Finite Group Databasebeta

← #7652173

Subgroups — #7652173

Order 512.

4737 conjugacy classes of subgroups.

The subgroup lattice has 1707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42785C212yesmaximal, complemented
2#42720C212yesmaximal, complemented
3#42672C212yesmaximal, complemented
4#42665C212yesmaximal, complemented
5#42661C212yesmaximal, complemented
6#42640C212yesmaximal, complemented
7#42549C212yesmaximal, complemented
8#42457C212yesmaximal, complemented
9#41513C214yesmaximal, complemented
10#40892C214yesmaximal, complemented
11#40078C212yesmaximal, complemented
12#40055C212yesmaximal, complemented
13#39905C212yesmaximal, complemented
14#39903C212yesmaximal, complemented
15#39784C212yesmaximal, complemented
16#39657C212yesmaximal, complemented
17#39609C212yesmaximal, complemented
18#39159C212yesmaximal, complemented
19#38598C214yesmaximal, complemented
20#38547C214yesmaximal, complemented
21#35672C211yesmaximal, characteristic, complemented
22#35668C211yesmaximal, characteristic, complemented
23#35630C211yesmaximal, characteristic, complemented
24#35628C211yesmaximal, characteristic, complemented
25#35576C211yesmaximal, characteristic, complemented
26#35542C211yesmaximal, characteristic
27#35306C211yesmaximal, characteristic
28#35279C211yesmaximal, characteristic, complemented
29#35160C211yesmaximal, characteristic, complemented
30C2×#2492C211yesmaximal, characteristic, complemented
31#34742C211yesmaximal, characteristic
32#34739C211yesmaximal, characteristic, complemented
33#34268C211yesmaximal, characteristic, complemented
34#34213C211yesmaximal, characteristic, complemented
35#34180C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#536C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C22×C4⋊Q8C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C22×C22⋊Q8C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2857C2212yes—
46#2857C2212yescomplemented
47#2857C2212yescomplemented
48#2852C2214yes—
49#2850C2212yes—
50#2839C2214yescomplemented
51#2838C2214yes—
52#2838C2214yescomplemented
53#2832C2214yes—
54#2801C2214yes—
55#2799C2214yescomplemented
56#2798C2214yes—
57#2779C2214yes—
58#2777C2214yescomplemented
59#2774C2214yescomplemented
60#2774C2214yescomplemented
61#2773C2214yes—
62#2770C2214yescomplemented
63#2767C2214yescomplemented
64#2762C2214yescomplemented
65#2759C2214yes—
66#2759C2214yescomplemented
67#2758C2214yescomplemented
68#2758C2214yescomplemented
69#2755C2214yescomplemented
70#2754C2214yes—
71#2754C2214yescomplemented
72#2745C2214yes—
73#2745C2214yes—
74#2742C2214yes—
75#2742C2214yes—
76#2741C2214yes—
77#2739C2214yescomplemented
78#2737C2214yes—
79#2731C2214yes—
80#2729C2214yescomplemented
81#2716C2214yescomplemented
82#2698C2214yescomplemented
83#2692C2214yes—
84#2687C2214yes—
85#2674C2214yes—
86#2666C2214yescomplemented
87#2665C2214yescomplemented
88#2663C2214yes—
89#2655C2214yescomplemented
90#2654C2214yes—
91#2654C2214yescomplemented
92#2653C2214yes—
93#2650C2214yes—
94#2650C2214yescomplemented
95#2645C2214yescomplemented
96#2643C2214yes—
97#2632C2214yes—
98#2628C2214yes—
99#2628C2212yescomplemented
100#2628C2212yescomplemented
101#2621C2212yes—
102#2620C2212yes—
103#2592C2212yescomplemented
104#2592C2212yescomplemented
105#2583C2214yes—
106#2568C2212yescomplemented
107#2568C2212yescomplemented
108#2568C2212yescomplemented
109#2568C2212yescomplemented
110#2567C2212yescomplemented
111#2567C2212yescomplemented
112#2565C2212yescomplemented
113#2565C2212yescomplemented
114#2563C2212yes—
115#2563C2212yescomplemented
116#2562C2212yes—
117#2562C2212yes—
118#2551C2212yescomplemented
119#2551C2212yescomplemented
120#2551C2212yescomplemented
121#2551C2212yescomplemented
122#2550C2212yescomplemented
123#2550C2212yescomplemented
124#2550C2212yescomplemented
125#2550C2212yescomplemented
126#2547C2212yes—
127#2542C2212yescomplemented
128#2532C2214yescomplemented
129#2530C2214yescomplemented
130#2525C2214yes—
131#2521C2214yes—
132#2520C2214yescomplemented
133#2514C2212yescomplemented
134#2514C2212yescomplemented
135#2514C2212yescomplemented
136#2514C2212yescomplemented
137#2514C2212yescomplemented
138#2513C2212yescomplemented
139#2512C2212yescomplemented
140#2511C2212yescomplemented
141#2511C2212yescomplemented
142#2511C2212yescomplemented
143#2511C2212yescomplemented
144#2511C2212yescomplemented
145#2509C2214yescomplemented
146#2497C2212yescomplemented
147#2496C2212yescomplemented
148#2495C2214yes—
149#2495C2212yescomplemented
150#2494C2212yescomplemented
151#2493C2214yes—
152#2493C2214yes—
153#2492C2212yes—
154#2492C2212yes—
155#2492C2212yes—
156#2492C2212yes—
157#2492C2212yes—
158#2492C2212yes—
159#2492C2212yes—
160#2492C2212yes—
161#2492C2214yes—
162#2492C2212yes—
163#2492C2212yescomplemented
164#2492C2212yescomplemented
165#2491C2212yes—
166#2490C2212yes—
167#2489C2212yes—
168#2489C2212yescomplemented
169#2489C2212yescomplemented
170#2488C2214yes—
171#2488C2214yes—
172#2488C2214yes—
173#2487C2214yes—
174#2484C2214yes—
175#2482C2214yes—
176#2479C2214yes—
177#2477C2214yes—
178#2472C2214yes—
179#2465C2214yescomplemented
180#2453C2212yescomplemented
181#2453C2212yescomplemented
182#2451C2212yescomplemented
183#2451C2214yescomplemented
184#2451C2212yescomplemented
185#2442C2211yescharacteristic
186#2442C2211yescharacteristic
187#2441C2211yescharacteristic
188#2441C2211yescharacteristic
189#2440C2211yescharacteristic
190#2440C2211yescharacteristic
191#2439C2211yescharacteristic
192#2439C2211yescharacteristic
193#2438C2212yes—
194#2438C2214yes—
195#2438C2214yes—
196#2438C2212yes—
197#2437C2212yes—
198#2437C2212yes—
199#2434C2214yes—
200#2423C2212yes—
201#2423C2212yes—
202#2423C2212yes—
203#2423C2212yes—
204#2423C2211yescharacteristic
205#2423C2211yescharacteristic
206#2422C2211yescharacteristic
207#2422C2211yescharacteristic
208#2421C2212yes—
209#2421C2212yes—
210#2421C2212yes—
211#2421C2212yes—
212#2421C2211yescharacteristic
213#2421C2211yescharacteristic
214#2420C2211yescharacteristic
215#2420C2211yescharacteristic
216#2419C2212yes—
217#2419C2212yes—
218#2418C2212yes—
219#2418C2212yes—
220#2417C2212yes—
221#2417C2212yes—
222#2415C2212yes—
223#2415C2212yes—
224#2413C2214yes—
225#2412C2214yes—
226#2409C2214yes—
227#2396C2212yes—
228#2396C2212yes—
229#2395C2212yes—
230#2395C2212yes—
231C2×#400C2212yes—
232C2×#393C2212yes—
233#2370C2212yescomplemented
234#2370C2212yescomplemented
235#2369C2212yescomplemented
236#2367C2212yescomplemented
237#2367C2212yescomplemented
238#2365C2212yescomplemented
239#2365C2212yescomplemented
240#2365C2212yescomplemented
241#2359C2214yes—
242#2359C2214yes—
243#2355C2212yescomplemented
244#2355C2212yescomplemented
245#2355C2212yescomplemented
246Q8×C4⋊C4C2212yescomplemented
247#2347C2212yes—
248#2346C2212yes—
249#2345C2212yes—
250#2344C2212yes—
251#2343C2214yes—
252#2342C2214yes—
253#2335C2214yes—
254#2332C2214yescomplemented
255#2331C2214yescomplemented
256#2329C2214yes—
257#2323C2214yes—
258#2323C2212yescomplemented
259#2323C2212yescomplemented
260#2317C2211yescharacteristic
261#2317C2211yescharacteristic
262#2317C2211yescharacteristic
263#2317C2211yescharacteristic
264#2317C2211yescharacteristic
265#2314C2212yes—
266#2314C2212yes—
267#2311C2211yescharacteristic
268#2311C2211yescharacteristic
269#2311C2211yescharacteristic
270#2310C2211yescharacteristic
271#2310C2211yescharacteristic
272C4×C22⋊Q8C2214yes—
273C4×C22⋊Q8C2212yes—
274C4×C22⋊Q8C2212yes—
275C4×C22⋊Q8C2212yescomplemented
276C4×C22⋊Q8C2212yescomplemented
277C4×#123C2212yes—
278C4×#123C2212yes—
279#2297C2211yescharacteristic
280#2296C2211yescharacteristic
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283C2×#391C2211yescharacteristic
284C2×#391C2211yescharacteristic
285C2×#391C2212yes—
286C2×#388C2212yes—
287#2285C2211yescharacteristic
288#2285C2211yescharacteristic
289#2285C2212yes—
290#2283C2212yes—
291#2280C2211yescharacteristic
292#2280C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296#2274C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×Q8C2311yescharacteristic
301C23×Q8C2312yes—
302C24×C4C2311yescharacteristic
303#544—44no—
304#536—28no—
305#533—28no—
306C2×C4⋊Q8—44no—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2314yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2314yes—
318C2×#126C2314yes—
319C2×#125C2311yescharacteristic
320C2×#125C2311yescharacteristic
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#124C2312yes—
324C2×#124C2314yes—
325#525—44no—
326C2×#123C2312yes—
327C2×#123C2314yes—
328C2×#123C2312yes—
329C2×#123C2312yes—
330C2×C22⋊Q8—44no—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2314yes—
346C2×#121C2311yescharacteristic
347C2×#121C2311yescharacteristic
348C2×#120C2312yes—
349#519—44no—
350C4×#41—44no—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2311yescharacteristic
366C2×#117—28no—
367C2×#117C2311yescharacteristic
368C2×#117C2311yescharacteristic
369C2×#117C2311yescharacteristic
370C2×#117C2311yescharacteristic
371C2×#117C2311yescharacteristic
372C2×#117C2312yes—
373C2×#117C2311yescharacteristic
374C2×#117C2312yes—
375C2×#117C2311yescharacteristic
376C2×#117C2311yescharacteristic
377C2×#117C2312yes—
378C2×#117C2314yes—
379C2×#117C2314yes—
380C2×#117C2311yescharacteristic
381C22×C4⋊C4C2311yescharacteristic
382C22×C4⋊C4C2311yescharacteristic
383C22×C4⋊C4C2311yescharacteristic
384C22×C4⋊C4C2311yescharacteristic
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C22⋊C4C2312yes—
389C22×C22⋊C4C2311yescharacteristic
390C22×C22⋊C4C2311yescharacteristic
391C22×C22⋊C4C2312yes—
392C22×C22⋊C4C2312yes—
393C22×C42C2312yes—
394C22×C42C2311yescharacteristic
395C22×C42C2311yescharacteristic
396C22×C42C2312yes—
397C22×C42C2312yes—
398#401C2314yes—
399#401C2314yes—
400#401C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2312yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2312yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2312yes—
426#400C2312yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2312yes—
433#399C2314yes—
434#399C2314yes—
435#399C2312yes—
436#399C2312yes—
437#399C2312yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2312yes—
446#398C2312yes—
447#398C2314yes—
448#398C2314yes—
449#398C2312yes—
450#398C2312yes—
451#398C2312yes—
452#398C2312yes—
453#398C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2312yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2312yes—
466#397C2312yes—
467#397C2312yes—
468#397C2312yes—
469#397C2314yes—
470#397C2314yes—
471#396C2312yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2312yes—
476#396C2312yes—
477#396C2312yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2314yes—
484#395C2314yes—
485#395C2314yes—
486#395C2314yes—
487#395C2312yes—
488#395C2312yes—
489#395C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2312yes—
493#394C2314yes—
494#394C2314yes—
495#394C2312yes—
496#394C2312yes—
497#394C2312yes—
498#393C2314yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2312yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#393C2312yes—
508#393C2314yes—
509#393C2314yes—
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#391C2314yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2314yes—
531#391C2314yes—
532#391C2312yes—
533#391C2314yes—
534#391C2314yes—
535#391C2314yes—
536#391C2314yes—
537#391C2314yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2314yes—
542#391C2314yes—
543#391C2312yes—
544#391C2312yes—
545#391C2312yes—
546#391C2314yes—
547#391C2314yes—
548#391C2312yes—
549#390C2314yes—
550#390C2312yes—
551#390C2312yes—
552#390C2312yes—
553#390C2311yescharacteristic
554#390C2311yescharacteristic
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#389C2311yescharacteristic
571#389C2311yescharacteristic
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2311yescharacteristic
584#389C2311yescharacteristic
585#389C2311yescharacteristic
586#389C2311yescharacteristic
587#389C2312yes—
588#389C2311yescharacteristic
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2312yes—
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#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2312yes—
621#388C2314yes—
622#388C2314yes—
623#388C2312yes—
624#388C2312yes—
625#388C2314yes—
626#388C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2312yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2312yes—
681#385C2312yes—
682#385C2312yes—
683#385C2312yes—
684#385C2312yes—
685#385C2314yes—
686#385C2314yes—
687#385C2312yes—
688#385C2312yes—
689#385C2312yes—
690#385C2312yes—
691#385C2312yes—
692#385C2312yes—
693#385C2312yes—
694#384C2311yescharacteristic
695#384C2312yes—
696#384C2311yescharacteristic
697#384C2312yes—
698#384C2312yes—
699#384C2312yes—
700#384C2312yes—
701#384C2311yescharacteristic
702#384C2311yescharacteristic
703#383C2314yes—
704#383C2314yes—
705#383C2314yes—
706#383C2314yes—
707#382C2314yes—
708#382C2312yes—
709#382C2312yes—
710#382C2311yescharacteristic
711#382C2311yescharacteristic
712#382C2314yes—
713#382C2314yes—
714#382C2312yes—
715#382C2312yes—
716#382C2312yes—
717#382C2314yes—
718#382C2311yescharacteristic
719#382C2311yescharacteristic
720#381C2314yes—
721#381C2314yes—
722#381C2312yes—
723#381C2314yes—
724#381C2312yes—
725#381C2312yes—
726#381C2312yes—
727#380C2312yes—
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2311yescharacteristic
735#380C2312yes—
736#380C2314yes—
737#380C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2311yescharacteristic
742#380C2312yes—
743#380C2314yes—
744#380C2312yes—
745#380C2314yes—
746#380C2314yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2311yescharacteristic
751#380C2311yescharacteristic
752#380C2311yescharacteristic
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756#379C2312yes—
757#379C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
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×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2311yescharacteristic
810#376C2314yes—
811C2×#95C2312yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2312yes—
815C2×#95C2312yes—
816C2×#95C2311yescharacteristic
817C2×#95C2311yescharacteristic
818C2×#95C2312yes—
819C25C2411yescharacteristic
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—24no—
823C22×Q8—24no—
824C22×Q8—24no—
825C22×Q8—24no—
826C22×Q8—44no—
827C22×Q8—44no—
828C22×Q8—82no—
829C22×Q8C2412yes—
830C22×Q8C2412yes—
831C22×Q8C2411yescharacteristic
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2414yes—
835C22×Q8C2414yes—
836C22×Q8C2414yes—
837C22×D4C2412yes—
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2412yes—
841C23×C4—24no—
842C23×C4—24no—
843C23×C4—24no—
844C23×C4C2412yes—
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2411yescharacteristic
863C4⋊Q8—24no—
864C4⋊Q8—24no—
865C4⋊Q8—28no—
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871C4⋊Q8—44no—
872C4⋊Q8—48no—
873C4⋊Q8—84no—
874#126—84no—
875#125—24no—
876#125—24no—
877#125—44no—
878#125—44no—
879#124—28no—
880#124—84no—
881#123—216no—
882#123—28no—
883#123—44no—
884#123—44no—
885C22⋊Q8—28no—
886C22⋊Q8—28no—
887C22⋊Q8—28no—
888C22⋊Q8—28no—
889C22⋊Q8—28no—
890C22⋊Q8—48no—
891C22⋊Q8—44no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—48no—
897C22⋊Q8—42no—
898C22⋊Q8—42no—
899C22⋊Q8—84no—
900#121—42no—
901#121—42no—
902#120—44no—
903C4×Q8—28no—
904C4×Q8—28no—
905C4×Q8—42no—
906C4×Q8—42no—
907C4×Q8—44no—
908C4×Q8—44no—
909C4×Q8—44no—
910C4×Q8—44no—
911C4×Q8—84no—
912C4×D4—42no—
913C4×D4—42no—
914C4×D4—44no—
915C4×D4—44no—
916C4×D4—44no—
917C4×D4—44no—
918#117—24no—
919#117—24no—
920#117—24no—
921#117—24no—
922#117—24no—
923#117—24no—
924#117—24no—
925#117—24no—
926#117—28no—
927#117—28no—
928#117—44no—
929#117—48no—
930#117—84no—
931#117#4118yes—
932C2×C4⋊C4—24no—
933C2×C4⋊C4—24no—
934C2×C4⋊C4—24no—
935C2×C4⋊C4—24no—
936C2×C4⋊C4—24no—
937C2×C4⋊C4—44no—
938C2×C4⋊C4—44no—
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C22⋊C4—28no—
1013C2×C22⋊C4—24no—
1014C2×C22⋊C4—42no—
1015C2×C22⋊C4—44no—
1016C2×C22⋊C4—82no—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C22⋊C4C2411yescharacteristic
1024C2×C22⋊C4C2411yescharacteristic
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2411yescharacteristic
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C42—24no—
1065C2×C42—24no—
1066C2×C42—28no—
1067C2×C42—44no—
1068C2×C42—82no—
1069C2×C42C2412yes—
1070C2×C42C2411yescharacteristic
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2414yes—
1086C2×C42C2414yes—
1087C2×C42C2414yes—
1088C2×C42C2414yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2414yes—
1092C2×C42C2414yes—
1093C2×C42C2414yes—
1094C2×C42C2414yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2412yes—
1098#95C2414yes—
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2411yescharacteristic
1102#95C2411yescharacteristic
1103#95C2411yescharacteristic
1104#95C2411yescharacteristic
1105#95C2411yescharacteristic
1106#95C2411yescharacteristic
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2412yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2414yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180C24—22no—
1181C24—22no—
1182C24—22no—
1183C24—22no—
1184C24—41no—
1185C24—41no—
1186C24—41no—
1187C24C2511yescharacteristic
1188C24C2512yes—
1189C24C2511yescharacteristic
1190C24C2511yescharacteristic
1191#41—416no—
1192C2×Q8—24no—
1193C2×Q8—24no—
1194C2×Q8—24no—
1195C2×Q8—22no—
1196C2×Q8—24no—
1197C2×Q8—24no—
1198C2×Q8—24no—
1199C2×Q8—22no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—22no—
1204C2×Q8—28no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×Q8—44no—
1208C2×Q8—44no—
1209C2×Q8—44no—
1210C2×Q8—44no—
1211C2×Q8—44no—
1212C2×Q8—42no—
1213C2×Q8—44no—
1214C2×Q8—44no—
1215C2×Q8—44no—
1216C2×Q8—416no—
1217C2×Q8—816no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—42no—
1226C2×D4—42no—
1227C2×D4—42no—
1228C2×D4—42no—
1229C2×D4—42no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—24no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—24no—
1236C22×C4—24no—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—22no—
1240C22×C4—24no—
1241C22×C4—22no—
1242C22×C4—24no—
1243C22×C4—24no—
1244C22×C4—22no—
1245C22×C4—24no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—24no—
1250C22×C4—24no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—41no—
1267C22×C4—42no—
1268C22×C4—42no—
1269C22×C4—41no—
1270C22×C4—42no—
1271C22×C4—41no—
1272C22×C4—42no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—41no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—42no—
1279C22×C4—42no—
1280C22×C4—42no—
1281C22×C4—42no—
1282C22×C4—41no—
1283C22×C4—42no—
1284C22×C4—416no—
1285C22×C4C2×#4114yes—
1286C22×C4H(5,𝔽2)14yes—
1287C22×C42−1+414yes—
1288C22×C4C2512yes—
1289C22×C4C2511yescharacteristic
1290C22×C4C2514yes—
1291C22×C4C2511yescharacteristic
1292C22×C4C2514yes—
1293C22×C4C2512yes—
1294C22×C4C2511yescharacteristic
1295C22×C4C2511yescharacteristic
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2514yes—
1308C22×C4C2512yes—
1309C22×C4C2514yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2512yes—
1313C22×C4C2512yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2511yescharacteristic
1317C22×C4C2511yescharacteristic
1318C22×C4C2511yescharacteristic
1319C4⋊C4—22no—
1320C4⋊C4—22no—
1321C4⋊C4—24no—
1322C4⋊C4—24no—
1323C4⋊C4—22no—
1324C4⋊C4—22no—
1325C4⋊C4—24no—
1326C4⋊C4—24no—
1327C4⋊C4—24no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—28no—
1332C4⋊C4—28no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—24no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4C2×#4114yes—
1391C4⋊C4C2×#4114yes—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—24no—
1397C22⋊C4—22no—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—28no—
1405C22⋊C4—22no—
1406C22⋊C4—22no—
1407C22⋊C4—24no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—41no—
1411C22⋊C4—41no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—44no—
1436C22⋊C4—42no—
1437C22⋊C4C2×#4118yes—
1438C22⋊C42−1+414yes—
1439C42—24no—
1440C42—24no—
1441C42—24no—
1442C42—22no—
1443C42—22no—
1444C42—22no—
1445C42—22no—
1446C42—24no—
1447C42—22no—
1448C42—22no—
1449C42—22no—
1450C42—22no—
1451C42—24no—
1452C42—24no—
1453C42—24no—
1454C42—24no—
1455C42—42no—
1456C42—42no—
1457C42—44no—
1458C42—44no—
1459C42—44no—
1460C42—44no—
1461C42—44no—
1462C42—44no—
1463C42—44no—
1464C42—44no—
1465C42—44no—
1466C42—44no—
1467C42C2×#4118yes—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—22no—
1480C23—21no—
1481C23—22no—
1482C23—21no—
1483C23—22no—
1484C23—21no—
1485C23—22no—
1486C23—21no—
1487C23—22no—
1488C23—22no—
1489C23—21no—
1490C23—21no—
1491C23—22no—
1492C23—44no—
1493C23—44no—
1494C23—44no—
1495C23—44no—
1496C23—82no—
1497C23—82no—
1498C23—82no—
1499C23C22×#4112yes—
1500C23C2×H(5,𝔽2)12yes—
1501C23C2×2−1+412yes—
1502C23C2×2−1+412yes—
1503C23C2611yescharacteristic
1504Q8—48no—
1505Q8—48no—
1506Q8—48no—
1507Q8—44no—
1508Q8—84no—
1509Q8—88no—
1510Q8—88no—
1511Q8—164no—
1512D4—48no—
1513D4—44no—
1514D4—84no—
1515D4—84no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—22no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—24no—
1535C2×C4—21no—
1536C2×C4—22no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—24no—
1547C2×C4—24no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—24no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—24no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—22no—
1577C2×C4—24no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—22no—
1584C2×C4—24no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—21no—
1588C2×C4—24no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—48no—
1599C2×C4—44no—
1600C2×C4—44no—
1601C2×C4—44no—
1602C2×C4—48no—
1603C2×C4—44no—
1604C2×C4—48no—
1605C2×C4—44no—
1606C2×C4—44no—
1607C2×C4—44no—
1608C2×C4—44no—
1609C2×C4—48no—
1610C2×C4—84no—
1611C2×C4—84no—
1612C2×C4—84no—
1613C2×C4—82no—
1614C2×C4—84no—
1615C2×C4—84no—
1616C2×C4#542116yes—
1617C2×C4C22×#4114yes—
1618C2×C4C22×#4114yes—
1619C2×C4C22×#4112yes—
1620C2×C4C22×#4112yes—
1621C2×C4C2×H(5,𝔽2)12yes—
1622C2×C4C2×H(5,𝔽2)12yes—
1623C2×C4C2×2−1+412yes—
1624C2×C4C2×2−1+412yes—
1625C2×C4C2×2−1+412yes—
1626C2×C4C2×2−1+412yes—
1627C2×C4#58512yes—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—42no—
1642C22—41no—
1643C22—42no—
1644C22—41no—
1645C22—42no—
1646C22—41no—
1647C22—42no—
1648C22—41no—
1649C22—42no—
1650C22—41no—
1651C22—41no—
1652C22—42no—
1653C22—42no—
1654C22—41no—
1655C22—88no—
1656C22C2×#54214yes—
1657C22C23×#4111yescharacteristic
1658C22C22×H(5,𝔽2)11yescharacteristic
1659C22C22×2−1+411yescharacteristic
1660C22C22×2−1+411yescharacteristic
1661C22C2×#58511yescharacteristic
1662C22H(7,𝔽2)11yescharacteristic
1663C222−1+611yescharacteristic
1664C4—24no—
1665C4—22no—
1666C4—24no—
1667C4—22no—
1668C4—22no—
1669C4—42no—
1670C4—41no—
1671C4—42no—
1672C4—42no—
1673C4—41no—
1674C4—41no—
1675C4—42no—
1676C4—42no—
1677C4—42no—
1678C4—44no—
1679C4—44no—
1680C4—41no—
1681C4—42no—
1682C4—44no—
1683C4—42no—
1684C4—42no—
1685C4—41no—
1686C4—41no—
1687C4—42no—
1688C4—44no—
1689C4—42no—
1690C4—41no—
1691C4—42no—
1692C4—42no—
1693C4C2×#54214yes—
1694C4C2×#54214yes—
1695C2—24no—
1696C2—42no—
1697C2—82no—
1698C2—81no—
1699C2C22×#54211yescharacteristic
1700C2#6283711yescharacteristic
1701C2#6287911yescharacteristic
1702C2#6292411yescharacteristic
1703C2#6294211yescharacteristic
1704C2#6300011yescharacteristic
1705C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42785C2semidirect
2. #42720C2semidirect
3. #42672C2semidirect
4. #42665C2semidirect
5. #42661C2semidirect
6. #42640C2semidirect
7. #42549C2semidirect
8. #42457C2semidirect
9. #41513C2semidirect
10. #40892C2semidirect
11. #40078C2semidirect
12. #40055C2semidirect
13. #39905C2semidirect
14. #39903C2semidirect
15. #39784C2semidirect
16. #39657C2semidirect
17. #39609C2semidirect
18. #39159C2semidirect
19. #38598C2semidirect
20. #38547C2semidirect
21. #35672C2semidirect
22. #35668C2semidirect
23. #35630C2semidirect
24. #35628C2semidirect
25. #35576C2semidirect
28. #35279C2semidirect
29. #35160C2semidirect
30. C2×#2492C2semidirect
32. #34739C2semidirect
33. #34268C2semidirect
34. #34213C2semidirect
35. #34180C2semidirect
46. #2857C22semidirect
47. #2857C22semidirect
50. #2839C22semidirect
52. #2838C22semidirect
55. #2799C22semidirect
58. #2777C22semidirect
59. #2774C22semidirect
60. #2774C22semidirect
62. #2770C22semidirect
63. #2767C22semidirect
64. #2762C22semidirect
66. #2759C22semidirect
67. #2758C22semidirect
68. #2758C22semidirect
69. #2755C22semidirect
71. #2754C22semidirect
77. #2739C22semidirect
80. #2729C22semidirect
81. #2716C22semidirect
82. #2698C22semidirect
86. #2666C22semidirect
87. #2665C22semidirect
89. #2655C22semidirect
91. #2654C22semidirect
94. #2650C22semidirect
95. #2645C22semidirect
99. #2628C22semidirect
100. #2628C22semidirect
103. #2592C22semidirect
104. #2592C22semidirect
106. #2568C22semidirect
107. #2568C22semidirect
108. #2568C22semidirect
109. #2568C22semidirect
110. #2567C22semidirect
111. #2567C22semidirect
112. #2565C22semidirect
113. #2565C22semidirect
115. #2563C22semidirect
118. #2551C22semidirect
119. #2551C22semidirect
120. #2551C22semidirect
121. #2551C22semidirect
122. #2550C22semidirect
123. #2550C22semidirect
124. #2550C22semidirect
125. #2550C22semidirect
127. #2542C22semidirect
128. #2532C22semidirect
129. #2530C22semidirect
132. #2520C22semidirect
133. #2514C22semidirect
134. #2514C22semidirect
135. #2514C22semidirect
136. #2514C22semidirect
137. #2514C22semidirect
138. #2513C22semidirect
139. #2512C22semidirect
140. #2511C22semidirect
141. #2511C22semidirect
142. #2511C22semidirect
143. #2511C22semidirect
144. #2511C22semidirect
145. #2509C22semidirect
146. #2497C22semidirect
147. #2496C22semidirect
149. #2495C22semidirect
150. #2494C22semidirect
163. #2492C22semidirect
164. #2492C22semidirect
168. #2489C22semidirect
169. #2489C22semidirect
179. #2465C22semidirect
180. #2453C22semidirect
181. #2453C22semidirect
182. #2451C22semidirect
183. #2451C22semidirect
184. #2451C22semidirect
233. #2370C22semidirect
234. #2370C22semidirect
235. #2369C22semidirect
236. #2367C22semidirect
237. #2367C22semidirect
238. #2365C22semidirect
239. #2365C22semidirect
240. #2365C22semidirect
243. #2355C22semidirect
244. #2355C22semidirect
245. #2355C22semidirect
246. Q8×C4⋊C4C22semidirect
254. #2332C22semidirect
255. #2331C22semidirect
258. #2323C22semidirect
259. #2323C22semidirect
275. C4×C22⋊Q8C22semidirect
276. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#427852
#427202
#426722
#426652
#426612
#426402
#425492
#424572
#415132
#408922
#400782
#400552
#399052
#399032
#397842
#396572
#396092
#391592
#385982
#385472
#356722
#356682
#356302
#356282
#355762
#355422
#353062
#352792
#351602
C2×#24922
#347422
#347392
#342682
#342132
#341802