C2212yescomplemented
224#2398C2212yes—
225#2396C2212yescomplemented
226#2395C2212yes—
227C2×#400C2214yescomplemented
228C2×#398C2214yescomplemented
229C2×#397C2214yes—
230C2×#397C2214yes—
231#2369C2212yescomplemented
232#2368C2214yescomplemented
233#2365C2211yescharacteristic, complemented
234#2365C2211yescharacteristic, complemented
235#2361C2212yescomplemented
236#2360C2212yescomplemented
237#2360C2212yescomplemented
238#2359C2214yescomplemented
239#2355C2211yescharacteristic, complemented
240#2354C2211yescharacteristic
241#2354C2211yescharacteristic
242#2352C2212yes—
243#2352C2212yes—
244#2349C2212yes—
245#2349C2212yes—
246D4×C4⋊C4C2211yescharacteristic
247D4×C4⋊C4C2211yescharacteristic
248D4×C4⋊C4C2211yescharacteristic
249D4×C4⋊C4C2212yes—
250D4×C4⋊C4C2211yescharacteristic
251D4×C4⋊C4C2211yescharacteristic, complemented
252#2344C2211yescharacteristic
253#2344C2211yescharacteristic
254#2344C2212yescomplemented
255#2342C2212yes—
256#2342C2212yes—
257Q8×C22⋊C4C2212yescomplemented
258#2339C2212yes—
259#2339C2212yes—
260#2339C2212yes—
261#2339C2212yes—
262D4×C22⋊C4C2211yescharacteristic
263D4×C22⋊C4C2212yes—
264D4×C22⋊C4C2211yescharacteristic
265#2331C2212yescomplemented
266#2329C2214yescomplemented
267#2324C2212yescomplemented
268#2323C2212yes—
269#2323C2212yescomplemented
270#2323C2212yescomplemented
271#2322C2214yescomplemented
272#2320C2212yescomplemented
273#2314C2212yes—
274C4×C4⋊Q8C2211yescharacteristic, complemented
275C4×C4⋊Q8C2211yescharacteristic, complemented
276C4×C4⋊Q8C2211yescharacteristic, complemented
277C4×#124C2211yescharacteristic, complemented
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2212yescomplemented
280C4×#121C2211yescharacteristic
281C4×#121C2212yescomplemented
282#2295C2211yescharacteristic, complemented
283C2×#391C2212yescomplemented
284C2×#391C2212yescomplemented
285#2293C2211yescharacteristic
286#2293C2211yescharacteristic
287#2293C2211yescharacteristic, complemented
288C2×#389C2212yescomplemented
289C2×#389C2212yescomplemented
290#2290C2212yes—
291#2290C2212yes—
292#2285C2211yescharacteristic
293#2280C2212yes—
294C2×#380C2212yes—
295#2275C2212yes—
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C22×#41C2312yes—
300C23×Q8C2312yes—
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303#554—48no—
304D4×Q8—28no—
305#547—28no—
306#546—48no—
307#542—48no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×#126C2314yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#124C2312yes—
318C2×#124C2312yes—
319C2×#124C2311yescharacteristic
320C2×#124C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×C22⋊Q8—48no—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×#121C2311yescharacteristic
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2312yes—
344C2×#121C2314yes—
345C2×#120C2314yes—
346#520—48no—
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×D4—28no—
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×#117—48no—
373C2×#117C2312yes—
374C2×#117C2311yescharacteristic
375C2×#117C2311yescharacteristic
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2312yes—
380C2×#117C2314yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C22×C4⋊C4C2311yescharacteristic
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2314yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2314yes—
393C22×C4⋊C4C2312yes—
394C22×C22⋊C4C2312yes—
395C22×C22⋊C4C2314yes—
396C22×C22⋊C4C2312yes—
397C22×C22⋊C4C2312yes—
398C22×C22⋊C4C2314yes—
399C22×C42C2311yescharacteristic
400C22×C42C2312yes—
401C22×C42C2312yes—
402#401C2314yes—
403#401C2314yes—
404#401C2312yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2312yes—
413#400C2314yes—
414#400C2314yes—
415#400C2312yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2312yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2312yes—
429#400C2312yes—
430#400C2312yes—
431#400C2312yes—
432#399C2314yes—
433#399C2314yes—
434#399C2314yes—
435#399C2314yes—
436#399C2312yes—
437#399C2312yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2312yes—
451#398C2312yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2312yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2312yes—
472#397C2312yes—
473#397C2312yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2312yes—
484#397C2312yes—
485#397C2312yes—
486#397C2312yes—
487#396C2314yes—
488#396C2314yes—
489#396C2312yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2312yes—
495#396C2312yes—
496#395C2314yes—
497#395C2314yes—
498#395C2314yes—
499#395C2314yes—
500#395C2314yes—
501#395C2314yes—
502#395C2312yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2312yes—
510#394C2312yes—
511#394C2312yes—
512#394C2312yes—
513#393C2312yes—
514#393C2314yes—
515#393C2314yes—
516#393C2312yes—
517#393C2314yes—
518#393C2314yes—
519#393C2314yes—
520#393C2314yes—
521#393C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2312yes—
528#391C2312yes—
529#391C2314yes—
530#391C2312yes—
531#391C2312yes—
532#391C2312yes—
533#391C2312yes—
534#391C2312yes—
535#391C2312yes—
536#391C2314yes—
537#391C2314yes—
538#391C2314yes—
539#391C2314yes—
540#391C2312yes—
541#391C2311yescharacteristic
542#391C2312yes—
543#391C2314yes—
544#391C2312yes—
545#391C2311yescharacteristic
546#391C2311yescharacteristic
547#391C2312yes—
548#391C2314yes—
549#391C2314yes—
550#391C2311yescharacteristic
551#391C2314yes—
552#391C2314yes—
553#390C2311yescharacteristic
554#390C2314yes—
555#390C2311yescharacteristic
556#390C2312yes—
557#390C2311yescharacteristic
558#390C2311yescharacteristic
559#390C2311yescharacteristic
560#390C2312yes—
561#390C2311yescharacteristic
562#390C2311yescharacteristic
563#390C2311yescharacteristic
564#390C2314yes—
565#389C2312yes—
566#389C2311yescharacteristic
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2311yescharacteristic
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2314yes—
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#389C2312yes—
579#389C2311yescharacteristic
580#389C2312yes—
581#389C2314yes—
582#389C2312yes—
583#389C2314yes—
584#389C2314yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2314yes—
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2311yescharacteristic
600#389C2312yes—
601#389C2311yescharacteristic
602#389C2311yescharacteristic
603#389C2312yes—
604#389C2312yes—
605#389C2314yes—
606#389C2311yescharacteristic
607#389C2311yescharacteristic
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2312yes—
615#388C2312yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2312yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2312yes—
629#388C2312yes—
630#388C2312yes—
631#388C2312yes—
632#388C2312yes—
633#388C2312yes—
634#388C2312yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2312yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2314yes—
653#387C2312yes—
654#387C2312yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2312yes—
674#386C2312yes—
675#386C2312yes—
676#386C2312yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2312yes—
684#386C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2312yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2314yes—
702#385C2314yes—
703#385C2312yes—
704#384C2311yescharacteristic
705#384C2311yescharacteristic
706#384C2311yescharacteristic
707#384C2311yescharacteristic
708#384C2312yes—
709#384C2312yes—
710#384C2311yescharacteristic
711#383C2314yes—
712#383C2314yes—
713#382C2312yes—
714#382C2312yes—
715#382C2314yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#382C2311yescharacteristic
721#382C2314yes—
722#381C2314yes—
723#381C2314yes—
724#381C2314yes—
725#381C2314yes—
726#381C2312yes—
727#381C2312yes—
728#381C2314yes—
729#380C2311yescharacteristic
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2314yes—
734#380C2312yes—
735#380C2314yes—
736#380C2312yes—
737#380C2312yes—
738#380C2311yescharacteristic
739#380C2311yescharacteristic
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2314yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2311yescharacteristic
753#380C2314yes—
754#380C2312yes—
755#380C2312yes—
756#380C2314yes—
757#380C2314yes—
758#379C2312yes—
759#379C2314yes—
760#379C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807#376C2311yescharacteristic
808#376C2312yes—
809#376C2311yescharacteristic
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2314yes—
813C2×#95C2314yes—
814C2×#95C2314yes—
815C2×#95C2314yes—
816C2×#95C2314yes—
817C43C2311yescharacteristic
818C43C2311yescharacteristic
819C25C2412yes—
820C2×#41—28no—
821C2×#41—28no—
822C2×#41—28no—
823C22×Q8—28no—
824C22×Q8—44no—
825C22×Q8—44no—
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2411yescharacteristic
829C22×Q8C2414yes—
830C22×Q8C2412yes—
831C22×Q8C2414yes—
832C22×D4—24no—
833C22×D4—24no—
834C22×D4—24no—
835C22×D4C2411yescharacteristic
836C22×D4C2414yes—
837C22×D4C2412yes—
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2414yes—
841C22×D4C2411yescharacteristic
842C23×C4—28no—
843C23×C4—28no—
844C23×C4—44no—
845C23×C4C2414yes—
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2414yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2414yes—
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C4⋊Q8—28no—
864C4⋊Q8—24no—
865C4⋊Q8—24no—
866C4⋊Q8—42no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869#126—48no—
870#125—44no—
871#125—44no—
872#124—42no—
873#124—44no—
874#124—44no—
875#124—48no—
876#123—216no—
877#123—48no—
878#123—48no—
879C22⋊Q8—28no—
880C22⋊Q8—24no—
881C22⋊Q8—28no—
882C22⋊Q8—28no—
883C22⋊Q8—216no—
884C22⋊Q8—48no—
885C22⋊Q8—48no—
886C22⋊Q8—48no—
887C22⋊Q8—48no—
888C22⋊Q8—48no—
889C22⋊Q8—48no—
890C22⋊Q8—44no—
891C22⋊Q8—44no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894#121—28no—
895#121—24no—
896#121—44no—
897#121—44no—
898#121—48no—
899#120—48no—
900C4×Q8—24no—
901C4×Q8—44no—
902C4×Q8—44no—
903C4×Q8—44no—
904C4×Q8—44no—
905C4×Q8—44no—
906C4×D4—24no—
907C4×D4—28no—
908C4×D4—24no—
909C4×D4—28no—
910C4×D4—28no—
911C4×D4—24no—
912C4×D4—24no—
913C4×D4—24no—
914C4×D4—28no—
915C4×D4—24no—
916C4×D4—28no—
917C4×D4—24no—
918C4×D4—24no—
919C4×D4—44no—
920C4×D4—44no—
921C4×D4—48no—
922C4×D4—48no—
923C4×D4#4118yes—
924#117—24no—
925#117—28no—
926#117—44no—
927#117—44no—
928#117—42no—
929#117—44no—
930#117—44no—
931#117—44no—
932#117—48no—
933#117—44no—
934#117—44no—
935C2×C4⋊C4—28no—
936C2×C4⋊C4—24no—
937C2×C4⋊C4—44no—
938C2×C4⋊C4—44no—
939C2×C4⋊C4—44no—
940C2×C4⋊C4—44no—
941C2×C4⋊C4—44no—
942C2×C4⋊C4—48no—
943C2×C4⋊C4—48no—
944C2×C4⋊C4—48no—
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C22⋊C4—28no—
1015C2×C22⋊C4—44no—
1016C2×C22⋊C4—44no—
1017C2×C22⋊C4—48no—
1018C2×C22⋊C4—48no—
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C42—24no—
1074C2×C42—44no—
1075C2×C42—44no—
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2412yes—
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2412yes—
1090C2×C42C2411yescharacteristic
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2412yes—
1096C2×C42C2414yes—
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2414yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2414yes—
1105C2×C42C2411yescharacteristic
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2411yescharacteristic
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2411yescharacteristic
1144#95C2411yescharacteristic
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184C24—24no—
1185C24—24no—
1186C24—24no—
1187C24—24no—
1188C24—42no—
1189C24—42no—
1190C24—42no—
1191C24C2512yes—
1192C24C2512yes—
1193C24C2511yescharacteristic
1194C24C2512yes—
1195#41—432no—
1196C2×Q8—22no—
1197C2×Q8—24no—
1198C2×Q8—24no—
1199C2×Q8—28no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—22no—
1203C2×Q8—24no—
1204C2×Q8—24no—
1205C2×Q8—22no—
1206C2×Q8—42no—
1207C2×Q8—44no—
1208C2×Q8—42no—
1209C2×Q8—44no—
1210C2×Q8—42no—
1211C2×Q8—44no—
1212C2×Q8—44no—
1213C2×Q8—44no—
1214C2×Q8—816no—
1215C2×D4—24no—
1216C2×D4—28no—
1217C2×D4—28no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—28no—
1221C2×D4—24no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—42no—
1229C2×D4—42no—
1230C2×D4—44no—
1231C2×D4—44no—
1232C2×D4—44no—
1233C2×D4—416no—
1234C2×D4C2×#4114yes—
1235C2×D4H(5,𝔽2)14yes—
1236C2×D42−1+414yes—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—22no—
1241C22×C4—28no—
1242C22×C4—24no—
1243C22×C4—28no—
1244C22×C4—24no—
1245C22×C4—28no—
1246C22×C4—28no—
1247C22×C4—28no—
1248C22×C4—24no—
1249C22×C4—28no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—22no—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—24no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—42no—
1268C22×C4—42no—
1269C22×C4—42no—
1270C22×C4—432no—
1271C22×C4—42no—
1272C22×C4—42no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—44no—
1276C22×C4—44no—
1277C22×C4—44no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—42no—
1281C22×C4—42no—
1282C22×C4—42no—
1283C22×C4—42no—
1284C22×C4—44no—
1285C22×C4—44no—
1286C22×C4—44no—
1287C22×C4—44no—
1288C22×C4—44no—
1289C22×C4—44no—
1290C22×C4C2×#4118yes—
1291C22×C4H(5,𝔽2)14yes—
1292C22×C4C2511yescharacteristic
1293C22×C4C2511yescharacteristic
1294C22×C4C2511yescharacteristic
1295C22×C4C2511yescharacteristic
1296C22×C4C2511yescharacteristic
1297C22×C4C2514yes—
1298C22×C4C2511yescharacteristic
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2514yes—
1307C22×C4C2514yes—
1308C22×C4C2512yes—
1309C22×C4C2512yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2512yes—
1313C22×C4C2514yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2511yescharacteristic
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2511yescharacteristic
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C4⋊C4—22no—
1324C4⋊C4—24no—
1325C4⋊C4—22no—
1326C4⋊C4—24no—
1327C4⋊C4—28no—
1328C4⋊C4—24no—
1329C4⋊C4—22no—
1330C4⋊C4—24no—
1331C4⋊C4—28no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—28no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—42no—
1353C4⋊C4—44no—
1354C4⋊C4—42no—
1355C4⋊C4—44no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—41no—
1378C4⋊C4—41no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—42no—
1391C4⋊C4C2×#4114yes—
1392C22⋊C4—24no—
1393C22⋊C4—28no—
1394C22⋊C4—22no—
1395C22⋊C4—22no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—28no—
1400C22⋊C4—24no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—24no—
1409C22⋊C4—28no—
1410C22⋊C4—24no—
1411C22⋊C4—42no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—42no—
1415C22⋊C4—42no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—41no—
1433C22⋊C4—41no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4C2×#4118yes—
1446C42—22no—
1447C42—22no—
1448C42—22no—
1449C42—24no—
1450C42—22no—
1451C42—22no—
1452C42—24no—
1453C42—24no—
1454C42—22no—
1455C42—24no—
1456C42—24no—
1457C42—22no—
1458C42—22no—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—42no—
1463C42—42no—
1464C42—42no—
1465C42—42no—
1466C42—41no—
1467C42—41no—
1468C42—41no—
1469C42—41no—
1470C42—44no—
1471C42—44no—
1472C42—44no—
1473C42—44no—
1474C42—44no—
1475C42C2×#4114yes—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—22no—
1487C23—22no—
1488C23—22no—
1489C23—22no—
1490C23—22no—
1491C23—22no—
1492C23—22no—
1493C23—22no—
1494C23—22no—
1495C23—22no—
1496C23—22no—
1497C23—22no—
1498C23—22no—
1499C23—22no—
1500C23—48no—
1501C23—48no—
1502C23—48no—
1503C23—48no—
1504C23—84no—
1505C23—84no—
1506C23—84no—
1507C23C22×#4114yes—
1508C23C2×H(5,𝔽2)12yes—
1509C23C2×H(5,𝔽2)14yes—
1510C23C2×2−1+414yes—
1511C23C2611yescharacteristic
1512Q8—48no—
1513Q8—48no—
1514Q8—44no—
1515Q8—88no—
1516Q8—84no—
1517Q8—164no—
1518D4—48no—
1519D4—416no—
1520D4—44no—
1521D4—44no—
1522D4—84no—
1523D4—164no—
1524D4#542116yescomplemented
1525C2×C4—21no—
1526C2×C4—22no—
1527C2×C4—21no—
1528C2×C4—22no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—28no—
1532C2×C4—216no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—24no—
1540C2×C4—24no—
1541C2×C4—21no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—22no—
1556C2×C4—21no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—24no—
1560C2×C4—24no—
1561C2×C4—24no—
1562C2×C4—22no—
1563C2×C4—24no—
1564C2×C4—24no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—24no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—24no—
1584C2×C4—24no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—24no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—24no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—48no—
1612C2×C4—48no—
1613C2×C4—48no—
1614C2×C4—416no—
1615C2×C4—44no—
1616C2×C4—48no—
1617C2×C4—48no—
1618C2×C4—82no—
1619C2×C4—84no—
1620C2×C4—88no—
1621C2×C4—84no—
1622C2×C4—88no—
1623C2×C4—84no—
1624C2×C4—84no—
1625C2×C4—88no—
1626C2×C4—164no—
1627C2×C4C22×#4112yes—
1628C2×C4C22×#4114yes—
1629C2×C4C22×#4112yes—
1630C2×C4C22×#4112yes—
1631C2×C4C2×H(5,𝔽2)12yes—
1632C2×C4C2×H(5,𝔽2)12yes—
1633C2×C4C2×H(5,𝔽2)12yes—
1634C2×C4C2×2−1+412yes—
1635C2×C4#58512yes—
1636C22—24no—
1637C22—24no—
1638C22—24no—
1639C22—24no—
1640C22—24no—
1641C22—24no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—42no—
1650C22—42no—
1651C22—42no—
1652C22—42no—
1653C22—42no—
1654C22—42no—
1655C22—42no—
1656C22—42no—
1657C22—42no—
1658C22—42no—
1659C22—42no—
1660C22—42no—
1661C22—42no—
1662C22—42no—
1663C22—816no—
1664C22C2×#54218yes—
1665C22C23×#4111yescharacteristic
1666C22C22×H(5,𝔽2)11yescharacteristic
1667C22C22×H(5,𝔽2)11yescharacteristic
1668C22C22×2−1+411yescharacteristic
1669C22C2×#58511yescharacteristic
1670C222−1+611yescharacteristic
1671C222−1+611yescharacteristic
1672C4—22no—
1673C4—24no—
1674C4—22no—
1675C4—42no—
1676C4—42no—
1677C4—44no—
1678C4—42no—
1679C4—41no—
1680C4—41no—
1681C4—41no—
1682C4—42no—
1683C4—42no—
1684C4—44no—
1685C4—42no—
1686C4—42no—
1687C4—41no—
1688C4—42no—
1689C4—44no—
1690C4—42no—
1691C4—41no—
1692C4—42no—
1693C4—41no—
1694C4—44no—
1695C4—42no—
1696C4—42no—
1697C4—41no—
1698C4—41no—
1699C4—41no—
1700C4—41no—
1701C4C2×#54214yes—
1702C4#351314yes—
1703C2—28no—
1704C2—42no—
1705C2—82no—
1706C2—82no—
1707C2C22×#54211yescharacteristic
1708C2C2×#351311yescharacteristic
1709C2#6286111yescharacteristic
1710C2#6291411yescharacteristic
1711C2#6292111yescharacteristic
1712C2#6294211yescharacteristic
1713C2#6295011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36153C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42628C2semidirect
2. #42621C2semidirect
3. #42574C2semidirect
4. #42568C2semidirect
5. #40870C2semidirect
6. #40865C2semidirect
7. #40761C2semidirect
8. #40756C2semidirect
9. #39478C2semidirect
10. #39350C2semidirect
11. #39200C2semidirect
12. #39193C2semidirect
13. #38124C2semidirect
14. #38111C2semidirect
15. #37853C2semidirect
16. #37665C2semidirect
17. #37631C2semidirect
18. #37627C2semidirect
19. #37503C2semidirect
20. #37494C2semidirect
21. #36303C2semidirect
22. #36261C2semidirect
24. D4×C22⋊Q8C2semidirect
25. #35976C2semidirect
26. #35888C2semidirect
27. #35847C2semidirect
28. #35806C2semidirect
29. #35291C2semidirect
30. #35260C2semidirect
31. #34619C2semidirect
32. C2×#2625C2semidirect
33. #34334C2semidirect
34. #34308C2semidirect
35. D4×#117C2semidirect
45. #2862C22semidirect
46. #2859C22semidirect
49. #2857C22semidirect
50. #2850C22semidirect
53. #2839C22semidirect
54. #2838C22semidirect
55. #2838C22semidirect
56. #2837C22semidirect
57. #2832C22semidirect
58. #2831C22semidirect
59. #2800C22semidirect
60. #2799C22semidirect
61. #2798C22semidirect
62. #2779C22semidirect
63. #2773C22semidirect
64. #2772C22semidirect
65. #2767C22semidirect
66. #2765C22semidirect
67. #2759C22semidirect
68. #2757C22semidirect
69. #2757C22semidirect
70. #2755C22semidirect
71. #2754C22semidirect
73. #2747C22semidirect
75. #2742C22semidirect
78. #2702C22semidirect
80. #2698C22semidirect
81. #2692C22semidirect
83. #2666C22semidirect
84. #2665C22semidirect
85. #2654C22semidirect
86. #2654C22semidirect
88. #2653C22semidirect
89. #2651C22semidirect
90. #2650C22semidirect
91. #2650C22semidirect
93. #2647C22semidirect
94. #2645C22semidirect
95. #2645C22semidirect
96. #2645C22semidirect
97. #2644C22semidirect
98. #2643C22semidirect
100. #2640C22semidirect
102. #2629C22semidirect
104. #2628C22semidirect
105. #2627C22semidirect
112. #2625C22semidirect
113. #2625C22semidirect
114. #2625C22semidirect
115. #2625C22semidirect
116. #2625C22semidirect
117. #2625C22semidirect
122. #2620C22semidirect
124. #2584C22semidirect
125. #2583C22semidirect
126. #2582C22semidirect
127. #2579C22semidirect
128. #2568C22semidirect
129. #2565C22semidirect
131. #2552C22semidirect
132. #2551C22semidirect
133. #2550C22semidirect
134. #2549C22semidirect
137. #2547C22semidirect
141. #2514C22semidirect
142. #2511C22semidirect
143. #2511C22semidirect
144. #2511C22semidirect
145. #2510C22semidirect
146. #2509C22semidirect
147. #2508C22semidirect
148. #2508C22semidirect
151. #2503C22semidirect
153. #2497C22semidirect
154. #2496C22semidirect
156. #2495C22semidirect
157. #2495C22semidirect
159. #2494C22semidirect
160. #2493C22semidirect
161. #2493C22semidirect
162. #2493C22semidirect
163. #2492C22semidirect
164. #2492C22semidirect
165. #2492C22semidirect
166. #2492C22semidirect
173. #2488C22semidirect
174. #2488C22semidirect
178. #2481C22semidirect
179. #2481C22semidirect
180. #2479C22semidirect
181. #2477C22semidirect
186. #2453C22semidirect
188. #2451C22semidirect
189. #2451C22semidirect
190. #2450C22semidirect
192. #2449C22semidirect
195. #2447C22semidirect
198. #2442C22semidirect
200. #2440C22semidirect
201. #2440C22semidirect
202. #2440C22semidirect
203. #2438C22semidirect
204. #2438C22semidirect
206. #2436C22semidirect
208. #2427C22semidirect
209. #2426C22semidirect
211. #2423C22semidirect
212. #2423C22semidirect
219. #2417C22semidirect
223. #2401C22semidirect
225. #2396C22semidirect
227. C2×#400C22semidirect
228. C2×#398C22semidirect
231. #2369C22semidirect
232. #2368C22semidirect
233. #2365C22semidirect
234. #2365C22semidirect
235. #2361C22semidirect
236. #2360C22semidirect
237. #2360C22semidirect
238. #2359C22semidirect
239. #2355C22semidirect
251. D4×C4⋊C4C22semidirect
254. #2344C22semidirect
257. Q8×C22⋊C4C22semidirect
265. #2331C22semidirect
266. #2329C22semidirect
267. #2324C22semidirect
269. #2323C22semidirect
270. #2323C22semidirect
271. #2322C22semidirect
272. #2320C22semidirect
274. C4×C4⋊Q8C22semidirect
275. C4×C4⋊Q8C22semidirect
276. C4×C4⋊Q8C22semidirect
277. C4×#124C22semidirect
279. C4×C22⋊Q8C22semidirect
281. C4×#121C22semidirect
282. #2295C22semidirect
283. C2×#391C22semidirect
284. C2×#391C22semidirect
287. #2293C22semidirect
288. C2×#389C22semidirect
289. C2×#389C22semidirect
1524. D4#542semidirect

Maximal subgroups

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

subgroupindex
#426282
#426212
#425742
#425682
#408702
#408652
#407612
#407562
#394782
#393502
#392002
#391932
#381242
#381112
#378532
#376652
#376312
#376272
#375032
#374942
#363032
#362612
#361532
D4×C22⋊Q82
#359762
#358882
#358472
#358062
#352912
#352602
#346192
C2×#26252
#343342
#343082
D4×#1172