Finite Group Databasebeta

← #7680484

Subgroups — #7680484

Order 512.

5020 conjugacy classes of subgroups.

The subgroup lattice has 1667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59960C212yesmaximal, complemented
2#59715C212yesmaximal, complemented
3#59563C212yesmaximal, complemented
4#59502C212yesmaximal, complemented
5#59488C212yesmaximal
6#59484C212yesmaximal
7#59460C212yesmaximal, complemented
8#59436C212yesmaximal, complemented
9#44730C214yesmaximal, complemented
10#44714C214yesmaximal, complemented
11#43885C214yesmaximal, complemented
12#43858C214yesmaximal, complemented
13#39734C211yesmaximal, characteristic, complemented
14#39609C211yesmaximal, characteristic, complemented
15#39058C212yesmaximal, complemented
16#39043C212yesmaximal, complemented
17#38967C211yesmaximal, characteristic, complemented
18#38954C211yesmaximal, characteristic, complemented
19#37859C212yesmaximal, complemented
20#37663C212yesmaximal, complemented
21#36477C211yesmaximal, characteristic, complemented
22#36454C211yesmaximal, characteristic, complemented
23#36161C211yesmaximal, characteristic
24D4×C22⋊Q8C211yesmaximal, characteristic
25#35665C212yesmaximal, complemented
26#35647C212yesmaximal, complemented
27#35325C212yesmaximal, complemented
28#35291C211yesmaximal, characteristic, complemented
29#34945C211yesmaximal, characteristic, complemented
30#34929C211yesmaximal, characteristic, complemented
31#34322C211yesmaximal, characteristic, complemented
32#34311C211yesmaximal, characteristic, complemented
33#34203C212yesmaximal, complemented
34D4×#117C211yesmaximal, characteristic
35C4×#541C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#541C2211yescharacteristic
39C2×#533C2212yescomplemented
40C22×C22⋊Q8C2212yes—
41C2×#519C2212yescomplemented
42C22×C4×D4C2211yescharacteristic
43C22×#117C2212yes—
44#2862C2211yescharacteristic, complemented
45#2859C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2855C2212yescomplemented
49#2855C2212yescomplemented
50#2848C2212yes—
51#2848C2212yes—
52#2788C2214yescomplemented
53#2776C2214yescomplemented
54#2774C2214yescomplemented
55#2766C2214yescomplemented
56#2765C2214yescomplemented
57#2763C2214yescomplemented
58#2762C2214yescomplemented
59#2750C2214yes—
60#2747C2214yes—
61#2747C2214yescomplemented
62#2746C2214yes—
63#2745C2214yescomplemented
64#2745C2214yescomplemented
65#2742C2214yes—
66#2742C2214yescomplemented
67#2739C2214yescomplemented
68#2736C2214yes—
69#2735C2214yes—
70#2704C2214yescomplemented
71#2698C2214yes—
72#2698C2214yescomplemented
73#2698C2214yescomplemented
74#2690C2214yescomplemented
75#2689C2214yes—
76#2645C2212yescomplemented
77#2628C2212yes—
78#2628C2212yescomplemented
79#2625C2212yes—
80#2621C2212yes—
81#2621C2212yescomplemented
82#2611C2214yes—
83#2611C2214yescomplemented
84#2609C2214yes—
85#2608C2214yescomplemented
86#2605C2214yescomplemented
87#2599C2214yes—
88#2599C2214yescomplemented
89#2599C2214yescomplemented
90#2599C2214yescomplemented
91#2590C2214yescomplemented
92#2587C2214yescomplemented
93#2587C2214yescomplemented
94#2587C2214yescomplemented
95#2583C2214yescomplemented
96#2581C2214yescomplemented
97#2578C2214yes—
98#2578C2214yes—
99#2576C2214yes—
100#2575C2214yes—
101#2575C2214yescomplemented
102#2575C2214yescomplemented
103#2574C2214yescomplemented
104#2573C2214yescomplemented
105#2573C2214yescomplemented
106#2572C2214yes—
107#2571C2211yescharacteristic, complemented
108#2570C2212yescomplemented
109#2570C2212yescomplemented
110#2568C2211yescharacteristic, complemented
111#2567C2212yescomplemented
112#2566C2212yes—
113#2563C2212yes—
114#2561C2214yes—
115#2556C2214yescomplemented
116#2551C2211yescharacteristic, complemented
117#2550C2212yescomplemented
118#2547C2211yescharacteristic
119#2546C2211yescharacteristic, complemented
120#2542C2211yescharacteristic
121#2538C2211yescharacteristic
122#2538C2211yescharacteristic
123#2530C2214yescomplemented
124#2530C2214yescomplemented
125#2528C2214yescomplemented
126#2527C2214yes—
127#2527C2214yescomplemented
128#2524C2214yescomplemented
129#2517C2214yescomplemented
130#2514C2212yescomplemented
131#2514C2212yescomplemented
132#2514C2212yescomplemented
133#2511C2212yescomplemented
134#2511C2212yescomplemented
135#2509C2212yescomplemented
136#2509C2212yescomplemented
137#2509C2212yescomplemented
138#2508C2212yescomplemented
139#2507C2212yescomplemented
140#2506C2212yescomplemented
141#2499C2212yescomplemented
142#2497C2212yescomplemented
143#2495C2212yes—
144#2495C2212yes—
145#2495C2214yescomplemented
146#2494C2212yes—
147#2494C2212yes—
148#2494C2214yescomplemented
149#2494C2212yescomplemented
150#2492C2212yes—
151#2492C2212yescomplemented
152#2489C2212yes—
153#2489C2212yescomplemented
154#2485C2212yes—
155#2484C2214yescomplemented
156#2482C2214yes—
157#2480C2214yes—
158#2480C2214yes—
159#2480C2214yes—
160#2477C2214yes—
161#2475C2214yescomplemented
162#2473C2214yescomplemented
163#2466C2214yes—
164#2465C2214yescomplemented
165#2462C2214yescomplemented
166#2454C2212yes—
167#2453C2212yescomplemented
168#2452C2212yes—
169#2452C2212yes—
170#2451C2212yescomplemented
171#2451C2212yescomplemented
172#2451C2212yescomplemented
173#2449C2214yes—
174#2447C2212yes—
175#2447C2212yes—
176#2447C2212yes—
177#2447C2212yes—
178#2447C2212yes—
179#2446C2212yescomplemented
180#2442C2214yescomplemented
181#2442C2212yescomplemented
182#2440C2212yes—
183#2439C2212yescomplemented
184#2437C2214yes—
185#2435C2212yes—
186#2434C2212yescomplemented
187#2429C2212yescomplemented
188#2429C2212yescomplemented
189#2423C2212yes—
190#2421C2212yes—
191#2421C2212yescomplemented
192#2421C2212yescomplemented
193#2417C2212yes—
194#2415C2212yes—
195#2409C2212yes—
196#2401C2214yescomplemented
197#2396C2214yescomplemented
198#2373C2214yescomplemented
199#2370C2212yescomplemented
200#2367C2212yes—
201#2367C2212yes—
202#2367C2212yes—
203#2365C2211yescharacteristic, complemented
204#2365C2212yescomplemented
205#2365C2211yescharacteristic, complemented
206#2362C2214yes—
207#2362C2214yes—
208#2362C2214yescomplemented
209#2362C2212yescomplemented
210#2360C2212yes—
211#2360C2212yescomplemented
212#2360C2214yescomplemented
213#2360C2214yescomplemented
214#2357C2212yes—
215#2355C2211yescharacteristic, complemented
216#2355C2212yescomplemented
217#2354C2212yes—
218#2354C2211yescharacteristic
219#2354C2211yescharacteristic
220#2354C2211yescharacteristic
221#2352C2212yes—
222#2352C2212yes—
223#2351C2212yescomplemented
224Q8×C4⋊C4C2211yescharacteristic, complemented
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2212yes—
227D4×C4⋊C4C2211yescharacteristic
228D4×C4⋊C4C2211yescharacteristic
229#2346C2212yescomplemented
230#2344C2211yescharacteristic
231#2344C2211yescharacteristic
232#2344C2214yescomplemented
233#2344C2214yescomplemented
234#2342C2212yes—
235#2342C2212yes—
236#2342C2214yes—
237#2342C2214yes—
238Q8×C22⋊C4C2212yescomplemented
239D4×C22⋊C4C2211yescharacteristic
240D4×C22⋊C4C2211yescharacteristic
241D4×C22⋊C4C2212yes—
242#2336C2212yescomplemented
243#2336C2212yescomplemented
244#2334C2212yes—
245#2334C2212yes—
246#2334C2214yescomplemented
247#2330C2211yescharacteristic, complemented
248#2327C2211yescharacteristic, complemented
249#2323C2212yes—
250#2323C2211yescharacteristic
251#2323C2211yescharacteristic
252#2323C2212yes—
253#2323C2212yes—
254#2323C2212yescomplemented
255#2323C2214yescomplemented
256#2323C2212yescomplemented
257#2320C2211yescharacteristic, complemented
258#2320C2211yescharacteristic, complemented
259#2320C2212yescomplemented
260#2316C2212yescomplemented
261#2314C2211yescharacteristic
262#2310C2212yescomplemented
263C4×C4⋊Q8C2212yescomplemented
264C4×C4⋊Q8C2211yescharacteristic, complemented
265C4×C4⋊Q8C2211yescharacteristic, complemented
266C4×C4⋊Q8C2211yescharacteristic, complemented
267C4×C4⋊Q8C2212yescomplemented
268C4×#125C2212yescomplemented
269C4×#125C2211yescharacteristic, complemented
270C4×#125C2212yescomplemented
271C4×#126C2212yes—
272C4×#126C2212yes—
273C4×#124C2212yes—
274C4×#124C2212yes—
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2211yescharacteristic
277C4×C22⋊Q8C2212yescomplemented
278C4×C22⋊Q8C2212yescomplemented
279C4×C22⋊Q8C2212yescomplemented
280C4×C22⋊Q8C2212yescomplemented
281#2295C2212yescomplemented
282#2295C2212yescomplemented
283#2293C2211yescharacteristic
284#2293C2212yes—
285#2293C2211yescharacteristic
286#2293C2212yes—
287#2290C2212yes—
288#2290C2212yes—
289#2285C2211yescharacteristic
290#2283C2212yescomplemented
291#2280C2212yes—
292#2280C2212yes—
293#2274C2212yescomplemented
294C42×Q8C2211yescharacteristic, complemented
295C42×Q8C2211yescharacteristic, complemented
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C23×Q8C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#556—28no—
303D4×Q8—28no—
304#541—28no—
305#533—48no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×#126C2312yes—
314C2×#126C2312yes—
315C2×#126C2314yes—
316C2×#125C2311yescharacteristic
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2314yes—
321C2×#124C2312yes—
322C2×#124C2312yes—
323C2×C22⋊Q8—216no—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2311yescharacteristic
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2311yescharacteristic
338#519—48no—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2314yes—
348C2×C4×Q8C2314yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2314yes—
354C2×C4×D4—28no—
355C2×C4×D4C2312yes—
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2311yescharacteristic
367C2×#117—48no—
368C2×#117C2312yes—
369C2×#117C2311yescharacteristic
370C2×#117C2311yescharacteristic
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2314yes—
376C2×#117C2312yes—
377C2×#117C2314yes—
378C2×#117C2312yes—
379C2×#117C2312yes—
380C2×#117C2314yes—
381C2×#117C2312yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2311yescharacteristic
384C22×C4⋊C4C2314yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C22⋊C4C2314yes—
388C22×C22⋊C4C2312yes—
389C22×C22⋊C4C2312yes—
390C22×C22⋊C4C2312yes—
391C22×C42C2311yescharacteristic
392C22×C42C2312yes—
393C22×C42C2312yes—
394#401C2314yes—
395#401C2314yes—
396#401C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#399C2314yes—
416#399C2314yes—
417#399C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#394C2314yes—
460#394C2314yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2311yescharacteristic
483#391C2311yescharacteristic
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#390C2311yescharacteristic
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2311yescharacteristic
498#390C2311yescharacteristic
499#390C2311yescharacteristic
500#390C2312yes—
501#389C2311yescharacteristic
502#389C2312yes—
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2311yescharacteristic
529#389C2311yescharacteristic
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2314yes—
542#389C2311yescharacteristic
543#389C2311yescharacteristic
544#389C2311yescharacteristic
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2312yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#386C2312yes—
647#386C2314yes—
648#386C2312yes—
649#386C2314yes—
650#386C2312yes—
651#386C2312yes—
652#385C2314yes—
653#385C2314yes—
654#385C2312yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2312yes—
665#385C2312yes—
666#385C2312yes—
667#385C2312yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2312yes—
674#385C2314yes—
675#385C2314yes—
676#384C2312yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2311yescharacteristic
680#384C2312yes—
681#384C2311yescharacteristic
682#384C2311yescharacteristic
683#383C2312yes—
684#383C2312yes—
685#383C2314yes—
686#383C2314yes—
687#383C2314yes—
688#382C2311yescharacteristic
689#382C2312yes—
690#382C2312yes—
691#382C2312yes—
692#382C2312yes—
693#382C2312yes—
694#382C2312yes—
695#382C2312yes—
696#382C2314yes—
697#382C2312yes—
698#382C2314yes—
699#382C2312yes—
700#382C2312yes—
701#382C2314yes—
702#381C2314yes—
703#381C2314yes—
704#381C2314yes—
705#381C2314yes—
706#381C2314yes—
707#381C2312yes—
708#381C2312yes—
709#381C2314yes—
710#380C2314yes—
711#380C2314yes—
712#380C2311yescharacteristic
713#380C2311yescharacteristic
714#380C2314yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2314yes—
720#380C2312yes—
721#380C2312yes—
722#380C2311yescharacteristic
723#380C2311yescharacteristic
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#379C2314yes—
735#379C2314yes—
736#379C2312yes—
737#379C2312yes—
738#379C2314yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C22⋊C4C2311yescharacteristic
786C4×C22⋊C4C2311yescharacteristic
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810#376C2311yescharacteristic
811#376C2311yescharacteristic
812#376C2314yes—
813#376C2314yes—
814C43C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2311yescharacteristic
818C25C2412yes—
819C22×Q8—28no—
820C22×Q8—28no—
821C22×Q8—44no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2412yes—
825C22×Q8C2414yes—
826C22×Q8C2411yescharacteristic
827C22×Q8C2414yes—
828C22×D4—24no—
829C22×D4—24no—
830C22×D4—42no—
831C22×D4C2412yes—
832C22×D4C2411yescharacteristic
833C22×D4C2411yescharacteristic
834C23×C4—28no—
835C23×C4—28no—
836C23×C4—44no—
837C23×C4C2411yescharacteristic
838C23×C4C2412yes—
839C23×C4C2414yes—
840C23×C4C2412yes—
841C23×C4C2412yes—
842C23×C4C2412yes—
843C23×C4C2412yes—
844C23×C4C2412yes—
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2414yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C4⋊Q8—24no—
852C4⋊Q8—28no—
853C4⋊Q8—24no—
854C4⋊Q8—24no—
855C4⋊Q8—44no—
856C4⋊Q8—44no—
857C4⋊Q8—44no—
858#126—28no—
859#126—28no—
860#126—216no—
861#125—24no—
862#125—28no—
863#125—28no—
864#125—44no—
865#125—48no—
866#124—28no—
867#124—28no—
868C22⋊Q8—28no—
869C22⋊Q8—28no—
870C22⋊Q8—24no—
871C22⋊Q8—28no—
872C22⋊Q8—28no—
873C22⋊Q8—28no—
874C22⋊Q8—216no—
875C22⋊Q8—216no—
876C22⋊Q8—216no—
877C22⋊Q8—48no—
878C22⋊Q8—44no—
879C22⋊Q8—44no—
880C22⋊Q8—44no—
881C22⋊Q8#4118yes—
882C4×Q8—24no—
883C4×Q8—24no—
884C4×Q8—28no—
885C4×Q8—24no—
886C4×Q8—24no—
887C4×Q8—24no—
888C4×Q8—28no—
889C4×Q8—24no—
890C4×Q8—48no—
891C4×Q8—48no—
892C4×Q8—48no—
893C4×Q8—44no—
894C4×Q8—44no—
895C4×Q8—44no—
896C4×Q8—44no—
897C4×D4—24no—
898C4×D4—28no—
899C4×D4—24no—
900C4×D4—24no—
901C4×D4—28no—
902C4×D4—24no—
903C4×D4—28no—
904C4×D4—24no—
905C4×D4—42no—
906C4×D4—44no—
907C4×D4—42no—
908C4×D4#4118yes—
909#117—24no—
910#117—28no—
911#117—24no—
912#117—28no—
913#117—44no—
914#117—44no—
915#117—48no—
916#117—44no—
917#117—44no—
918#117—44no—
919#117—44no—
920#117—48no—
921#117—48no—
922#117—44no—
923C2×C4⋊C4—24no—
924C2×C4⋊C4—28no—
925C2×C4⋊C4—216no—
926C2×C4⋊C4—44no—
927C2×C4⋊C4—44no—
928C2×C4⋊C4C2411yescharacteristic
929C2×C4⋊C4C2411yescharacteristic
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2411yescharacteristic
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C22⋊C4—28no—
1004C2×C22⋊C4—216no—
1005C2×C22⋊C4—44no—
1006C2×C22⋊C4—44no—
1007C2×C22⋊C4C2411yescharacteristic
1008C2×C22⋊C4C2411yescharacteristic
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2411yescharacteristic
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C42—24no—
1050C2×C42—28no—
1051C2×C42—44no—
1052C2×C42C2411yescharacteristic
1053C2×C42C2412yes—
1054C2×C42C2412yes—
1055C2×C42C2414yes—
1056C2×C42C2412yes—
1057C2×C42C2412yes—
1058C2×C42C2412yes—
1059C2×C42C2412yes—
1060C2×C42C2411yescharacteristic
1061C2×C42C2414yes—
1062C2×C42C2411yescharacteristic
1063C2×C42C2411yescharacteristic
1064C2×C42C2411yescharacteristic
1065C2×C42C2411yescharacteristic
1066C2×C42C2411yescharacteristic
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2411yescharacteristic
1070C2×C42C2411yescharacteristic
1071C2×C42C2411yescharacteristic
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2414yes—
1079C2×C42C2414yes—
1080C2×C42C2414yes—
1081C2×C42C2414yes—
1082C2×C42C2414yes—
1083C2×C42C2412yes—
1084C2×C42C2412yes—
1085C2×C42C2412yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2412yes—
1091C2×C42C2414yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094#95C2412yes—
1095#95C2411yescharacteristic
1096#95C2411yescharacteristic
1097#95C2411yescharacteristic
1098#95C2411yescharacteristic
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2411yescharacteristic
1102#95C2411yescharacteristic
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174C24—24no—
1175C24—24no—
1176C24—24no—
1177C24—42no—
1178C24—42no—
1179C24—42no—
1180C24—42no—
1181C24C2511yescharacteristic
1182C24C2512yes—
1183C24C2512yes—
1184C2×Q8—22no—
1185C2×Q8—22no—
1186C2×Q8—22no—
1187C2×Q8—24no—
1188C2×Q8—28no—
1189C2×Q8—24no—
1190C2×Q8—28no—
1191C2×Q8—24no—
1192C2×Q8—22no—
1193C2×Q8—24no—
1194C2×Q8—22no—
1195C2×Q8—24no—
1196C2×Q8—24no—
1197C2×Q8—44no—
1198C2×Q8—44no—
1199C2×Q8—44no—
1200C2×Q8—44no—
1201C2×Q8—432no—
1202C2×Q8C2×#4114yes—
1203C2×D4—24no—
1204C2×D4—24no—
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—22no—
1209C2×D4—42no—
1210C2×D4—416no—
1211C2×D4C2×#4114yes—
1212C2×D42−1+414yes—
1213C22×C4—22no—
1214C22×C4—24no—
1215C22×C4—22no—
1216C22×C4—24no—
1217C22×C4—24no—
1218C22×C4—28no—
1219C22×C4—24no—
1220C22×C4—24no—
1221C22×C4—24no—
1222C22×C4—22no—
1223C22×C4—24no—
1224C22×C4—28no—
1225C22×C4—24no—
1226C22×C4—24no—
1227C22×C4—24no—
1228C22×C4—24no—
1229C22×C4—24no—
1230C22×C4—24no—
1231C22×C4—24no—
1232C22×C4—22no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—28no—
1236C22×C4—24no—
1237C22×C4—42no—
1238C22×C4—42no—
1239C22×C4—42no—
1240C22×C4—44no—
1241C22×C4—42no—
1242C22×C4—432no—
1243C22×C4—42no—
1244C22×C4—42no—
1245C22×C4—42no—
1246C22×C4—44no—
1247C22×C4—42no—
1248C22×C4—42no—
1249C22×C4—41no—
1250C22×C4—41no—
1251C22×C4—44no—
1252C22×C4—42no—
1253C22×C4—42no—
1254C22×C4C2×#4118yes—
1255C22×C4C2×#4114yes—
1256C22×C4C2511yescharacteristic
1257C22×C4C2511yescharacteristic
1258C22×C4C2511yescharacteristic
1259C22×C4C2511yescharacteristic
1260C22×C4C2512yes—
1261C22×C4C2514yes—
1262C22×C4C2511yescharacteristic
1263C22×C4C2512yes—
1264C22×C4C2512yes—
1265C22×C4C2512yes—
1266C22×C4C2514yes—
1267C22×C4C2512yes—
1268C22×C4C2512yes—
1269C22×C4C2511yescharacteristic
1270C22×C4C2512yes—
1271C22×C4C2511yescharacteristic
1272C22×C4C2512yes—
1273C22×C4C2511yescharacteristic
1274C22×C4C2512yes—
1275C22×C4C2514yes—
1276C22×C4C2512yes—
1277C22×C4C2514yes—
1278C22×C4C2512yes—
1279C22×C4C2511yescharacteristic
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2511yescharacteristic
1284C22×C4C2511yescharacteristic
1285C22×C4C2511yescharacteristic
1286C22×C4C2511yescharacteristic
1287C22×C4C2511yescharacteristic
1288C4⋊C4—24no—
1289C4⋊C4—22no—
1290C4⋊C4—28no—
1291C4⋊C4—24no—
1292C4⋊C4—28no—
1293C4⋊C4—28no—
1294C4⋊C4—28no—
1295C4⋊C4—22no—
1296C4⋊C4—24no—
1297C4⋊C4—22no—
1298C4⋊C4—22no—
1299C4⋊C4—24no—
1300C4⋊C4—24no—
1301C4⋊C4—22no—
1302C4⋊C4—22no—
1303C4⋊C4—28no—
1304C4⋊C4—24no—
1305C4⋊C4—24no—
1306C4⋊C4—24no—
1307C4⋊C4—28no—
1308C4⋊C4—24no—
1309C4⋊C4—24no—
1310C4⋊C4—24no—
1311C4⋊C4—24no—
1312C4⋊C4—24no—
1313C4⋊C4—24no—
1314C4⋊C4—24no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—22no—
1321C4⋊C4—28no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—22no—
1325C4⋊C4—22no—
1326C4⋊C4—22no—
1327C4⋊C4—22no—
1328C4⋊C4—24no—
1329C4⋊C4—22no—
1330C4⋊C4—24no—
1331C4⋊C4—42no—
1332C4⋊C4—42no—
1333C4⋊C4—42no—
1334C4⋊C4—42no—
1335C4⋊C4—42no—
1336C4⋊C4—42no—
1337C4⋊C4—42no—
1338C4⋊C4—42no—
1339C4⋊C4—42no—
1340C4⋊C4—42no—
1341C4⋊C4—42no—
1342C4⋊C4—42no—
1343C4⋊C4—42no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—42no—
1347C4⋊C4—44no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—44no—
1353C4⋊C4—44no—
1354C4⋊C4—44no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4C2×#4114yes—
1361C4⋊C4C2×#4118yes—
1362C4⋊C4C2×#4114yes—
1363C22⋊C4—24no—
1364C22⋊C4—28no—
1365C22⋊C4—28no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—28no—
1369C22⋊C4—28no—
1370C22⋊C4—24no—
1371C22⋊C4—24no—
1372C22⋊C4—24no—
1373C22⋊C4—28no—
1374C22⋊C4—28no—
1375C22⋊C4—24no—
1376C22⋊C4—24no—
1377C22⋊C4—28no—
1378C22⋊C4—28no—
1379C22⋊C4—22no—
1380C22⋊C4—22no—
1381C22⋊C4—24no—
1382C22⋊C4—24no—
1383C22⋊C4—42no—
1384C22⋊C4—42no—
1385C22⋊C4—42no—
1386C22⋊C4—42no—
1387C22⋊C4—42no—
1388C22⋊C4—42no—
1389C22⋊C4—42no—
1390C22⋊C4—44no—
1391C22⋊C4—44no—
1392C22⋊C4—44no—
1393C22⋊C4—42no—
1394C22⋊C4—42no—
1395C22⋊C4—42no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—42no—
1400C22⋊C4—42no—
1401C22⋊C4—44no—
1402C22⋊C4—44no—
1403C22⋊C4C2×#4118yes—
1404C22⋊C4C2×#4118yes—
1405C42—22no—
1406C42—22no—
1407C42—22no—
1408C42—22no—
1409C42—28no—
1410C42—22no—
1411C42—24no—
1412C42—24no—
1413C42—24no—
1414C42—24no—
1415C42—24no—
1416C42—24no—
1417C42—24no—
1418C42—22no—
1419C42—24no—
1420C42—24no—
1421C42—28no—
1422C42—24no—
1423C42—22no—
1424C42—22no—
1425C42—24no—
1426C42—22no—
1427C42—24no—
1428C42—22no—
1429C42—42no—
1430C42—42no—
1431C42—41no—
1432C42—41no—
1433C42—42no—
1434C42—42no—
1435C42—41no—
1436C42—41no—
1437C42—42no—
1438C42—42no—
1439C42—44no—
1440C42—44no—
1441C42—44no—
1442C42—44no—
1443C42—44no—
1444C42—44no—
1445C42C2×#4114yes—
1446C42H(5,𝔽2)14yes—
1447C23—22no—
1448C23—22no—
1449C23—22no—
1450C23—21no—
1451C23—22no—
1452C23—21no—
1453C23—22no—
1454C23—21no—
1455C23—22no—
1456C23—21no—
1457C23—22no—
1458C23—22no—
1459C23—22no—
1460C23—22no—
1461C23—22no—
1462C23—22no—
1463C23—21no—
1464C23—21no—
1465C23—48no—
1466C23—48no—
1467C23—48no—
1468C23—84no—
1469C23—84no—
1470C23—84no—
1471C23—84no—
1472C23C22×#4112yes—
1473C23C22×#4114yes—
1474C23C2×2−1+414yes—
1475C23C2611yescharacteristic
1476Q8—28no—
1477Q8—416no—
1478Q8—44no—
1479Q8—48no—
1480Q8—48no—
1481Q8—88no—
1482D4—28no—
1483D4—28no—
1484D4—48no—
1485C2×C4—21no—
1486C2×C4—22no—
1487C2×C4—22no—
1488C2×C4—22no—
1489C2×C4—22no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—22no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—22no—
1499C2×C4—28no—
1500C2×C4—216no—
1501C2×C4—22no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—22no—
1507C2×C4—24no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—22no—
1511C2×C4—21no—
1512C2×C4—22no—
1513C2×C4—24no—
1514C2×C4—22no—
1515C2×C4—24no—
1516C2×C4—24no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—24no—
1527C2×C4—24no—
1528C2×C4—22no—
1529C2×C4—22no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—21no—
1535C2×C4—24no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—22no—
1542C2×C4—21no—
1543C2×C4—22no—
1544C2×C4—24no—
1545C2×C4—24no—
1546C2×C4—24no—
1547C2×C4—22no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—24no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—48no—
1571C2×C4—48no—
1572C2×C4—48no—
1573C2×C4—48no—
1574C2×C4—416no—
1575C2×C4—48no—
1576C2×C4—44no—
1577C2×C4—88no—
1578C2×C4—82no—
1579C2×C4—84no—
1580C2×C4—84no—
1581C2×C4—84no—
1582C2×C4C22×#4114yes—
1583C2×C4C22×#4112yes—
1584C2×C4C22×#4114yes—
1585C2×C4C22×#4114yes—
1586C2×C4C22×#4112yes—
1587C2×C4C22×#4112yes—
1588C2×C4C22×#4112yes—
1589C2×C4C22×#4112yes—
1590C2×C4C2×H(5,𝔽2)12yes—
1591C2×C4C2×H(5,𝔽2)12yes—
1592C2×C4C2×H(5,𝔽2)12yes—
1593C2×C4C2×2−1+412yes—
1594C2×C4#58512yes—
1595C22—22no—
1596C22—24no—
1597C22—22no—
1598C22—24no—
1599C22—24no—
1600C22—24no—
1601C22—24no—
1602C22—24no—
1603C22—22no—
1604C22—42no—
1605C22—42no—
1606C22—42no—
1607C22—41no—
1608C22—41no—
1609C22—42no—
1610C22—42no—
1611C22—41no—
1612C22—42no—
1613C22—42no—
1614C22—41no—
1615C22—42no—
1616C22—816no—
1617C22C23×#4111yescharacteristic
1618C22C23×#4111yescharacteristic
1619C22C22×H(5,𝔽2)11yescharacteristic
1620C22C22×2−1+411yescharacteristic
1621C22C2×#58511yescharacteristic
1622C222−1+611yescharacteristic
1623C222−1+611yescharacteristic
1624C4—24no—
1625C4—22no—
1626C4—22no—
1627C4—22no—
1628C4—22no—
1629C4—24no—
1630C4—24no—
1631C4—41no—
1632C4—41no—
1633C4—42no—
1634C4—41no—
1635C4—41no—
1636C4—44no—
1637C4—41no—
1638C4—44no—
1639C4—42no—
1640C4—42no—
1641C4—41no—
1642C4—42no—
1643C4—42no—
1644C4—42no—
1645C4—41no—
1646C4—42no—
1647C4—41no—
1648C4—42no—
1649C4—44no—
1650C4—42no—
1651C4—42no—
1652C4—44no—
1653C4—42no—
1654C4#348114yes—
1655C4#349514yes—
1656C2—44no—
1657C2—44no—
1658C2—42no—
1659C2C2×#348111yescharacteristic
1660C2C2×#349511yescharacteristic
1661C2#6286111yescharacteristic
1662C2#6294211yescharacteristic
1663C2#6296011yescharacteristic
1664C2#6299811yescharacteristic
1665C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59960C2semidirect
2. #59715C2semidirect
3. #59563C2semidirect
4. #59502C2semidirect
7. #59460C2semidirect
8. #59436C2semidirect
9. #44730C2semidirect
10. #44714C2semidirect
11. #43885C2semidirect
12. #43858C2semidirect
13. #39734C2semidirect
14. #39609C2semidirect
15. #39058C2semidirect
16. #39043C2semidirect
17. #38967C2semidirect
18. #38954C2semidirect
19. #37859C2semidirect
20. #37663C2semidirect
21. #36477C2semidirect
22. #36454C2semidirect
25. #35665C2semidirect
26. #35647C2semidirect
27. #35325C2semidirect
28. #35291C2semidirect
29. #34945C2semidirect
30. #34929C2semidirect
31. #34322C2semidirect
32. #34311C2semidirect
33. #34203C2semidirect
35. C4×#541C2semidirect
39. C2×#533C22semidirect
41. C2×#519C22semidirect
44. #2862C22semidirect
45. #2859C22semidirect
48. #2855C22semidirect
49. #2855C22semidirect
52. #2788C22semidirect
53. #2776C22semidirect
54. #2774C22semidirect
55. #2766C22semidirect
56. #2765C22semidirect
57. #2763C22semidirect
58. #2762C22semidirect
61. #2747C22semidirect
63. #2745C22semidirect
64. #2745C22semidirect
66. #2742C22semidirect
67. #2739C22semidirect
70. #2704C22semidirect
72. #2698C22semidirect
73. #2698C22semidirect
74. #2690C22semidirect
76. #2645C22semidirect
78. #2628C22semidirect
81. #2621C22semidirect
83. #2611C22semidirect
85. #2608C22semidirect
86. #2605C22semidirect
88. #2599C22semidirect
89. #2599C22semidirect
90. #2599C22semidirect
91. #2590C22semidirect
92. #2587C22semidirect
93. #2587C22semidirect
94. #2587C22semidirect
95. #2583C22semidirect
96. #2581C22semidirect
101. #2575C22semidirect
102. #2575C22semidirect
103. #2574C22semidirect
104. #2573C22semidirect
105. #2573C22semidirect
107. #2571C22semidirect
108. #2570C22semidirect
109. #2570C22semidirect
110. #2568C22semidirect
111. #2567C22semidirect
115. #2556C22semidirect
116. #2551C22semidirect
117. #2550C22semidirect
119. #2546C22semidirect
123. #2530C22semidirect
124. #2530C22semidirect
125. #2528C22semidirect
127. #2527C22semidirect
128. #2524C22semidirect
129. #2517C22semidirect
130. #2514C22semidirect
131. #2514C22semidirect
132. #2514C22semidirect
133. #2511C22semidirect
134. #2511C22semidirect
135. #2509C22semidirect
136. #2509C22semidirect
137. #2509C22semidirect
138. #2508C22semidirect
139. #2507C22semidirect
140. #2506C22semidirect
141. #2499C22semidirect
142. #2497C22semidirect
145. #2495C22semidirect
148. #2494C22semidirect
149. #2494C22semidirect
151. #2492C22semidirect
153. #2489C22semidirect
155. #2484C22semidirect
161. #2475C22semidirect
162. #2473C22semidirect
164. #2465C22semidirect
165. #2462C22semidirect
167. #2453C22semidirect
170. #2451C22semidirect
171. #2451C22semidirect
172. #2451C22semidirect
179. #2446C22semidirect
180. #2442C22semidirect
181. #2442C22semidirect
183. #2439C22semidirect
186. #2434C22semidirect
187. #2429C22semidirect
188. #2429C22semidirect
191. #2421C22semidirect
192. #2421C22semidirect
196. #2401C22semidirect
197. #2396C22semidirect
198. #2373C22semidirect
199. #2370C22semidirect
203. #2365C22semidirect
204. #2365C22semidirect
205. #2365C22semidirect
208. #2362C22semidirect
209. #2362C22semidirect
211. #2360C22semidirect
212. #2360C22semidirect
213. #2360C22semidirect
215. #2355C22semidirect
216. #2355C22semidirect
223. #2351C22semidirect
224. Q8×C4⋊C4C22semidirect
229. #2346C22semidirect
232. #2344C22semidirect
233. #2344C22semidirect
238. Q8×C22⋊C4C22semidirect
242. #2336C22semidirect
243. #2336C22semidirect
246. #2334C22semidirect
247. #2330C22semidirect
248. #2327C22semidirect
254. #2323C22semidirect
255. #2323C22semidirect
256. #2323C22semidirect
257. #2320C22semidirect
258. #2320C22semidirect
259. #2320C22semidirect
260. #2316C22semidirect
262. #2310C22semidirect
263. C4×C4⋊Q8C22semidirect
264. C4×C4⋊Q8C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×C4⋊Q8C22semidirect
267. C4×C4⋊Q8C22semidirect
268. C4×#125C22semidirect
269. C4×#125C22semidirect
270. C4×#125C22semidirect
277. C4×C22⋊Q8C22semidirect
278. C4×C22⋊Q8C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
281. #2295C22semidirect
282. #2295C22semidirect
290. #2283C22semidirect
293. #2274C22semidirect
294. C42×Q8C22semidirect
295. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#599602
#597152
#595632
#595022
#594882
#594842
#594602
#594362
#447302
#447142
#438852
#438582
#397342
#396092
#390582
#390432
#389672
#389542
#378592
#376632
#364772
#364542
#361612
D4×C22⋊Q82
#356652
#356472
#353252
#352912
#349452
#349292
#343222
#343112
#342032
D4×#1172
C4×#5412