Finite Group Databasebeta

← #7690138

Subgroups — #7690138

Order 512.

5340 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59842C212yesmaximal, complemented
2#59804C214yesmaximal, complemented
3#59691C212yesmaximal, complemented
4#59562C212yesmaximal, complemented
5#59488C212yesmaximal, complemented
6#59457C211yesmaximal, characteristic, complemented
7#59143C211yesmaximal, characteristic, complemented
8#59070C211yesmaximal, characteristic, complemented
9#45068C212yesmaximal, complemented
10#44901C212yesmaximal, complemented
11#44592C214yesmaximal, complemented
12#43231C214yesmaximal, complemented
13#39533C212yesmaximal, complemented
14#39480C211yesmaximal, characteristic, complemented
15#39024C212yesmaximal, complemented
16#38985C211yesmaximal, characteristic, complemented
17#38694C214yesmaximal, complemented
18#38254C212yesmaximal, complemented
19#36527C212yesmaximal, complemented
20#36460C211yesmaximal, characteristic, complemented
21#36302C211yesmaximal, characteristic, complemented
22#36300C211yesmaximal, characteristic, complemented
23#36287C211yesmaximal, characteristic, complemented
24#36270C212yesmaximal, complemented
25#36240C212yesmaximal, complemented
26#36121C211yesmaximal, characteristic
27#36075C212yesmaximal, complemented
28#35890C212yesmaximal, complemented
29#34918C212yesmaximal, complemented
30#34793C211yesmaximal, characteristic, complemented
31#34331C211yesmaximal, characteristic, complemented
32#34261C212yesmaximal, complemented
33#34210C211yesmaximal, characteristic, complemented
34C4×#556C211yesmaximal, characteristic, complemented
35#34155C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×#556C2211yescharacteristic
38C2×#552C2214yescomplemented
39C2×#546C2212yes—
40C2×#532C2211yescharacteristic
41C22×#127C2211yescharacteristic
42C2×#518C2212yes—
43#2861C2212yescomplemented
44#2860C2212yescomplemented
45#2860C2212yescomplemented
46#2859C2212yescomplemented
47#2858C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2852C2214yescomplemented
51#2797C2214yescomplemented
52#2796C2214yescomplemented
53#2786C2214yescomplemented
54#2780C2214yescomplemented
55#2778C2214yescomplemented
56#2762C2214yescomplemented
57#2756C2214yescomplemented
58#2746C2214yescomplemented
59#2735C2214yes—
60#2735C2214yes—
61#2735C2214yes—
62#2717C2214yescomplemented
63#2715C2214yescomplemented
64#2711C2214yescomplemented
65#2709C2214yes—
66#2707C2214yescomplemented
67#2705C2214yescomplemented
68#2702C2214yescomplemented
69#2700C2214yescomplemented
70#2690C2214yes—
71#2685C2214yes—
72#2648C2214yescomplemented
73#2644C2212yescomplemented
74#2636C2214yescomplemented
75#2625C2212yes—
76#2612C2214yescomplemented
77#2609C2214yescomplemented
78#2603C2214yescomplemented
79#2601C2214yescomplemented
80#2601C2214yescomplemented
81#2597C2214yescomplemented
82#2595C2214yescomplemented
83#2595C2214yescomplemented
84#2592C2212yescomplemented
85#2580C2212yescomplemented
86#2578C2214yescomplemented
87#2576C2214yescomplemented
88#2576C2214yescomplemented
89#2571C2211yescharacteristic, complemented
90#2570C2212yescomplemented
91#2567C2211yescharacteristic, complemented
92#2567C2211yescharacteristic, complemented
93#2566C2212yescomplemented
94#2566C2212yescomplemented
95#2562C2214yescomplemented
96#2559C2214yescomplemented
97#2558C2214yescomplemented
98#2558C2214yescomplemented
99#2556C2214yes—
100#2552C2211yescharacteristic, complemented
101#2548C2211yescharacteristic
102#2548C2211yescharacteristic
103#2544C2212yes—
104#2544C2212yes—
105#2544C2212yes—
106#2538C2212yescomplemented
107#2538C2212yescomplemented
108#2536C2214yescomplemented
109#2531C2214yescomplemented
110#2530C2212yes—
111#2528C2212yescomplemented
112#2526C2214yescomplemented
113#2521C2214yescomplemented
114#2518C2214yescomplemented
115#2517C2212yescomplemented
116#2516C2214yescomplemented
117#2514C2212yescomplemented
118#2513C2212yescomplemented
119#2513C2212yescomplemented
120#2512C2212yescomplemented
121#2512C2212yescomplemented
122#2512C2212yescomplemented
123#2512C2212yescomplemented
124#2511C2211yescharacteristic, complemented
125#2510C2214yescomplemented
126#2510C2214yescomplemented
127#2506C2212yescomplemented
128#2506C2212yescomplemented
129#2506C2212yescomplemented
130#2506C2211yescharacteristic, complemented
131#2500C2212yescomplemented
132#2500C2212yescomplemented
133#2499C2211yescharacteristic, complemented
134#2497C2212yes—
135#2495C2212yes—
136#2494C2212yes—
137#2494C2211yescharacteristic
138#2490C2214yescomplemented
139#2490C2212yescomplemented
140#2489C2211yescharacteristic
141#2485C2211yescharacteristic
142#2482C2214yes—
143#2481C2214yescomplemented
144#2480C2214yes—
145#2480C2214yes—
146#2480C2214yes—
147#2480C2214yes—
148#2477C2214yescomplemented
149#2476C2214yescomplemented
150#2474C2214yescomplemented
151#2472C2214yes—
152#2472C2214yes—
153#2471C2214yescomplemented
154#2466C2214yescomplemented
155#2460C2212yes—
156#2460C2214yescomplemented
157#2458C2214yescomplemented
158#2454C2212yescomplemented
159#2454C2212yescomplemented
160#2452C2212yescomplemented
161#2452C2212yescomplemented
162#2450C2214yescomplemented
163#2448C2212yescomplemented
164#2447C2212yescomplemented
165#2447C2212yescomplemented
166#2447C2212yescomplemented
167#2445C2212yes—
168#2445C2212yes—
169#2445C2212yes—
170#2445C2212yes—
171#2444C2214yescomplemented
172#2441C2212yes—
173#2441C2211yescharacteristic, complemented
174#2435C2212yes—
175#2435C2212yes—
176#2435C2212yes—
177#2431C2212yes—
178#2428C2212yes—
179#2428C2212yes—
180#2427C2212yescomplemented
181#2427C2212yescomplemented
182#2427C2212yescomplemented
183#2426C2212yescomplemented
184#2425C2214yescomplemented
185#2423C2212yes—
186#2422C2212yescomplemented
187#2422C2212yescomplemented
188#2420C2212yescomplemented
189#2415C2211yescharacteristic
190#2411C2214yes—
191#2408C2212yes—
192#2408C2212yes—
193#2406C2214yescomplemented
194#2405C2214yes—
195#2401C2212yescomplemented
196#2398C2214yescomplemented
197#2395C2212yes—
198#2395C2214yescomplemented
199#2373C2212yes—
200#2373C2212yescomplemented
201#2372C2214yescomplemented
202#2370C2212yescomplemented
203#2369C2211yescharacteristic, complemented
204#2369C2211yescharacteristic, complemented
205#2367C2212yes—
206#2367C2212yescomplemented
207#2367C2212yescomplemented
208#2367C2212yescomplemented
209#2366C2211yescharacteristic
210#2366C2212yes—
211#2366C2211yescharacteristic
212#2366C2212yes—
213#2366C2211yescharacteristic
214#2366C2211yescharacteristic
215#2366C2211yescharacteristic
216#2365C2211yescharacteristic, complemented
217#2363C2212yescomplemented
218#2363C2212yescomplemented
219#2363C2212yescomplemented
220#2363C2212yescomplemented
221#2363C2212yescomplemented
222#2363C2212yescomplemented
223#2362C2211yescharacteristic
224#2362C2211yescharacteristic, complemented
225#2359C2214yescomplemented
226#2357C2212yescomplemented
227#2356C2212yescomplemented
228#2355C2211yescharacteristic, complemented
229#2355C2211yescharacteristic, complemented
230#2354C2211yescharacteristic
231#2354C2212yescomplemented
232#2354C2212yescomplemented
233#2354C2212yescomplemented
234#2353C2214yescomplemented
235#2352C2214yescomplemented
236Q8×C4⋊C4C2211yescharacteristic, complemented
237#2349C2212yescomplemented
238#2349C2212yescomplemented
239#2349C2212yescomplemented
240D4×C4⋊C4C2212yescomplemented
241D4×C4⋊C4C2212yescomplemented
242#2347C2211yescharacteristic
243#2347C2211yescharacteristic, complemented
244#2346C2212yes—
245#2342C2214yes—
246#2342C2214yes—
247D4×C22⋊C4C2212yes—
248D4×C22⋊C4C2212yes—
249D4×C22⋊C4C2212yes—
250D4×C22⋊C4C2212yes—
251D4×C22⋊C4C2212yes—
252D4×C22⋊C4C2212yes—
253D4×C22⋊C4C2214yes—
254#2335C2214yescomplemented
255#2328C2214yes—
256#2326C2212yescomplemented
257#2319C2212yescomplemented
258#2318C2214yescomplemented
259#2314C2212yes—
260#2312C2214yes—
261#2309C2212yes—
262C4×C4⋊Q8C2211yescharacteristic, complemented
263C4×#127C2211yescharacteristic
264C4×#127C2212yes—
265C4×#127C2212yes—
266C4×#125C2211yescharacteristic, complemented
267C4×#125C2212yescomplemented
268C4×#126C2212yes—
269C4×#126C2212yescomplemented
270C4×#124C2212yes—
271C4×#124C2212yescomplemented
272C4×#124C2212yescomplemented
273C4×C22⋊Q8C2211yescharacteristic
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2211yescharacteristic, complemented
276C4×C22⋊Q8C2211yescharacteristic, complemented
277C4×#123C2214yescomplemented
278#2298C2212yes—
279#2297C2214yescomplemented
280#2295C2211yescharacteristic, complemented
281#2295C2212yescomplemented
282#2293C2212yescomplemented
283#2293C2212yescomplemented
284#2293C2212yescomplemented
285#2293C2212yescomplemented
286#2293C2212yescomplemented
287#2290C2214yescomplemented
288C2×#388C2214yes—
289#2285C2211yescharacteristic
290#2275C2212yescomplemented
291C42×Q8C2211yescharacteristic, complemented
292C42×Q8C2212yescomplemented
293C42×D4C2211yescharacteristic
294C42×D4C2212yescomplemented
295C42×D4C2212yescomplemented
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic, complemented
298C4×#117C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C23×D4C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303#559—28no—
304#556—28no—
305#552—416no—
306#546—48no—
307#532—28no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×#127—28no—
311C2×#127C2312yes—
312C2×#127C2312yes—
313C2×#127C2311yescharacteristic
314C2×#127C2312yes—
315C2×#127C2311yescharacteristic
316C2×#126C2312yes—
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#125C2312yes—
322C2×#125C2311yescharacteristic
323C2×#125C2314yes—
324C2×#125C2312yes—
325C2×#125C2314yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2314yes—
351C2×#120C2314yes—
352#518—216no—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2314yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2314yes—
385C2×#117C2312yes—
386C2×#117C2311yescharacteristic
387C2×#117C2311yescharacteristic
388C2×#117C2314yes—
389C2×#117C2314yes—
390C2×#117C2314yes—
391C2×#117C2311yescharacteristic
392C2×#117C2311yescharacteristic
393C2×#117C2311yescharacteristic
394C2×#117C2314yes—
395C2×#117C2311yescharacteristic
396C22×C4⋊C4C2314yes—
397C22×C22⋊C4C2314yes—
398C22×C22⋊C4C2314yes—
399C22×C22⋊C4C2314yes—
400C22×C22⋊C4C2314yes—
401C22×C42C2311yescharacteristic
402C22×C42C2311yescharacteristic
403C22×C42C2314yes—
404#401C2314yes—
405#401C2312yes—
406#400C2312yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2312yes—
411#400C2312yes—
412#400C2312yes—
413#400C2314yes—
414#400C2314yes—
415#399C2314yes—
416#399C2312yes—
417#399C2314yes—
418#399C2314yes—
419#398C2314yes—
420#398C2312yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2312yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2312yes—
438#397C2312yes—
439#397C2312yes—
440#397C2312yes—
441#397C2312yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2312yes—
454#396C2314yes—
455#396C2314yes—
456#395C2314yes—
457#395C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#393C2314yes—
479#393C2314yes—
480#392C2314yes—
481#392C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2312yes—
491#391C2314yes—
492#391C2311yescharacteristic
493#391C2314yes—
494#391C2311yescharacteristic
495#391C2311yescharacteristic
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2314yes—
504#390C2314yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2314yes—
525#390C2312yes—
526#390C2312yes—
527#390C2314yes—
528#390C2312yes—
529#390C2312yes—
530#390C2314yes—
531#389C2311yescharacteristic
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#389C2312yes—
550#389C2311yescharacteristic
551#389C2311yescharacteristic
552#389C2311yescharacteristic
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2311yescharacteristic
557#389C2311yescharacteristic
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2311yescharacteristic
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2312yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2312yes—
599#388C2312yes—
600#388C2314yes—
601#388C2312yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2312yes—
608#388C2312yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2312yes—
613#387C2312yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2312yes—
683#385C2312yes—
684#385C2312yes—
685#385C2312yes—
686#384C2311yescharacteristic
687#384C2311yescharacteristic
688#384C2311yescharacteristic
689#384C2311yescharacteristic
690#384C2312yes—
691#384C2312yes—
692#384C2312yes—
693#384C2312yes—
694#383C2312yes—
695#383C2312yes—
696#383C2314yes—
697#382C2312yes—
698#382C2311yescharacteristic
699#382C2312yes—
700#382C2312yes—
701#382C2312yes—
702#382C2314yes—
703#382C2312yes—
704#382C2312yes—
705#381C2314yes—
706#381C2314yes—
707#381C2314yes—
708#380C2314yes—
709#380C2314yes—
710#380C2314yes—
711#380C2314yes—
712#380C2314yes—
713#380C2311yescharacteristic
714#380C2312yes—
715#380C2314yes—
716#380C2314yes—
717#380C2311yescharacteristic
718#380C2312yes—
719#380C2311yescharacteristic
720#380C2311yescharacteristic
721#380C2312yes—
722#380C2311yescharacteristic
723#380C2314yes—
724#380C2311yescharacteristic
725#379C2314yes—
726#379C2314yes—
727#379C2314yes—
728#379C2314yes—
729#379C2314yes—
730#379C2314yes—
731#379C2314yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C22⋊C4C2311yescharacteristic
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2311yescharacteristic
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805#376C2312yes—
806#376C2312yes—
807#376C2314yes—
808#376C2312yes—
809#376C2312yes—
810C2×#95C2314yes—
811C2×#95C2314yes—
812C43C2312yes—
813C43C2312yes—
814C43C2311yescharacteristic
815C43C2312yes—
816C43C2312yes—
817C25C2414yes—
818C2×#41—28no—
819C2×#41—44no—
820C2×#41—82no—
821C22×Q8C2411yescharacteristic
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2412yes—
825C22×D4—28no—
826C22×D4—28no—
827C22×D4—28no—
828C22×D4—28no—
829C22×D4—44no—
830C22×D4—44no—
831C22×D4—44no—
832C22×D4—44no—
833C22×D4—82no—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2411yescharacteristic
837C22×D4C2414yes—
838C22×D4C2414yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2414yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2414yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2414yes—
854C23×C4C2414yes—
855C23×C4C2414yes—
856C23×C4C2414yes—
857C23×C4C2414yes—
858C23×C4C2414yes—
859C23×C4C2414yes—
860C4⋊Q8—24no—
861C4⋊Q8—24no—
862#127—28no—
863#127—28no—
864#127—28no—
865#127—24no—
866#127#4118yes—
867#126—28no—
868#126—28no—
869#126—48no—
870#126—48no—
871#126—84no—
872#125—28no—
873#125—42no—
874#125—44no—
875#125—48no—
876#125—48no—
877#124—28no—
878#124—28no—
879#124—28no—
880#124—28no—
881#124—44no—
882#124—44no—
883#124—44no—
884#124—82no—
885#123—216no—
886#123—216no—
887#123—48no—
888#123—84no—
889C22⋊Q8—24no—
890C22⋊Q8—24no—
891C22⋊Q8—48no—
892C22⋊Q8—48no—
893C22⋊Q8—44no—
894C22⋊Q8—42no—
895C22⋊Q8—42no—
896#121—28no—
897#121—28no—
898#121—44no—
899#121—48no—
900#121—44no—
901#121—44no—
902#120—48no—
903C4×Q8—24no—
904C4×Q8—28no—
905C4×Q8—28no—
906C4×Q8—24no—
907C4×Q8—24no—
908C4×Q8—44no—
909C4×Q8—42no—
910C4×Q8—44no—
911C4×D4—28no—
912C4×D4—28no—
913C4×D4—28no—
914C4×D4—28no—
915C4×D4—24no—
916C4×D4—28no—
917C4×D4—28no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—24no—
921C4×D4—216no—
922C4×D4—216no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—44no—
932C4×D4—48no—
933C4×D4—42no—
934C4×D4—84no—
935#117—28no—
936#117—24no—
937#117—48no—
938#117—48no—
939#117—48no—
940#117—42no—
941#117—42no—
942#117—42no—
943#117—42no—
944#117—84no—
945#117#4118yescomplemented
946C2×C4⋊C4—48no—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C22⋊C4—216no—
1010C2×C22⋊C4—216no—
1011C2×C22⋊C4—48no—
1012C2×C22⋊C4—84no—
1013C2×C22⋊C4C2411yescharacteristic
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2411yescharacteristic
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2411yescharacteristic
1029C2×C22⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C42—24no—
1075C2×C42—24no—
1076C2×C42—84no—
1077C2×C42C2412yes—
1078C2×C42C2412yes—
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2412yes—
1085C2×C42C2412yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2411yescharacteristic
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2414yes—
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2414yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2414yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2414yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2411yescharacteristic
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2411yescharacteristic
1146#95C2411yescharacteristic
1147#95C2414yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2411yescharacteristic
1151#95C2411yescharacteristic
1152#95C2411yescharacteristic
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2411yescharacteristic
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2414yes—
1186C24—28no—
1187C24—28no—
1188C24—44no—
1189C24—44no—
1190C24—44no—
1191C24—44no—
1192C24—44no—
1193C24C2514yes—
1194C24C2511yescharacteristic
1195C24C2511yescharacteristic
1196C24C2514yes—
1197#41—816no—
1198C2×Q8—22no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—22no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—42no—
1208C2×Q8—42no—
1209C2×Q8—42no—
1210C2×D4—22no—
1211C2×D4—28no—
1212C2×D4—28no—
1213C2×D4—28no—
1214C2×D4—28no—
1215C2×D4—24no—
1216C2×D4—28no—
1217C2×D4—24no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—22no—
1222C2×D4—28no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—432no—
1230C2×D4—42no—
1231C2×D4—41no—
1232C2×D4—44no—
1233C2×D4—44no—
1234C2×D4—42no—
1235C2×D4—44no—
1236C2×D4—42no—
1237C2×D4—44no—
1238C2×D4—42no—
1239C2×D4—44no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—816no—
1245C2×D4—816no—
1246C2×D4C2×#4118yes—
1247C2×D4C2×#4118yes—
1248C2×D4C2×#4118yes—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—28no—
1252C22×C4—28no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—28no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—28no—
1268C22×C4—28no—
1269C22×C4—28no—
1270C22×C4—28no—
1271C22×C4—44no—
1272C22×C4—41no—
1273C22×C4—41no—
1274C22×C4—44no—
1275C22×C4—44no—
1276C22×C4—44no—
1277C22×C4—44no—
1278C22×C4—44no—
1279C22×C4—44no—
1280C22×C4—44no—
1281C22×C4—44no—
1282C22×C4—44no—
1283C22×C4—44no—
1284C22×C4—44no—
1285C22×C4—44no—
1286C22×C4—44no—
1287C22×C4—44no—
1288C22×C4—44no—
1289C22×C4—44no—
1290C22×C4C2×#4114yes—
1291C22×C4C2511yescharacteristic
1292C22×C4C2511yescharacteristic
1293C22×C4C2511yescharacteristic
1294C22×C4C2511yescharacteristic
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2514yes—
1303C22×C4C2514yes—
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2512yes—
1309C22×C4C2512yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2512yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2512yes—
1316C22×C4C2512yes—
1317C22×C4C2511yescharacteristic
1318C22×C4C2511yescharacteristic
1319C22×C4C2511yescharacteristic
1320C22×C4C2511yescharacteristic
1321C22×C4C2511yescharacteristic
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—22no—
1325C4⋊C4—22no—
1326C4⋊C4—22no—
1327C4⋊C4—22no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—28no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—41no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—44no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4C2×#4114yes—
1382C4⋊C4C2×#4114yes—
1383C4⋊C4H(5,𝔽2)14yes—
1384C22⋊C4—24no—
1385C22⋊C4—24no—
1386C22⋊C4—28no—
1387C22⋊C4—28no—
1388C22⋊C4—28no—
1389C22⋊C4—28no—
1390C22⋊C4—22no—
1391C22⋊C4—24no—
1392C22⋊C4—28no—
1393C22⋊C4—28no—
1394C22⋊C4—28no—
1395C22⋊C4—28no—
1396C22⋊C4—28no—
1397C22⋊C4—24no—
1398C22⋊C4—22no—
1399C22⋊C4—24no—
1400C22⋊C4—22no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—22no—
1404C22⋊C4—28no—
1405C22⋊C4—44no—
1406C22⋊C4—44no—
1407C22⋊C4—42no—
1408C22⋊C4—42no—
1409C22⋊C4—44no—
1410C22⋊C4—44no—
1411C22⋊C4—42no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—42no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—41no—
1428C22⋊C4—41no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—44no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4C2×#4118yes—
1445C42—22no—
1446C42—22no—
1447C42—22no—
1448C42—22no—
1449C42—22no—
1450C42—22no—
1451C42—24no—
1452C42—24no—
1453C42—24no—
1454C42—24no—
1455C42—24no—
1456C42—22no—
1457C42—24no—
1458C42—24no—
1459C42—24no—
1460C42—24no—
1461C42—22no—
1462C42—24no—
1463C42—24no—
1464C42—24no—
1465C42—22no—
1466C42—22no—
1467C42—22no—
1468C42—24no—
1469C42—24no—
1470C42—42no—
1471C42—42no—
1472C42—44no—
1473C42—44no—
1474C42—42no—
1475C42—42no—
1476C42—42no—
1477C42—42no—
1478C42—44no—
1479C42—42no—
1480C42—42no—
1481C42—44no—
1482C42—42no—
1483C42—41no—
1484C42C2×#4114yes—
1485C42C2×#4118yes—
1486C23—24no—
1487C23—21no—
1488C23—21no—
1489C23—24no—
1490C23—21no—
1491C23—21no—
1492C23—24no—
1493C23—24no—
1494C23—24no—
1495C23—21no—
1496C23—21no—
1497C23—24no—
1498C23—21no—
1499C23—24no—
1500C23—21no—
1501C23—24no—
1502C23—24no—
1503C23—21no—
1504C23—21no—
1505C23—24no—
1506C23—24no—
1507C23—21no—
1508C23—21no—
1509C23—24no—
1510C23—24no—
1511C23—21no—
1512C23—416no—
1513C23—88no—
1514C23—88no—
1515C23—88no—
1516C23—88no—
1517C23—164no—
1518C23—164no—
1519C23C22×#4112yes—
1520C23C22×#4118yes—
1521C23C2611yescharacteristic
1522Q8—48no—
1523Q8—44no—
1524Q8—44no—
1525Q8—84no—
1526D4—216no—
1527D4—216no—
1528D4—48no—
1529D4—44no—
1530D4—416no—
1531D4—416no—
1532D4—48no—
1533D4—48no—
1534D4—84no—
1535D4—88no—
1536D4—88no—
1537D4—164no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—22no—
1543C2×C4—21no—
1544C2×C4—22no—
1545C2×C4—21no—
1546C2×C4—22no—
1547C2×C4—21no—
1548C2×C4—22no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—28no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—24no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—24no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—24no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—24no—
1614C2×C4—22no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—44no—
1620C2×C4—44no—
1621C2×C4—416no—
1622C2×C4—44no—
1623C2×C4—44no—
1624C2×C4—44no—
1625C2×C4—88no—
1626C2×C4—88no—
1627C2×C4—88no—
1628C2×C4—88no—
1629C2×C4—88no—
1630C2×C4—88no—
1631C2×C4—164no—
1632C2×C4C22×#4114yes—
1633C2×C4C22×#4112yes—
1634C2×C4C22×#4112yes—
1635C2×C4C22×#4114yes—
1636C2×C4C22×#4112yes—
1637C2×C4C22×#4112yes—
1638C2×C4C22×#4112yes—
1639C2×C4C2×H(5,𝔽2)12yes—
1640C2×C4C2×H(5,𝔽2)12yes—
1641C2×C4C2×H(5,𝔽2)12yes—
1642C2×C4#58512yes—
1643C2×C4#58512yes—
1644C2×C4#58512yes—
1645C22—28no—
1646C22—22no—
1647C22—28no—
1648C22—22no—
1649C22—22no—
1650C22—28no—
1651C22—41no—
1652C22—44no—
1653C22—44no—
1654C22—41no—
1655C22—41no—
1656C22—44no—
1657C22—44no—
1658C22—41no—
1659C22—41no—
1660C22—44no—
1661C22—44no—
1662C22—41no—
1663C22—41no—
1664C22—44no—
1665C22—41no—
1666C22—44no—
1667C22—44no—
1668C22—41no—
1669C22—41no—
1670C22—44no—
1671C22—41no—
1672C22—44no—
1673C22—1616no—
1674C22C23×#4111yescharacteristic
1675C22C23×#4111yescharacteristic
1676C22C22×H(5,𝔽2)11yescharacteristic
1677C22C2×#58511yescharacteristic
1678C22C2×#58511yescharacteristic
1679C22C2×#58511yescharacteristic
1680C22H(7,𝔽2)11yescharacteristic
1681C4—22no—
1682C4—22no—
1683C4—22no—
1684C4—24no—
1685C4—24no—
1686C4—22no—
1687C4—22no—
1688C4—44no—
1689C4—42no—
1690C4—42no—
1691C4—41no—
1692C4—42no—
1693C4—42no—
1694C4—42no—
1695C4—42no—
1696C4—41no—
1697C4—44no—
1698C4—41no—
1699C4—41no—
1700C4—42no—
1701C4—42no—
1702C4—42no—
1703C4—42no—
1704C4—41no—
1705C4—42no—
1706C4—41no—
1707C4—42no—
1708C4—42no—
1709C4—42no—
1710C4#347514yes—
1711C4#352114yes—
1712C2—48no—
1713C2—42no—
1714C2—81no—
1715C2—84no—
1716C2C2×#347511yescharacteristic
1717C2C2×#352111yescharacteristic
1718C2#6280011yescharacteristic
1719C2#6296911yescharacteristic
1720C2#6298311yescharacteristic
1721C2#6301011yescharacteristic
1722C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59842C2semidirect
2. #59804C2semidirect
3. #59691C2semidirect
4. #59562C2semidirect
5. #59488C2semidirect
6. #59457C2semidirect
7. #59143C2semidirect
8. #59070C2semidirect
9. #45068C2semidirect
10. #44901C2semidirect
11. #44592C2semidirect
12. #43231C2semidirect
13. #39533C2semidirect
14. #39480C2semidirect
15. #39024C2semidirect
16. #38985C2semidirect
17. #38694C2semidirect
18. #38254C2semidirect
19. #36527C2semidirect
20. #36460C2semidirect
21. #36302C2semidirect
22. #36300C2semidirect
23. #36287C2semidirect
24. #36270C2semidirect
25. #36240C2semidirect
27. #36075C2semidirect
28. #35890C2semidirect
29. #34918C2semidirect
30. #34793C2semidirect
31. #34331C2semidirect
32. #34261C2semidirect
33. #34210C2semidirect
34. C4×#556C2semidirect
35. #34155C2semidirect
38. C2×#552C22semidirect
43. #2861C22semidirect
44. #2860C22semidirect
45. #2860C22semidirect
46. #2859C22semidirect
50. #2852C22semidirect
51. #2797C22semidirect
52. #2796C22semidirect
53. #2786C22semidirect
54. #2780C22semidirect
55. #2778C22semidirect
56. #2762C22semidirect
57. #2756C22semidirect
58. #2746C22semidirect
62. #2717C22semidirect
63. #2715C22semidirect
64. #2711C22semidirect
66. #2707C22semidirect
67. #2705C22semidirect
68. #2702C22semidirect
69. #2700C22semidirect
72. #2648C22semidirect
73. #2644C22semidirect
74. #2636C22semidirect
76. #2612C22semidirect
77. #2609C22semidirect
78. #2603C22semidirect
79. #2601C22semidirect
80. #2601C22semidirect
81. #2597C22semidirect
82. #2595C22semidirect
83. #2595C22semidirect
84. #2592C22semidirect
85. #2580C22semidirect
86. #2578C22semidirect
87. #2576C22semidirect
88. #2576C22semidirect
89. #2571C22semidirect
90. #2570C22semidirect
91. #2567C22semidirect
92. #2567C22semidirect
93. #2566C22semidirect
94. #2566C22semidirect
95. #2562C22semidirect
96. #2559C22semidirect
97. #2558C22semidirect
98. #2558C22semidirect
100. #2552C22semidirect
106. #2538C22semidirect
107. #2538C22semidirect
108. #2536C22semidirect
109. #2531C22semidirect
111. #2528C22semidirect
112. #2526C22semidirect
113. #2521C22semidirect
114. #2518C22semidirect
115. #2517C22semidirect
116. #2516C22semidirect
117. #2514C22semidirect
118. #2513C22semidirect
119. #2513C22semidirect
120. #2512C22semidirect
121. #2512C22semidirect
122. #2512C22semidirect
123. #2512C22semidirect
124. #2511C22semidirect
125. #2510C22semidirect
126. #2510C22semidirect
127. #2506C22semidirect
128. #2506C22semidirect
129. #2506C22semidirect
130. #2506C22semidirect
131. #2500C22semidirect
132. #2500C22semidirect
133. #2499C22semidirect
138. #2490C22semidirect
139. #2490C22semidirect
143. #2481C22semidirect
148. #2477C22semidirect
149. #2476C22semidirect
150. #2474C22semidirect
153. #2471C22semidirect
154. #2466C22semidirect
156. #2460C22semidirect
157. #2458C22semidirect
158. #2454C22semidirect
159. #2454C22semidirect
160. #2452C22semidirect
161. #2452C22semidirect
162. #2450C22semidirect
163. #2448C22semidirect
164. #2447C22semidirect
165. #2447C22semidirect
166. #2447C22semidirect
171. #2444C22semidirect
173. #2441C22semidirect
180. #2427C22semidirect
181. #2427C22semidirect
182. #2427C22semidirect
183. #2426C22semidirect
184. #2425C22semidirect
186. #2422C22semidirect
187. #2422C22semidirect
188. #2420C22semidirect
193. #2406C22semidirect
195. #2401C22semidirect
196. #2398C22semidirect
198. #2395C22semidirect
200. #2373C22semidirect
201. #2372C22semidirect
202. #2370C22semidirect
203. #2369C22semidirect
204. #2369C22semidirect
206. #2367C22semidirect
207. #2367C22semidirect
208. #2367C22semidirect
216. #2365C22semidirect
217. #2363C22semidirect
218. #2363C22semidirect
219. #2363C22semidirect
220. #2363C22semidirect
221. #2363C22semidirect
222. #2363C22semidirect
224. #2362C22semidirect
225. #2359C22semidirect
226. #2357C22semidirect
227. #2356C22semidirect
228. #2355C22semidirect
229. #2355C22semidirect
231. #2354C22semidirect
232. #2354C22semidirect
233. #2354C22semidirect
234. #2353C22semidirect
235. #2352C22semidirect
236. Q8×C4⋊C4C22semidirect
237. #2349C22semidirect
238. #2349C22semidirect
239. #2349C22semidirect
240. D4×C4⋊C4C22semidirect
241. D4×C4⋊C4C22semidirect
243. #2347C22semidirect
254. #2335C22semidirect
256. #2326C22semidirect
257. #2319C22semidirect
258. #2318C22semidirect
262. C4×C4⋊Q8C22semidirect
266. C4×#125C22semidirect
267. C4×#125C22semidirect
269. C4×#126C22semidirect
271. C4×#124C22semidirect
272. C4×#124C22semidirect
275. C4×C22⋊Q8C22semidirect
276. C4×C22⋊Q8C22semidirect
277. C4×#123C22semidirect
279. #2297C22semidirect
280. #2295C22semidirect
281. #2295C22semidirect
282. #2293C22semidirect
283. #2293C22semidirect
284. #2293C22semidirect
285. #2293C22semidirect
286. #2293C22semidirect
287. #2290C22semidirect
290. #2275C22semidirect
291. C42×Q8C22semidirect
292. C42×Q8C22semidirect
294. C42×D4C22semidirect
295. C42×D4C22semidirect
297. C4×#117C22semidirect
298. C4×#117C22semidirect
945. #117#41semidirect

Maximal subgroups

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

subgroupindex
#598422
#598042
#596912
#595622
#594882
#594572
#591432
#590702
#450682
#449012
#445922
#432312
#395332
#394802
#390242
#389852
#386942
#382542
#365272
#364602
#363022
#363002
#362872
#362702
#362402
#361212
#360752
#358902
#349182
#347932
#343312
#342612
#342102
C4×#5562
#341552