Finite Group Databasebeta

← #7647674

Subgroups — #7647674

Order 512.

4951 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#42783C212yesmaximal, complemented
2#42625C212yesmaximal, complemented
3#42613C212yesmaximal, complemented
4#42599C212yesmaximal, complemented
5#40727C214yesmaximal, complemented
6#40694C214yesmaximal, complemented
7#40188C212yesmaximal, complemented
8#40058C212yesmaximal, complemented
9#39781C212yesmaximal, complemented
10#39002C212yesmaximal, complemented
11#38566C214yesmaximal, complemented
12#38134C214yesmaximal, complemented
13#37593C212yesmaximal, complemented
14#37591C212yesmaximal, complemented
15#37435C212yesmaximal, complemented
16#37321C212yesmaximal, complemented
17#37293C212yesmaximal, complemented
18#37292C212yesmaximal, complemented
19#35639C211yesmaximal, characteristic, complemented
20#35540C211yesmaximal, characteristic, complemented
21#35516C211yesmaximal, characteristic, complemented
22#35515C211yesmaximal, characteristic, complemented
23#35335C211yesmaximal, characteristic, complemented
24#35288C212yesmaximal, complemented
25#35266C211yesmaximal, characteristic, complemented
26#35264C211yesmaximal, characteristic, complemented
27#35253C211yesmaximal, characteristic, complemented
28#35252C211yesmaximal, characteristic
29#35160C211yesmaximal, characteristic, complemented
30#35135C212yesmaximal, complemented
31#34813C211yesmaximal, characteristic, complemented
32C2×#2490C211yesmaximal, characteristic, complemented
33#34275C211yesmaximal, characteristic, complemented
34#34109C211yesmaximal, characteristic, complemented
35C4×#544C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#535C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C22×#125C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C22×#121C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#518C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2861C2212yescomplemented
46#2860C2212yescomplemented
47#2860C2212yescomplemented
48#2859C2212yescomplemented
49#2859C2212yescomplemented
50#2858C2212yescomplemented
51#2857C2212yescomplemented
52#2856C2212yes—
53#2852C2214yes—
54#2851C2212yescomplemented
55#2850C2212yes—
56#2832C2214yescomplemented
57#2831C2214yescomplemented
58#2830C2214yescomplemented
59#2829C2214yescomplemented
60#2801C2214yescomplemented
61#2800C2214yescomplemented
62#2796C2214yescomplemented
63#2796C2214yescomplemented
64#2779C2214yescomplemented
65#2777C2214yescomplemented
66#2772C2214yescomplemented
67#2772C2214yescomplemented
68#2765C2214yescomplemented
69#2764C2214yescomplemented
70#2761C2214yescomplemented
71#2759C2214yescomplemented
72#2757C2214yescomplemented
73#2757C2214yescomplemented
74#2746C2214yescomplemented
75#2739C2214yescomplemented
76#2737C2214yescomplemented
77#2737C2214yescomplemented
78#2723C2214yescomplemented
79#2715C2214yescomplemented
80#2715C2214yescomplemented
81#2710C2214yescomplemented
82#2710C2214yescomplemented
83#2705C2214yescomplemented
84#2705C2214yescomplemented
85#2702C2214yescomplemented
86#2701C2214yescomplemented
87#2698C2214yescomplemented
88#2692C2214yescomplemented
89#2691C2214yescomplemented
90#2686C2214yescomplemented
91#2672C2214yescomplemented
92#2663C2214yescomplemented
93#2662C2214yescomplemented
94#2660C2212yescomplemented
95#2660C2212yescomplemented
96#2654C2214yescomplemented
97#2652C2214yescomplemented
98#2651C2214yescomplemented
99#2651C2214yescomplemented
100#2650C2214yescomplemented
101#2649C2214yescomplemented
102#2644C2212yescomplemented
103#2644C2214yescomplemented
104#2644C2212yescomplemented
105#2643C2214yes—
106#2641C2212yescomplemented
107#2640C2212yescomplemented
108#2638C2214yescomplemented
109#2630C2214yescomplemented
110#2629C2212yescomplemented
111#2628C2212yescomplemented
112#2624C2214yescomplemented
113#2620C2212yes—
114#2619C2212yes—
115#2584C2212yescomplemented
116#2584C2212yescomplemented
117#2584C2212yescomplemented
118#2584C2212yescomplemented
119#2583C2214yes—
120#2583C2214yes—
121#2580C2212yescomplemented
122#2580C2212yescomplemented
123#2579C2214yes—
124#2538C2212yescomplemented
125#2538C2212yescomplemented
126#2530C2214yescomplemented
127#2529C2214yescomplemented
128#2514C2212yescomplemented
129#2513C2212yescomplemented
130#2513C2212yescomplemented
131#2513C2212yescomplemented
132#2512C2212yescomplemented
133#2512C2212yescomplemented
134#2512C2212yescomplemented
135#2511C2212yescomplemented
136#2497C2212yescomplemented
137#2496C2212yescomplemented
138#2495C2212yescomplemented
139#2494C2212yescomplemented
140#2492C2211yescharacteristic, complemented
141#2492C2211yescharacteristic, complemented
142#2491C2212yescomplemented
143#2491C2212yescomplemented
144#2491C2211yescharacteristic, complemented
145#2491C2211yescharacteristic, complemented
146#2490C2212yes—
147#2490C2212yes—
148#2490C2212yes—
149#2490C2212yes—
150#2490C2212yes—
151#2490C2212yes—
152#2490C2212yes—
153#2490C2212yes—
154#2490C2212yescomplemented
155#2490C2212yescomplemented
156#2490C2211yescharacteristic, complemented
157#2490C2211yescharacteristic, complemented
158#2489C2211yescharacteristic, complemented
159#2489C2211yescharacteristic, complemented
160#2488C2212yes—
161#2488C2212yes—
162#2487C2214yes—
163#2487C2212yescomplemented
164#2486C2212yescomplemented
165#2485C2212yescomplemented
166#2485C2212yescomplemented
167#2483C2214yes—
168#2480C2214yes—
169#2480C2214yes—
170#2479C2214yescomplemented
171#2472C2212yes—
172#2472C2214yes—
173#2472C2212yes—
174#2472C2214yes—
175#2470C2214yescomplemented
176#2468C2214yescomplemented
177#2465C2214yescomplemented
178#2461C2214yescomplemented
179#2458C2214yescomplemented
180#2454C2212yescomplemented
181#2454C2212yescomplemented
182#2454C2212yescomplemented
183#2454C2212yescomplemented
184#2453C2212yescomplemented
185#2453C2212yescomplemented
186#2452C2212yescomplemented
187#2452C2212yescomplemented
188#2448C2214yescomplemented
189#2447C2214yescomplemented
190#2442C2212yescomplemented
191#2442C2212yescomplemented
192#2442C2212yescomplemented
193#2441C2212yescomplemented
194#2441C2212yescomplemented
195#2441C2212yescomplemented
196#2440C2212yescomplemented
197#2439C2212yescomplemented
198#2438C2214yes—
199#2437C2214yes—
200#2437C2214yes—
201#2437C2214yes—
202#2427C2214yescomplemented
203#2426C2214yescomplemented
204#2423C2212yescomplemented
205#2422C2212yes—
206#2422C2212yes—
207#2422C2212yes—
208#2422C2212yes—
209#2422C2212yescomplemented
210#2421C2212yescomplemented
211#2420C2212yes—
212#2420C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2420C2212yescomplemented
216#2419C2214yes—
217#2418C2214yes—
218#2416C2212yes—
219#2416C2212yes—
220#2414C2212yes—
221#2414C2212yes—
222#2411C2214yes—
223#2410C2214yes—
224#2405C2214yes—
225#2398C2212yescomplemented
226#2398C2212yescomplemented
227C2×#397C2212yes—
228C2×#394C2212yes—
229#2363C2212yescomplemented
230#2363C2212yescomplemented
231#2361C2212yescomplemented
232#2361C2212yescomplemented
233#2358C2214yes—
234#2358C2214yes—
235#2347C2211yescharacteristic, complemented
236#2347C2211yescharacteristic, complemented
237#2346C2211yescharacteristic, complemented
238#2346C2211yescharacteristic, complemented
239#2345C2211yescharacteristic, complemented
240#2345C2211yescharacteristic, complemented
241#2344C2211yescharacteristic, complemented
242#2344C2211yescharacteristic, complemented
243#2343C2212yes—
244#2343C2212yes—
245#2342C2212yes—
246#2342C2212yes—
247#2335C2214yescomplemented
248#2334C2214yescomplemented
249#2331C2212yescomplemented
250#2331C2212yescomplemented
251#2330C2212yescomplemented
252#2330C2212yescomplemented
253#2329C2214yes—
254#2328C2212yescomplemented
255#2326C2212yescomplemented
256#2324C2214yescomplemented
257#2319C2214yescomplemented
258#2317C2211yescharacteristic
259#2317C2211yescharacteristic
260#2317C2211yescharacteristic
261#2317C2211yescharacteristic
262#2317C2211yescharacteristic
263#2317C2211yescharacteristic
264#2316C2211yescharacteristic
265#2316C2211yescharacteristic
266#2311C2211yescharacteristic
267#2311C2211yescharacteristic
268#2309C2211yescharacteristic
269#2309C2211yescharacteristic
270C4×C4⋊Q8C2212yescomplemented
271C4×C4⋊Q8C2212yescomplemented
272C4×#127C2212yescomplemented
273C4×#125C2212yescomplemented
274C4×#125C2212yescomplemented
275C4×#124C2212yescomplemented
276C4×#124C2212yescomplemented
277C4×#124C2212yescomplemented
278C4×C22⋊Q8C2214yes—
279#2298C2212yescomplemented
280#2298C2212yescomplemented
281#2297C2211yescharacteristic
282#2297C2211yescharacteristic
283#2296C2211yescharacteristic
284#2296C2211yescharacteristic
285C2×#390C2212yes—
286C2×#390C2211yescharacteristic
287C2×#390C2211yescharacteristic
288C2×#388C2212yes—
289#2283C2212yescomplemented
290#2280C2211yescharacteristic
291#2280C2211yescharacteristic
292C2×#380C2211yescharacteristic
293C4×#117C2211yescharacteristic
294C4×#117C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C4×#117C2212yescomplemented
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C23×D4C2312yes—
302C24×C4C2311yescharacteristic
303#544—28no—
304#535—28no—
305#533—44no—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×#127C2312yes—
311C2×#126C2314yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#125—44no—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2311yescharacteristic
321C2×#125C2311yescharacteristic
322C2×#125C2312yes—
323C2×#124C2312yes—
324C2×#124C2312yes—
325C2×#124C2312yes—
326C2×#124C2314yes—
327C2×#124C2314yes—
328#525—44no—
329C2×#123C2314yes—
330C2×#123C2312yes—
331C2×#123C2314yes—
332C2×#123C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×#121—44no—
342C2×#121C2312yes—
343C2×#121C2312yes—
344C2×#121C2314yes—
345C2×#121C2312yes—
346C2×#121C2311yescharacteristic
347C2×#121C2311yescharacteristic
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2314yes—
352C2×#120C2314yes—
353C2×#120C2312yes—
354#520—44no—
355#518—44no—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2314yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2314yes—
370C2×#117—28no—
371C2×#117C2311yescharacteristic
372C2×#117C2311yescharacteristic
373C2×#117C2311yescharacteristic
374C2×#117C2311yescharacteristic
375C2×#117C2311yescharacteristic
376C2×#117C2311yescharacteristic
377C2×#117C2312yes—
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2311yescharacteristic
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2311yescharacteristic
387C22×C4⋊C4C2311yescharacteristic
388C22×C4⋊C4C2311yescharacteristic
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C22⋊C4C2312yes—
394C22×C22⋊C4C2311yescharacteristic
395C22×C22⋊C4C2311yescharacteristic
396C22×C22⋊C4C2314yes—
397C22×C22⋊C4C2312yes—
398C22×C22⋊C4C2312yes—
399C22×C22⋊C4C2312yes—
400C22×C22⋊C4C2312yes—
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2312yes—
403C22×C42C2312yes—
404C22×C42C2311yescharacteristic
405C22×C42C2311yescharacteristic
406C22×C42C2312yes—
407#401C2314yes—
408#400C2312yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2312yes—
417#400C2312yes—
418#400C2312yes—
419#399C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2314yes—
424#399C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2312yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2312yes—
457#397C2312yes—
458#397C2312yes—
459#397C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#395C2314yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#395C2314yes—
478#394C2312yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2312yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2312yes—
499#394C2312yes—
500#393C2312yes—
501#393C2314yes—
502#393C2314yes—
503#393C2312yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#393C2312yes—
508#393C2312yes—
509#392C2314yes—
510#392C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2312yes—
515#391C2311yescharacteristic
516#391C2314yes—
517#391C2314yes—
518#391C2311yescharacteristic
519#391C2311yescharacteristic
520#391C2312yes—
521#391C2312yes—
522#391C2311yescharacteristic
523#390C2311yescharacteristic
524#390C2314yes—
525#390C2314yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2314yes—
538#390C2314yes—
539#390C2312yes—
540#390C2314yes—
541#390C2314yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2311yescharacteristic
546#390C2314yes—
547#390C2311yescharacteristic
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2311yescharacteristic
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2314yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2311yescharacteristic
583#389C2311yescharacteristic
584#389C2314yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2314yes—
590#389C2314yes—
591#389C2314yes—
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2311yescharacteristic
596#389C2311yescharacteristic
597#389C2311yescharacteristic
598#389C2314yes—
599#388C2312yes—
600#388C2312yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2312yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2312yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
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#388C2312yes—
632#388C2312yes—
633#388C2314yes—
634#388C2312yes—
635#388C2312yes—
636#388C2314yes—
637#388C2314yes—
638#388C2312yes—
639#388C2312yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2312yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2312yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2312yes—
675#386C2312yes—
676#386C2314yes—
677#386C2312yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2312yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#385C2314yes—
700#385C2314yes—
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#383C2314yes—
708#383C2312yes—
709#383C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2312yes—
714#382C2312yes—
715#382C2312yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#381C2314yes—
721#381C2314yes—
722#381C2312yes—
723#381C2312yes—
724#381C2312yes—
725#381C2314yes—
726#381C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2314yes—
733#380C2314yes—
734#380C2314yes—
735#380C2314yes—
736#380C2314yes—
737#380C2311yescharacteristic
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2311yescharacteristic
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746#380C2311yescharacteristic
747#380C2312yes—
748#380C2311yescharacteristic
749#380C2314yes—
750#380C2312yes—
751#380C2312yes—
752#379C2314yes—
753#379C2314yes—
754#379C2312yes—
755#379C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2314yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2311yescharacteristic
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807#376C2312yes—
808#376C2312yes—
809#376C2312yes—
810#376C2312yes—
811#376C2312yes—
812C2×#95C2312yes—
813C2×#95C2311yescharacteristic
814C2×#95C2311yescharacteristic
815C2×#95C2312yes—
816C43C2312yes—
817C43C2312yes—
818C43C2312yes—
819C25C2411yescharacteristic
820C25C2412yes—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C22×Q8C2411yescharacteristic
825C22×Q8C2414yes—
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×D4—24no—
829C22×D4—24no—
830C22×D4—24no—
831C22×D4—44no—
832C22×D4—44no—
833C22×D4—82no—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2414yes—
840C22×D4C2414yes—
841C22×D4C2414yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C23×C4—24no—
845C23×C4—24no—
846C23×C4—24no—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2411yescharacteristic
866C4⋊Q8—28no—
867C4⋊Q8—28no—
868C4⋊Q8—42no—
869C4⋊Q8—42no—
870#127—28no—
871#126—48no—
872#126—84no—
873#126—84no—
874#125—28no—
875#125—28no—
876#125—44no—
877#125—44no—
878#125—44no—
879#125—44no—
880#125—42no—
881#125—42no—
882#124—28no—
883#124—44no—
884#124—44no—
885#124—84no—
886#124—84no—
887#123—48no—
888#123—44no—
889#123—84no—
890#123—84no—
891C22⋊Q8—216no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894C22⋊Q8—42no—
895C22⋊Q8—42no—
896C22⋊Q8—84no—
897C22⋊Q8—84no—
898C22⋊Q8—84no—
899#121—28no—
900#121—28no—
901#121—44no—
902#121—44no—
903#121—44no—
904#121—44no—
905#121—42no—
906#121—42no—
907#121—48no—
908#121—84no—
909#120—216no—
910#120—44no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×Q8—44no—
914C4×Q8—84no—
915C4×D4—48no—
916C4×D4—44no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—44no—
920C4×D4—44no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—48no—
924C4×D4—84no—
925#117—24no—
926#117—24no—
927#117—24no—
928#117—24no—
929#117—24no—
930#117—24no—
931#117—24no—
932#117—24no—
933#117—28no—
934#117—28no—
935#117—44no—
936#117—44no—
937#117—44no—
938#117#4118yes—
939C2×C4⋊C4—24no—
940C2×C4⋊C4—24no—
941C2×C4⋊C4—24no—
942C2×C4⋊C4—24no—
943C2×C4⋊C4—24no—
944C2×C4⋊C4—44no—
945C2×C4⋊C4—44no—
946C2×C4⋊C4—44no—
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C22⋊C4—28no—
1010C2×C22⋊C4—42no—
1011C2×C22⋊C4—44no—
1012C2×C22⋊C4—42no—
1013C2×C22⋊C4—48no—
1014C2×C22⋊C4—44no—
1015C2×C22⋊C4—82no—
1016C2×C22⋊C4—82no—
1017C2×C22⋊C4—82no—
1018C2×C22⋊C4—82no—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2411yescharacteristic
1028C2×C22⋊C4C2411yescharacteristic
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C42—24no—
1086C2×C42—24no—
1087C2×C42—28no—
1088C2×C42—82no—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2412yes—
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2412yes—
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2414yes—
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2414yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2414yes—
1120C2×C42C2412yes—
1121#95C2411yescharacteristic
1122#95C2411yescharacteristic
1123#95C2411yescharacteristic
1124#95C2411yescharacteristic
1125#95C2411yescharacteristic
1126#95C2411yescharacteristic
1127#95C2411yescharacteristic
1128#95C2411yescharacteristic
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
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#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189C24—22no—
1190C24—22no—
1191C24—22no—
1192C24—22no—
1193C24—24no—
1194C24—24no—
1195C24—24no—
1196C24—41no—
1197C24—41no—
1198C24—41no—
1199C24—42no—
1200C24—42no—
1201C24—42no—
1202C24—42no—
1203C24C2511yescharacteristic
1204C24C2514yes—
1205C24C2512yes—
1206C24C2511yescharacteristic
1207C24C2511yescharacteristic
1208#41—416no—
1209C2×Q8—22no—
1210C2×Q8—28no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—42no—
1214C2×Q8—42no—
1215C2×Q8—44no—
1216C2×Q8—42no—
1217C2×Q8—42no—
1218C2×Q8—44no—
1219C2×Q8—42no—
1220C2×Q8—42no—
1221C2×D4—24no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—28no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—22no—
1229C2×D4—28no—
1230C2×D4—28no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—22no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—44no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—42no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—42no—
1248C2×D4—44no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—416no—
1252C2×D4—816no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—24no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—24no—
1259C22×C4—24no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—24no—
1270C22×C4—24no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—24no—
1280C22×C4—22no—
1281C22×C4—24no—
1282C22×C4—41no—
1283C22×C4—42no—
1284C22×C4—42no—
1285C22×C4—42no—
1286C22×C4—42no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—42no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
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×C4—44no—
1307C22×C4—416no—
1308C22×C4C2×#4114yes—
1309C22×C4H(5,𝔽2)14yes—
1310C22×C42−1+414yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2512yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2511yescharacteristic
1317C22×C4C2512yes—
1318C22×C4C2512yes—
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2514yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2514yes—
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2514yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2511yescharacteristic
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—28no—
1350C4⋊C4—28no—
1351C4⋊C4—28no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—22no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—24no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
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—44no—
1398C4⋊C4—44no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4C2×#4114yes—
1402C4⋊C4C2×#4114yes—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—24no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—28no—
1416C22⋊C4—28no—
1417C22⋊C4—22no—
1418C22⋊C4—28no—
1419C22⋊C4—22no—
1420C22⋊C4—24no—
1421C22⋊C4—41no—
1422C22⋊C4—41no—
1423C22⋊C4—41no—
1424C22⋊C4—41no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—44no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—42no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—42no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4C2×#4118yes—
1469C42—24no—
1470C42—24no—
1471C42—24no—
1472C42—24no—
1473C42—22no—
1474C42—22no—
1475C42—22no—
1476C42—22no—
1477C42—24no—
1478C42—24no—
1479C42—24no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—22no—
1484C42—24no—
1485C42—24no—
1486C42—24no—
1487C42—44no—
1488C42—44no—
1489C42—42no—
1490C42—42no—
1491C42—42no—
1492C42—44no—
1493C42—42no—
1494C42—42no—
1495C42—42no—
1496C42—42no—
1497C42—42no—
1498C42—42no—
1499C42—42no—
1500C42C2×#4118yes—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—24no—
1513C23—22no—
1514C23—22no—
1515C23—24no—
1516C23—21no—
1517C23—21no—
1518C23—22no—
1519C23—24no—
1520C23—24no—
1521C23—21no—
1522C23—22no—
1523C23—22no—
1524C23—24no—
1525C23—21no—
1526C23—24no—
1527C23—22no—
1528C23—21no—
1529C23—22no—
1530C23—24no—
1531C23—21no—
1532C23—44no—
1533C23—44no—
1534C23—44no—
1535C23—44no—
1536C23—48no—
1537C23—82no—
1538C23—82no—
1539C23—82no—
1540C23—84no—
1541C23—84no—
1542C23—84no—
1543C23—84no—
1544C23—84no—
1545C23—84no—
1546C23C22×#4112yes—
1547C23C2×H(5,𝔽2)12yes—
1548C23C2×2−1+412yes—
1549C23#58512yes—
1550C23C2611yescharacteristic
1551Q8—44no—
1552Q8—88no—
1553Q8—84no—
1554Q8—84no—
1555D4—48no—
1556D4—48no—
1557D4—48no—
1558D4—44no—
1559D4—88no—
1560D4—88no—
1561D4—84no—
1562D4—88no—
1563D4—84no—
1564D4—88no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—24no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—24no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—24no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—24no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—24no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—24no—
1639C2×C4—22no—
1640C2×C4—24no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—48no—
1647C2×C4—44no—
1648C2×C4—48no—
1649C2×C4—44no—
1650C2×C4—44no—
1651C2×C4—44no—
1652C2×C4—44no—
1653C2×C4—44no—
1654C2×C4—48no—
1655C2×C4—84no—
1656C2×C4—84no—
1657C2×C4—82no—
1658C2×C4—82no—
1659C2×C4—84no—
1660C2×C4—82no—
1661C2×C4—164no—
1662C2×C4—164no—
1663C2×C4—164no—
1664C2×C4#542116yes—
1665C2×C4C22×#4114yes—
1666C2×C4C22×#4114yes—
1667C2×C4C22×#4112yes—
1668C2×C4C22×#4112yes—
1669C2×C4C2×H(5,𝔽2)12yes—
1670C2×C4C2×H(5,𝔽2)12yes—
1671C2×C4C2×2−1+412yes—
1672C2×C4C2×2−1+412yes—
1673C2×C4#58512yes—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—22no—
1679C22—22no—
1680C22—22no—
1681C22—22no—
1682C22—22no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—41no—
1687C22—42no—
1688C22—44no—
1689C22—41no—
1690C22—42no—
1691C22—44no—
1692C22—41no—
1693C22—44no—
1694C22—41no—
1695C22—42no—
1696C22—41no—
1697C22—42no—
1698C22—44no—
1699C22—42no—
1700C22—44no—
1701C22—41no—
1702C22—42no—
1703C22—42no—
1704C22—41no—
1705C22—41no—
1706C22—44no—
1707C22—44no—
1708C22—88no—
1709C22—168no—
1710C22C2×#54214yes—
1711C22C23×#4111yescharacteristic
1712C22C22×H(5,𝔽2)11yescharacteristic
1713C22C22×2−1+411yescharacteristic
1714C22C2×#58511yescharacteristic
1715C22C2×#58511yescharacteristic
1716C22H(7,𝔽2)11yescharacteristic
1717C22H(7,𝔽2)11yescharacteristic
1718C4—24no—
1719C4—24no—
1720C4—22no—
1721C4—42no—
1722C4—42no—
1723C4—42no—
1724C4—44no—
1725C4—42no—
1726C4—44no—
1727C4—41no—
1728C4—41no—
1729C4—42no—
1730C4—42no—
1731C4—42no—
1732C4—41no—
1733C4—41no—
1734C4—42no—
1735C4—41no—
1736C4—44no—
1737C4—41no—
1738C4—42no—
1739C4—42no—
1740C4—42no—
1741C4—42no—
1742C4—42no—
1743C4—41no—
1744C4—41no—
1745C4—41no—
1746C4C2×#54214yes—
1747C4C2×#54214yes—
1748C2—24no—
1749C2—42no—
1750C2—82no—
1751C2—81no—
1752C2—84no—
1753C2C22×#54211yescharacteristic
1754C2#6281011yescharacteristic
1755C2#6285811yescharacteristic
1756C2#6292411yescharacteristic
1757C2#6295511yescharacteristic
1758C2#6295811yescharacteristic
1759C2#6295811yescharacteristic
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. #42783C2semidirect
2. #42625C2semidirect
3. #42613C2semidirect
4. #42599C2semidirect
5. #40727C2semidirect
6. #40694C2semidirect
7. #40188C2semidirect
8. #40058C2semidirect
9. #39781C2semidirect
10. #39002C2semidirect
11. #38566C2semidirect
12. #38134C2semidirect
13. #37593C2semidirect
14. #37591C2semidirect
15. #37435C2semidirect
16. #37321C2semidirect
17. #37293C2semidirect
18. #37292C2semidirect
19. #35639C2semidirect
20. #35540C2semidirect
21. #35516C2semidirect
22. #35515C2semidirect
23. #35335C2semidirect
24. #35288C2semidirect
25. #35266C2semidirect
26. #35264C2semidirect
27. #35253C2semidirect
29. #35160C2semidirect
30. #35135C2semidirect
31. #34813C2semidirect
32. C2×#2490C2semidirect
33. #34275C2semidirect
34. #34109C2semidirect
35. C4×#544C2semidirect
45. #2861C22semidirect
46. #2860C22semidirect
47. #2860C22semidirect
48. #2859C22semidirect
49. #2859C22semidirect
50. #2858C22semidirect
51. #2857C22semidirect
54. #2851C22semidirect
56. #2832C22semidirect
57. #2831C22semidirect
58. #2830C22semidirect
59. #2829C22semidirect
60. #2801C22semidirect
61. #2800C22semidirect
62. #2796C22semidirect
63. #2796C22semidirect
64. #2779C22semidirect
65. #2777C22semidirect
66. #2772C22semidirect
67. #2772C22semidirect
68. #2765C22semidirect
69. #2764C22semidirect
70. #2761C22semidirect
71. #2759C22semidirect
72. #2757C22semidirect
73. #2757C22semidirect
74. #2746C22semidirect
75. #2739C22semidirect
76. #2737C22semidirect
77. #2737C22semidirect
78. #2723C22semidirect
79. #2715C22semidirect
80. #2715C22semidirect
81. #2710C22semidirect
82. #2710C22semidirect
83. #2705C22semidirect
84. #2705C22semidirect
85. #2702C22semidirect
86. #2701C22semidirect
87. #2698C22semidirect
88. #2692C22semidirect
89. #2691C22semidirect
90. #2686C22semidirect
91. #2672C22semidirect
92. #2663C22semidirect
93. #2662C22semidirect
94. #2660C22semidirect
95. #2660C22semidirect
96. #2654C22semidirect
97. #2652C22semidirect
98. #2651C22semidirect
99. #2651C22semidirect
100. #2650C22semidirect
101. #2649C22semidirect
102. #2644C22semidirect
103. #2644C22semidirect
104. #2644C22semidirect
106. #2641C22semidirect
107. #2640C22semidirect
108. #2638C22semidirect
109. #2630C22semidirect
110. #2629C22semidirect
111. #2628C22semidirect
112. #2624C22semidirect
115. #2584C22semidirect
116. #2584C22semidirect
117. #2584C22semidirect
118. #2584C22semidirect
121. #2580C22semidirect
122. #2580C22semidirect
124. #2538C22semidirect
125. #2538C22semidirect
126. #2530C22semidirect
127. #2529C22semidirect
128. #2514C22semidirect
129. #2513C22semidirect
130. #2513C22semidirect
131. #2513C22semidirect
132. #2512C22semidirect
133. #2512C22semidirect
134. #2512C22semidirect
135. #2511C22semidirect
136. #2497C22semidirect
137. #2496C22semidirect
138. #2495C22semidirect
139. #2494C22semidirect
140. #2492C22semidirect
141. #2492C22semidirect
142. #2491C22semidirect
143. #2491C22semidirect
144. #2491C22semidirect
145. #2491C22semidirect
154. #2490C22semidirect
155. #2490C22semidirect
156. #2490C22semidirect
157. #2490C22semidirect
158. #2489C22semidirect
159. #2489C22semidirect
163. #2487C22semidirect
164. #2486C22semidirect
165. #2485C22semidirect
166. #2485C22semidirect
170. #2479C22semidirect
175. #2470C22semidirect
176. #2468C22semidirect
177. #2465C22semidirect
178. #2461C22semidirect
179. #2458C22semidirect
180. #2454C22semidirect
181. #2454C22semidirect
182. #2454C22semidirect
183. #2454C22semidirect
184. #2453C22semidirect
185. #2453C22semidirect
186. #2452C22semidirect
187. #2452C22semidirect
188. #2448C22semidirect
189. #2447C22semidirect
190. #2442C22semidirect
191. #2442C22semidirect
192. #2442C22semidirect
193. #2441C22semidirect
194. #2441C22semidirect
195. #2441C22semidirect
196. #2440C22semidirect
197. #2439C22semidirect
202. #2427C22semidirect
203. #2426C22semidirect
204. #2423C22semidirect
209. #2422C22semidirect
210. #2421C22semidirect
215. #2420C22semidirect
225. #2398C22semidirect
226. #2398C22semidirect
229. #2363C22semidirect
230. #2363C22semidirect
231. #2361C22semidirect
232. #2361C22semidirect
235. #2347C22semidirect
236. #2347C22semidirect
237. #2346C22semidirect
238. #2346C22semidirect
239. #2345C22semidirect
240. #2345C22semidirect
241. #2344C22semidirect
242. #2344C22semidirect
247. #2335C22semidirect
248. #2334C22semidirect
249. #2331C22semidirect
250. #2331C22semidirect
251. #2330C22semidirect
252. #2330C22semidirect
254. #2328C22semidirect
255. #2326C22semidirect
256. #2324C22semidirect
257. #2319C22semidirect
270. C4×C4⋊Q8C22semidirect
271. C4×C4⋊Q8C22semidirect
272. C4×#127C22semidirect
273. C4×#125C22semidirect
274. C4×#125C22semidirect
275. C4×#124C22semidirect
276. C4×#124C22semidirect
277. C4×#124C22semidirect
279. #2298C22semidirect
280. #2298C22semidirect
289. #2283C22semidirect
296. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#427832
#426252
#426132
#425992
#407272
#406942
#401882
#400582
#397812
#390022
#385662
#381342
#375932
#375912
#374352
#373212
#372932
#372922
#356392
#355402
#355162
#355152
#353352
#352882
#352662
#352642
#352532
#352522
#351602
#351352
#348132
C2×#24902
#342752
#341092
C4×#5442