Finite Group Databasebeta

← #7680339

Subgroups — #7680339

Order 512.

5087 conjugacy classes of subgroups.

The subgroup lattice has 1761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59859C212yesmaximal, complemented
2#59855C212yesmaximal, complemented
3#59768C212yesmaximal, complemented
4#59440C212yesmaximal, complemented
5#59388C214yesmaximal, complemented
6#59387C214yesmaximal, complemented
7#45397C212yesmaximal, complemented
8#45371C212yesmaximal, complemented
9#45162C212yesmaximal, complemented
10#45161C212yesmaximal, complemented
11#43709C214yesmaximal, complemented
12#43308C214yesmaximal, complemented
13#39286C212yesmaximal, complemented
14#39285C212yesmaximal, complemented
15#39284C212yesmaximal, complemented
16#39283C212yesmaximal, complemented
17#39149C212yesmaximal, complemented
18#39142C212yesmaximal, complemented
19#36513C212yesmaximal, complemented
20#36449C212yesmaximal, complemented
21#35633C211yesmaximal, characteristic, complemented
22#35627C211yesmaximal, characteristic, complemented
23#35621C211yesmaximal, characteristic, complemented
24#35516C211yesmaximal, characteristic, complemented
25#35313C211yesmaximal, characteristic, complemented
26#35306C211yesmaximal, characteristic, complemented
27#35267C211yesmaximal, characteristic, complemented
28#34743C211yesmaximal, characteristic
29C2×#2421C211yesmaximal, characteristic, complemented
30#34266C211yesmaximal, characteristic, complemented
31#34250C211yesmaximal, characteristic, complemented
32#34208C211yesmaximal, characteristic, complemented
33#34202C211yesmaximal, characteristic, complemented
34#34109C211yesmaximal, characteristic, complemented
35C4×#536C211yesmaximal, characteristic, complemented
36C2×#536C2211yescharacteristic
37C2×#536C2211yescharacteristic
38C2×#532C2211yescharacteristic
39C2×#525C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C22×C22⋊Q8C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#520C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×#117C2211yescharacteristic
48#2863C2212yescomplemented
49#2863C2212yescomplemented
50#2863C2212yescomplemented
51#2860C2212yescomplemented
52#2857C2212yes—
53#2850C2212yes—
54#2802C2214yescomplemented
55#2800C2214yes—
56#2796C2214yes—
57#2795C2214yes—
58#2793C2214yescomplemented
59#2787C2214yescomplemented
60#2782C2214yescomplemented
61#2781C2214yescomplemented
62#2779C2214yescomplemented
63#2778C2214yes—
64#2778C2214yes—
65#2777C2214yes—
66#2776C2214yescomplemented
67#2776C2214yescomplemented
68#2772C2214yes—
69#2772C2214yescomplemented
70#2766C2214yescomplemented
71#2753C2214yes—
72#2750C2214yescomplemented
73#2747C2214yescomplemented
74#2741C2214yes—
75#2739C2214yes—
76#2739C2214yes—
77#2708C2214yes—
78#2645C2212yescomplemented
79#2645C2212yescomplemented
80#2645C2212yescomplemented
81#2644C2212yescomplemented
82#2621C2212yes—
83#2620C2212yes—
84#2608C2214yescomplemented
85#2601C2214yes—
86#2597C2214yes—
87#2596C2214yes—
88#2595C2214yes—
89#2594C2214yes—
90#2591C2214yes—
91#2590C2214yescomplemented
92#2587C2214yescomplemented
93#2585C2214yescomplemented
94#2578C2214yes—
95#2578C2214yes—
96#2578C2214yescomplemented
97#2577C2214yescomplemented
98#2576C2214yescomplemented
99#2573C2214yescomplemented
100#2571C2212yescomplemented
101#2571C2212yescomplemented
102#2570C2212yescomplemented
103#2570C2212yescomplemented
104#2570C2214yescomplemented
105#2569C2214yescomplemented
106#2559C2214yes—
107#2547C2212yescomplemented
108#2546C2212yescomplemented
109#2545C2212yescomplemented
110#2544C2212yescomplemented
111#2534C2214yes—
112#2530C2214yescomplemented
113#2530C2214yescomplemented
114#2529C2214yescomplemented
115#2525C2214yescomplemented
116#2518C2214yes—
117#2518C2214yes—
118#2514C2212yescomplemented
119#2514C2212yescomplemented
120#2511C2212yescomplemented
121#2511C2212yescomplemented
122#2510C2214yes—
123#2510C2214yes—
124#2510C2214yescomplemented
125#2509C2212yescomplemented
126#2509C2212yescomplemented
127#2509C2214yescomplemented
128#2508C2212yescomplemented
129#2508C2212yescomplemented
130#2505C2214yes—
131#2505C2214yes—
132#2497C2214yes—
133#2497C2212yescomplemented
134#2496C2212yescomplemented
135#2495C2214yescomplemented
136#2495C2212yescomplemented
137#2494C2214yes—
138#2494C2212yescomplemented
139#2493C2214yes—
140#2493C2214yes—
141#2487C2212yes—
142#2486C2214yes—
143#2486C2212yes—
144#2485C2214yes—
145#2485C2212yes—
146#2485C2212yes—
147#2481C2214yes—
148#2481C2214yescomplemented
149#2470C2214yes—
150#2457C2214yes—
151#2444C2214yes—
152#2429C2212yes—
153#2429C2212yes—
154#2429C2211yescharacteristic
155#2429C2211yescharacteristic
156#2428C2211yescharacteristic
157#2428C2211yescharacteristic
158#2427C2212yes—
159#2427C2212yes—
160#2427C2211yescharacteristic
161#2427C2211yescharacteristic
162#2426C2211yescharacteristic
163#2426C2211yescharacteristic
164#2425C2214yes—
165#2425C2214yes—
166#2425C2212yes—
167#2425C2212yes—
168#2424C2212yes—
169#2424C2212yes—
170#2423C2212yes—
171#2422C2212yes—
172#2421C2212yes—
173#2421C2212yes—
174#2421C2212yes—
175#2421C2212yes—
176#2421C2212yes—
177#2421C2212yes—
178#2421C2212yes—
179#2421C2212yes—
180#2421C2212yes—
181#2420C2212yes—
182#2419C2214yes—
183#2418C2214yes—
184#2417C2212yes—
185#2417C2212yes—
186#2417C2212yes—
187#2417C2212yes—
188#2417C2212yescomplemented
189#2417C2212yescomplemented
190#2415C2212yes—
191#2415C2212yes—
192#2415C2212yes—
193#2415C2212yes—
194#2415C2212yescomplemented
195#2415C2212yescomplemented
196#2413C2214yes—
197#2412C2214yes—
198C2×#400C2212yes—
199#2392C2212yes—
200#2392C2212yes—
201C2×#397C2212yes—
202#2374C2214yes—
203#2373C2214yescomplemented
204#2367C2212yescomplemented
205#2367C2212yescomplemented
206#2365C2212yescomplemented
207#2365C2212yescomplemented
208#2364C2214yes—
209#2364C2214yes—
210#2362C2212yescomplemented
211#2362C2212yescomplemented
212#2360C2212yescomplemented
213#2360C2212yescomplemented
214#2359C2214yes—
215#2358C2214yes—
216#2354C2212yes—
217#2352C2214yes—
218#2352C2212yes—
219#2352C2212yes—
220#2352C2212yescomplemented
221#2352C2212yescomplemented
222#2352C2212yescomplemented
223#2352C2212yescomplemented
224#2351C2212yescomplemented
225Q8×C4⋊C4C2212yescomplemented
226#2349C2214yes—
227#2349C2212yescomplemented
228D4×C4⋊C4C2212yes—
229D4×C4⋊C4C2214yes—
230D4×C4⋊C4C2212yescomplemented
231#2347C2211yescharacteristic
232#2347C2211yescharacteristic
233#2346C2211yescharacteristic
234#2346C2211yescharacteristic
235#2345C2211yescharacteristic
236#2345C2211yescharacteristic
237#2345C2214yescomplemented
238#2344C2211yescharacteristic
239#2344C2211yescharacteristic
240#2343C2212yes—
241#2343C2212yes—
242#2342C2212yes—
243#2342C2212yes—
244#2328C2212yescomplemented
245#2327C2212yescomplemented
246#2327C2212yescomplemented
247#2326C2212yescomplemented
248#2324C2212yes—
249#2323C2212yes—
250#2323C2212yescomplemented
251#2323C2212yescomplemented
252#2322C2214yes—
253#2322C2214yes—
254#2317C2211yescharacteristic
255#2317C2211yescharacteristic
256#2317C2211yescharacteristic
257#2317C2212yescomplemented
258#2316C2211yescharacteristic
259#2316C2211yescharacteristic
260#2316C2212yescomplemented
261#2311C2211yescharacteristic
262#2311C2211yescharacteristic
263#2311C2211yescharacteristic
264#2310C2211yescharacteristic
265#2310C2211yescharacteristic
266C4×C4⋊Q8C2212yescomplemented
267C4×#124C2212yescomplemented
268C4×#124C2212yescomplemented
269C4×#124C2212yescomplemented
270C4×C22⋊Q8C2212yes—
271C4×C22⋊Q8C2212yescomplemented
272C4×C22⋊Q8C2212yescomplemented
273C4×#123C2214yes—
274C4×#123C2214yes—
275C4×#121C2212yes—
276C4×#121C2212yes—
277C4×#121C2212yes—
278#2298C2212yes—
279#2298C2212yes—
280#2297C2211yescharacteristic
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283#2296C2211yescharacteristic
284#2296C2212yescomplemented
285C2×#391C2211yescharacteristic
286C2×#389C2211yescharacteristic
287C2×#389C2212yescomplemented
288C2×#388C2212yes—
289C2×#387C2212yes—
290#2283C2212yes—
291C2×#382C2211yescharacteristic
292#2280C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C4×#117C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C23×Q8C2311yescharacteristic
302C24×C4C2311yescharacteristic
303#536—28no—
304#536—28no—
305#532—28no—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×#127C2311yescharacteristic
310C2×#126C2314yes—
311C2×#124C2312yes—
312C2×#124C2312yes—
313C2×#124C2311yescharacteristic
314C2×#124C2311yescharacteristic
315#525—28no—
316#525—44no—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2312yes—
320C2×#123C2314yes—
321C2×#123C2312yes—
322C2×C22⋊Q8—44no—
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2311yescharacteristic
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2311yescharacteristic
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×#121C2311yescharacteristic
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#121C2311yescharacteristic
339C2×#121C2312yes—
340C2×#121C2311yescharacteristic
341C2×#121C2311yescharacteristic
342C2×#121C2312yes—
343C2×#120C2312yes—
344C2×#120C2312yes—
345#520—28no—
346#520—44no—
347#520—44no—
348C4×#41—44no—
349C2×C4×Q8—44no—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×#117—28no—
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2311yescharacteristic
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2311yescharacteristic
386C2×#117C2311yescharacteristic
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2311yescharacteristic
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2311yescharacteristic
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2312yes—
397C22×C4⋊C4C2311yescharacteristic
398C22×C4⋊C4C2311yescharacteristic
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2314yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2312yes—
405C22×C22⋊C4C2312yes—
406C22×C22⋊C4C2311yescharacteristic
407C22×C22⋊C4C2311yescharacteristic
408C22×C22⋊C4C2312yes—
409C22×C22⋊C4C2312yes—
410C22×C42C2312yes—
411C22×C42C2311yescharacteristic
412C22×C42C2311yescharacteristic
413C22×C42C2312yes—
414C22×C42C2312yes—
415#401C2314yes—
416#401C2314yes—
417#401C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2314yes—
438#399C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2312yes—
450#397C2314yes—
451#397C2314yes—
452#397C2312yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2312yes—
466#397C2314yes—
467#397C2314yes—
468#396C2314yes—
469#396C2312yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2312yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#396C2312yes—
479#394C2314yes—
480#394C2312yes—
481#394C2314yes—
482#394C2312yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2312yes—
487#394C2314yes—
488#394C2312yes—
489#394C2312yes—
490#394C2312yes—
491#394C2314yes—
492#394C2314yes—
493#392C2312yes—
494#392C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2312yes—
508#391C2311yescharacteristic
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2314yes—
516#390C2312yes—
517#390C2312yes—
518#390C2311yescharacteristic
519#390C2311yescharacteristic
520#389C2314yes—
521#389C2314yes—
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2311yescharacteristic
529#389C2311yescharacteristic
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2311yescharacteristic
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2311yescharacteristic
558#389C2311yescharacteristic
559#389C2311yescharacteristic
560#389C2311yescharacteristic
561#389C2311yescharacteristic
562#389C2311yescharacteristic
563#389C2314yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2312yes—
587#388C2314yes—
588#388C2314yes—
589#388C2312yes—
590#388C2314yes—
591#388C2314yes—
592#388C2312yes—
593#388C2314yes—
594#388C2314yes—
595#388C2312yes—
596#388C2312yes—
597#388C2314yes—
598#388C2312yes—
599#388C2312yes—
600#388C2312yes—
601#388C2312yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2312yes—
609#388C2314yes—
610#388C2314yes—
611#388C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2312yes—
628#387C2314yes—
629#387C2312yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2312yes—
643#387C2314yes—
644#387C2314yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2312yes—
657#386C2314yes—
658#386C2312yes—
659#386C2312yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2312yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2312yes—
689#385C2312yes—
690#385C2312yes—
691#385C2314yes—
692#385C2314yes—
693#385C2312yes—
694#385C2312yes—
695#384C2312yes—
696#384C2314yes—
697#384C2312yes—
698#384C2312yes—
699#383C2314yes—
700#383C2314yes—
701#383C2314yes—
702#383C2312yes—
703#383C2312yes—
704#382C2312yes—
705#382C2312yes—
706#382C2314yes—
707#382C2312yes—
708#382C2312yes—
709#382C2312yes—
710#382C2314yes—
711#382C2312yes—
712#382C2314yes—
713#382C2312yes—
714#382C2312yes—
715#382C2312yes—
716#381C2314yes—
717#381C2314yes—
718#381C2314yes—
719#381C2312yes—
720#381C2312yes—
721#381C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2314yes—
731#380C2314yes—
732#380C2314yes—
733#380C2314yes—
734#380C2314yes—
735#380C2314yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2311yescharacteristic
740#380C2311yescharacteristic
741#380C2312yes—
742#380C2314yes—
743#380C2314yes—
744#380C2314yes—
745#380C2311yescharacteristic
746#380C2311yescharacteristic
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#379C2312yes—
751C4×C4⋊C4C2314yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2314yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807#376C2312yes—
808#376C2312yes—
809#376C2312yes—
810#376C2312yes—
811C2×#95C2314yes—
812C2×#95C2311yescharacteristic
813C2×#95C2311yescharacteristic
814C2×#95C2312yes—
815C2×#95C2312yes—
816C2×#95C2312yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C2×#95C2312yes—
820C43C2312yes—
821C43C2312yes—
822C25C2411yescharacteristic
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C2×#41—24no—
827C2×#41—24no—
828C2×#41#4118yes—
829C22×Q8—24no—
830C22×Q8—24no—
831C22×Q8—24no—
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2411yescharacteristic
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C23×C4—24no—
847C23×C4—24no—
848C23×C4—24no—
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2411yescharacteristic
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2411yescharacteristic
866C23×C4C2414yes—
867C23×C4C2412yes—
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2412yes—
871C23×C4C2411yescharacteristic
872C4⋊Q8—24no—
873C4⋊Q8—28no—
874C4⋊Q8—28no—
875#127—24no—
876#126—48no—
877#124—24no—
878#124—24no—
879#124—28no—
880#124—28no—
881#123—28no—
882#123—216no—
883#123—216no—
884#123—48no—
885#123—44no—
886C22⋊Q8—24no—
887C22⋊Q8—24no—
888C22⋊Q8—28no—
889C22⋊Q8—28no—
890C22⋊Q8—28no—
891C22⋊Q8—28no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—42no—
897C22⋊Q8—42no—
898#121—24no—
899#121—24no—
900#121—28no—
901#121—28no—
902#121—44no—
903#121—44no—
904#121—42no—
905#121—42no—
906#120—28no—
907#120—44no—
908C4×Q8—28no—
909C4×Q8—44no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×Q8—42no—
914C4×Q8—42no—
915C4×Q8—44no—
916C4×Q8—44no—
917C4×D4—28no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—28no—
921C4×D4—216no—
922C4×D4—28no—
923C4×D4—42no—
924C4×D4—42no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—48no—
930C4×D4—44no—
931C4×D4—44no—
932C4×D4—48no—
933C4×D4—48no—
934#117—24no—
935#117—24no—
936#117—24no—
937#117—24no—
938#117—24no—
939#117—24no—
940#117—24no—
941#117—28no—
942#117—28no—
943#117—28no—
944#117—44no—
945#117—44no—
946#117—44no—
947#117—44no—
948#117—44no—
949#117#4118yes—
950C2×C4⋊C4—24no—
951C2×C4⋊C4—24no—
952C2×C4⋊C4—24no—
953C2×C4⋊C4—24no—
954C2×C4⋊C4—24no—
955C2×C4⋊C4—28no—
956C2×C4⋊C4—48no—
957C2×C4⋊C4—44no—
958C2×C4⋊C4—44no—
959C2×C4⋊C4—44no—
960C2×C4⋊C4—44no—
961C2×C4⋊C4—44no—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C22⋊C4—28no—
1026C2×C22⋊C4—42no—
1027C2×C22⋊C4—42no—
1028C2×C22⋊C4—44no—
1029C2×C22⋊C4—44no—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C42—24no—
1086C2×C42—24no—
1087C2×C42—28no—
1088C2×C42—44no—
1089C2×C42—44no—
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2412yes—
1096C2×C42C2412yes—
1097C2×C42C2414yes—
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2414yes—
1108C2×C42C2414yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2414yes—
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2414yes—
1122C2×C42C2412yes—
1123#95C2412yes—
1124#95C2414yes—
1125#95C2411yescharacteristic
1126#95C2411yescharacteristic
1127#95C2411yescharacteristic
1128#95C2414yes—
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2414yes—
1132#95C2411yescharacteristic
1133#95C2411yescharacteristic
1134#95C2411yescharacteristic
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197C24—22no—
1198C24—22no—
1199C24—22no—
1200C24—22no—
1201C24—41no—
1202C24—41no—
1203C24—41no—
1204C24C2511yescharacteristic
1205C24C2512yes—
1206C24C2512yes—
1207C24C2511yescharacteristic
1208C24C2511yescharacteristic
1209#41—232no—
1210#41—416no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—24no—
1214C2×Q8—24no—
1215C2×Q8—24no—
1216C2×Q8—22no—
1217C2×Q8—22no—
1218C2×Q8—22no—
1219C2×Q8—24no—
1220C2×Q8—24no—
1221C2×Q8—22no—
1222C2×Q8—416no—
1223C2×Q8C2×#4114yes—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—42no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4C2×#4118yes—
1253C2×D4C2×#4114yes—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—24no—
1259C22×C4—24no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—24no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—24no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—24no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—24no—
1288C22×C4—28no—
1289C22×C4—24no—
1290C22×C4—42no—
1291C22×C4—41no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—44no—
1300C22×C4—42no—
1301C22×C4—42no—
1302C22×C4—44no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—42no—
1307C22×C4—41no—
1308C22×C4—41no—
1309C22×C4—41no—
1310C22×C4—42no—
1311C22×C4—42no—
1312C22×C4—42no—
1313C22×C4—44no—
1314C22×C4—44no—
1315C22×C4—44no—
1316C22×C4—44no—
1317C22×C4—44no—
1318C22×C4—44no—
1319C22×C4—416no—
1320C22×C4C2×#4118yes—
1321C22×C4C2×#4114yes—
1322C22×C4C2×#4114yes—
1323C22×C4H(5,𝔽2)14yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2512yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2514yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2512yes—
1336C22×C4C2514yes—
1337C22×C4C2511yescharacteristic
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2514yes—
1341C22×C4C2512yes—
1342C22×C4C2512yes—
1343C22×C4C2512yes—
1344C22×C4C2514yes—
1345C22×C4C2511yescharacteristic
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2511yescharacteristic
1352C22×C4C2511yescharacteristic
1353C22×C4C2511yescharacteristic
1354C4⋊C4—24no—
1355C4⋊C4—22no—
1356C4⋊C4—22no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—28no—
1360C4⋊C4—24no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—28no—
1370C4⋊C4—28no—
1371C4⋊C4—28no—
1372C4⋊C4—28no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—22no—
1378C4⋊C4—22no—
1379C4⋊C4—22no—
1380C4⋊C4—22no—
1381C4⋊C4—24no—
1382C4⋊C4—28no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—42no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—44no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—44no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4C2×#4114yes—
1416C4⋊C4C2×#4114yes—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—28no—
1425C22⋊C4—28no—
1426C22⋊C4—24no—
1427C22⋊C4—24no—
1428C22⋊C4—22no—
1429C22⋊C4—28no—
1430C22⋊C4—22no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—28no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—24no—
1439C22⋊C4—28no—
1440C22⋊C4—28no—
1441C22⋊C4—22no—
1442C22⋊C4—22no—
1443C22⋊C4—24no—
1444C22⋊C4—41no—
1445C22⋊C4—41no—
1446C22⋊C4—41no—
1447C22⋊C4—44no—
1448C22⋊C4—41no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—42no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4C2×#4118yes—
1472C42—24no—
1473C42—24no—
1474C42—24no—
1475C42—22no—
1476C42—22no—
1477C42—22no—
1478C42—22no—
1479C42—24no—
1480C42—28no—
1481C42—24no—
1482C42—22no—
1483C42—22no—
1484C42—22no—
1485C42—22no—
1486C42—24no—
1487C42—24no—
1488C42—24no—
1489C42—42no—
1490C42—42no—
1491C42—44no—
1492C42—44no—
1493C42—44no—
1494C42—42no—
1495C42—42no—
1496C42—42no—
1497C42—42no—
1498C42—42no—
1499C42—42no—
1500C42—42no—
1501C42—44no—
1502C42—44no—
1503C42—44no—
1504C42C2×#4118yes—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—22no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—22no—
1514C23—21no—
1515C23—22no—
1516C23—22no—
1517C23—22no—
1518C23—22no—
1519C23—21no—
1520C23—21no—
1521C23—21no—
1522C23—22no—
1523C23—21no—
1524C23—22no—
1525C23—21no—
1526C23—22no—
1527C23—22no—
1528C23—21no—
1529C23—21no—
1530C23—22no—
1531C23—22no—
1532C23—21no—
1533C23—21no—
1534C23—22no—
1535C23—44no—
1536C23—44no—
1537C23—44no—
1538C23—44no—
1539C23—82no—
1540C23—82no—
1541C23—82no—
1542C23C22×#4114yes—
1543C23C22×#4112yes—
1544C23C22×#4112yes—
1545C23C2×H(5,𝔽2)12yes—
1546C23#58512yes—
1547C23C2611yescharacteristic
1548Q8—28no—
1549Q8—48no—
1550Q8—48no—
1551Q8—44no—
1552D4—216no—
1553D4—28no—
1554D4—48no—
1555D4—48no—
1556D4—44no—
1557D4—84no—
1558D4—84no—
1559D4—84no—
1560D4—84no—
1561D4—84no—
1562C2×C4—22no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—216no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—24no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—24no—
1600C2×C4—24no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—24no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—24no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—24no—
1621C2×C4—24no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—24no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—24no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—48no—
1644C2×C4—44no—
1645C2×C4—44no—
1646C2×C4—48no—
1647C2×C4—44no—
1648C2×C4—44no—
1649C2×C4—44no—
1650C2×C4—44no—
1651C2×C4—48no—
1652C2×C4—88no—
1653C2×C4—84no—
1654C2×C4—84no—
1655C2×C4—82no—
1656C2×C4—82no—
1657C2×C4—84no—
1658C2×C4—82no—
1659C2×C4—84no—
1660C2×C4—84no—
1661C2×C4—84no—
1662C2×C4—164no—
1663C2×C4—164no—
1664C2×C4#553116yes—
1665C2×C4C22×#4114yes—
1666C2×C4C22×#4114yes—
1667C2×C4C22×#4114yes—
1668C2×C4C22×#4112yes—
1669C2×C4C22×#4112yes—
1670C2×C4C22×#4112yes—
1671C2×C4C22×#4112yes—
1672C2×C4C2×H(5,𝔽2)12yes—
1673C2×C4C2×H(5,𝔽2)12yes—
1674C2×C4#58512yes—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—22no—
1679C22—22no—
1680C22—22no—
1681C22—22no—
1682C22—24no—
1683C22—24no—
1684C22—22no—
1685C22—22no—
1686C22—24no—
1687C22—41no—
1688C22—42no—
1689C22—41no—
1690C22—42no—
1691C22—42no—
1692C22—42no—
1693C22—41no—
1694C22—41no—
1695C22—42no—
1696C22—41no—
1697C22—41no—
1698C22—42no—
1699C22—42no—
1700C22—41no—
1701C22—42no—
1702C22—41no—
1703C22—42no—
1704C22—41no—
1705C22—42no—
1706C22—41no—
1707C22—41no—
1708C22—42no—
1709C22—88no—
1710C22C2×#55314yes—
1711C22C23×#4111yescharacteristic
1712C22C23×#4111yescharacteristic
1713C22C22×H(5,𝔽2)11yescharacteristic
1714C22C2×#58511yescharacteristic
1715C22C2×#58511yescharacteristic
1716C222−1+611yescharacteristic
1717C222−1+611yescharacteristic
1718C4—24no—
1719C4—24no—
1720C4—22no—
1721C4—24no—
1722C4—42no—
1723C4—41no—
1724C4—41no—
1725C4—42no—
1726C4—42no—
1727C4—41no—
1728C4—41no—
1729C4—42no—
1730C4—42no—
1731C4—44no—
1732C4—42no—
1733C4—41no—
1734C4—41no—
1735C4—41no—
1736C4—44no—
1737C4—44no—
1738C4—42no—
1739C4—42no—
1740C4—42no—
1741C4—42no—
1742C4—41no—
1743C4—41no—
1744C4—42no—
1745C4—44no—
1746C4C2×#55314yes—
1747C4C2×#55314yes—
1748C2—24no—
1749C2—44no—
1750C2—42no—
1751C2—82no—
1752C2—81no—
1753C2C22×#55311yescharacteristic
1754C2#6281011yescharacteristic
1755C2#6286111yescharacteristic
1756C2#6295411yescharacteristic
1757C2#6295411yescharacteristic
1758C2#6299311yescharacteristic
1759C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34743C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59859C2semidirect
2. #59855C2semidirect
3. #59768C2semidirect
4. #59440C2semidirect
5. #59388C2semidirect
6. #59387C2semidirect
7. #45397C2semidirect
8. #45371C2semidirect
9. #45162C2semidirect
10. #45161C2semidirect
11. #43709C2semidirect
12. #43308C2semidirect
13. #39286C2semidirect
14. #39285C2semidirect
15. #39284C2semidirect
16. #39283C2semidirect
17. #39149C2semidirect
18. #39142C2semidirect
19. #36513C2semidirect
20. #36449C2semidirect
21. #35633C2semidirect
22. #35627C2semidirect
23. #35621C2semidirect
24. #35516C2semidirect
25. #35313C2semidirect
26. #35306C2semidirect
27. #35267C2semidirect
29. C2×#2421C2semidirect
30. #34266C2semidirect
31. #34250C2semidirect
32. #34208C2semidirect
33. #34202C2semidirect
34. #34109C2semidirect
35. C4×#536C2semidirect
48. #2863C22semidirect
49. #2863C22semidirect
50. #2863C22semidirect
51. #2860C22semidirect
54. #2802C22semidirect
58. #2793C22semidirect
59. #2787C22semidirect
60. #2782C22semidirect
61. #2781C22semidirect
62. #2779C22semidirect
66. #2776C22semidirect
67. #2776C22semidirect
69. #2772C22semidirect
70. #2766C22semidirect
72. #2750C22semidirect
73. #2747C22semidirect
78. #2645C22semidirect
79. #2645C22semidirect
80. #2645C22semidirect
81. #2644C22semidirect
84. #2608C22semidirect
91. #2590C22semidirect
92. #2587C22semidirect
93. #2585C22semidirect
96. #2578C22semidirect
97. #2577C22semidirect
98. #2576C22semidirect
99. #2573C22semidirect
100. #2571C22semidirect
101. #2571C22semidirect
102. #2570C22semidirect
103. #2570C22semidirect
104. #2570C22semidirect
105. #2569C22semidirect
107. #2547C22semidirect
108. #2546C22semidirect
109. #2545C22semidirect
110. #2544C22semidirect
112. #2530C22semidirect
113. #2530C22semidirect
114. #2529C22semidirect
115. #2525C22semidirect
118. #2514C22semidirect
119. #2514C22semidirect
120. #2511C22semidirect
121. #2511C22semidirect
124. #2510C22semidirect
125. #2509C22semidirect
126. #2509C22semidirect
127. #2509C22semidirect
128. #2508C22semidirect
129. #2508C22semidirect
133. #2497C22semidirect
134. #2496C22semidirect
135. #2495C22semidirect
136. #2495C22semidirect
138. #2494C22semidirect
148. #2481C22semidirect
188. #2417C22semidirect
189. #2417C22semidirect
194. #2415C22semidirect
195. #2415C22semidirect
203. #2373C22semidirect
204. #2367C22semidirect
205. #2367C22semidirect
206. #2365C22semidirect
207. #2365C22semidirect
210. #2362C22semidirect
211. #2362C22semidirect
212. #2360C22semidirect
213. #2360C22semidirect
220. #2352C22semidirect
221. #2352C22semidirect
222. #2352C22semidirect
223. #2352C22semidirect
224. #2351C22semidirect
225. Q8×C4⋊C4C22semidirect
227. #2349C22semidirect
230. D4×C4⋊C4C22semidirect
237. #2345C22semidirect
244. #2328C22semidirect
245. #2327C22semidirect
246. #2327C22semidirect
247. #2326C22semidirect
250. #2323C22semidirect
251. #2323C22semidirect
257. #2317C22semidirect
260. #2316C22semidirect
266. C4×C4⋊Q8C22semidirect
267. C4×#124C22semidirect
268. C4×#124C22semidirect
269. C4×#124C22semidirect
271. C4×C22⋊Q8C22semidirect
272. C4×C22⋊Q8C22semidirect
284. #2296C22semidirect
287. C2×#389C22semidirect

Maximal subgroups

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

subgroupindex
#598592
#598552
#597682
#594402
#593882
#593872
#453972
#453712
#451622
#451612
#437092
#433082
#392862
#392852
#392842
#392832
#391492
#391422
#365132
#364492
#356332
#356272
#356212
#355162
#353132
#353062
#352672
#347432
C2×#24212
#342662
#342502
#342082
#342022
#341092
C4×#5362