Finite Group Databasebeta

← #7652446

Subgroups — #7652446

Order 512.

4955 conjugacy classes of subgroups.

The subgroup lattice has 1769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42768C212yesmaximal, complemented
2#42740C212yesmaximal, complemented
3#42659C212yesmaximal, complemented
4#42618C212yesmaximal, complemented
5#42579C212yesmaximal, complemented
6#42472C212yesmaximal, complemented
7#42467C212yesmaximal, complemented
8#42459C212yesmaximal, complemented
9#40785C214yesmaximal, complemented
10#40694C214yesmaximal, complemented
11#40171C212yesmaximal, complemented
12#40147C212yesmaximal, complemented
13#39905C212yesmaximal, complemented
14#39903C212yesmaximal, complemented
15#39736C212yesmaximal, complemented
16#39236C212yesmaximal, complemented
17#39213C212yesmaximal, complemented
18#39147C212yesmaximal, complemented
19#38566C214yesmaximal, complemented
20#38514C214yesmaximal, complemented
21#35640C211yesmaximal, characteristic, complemented
22#35558C211yesmaximal, characteristic, complemented
23#35556C211yesmaximal, characteristic, complemented
24#35542C211yesmaximal, characteristic, complemented
25#35540C211yesmaximal, characteristic, complemented
26#35529C211yesmaximal, characteristic, complemented
27#35333C211yesmaximal, characteristic, complemented
28#35252C211yesmaximal, characteristic
29#35160C211yesmaximal, characteristic, complemented
30C2×#2490C211yesmaximal, characteristic, complemented
31#34742C211yesmaximal, characteristic, complemented
32#34739C211yesmaximal, characteristic, complemented
33#34269C211yesmaximal, characteristic, complemented
34#34213C211yesmaximal, characteristic, complemented
35#34180C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#535C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C22×#125C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C22×#121C2211yescharacteristic
42C2×#518C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2856C2212yes—
46#2852C2214yes—
47#2851C2212yescomplemented
48#2851C2212yescomplemented
49#2850C2212yes—
50#2837C2214yescomplemented
51#2831C2214yescomplemented
52#2830C2214yescomplemented
53#2829C2214yescomplemented
54#2800C2214yescomplemented
55#2796C2214yescomplemented
56#2795C2214yescomplemented
57#2793C2214yescomplemented
58#2790C2214yescomplemented
59#2772C2214yescomplemented
60#2770C2214yescomplemented
61#2765C2214yescomplemented
62#2761C2214yescomplemented
63#2761C2214yescomplemented
64#2759C2214yescomplemented
65#2757C2214yescomplemented
66#2757C2214yescomplemented
67#2757C2214yescomplemented
68#2754C2214yescomplemented
69#2751C2214yescomplemented
70#2741C2214yescomplemented
71#2737C2214yescomplemented
72#2730C2214yescomplemented
73#2718C2214yescomplemented
74#2715C2214yescomplemented
75#2712C2214yescomplemented
76#2710C2214yescomplemented
77#2705C2214yescomplemented
78#2701C2214yescomplemented
79#2701C2214yescomplemented
80#2700C2214yescomplemented
81#2698C2214yescomplemented
82#2692C2214yescomplemented
83#2691C2214yescomplemented
84#2691C2214yescomplemented
85#2687C2214yescomplemented
86#2662C2214yescomplemented
87#2654C2214yescomplemented
88#2653C2214yescomplemented
89#2653C2214yescomplemented
90#2652C2214yescomplemented
91#2651C2214yescomplemented
92#2651C2214yescomplemented
93#2644C2214yescomplemented
94#2643C2214yes—
95#2638C2214yescomplemented
96#2637C2214yescomplemented
97#2630C2214yescomplemented
98#2629C2212yescomplemented
99#2629C2212yescomplemented
100#2620C2212yes—
101#2620C2214yescomplemented
102#2619C2212yes—
103#2592C2212yescomplemented
104#2592C2212yescomplemented
105#2583C2214yes—
106#2579C2214yes—
107#2579C2214yes—
108#2566C2212yescomplemented
109#2566C2212yescomplemented
110#2566C2212yescomplemented
111#2566C2212yescomplemented
112#2565C2212yescomplemented
113#2565C2212yescomplemented
114#2563C2212yescomplemented
115#2563C2212yescomplemented
116#2562C2212yescomplemented
117#2562C2212yescomplemented
118#2552C2212yescomplemented
119#2552C2212yescomplemented
120#2552C2212yescomplemented
121#2552C2212yescomplemented
122#2550C2212yescomplemented
123#2550C2212yescomplemented
124#2550C2212yescomplemented
125#2550C2212yescomplemented
126#2548C2212yescomplemented
127#2548C2212yescomplemented
128#2547C2212yescomplemented
129#2542C2212yescomplemented
130#2532C2214yescomplemented
131#2530C2214yescomplemented
132#2515C2214yescomplemented
133#2514C2212yescomplemented
134#2513C2212yescomplemented
135#2513C2212yescomplemented
136#2513C2212yescomplemented
137#2513C2212yescomplemented
138#2513C2212yescomplemented
139#2512C2214yescomplemented
140#2512C2212yescomplemented
141#2512C2212yescomplemented
142#2512C2212yescomplemented
143#2512C2212yescomplemented
144#2512C2212yescomplemented
145#2511C2212yescomplemented
146#2502C2214yes—
147#2497C2212yescomplemented
148#2496C2212yescomplemented
149#2495C2212yescomplemented
150#2494C2212yescomplemented
151#2492C2212yescomplemented
152#2491C2212yescomplemented
153#2491C2212yescomplemented
154#2491C2212yescomplemented
155#2490C2212yes—
156#2490C2212yes—
157#2490C2212yes—
158#2490C2212yes—
159#2490C2212yes—
160#2490C2212yes—
161#2490C2212yes—
162#2490C2212yes—
163#2490C2212yescomplemented
164#2490C2212yescomplemented
165#2490C2212yescomplemented
166#2489C2212yescomplemented
167#2488C2214yes—
168#2483C2214yes—
169#2480C2214yes—
170#2480C2214yes—
171#2479C2214yescomplemented
172#2477C2214yescomplemented
173#2472C2214yes—
174#2472C2214yes—
175#2472C2214yes—
176#2468C2214yescomplemented
177#2461C2214yescomplemented
178#2458C2214yescomplemented
179#2454C2212yescomplemented
180#2454C2212yescomplemented
181#2452C2212yescomplemented
182#2452C2212yescomplemented
183#2447C2214yescomplemented
184#2442C2211yescharacteristic, complemented
185#2442C2211yescharacteristic, complemented
186#2441C2211yescharacteristic, complemented
187#2441C2211yescharacteristic, complemented
188#2440C2211yescharacteristic, complemented
189#2440C2211yescharacteristic, complemented
190#2439C2211yescharacteristic, complemented
191#2439C2211yescharacteristic, complemented
192#2438C2212yes—
193#2438C2212yes—
194#2437C2212yes—
195#2437C2214yes—
196#2437C2214yes—
197#2437C2212yes—
198#2426C2214yescomplemented
199#2423C2211yescharacteristic, complemented
200#2423C2211yescharacteristic, complemented
201#2422C2212yes—
202#2422C2212yes—
203#2422C2212yes—
204#2422C2212yes—
205#2422C2214yescomplemented
206#2422C2211yescharacteristic, complemented
207#2422C2211yescharacteristic, complemented
208#2421C2211yescharacteristic, complemented
209#2421C2211yescharacteristic, complemented
210#2420C2212yes—
211#2420C2212yes—
212#2420C2212yes—
213#2420C2212yes—
214#2420C2211yescharacteristic, complemented
215#2420C2211yescharacteristic, complemented
216#2419C2212yes—
217#2419C2212yes—
218#2418C2212yes—
219#2418C2212yes—
220#2416C2212yes—
221#2416C2212yes—
222#2414C2212yes—
223#2414C2212yes—
224#2411C2214yes—
225#2410C2214yes—
226#2405C2214yes—
227#2396C2212yescomplemented
228#2396C2212yescomplemented
229#2395C2212yescomplemented
230#2395C2212yescomplemented
231C2×#397C2212yes—
232C2×#394C2212yes—
233#2370C2212yescomplemented
234#2370C2212yescomplemented
235#2369C2212yescomplemented
236#2367C2212yescomplemented
237#2367C2212yescomplemented
238#2366C2212yescomplemented
239#2366C2212yescomplemented
240#2365C2212yescomplemented
241#2358C2214yes—
242#2358C2214yes—
243#2355C2212yescomplemented
244#2355C2212yescomplemented
245#2355C2212yescomplemented
246Q8×C4⋊C4C2212yescomplemented
247#2347C2212yescomplemented
248#2346C2212yescomplemented
249#2345C2212yescomplemented
250#2344C2212yescomplemented
251#2343C2214yes—
252#2342C2214yes—
253#2335C2214yescomplemented
254#2332C2214yescomplemented
255#2329C2214yes—
256#2326C2214yescomplemented
257#2324C2212yescomplemented
258#2324C2214yescomplemented
259#2324C2212yescomplemented
260#2317C2211yescharacteristic
261#2317C2211yescharacteristic
262#2317C2211yescharacteristic
263#2317C2211yescharacteristic
264#2317C2211yescharacteristic
265#2314C2212yescomplemented
266#2314C2212yescomplemented
267#2311C2211yescharacteristic
268#2311C2211yescharacteristic
269#2311C2211yescharacteristic
270#2309C2211yescharacteristic
271#2309C2211yescharacteristic
272C4×C22⋊Q8C2214yes—
273C4×C22⋊Q8C2212yescomplemented
274C4×C22⋊Q8C2212yescomplemented
275C4×#123C2212yescomplemented
276C4×#123C2212yescomplemented
277C4×#121C2212yescomplemented
278C4×#121C2212yescomplemented
279#2297C2211yescharacteristic
280#2296C2211yescharacteristic
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283C2×#390C2212yes—
284C2×#390C2211yescharacteristic
285C2×#390C2211yescharacteristic
286C2×#388C2212yes—
287#2285C2211yescharacteristic
288#2285C2211yescharacteristic
289#2285C2212yescomplemented
290#2283C2212yescomplemented
291#2280C2211yescharacteristic
292#2280C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296#2274C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C23×D4C2312yes—
302C24×C4C2311yescharacteristic
303#544—44no—
304#535—28no—
305#533—28no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×#127C2312yes—
311C2×#126C2314yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#125—44no—
315C2×#125C2311yescharacteristic
316C2×#125C2311yescharacteristic
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#124C2312yes—
324C2×#124C2314yes—
325C2×#124C2314yes—
326C2×#124C2314yes—
327#525—44no—
328C2×#123C2314yes—
329C2×#123C2312yes—
330C2×#123C2312yes—
331C2×#123C2312yes—
332C2×#123C2314yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2314yes—
342C2×#121—44no—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2314yes—
346C2×#121C2312yes—
347C2×#121C2311yescharacteristic
348C2×#121C2311yescharacteristic
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2312yes—
352C2×#121C2314yes—
353C2×#120C2314yes—
354C2×#120C2312yes—
355#518—44no—
356C4×#41—44no—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×#117—28no—
375C2×#117C2311yescharacteristic
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2311yescharacteristic
382C2×#117C2312yes—
383C2×#117C2311yescharacteristic
384C2×#117C2311yescharacteristic
385C2×#117C2312yes—
386C2×#117C2314yes—
387C2×#117C2311yescharacteristic
388C22×C4⋊C4C2311yescharacteristic
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2311yescharacteristic
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2312yes—
395C22×C22⋊C4C2312yes—
396C22×C22⋊C4C2314yes—
397C22×C22⋊C4C2311yescharacteristic
398C22×C22⋊C4C2312yes—
399C22×C22⋊C4C2311yescharacteristic
400C22×C22⋊C4C2312yes—
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2312yes—
403C22×C22⋊C4C2312yes—
404C22×C22⋊C4C2312yes—
405C22×C42C2312yes—
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2312yes—
409C22×C42C2312yes—
410#401C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2312yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2312yes—
418#400C2312yes—
419#400C2312yes—
420#399C2314yes—
421#399C2312yes—
422#399C2312yes—
423#399C2312yes—
424#399C2312yes—
425#399C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2312yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2312yes—
437#398C2312yes—
438#398C2312yes—
439#398C2312yes—
440#398C2312yes—
441#398C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2312yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2312yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2312yes—
463#397C2312yes—
464#397C2312yes—
465#397C2312yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2312yes—
484#396C2312yes—
485#396C2312yes—
486#395C2314yes—
487#395C2312yes—
488#395C2314yes—
489#395C2312yes—
490#394C2314yes—
491#394C2314yes—
492#394C2312yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2312yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2312yes—
508#394C2312yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#393C2314yes—
513#393C2314yes—
514#393C2314yes—
515#393C2314yes—
516#393C2314yes—
517#393C2314yes—
518#393C2312yes—
519#393C2312yes—
520#392C2314yes—
521#392C2314yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2314yes—
526#391C2312yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2311yescharacteristic
531#391C2311yescharacteristic
532#391C2314yes—
533#391C2314yes—
534#391C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2314yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2314yes—
550#390C2314yes—
551#390C2312yes—
552#390C2314yes—
553#390C2314yes—
554#390C2314yes—
555#390C2314yes—
556#390C2312yes—
557#390C2312yes—
558#390C2314yes—
559#390C2314yes—
560#390C2311yescharacteristic
561#390C2311yescharacteristic
562#390C2314yes—
563#390C2312yes—
564#390C2312yes—
565#390C2314yes—
566#390C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2312yes—
587#389C2311yescharacteristic
588#389C2311yescharacteristic
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2312yes—
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2311yescharacteristic
596#389C2311yescharacteristic
597#389C2311yescharacteristic
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2312yes—
629#388C2312yes—
630#388C2312yes—
631#388C2314yes—
632#388C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2312yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2312yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2312yes—
671#386C2312yes—
672#386C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2312yes—
689#385C2314yes—
690#385C2312yes—
691#385C2312yes—
692#385C2312yes—
693#385C2312yes—
694#385C2312yes—
695#385C2312yes—
696#385C2312yes—
697#385C2314yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2311yescharacteristic
705#384C2312yes—
706#384C2312yes—
707#384C2312yes—
708#384C2314yes—
709#384C2311yescharacteristic
710#384C2314yes—
711#384C2311yescharacteristic
712#384C2311yescharacteristic
713#383C2314yes—
714#383C2314yes—
715#382C2311yescharacteristic
716#382C2312yes—
717#382C2314yes—
718#382C2312yes—
719#382C2311yescharacteristic
720#382C2312yes—
721#382C2312yes—
722#382C2312yes—
723#382C2311yescharacteristic
724#382C2311yescharacteristic
725#382C2314yes—
726#381C2314yes—
727#381C2314yes—
728#381C2312yes—
729#381C2314yes—
730#381C2312yes—
731#381C2312yes—
732#381C2312yes—
733#380C2312yes—
734#380C2311yescharacteristic
735#380C2311yescharacteristic
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2312yes—
742#380C2314yes—
743#380C2314yes—
744#380C2312yes—
745#380C2312yes—
746#380C2311yescharacteristic
747#380C2311yescharacteristic
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2311yescharacteristic
756#380C2311yescharacteristic
757#380C2311yescharacteristic
758#380C2312yes—
759#380C2312yes—
760#379C2314yes—
761#379C2314yes—
762#379C2312yes—
763#379C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2314yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
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×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2311yescharacteristic
814#376C2314yes—
815C2×#95C2312yes—
816C2×#95C2312yes—
817C2×#95C2311yescharacteristic
818C2×#95C2311yescharacteristic
819C25C2411yescharacteristic
820C25C2412yes—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C22×Q8C2411yescharacteristic
825C22×Q8C2412yes—
826C22×Q8C2412yes—
827C22×Q8C2414yes—
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×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
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×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2411yescharacteristic
867C4⋊Q8—24no—
868C4⋊Q8—24no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871#127—28no—
872#126—84no—
873#126—84no—
874#126—84no—
875#125—24no—
876#125—24no—
877#125—44no—
878#125—44no—
879#125—44no—
880#125—44no—
881#125—44no—
882#125—44no—
883#124—28no—
884#124—48no—
885#124—84no—
886#124—84no—
887#123—44no—
888#123—44no—
889#123—48no—
890#123—44no—
891#123—84no—
892C22⋊Q8—28no—
893C22⋊Q8—28no—
894C22⋊Q8—44no—
895C22⋊Q8—48no—
896C22⋊Q8—48no—
897C22⋊Q8—44no—
898C22⋊Q8—42no—
899C22⋊Q8—42no—
900C22⋊Q8—84no—
901#121—28no—
902#121—28no—
903#121—44no—
904#121—44no—
905#121—44no—
906#121—44no—
907#121—42no—
908#121—42no—
909#121—48no—
910#121—84no—
911#120—216no—
912#120—44no—
913C4×Q8—28no—
914C4×Q8—28no—
915C4×Q8—42no—
916C4×Q8—42no—
917C4×Q8—84no—
918C4×D4—42no—
919C4×D4—42no—
920C4×D4—44no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—84no—
929C4×D4—84no—
930#117—24no—
931#117—24no—
932#117—24no—
933#117—24no—
934#117—24no—
935#117—24no—
936#117—24no—
937#117—24no—
938#117—28no—
939#117—28no—
940#117—44no—
941#117—84no—
942#117#4118yes—
943C2×C4⋊C4—24no—
944C2×C4⋊C4—24no—
945C2×C4⋊C4—24no—
946C2×C4⋊C4—24no—
947C2×C4⋊C4—24no—
948C2×C4⋊C4—44no—
949C2×C4⋊C4—44no—
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C22⋊C4—28no—
1020C2×C22⋊C4—42no—
1021C2×C22⋊C4—44no—
1022C2×C22⋊C4—42no—
1023C2×C22⋊C4—48no—
1024C2×C22⋊C4—44no—
1025C2×C22⋊C4—82no—
1026C2×C22⋊C4—82no—
1027C2×C22⋊C4—82no—
1028C2×C22⋊C4—82no—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2411yescharacteristic
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C42—24no—
1095C2×C42—24no—
1096C2×C42—28no—
1097C2×C42—44no—
1098C2×C42—82no—
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2414yes—
1124C2×C42C2414yes—
1125C2×C42C2412yes—
1126#95C2414yes—
1127#95C2411yescharacteristic
1128#95C2411yescharacteristic
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2411yescharacteristic
1132#95C2411yescharacteristic
1133#95C2411yescharacteristic
1134#95C2411yescharacteristic
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
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#95C2414yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192C24—22no—
1193C24—22no—
1194C24—22no—
1195C24—22no—
1196C24—24no—
1197C24—24no—
1198C24—24no—
1199C24—41no—
1200C24—41no—
1201C24—41no—
1202C24—42no—
1203C24—42no—
1204C24—42no—
1205C24—42no—
1206C24C2511yescharacteristic
1207C24C2514yes—
1208C24C2512yes—
1209C24C2511yescharacteristic
1210C24C2511yescharacteristic
1211#41—416no—
1212C2×Q8—24no—
1213C2×Q8—22no—
1214C2×Q8—24no—
1215C2×Q8—22no—
1216C2×Q8—22no—
1217C2×Q8—24no—
1218C2×Q8—42no—
1219C2×Q8—42no—
1220C2×Q8—42no—
1221C2×Q8—44no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—28no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—22no—
1232C2×D4—28no—
1233C2×D4—28no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—22no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—22no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—42no—
1248C2×D4—44no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—42no—
1253C2×D4—44no—
1254C2×D4—416no—
1255C2×D4—816no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—24no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—22no—
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—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—24no—
1283C22×C4—22no—
1284C22×C4—24no—
1285C22×C4—41no—
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—41no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—42no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—416no—
1314C22×C4C2×#4114yes—
1315C22×C4H(5,𝔽2)14yes—
1316C22×C42−1+414yes—
1317C22×C4C2511yescharacteristic
1318C22×C4C2512yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2514yes—
1323C22×C4C2512yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2511yescharacteristic
1336C22×C4C2514yes—
1337C22×C4C2514yes—
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C22×C4C2512yes—
1343C22×C4C2512yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2511yescharacteristic
1346C22×C4C2511yescharacteristic
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—24no—
1370C4⋊C4—24no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—44no—
1405C4⋊C4—42no—
1406C4⋊C4—44no—
1407C4⋊C4—44no—
1408C4⋊C4—44no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4C2×#4114yes—
1415C4⋊C4C2×#4114yes—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—22no—
1423C22⋊C4—22no—
1424C22⋊C4—24no—
1425C22⋊C4—24no—
1426C22⋊C4—24no—
1427C22⋊C4—24no—
1428C22⋊C4—28no—
1429C22⋊C4—28no—
1430C22⋊C4—22no—
1431C22⋊C4—28no—
1432C22⋊C4—22no—
1433C22⋊C4—24no—
1434C22⋊C4—44no—
1435C22⋊C4—41no—
1436C22⋊C4—41no—
1437C22⋊C4—41no—
1438C22⋊C4—41no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—42no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
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⋊C4C2×#4118yes—
1481C42—24no—
1482C42—24no—
1483C42—24no—
1484C42—22no—
1485C42—22no—
1486C42—22no—
1487C42—22no—
1488C42—24no—
1489C42—22no—
1490C42—22no—
1491C42—22no—
1492C42—22no—
1493C42—24no—
1494C42—24no—
1495C42—24no—
1496C42—24no—
1497C42—42no—
1498C42—42no—
1499C42—44no—
1500C42—44no—
1501C42—44no—
1502C42—44no—
1503C42—44no—
1504C42—44no—
1505C42—44no—
1506C42—44no—
1507C42C2×#4118yes—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—21no—
1519C23—24no—
1520C23—22no—
1521C23—22no—
1522C23—24no—
1523C23—21no—
1524C23—21no—
1525C23—22no—
1526C23—24no—
1527C23—24no—
1528C23—21no—
1529C23—22no—
1530C23—22no—
1531C23—24no—
1532C23—21no—
1533C23—24no—
1534C23—21no—
1535C23—22no—
1536C23—22no—
1537C23—24no—
1538C23—21no—
1539C23—44no—
1540C23—44no—
1541C23—44no—
1542C23—44no—
1543C23—48no—
1544C23—82no—
1545C23—82no—
1546C23—82no—
1547C23—84no—
1548C23—84no—
1549C23—84no—
1550C23—84no—
1551C23—84no—
1552C23—84no—
1553C23C22×#4112yes—
1554C23C2×H(5,𝔽2)12yes—
1555C23C2×2−1+412yes—
1556C23#58512yes—
1557C23C2611yescharacteristic
1558Q8—48no—
1559Q8—44no—
1560Q8—84no—
1561Q8—164no—
1562D4—48no—
1563D4—48no—
1564D4—48no—
1565D4—44no—
1566D4—88no—
1567D4—88no—
1568D4—84no—
1569D4—88no—
1570D4—84no—
1571D4—88no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—24no—
1602C2×C4—24no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—24no—
1611C2×C4—22no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—21no—
1632C2×C4—24no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—24no—
1641C2×C4—24no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—48no—
1654C2×C4—44no—
1655C2×C4—48no—
1656C2×C4—44no—
1657C2×C4—44no—
1658C2×C4—44no—
1659C2×C4—44no—
1660C2×C4—44no—
1661C2×C4—48no—
1662C2×C4—84no—
1663C2×C4—82no—
1664C2×C4—84no—
1665C2×C4—82no—
1666C2×C4—82no—
1667C2×C4—84no—
1668C2×C4—84no—
1669C2×C4—84no—
1670C2×C4—164no—
1671C2×C4—164no—
1672C2×C4#542116yes—
1673C2×C4C22×#4114yes—
1674C2×C4C22×#4114yes—
1675C2×C4C22×#4112yes—
1676C2×C4C22×#4112yes—
1677C2×C4C2×H(5,𝔽2)12yes—
1678C2×C4C2×H(5,𝔽2)12yes—
1679C2×C4C2×2−1+412yes—
1680C2×C4C2×2−1+412yes—
1681C2×C4#58512yes—
1682C22—22no—
1683C22—22no—
1684C22—22no—
1685C22—22no—
1686C22—22no—
1687C22—22no—
1688C22—22no—
1689C22—22no—
1690C22—22no—
1691C22—41no—
1692C22—41no—
1693C22—41no—
1694C22—41no—
1695C22—42no—
1696C22—42no—
1697C22—44no—
1698C22—44no—
1699C22—41no—
1700C22—41no—
1701C22—42no—
1702C22—41no—
1703C22—44no—
1704C22—42no—
1705C22—41no—
1706C22—44no—
1707C22—42no—
1708C22—44no—
1709C22—41no—
1710C22—41no—
1711C22—42no—
1712C22—44no—
1713C22—42no—
1714C22—44no—
1715C22—41no—
1716C22—88no—
1717C22—168no—
1718C22C2×#54214yes—
1719C22C23×#4111yescharacteristic
1720C22C22×H(5,𝔽2)11yescharacteristic
1721C22C22×2−1+411yescharacteristic
1722C22C2×#58511yescharacteristic
1723C22C2×#58511yescharacteristic
1724C22H(7,𝔽2)11yescharacteristic
1725C22H(7,𝔽2)11yescharacteristic
1726C4—24no—
1727C4—22no—
1728C4—24no—
1729C4—41no—
1730C4—42no—
1731C4—42no—
1732C4—41no—
1733C4—41no—
1734C4—42no—
1735C4—42no—
1736C4—42no—
1737C4—42no—
1738C4—44no—
1739C4—44no—
1740C4—41no—
1741C4—41no—
1742C4—42no—
1743C4—42no—
1744C4—42no—
1745C4—41no—
1746C4—41no—
1747C4—42no—
1748C4—41no—
1749C4—41no—
1750C4—42no—
1751C4—44no—
1752C4—42no—
1753C4—42no—
1754C4C2×#54214yes—
1755C4C2×#54214yes—
1756C2—24no—
1757C2—42no—
1758C2—82no—
1759C2—81no—
1760C2—84no—
1761C2C22×#54211yescharacteristic
1762C2#6283111yescharacteristic
1763C2#6288111yescharacteristic
1764C2#6292411yescharacteristic
1765C2#6295511yescharacteristic
1766C2#6300811yescharacteristic
1767C2#6300811yescharacteristic
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. #42768C2semidirect
2. #42740C2semidirect
3. #42659C2semidirect
4. #42618C2semidirect
5. #42579C2semidirect
6. #42472C2semidirect
7. #42467C2semidirect
8. #42459C2semidirect
9. #40785C2semidirect
10. #40694C2semidirect
11. #40171C2semidirect
12. #40147C2semidirect
13. #39905C2semidirect
14. #39903C2semidirect
15. #39736C2semidirect
16. #39236C2semidirect
17. #39213C2semidirect
18. #39147C2semidirect
19. #38566C2semidirect
20. #38514C2semidirect
21. #35640C2semidirect
22. #35558C2semidirect
23. #35556C2semidirect
24. #35542C2semidirect
25. #35540C2semidirect
26. #35529C2semidirect
27. #35333C2semidirect
29. #35160C2semidirect
30. C2×#2490C2semidirect
31. #34742C2semidirect
32. #34739C2semidirect
33. #34269C2semidirect
34. #34213C2semidirect
35. #34180C2semidirect
47. #2851C22semidirect
48. #2851C22semidirect
50. #2837C22semidirect
51. #2831C22semidirect
52. #2830C22semidirect
53. #2829C22semidirect
54. #2800C22semidirect
55. #2796C22semidirect
56. #2795C22semidirect
57. #2793C22semidirect
58. #2790C22semidirect
59. #2772C22semidirect
60. #2770C22semidirect
61. #2765C22semidirect
62. #2761C22semidirect
63. #2761C22semidirect
64. #2759C22semidirect
65. #2757C22semidirect
66. #2757C22semidirect
67. #2757C22semidirect
68. #2754C22semidirect
69. #2751C22semidirect
70. #2741C22semidirect
71. #2737C22semidirect
72. #2730C22semidirect
73. #2718C22semidirect
74. #2715C22semidirect
75. #2712C22semidirect
76. #2710C22semidirect
77. #2705C22semidirect
78. #2701C22semidirect
79. #2701C22semidirect
80. #2700C22semidirect
81. #2698C22semidirect
82. #2692C22semidirect
83. #2691C22semidirect
84. #2691C22semidirect
85. #2687C22semidirect
86. #2662C22semidirect
87. #2654C22semidirect
88. #2653C22semidirect
89. #2653C22semidirect
90. #2652C22semidirect
91. #2651C22semidirect
92. #2651C22semidirect
93. #2644C22semidirect
95. #2638C22semidirect
96. #2637C22semidirect
97. #2630C22semidirect
98. #2629C22semidirect
99. #2629C22semidirect
101. #2620C22semidirect
103. #2592C22semidirect
104. #2592C22semidirect
108. #2566C22semidirect
109. #2566C22semidirect
110. #2566C22semidirect
111. #2566C22semidirect
112. #2565C22semidirect
113. #2565C22semidirect
114. #2563C22semidirect
115. #2563C22semidirect
116. #2562C22semidirect
117. #2562C22semidirect
118. #2552C22semidirect
119. #2552C22semidirect
120. #2552C22semidirect
121. #2552C22semidirect
122. #2550C22semidirect
123. #2550C22semidirect
124. #2550C22semidirect
125. #2550C22semidirect
126. #2548C22semidirect
127. #2548C22semidirect
128. #2547C22semidirect
129. #2542C22semidirect
130. #2532C22semidirect
131. #2530C22semidirect
132. #2515C22semidirect
133. #2514C22semidirect
134. #2513C22semidirect
135. #2513C22semidirect
136. #2513C22semidirect
137. #2513C22semidirect
138. #2513C22semidirect
139. #2512C22semidirect
140. #2512C22semidirect
141. #2512C22semidirect
142. #2512C22semidirect
143. #2512C22semidirect
144. #2512C22semidirect
145. #2511C22semidirect
147. #2497C22semidirect
148. #2496C22semidirect
149. #2495C22semidirect
150. #2494C22semidirect
151. #2492C22semidirect
152. #2491C22semidirect
153. #2491C22semidirect
154. #2491C22semidirect
163. #2490C22semidirect
164. #2490C22semidirect
165. #2490C22semidirect
166. #2489C22semidirect
171. #2479C22semidirect
172. #2477C22semidirect
176. #2468C22semidirect
177. #2461C22semidirect
178. #2458C22semidirect
179. #2454C22semidirect
180. #2454C22semidirect
181. #2452C22semidirect
182. #2452C22semidirect
183. #2447C22semidirect
184. #2442C22semidirect
185. #2442C22semidirect
186. #2441C22semidirect
187. #2441C22semidirect
188. #2440C22semidirect
189. #2440C22semidirect
190. #2439C22semidirect
191. #2439C22semidirect
198. #2426C22semidirect
199. #2423C22semidirect
200. #2423C22semidirect
205. #2422C22semidirect
206. #2422C22semidirect
207. #2422C22semidirect
208. #2421C22semidirect
209. #2421C22semidirect
214. #2420C22semidirect
215. #2420C22semidirect
227. #2396C22semidirect
228. #2396C22semidirect
229. #2395C22semidirect
230. #2395C22semidirect
233. #2370C22semidirect
234. #2370C22semidirect
235. #2369C22semidirect
236. #2367C22semidirect
237. #2367C22semidirect
238. #2366C22semidirect
239. #2366C22semidirect
240. #2365C22semidirect
243. #2355C22semidirect
244. #2355C22semidirect
245. #2355C22semidirect
246. Q8×C4⋊C4C22semidirect
247. #2347C22semidirect
248. #2346C22semidirect
249. #2345C22semidirect
250. #2344C22semidirect
253. #2335C22semidirect
254. #2332C22semidirect
256. #2326C22semidirect
257. #2324C22semidirect
258. #2324C22semidirect
259. #2324C22semidirect
265. #2314C22semidirect
266. #2314C22semidirect
273. C4×C22⋊Q8C22semidirect
274. C4×C22⋊Q8C22semidirect
275. C4×#123C22semidirect
276. C4×#123C22semidirect
277. C4×#121C22semidirect
278. C4×#121C22semidirect
289. #2285C22semidirect
290. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#427682
#427402
#426592
#426182
#425792
#424722
#424672
#424592
#407852
#406942
#401712
#401472
#399052
#399032
#397362
#392362
#392132
#391472
#385662
#385142
#356402
#355582
#355562
#355422
#355402
#355292
#353332
#352522
#351602
C2×#24902
#347422
#347392
#342692
#342132
#341802