Finite Group Databasebeta

← #7693211

Subgroups — #7693211

Order 512.

5377 conjugacy classes of subgroups.

The subgroup lattice has 1733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59585C212yesmaximal, complemented
2#59488C212yesmaximal, complemented
3#59457C211yesmaximal, characteristic, complemented
4#59446C212yesmaximal, complemented
5#59378C212yesmaximal, complemented
6#59372C214yesmaximal, complemented
7#59143C211yesmaximal, characteristic, complemented
8#59064C211yesmaximal, characteristic, complemented
9#45368C212yesmaximal, complemented
10#44961C212yesmaximal, complemented
11#44584C214yesmaximal, complemented
12#43359C214yesmaximal, complemented
13#40169C212yesmaximal, complemented
14#40165C212yesmaximal, complemented
15#40138C214yesmaximal, complemented
16#39736C211yesmaximal, characteristic, complemented
17#39734C211yesmaximal, characteristic, complemented
18#38947C212yesmaximal, complemented
19#36591C211yesmaximal, characteristic, complemented
20#36587C211yesmaximal, characteristic, complemented
21#36527C212yesmaximal, complemented
22#36502C212yesmaximal, complemented
23#36450C211yesmaximal, characteristic, complemented
24#36271C211yesmaximal, characteristic, complemented
25#36240C212yesmaximal, complemented
26#36121C211yesmaximal, characteristic
27#36033C212yesmaximal, complemented
28#35787C212yesmaximal, complemented
29#34970C212yesmaximal, complemented
30#34941C211yesmaximal, characteristic, complemented
31#34309C212yesmaximal, complemented
32#34210C211yesmaximal, characteristic, complemented
33#34206C211yesmaximal, characteristic, complemented
34C4×#559C211yesmaximal, characteristic, complemented
35C4×#552C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×#556C2212yescomplemented
38C2×#552C2211yescharacteristic
39C2×#546C2212yes—
40C2×#532C2211yescharacteristic
41C22×#127C2211yescharacteristic
42C2×#520C2212yescomplemented
43C2×#518C2212yes—
44#2863C2212yescomplemented
45#2861C2212yescomplemented
46#2860C2212yescomplemented
47#2858C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2852C2214yescomplemented
51#2850C2212yescomplemented
52#2780C2214yescomplemented
53#2779C2214yescomplemented
54#2766C2214yescomplemented
55#2761C2214yescomplemented
56#2761C2214yescomplemented
57#2760C2214yescomplemented
58#2757C2214yescomplemented
59#2749C2214yescomplemented
60#2747C2214yes—
61#2746C2214yescomplemented
62#2737C2214yescomplemented
63#2735C2214yes—
64#2735C2214yes—
65#2723C2214yescomplemented
66#2709C2214yes—
67#2708C2214yescomplemented
68#2707C2214yescomplemented
69#2707C2214yescomplemented
70#2697C2214yes—
71#2697C2214yes—
72#2691C2214yescomplemented
73#2638C2214yescomplemented
74#2636C2214yescomplemented
75#2621C2212yes—
76#2620C2212yescomplemented
77#2609C2214yescomplemented
78#2601C2214yescomplemented
79#2601C2214yescomplemented
80#2598C2214yescomplemented
81#2597C2214yescomplemented
82#2595C2214yescomplemented
83#2595C2214yescomplemented
84#2592C2212yescomplemented
85#2580C2212yescomplemented
86#2578C2214yescomplemented
87#2577C2214yes—
88#2576C2214yescomplemented
89#2576C2214yescomplemented
90#2576C2214yescomplemented
91#2574C2212yes—
92#2574C2212yescomplemented
93#2571C2211yescharacteristic, complemented
94#2570C2212yescomplemented
95#2568C2211yescharacteristic, complemented
96#2567C2211yescharacteristic, complemented
97#2566C2212yescomplemented
98#2566C2212yescomplemented
99#2566C2212yescomplemented
100#2563C2211yescharacteristic
101#2561C2214yes—
102#2561C2214yes—
103#2560C2214yescomplemented
104#2558C2214yescomplemented
105#2552C2211yescharacteristic, complemented
106#2552C2211yescharacteristic, complemented
107#2548C2211yescharacteristic
108#2548C2211yescharacteristic
109#2547C2212yescomplemented
110#2546C2211yescharacteristic, complemented
111#2545C2212yescomplemented
112#2544C2212yes—
113#2544C2212yes—
114#2544C2212yes—
115#2538C2211yescharacteristic
116#2538C2212yescomplemented
117#2531C2214yescomplemented
118#2531C2214yescomplemented
119#2528C2214yescomplemented
120#2526C2214yescomplemented
121#2518C2214yescomplemented
122#2516C2214yescomplemented
123#2514C2212yescomplemented
124#2514C2212yescomplemented
125#2513C2212yescomplemented
126#2513C2212yescomplemented
127#2513C2212yescomplemented
128#2512C2212yescomplemented
129#2512C2212yescomplemented
130#2512C2212yescomplemented
131#2510C2214yescomplemented
132#2510C2214yescomplemented
133#2508C2212yescomplemented
134#2507C2212yescomplemented
135#2504C2212yescomplemented
136#2499C2212yes—
137#2497C2211yescharacteristic
138#2497C2211yescharacteristic, complemented
139#2495C2212yes—
140#2494C2212yes—
141#2494C2212yes—
142#2490C2212yescomplemented
143#2489C2212yes—
144#2482C2214yes—
145#2481C2214yescomplemented
146#2480C2214yes—
147#2480C2214yes—
148#2480C2214yes—
149#2480C2214yes—
150#2480C2214yes—
151#2476C2214yescomplemented
152#2476C2214yescomplemented
153#2471C2214yescomplemented
154#2468C2214yescomplemented
155#2468C2214yescomplemented
156#2467C2214yescomplemented
157#2466C2214yescomplemented
158#2463C2214yescomplemented
159#2460C2214yescomplemented
160#2454C2212yes—
161#2454C2212yescomplemented
162#2452C2212yescomplemented
163#2452C2212yescomplemented
164#2450C2214yescomplemented
165#2449C2214yescomplemented
166#2448C2212yescomplemented
167#2448C2212yescomplemented
168#2447C2212yescomplemented
169#2447C2212yescomplemented
170#2447C2212yescomplemented
171#2447C2212yescomplemented
172#2447C2212yescomplemented
173#2446C2212yescomplemented
174#2445C2212yes—
175#2445C2212yes—
176#2445C2212yes—
177#2445C2212yes—
178#2444C2214yescomplemented
179#2435C2212yes—
180#2435C2212yes—
181#2435C2212yes—
182#2432C2212yescomplemented
183#2431C2212yes—
184#2428C2212yes—
185#2428C2212yes—
186#2427C2212yescomplemented
187#2423C2211yescharacteristic
188#2423C2211yescharacteristic, complemented
189#2420C2212yescomplemented
190#2420C2212yescomplemented
191#2419C2214yescomplemented
192#2419C2214yescomplemented
193#2408C2212yes—
194#2408C2212yes—
195#2405C2214yes—
196#2396C2212yes—
197#2396C2212yescomplemented
198#2395C2214yescomplemented
199#2392C2214yescomplemented
200#2374C2214yescomplemented
201#2373C2212yes—
202#2371C2212yescomplemented
203#2370C2211yescharacteristic, complemented
204#2367C2212yescomplemented
205#2367C2212yescomplemented
206#2367C2212yescomplemented
207#2367C2212yescomplemented
208#2367C2212yescomplemented
209#2367C2212yescomplemented
210#2366C2211yescharacteristic
211#2366C2211yescharacteristic
212#2366C2212yes—
213#2366C2211yescharacteristic
214#2366C2211yescharacteristic
215#2366C2211yescharacteristic
216#2366C2212yes—
217#2365C2211yescharacteristic, complemented
218#2365C2211yescharacteristic, complemented
219#2364C2214yescomplemented
220#2362C2212yes—
221#2362C2211yescharacteristic
222#2361C2212yescomplemented
223#2360C2211yescharacteristic, complemented
224#2359C2212yes—
225#2359C2214yescomplemented
226#2358C2214yes—
227#2357C2212yescomplemented
228#2357C2212yescomplemented
229#2357C2212yescomplemented
230#2357C2212yescomplemented
231#2356C2211yescharacteristic, complemented
232#2355C2211yescharacteristic, complemented
233#2355C2211yescharacteristic, complemented
234#2355C2212yescomplemented
235#2354C2212yescomplemented
236#2353C2214yescomplemented
237#2352C2211yescharacteristic
238#2352C2214yescomplemented
239#2349C2212yescomplemented
240#2349C2212yescomplemented
241#2349C2212yescomplemented
242D4×C4⋊C4C2212yescomplemented
243#2346C2211yescharacteristic
244#2344C2211yescharacteristic, complemented
245#2343C2212yescomplemented
246#2342C2214yes—
247#2339C2212yescomplemented
248D4×C22⋊C4C2212yes—
249D4×C22⋊C4C2212yes—
250D4×C22⋊C4C2212yes—
251D4×C22⋊C4C2212yes—
252D4×C22⋊C4C2214yes—
253D4×C22⋊C4C2212yes—
254D4×C22⋊C4C2212yes—
255#2328C2214yes—
256#2325C2214yescomplemented
257#2324C2212yescomplemented
258#2323C2212yes—
259#2322C2214yescomplemented
260#2321C2214yes—
261#2311C2212yescomplemented
262#2309C2212yes—
263C4×C4⋊Q8C2211yescharacteristic, complemented
264C4×#127C2211yescharacteristic
265C4×#127C2212yes—
266C4×#127C2212yes—
267C4×#125C2212yescomplemented
268C4×#125C2212yescomplemented
269C4×#125C2211yescharacteristic, complemented
270C4×#125C2212yescomplemented
271C4×#126C2212yes—
272C4×#124C2212yescomplemented
273C4×#124C2212yescomplemented
274C4×#124C2212yescomplemented
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2211yescharacteristic
277C4×C22⋊Q8C2211yescharacteristic, complemented
278C4×C22⋊Q8C2211yescharacteristic, complemented
279C4×#123C2212yes—
280C4×#123C2214yescomplemented
281C4×#123C2214yescomplemented
282C4×#121C2214yescomplemented
283C4×#121C2212yescomplemented
284C4×#121C2212yescomplemented
285C4×#121C2212yescomplemented
286#2293C2212yes—
287#2293C2212yescomplemented
288C2×#388C2214yes—
289#2285C2211yescharacteristic
290#2285C2211yescharacteristic, complemented
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#556—48no—
305#552—28no—
306#546—216no—
307#532—28no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×#127—28no—
312C2×#127C2312yes—
313C2×#127C2312yes—
314C2×#127C2311yescharacteristic
315C2×#127C2312yes—
316C2×#127C2311yescharacteristic
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#125C2311yescharacteristic
322C2×#125C2312yes—
323C2×#125C2312yes—
324C2×#125C2312yes—
325C2×#124C2312yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#123C2314yes—
333C2×#123C2312yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2314yes—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2314yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#120C2314yes—
350#520—48no—
351#518—48no—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2314yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2314yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2314yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2314yes—
387C2×C4×D4C2311yescharacteristic
388C2×#117C2311yescharacteristic
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C2×#117C2312yes—
392C2×#117C2312yes—
393C2×#117C2314yes—
394C2×#117C2312yes—
395C2×#117C2314yes—
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2311yescharacteristic
398C22×C4⋊C4C2314yes—
399C22×C22⋊C4C2314yes—
400C22×C22⋊C4C2314yes—
401C22×C22⋊C4C2314yes—
402C22×C22⋊C4C2314yes—
403C22×C42C2311yescharacteristic
404C22×C42C2311yescharacteristic
405C22×C42C2312yes—
406C22×C42C2314yes—
407#401C2314yes—
408#401C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2312yes—
415#400C2312yes—
416#399C2314yes—
417#399C2312yes—
418#399C2314yes—
419#399C2312yes—
420#398C2314yes—
421#398C2314yes—
422#398C2312yes—
423#398C2312yes—
424#398C2314yes—
425#398C2312yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
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#397C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2312yes—
454#396C2312yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2312yes—
460#396C2312yes—
461#395C2312yes—
462#395C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#393C2314yes—
480#393C2312yes—
481#393C2314yes—
482#393C2312yes—
483#392C2314yes—
484#392C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2311yescharacteristic
498#391C2311yescharacteristic
499#390C2312yes—
500#390C2314yes—
501#390C2314yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2312yes—
537#389C2311yescharacteristic
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2312yes—
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2311yescharacteristic
552#389C2312yes—
553#389C2312yes—
554#389C2311yescharacteristic
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
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#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2314yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2314yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2312yes—
631#387C2314yes—
632#387C2314yes—
633#387C2312yes—
634#387C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2312yes—
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#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2312yes—
669#385C2312yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2312yes—
679#385C2312yes—
680#385C2314yes—
681#385C2314yes—
682#385C2312yes—
683#385C2314yes—
684#384C2311yescharacteristic
685#384C2311yescharacteristic
686#384C2311yescharacteristic
687#384C2311yescharacteristic
688#384C2311yescharacteristic
689#384C2312yes—
690#384C2311yescharacteristic
691#383C2312yes—
692#383C2314yes—
693#383C2314yes—
694#382C2312yes—
695#382C2312yes—
696#382C2312yes—
697#382C2311yescharacteristic
698#382C2312yes—
699#382C2312yes—
700#382C2312yes—
701#382C2312yes—
702#382C2312yes—
703#382C2314yes—
704#382C2312yes—
705#381C2314yes—
706#381C2314yes—
707#381C2314yes—
708#381C2314yes—
709#381C2314yes—
710#381C2314yes—
711#381C2312yes—
712#380C2311yescharacteristic
713#380C2311yescharacteristic
714#380C2311yescharacteristic
715#380C2311yescharacteristic
716#380C2314yes—
717#380C2314yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2314yes—
722#380C2311yescharacteristic
723#380C2311yescharacteristic
724#380C2311yescharacteristic
725#380C2312yes—
726#380C2314yes—
727#380C2314yes—
728#380C2314yes—
729#380C2311yescharacteristic
730#379C2314yes—
731#379C2314yes—
732#379C2314yes—
733#379C2314yes—
734#379C2314yes—
735#379C2314yes—
736#379C2314yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C22⋊C4C2311yescharacteristic
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2311yescharacteristic
788C4×C22⋊C4C2311yescharacteristic
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2314yes—
808#376C2312yes—
809#376C2312yes—
810#376C2312yes—
811C2×#95C2312yes—
812C2×#95C2314yes—
813C2×#95C2314yes—
814C43C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2312yes—
818C25C2414yes—
819C2×#41—28no—
820C2×#41—28no—
821C2×#41—44no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2411yescharacteristic
824C22×Q8C2412yes—
825C22×Q8C2412yes—
826C22×D4—28no—
827C22×D4—28no—
828C22×D4—28no—
829C22×D4—28no—
830C22×D4—44no—
831C22×D4—44no—
832C22×D4—44no—
833C22×D4—44no—
834C22×D4—82no—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2414yes—
838C22×D4C2414yes—
839C22×D4C2414yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2412yes—
844C22×D4C2414yes—
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2414yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2414yes—
854C23×C4C2414yes—
855C23×C4C2414yes—
856C23×C4C2414yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2414yes—
861C23×C4C2414yes—
862C23×C4C2414yes—
863C4⋊Q8—24no—
864C4⋊Q8—42no—
865C4⋊Q8—44no—
866#127—28no—
867#127—28no—
868#127—28no—
869#127—24no—
870#127#4118yes—
871#126—28no—
872#126—48no—
873#126—48no—
874#126—84no—
875#125—28no—
876#125—24no—
877#125—44no—
878#125—44no—
879#124—28no—
880#124—28no—
881#124—28no—
882#124—28no—
883#124—44no—
884#124—44no—
885#124—44no—
886#123—28no—
887#123—216no—
888#123—216no—
889#123—48no—
890C22⋊Q8—28no—
891C22⋊Q8—24no—
892C22⋊Q8—24no—
893C22⋊Q8—48no—
894C22⋊Q8—42no—
895C22⋊Q8—42no—
896C22⋊Q8—84no—
897#121—28no—
898#121—28no—
899#121—28no—
900#121—216no—
901#121—44no—
902#121—82no—
903#120—216no—
904C4×Q8—28no—
905C4×Q8—24no—
906C4×Q8—24no—
907C4×Q8—24no—
908C4×Q8—24no—
909C4×Q8—44no—
910C4×Q8—42no—
911C4×Q8—42no—
912C4×Q8—44no—
913C4×D4—28no—
914C4×D4—28no—
915C4×D4—28no—
916C4×D4—28no—
917C4×D4—28no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—48no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—48no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—42no—
932C4×D4—48no—
933C4×D4—48no—
934C4×D4—42no—
935C4×D4—48no—
936C4×D4—84no—
937C4×D4—82no—
938C4×D4—84no—
939C4×D4#4118yes—
940#117—24no—
941#117—24no—
942#117—28no—
943#117—44no—
944#117—44no—
945#117—48no—
946#117—44no—
947#117—48no—
948C2×C4⋊C4—24no—
949C2×C4⋊C4—24no—
950C2×C4⋊C4—48no—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C22⋊C4—216no—
1016C2×C22⋊C4—48no—
1017C2×C22⋊C4—48no—
1018C2×C22⋊C4—84no—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2411yescharacteristic
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2411yescharacteristic
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2411yescharacteristic
1077C2×C22⋊C4C2411yescharacteristic
1078C2×C42—24no—
1079C2×C42—24no—
1080C2×C42—44no—
1081C2×C42—84no—
1082C2×C42C2412yes—
1083C2×C42C2414yes—
1084C2×C42C2412yes—
1085C2×C42C2412yes—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2414yes—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2414yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2414yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2411yescharacteristic
1134#95C2411yescharacteristic
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2411yescharacteristic
1153#95C2412yes—
1154#95C2411yescharacteristic
1155#95C2414yes—
1156#95C2411yescharacteristic
1157#95C2411yescharacteristic
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189C24—28no—
1190C24—28no—
1191C24—44no—
1192C24—44no—
1193C24—44no—
1194C24—44no—
1195C24—44no—
1196C24C2514yes—
1197C24C2511yescharacteristic
1198C24C2514yes—
1199C24C2511yescharacteristic
1200#41—432no—
1201C2×Q8—22no—
1202C2×Q8—22no—
1203C2×Q8—22no—
1204C2×Q8—24no—
1205C2×Q8—24no—
1206C2×Q8—24no—
1207C2×Q8—22no—
1208C2×Q8—22no—
1209C2×Q8—22no—
1210C2×Q8—42no—
1211C2×Q8—42no—
1212C2×Q8—42no—
1213C2×D4—28no—
1214C2×D4—28no—
1215C2×D4—28no—
1216C2×D4—28no—
1217C2×D4—28no—
1218C2×D4—28no—
1219C2×D4—24no—
1220C2×D4—28no—
1221C2×D4—24no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—28no—
1231C2×D4—24no—
1232C2×D4—432no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—44no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—42no—
1243C2×D4—42no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—816no—
1247C2×D4—816no—
1248C2×D4C2×#4118yes—
1249C2×D4C2×#4118yes—
1250C2×D4C2×#4118yes—
1251C2×D4C2×#4114yes—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—24no—
1257C22×C4—28no—
1258C22×C4—28no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—28no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—28no—
1270C22×C4—28no—
1271C22×C4—28no—
1272C22×C4—24no—
1273C22×C4—42no—
1274C22×C4—44no—
1275C22×C4—42no—
1276C22×C4—41no—
1277C22×C4—42no—
1278C22×C4—44no—
1279C22×C4—44no—
1280C22×C4—44no—
1281C22×C4—44no—
1282C22×C4—44no—
1283C22×C4—44no—
1284C22×C4—41no—
1285C22×C4—42no—
1286C22×C4—44no—
1287C22×C4—41no—
1288C22×C4—44no—
1289C22×C4—44no—
1290C22×C4—44no—
1291C22×C4—44no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4—44no—
1297C22×C4—44no—
1298C22×C4C2×#4114yes—
1299C22×C4C2×#4114yes—
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2511yescharacteristic
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2514yes—
1309C22×C4C2514yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2512yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2511yescharacteristic
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2512yes—
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C4⋊C4—22no—
1332C4⋊C4—22no—
1333C4⋊C4—24no—
1334C4⋊C4—22no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—28no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—24no—
1349C4⋊C4—22no—
1350C4⋊C4—28no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—22no—
1357C4⋊C4—24no—
1358C4⋊C4—22no—
1359C4⋊C4—22no—
1360C4⋊C4—24no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—42no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—44no—
1372C4⋊C4—41no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—44no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—44no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—44no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4C2×#4114yes—
1394C4⋊C4H(5,𝔽2)14yes—
1395C22⋊C4—28no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—28no—
1399C22⋊C4—28no—
1400C22⋊C4—28no—
1401C22⋊C4—28no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—28no—
1405C22⋊C4—28no—
1406C22⋊C4—28no—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—28no—
1410C22⋊C4—28no—
1411C22⋊C4—22no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—42no—
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—44no—
1434C22⋊C4—41no—
1435C22⋊C4—41no—
1436C22⋊C4—41no—
1437C22⋊C4—42no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4C2×#4114yes—
1453C22⋊C4C2×#4114yes—
1454C42—22no—
1455C42—22no—
1456C42—22no—
1457C42—22no—
1458C42—22no—
1459C42—22no—
1460C42—24no—
1461C42—24no—
1462C42—24no—
1463C42—24no—
1464C42—24no—
1465C42—24no—
1466C42—28no—
1467C42—24no—
1468C42—24no—
1469C42—24no—
1470C42—22no—
1471C42—24no—
1472C42—24no—
1473C42—24no—
1474C42—22no—
1475C42—24no—
1476C42—22no—
1477C42—42no—
1478C42—42no—
1479C42—42no—
1480C42—42no—
1481C42—44no—
1482C42—44no—
1483C42—42no—
1484C42—44no—
1485C42—41no—
1486C42—41no—
1487C42—42no—
1488C42—42no—
1489C42—42no—
1490C42—42no—
1491C42C2×#4114yes—
1492C42C2×#4114yes—
1493C23—24no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—24no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—24no—
1503C23—24no—
1504C23—24no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—24no—
1510C23—21no—
1511C23—24no—
1512C23—24no—
1513C23—24no—
1514C23—24no—
1515C23—24no—
1516C23—24no—
1517C23—24no—
1518C23—416no—
1519C23—88no—
1520C23—88no—
1521C23—88no—
1522C23—88no—
1523C23—164no—
1524C23—164no—
1525C23C22×#4112yes—
1526C23C22×#4118yes—
1527C23C22×#4112yes—
1528C23C2611yescharacteristic
1529Q8—44no—
1530Q8—48no—
1531Q8—44no—
1532Q8—84no—
1533D4—216no—
1534D4—216no—
1535D4—48no—
1536D4—44no—
1537D4—416no—
1538D4—416no—
1539D4—416no—
1540D4—48no—
1541D4—48no—
1542D4—84no—
1543D4—88no—
1544D4—88no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—22no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—28no—
1560C2×C4—28no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—24no—
1572C2×C4—24no—
1573C2×C4—24no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—24no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—24no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—24no—
1621C2×C4—22no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—44no—
1628C2×C4—416no—
1629C2×C4—48no—
1630C2×C4—44no—
1631C2×C4—44no—
1632C2×C4—82no—
1633C2×C4—88no—
1634C2×C4—88no—
1635C2×C4—88no—
1636C2×C4—84no—
1637C2×C4—88no—
1638C2×C4—164no—
1639C2×C4—164no—
1640C2×C4—164no—
1641C2×C4C22×#4112yes—
1642C2×C4C22×#4112yes—
1643C2×C4C22×#4112yes—
1644C2×C4C22×#4112yes—
1645C2×C4C22×#4112yes—
1646C2×C4C22×#4112yes—
1647C2×C4C22×#4112yes—
1648C2×C4C22×#4112yes—
1649C2×C4C2×H(5,𝔽2)14yes—
1650C2×C4C2×H(5,𝔽2)12yes—
1651C2×C4#58512yes—
1652C2×C4#58512yes—
1653C2×C4#58512yes—
1654C22—28no—
1655C22—22no—
1656C22—22no—
1657C22—28no—
1658C22—22no—
1659C22—22no—
1660C22—22no—
1661C22—22no—
1662C22—28no—
1663C22—41no—
1664C22—41no—
1665C22—44no—
1666C22—44no—
1667C22—41no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—44no—
1672C22—41no—
1673C22—44no—
1674C22—41no—
1675C22—44no—
1676C22—44no—
1677C22—44no—
1678C22—44no—
1679C22—44no—
1680C22—44no—
1681C22—44no—
1682C22—1616no—
1683C22C23×#4111yescharacteristic
1684C22C23×#4111yescharacteristic
1685C22C22×H(5,𝔽2)11yescharacteristic
1686C22C2×#58511yescharacteristic
1687C22C2×#58511yescharacteristic
1688C22C2×#58511yescharacteristic
1689C22H(7,𝔽2)11yescharacteristic
1690C4—22no—
1691C4—22no—
1692C4—22no—
1693C4—22no—
1694C4—24no—
1695C4—22no—
1696C4—22no—
1697C4—41no—
1698C4—42no—
1699C4—42no—
1700C4—42no—
1701C4—44no—
1702C4—42no—
1703C4—41no—
1704C4—42no—
1705C4—42no—
1706C4—42no—
1707C4—41no—
1708C4—41no—
1709C4—42no—
1710C4—42no—
1711C4—42no—
1712C4—42no—
1713C4—42no—
1714C4—42no—
1715C4—42no—
1716C4—41no—
1717C4—44no—
1718C4—42no—
1719C4#348114yes—
1720C4#352114yes—
1721C2—42no—
1722C2—48no—
1723C2—42no—
1724C2—84no—
1725C2C2×#348111yescharacteristic
1726C2C2×#352111yescharacteristic
1727C2#6281511yescharacteristic
1728C2#6292011yescharacteristic
1729C2#6299011yescharacteristic
1730C2#6301011yescharacteristic
1731C2#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. #59585C2semidirect
2. #59488C2semidirect
3. #59457C2semidirect
4. #59446C2semidirect
5. #59378C2semidirect
6. #59372C2semidirect
7. #59143C2semidirect
8. #59064C2semidirect
9. #45368C2semidirect
10. #44961C2semidirect
11. #44584C2semidirect
12. #43359C2semidirect
13. #40169C2semidirect
14. #40165C2semidirect
15. #40138C2semidirect
16. #39736C2semidirect
17. #39734C2semidirect
18. #38947C2semidirect
19. #36591C2semidirect
20. #36587C2semidirect
21. #36527C2semidirect
22. #36502C2semidirect
23. #36450C2semidirect
24. #36271C2semidirect
25. #36240C2semidirect
27. #36033C2semidirect
28. #35787C2semidirect
29. #34970C2semidirect
30. #34941C2semidirect
31. #34309C2semidirect
32. #34210C2semidirect
33. #34206C2semidirect
34. C4×#559C2semidirect
35. C4×#552C2semidirect
37. C2×#556C22semidirect
42. C2×#520C22semidirect
44. #2863C22semidirect
45. #2861C22semidirect
46. #2860C22semidirect
50. #2852C22semidirect
51. #2850C22semidirect
52. #2780C22semidirect
53. #2779C22semidirect
54. #2766C22semidirect
55. #2761C22semidirect
56. #2761C22semidirect
57. #2760C22semidirect
58. #2757C22semidirect
59. #2749C22semidirect
61. #2746C22semidirect
62. #2737C22semidirect
65. #2723C22semidirect
67. #2708C22semidirect
68. #2707C22semidirect
69. #2707C22semidirect
72. #2691C22semidirect
73. #2638C22semidirect
74. #2636C22semidirect
76. #2620C22semidirect
77. #2609C22semidirect
78. #2601C22semidirect
79. #2601C22semidirect
80. #2598C22semidirect
81. #2597C22semidirect
82. #2595C22semidirect
83. #2595C22semidirect
84. #2592C22semidirect
85. #2580C22semidirect
86. #2578C22semidirect
88. #2576C22semidirect
89. #2576C22semidirect
90. #2576C22semidirect
92. #2574C22semidirect
93. #2571C22semidirect
94. #2570C22semidirect
95. #2568C22semidirect
96. #2567C22semidirect
97. #2566C22semidirect
98. #2566C22semidirect
99. #2566C22semidirect
103. #2560C22semidirect
104. #2558C22semidirect
105. #2552C22semidirect
106. #2552C22semidirect
109. #2547C22semidirect
110. #2546C22semidirect
111. #2545C22semidirect
116. #2538C22semidirect
117. #2531C22semidirect
118. #2531C22semidirect
119. #2528C22semidirect
120. #2526C22semidirect
121. #2518C22semidirect
122. #2516C22semidirect
123. #2514C22semidirect
124. #2514C22semidirect
125. #2513C22semidirect
126. #2513C22semidirect
127. #2513C22semidirect
128. #2512C22semidirect
129. #2512C22semidirect
130. #2512C22semidirect
131. #2510C22semidirect
132. #2510C22semidirect
133. #2508C22semidirect
134. #2507C22semidirect
135. #2504C22semidirect
138. #2497C22semidirect
142. #2490C22semidirect
145. #2481C22semidirect
151. #2476C22semidirect
152. #2476C22semidirect
153. #2471C22semidirect
154. #2468C22semidirect
155. #2468C22semidirect
156. #2467C22semidirect
157. #2466C22semidirect
158. #2463C22semidirect
159. #2460C22semidirect
161. #2454C22semidirect
162. #2452C22semidirect
163. #2452C22semidirect
164. #2450C22semidirect
165. #2449C22semidirect
166. #2448C22semidirect
167. #2448C22semidirect
168. #2447C22semidirect
169. #2447C22semidirect
170. #2447C22semidirect
171. #2447C22semidirect
172. #2447C22semidirect
173. #2446C22semidirect
178. #2444C22semidirect
182. #2432C22semidirect
186. #2427C22semidirect
188. #2423C22semidirect
189. #2420C22semidirect
190. #2420C22semidirect
191. #2419C22semidirect
192. #2419C22semidirect
197. #2396C22semidirect
198. #2395C22semidirect
199. #2392C22semidirect
200. #2374C22semidirect
202. #2371C22semidirect
203. #2370C22semidirect
204. #2367C22semidirect
205. #2367C22semidirect
206. #2367C22semidirect
207. #2367C22semidirect
208. #2367C22semidirect
209. #2367C22semidirect
217. #2365C22semidirect
218. #2365C22semidirect
219. #2364C22semidirect
222. #2361C22semidirect
223. #2360C22semidirect
225. #2359C22semidirect
227. #2357C22semidirect
228. #2357C22semidirect
229. #2357C22semidirect
230. #2357C22semidirect
231. #2356C22semidirect
232. #2355C22semidirect
233. #2355C22semidirect
234. #2355C22semidirect
235. #2354C22semidirect
236. #2353C22semidirect
238. #2352C22semidirect
239. #2349C22semidirect
240. #2349C22semidirect
241. #2349C22semidirect
242. D4×C4⋊C4C22semidirect
244. #2344C22semidirect
245. #2343C22semidirect
247. #2339C22semidirect
256. #2325C22semidirect
257. #2324C22semidirect
259. #2322C22semidirect
261. #2311C22semidirect
263. C4×C4⋊Q8C22semidirect
267. C4×#125C22semidirect
268. C4×#125C22semidirect
269. C4×#125C22semidirect
270. C4×#125C22semidirect
272. C4×#124C22semidirect
273. C4×#124C22semidirect
274. C4×#124C22semidirect
277. C4×C22⋊Q8C22semidirect
278. C4×C22⋊Q8C22semidirect
280. C4×#123C22semidirect
281. C4×#123C22semidirect
282. C4×#121C22semidirect
283. C4×#121C22semidirect
284. C4×#121C22semidirect
285. C4×#121C22semidirect
287. #2293C22semidirect
290. #2285C22semidirect
291. C42×Q8C22semidirect
292. C42×Q8C22semidirect
294. C42×D4C22semidirect
295. C42×D4C22semidirect
297. C4×#117C22semidirect
298. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#595852
#594882
#594572
#594462
#593782
#593722
#591432
#590642
#453682
#449612
#445842
#433592
#401692
#401652
#401382
#397362
#397342
#389472
#365912
#365872
#365272
#365022
#364502
#362712
#362402
#361212
#360332
#357872
#349702
#349412
#343092
#342102
#342062
C4×#5592
C4×#5522