Finite Group Databasebeta

← #7644403

Subgroups — #7644403

Order 512.

4918 conjugacy classes of subgroups.

The subgroup lattice has 1770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42949C212yesmaximal, complemented
2#42947C212yesmaximal, complemented
3#42946C212yesmaximal, complemented
4#42925C212yesmaximal, complemented
5#42465C212yesmaximal, complemented
6#42464C212yesmaximal, complemented
7#42453C212yesmaximal, complemented
8#42450C212yesmaximal, complemented
9#41974C214yesmaximal, complemented
10#41964C214yesmaximal, complemented
11#40539C214yesmaximal, complemented
12#40538C214yesmaximal, complemented
13#37524C212yesmaximal, complemented
14#37523C212yesmaximal, complemented
15#37521C212yesmaximal, complemented
16#37520C212yesmaximal, complemented
17#37430C212yesmaximal, complemented
18#37326C212yesmaximal, complemented
19#37318C212yesmaximal, complemented
20#37315C212yesmaximal, complemented
21#35585C211yesmaximal, characteristic, complemented
22#35575C211yesmaximal, characteristic, complemented
23#35558C211yesmaximal, characteristic, complemented
24#35545C211yesmaximal, characteristic, complemented
25#35543C211yesmaximal, characteristic, complemented
26#35541C211yesmaximal, characteristic, complemented
27#35531C211yesmaximal, characteristic, complemented
28#35529C211yesmaximal, characteristic, complemented
29#35253C211yesmaximal, characteristic, complemented
30#35252C211yesmaximal, characteristic
31#34635C211yesmaximal, characteristic, complemented
32C2×#2624C211yesmaximal, characteristic, complemented
33#34204C211yesmaximal, characteristic, complemented
34#34202C211yesmaximal, characteristic, complemented
35#34052C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#535C2211yescharacteristic
38C2×#525C2211yescharacteristic
39C22×#121C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#518C2211yescharacteristic
42C22×#117C2211yescharacteristic
43C22×#117C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2857C2212yescomplemented
46#2856C2212yes—
47#2851C2212yescomplemented
48#2850C2212yes—
49#2838C2214yescomplemented
50#2837C2214yescomplemented
51#2837C2214yescomplemented
52#2836C2214yescomplemented
53#2827C2214yescomplemented
54#2827C2214yescomplemented
55#2826C2214yescomplemented
56#2824C2214yescomplemented
57#2808C2214yescomplemented
58#2807C2214yescomplemented
59#2798C2214yescomplemented
60#2796C2214yescomplemented
61#2796C2214yescomplemented
62#2796C2214yescomplemented
63#2787C2214yescomplemented
64#2786C2214yescomplemented
65#2783C2214yescomplemented
66#2782C2214yescomplemented
67#2777C2214yescomplemented
68#2773C2214yescomplemented
69#2771C2214yescomplemented
70#2757C2214yescomplemented
71#2750C2214yescomplemented
72#2746C2214yescomplemented
73#2732C2214yescomplemented
74#2728C2214yescomplemented
75#2727C2214yescomplemented
76#2724C2214yescomplemented
77#2723C2214yescomplemented
78#2711C2214yescomplemented
79#2711C2214yescomplemented
80#2708C2214yescomplemented
81#2708C2214yescomplemented
82#2694C2214yescomplemented
83#2694C2214yescomplemented
84#2691C2214yescomplemented
85#2691C2214yescomplemented
86#2689C2214yescomplemented
87#2681C2214yescomplemented
88#2681C2214yescomplemented
89#2667C2214yescomplemented
90#2664C2214yescomplemented
91#2663C2214yescomplemented
92#2663C2214yescomplemented
93#2654C2214yescomplemented
94#2653C2214yescomplemented
95#2652C2214yescomplemented
96#2649C2214yescomplemented
97#2649C2214yescomplemented
98#2649C2214yescomplemented
99#2638C2214yescomplemented
100#2636C2214yescomplemented
101#2636C2214yescomplemented
102#2633C2214yescomplemented
103#2630C2214yescomplemented
104#2630C2214yescomplemented
105#2629C2212yescomplemented
106#2628C2212yescomplemented
107#2625C2211yescharacteristic, complemented
108#2625C2211yescharacteristic, complemented
109#2625C2211yescharacteristic, complemented
110#2625C2211yescharacteristic, complemented
111#2624C2212yes—
112#2624C2212yes—
113#2624C2212yes—
114#2624C2212yes—
115#2624C2212yes—
116#2624C2212yes—
117#2624C2212yes—
118#2624C2212yes—
119#2624C2211yescharacteristic, complemented
120#2624C2211yescharacteristic, complemented
121#2624C2211yescharacteristic, complemented
122#2624C2211yescharacteristic, complemented
123#2623C2212yes—
124#2623C2212yes—
125#2622C2212yes—
126#2622C2212yes—
127#2620C2212yes—
128#2619C2212yes—
129#2573C2214yescomplemented
130#2571C2212yescomplemented
131#2570C2212yescomplemented
132#2570C2212yescomplemented
133#2569C2214yes—
134#2566C2212yescomplemented
135#2566C2212yescomplemented
136#2564C2214yes—
137#2563C2212yescomplemented
138#2556C2214yescomplemented
139#2553C2214yescomplemented
140#2553C2214yescomplemented
141#2552C2212yescomplemented
142#2542C2212yescomplemented
143#2514C2212yescomplemented
144#2513C2212yescomplemented
145#2513C2212yescomplemented
146#2513C2212yescomplemented
147#2513C2212yescomplemented
148#2513C2212yescomplemented
149#2512C2212yescomplemented
150#2512C2212yescomplemented
151#2512C2212yescomplemented
152#2512C2212yescomplemented
153#2512C2212yescomplemented
154#2511C2212yescomplemented
155#2510C2214yes—
156#2509C2212yescomplemented
157#2509C2212yescomplemented
158#2509C2212yescomplemented
159#2508C2212yescomplemented
160#2508C2212yescomplemented
161#2508C2212yescomplemented
162#2507C2212yescomplemented
163#2507C2212yescomplemented
164#2507C2212yescomplemented
165#2506C2212yescomplemented
166#2506C2212yescomplemented
167#2506C2212yescomplemented
168#2505C2214yes—
169#2504C2212yescomplemented
170#2501C2212yescomplemented
171#2500C2212yescomplemented
172#2500C2212yescomplemented
173#2497C2212yescomplemented
174#2496C2212yescomplemented
175#2495C2212yescomplemented
176#2494C2212yescomplemented
177#2481C2214yes—
178#2480C2214yes—
179#2480C2214yes—
180#2473C2214yes—
181#2466C2214yescomplemented
182#2463C2214yescomplemented
183#2460C2214yescomplemented
184#2455C2214yescomplemented
185#2454C2212yescomplemented
186#2454C2212yescomplemented
187#2454C2212yescomplemented
188#2453C2212yescomplemented
189#2452C2212yescomplemented
190#2452C2212yescomplemented
191#2452C2212yescomplemented
192#2451C2212yescomplemented
193#2448C2212yescomplemented
194#2448C2212yescomplemented
195#2447C2212yescomplemented
196#2447C2212yescomplemented
197#2445C2212yescomplemented
198#2445C2212yescomplemented
199#2445C2212yescomplemented
200#2445C2212yescomplemented
201#2442C2214yes—
202#2442C2212yescomplemented
203#2442C2212yescomplemented
204#2441C2212yescomplemented
205#2441C2212yescomplemented
206#2440C2212yescomplemented
207#2440C2212yescomplemented
208#2439C2212yescomplemented
209#2439C2212yescomplemented
210#2438C2214yes—
211#2437C2214yes—
212#2437C2214yes—
213#2437C2214yes—
214#2422C2212yescomplemented
215#2422C2212yescomplemented
216#2420C2212yescomplemented
217#2420C2212yescomplemented
218#2418C2214yes—
219#2418C2214yes—
220#2417C2214yes—
221#2416C2212yes—
222#2416C2212yes—
223#2414C2212yes—
224#2414C2212yes—
225#2412C2214yes—
226#2412C2214yes—
227#2411C2214yes—
228#2410C2214yes—
229#2395C2212yescomplemented
230#2395C2212yescomplemented
231#2395C2212yescomplemented
232#2395C2212yescomplemented
233C2×#399C2212yes—
234C2×#397C2212yes—
235C2×#394C2212yes—
236C2×#394C2212yes—
237#2363C2212yes—
238#2363C2212yes—
239#2361C2212yes—
240#2361C2212yes—
241#2359C2214yes—
242#2358C2214yes—
243#2354C2212yescomplemented
244#2352C2212yescomplemented
245#2352C2212yescomplemented
246D4×C4⋊C4C2212yescomplemented
247#2342C2214yes—
248D4×C22⋊C4C2214yes—
249#2324C2212yes—
250#2324C2212yes—
251#2324C2212yescomplemented
252#2323C2212yescomplemented
253#2317C2211yescharacteristic
254#2317C2211yescharacteristic
255#2317C2211yescharacteristic
256#2317C2211yescharacteristic
257#2317C2211yescharacteristic, complemented
258#2317C2211yescharacteristic, complemented
259#2317C2211yescharacteristic, complemented
260#2317C2211yescharacteristic, complemented
261#2317C2211yescharacteristic, complemented
262#2317C2211yescharacteristic, complemented
263#2317C2211yescharacteristic, complemented
264#2317C2211yescharacteristic, complemented
265#2316C2211yescharacteristic
266#2316C2211yescharacteristic
267#2316C2212yes—
268#2316C2212yes—
269#2315C2212yes—
270#2315C2212yes—
271#2311C2211yescharacteristic
272#2311C2211yescharacteristic
273#2309C2211yescharacteristic
274#2309C2211yescharacteristic
275C4×C22⋊Q8C2212yescomplemented
276C4×#121C2212yes—
277C4×#121C2212yes—
278C4×#121C2212yescomplemented
279#2297C2211yescharacteristic
280#2297C2211yescharacteristic
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283#2296C2212yescomplemented
284#2296C2212yescomplemented
285#2296C2212yescomplemented
286#2296C2212yescomplemented
287C2×#390C2211yescharacteristic
288C2×#390C2211yescharacteristic
289C2×#389C2211yescharacteristic
290C2×#389C2211yescharacteristic
291#2285C2211yescharacteristic
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic
294#2285C2211yescharacteristic
295#2280C2211yescharacteristic
296C2×#380C2211yescharacteristic
297#2274C2211yescharacteristic
298#2274C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C23×D4C2312yes—
302C24×C4C2311yescharacteristic
303#544—44no—
304#535—44no—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×#127C2312yes—
308C2×#126C2314yes—
309C2×#126C2314yes—
310C2×#126C2314yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#124C2312yes—
316#525—28no—
317C2×#123C2312yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×#121—28no—
330C2×#121C2312yes—
331C2×#121C2311yescharacteristic
332C2×#121C2312yes—
333C2×#121C2312yes—
334C2×#121C2311yescharacteristic
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#120C2312yes—
341C2×#120C2314yes—
342#520—44no—
343#518—44no—
344C2×C4×Q8C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×#117—28no—
357C2×#117—44no—
358C2×#117—44no—
359C2×#117C2311yescharacteristic
360C2×#117C2311yescharacteristic
361C2×#117C2311yescharacteristic
362C2×#117C2311yescharacteristic
363C2×#117C2311yescharacteristic
364C2×#117C2311yescharacteristic
365C2×#117C2311yescharacteristic
366C2×#117C2311yescharacteristic
367C2×#117C2311yescharacteristic
368C2×#117C2311yescharacteristic
369C2×#117C2311yescharacteristic
370C2×#117C2311yescharacteristic
371C2×#117C2311yescharacteristic
372C2×#117C2311yescharacteristic
373C2×#117C2311yescharacteristic
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C22×C4⋊C4C2311yescharacteristic
384C22×C4⋊C4C2311yescharacteristic
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2311yescharacteristic
387C22×C4⋊C4C2311yescharacteristic
388C22×C4⋊C4C2311yescharacteristic
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2312yes—
395C22×C22⋊C4C2311yescharacteristic
396C22×C22⋊C4C2311yescharacteristic
397C22×C22⋊C4C2312yes—
398C22×C22⋊C4C2312yes—
399C22×C22⋊C4C2312yes—
400C22×C22⋊C4C2314yes—
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2312yes—
403C22×C22⋊C4C2312yes—
404C22×C22⋊C4C2312yes—
405C22×C22⋊C4C2312yes—
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2312yes—
409C22×C42C2312yes—
410#401C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2312yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2312yes—
426#400C2312yes—
427#400C2312yes—
428#399C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#399C2312yes—
434#399C2314yes—
435#399C2314yes—
436#399C2312yes—
437#399C2312yes—
438#399C2312yes—
439#399C2314yes—
440#399C2314yes—
441#399C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2312yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2312yes—
456#398C2312yes—
457#398C2312yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2312yes—
463#397C2312yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2312yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2312yes—
478#397C2312yes—
479#397C2312yes—
480#397C2312yes—
481#397C2312yes—
482#397C2312yes—
483#397C2312yes—
484#397C2312yes—
485#397C2312yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#395C2314yes—
503#395C2314yes—
504#394C2312yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2312yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2312yes—
521#394C2312yes—
522#394C2312yes—
523#394C2312yes—
524#394C2312yes—
525#394C2312yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2314yes—
536#392C2314yes—
537#392C2314yes—
538#391C2312yes—
539#391C2312yes—
540#391C2314yes—
541#391C2311yescharacteristic
542#391C2311yescharacteristic
543#391C2311yescharacteristic
544#391C2311yescharacteristic
545#391C2314yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2312yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2314yes—
559#390C2314yes—
560#390C2314yes—
561#390C2314yes—
562#390C2314yes—
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2312yes—
567#390C2312yes—
568#390C2312yes—
569#390C2311yescharacteristic
570#390C2311yescharacteristic
571#390C2311yescharacteristic
572#390C2311yescharacteristic
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2312yes—
608#389C2314yes—
609#389C2314yes—
610#389C2312yes—
611#389C2312yes—
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2311yescharacteristic
617#389C2311yescharacteristic
618#389C2311yescharacteristic
619#389C2311yescharacteristic
620#389C2311yescharacteristic
621#389C2311yescharacteristic
622#389C2311yescharacteristic
623#389C2311yescharacteristic
624#389C2314yes—
625#389C2314yes—
626#389C2314yes—
627#389C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#386C2312yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2312yes—
693#385C2312yes—
694#385C2314yes—
695#385C2312yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#385C2312yes—
703#385C2312yes—
704#385C2312yes—
705#385C2312yes—
706#385C2312yes—
707#385C2312yes—
708#385C2312yes—
709#385C2312yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2312yes—
720#385C2312yes—
721#385C2312yes—
722#385C2314yes—
723#385C2314yes—
724#384C2311yescharacteristic
725#384C2312yes—
726#384C2311yescharacteristic
727#384C2312yes—
728#384C2312yes—
729#384C2312yes—
730#384C2311yescharacteristic
731#384C2311yescharacteristic
732#384C2311yescharacteristic
733#384C2311yescharacteristic
734#384C2311yescharacteristic
735#384C2311yescharacteristic
736#383C2314yes—
737#382C2311yescharacteristic
738#382C2312yes—
739#382C2311yescharacteristic
740#382C2312yes—
741#382C2311yescharacteristic
742#382C2311yescharacteristic
743#382C2314yes—
744#382C2312yes—
745#382C2312yes—
746#382C2311yescharacteristic
747#382C2311yescharacteristic
748#382C2311yescharacteristic
749#382C2311yescharacteristic
750#382C2314yes—
751#381C2314yes—
752#381C2312yes—
753#381C2314yes—
754#380C2314yes—
755#380C2314yes—
756#380C2312yes—
757#380C2314yes—
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2314yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2311yescharacteristic
772#380C2311yescharacteristic
773#380C2314yes—
774#380C2312yes—
775#380C2312yes—
776#380C2312yes—
777#380C2311yescharacteristic
778#380C2311yescharacteristic
779#380C2314yes—
780#379C2314yes—
781#379C2314yes—
782#379C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2314yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2312yes—
802C4×C4⋊C4C2312yes—
803C4×C4⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2314yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C2×#95C2312yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C25C2412yes—
820C25C2411yescharacteristic
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C22×Q8C2411yescharacteristic
825C22×Q8C2414yes—
826C22×D4—28no—
827C22×D4—24no—
828C22×D4—24no—
829C22×D4—24no—
830C22×D4—82no—
831C22×D4—82no—
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2412yes—
835C22×D4C2411yescharacteristic
836C22×D4C2412yes—
837C22×D4C2414yes—
838C22×D4C2412yes—
839C22×D4C2414yes—
840C22×D4C2414yes—
841C22×D4C2414yes—
842C23×C4—24no—
843C23×C4—24no—
844C23×C4#4118yes—
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2411yescharacteristic
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868#127—44no—
869#126—84no—
870#126—84no—
871#126—84no—
872#125—44no—
873#125—44no—
874#125—84no—
875#125—84no—
876#124—44no—
877#123—28no—
878#123—84no—
879#123—84no—
880#123—84no—
881#123—84no—
882C22⋊Q8—24no—
883C22⋊Q8—24no—
884C22⋊Q8—48no—
885C22⋊Q8—84no—
886C22⋊Q8—84no—
887C22⋊Q8—84no—
888C22⋊Q8—84no—
889#121—28no—
890#121—28no—
891#121—28no—
892#121—28no—
893#121—24no—
894#121—24no—
895#121—44no—
896#121—44no—
897#121—84no—
898#121—84no—
899#120—28no—
900#120—48no—
901C4×Q8—44no—
902C4×D4—28no—
903C4×D4—28no—
904C4×D4—44no—
905C4×D4—44no—
906C4×D4—44no—
907C4×D4—44no—
908C4×D4—44no—
909C4×D4—48no—
910C4×D4—84no—
911C4×D4—84no—
912C4×D4—84no—
913#117—24no—
914#117—24no—
915#117—24no—
916#117—24no—
917#117—24no—
918#117—24no—
919#117—24no—
920#117—24no—
921#117—24no—
922#117—24no—
923#117—24no—
924#117—24no—
925#117—24no—
926#117—24no—
927#117—24no—
928#117—44no—
929#117—44no—
930#117—44no—
931#117—44no—
932#117—42no—
933#117—42no—
934#117—42no—
935#117—42no—
936#117—44no—
937C2×C4⋊C4—24no—
938C2×C4⋊C4—24no—
939C2×C4⋊C4—24no—
940C2×C4⋊C4—24no—
941C2×C4⋊C4—24no—
942C2×C4⋊C4—42no—
943C2×C4⋊C4—42no—
944C2×C4⋊C4—42no—
945C2×C4⋊C4—42no—
946C2×C4⋊C4—44no—
947C2×C4⋊C4—82no—
948C2×C4⋊C4—82no—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C22⋊C4—24no—
1028C2×C22⋊C4—24no—
1029C2×C22⋊C4—28no—
1030C2×C22⋊C4—44no—
1031C2×C22⋊C4—44no—
1032C2×C22⋊C4—48no—
1033C2×C22⋊C4—82no—
1034C2×C22⋊C4—82no—
1035C2×C22⋊C4—82no—
1036C2×C22⋊C4—82no—
1037C2×C22⋊C4—82no—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2411yescharacteristic
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C42—24no—
1103C2×C42—24no—
1104C2×C42—44no—
1105C2×C42—44no—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2414yes—
1126C2×C42C2414yes—
1127C2×C42C2414yes—
1128C2×C42C2414yes—
1129C2×C42C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
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#95C2412yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192C24—22no—
1193C24—22no—
1194C24—24no—
1195C24—24no—
1196C24—24no—
1197C24—41no—
1198C24—41no—
1199C24—41no—
1200C24—41no—
1201C24—42no—
1202C24—42no—
1203C24—42no—
1204C24—42no—
1205C24C2×#4114yes—
1206C24C2514yes—
1207C24C2512yes—
1208C24C2511yescharacteristic
1209C24C2511yescharacteristic
1210C24C2511yescharacteristic
1211#41—416no—
1212C2×Q8—22no—
1213C2×Q8—22no—
1214C2×Q8—22no—
1215C2×Q8—44no—
1216C2×Q8—44no—
1217C2×Q8—44no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—28no—
1221C2×D4—24no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—28no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—22no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—42no—
1235C2×D4—44no—
1236C2×D4—44no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—44no—
1248C2×D4—416no—
1249C2×D4—816no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—232no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—24no—
1271C22×C4—42no—
1272C22×C4—42no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—42no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—42no—
1281C22×C4—42no—
1282C22×C4—42no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—42no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—44no—
1298C22×C4—44no—
1299C22×C4—44no—
1300C22×C4—44no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4C2×#4114yes—
1307C22×C4C2×#4114yes—
1308C22×C4C2×#4114yes—
1309C22×C4C2×#4114yes—
1310C22×C4C2×#4114yes—
1311C22×C4C2×#4114yes—
1312C22×C4H(5,𝔽2)14yes—
1313C22×C42−1+414yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2511yescharacteristic
1320C22×C4C2511yescharacteristic
1321C22×C4C2511yescharacteristic
1322C22×C4C2514yes—
1323C22×C4C2514yes—
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2511yescharacteristic
1333C22×C4C2511yescharacteristic
1334C22×C4C2511yescharacteristic
1335C22×C4C2511yescharacteristic
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2514yes—
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C22×C4C2511yescharacteristic
1343C22×C4C2511yescharacteristic
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—22no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—44no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C22⋊C4—22no—
1423C22⋊C4—22no—
1424C22⋊C4—22no—
1425C22⋊C4—22no—
1426C22⋊C4—22no—
1427C22⋊C4—22no—
1428C22⋊C4—22no—
1429C22⋊C4—22no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—24no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—24no—
1439C22⋊C4—28no—
1440C22⋊C4—28no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—42no—
1446C22⋊C4—42no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—42no—
1464C22⋊C4—44no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—44no—
1472C22⋊C4—44no—
1473C22⋊C4—44no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—44no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—42no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—42no—
1486C42—22no—
1487C42—22no—
1488C42—22no—
1489C42—22no—
1490C42—22no—
1491C42—22no—
1492C42—22no—
1493C42—22no—
1494C42—24no—
1495C42—24no—
1496C42—24no—
1497C42—24no—
1498C42—24no—
1499C42—24no—
1500C42—24no—
1501C42—42no—
1502C42—42no—
1503C42—42no—
1504C42—42no—
1505C42—44no—
1506C42—44no—
1507C42—44no—
1508C42—44no—
1509C42—44no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—21no—
1519C23—21no—
1520C23—21no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—21no—
1525C23—21no—
1526C23—28no—
1527C23—22no—
1528C23—24no—
1529C23—24no—
1530C23—22no—
1531C23—22no—
1532C23—24no—
1533C23—24no—
1534C23—22no—
1535C23—22no—
1536C23—22no—
1537C23—24no—
1538C23—24no—
1539C23—24no—
1540C23—22no—
1541C23—44no—
1542C23—44no—
1543C23—48no—
1544C23—82no—
1545C23—82no—
1546C23—82no—
1547C23—82no—
1548C23—84no—
1549C23—84no—
1550C23—84no—
1551C23—84no—
1552C23—84no—
1553C23—84no—
1554C23C22×#4112yes—
1555C23C22×#4112yes—
1556C23C22×#4112yes—
1557C23C2×H(5,𝔽2)12yes—
1558C23C2×2−1+412yes—
1559C23C2611yescharacteristic
1560Q8—44no—
1561Q8—164no—
1562D4—48no—
1563D4—416no—
1564D4—48no—
1565D4—48no—
1566D4—48no—
1567D4—44no—
1568D4—84no—
1569D4—88no—
1570D4—164no—
1571D4—164no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—28no—
1577C2×C4—28no—
1578C2×C4—28no—
1579C2×C4—28no—
1580C2×C4—28no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—24no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—24no—
1618C2×C4—24no—
1619C2×C4—24no—
1620C2×C4—24no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—22no—
1631C2×C4—24no—
1632C2×C4—22no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—24no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—48no—
1660C2×C4—82no—
1661C2×C4—82no—
1662C2×C4—82no—
1663C2×C4—82no—
1664C2×C4—84no—
1665C2×C4—84no—
1666C2×C4—84no—
1667C2×C4—84no—
1668C2×C4—84no—
1669C2×C4—84no—
1670C2×C4—84no—
1671C2×C4—164no—
1672C2×C4—164no—
1673C2×C4—164no—
1674C2×C4#539116yes—
1675C2×C4C22×#4112yes—
1676C2×C4C22×#4112yes—
1677C2×C4C22×#4112yes—
1678C2×C4C22×#4112yes—
1679C2×C4C2×H(5,𝔽2)12yes—
1680C2×C4C2×H(5,𝔽2)12yes—
1681C2×C4C2×2−1+412yes—
1682C2×C4C2×2−1+412yes—
1683C22—22no—
1684C22—22no—
1685C22—22no—
1686C22—22no—
1687C22—22no—
1688C22—22no—
1689C22—22no—
1690C22—22no—
1691C22—22no—
1692C22—22no—
1693C22—22no—
1694C22—22no—
1695C22—41no—
1696C22—41no—
1697C22—41no—
1698C22—41no—
1699C22—41no—
1700C22—41no—
1701C22—41no—
1702C22—41no—
1703C22—44no—
1704C22—42no—
1705C22—42no—
1706C22—44no—
1707C22—44no—
1708C22—42no—
1709C22—42no—
1710C22—44no—
1711C22—42no—
1712C22—44no—
1713C22—42no—
1714C22—44no—
1715C22—42no—
1716C22—44no—
1717C22—88no—
1718C22—168no—
1719C22C2×#53914yes—
1720C22C23×#4111yescharacteristic
1721C22C22×H(5,𝔽2)11yescharacteristic
1722C22C22×2−1+411yescharacteristic
1723C22H(7,𝔽2)11yescharacteristic
1724C22H(7,𝔽2)11yescharacteristic
1725C22H(7,𝔽2)11yescharacteristic
1726C222−1+611yescharacteristic
1727C4—22no—
1728C4—22no—
1729C4—41no—
1730C4—41no—
1731C4—41no—
1732C4—41no—
1733C4—44no—
1734C4—42no—
1735C4—41no—
1736C4—41no—
1737C4—41no—
1738C4—41no—
1739C4—42no—
1740C4—42no—
1741C4—42no—
1742C4—42no—
1743C4—42no—
1744C4—42no—
1745C4—42no—
1746C4—42no—
1747C4—42no—
1748C4—44no—
1749C4—42no—
1750C4—42no—
1751C4—42no—
1752C4—42no—
1753C4—44no—
1754C4—42no—
1755C4C2×#53914yes—
1756C4C2×#53914yes—
1757C2—24no—
1758C2—42no—
1759C2—42no—
1760C2—82no—
1761C2—84no—
1762C2C22×#53911yescharacteristic
1763C2#6285511yescharacteristic
1764C2#6285611yescharacteristic
1765C2#6287811yescharacteristic
1766C2#6287911yescharacteristic
1767C2#6288011yescharacteristic
1768C2#6288111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35252C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42949C2semidirect
2. #42947C2semidirect
3. #42946C2semidirect
4. #42925C2semidirect
5. #42465C2semidirect
6. #42464C2semidirect
7. #42453C2semidirect
8. #42450C2semidirect
9. #41974C2semidirect
10. #41964C2semidirect
11. #40539C2semidirect
12. #40538C2semidirect
13. #37524C2semidirect
14. #37523C2semidirect
15. #37521C2semidirect
16. #37520C2semidirect
17. #37430C2semidirect
18. #37326C2semidirect
19. #37318C2semidirect
20. #37315C2semidirect
21. #35585C2semidirect
22. #35575C2semidirect
23. #35558C2semidirect
24. #35545C2semidirect
25. #35543C2semidirect
26. #35541C2semidirect
27. #35531C2semidirect
28. #35529C2semidirect
29. #35253C2semidirect
31. #34635C2semidirect
32. C2×#2624C2semidirect
33. #34204C2semidirect
34. #34202C2semidirect
35. #34052C2semidirect
45. #2857C22semidirect
47. #2851C22semidirect
49. #2838C22semidirect
50. #2837C22semidirect
51. #2837C22semidirect
52. #2836C22semidirect
53. #2827C22semidirect
54. #2827C22semidirect
55. #2826C22semidirect
56. #2824C22semidirect
57. #2808C22semidirect
58. #2807C22semidirect
59. #2798C22semidirect
60. #2796C22semidirect
61. #2796C22semidirect
62. #2796C22semidirect
63. #2787C22semidirect
64. #2786C22semidirect
65. #2783C22semidirect
66. #2782C22semidirect
67. #2777C22semidirect
68. #2773C22semidirect
69. #2771C22semidirect
70. #2757C22semidirect
71. #2750C22semidirect
72. #2746C22semidirect
73. #2732C22semidirect
74. #2728C22semidirect
75. #2727C22semidirect
76. #2724C22semidirect
77. #2723C22semidirect
78. #2711C22semidirect
79. #2711C22semidirect
80. #2708C22semidirect
81. #2708C22semidirect
82. #2694C22semidirect
83. #2694C22semidirect
84. #2691C22semidirect
85. #2691C22semidirect
86. #2689C22semidirect
87. #2681C22semidirect
88. #2681C22semidirect
89. #2667C22semidirect
90. #2664C22semidirect
91. #2663C22semidirect
92. #2663C22semidirect
93. #2654C22semidirect
94. #2653C22semidirect
95. #2652C22semidirect
96. #2649C22semidirect
97. #2649C22semidirect
98. #2649C22semidirect
99. #2638C22semidirect
100. #2636C22semidirect
101. #2636C22semidirect
102. #2633C22semidirect
103. #2630C22semidirect
104. #2630C22semidirect
105. #2629C22semidirect
106. #2628C22semidirect
107. #2625C22semidirect
108. #2625C22semidirect
109. #2625C22semidirect
110. #2625C22semidirect
119. #2624C22semidirect
120. #2624C22semidirect
121. #2624C22semidirect
122. #2624C22semidirect
129. #2573C22semidirect
130. #2571C22semidirect
131. #2570C22semidirect
132. #2570C22semidirect
134. #2566C22semidirect
135. #2566C22semidirect
137. #2563C22semidirect
138. #2556C22semidirect
139. #2553C22semidirect
140. #2553C22semidirect
141. #2552C22semidirect
142. #2542C22semidirect
143. #2514C22semidirect
144. #2513C22semidirect
145. #2513C22semidirect
146. #2513C22semidirect
147. #2513C22semidirect
148. #2513C22semidirect
149. #2512C22semidirect
150. #2512C22semidirect
151. #2512C22semidirect
152. #2512C22semidirect
153. #2512C22semidirect
154. #2511C22semidirect
156. #2509C22semidirect
157. #2509C22semidirect
158. #2509C22semidirect
159. #2508C22semidirect
160. #2508C22semidirect
161. #2508C22semidirect
162. #2507C22semidirect
163. #2507C22semidirect
164. #2507C22semidirect
165. #2506C22semidirect
166. #2506C22semidirect
167. #2506C22semidirect
169. #2504C22semidirect
170. #2501C22semidirect
171. #2500C22semidirect
172. #2500C22semidirect
173. #2497C22semidirect
174. #2496C22semidirect
175. #2495C22semidirect
176. #2494C22semidirect
181. #2466C22semidirect
182. #2463C22semidirect
183. #2460C22semidirect
184. #2455C22semidirect
185. #2454C22semidirect
186. #2454C22semidirect
187. #2454C22semidirect
188. #2453C22semidirect
189. #2452C22semidirect
190. #2452C22semidirect
191. #2452C22semidirect
192. #2451C22semidirect
193. #2448C22semidirect
194. #2448C22semidirect
195. #2447C22semidirect
196. #2447C22semidirect
197. #2445C22semidirect
198. #2445C22semidirect
199. #2445C22semidirect
200. #2445C22semidirect
202. #2442C22semidirect
203. #2442C22semidirect
204. #2441C22semidirect
205. #2441C22semidirect
206. #2440C22semidirect
207. #2440C22semidirect
208. #2439C22semidirect
209. #2439C22semidirect
214. #2422C22semidirect
215. #2422C22semidirect
216. #2420C22semidirect
217. #2420C22semidirect
229. #2395C22semidirect
230. #2395C22semidirect
231. #2395C22semidirect
232. #2395C22semidirect
243. #2354C22semidirect
244. #2352C22semidirect
245. #2352C22semidirect
246. D4×C4⋊C4C22semidirect
251. #2324C22semidirect
252. #2323C22semidirect
257. #2317C22semidirect
258. #2317C22semidirect
259. #2317C22semidirect
260. #2317C22semidirect
261. #2317C22semidirect
262. #2317C22semidirect
263. #2317C22semidirect
264. #2317C22semidirect
275. C4×C22⋊Q8C22semidirect
278. C4×#121C22semidirect
283. #2296C22semidirect
284. #2296C22semidirect
285. #2296C22semidirect
286. #2296C22semidirect

Maximal subgroups

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

subgroupindex
#429492
#429472
#429462
#429252
#424652
#424642
#424532
#424502
#419742
#419642
#405392
#405382
#375242
#375232
#375212
#375202
#374302
#373262
#373182
#373152
#355852
#355752
#355582
#355452
#355432
#355412
#355312
#355292
#352532
#352522
#346352
C2×#26242
#342042
#342022
#340522