Finite Group Databasebeta

← #7673915

Subgroups — #7673915

Order 512.

4966 conjugacy classes of subgroups.

The subgroup lattice has 1754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45345C212yesmaximal, complemented
2#45302C212yesmaximal, complemented
3#45226C212yesmaximal, complemented
4#45225C212yesmaximal, complemented
5#45225C212yesmaximal, complemented
6#45205C212yesmaximal, complemented
7#45076C212yesmaximal, complemented
8#45075C212yesmaximal, complemented
9#39274C212yesmaximal, complemented
10#39273C212yesmaximal, complemented
11#39271C212yesmaximal, complemented
12#39268C212yesmaximal, complemented
13#39267C214yesmaximal, complemented
14#39266C214yesmaximal, complemented
15#39203C212yesmaximal, complemented
16#39200C212yesmaximal, complemented
17#39199C214yesmaximal, complemented
18#39197C212yesmaximal, complemented
19#39196C212yesmaximal, complemented
20#39195C214yesmaximal, complemented
21#35644C211yesmaximal, characteristic, complemented
22#35634C211yesmaximal, characteristic
23#35542C211yesmaximal, characteristic, complemented
24#35516C211yesmaximal, characteristic, complemented
25#35312C211yesmaximal, characteristic, complemented
26#35307C211yesmaximal, characteristic, complemented
27#35182C211yesmaximal, characteristic, complemented
28#35158C211yesmaximal, characteristic, complemented
29#34635C211yesmaximal, characteristic, complemented
30#34272C211yesmaximal, characteristic, complemented
31#34271C211yesmaximal, characteristic, complemented
32#34267C211yesmaximal, characteristic, complemented
33#34266C211yesmaximal, characteristic, complemented
34#34065C211yesmaximal, characteristic, complemented
35C2×#2323C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#544C2211yescharacteristic
38C2×#537C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2211yescharacteristic
41C2×#525C2211yescharacteristic
42C2×#525C2211yescharacteristic
43C22×C22⋊Q8C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×#117C2211yescharacteristic
48#2862C2212yescomplemented
49#2861C2212yescomplemented
50#2855C2212yescomplemented
51#2855C2212yescomplemented
52#2853C2214yes—
53#2850C2214yes—
54#2808C2214yes—
55#2808C2214yes—
56#2807C2214yescomplemented
57#2807C2214yescomplemented
58#2803C2214yes—
59#2803C2214yes—
60#2798C2214yes—
61#2798C2214yes—
62#2798C2214yescomplemented
63#2798C2214yescomplemented
64#2798C2214yescomplemented
65#2797C2214yes—
66#2796C2214yes—
67#2796C2214yescomplemented
68#2794C2214yescomplemented
69#2794C2214yescomplemented
70#2773C2214yes—
71#2773C2214yes—
72#2773C2214yescomplemented
73#2773C2214yescomplemented
74#2773C2214yescomplemented
75#2771C2214yescomplemented
76#2771C2214yescomplemented
77#2754C2214yes—
78#2754C2214yes—
79#2754C2214yescomplemented
80#2754C2214yescomplemented
81#2752C2214yes—
82#2751C2214yes—
83#2751C2214yescomplemented
84#2712C2214yes—
85#2710C2214yes—
86#2642C2212yescomplemented
87#2640C2212yescomplemented
88#2639C2214yes—
89#2625C2211yescharacteristic
90#2625C2211yescharacteristic
91#2625C2211yescharacteristic
92#2625C2211yescharacteristic
93#2625C2212yescomplemented
94#2625C2212yescomplemented
95#2624C2211yescharacteristic
96#2624C2211yescharacteristic
97#2624C2211yescharacteristic
98#2624C2211yescharacteristic
99#2623C2214yes—
100#2623C2212yes—
101#2623C2212yes—
102#2622C2212yes—
103#2622C2212yes—
104#2607C2214yescomplemented
105#2602C2214yes—
106#2597C2214yes—
107#2597C2214yes—
108#2596C2214yes—
109#2596C2214yes—
110#2595C2214yes—
111#2595C2214yescomplemented
112#2593C2214yes—
113#2593C2214yes—
114#2592C2214yes—
115#2589C2214yescomplemented
116#2582C2214yescomplemented
117#2580C2214yescomplemented
118#2575C2214yescomplemented
119#2571C2214yescomplemented
120#2570C2214yescomplemented
121#2570C2214yescomplemented
122#2563C2212yes—
123#2562C2212yes—
124#2562C2212yes—
125#2561C2214yes—
126#2547C2212yes—
127#2542C2212yes—
128#2542C2212yes—
129#2542C2212yes—
130#2542C2212yes—
131#2540C2212yes—
132#2540C2212yes—
133#2540C2212yes—
134#2540C2212yes—
135#2539C2214yes—
136#2517C2214yescomplemented
137#2516C2214yes—
138#2516C2214yescomplemented
139#2513C2214yes—
140#2513C2214yes—
141#2513C2214yescomplemented
142#2511C2214yescomplemented
143#2511C2214yescomplemented
144#2503C2214yes—
145#2501C2214yes—
146#2492C2212yes—
147#2492C2212yes—
148#2492C2212yes—
149#2492C2212yes—
150#2492C2212yes—
151#2492C2212yescomplemented
152#2492C2212yescomplemented
153#2492C2212yescomplemented
154#2492C2212yescomplemented
155#2491C2212yes—
156#2491C2212yescomplemented
157#2491C2212yescomplemented
158#2490C2212yes—
159#2490C2212yescomplemented
160#2490C2212yescomplemented
161#2489C2212yes—
162#2489C2212yes—
163#2489C2212yes—
164#2489C2212yes—
165#2489C2212yes—
166#2489C2212yescomplemented
167#2489C2212yescomplemented
168#2489C2212yescomplemented
169#2489C2212yescomplemented
170#2488C2214yes—
171#2488C2214yes—
172#2488C2214yes—
173#2487C2212yes—
174#2486C2212yes—
175#2485C2212yes—
176#2485C2212yes—
177#2472C2214yes—
178#2459C2214yes—
179#2458C2214yes—
180#2458C2214yes—
181#2448C2214yes—
182#2448C2212yescomplemented
183#2448C2214yescomplemented
184#2448C2212yescomplemented
185#2447C2214yescomplemented
186#2447C2212yescomplemented
187#2447C2212yescomplemented
188#2446C2212yescomplemented
189#2446C2212yescomplemented
190#2446C2212yescomplemented
191#2446C2212yescomplemented
192#2423C2212yes—
193#2423C2212yescomplemented
194#2423C2212yescomplemented
195#2422C2212yes—
196#2421C2212yes—
197#2421C2212yescomplemented
198#2421C2212yescomplemented
199#2420C2212yes—
200#2419C2214yes—
201#2419C2214yes—
202#2419C2214yes—
203#2418C2214yes—
204#2395C2212yes—
205#2395C2212yes—
206#2395C2212yes—
207#2395C2212yes—
208#2370C2212yescomplemented
209#2370C2212yescomplemented
210#2370C2212yescomplemented
211#2370C2212yescomplemented
212#2370C2212yescomplemented
213#2370C2212yescomplemented
214#2369C2212yescomplemented
215#2369C2212yescomplemented
216#2369C2212yescomplemented
217#2368C2214yes—
218#2367C2212yescomplemented
219#2367C2212yescomplemented
220#2365C2212yescomplemented
221#2365C2212yescomplemented
222#2365C2212yescomplemented
223#2365C2212yescomplemented
224#2365C2212yescomplemented
225#2364C2214yes—
226#2363C2212yescomplemented
227#2362C2212yescomplemented
228#2362C2212yescomplemented
229#2362C2212yescomplemented
230#2361C2214yes—
231#2361C2212yescomplemented
232#2360C2214yes—
233#2360C2212yescomplemented
234#2360C2212yescomplemented
235#2360C2212yescomplemented
236#2331C2212yescomplemented
237#2330C2212yescomplemented
238#2329C2214yes—
239#2324C2211yescharacteristic
240#2324C2211yescharacteristic
241#2324C2211yescharacteristic
242#2324C2211yescharacteristic
243#2324C2212yescomplemented
244#2323C2212yes—
245#2323C2212yes—
246#2323C2212yes—
247#2323C2212yes—
248#2323C2212yes—
249#2323C2212yes—
250#2323C2212yes—
251#2323C2212yes—
252#2323C2211yescharacteristic
253#2323C2211yescharacteristic
254#2323C2211yescharacteristic
255#2323C2211yescharacteristic
256#2323C2212yescomplemented
257#2322C2212yes—
258#2322C2212yes—
259#2322C2214yes—
260#2321C2212yes—
261#2321C2212yes—
262#2317C2211yescharacteristic
263#2316C2211yescharacteristic
264#2311C2211yescharacteristic
265#2311C2211yescharacteristic
266#2311C2211yescharacteristic
267#2310C2211yescharacteristic
268#2310C2211yescharacteristic
269C4×C4⋊Q8C2212yescomplemented
270C4×#125C2212yescomplemented
271C4×C22⋊Q8C2214yes—
272C4×C22⋊Q8C2212yescomplemented
273C4×#123C2214yes—
274C4×#121C2212yescomplemented
275#2297C2211yescharacteristic
276#2297C2211yescharacteristic
277#2297C2211yescharacteristic
278#2296C2211yescharacteristic
279#2296C2211yescharacteristic
280#2296C2211yescharacteristic
281C2×#391C2211yescharacteristic
282#2293C2212yes—
283#2293C2212yes—
284C2×#389C2212yes—
285C2×#389C2211yescharacteristic
286#2290C2212yes—
287#2290C2212yes—
288C2×#388C2212yes—
289C2×#388C2212yes—
290C2×#387C2212yes—
291#2280C2211yescharacteristic
292#2280C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296#2274C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C23×Q8C2311yescharacteristic
302C24×C4C2311yescharacteristic
303#544—28no—
304#544—28no—
305#537—28no—
306#536—28no—
307#536—44no—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#124C2312yes—
319C2×#124C2312yes—
320C2×#124C2314yes—
321C2×#124C2314yes—
322#525—28no—
323#525—44no—
324C2×#123C2312yes—
325C2×#123C2314yes—
326C2×#123C2314yes—
327C2×#123C2312yes—
328C2×#123C2314yes—
329C2×C22⋊Q8—28no—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×#121C2311yescharacteristic
347C2×#121C2311yescharacteristic
348C2×#121C2312yes—
349C2×#121C2314yes—
350C2×#121C2312yes—
351C2×#121C2311yescharacteristic
352C2×#121C2311yescharacteristic
353C2×#120C2312yes—
354C2×#120C2312yes—
355#520—44no—
356C4×#41—44no—
357C2×C4×Q8—44no—
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2314yes—
366C2×C4×Q8C2314yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×#117—44no—
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2311yescharacteristic
382C2×#117C2311yescharacteristic
383C2×#117C2311yescharacteristic
384C2×#117C2311yescharacteristic
385C2×#117C2311yescharacteristic
386C2×#117C2311yescharacteristic
387C2×#117C2311yescharacteristic
388C2×#117C2311yescharacteristic
389C2×#117C2311yescharacteristic
390C2×#117C2311yescharacteristic
391C2×#117C2311yescharacteristic
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2311yescharacteristic
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2311yescharacteristic
399C22×C4⋊C4C2311yescharacteristic
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2311yescharacteristic
404C22×C22⋊C4C2312yes—
405C22×C22⋊C4C2311yescharacteristic
406C22×C22⋊C4C2311yescharacteristic
407C22×C22⋊C4C2312yes—
408C22×C42C2311yescharacteristic
409C22×C42C2311yescharacteristic
410C22×C42C2312yes—
411C22×C42C2312yes—
412C22×C42C2312yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2312yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2312yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2312yes—
431#400C2312yes—
432#400C2314yes—
433#400C2314yes—
434#399C2314yes—
435#399C2312yes—
436#399C2314yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2312yes—
441#399C2314yes—
442#399C2312yes—
443#399C2312yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#398C2312yes—
448#398C2312yes—
449#398C2314yes—
450#398C2314yes—
451#398C2312yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2312yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2314yes—
461#397C2312yes—
462#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2312yes—
466#397C2312yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2312yes—
472#397C2312yes—
473#397C2312yes—
474#397C2312yes—
475#397C2312yes—
476#397C2312yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2312yes—
488#394C2312yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2312yes—
493#394C2312yes—
494#394C2312yes—
495#394C2314yes—
496#394C2312yes—
497#394C2312yes—
498#394C2312yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#392C2314yes—
508#392C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#391C2312yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2311yescharacteristic
524#391C2311yescharacteristic
525#391C2312yes—
526#391C2312yes—
527#391C2311yescharacteristic
528#391C2314yes—
529#391C2314yes—
530#391C2314yes—
531#391C2314yes—
532#391C2314yes—
533#391C2314yes—
534#391C2314yes—
535#391C2314yes—
536#391C2314yes—
537#391C2314yes—
538#391C2311yescharacteristic
539#391C2311yescharacteristic
540#391C2314yes—
541#391C2311yescharacteristic
542#390C2314yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2311yescharacteristic
551#390C2311yescharacteristic
552#390C2311yescharacteristic
553#390C2314yes—
554#390C2314yes—
555#390C2314yes—
556#390C2314yes—
557#390C2314yes—
558#390C2314yes—
559#390C2314yes—
560#390C2311yescharacteristic
561#390C2311yescharacteristic
562#390C2311yescharacteristic
563#390C2314yes—
564#389C2311yescharacteristic
565#389C2312yes—
566#389C2311yescharacteristic
567#389C2314yes—
568#389C2312yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2312yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2314yes—
585#389C2314yes—
586#389C2314yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2311yescharacteristic
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2314yes—
595#389C2311yescharacteristic
596#389C2314yes—
597#389C2311yescharacteristic
598#389C2311yescharacteristic
599#389C2311yescharacteristic
600#389C2311yescharacteristic
601#389C2311yescharacteristic
602#389C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2312yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
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#388C2314yes—
652#388C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2312yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2312yes—
693#386C2312yes—
694#386C2312yes—
695#386C2312yes—
696#386C2312yes—
697#386C2312yes—
698#386C2312yes—
699#386C2314yes—
700#386C2314yes—
701#386C2312yes—
702#386C2314yes—
703#386C2312yes—
704#386C2312yes—
705#385C2314yes—
706#385C2312yes—
707#385C2312yes—
708#385C2312yes—
709#385C2312yes—
710#385C2312yes—
711#385C2312yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2312yes—
718#385C2314yes—
719#385C2312yes—
720#385C2314yes—
721#385C2312yes—
722#385C2312yes—
723#384C2312yes—
724#384C2314yes—
725#384C2314yes—
726#382C2312yes—
727#382C2314yes—
728#382C2314yes—
729#382C2314yes—
730#382C2314yes—
731#382C2314yes—
732#382C2314yes—
733#381C2314yes—
734#381C2314yes—
735#381C2314yes—
736#381C2312yes—
737#381C2314yes—
738#381C2314yes—
739#381C2312yes—
740#380C2312yes—
741#380C2311yescharacteristic
742#380C2311yescharacteristic
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2311yescharacteristic
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2314yes—
752#380C2312yes—
753#380C2312yes—
754#380C2311yescharacteristic
755#380C2311yescharacteristic
756#380C2311yescharacteristic
757#380C2311yescharacteristic
758#380C2311yescharacteristic
759#379C2312yes—
760#379C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2314yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815#376C2312yes—
816C2×#95C2312yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C2×#95C2312yes—
820C2×#95C2312yes—
821C43C2312yes—
822C25C2411yescharacteristic
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C2×#41—24no—
827C2×#41—24no—
828C2×#41—24no—
829C22×Q8—24no—
830C22×Q8—24no—
831C22×Q8—24no—
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2411yescharacteristic
836C22×Q8C2414yes—
837C22×Q8C2414yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2411yescharacteristic
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2414yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C23×C4—24no—
848C23×C4—24no—
849C23×C4—24no—
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C23×C4C2412yes—
860C23×C4C2411yescharacteristic
861C23×C4C2411yescharacteristic
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2414yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C4⋊Q8—28no—
870C4⋊Q8—28no—
871C4⋊Q8—28no—
872C4⋊Q8—28no—
873C4⋊Q8—28no—
874C4⋊Q8—44no—
875#125—28no—
876#125—28no—
877#125—28no—
878#125—28no—
879#124—28no—
880#124—44no—
881#124—84no—
882#124—84no—
883#123—28no—
884#123—216no—
885#123—44no—
886#123—48no—
887#123—84no—
888C22⋊Q8—216no—
889C22⋊Q8—28no—
890C22⋊Q8—28no—
891C22⋊Q8—28no—
892C22⋊Q8—28no—
893C22⋊Q8—24no—
894C22⋊Q8—24no—
895C22⋊Q8—28no—
896C22⋊Q8—28no—
897C22⋊Q8—28no—
898C22⋊Q8—28no—
899C22⋊Q8—216no—
900C22⋊Q8—42no—
901C22⋊Q8—42no—
902C22⋊Q8—44no—
903C22⋊Q8—44no—
904#121—216no—
905#121—24no—
906#121—24no—
907#121—28no—
908#121—28no—
909#121—42no—
910#121—42no—
911#120—28no—
912#120—44no—
913C4×Q8—44no—
914C4×Q8—44no—
915C4×Q8—44no—
916C4×Q8—44no—
917C4×Q8—42no—
918C4×Q8—42no—
919C4×Q8—44no—
920C4×Q8—84no—
921C4×Q8—84no—
922C4×D4—28no—
923C4×D4—28no—
924C4×D4—42no—
925C4×D4—42no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—48no—
932C4×D4—84no—
933#117—24no—
934#117—24no—
935#117—24no—
936#117—24no—
937#117—24no—
938#117—42no—
939#117—42no—
940#117—42no—
941#117—42no—
942#117—42no—
943#117—42no—
944#117—42no—
945#117—42no—
946#117—44no—
947#117—44no—
948#117#4118yes—
949C2×C4⋊C4—28no—
950C2×C4⋊C4—24no—
951C2×C4⋊C4—24no—
952C2×C4⋊C4—44no—
953C2×C4⋊C4—42no—
954C2×C4⋊C4—42no—
955C2×C4⋊C4—44no—
956C2×C4⋊C4—82no—
957C2×C4⋊C4#4118yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C22⋊C4—28no—
1025C2×C22⋊C4—42no—
1026C2×C22⋊C4—42no—
1027C2×C22⋊C4—82no—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C42—24no—
1090C2×C42—24no—
1091C2×C42—44no—
1092C2×C42—44no—
1093C2×C42—82no—
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2414yes—
1108C2×C42C2414yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2414yes—
1113C2×C42C2414yes—
1114C2×C42C2414yes—
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2414yes—
1124C2×C42C2412yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2412yes—
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#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195C24—22no—
1196C24—22no—
1197C24—22no—
1198C24—41no—
1199C24—41no—
1200C24—41no—
1201C24—41no—
1202C24C2511yescharacteristic
1203C24C2511yescharacteristic
1204C24C2512yes—
1205C24C2512yes—
1206C24C2511yescharacteristic
1207#41—416no—
1208#41—416no—
1209C2×Q8—24no—
1210C2×Q8—24no—
1211C2×Q8—24no—
1212C2×Q8—22no—
1213C2×Q8—22no—
1214C2×Q8—22no—
1215C2×Q8—24no—
1216C2×Q8—22no—
1217C2×Q8—28no—
1218C2×Q8—28no—
1219C2×Q8—24no—
1220C2×Q8—22no—
1221C2×Q8—24no—
1222C2×Q8—22no—
1223C2×Q8—44no—
1224C2×Q8—44no—
1225C2×Q8—44no—
1226C2×Q8—44no—
1227C2×Q8—416no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—28no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—44no—
1246C2×D4—42no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C22×C4—24no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—24no—
1259C22×C4—22no—
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—22no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—41no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—41no—
1296C22×C4—42no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—42no—
1300C22×C4—41no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—416no—
1309C22×C4C2×#4118yes—
1310C22×C4C2×#4114yes—
1311C22×C4C2×#4114yes—
1312C22×C4H(5,𝔽2)14yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2512yes—
1319C22×C4C2512yes—
1320C22×C4C2514yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2512yes—
1327C22×C4C2512yes—
1328C22×C4C2514yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2511yescharacteristic
1332C22×C4C2511yescharacteristic
1333C22×C4C2514yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2514yes—
1341C22×C4C2511yescharacteristic
1342C22×C4C2511yescharacteristic
1343C4⋊C4—28no—
1344C4⋊C4—28no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—28no—
1356C4⋊C4—28no—
1357C4⋊C4—28no—
1358C4⋊C4—28no—
1359C4⋊C4—28no—
1360C4⋊C4—28no—
1361C4⋊C4—28no—
1362C4⋊C4—28no—
1363C4⋊C4—28no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—22no—
1370C4⋊C4—41no—
1371C4⋊C4—41no—
1372C4⋊C4—41no—
1373C4⋊C4—41no—
1374C4⋊C4—41no—
1375C4⋊C4—41no—
1376C4⋊C4—41no—
1377C4⋊C4—41no—
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—42no—
1390C4⋊C4—44no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4—44no—
1405C4⋊C4C2×#4118yes—
1406C4⋊C4C2×#4118yes—
1407C4⋊C4C2×#4114yes—
1408C4⋊C4C2×#4114yes—
1409C22⋊C4—24no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—28no—
1415C22⋊C4—28no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—28no—
1421C22⋊C4—28no—
1422C22⋊C4—28no—
1423C22⋊C4—28no—
1424C22⋊C4—41no—
1425C22⋊C4—41no—
1426C22⋊C4—41no—
1427C22⋊C4—41no—
1428C22⋊C4—41no—
1429C22⋊C4—41no—
1430C22⋊C4—41no—
1431C22⋊C4—41no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—42no—
1446C22⋊C4—44no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—44no—
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—44no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—44no—
1468C22⋊C4—42no—
1469C22⋊C4C2×#4118yes—
1470C42—24no—
1471C42—24no—
1472C42—24no—
1473C42—22no—
1474C42—22no—
1475C42—22no—
1476C42—22no—
1477C42—22no—
1478C42—22no—
1479C42—22no—
1480C42—22no—
1481C42—24no—
1482C42—24no—
1483C42—42no—
1484C42—42no—
1485C42—44no—
1486C42—44no—
1487C42—44no—
1488C42—44no—
1489C42—44no—
1490C42—44no—
1491C42—42no—
1492C42—42no—
1493C42—44no—
1494C42—42no—
1495C42—44no—
1496C42—44no—
1497C42—44no—
1498C42—42no—
1499C42—44no—
1500C42C2×#4118yes—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—22no—
1508C23—21no—
1509C23—21no—
1510C23—22no—
1511C23—22no—
1512C23—22no—
1513C23—21no—
1514C23—21no—
1515C23—22no—
1516C23—22no—
1517C23—21no—
1518C23—21no—
1519C23—22no—
1520C23—22no—
1521C23—22no—
1522C23—21no—
1523C23—21no—
1524C23—22no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—21no—
1529C23—21no—
1530C23—22no—
1531C23—21no—
1532C23—21no—
1533C23—44no—
1534C23—44no—
1535C23—44no—
1536C23—82no—
1537C23—82no—
1538C23—82no—
1539C23—82no—
1540C23C22×#4112yes—
1541C23C22×#4112yes—
1542C23C2×H(5,𝔽2)12yes—
1543C23C2611yescharacteristic
1544Q8—48no—
1545Q8—48no—
1546Q8—44no—
1547Q8—44no—
1548Q8—88no—
1549Q8—88no—
1550D4—48no—
1551D4—48no—
1552D4—44no—
1553D4—44no—
1554D4—88no—
1555D4—84no—
1556D4—84no—
1557D4—84no—
1558D4—84no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—24no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—24no—
1577C2×C4—24no—
1578C2×C4—24no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—24no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—24no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—24no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—24no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—24no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—48no—
1641C2×C4—44no—
1642C2×C4—44no—
1643C2×C4—44no—
1644C2×C4—48no—
1645C2×C4—44no—
1646C2×C4—44no—
1647C2×C4—44no—
1648C2×C4—44no—
1649C2×C4—48no—
1650C2×C4—48no—
1651C2×C4—84no—
1652C2×C4—82no—
1653C2×C4—84no—
1654C2×C4—82no—
1655C2×C4—84no—
1656C2×C4—84no—
1657C2×C4—164no—
1658C2×C4#559116yes—
1659C2×C4C22×#4114yes—
1660C2×C4C22×#4114yes—
1661C2×C4C22×#4118yes—
1662C2×C4C22×#4112yes—
1663C2×C4C22×#4112yes—
1664C2×C4C22×#4112yes—
1665C2×C4C22×#4112yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4C2×H(5,𝔽2)12yes—
1668C22—22no—
1669C22—22no—
1670C22—22no—
1671C22—22no—
1672C22—22no—
1673C22—22no—
1674C22—42no—
1675C22—42no—
1676C22—41no—
1677C22—41no—
1678C22—42no—
1679C22—42no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—42no—
1684C22—42no—
1685C22—41no—
1686C22—41no—
1687C22—42no—
1688C22—42no—
1689C22—41no—
1690C22—42no—
1691C22—42no—
1692C22—41no—
1693C22—41no—
1694C22—42no—
1695C22—41no—
1696C22—42no—
1697C22—41no—
1698C22—41no—
1699C22—41no—
1700C22—42no—
1701C22—42no—
1702C22—88no—
1703C22C2×#55914yes—
1704C22C23×#4111yescharacteristic
1705C22C23×#4111yescharacteristic
1706C22C22×H(5,𝔽2)11yescharacteristic
1707C22H(7,𝔽2)11yescharacteristic
1708C222−1+611yescharacteristic
1709C222−1+611yescharacteristic
1710C222−1+611yescharacteristic
1711C4—28no—
1712C4—24no—
1713C4—24no—
1714C4—42no—
1715C4—42no—
1716C4—42no—
1717C4—42no—
1718C4—44no—
1719C4—42no—
1720C4—42no—
1721C4—41no—
1722C4—41no—
1723C4—41no—
1724C4—41no—
1725C4—44no—
1726C4—42no—
1727C4—42no—
1728C4—41no—
1729C4—41no—
1730C4—41no—
1731C4—42no—
1732C4—41no—
1733C4—42no—
1734C4—41no—
1735C4—41no—
1736C4—42no—
1737C4—42no—
1738C4—44no—
1739C4C2×#55914yes—
1740C4C2×#55914yes—
1741C2—24no—
1742C2—82no—
1743C2—82no—
1744C2—81no—
1745C2—81no—
1746C2C22×#55911yescharacteristic
1747C2#6284711yescharacteristic
1748C2#6285011yescharacteristic
1749C2#6285711yescharacteristic
1750C2#6286111yescharacteristic
1751C2#6287511yescharacteristic
1752C2#6288611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35634C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45345C2semidirect
2. #45302C2semidirect
3. #45226C2semidirect
4. #45225C2semidirect
5. #45225C2semidirect
6. #45205C2semidirect
7. #45076C2semidirect
8. #45075C2semidirect
9. #39274C2semidirect
10. #39273C2semidirect
11. #39271C2semidirect
12. #39268C2semidirect
13. #39267C2semidirect
14. #39266C2semidirect
15. #39203C2semidirect
16. #39200C2semidirect
17. #39199C2semidirect
18. #39197C2semidirect
19. #39196C2semidirect
20. #39195C2semidirect
21. #35644C2semidirect
23. #35542C2semidirect
24. #35516C2semidirect
25. #35312C2semidirect
26. #35307C2semidirect
27. #35182C2semidirect
28. #35158C2semidirect
29. #34635C2semidirect
30. #34272C2semidirect
31. #34271C2semidirect
32. #34267C2semidirect
33. #34266C2semidirect
34. #34065C2semidirect
35. C2×#2323C2semidirect
48. #2862C22semidirect
49. #2861C22semidirect
50. #2855C22semidirect
51. #2855C22semidirect
56. #2807C22semidirect
57. #2807C22semidirect
62. #2798C22semidirect
63. #2798C22semidirect
64. #2798C22semidirect
67. #2796C22semidirect
68. #2794C22semidirect
69. #2794C22semidirect
72. #2773C22semidirect
73. #2773C22semidirect
74. #2773C22semidirect
75. #2771C22semidirect
76. #2771C22semidirect
79. #2754C22semidirect
80. #2754C22semidirect
83. #2751C22semidirect
86. #2642C22semidirect
87. #2640C22semidirect
93. #2625C22semidirect
94. #2625C22semidirect
104. #2607C22semidirect
111. #2595C22semidirect
115. #2589C22semidirect
116. #2582C22semidirect
117. #2580C22semidirect
118. #2575C22semidirect
119. #2571C22semidirect
120. #2570C22semidirect
121. #2570C22semidirect
136. #2517C22semidirect
138. #2516C22semidirect
141. #2513C22semidirect
142. #2511C22semidirect
143. #2511C22semidirect
151. #2492C22semidirect
152. #2492C22semidirect
153. #2492C22semidirect
154. #2492C22semidirect
156. #2491C22semidirect
157. #2491C22semidirect
159. #2490C22semidirect
160. #2490C22semidirect
166. #2489C22semidirect
167. #2489C22semidirect
168. #2489C22semidirect
169. #2489C22semidirect
182. #2448C22semidirect
183. #2448C22semidirect
184. #2448C22semidirect
185. #2447C22semidirect
186. #2447C22semidirect
187. #2447C22semidirect
188. #2446C22semidirect
189. #2446C22semidirect
190. #2446C22semidirect
191. #2446C22semidirect
193. #2423C22semidirect
194. #2423C22semidirect
197. #2421C22semidirect
198. #2421C22semidirect
208. #2370C22semidirect
209. #2370C22semidirect
210. #2370C22semidirect
211. #2370C22semidirect
212. #2370C22semidirect
213. #2370C22semidirect
214. #2369C22semidirect
215. #2369C22semidirect
216. #2369C22semidirect
218. #2367C22semidirect
219. #2367C22semidirect
220. #2365C22semidirect
221. #2365C22semidirect
222. #2365C22semidirect
223. #2365C22semidirect
224. #2365C22semidirect
226. #2363C22semidirect
227. #2362C22semidirect
228. #2362C22semidirect
229. #2362C22semidirect
231. #2361C22semidirect
233. #2360C22semidirect
234. #2360C22semidirect
235. #2360C22semidirect
236. #2331C22semidirect
237. #2330C22semidirect
243. #2324C22semidirect
256. #2323C22semidirect
269. C4×C4⋊Q8C22semidirect
270. C4×#125C22semidirect
272. C4×C22⋊Q8C22semidirect
274. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#453452
#453022
#452262
#452252
#452052
#450762
#450752
#392742
#392732
#392712
#392682
#392672
#392662
#392032
#392002
#391992
#391972
#391962
#391952
#356442
#356342
#355422
#355162
#353122
#353072
#351822
#351582
#346352
#342722
#342712
#342672
#342662
#340652
C2×#23232