Finite Group Databasebeta

← #7690714

Subgroups — #7690714

Order 512.

5359 conjugacy classes of subgroups.

The subgroup lattice has 1726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59702C212yesmaximal, complemented
2#59484C212yesmaximal, complemented
3#59465C211yesmaximal, characteristic, complemented
4#59442C212yesmaximal, complemented
5#59382C212yesmaximal, complemented
6#59143C211yesmaximal, characteristic, complemented
7#59070C211yesmaximal, characteristic, complemented
8#59032C214yesmaximal, complemented
9#45376C212yesmaximal, complemented
10#45188C212yesmaximal, complemented
11#44229C214yesmaximal, complemented
12#43674C214yesmaximal, complemented
13#40306C214yesmaximal, complemented
14#39524C212yesmaximal, complemented
15#39480C211yesmaximal, characteristic, complemented
16#39070C212yesmaximal, complemented
17#39020C212yesmaximal, complemented
18#38941C211yesmaximal, characteristic, complemented
19#36587C211yesmaximal, characteristic, complemented
20#36502C212yesmaximal, complemented
21#36480C211yesmaximal, characteristic, complemented
22#36300C211yesmaximal, characteristic, complemented
23#36300C211yesmaximal, characteristic, complemented
24#36240C212yesmaximal, complemented
25#36121C211yesmaximal, characteristic
26#36113C212yesmaximal, complemented
27#35982C212yesmaximal, complemented
28#35970C212yesmaximal, complemented
29#34914C212yesmaximal, complemented
30#34898C211yesmaximal, characteristic, complemented
31#34261C212yesmaximal, complemented
32#34236C211yesmaximal, characteristic, complemented
33#34210C211yesmaximal, characteristic, complemented
34C4×#559C211yesmaximal, characteristic, complemented
35C4×#552C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×#552C2211yescharacteristic
38C2×#546C2212yes—
39C2×#532C2211yescharacteristic
40C22×#127C2211yescharacteristic
41C2×#529C2214yescomplemented
42C2×#518C2212yes—
43#2863C2212yescomplemented
44#2860C2212yescomplemented
45#2860C2212yescomplemented
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2852C2214yescomplemented
50#2850C2212yescomplemented
51#2796C2214yescomplemented
52#2786C2214yescomplemented
53#2784C2214yescomplemented
54#2778C2214yescomplemented
55#2762C2214yescomplemented
56#2751C2214yescomplemented
57#2751C2214yescomplemented
58#2750C2214yescomplemented
59#2743C2214yescomplemented
60#2741C2214yescomplemented
61#2740C2214yescomplemented
62#2737C2214yescomplemented
63#2736C2214yes—
64#2736C2214yes—
65#2735C2214yes—
66#2717C2214yescomplemented
67#2709C2214yes—
68#2694C2214yescomplemented
69#2690C2214yes—
70#2686C2214yescomplemented
71#2684C2214yes—
72#2653C2214yescomplemented
73#2640C2212yescomplemented
74#2633C2214yescomplemented
75#2625C2212yes—
76#2605C2214yescomplemented
77#2598C2214yescomplemented
78#2598C2214yescomplemented
79#2597C2214yescomplemented
80#2595C2214yescomplemented
81#2578C2214yescomplemented
82#2578C2214yescomplemented
83#2577C2212yes—
84#2575C2212yescomplemented
85#2572C2214yescomplemented
86#2571C2211yescharacteristic, complemented
87#2570C2211yescharacteristic, complemented
88#2570C2212yescomplemented
89#2567C2211yescharacteristic, complemented
90#2567C2211yescharacteristic, complemented
91#2565C2211yescharacteristic, complemented
92#2564C2214yescomplemented
93#2563C2212yescomplemented
94#2563C2212yescomplemented
95#2563C2212yescomplemented
96#2562C2211yescharacteristic
97#2562C2214yescomplemented
98#2561C2214yes—
99#2560C2214yescomplemented
100#2559C2214yescomplemented
101#2558C2214yescomplemented
102#2557C2214yescomplemented
103#2551C2211yescharacteristic, complemented
104#2548C2211yescharacteristic
105#2548C2211yescharacteristic
106#2544C2212yes—
107#2544C2212yes—
108#2544C2212yes—
109#2536C2211yescharacteristic
110#2534C2214yes—
111#2531C2214yescomplemented
112#2524C2212yescomplemented
113#2521C2214yescomplemented
114#2521C2214yescomplemented
115#2514C2212yescomplemented
116#2513C2212yescomplemented
117#2513C2212yescomplemented
118#2513C2212yescomplemented
119#2513C2212yescomplemented
120#2513C2212yescomplemented
121#2512C2212yescomplemented
122#2512C2212yescomplemented
123#2510C2214yescomplemented
124#2510C2214yescomplemented
125#2509C2212yescomplemented
126#2506C2212yescomplemented
127#2506C2212yescomplemented
128#2504C2212yescomplemented
129#2497C2212yes—
130#2496C2211yescharacteristic, complemented
131#2495C2212yes—
132#2495C2211yescharacteristic
133#2494C2212yes—
134#2492C2212yes—
135#2491C2212yescomplemented
136#2491C2212yescomplemented
137#2486C2214yescomplemented
138#2485C2214yescomplemented
139#2481C2214yescomplemented
140#2480C2214yes—
141#2480C2214yes—
142#2480C2214yes—
143#2480C2214yes—
144#2477C2214yescomplemented
145#2476C2214yescomplemented
146#2474C2214yescomplemented
147#2474C2214yescomplemented
148#2468C2212yes—
149#2468C2214yescomplemented
150#2467C2214yescomplemented
151#2465C2214yes—
152#2460C2214yescomplemented
153#2459C2214yescomplemented
154#2458C2214yescomplemented
155#2458C2214yescomplemented
156#2457C2214yescomplemented
157#2454C2212yescomplemented
158#2454C2212yescomplemented
159#2454C2212yescomplemented
160#2454C2212yescomplemented
161#2452C2212yescomplemented
162#2452C2212yescomplemented
163#2448C2212yescomplemented
164#2448C2212yescomplemented
165#2447C2212yescomplemented
166#2447C2212yescomplemented
167#2447C2212yescomplemented
168#2445C2212yes—
169#2445C2212yes—
170#2445C2212yes—
171#2445C2212yes—
172#2444C2214yescomplemented
173#2439C2212yes—
174#2435C2212yes—
175#2435C2212yes—
176#2435C2212yes—
177#2431C2212yes—
178#2428C2212yes—
179#2428C2212yes—
180#2427C2212yescomplemented
181#2427C2212yescomplemented
182#2427C2212yescomplemented
183#2423C2211yescharacteristic, complemented
184#2422C2212yescomplemented
185#2422C2212yescomplemented
186#2421C2211yescharacteristic
187#2420C2212yescomplemented
188#2419C2214yescomplemented
189#2418C2214yes—
190#2418C2214yes—
191#2408C2212yes—
192#2408C2212yes—
193#2406C2214yescomplemented
194#2405C2214yes—
195#2402C2212yescomplemented
196#2398C2214yescomplemented
197#2395C2212yes—
198#2392C2214yescomplemented
199#2374C2214yescomplemented
200#2373C2212yes—
201#2371C2212yescomplemented
202#2370C2211yescharacteristic, complemented
203#2369C2211yescharacteristic, complemented
204#2369C2211yescharacteristic, complemented
205#2367C2212yescomplemented
206#2367C2212yescomplemented
207#2367C2212yescomplemented
208#2367C2212yescomplemented
209#2366C2211yescharacteristic
210#2366C2212yes—
211#2366C2211yescharacteristic
212#2366C2212yes—
213#2366C2211yescharacteristic
214#2366C2211yescharacteristic
215#2366C2211yescharacteristic
216#2365C2212yescomplemented
217#2364C2214yescomplemented
218#2362C2211yescharacteristic
219#2361C2212yescomplemented
220#2361C2212yescomplemented
221#2361C2212yescomplemented
222#2360C2211yescharacteristic, complemented
223#2359C2212yes—
224#2357C2212yescomplemented
225#2357C2212yescomplemented
226#2357C2212yescomplemented
227#2357C2212yescomplemented
228#2356C2211yescharacteristic, complemented
229#2355C2211yescharacteristic, complemented
230#2355C2211yescharacteristic, complemented
231#2354C2212yescomplemented
232#2354C2212yescomplemented
233#2353C2214yescomplemented
234#2352C2211yescharacteristic
235#2352C2214yescomplemented
236#2349C2212yescomplemented
237#2349C2212yescomplemented
238#2349C2212yescomplemented
239D4×C4⋊C4C2212yescomplemented
240D4×C4⋊C4C2212yescomplemented
241#2347C2212yes—
242#2346C2211yescharacteristic
243#2344C2211yescharacteristic, complemented
244#2343C2212yescomplemented
245#2342C2214yes—
246#2342C2214yes—
247#2339C2214yescomplemented
248D4×C22⋊C4C2212yes—
249D4×C22⋊C4C2212yes—
250D4×C22⋊C4C2212yes—
251D4×C22⋊C4C2212yes—
252D4×C22⋊C4C2212yes—
253D4×C22⋊C4C2212yes—
254D4×C22⋊C4C2214yes—
255#2337C2214yescomplemented
256#2328C2214yes—
257#2319C2212yescomplemented
258#2319C2212yescomplemented
259#2318C2214yescomplemented
260#2314C2212yes—
261#2312C2214yes—
262#2309C2212yes—
263C4×C4⋊Q8C2212yescomplemented
264C4×#127C2211yescharacteristic
265C4×#127C2212yes—
266C4×#127C2212yes—
267C4×#125C2212yescomplemented
268C4×#125C2211yescharacteristic, complemented
269C4×#125C2211yescharacteristic, complemented
270C4×#126C2212yes—
271C4×#126C2212yescomplemented
272C4×#124C2212yescomplemented
273C4×#124C2212yescomplemented
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2211yescharacteristic, complemented
277C4×C22⋊Q8C2211yescharacteristic, complemented
278C4×#123C2212yes—
279C4×#123C2214yescomplemented
280C4×#121C2212yescomplemented
281C4×#121C2212yescomplemented
282C4×#121C2212yescomplemented
283#2298C2212yes—
284#2293C2212yescomplemented
285#2293C2212yescomplemented
286#2290C2214yescomplemented
287C2×#388C2214yes—
288#2285C2211yescharacteristic
289#2283C2211yescharacteristic, complemented
290#2275C2212yescomplemented
291C42×Q8C2211yescharacteristic, complemented
292C42×Q8C2211yescharacteristic, complemented
293C42×D4C2211yescharacteristic
294C42×D4C2212yescomplemented
295C42×D4C2212yescomplemented
296C4×#117C2211yescharacteristic
297C4×#117C2212yescomplemented
298C2×C4×C4⋊C4C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C23×D4C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303#559—28no—
304#552—28no—
305#546—48no—
306#532—28no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×#127—28no—
311C2×#127C2312yes—
312C2×#127C2312yes—
313C2×#127C2311yescharacteristic
314C2×#127C2312yes—
315C2×#127C2311yescharacteristic
316#529—416no—
317C2×#126C2312yes—
318C2×#126C2312yes—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#125C2312yes—
322C2×#125C2311yescharacteristic
323C2×#125C2311yescharacteristic
324C2×#125C2314yes—
325C2×#124C2312yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2314yes—
332C2×#124C2312yes—
333C2×#123C2312yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×#121C2312yes—
345C2×#121C2314yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#120C2314yes—
351#518—216no—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2314yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×D4C2314yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2314yes—
385C2×C4×D4C2314yes—
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2311yescharacteristic
390C2×#117C2314yes—
391C2×#117C2314yes—
392C2×#117C2311yescharacteristic
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2311yescharacteristic
395C22×C4⋊C4C2314yes—
396C22×C22⋊C4C2314yes—
397C22×C22⋊C4C2314yes—
398C22×C22⋊C4C2314yes—
399C22×C22⋊C4C2314yes—
400C22×C42C2311yescharacteristic
401C22×C42C2311yescharacteristic
402C22×C42C2312yes—
403C22×C42C2314yes—
404#401C2314yes—
405#400C2312yes—
406#400C2312yes—
407#400C2314yes—
408#400C2314yes—
409#400C2312yes—
410#400C2312yes—
411#400C2312yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#399C2314yes—
417#399C2312yes—
418#399C2314yes—
419#399C2314yes—
420#398C2314yes—
421#398C2312yes—
422#398C2312yes—
423#398C2312yes—
424#398C2314yes—
425#398C2312yes—
426#398C2312yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2312yes—
432#397C2312yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#394C2314yes—
456#394C2312yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2312yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#392C2314yes—
481#392C2314yes—
482#391C2314yes—
483#391C2311yescharacteristic
484#391C2311yescharacteristic
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#390C2314yes—
496#390C2312yes—
497#390C2312yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2314yes—
503#390C2312yes—
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#390C2312yes—
524#390C2312yes—
525#389C2311yescharacteristic
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2312yes—
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2312yes—
541#389C2311yescharacteristic
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2311yescharacteristic
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2314yes—
561#388C2312yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
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#388C2312yes—
594#388C2314yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#387C2314yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2314yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2312yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2312yes—
631#387C2312yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
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#386C2312yes—
657#386C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2312yes—
663#385C2312yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2312yes—
671#385C2314yes—
672#385C2314yes—
673#385C2312yes—
674#385C2314yes—
675#385C2312yes—
676#385C2314yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2311yescharacteristic
680#384C2312yes—
681#384C2312yes—
682#383C2312yes—
683#383C2312yes—
684#383C2314yes—
685#383C2314yes—
686#383C2312yes—
687#382C2311yescharacteristic
688#382C2311yescharacteristic
689#382C2312yes—
690#382C2311yescharacteristic
691#382C2312yes—
692#382C2312yes—
693#382C2312yes—
694#382C2311yescharacteristic
695#382C2312yes—
696#382C2312yes—
697#381C2314yes—
698#381C2314yes—
699#381C2314yes—
700#381C2314yes—
701#381C2312yes—
702#381C2312yes—
703#381C2314yes—
704#380C2311yescharacteristic
705#380C2311yescharacteristic
706#380C2311yescharacteristic
707#380C2311yescharacteristic
708#380C2314yes—
709#380C2314yes—
710#380C2314yes—
711#380C2314yes—
712#380C2314yes—
713#380C2314yes—
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2311yescharacteristic
718#380C2312yes—
719#380C2314yes—
720#380C2314yes—
721#380C2312yes—
722#380C2311yescharacteristic
723#380C2312yes—
724#380C2311yescharacteristic
725#380C2311yescharacteristic
726#379C2314yes—
727#379C2314yes—
728#379C2314yes—
729#379C2314yes—
730#379C2314yes—
731#379C2314yes—
732#379C2314yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C22⋊C4C2311yescharacteristic
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2311yescharacteristic
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2311yescharacteristic
806#376C2312yes—
807#376C2312yes—
808#376C2312yes—
809#376C2312yes—
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2312yes—
813C43C2312yes—
814C43C2312yes—
815C43C2311yescharacteristic
816C43C2312yes—
817C25C2414yes—
818C2×#41—28no—
819C2×#41—44no—
820C2×#41—82no—
821C22×Q8C2411yescharacteristic
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2414yes—
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×D4C2414yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2412yes—
844C22×D4C2414yes—
845C22×D4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2414yes—
854C23×C4C2414yes—
855C23×C4C2414yes—
856C23×C4C2414yes—
857C23×C4C2414yes—
858C23×C4C2414yes—
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2412yes—
862C4⋊Q8—24no—
863C4⋊Q8—44no—
864C4⋊Q8—44no—
865#127—28no—
866#127—28no—
867#127—28no—
868#127—24no—
869#127#4118yes—
870#126—28no—
871#126—28no—
872#126—48no—
873#126—84no—
874#125—24no—
875#125—28no—
876#125—42no—
877#125—48no—
878#124—28no—
879#124—28no—
880#124—28no—
881#124—44no—
882#124—44no—
883#124—44no—
884#124—48no—
885#124—82no—
886#123—216no—
887#123—28no—
888#123—48no—
889#123—48no—
890#123—48no—
891C22⋊Q8—24no—
892C22⋊Q8—24no—
893C22⋊Q8—48no—
894C22⋊Q8—44no—
895C22⋊Q8—42no—
896C22⋊Q8—42no—
897#121—28no—
898#121—28no—
899#121—216no—
900#121—44no—
901#121—44no—
902#121—44no—
903#120—48no—
904C4×Q8—24no—
905C4×Q8—24no—
906C4×Q8—24no—
907C4×Q8—48no—
908C4×Q8—42no—
909C4×Q8—42no—
910C4×Q8—42no—
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—48no—
932C4×D4—42no—
933C4×D4—44no—
934C4×D4—48no—
935C4×D4—48no—
936C4×D4—84no—
937C4×D4—84no—
938#117—28no—
939#117—28no—
940#117—28no—
941#117—48no—
942#117—42no—
943#117—84no—
944#117#4118yescomplemented
945C2×C4⋊C4—24no—
946C2×C4⋊C4—42no—
947C2×C4⋊C4—84no—
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C22⋊C4—216no—
1009C2×C22⋊C4—216no—
1010C2×C22⋊C4—48no—
1011C2×C22⋊C4—84no—
1012C2×C22⋊C4C2411yescharacteristic
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2411yescharacteristic
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2411yescharacteristic
1071C2×C42—24no—
1072C2×C42—24no—
1073C2×C42—48no—
1074C2×C42—44no—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2412yes—
1079C2×C42C2412yes—
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2412yes—
1084C2×C42C2412yes—
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2412yes—
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2414yes—
1100C2×C42C2414yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2414yes—
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2411yescharacteristic
1108C2×C42C2414yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2411yescharacteristic
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2411yescharacteristic
1126#95C2411yescharacteristic
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#95C2414yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2411yescharacteristic
1145#95C2411yescharacteristic
1146#95C2411yescharacteristic
1147#95C2414yes—
1148#95C2411yescharacteristic
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186C24—28no—
1187C24—28no—
1188C24—44no—
1189C24—44no—
1190C24—44no—
1191C24—44no—
1192C24—44no—
1193C24C2514yes—
1194C24C2511yescharacteristic
1195C24C2514yes—
1196C24C2511yescharacteristic
1197#41—816no—
1198C2×Q8—22no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—24no—
1202C2×Q8—22no—
1203C2×Q8—22no—
1204C2×Q8—22no—
1205C2×Q8—44no—
1206C2×Q8—42no—
1207C2×Q8—42no—
1208C2×Q8—44no—
1209C2×Q8—44no—
1210C2×D4—22no—
1211C2×D4—28no—
1212C2×D4—28no—
1213C2×D4—28no—
1214C2×D4—22no—
1215C2×D4—28no—
1216C2×D4—28no—
1217C2×D4—28no—
1218C2×D4—24no—
1219C2×D4—28no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—28no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—432no—
1232C2×D4—42no—
1233C2×D4—41no—
1234C2×D4—44no—
1235C2×D4—44no—
1236C2×D4—44no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—44no—
1240C2×D4—44no—
1241C2×D4—42no—
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—24no—
1252C22×C4—22no—
1253C22×C4—28no—
1254C22×C4—28no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—24no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—28no—
1269C22×C4—28no—
1270C22×C4—28no—
1271C22×C4—28no—
1272C22×C4—28no—
1273C22×C4—42no—
1274C22×C4—41no—
1275C22×C4—41no—
1276C22×C4—44no—
1277C22×C4—44no—
1278C22×C4—42no—
1279C22×C4—44no—
1280C22×C4—44no—
1281C22×C4—42no—
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×C4—44no—
1291C22×C4—44no—
1292C22×C4—42no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4C2×#4114yes—
1297C22×C4C2511yescharacteristic
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2511yescharacteristic
1305C22×C4C2514yes—
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2512yes—
1309C22×C4C2512yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2514yes—
1313C22×C4C2512yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2511yescharacteristic
1321C22×C4C2511yescharacteristic
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C4⋊C4—22no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—22no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—28no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—22no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—22no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—41no—
1370C4⋊C4—42no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4C2×#4114yes—
1387C4⋊C4C2×#4114yes—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—28no—
1391C22⋊C4—28no—
1392C22⋊C4—28no—
1393C22⋊C4—28no—
1394C22⋊C4—22no—
1395C22⋊C4—24no—
1396C22⋊C4—28no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—28no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—28no—
1404C22⋊C4—22no—
1405C22⋊C4—24no—
1406C22⋊C4—22no—
1407C22⋊C4—28no—
1408C22⋊C4—44no—
1409C22⋊C4—44no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—42no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—41no—
1418C22⋊C4—41no—
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—44no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4C2×#4118yes—
1446C22⋊C4H(5,𝔽2)14yes—
1447C42—22no—
1448C42—22no—
1449C42—22no—
1450C42—22no—
1451C42—22no—
1452C42—22no—
1453C42—24no—
1454C42—24no—
1455C42—24no—
1456C42—24no—
1457C42—24no—
1458C42—22no—
1459C42—24no—
1460C42—24no—
1461C42—24no—
1462C42—22no—
1463C42—24no—
1464C42—24no—
1465C42—22no—
1466C42—22no—
1467C42—24no—
1468C42—22no—
1469C42—24no—
1470C42—42no—
1471C42—42no—
1472C42—44no—
1473C42—44no—
1474C42—42no—
1475C42—44no—
1476C42—42no—
1477C42—44no—
1478C42—42no—
1479C42—42no—
1480C42—42no—
1481C42—42no—
1482C42—41no—
1483C42—42no—
1484C42C2×#4114yes—
1485C42C2×#4118yes—
1486C23—21no—
1487C23—24no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—24no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—24no—
1496C23—24no—
1497C23—24no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—21no—
1503C23—24no—
1504C23—24no—
1505C23—24no—
1506C23—24no—
1507C23—24no—
1508C23—24no—
1509C23—24no—
1510C23—24no—
1511C23—416no—
1512C23—88no—
1513C23—88no—
1514C23—88no—
1515C23—88no—
1516C23—164no—
1517C23—164no—
1518C23C22×#4112yes—
1519C23C22×#4118yes—
1520C23C2×H(5,𝔽2)12yes—
1521C23C2611yescharacteristic
1522Q8—44no—
1523Q8—44no—
1524Q8—84no—
1525Q8—88no—
1526D4—216no—
1527D4—216no—
1528D4—48no—
1529D4—416no—
1530D4—416no—
1531D4—44no—
1532D4—416no—
1533D4—48no—
1534D4—48no—
1535D4—84no—
1536D4—88no—
1537D4—88no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—22no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—22no—
1549C2×C4—21no—
1550C2×C4—28no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—21no—
1566C2×C4—24no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—24no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—24no—
1605C2×C4—24no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—24no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—44no—
1621C2×C4—48no—
1622C2×C4—44no—
1623C2×C4—44no—
1624C2×C4—44no—
1625C2×C4—44no—
1626C2×C4—88no—
1627C2×C4—88no—
1628C2×C4—88no—
1629C2×C4—88no—
1630C2×C4—88no—
1631C2×C4—88no—
1632C2×C4—88no—
1633C2×C4—84no—
1634C2×C4—164no—
1635C2×C4C22×#4112yes—
1636C2×C4C22×#4114yes—
1637C2×C4C22×#4112yes—
1638C2×C4C22×#4114yes—
1639C2×C4C22×#4112yes—
1640C2×C4C22×#4112yes—
1641C2×C4C22×#4112yes—
1642C2×C4C2×H(5,𝔽2)12yes—
1643C2×C4C2×H(5,𝔽2)12yes—
1644C2×C4#58512yes—
1645C2×C4#58512yes—
1646C2×C4#58512yes—
1647C22—22no—
1648C22—28no—
1649C22—22no—
1650C22—22no—
1651C22—28no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—28no—
1656C22—41no—
1657C22—44no—
1658C22—41no—
1659C22—44no—
1660C22—41no—
1661C22—41no—
1662C22—41no—
1663C22—44no—
1664C22—41no—
1665C22—41no—
1666C22—44no—
1667C22—41no—
1668C22—44no—
1669C22—44no—
1670C22—44no—
1671C22—44no—
1672C22—44no—
1673C22—44no—
1674C22—44no—
1675C22—1616no—
1676C22C23×#4111yescharacteristic
1677C22C23×#4111yescharacteristic
1678C22C22×H(5,𝔽2)11yescharacteristic
1679C22C2×#58511yescharacteristic
1680C22C2×#58511yescharacteristic
1681C22C2×#58511yescharacteristic
1682C22H(7,𝔽2)11yescharacteristic
1683C4—22no—
1684C4—22no—
1685C4—24no—
1686C4—22no—
1687C4—24no—
1688C4—22no—
1689C4—41no—
1690C4—42no—
1691C4—42no—
1692C4—44no—
1693C4—41no—
1694C4—42no—
1695C4—42no—
1696C4—44no—
1697C4—42no—
1698C4—42no—
1699C4—41no—
1700C4—41no—
1701C4—42no—
1702C4—42no—
1703C4—42no—
1704C4—42no—
1705C4—41no—
1706C4—41no—
1707C4—42no—
1708C4—41no—
1709C4—42no—
1710C4—42no—
1711C4—42no—
1712C4#347514yes—
1713C4#352114yes—
1714C2—42no—
1715C2—48no—
1716C2—42no—
1717C2—84no—
1718C2C2×#347511yescharacteristic
1719C2C2×#352111yescharacteristic
1720C2#6280011yescharacteristic
1721C2#6296611yescharacteristic
1722C2#6298311yescharacteristic
1723C2#6301011yescharacteristic
1724C2#6302111yescharacteristic
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. #59702C2semidirect
2. #59484C2semidirect
3. #59465C2semidirect
4. #59442C2semidirect
5. #59382C2semidirect
6. #59143C2semidirect
7. #59070C2semidirect
8. #59032C2semidirect
9. #45376C2semidirect
10. #45188C2semidirect
11. #44229C2semidirect
12. #43674C2semidirect
13. #40306C2semidirect
14. #39524C2semidirect
15. #39480C2semidirect
16. #39070C2semidirect
17. #39020C2semidirect
18. #38941C2semidirect
19. #36587C2semidirect
20. #36502C2semidirect
21. #36480C2semidirect
22. #36300C2semidirect
23. #36300C2semidirect
24. #36240C2semidirect
26. #36113C2semidirect
27. #35982C2semidirect
28. #35970C2semidirect
29. #34914C2semidirect
30. #34898C2semidirect
31. #34261C2semidirect
32. #34236C2semidirect
33. #34210C2semidirect
34. C4×#559C2semidirect
35. C4×#552C2semidirect
41. C2×#529C22semidirect
43. #2863C22semidirect
44. #2860C22semidirect
45. #2860C22semidirect
49. #2852C22semidirect
50. #2850C22semidirect
51. #2796C22semidirect
52. #2786C22semidirect
53. #2784C22semidirect
54. #2778C22semidirect
55. #2762C22semidirect
56. #2751C22semidirect
57. #2751C22semidirect
58. #2750C22semidirect
59. #2743C22semidirect
60. #2741C22semidirect
61. #2740C22semidirect
62. #2737C22semidirect
66. #2717C22semidirect
68. #2694C22semidirect
70. #2686C22semidirect
72. #2653C22semidirect
73. #2640C22semidirect
74. #2633C22semidirect
76. #2605C22semidirect
77. #2598C22semidirect
78. #2598C22semidirect
79. #2597C22semidirect
80. #2595C22semidirect
81. #2578C22semidirect
82. #2578C22semidirect
84. #2575C22semidirect
85. #2572C22semidirect
86. #2571C22semidirect
87. #2570C22semidirect
88. #2570C22semidirect
89. #2567C22semidirect
90. #2567C22semidirect
91. #2565C22semidirect
92. #2564C22semidirect
93. #2563C22semidirect
94. #2563C22semidirect
95. #2563C22semidirect
97. #2562C22semidirect
99. #2560C22semidirect
100. #2559C22semidirect
101. #2558C22semidirect
102. #2557C22semidirect
103. #2551C22semidirect
111. #2531C22semidirect
112. #2524C22semidirect
113. #2521C22semidirect
114. #2521C22semidirect
115. #2514C22semidirect
116. #2513C22semidirect
117. #2513C22semidirect
118. #2513C22semidirect
119. #2513C22semidirect
120. #2513C22semidirect
121. #2512C22semidirect
122. #2512C22semidirect
123. #2510C22semidirect
124. #2510C22semidirect
125. #2509C22semidirect
126. #2506C22semidirect
127. #2506C22semidirect
128. #2504C22semidirect
130. #2496C22semidirect
135. #2491C22semidirect
136. #2491C22semidirect
137. #2486C22semidirect
138. #2485C22semidirect
139. #2481C22semidirect
144. #2477C22semidirect
145. #2476C22semidirect
146. #2474C22semidirect
147. #2474C22semidirect
149. #2468C22semidirect
150. #2467C22semidirect
152. #2460C22semidirect
153. #2459C22semidirect
154. #2458C22semidirect
155. #2458C22semidirect
156. #2457C22semidirect
157. #2454C22semidirect
158. #2454C22semidirect
159. #2454C22semidirect
160. #2454C22semidirect
161. #2452C22semidirect
162. #2452C22semidirect
163. #2448C22semidirect
164. #2448C22semidirect
165. #2447C22semidirect
166. #2447C22semidirect
167. #2447C22semidirect
172. #2444C22semidirect
180. #2427C22semidirect
181. #2427C22semidirect
182. #2427C22semidirect
183. #2423C22semidirect
184. #2422C22semidirect
185. #2422C22semidirect
187. #2420C22semidirect
188. #2419C22semidirect
193. #2406C22semidirect
195. #2402C22semidirect
196. #2398C22semidirect
198. #2392C22semidirect
199. #2374C22semidirect
201. #2371C22semidirect
202. #2370C22semidirect
203. #2369C22semidirect
204. #2369C22semidirect
205. #2367C22semidirect
206. #2367C22semidirect
207. #2367C22semidirect
208. #2367C22semidirect
216. #2365C22semidirect
217. #2364C22semidirect
219. #2361C22semidirect
220. #2361C22semidirect
221. #2361C22semidirect
222. #2360C22semidirect
224. #2357C22semidirect
225. #2357C22semidirect
226. #2357C22semidirect
227. #2357C22semidirect
228. #2356C22semidirect
229. #2355C22semidirect
230. #2355C22semidirect
231. #2354C22semidirect
232. #2354C22semidirect
233. #2353C22semidirect
235. #2352C22semidirect
236. #2349C22semidirect
237. #2349C22semidirect
238. #2349C22semidirect
239. D4×C4⋊C4C22semidirect
240. D4×C4⋊C4C22semidirect
243. #2344C22semidirect
244. #2343C22semidirect
247. #2339C22semidirect
255. #2337C22semidirect
257. #2319C22semidirect
258. #2319C22semidirect
259. #2318C22semidirect
263. C4×C4⋊Q8C22semidirect
267. C4×#125C22semidirect
268. C4×#125C22semidirect
269. C4×#125C22semidirect
271. C4×#126C22semidirect
272. C4×#124C22semidirect
273. C4×#124C22semidirect
276. C4×C22⋊Q8C22semidirect
277. C4×C22⋊Q8C22semidirect
279. C4×#123C22semidirect
280. C4×#121C22semidirect
281. C4×#121C22semidirect
282. C4×#121C22semidirect
284. #2293C22semidirect
285. #2293C22semidirect
286. #2290C22semidirect
289. #2283C22semidirect
290. #2275C22semidirect
291. C42×Q8C22semidirect
292. C42×Q8C22semidirect
294. C42×D4C22semidirect
295. C42×D4C22semidirect
297. C4×#117C22semidirect
298. C2×C4×C4⋊C4C22semidirect
944. #117#41semidirect

Maximal subgroups

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

subgroupindex
#597022
#594842
#594652
#594422
#593822
#591432
#590702
#590322
#453762
#451882
#442292
#436742
#403062
#395242
#394802
#390702
#390202
#389412
#365872
#365022
#364802
#363002
#362402
#361212
#361132
#359822
#359702
#349142
#348982
#342612
#342362
#342102
C4×#5592
C4×#5522