Finite Group Databasebeta

← #7987581

Subgroups — #7987581

Order 512.

4941 conjugacy classes of subgroups.

The subgroup lattice has 1735 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59679C211yesmaximal, characteristic, complemented
2#59484C212yesmaximal, complemented
3#59272C212yesmaximal, complemented
4#59234C211yesmaximal, characteristic, complemented
5#59211C211yesmaximal, characteristic, complemented
6#49292C214yesmaximal, complemented
7#49180C214yesmaximal, complemented
8#46087C214yesmaximal, complemented
9#45398C212yesmaximal, complemented
10#45187C212yesmaximal, complemented
11#45049C212yesmaximal, complemented
12#44903C212yesmaximal, complemented
13#42975C212yesmaximal, complemented
14#42947C212yesmaximal, complemented
15#42778C212yesmaximal, complemented
16#42740C212yesmaximal, complemented
17#39379C211yesmaximal, characteristic, complemented
18#39351C211yesmaximal, characteristic, complemented
19#38967C211yesmaximal, characteristic, complemented
20#38910C211yesmaximal, characteristic, complemented
21#38589C214yesmaximal, complemented
22#38202C212yesmaximal, complemented
23#37980C212yesmaximal, complemented
24#36589C212yesmaximal, complemented
25#36461C212yesmaximal, complemented
26#36460C211yesmaximal, characteristic, complemented
27#36258C211yesmaximal, characteristic, complemented
28#36211C211yesmaximal, characteristic, complemented
29#35266C212yesmaximal, complemented
30#35220C212yesmaximal, complemented
31#34797C211yesmaximal, characteristic, complemented
32#34724C211yesmaximal, characteristic, complemented
33#34493C211yesmaximal, characteristic, complemented
34#34383C211yesmaximal, characteristic, complemented
35#34129C211yesmaximal, characteristic, complemented
36C2×#546C2212yes—
37C2×D42C2211yescharacteristic
38C2×#542C2212yescomplemented
39C2×#541C2212yescomplemented
40C2×#529C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42#2861C2214yescomplemented
43#2860C2214yescomplemented
44#2860C2212yescomplemented
45#2860C2214yescomplemented
46#2859C2211yescharacteristic, complemented
47#2856C2211yescharacteristic
48#2856C2211yescharacteristic
49#2854C2212yes—
50#2837C2214yescomplemented
51#2828C2214yescomplemented
52#2803C2214yescomplemented
53#2800C2214yescomplemented
54#2788C2214yescomplemented
55#2779C2214yescomplemented
56#2775C2214yescomplemented
57#2773C2214yescomplemented
58#2761C2214yescomplemented
59#2757C2214yescomplemented
60#2757C2214yescomplemented
61#2756C2214yescomplemented
62#2753C2214yescomplemented
63#2752C2214yescomplemented
64#2750C2214yescomplemented
65#2742C2214yescomplemented
66#2736C2214yescomplemented
67#2735C2214yescomplemented
68#2730C2214yescomplemented
69#2725C2214yescomplemented
70#2725C2214yescomplemented
71#2723C2214yescomplemented
72#2711C2214yescomplemented
73#2703C2214yescomplemented
74#2698C2214yescomplemented
75#2694C2214yescomplemented
76#2691C2214yescomplemented
77#2687C2214yescomplemented
78#2685C2214yes—
79#2685C2214yescomplemented
80#2685C2214yescomplemented
81#2685C2214yescomplemented
82#2678C2214yes—
83#2672C2214yescomplemented
84#2670C2214yescomplemented
85#2664C2214yescomplemented
86#2662C2214yescomplemented
87#2662C2214yescomplemented
88#2649C2214yescomplemented
89#2644C2214yescomplemented
90#2644C2214yescomplemented
91#2629C2212yescomplemented
92#2628C2212yescomplemented
93#2624C2212yes—
94#2624C2212yescomplemented
95#2597C2214yescomplemented
96#2596C2214yescomplemented
97#2593C2214yescomplemented
98#2578C2214yescomplemented
99#2573C2214yescomplemented
100#2572C2214yescomplemented
101#2571C2211yescharacteristic, complemented
102#2570C2212yescomplemented
103#2566C2212yescomplemented
104#2563C2212yes—
105#2561C2214yescomplemented
106#2560C2214yescomplemented
107#2559C2214yescomplemented
108#2558C2214yescomplemented
109#2558C2214yescomplemented
110#2557C2214yescomplemented
111#2556C2214yescomplemented
112#2554C2214yescomplemented
113#2554C2214yescomplemented
114#2551C2211yescharacteristic, complemented
115#2550C2212yescomplemented
116#2548C2211yescharacteristic
117#2548C2211yescharacteristic
118#2547C2212yescomplemented
119#2545C2212yescomplemented
120#2542C2212yescomplemented
121#2540C2212yes—
122#2538C2211yescharacteristic
123#2538C2211yescharacteristic
124#2536C2212yescomplemented
125#2535C2212yescomplemented
126#2532C2214yescomplemented
127#2531C2212yescomplemented
128#2529C2212yescomplemented
129#2526C2214yescomplemented
130#2526C2214yescomplemented
131#2525C2214yescomplemented
132#2525C2214yescomplemented
133#2518C2212yescomplemented
134#2516C2214yescomplemented
135#2513C2212yes—
136#2513C2212yes—
137#2513C2212yescomplemented
138#2513C2212yescomplemented
139#2513C2212yescomplemented
140#2512C2212yes—
141#2512C2211yescharacteristic
142#2512C2212yes—
143#2512C2212yescomplemented
144#2512C2212yescomplemented
145#2512C2212yescomplemented
146#2512C2212yescomplemented
147#2509C2212yescomplemented
148#2507C2211yescharacteristic, complemented
149#2506C2212yescomplemented
150#2506C2212yescomplemented
151#2500C2212yes—
152#2500C2211yescharacteristic
153#2500C2212yescomplemented
154#2495C2212yescomplemented
155#2495C2212yescomplemented
156#2495C2211yescharacteristic, complemented
157#2492C2212yescomplemented
158#2491C2212yes—
159#2491C2212yescomplemented
160#2490C2211yescharacteristic
161#2490C2212yes—
162#2490C2212yescomplemented
163#2490C2214yescomplemented
164#2490C2212yescomplemented
165#2485C2212yescomplemented
166#2485C2211yescharacteristic, complemented
167#2480C2214yescomplemented
168#2480C2214yescomplemented
169#2480C2214yescomplemented
170#2480C2214yescomplemented
171#2480C2214yescomplemented
172#2479C2214yescomplemented
173#2478C2212yescomplemented
174#2477C2214yescomplemented
175#2474C2214yescomplemented
176#2472C2214yescomplemented
177#2470C2212yescomplemented
178#2467C2212yescomplemented
179#2466C2214yescomplemented
180#2466C2212yescomplemented
181#2455C2212yescomplemented
182#2454C2212yes—
183#2453C2211yescharacteristic, complemented
184#2452C2212yescomplemented
185#2448C2212yescomplemented
186#2447C2211yescharacteristic
187#2447C2212yescomplemented
188#2442C2212yescomplemented
189#2441C2211yescharacteristic, complemented
190#2441C2211yescharacteristic, complemented
191#2439C2212yescomplemented
192#2435C2212yes—
193#2432C2211yescharacteristic
194#2429C2211yescharacteristic, complemented
195#2426C2212yes—
196#2426C2212yescomplemented
197#2424C2214yes—
198#2422C2211yescharacteristic
199#2422C2212yescomplemented
200#2421C2212yescomplemented
201#2421C2212yescomplemented
202#2420C2212yescomplemented
203#2420C2212yescomplemented
204#2420C2212yescomplemented
205#2416C2212yes—
206#2415C2211yescharacteristic, complemented
207#2415C2212yescomplemented
208#2414C2212yes—
209#2414C2212yes—
210#2414C2211yescharacteristic
211#2414C2212yescomplemented
212#2414C2212yescomplemented
213#2412C2214yescomplemented
214#2411C2214yes—
215#2411C2214yescomplemented
216#2408C2212yes—
217#2408C2212yes—
218#2408C2212yes—
219#2407C2211yescharacteristic
220#2395C2212yescomplemented
221#2395C2212yescomplemented
222#2392C2212yescomplemented
223#2392C2212yescomplemented
224#2376C2214yescomplemented
225#2375C2214yes—
226#2370C2212yescomplemented
227#2369C2212yescomplemented
228#2367C2212yes—
229#2367C2212yescomplemented
230#2366C2211yescharacteristic
231#2363C2212yes—
232#2363C2212yes—
233#2363C2212yescomplemented
234#2363C2212yescomplemented
235#2363C2212yescomplemented
236#2362C2212yescomplemented
237#2357C2212yescomplemented
238#2357C2212yescomplemented
239#2357C2212yescomplemented
240#2355C2211yescharacteristic, complemented
241#2354C2211yescharacteristic
242#2354C2211yescharacteristic
243#2354C2211yescharacteristic
244#2354C2212yescomplemented
245#2354C2212yescomplemented
246#2354C2212yescomplemented
247#2352C2212yescomplemented
248Q8×C4⋊C4C2211yescharacteristic, complemented
249Q8×C4⋊C4C2211yescharacteristic, complemented
250Q8×C4⋊C4C2211yescharacteristic, complemented
251D4×C4⋊C4C2211yescharacteristic
252#2347C2212yescomplemented
253#2347C2212yescomplemented
254#2346C2212yescomplemented
255#2346C2214yescomplemented
256#2342C2214yescomplemented
257#2341C2212yes—
258D4×C22⋊C4C2212yes—
259D4×C22⋊C4C2212yes—
260D4×C22⋊C4C2212yes—
261#2334C2214yescomplemented
262#2324C2212yes—
263#2324C2212yes—
264#2324C2212yes—
265#2323C2212yescomplemented
266#2321C2214yes—
267#2317C2212yescomplemented
268#2316C2212yescomplemented
269#2314C2212yescomplemented
270#2309C2212yes—
271#2309C2212yes—
272#2309C2212yes—
273C4×C4⋊Q8C2211yescharacteristic, complemented
274C4×#127C2211yescharacteristic
275C4×#125C2211yescharacteristic, complemented
276C4×#126C2212yescomplemented
277C4×#126C2214yescomplemented
278C4×#124C2212yescomplemented
279C4×C22⋊Q8C2211yescharacteristic, complemented
280C4×C22⋊Q8C2211yescharacteristic, complemented
281C4×#123C2212yescomplemented
282C4×#121C2211yescharacteristic
283C4×#121C2211yescharacteristic
284#2296C2212yescomplemented
285#2293C2211yescharacteristic
286#2293C2212yes—
287#2293C2211yescharacteristic
288#2293C2214yescomplemented
289#2293C2212yescomplemented
290C2×#390C2212yes—
291#2285C2211yescharacteristic, complemented
292#2285C2211yescharacteristic, complemented
293#2285C2212yescomplemented
294#2285C2211yescharacteristic, complemented
295C42×Q8C2212yescomplemented
296C42×D4C2211yescharacteristic, complemented
297C4×#117C2211yescharacteristic, complemented
298C4×#117C2212yescomplemented
299C22×#41C2311yescharacteristic
300C23×D4C2312yes—
301C23×D4C2312yes—
302#546—48no—
303D42—28no—
304#542—48no—
305#541—48no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×#127C2311yescharacteristic
310#529—28no—
311C2×#126C2312yes—
312C2×#126C2312yes—
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#126C2314yes—
318C2×#125C2311yescharacteristic
319C2×#125C2311yescharacteristic
320C2×#125C2312yes—
321C2×#125C2314yes—
322C2×#125C2314yes—
323C2×#124C2311yescharacteristic
324C2×#124C2312yes—
325C2×#124C2314yes—
326C2×#124C2312yes—
327C2×#124C2314yes—
328C2×#123C2312yes—
329C2×#123C2314yes—
330C2×#123C2312yes—
331C2×#123C2314yes—
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2314yes—
339C2×#121C2311yescharacteristic
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2311yescharacteristic
348C2×#121C2311yescharacteristic
349C2×#121C2314yes—
350C2×#121C2312yes—
351C2×#120C2314yes—
352C2×#120C2314yes—
353C2×#120C2314yes—
354C4×#41—28no—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2312yes—
377C2×C4×D4C2311yescharacteristic
378C2×#117C2312yes—
379C2×#117C2312yes—
380C2×#117C2311yescharacteristic
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2311yescharacteristic
389C2×#117C2311yescharacteristic
390C2×#117C2314yes—
391C2×#117C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C22⋊C4C2314yes—
394C22×C22⋊C4C2314yes—
395C22×C22⋊C4C2314yes—
396C22×C42C2312yes—
397C22×C42C2311yescharacteristic
398C22×C42C2311yescharacteristic
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2312yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2312yes—
408#399C2312yes—
409#399C2312yes—
410#399C2314yes—
411#399C2314yes—
412#399C2314yes—
413#399C2314yes—
414#398C2312yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2312yes—
419#398C2314yes—
420#398C2312yes—
421#398C2312yes—
422#397C2314yes—
423#397C2312yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2312yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2312yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2312yes—
443#397C2312yes—
444#397C2312yes—
445#397C2312yes—
446#397C2312yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2312yes—
454#396C2314yes—
455#396C2312yes—
456#396C2312yes—
457#396C2312yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#395C2314yes—
463#395C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2312yes—
479#394C2312yes—
480#394C2312yes—
481#394C2312yes—
482#394C2312yes—
483#394C2312yes—
484#394C2312yes—
485#394C2312yes—
486#394C2312yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#393C2314yes—
492#393C2314yes—
493#393C2314yes—
494#393C2314yes—
495#392C2312yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2312yes—
500#392C2314yes—
501#391C2314yes—
502#391C2311yescharacteristic
503#391C2311yescharacteristic
504#391C2314yes—
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2314yes—
508#391C2311yescharacteristic
509#390C2314yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2311yescharacteristic
514#390C2312yes—
515#390C2311yescharacteristic
516#390C2311yescharacteristic
517#390C2311yescharacteristic
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2312yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2314yes—
526#390C2312yes—
527#390C2312yes—
528#390C2314yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2311yescharacteristic
534#390C2312yes—
535#390C2312yes—
536#390C2314yes—
537#390C2314yes—
538#390C2314yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2314yes—
546#390C2314yes—
547#390C2314yes—
548#390C2314yes—
549#390C2314yes—
550#390C2312yes—
551#390C2312yes—
552#390C2312yes—
553#390C2311yescharacteristic
554#389C2311yescharacteristic
555#389C2311yescharacteristic
556#389C2312yes—
557#389C2312yes—
558#389C2311yescharacteristic
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2312yes—
566#389C2314yes—
567#389C2314yes—
568#389C2312yes—
569#389C2311yescharacteristic
570#389C2311yescharacteristic
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2311yescharacteristic
575#389C2312yes—
576#389C2314yes—
577#389C2312yes—
578#389C2314yes—
579#389C2311yescharacteristic
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2311yescharacteristic
586#389C2311yescharacteristic
587#389C2312yes—
588#389C2314yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2311yescharacteristic
593#389C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2312yes—
599#388C2314yes—
600#388C2312yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2312yes—
614#388C2312yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2312yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2312yes—
643#388C2312yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2312yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#388C2312yes—
652#388C2312yes—
653#388C2312yes—
654#388C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2314yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2312yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2312yes—
685#386C2312yes—
686#386C2312yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2312yes—
695#385C2314yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#384C2311yescharacteristic
703#384C2311yescharacteristic
704#384C2312yes—
705#384C2311yescharacteristic
706#384C2311yescharacteristic
707#384C2311yescharacteristic
708#384C2312yes—
709#384C2311yescharacteristic
710#384C2312yes—
711#383C2312yes—
712#383C2314yes—
713#383C2314yes—
714#382C2311yescharacteristic
715#382C2312yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2312yes—
722#382C2314yes—
723#381C2314yes—
724#381C2314yes—
725#381C2312yes—
726#381C2314yes—
727#380C2314yes—
728#380C2314yes—
729#380C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2314yes—
736#380C2312yes—
737#380C2311yescharacteristic
738#380C2312yes—
739#380C2311yescharacteristic
740#380C2312yes—
741#380C2311yescharacteristic
742#380C2312yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2312yes—
746#380C2311yescharacteristic
747#380C2311yescharacteristic
748#379C2314yes—
749#379C2314yes—
750#379C2314yes—
751#379C2314yes—
752#379C2314yes—
753#379C2314yes—
754#379C2314yes—
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2314yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811#376C2314yes—
812#376C2312yes—
813C43C2314yes—
814C43C2312yes—
815C43C2311yescharacteristic
816C25C2414yes—
817C2×#41—24no—
818C2×#41—24no—
819C2×#41—42no—
820C22×Q8C2411yescharacteristic
821C22×Q8C2411yescharacteristic
822C22×Q8C2414yes—
823C22×D4—28no—
824C22×D4—28no—
825C22×D4—44no—
826C22×D4—44no—
827C22×D4—44no—
828C22×D4—44no—
829C22×D4C2412yes—
830C22×D4C2412yes—
831C22×D4C2411yescharacteristic
832C22×D4C2412yes—
833C22×D4C2411yescharacteristic
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2414yes—
837C22×D4C2414yes—
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2414yes—
842C22×D4C2414yes—
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2414yes—
854C23×C4C2414yes—
855C23×C4C2414yes—
856C4⋊Q8—24no—
857C4⋊Q8—44no—
858C4⋊Q8—44no—
859#127—24no—
860#126—28no—
861#126—44no—
862#126—48no—
863#126—48no—
864#126—48no—
865#126—48no—
866#126—84no—
867#125—24no—
868#125—42no—
869#125—44no—
870#125—48no—
871#125—48no—
872#124—28no—
873#124—24no—
874#124—48no—
875#124—44no—
876#124—84no—
877#123—28no—
878#123—48no—
879#123—44no—
880#123—48no—
881C22⋊Q8—28no—
882C22⋊Q8—24no—
883C22⋊Q8—24no—
884C22⋊Q8—48no—
885C22⋊Q8—42no—
886C22⋊Q8—44no—
887C22⋊Q8—84no—
888#121—24no—
889#121—28no—
890#121—28no—
891#121—44no—
892#121—48no—
893#121—44no—
894#121—42no—
895#121—44no—
896#121—42no—
897#121—44no—
898#121—44no—
899#121—82no—
900#120—216no—
901#120—48no—
902#120—84no—
903C4×Q8—28no—
904C4×Q8—24no—
905C4×Q8—24no—
906C4×Q8—24no—
907C4×Q8—44no—
908C4×Q8—44no—
909C4×D4—24no—
910C4×D4—28no—
911C4×D4—28no—
912C4×D4—28no—
913C4×D4—24no—
914C4×D4—44no—
915C4×D4—44no—
916C4×D4—44no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—42no—
920C4×D4—42no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—42no—
924C4×D4—82no—
925C4×D4#4118yes—
926#117—28no—
927#117—24no—
928#117—28no—
929#117—44no—
930#117—44no—
931#117—44no—
932#117—44no—
933#117—44no—
934#117—42no—
935#117—42no—
936#117—44no—
937#117—44no—
938#117—84no—
939#117—82no—
940C2×C4⋊C4—44no—
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2411yescharacteristic
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C22⋊C4—48no—
1008C2×C22⋊C4—48no—
1009C2×C22⋊C4—84no—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2411yescharacteristic
1054C2×C22⋊C4C2411yescharacteristic
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C42—28no—
1083C2×C42—24no—
1084C2×C42—24no—
1085C2×C42C2412yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2412yes—
1090C2×C42C2411yescharacteristic
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2412yes—
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2414yes—
1101C2×C42C2411yescharacteristic
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2412yes—
1106C2×C42C2414yes—
1107C2×C42C2412yes—
1108C2×C42C2414yes—
1109C2×C42C2412yes—
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2414yes—
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2411yescharacteristic
1119#95C2412yes—
1120#95C2412yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2414yes—
1124#95C2412yes—
1125#95C2414yes—
1126#95C2411yescharacteristic
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2411yescharacteristic
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2411yescharacteristic
1136#95C2411yescharacteristic
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179C24—28no—
1180C24—44no—
1181C24—44no—
1182C24—44no—
1183C24—44no—
1184C24—44no—
1185C24—44no—
1186C24C2512yes—
1187C24C2514yes—
1188C24C2511yescharacteristic
1189C24C2511yescharacteristic
1190C24C2512yes—
1191#41—416no—
1192C2×Q8—22no—
1193C2×Q8—22no—
1194C2×Q8—22no—
1195C2×Q8—22no—
1196C2×Q8—22no—
1197C2×Q8—44no—
1198C2×Q8—44no—
1199C2×Q8—44no—
1200C2×Q8H(5,𝔽2)14yes—
1201C2×D4—24no—
1202C2×D4—24no—
1203C2×D4—28no—
1204C2×D4—22no—
1205C2×D4—24no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—28no—
1209C2×D4—22no—
1210C2×D4—24no—
1211C2×D4—24no—
1212C2×D4—22no—
1213C2×D4—24no—
1214C2×D4—24no—
1215C2×D4—24no—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—42no—
1222C2×D4—42no—
1223C2×D4—42no—
1224C2×D4—42no—
1225C2×D4—42no—
1226C2×D4—42no—
1227C2×D4—44no—
1228C2×D4—42no—
1229C2×D4—42no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—44no—
1236C2×D4—44no—
1237C2×D4—44no—
1238C2×D4—44no—
1239C2×D4—44no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—816no—
1243C2×D4—816no—
1244C2×D4C2×#4114yes—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—22no—
1257C22×C4—24no—
1258C22×C4—22no—
1259C22×C4—24no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—41no—
1270C22×C4—42no—
1271C22×C4—42no—
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×C4C2×#4118yes—
1284C22×C4C2511yescharacteristic
1285C22×C4C2511yescharacteristic
1286C22×C4C2511yescharacteristic
1287C22×C4C2511yescharacteristic
1288C22×C4C2511yescharacteristic
1289C22×C4C2512yes—
1290C22×C4C2512yes—
1291C22×C4C2512yes—
1292C22×C4C2514yes—
1293C22×C4C2512yes—
1294C22×C4C2512yes—
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2511yescharacteristic
1299C22×C4C2514yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2514yes—
1304C22×C4C2511yescharacteristic
1305C22×C4C2512yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2511yescharacteristic
1308C22×C4C2512yes—
1309C22×C4C2511yescharacteristic
1310C22×C4C2512yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C4⋊C4—24no—
1315C4⋊C4—24no—
1316C4⋊C4—22no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—22no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—28no—
1327C4⋊C4—28no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—22no—
1332C4⋊C4—24no—
1333C4⋊C4—22no—
1334C4⋊C4—22no—
1335C4⋊C4—24no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—24no—
1339C4⋊C4—22no—
1340C4⋊C4—24no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—44no—
1345C4⋊C4—42no—
1346C4⋊C4—42no—
1347C4⋊C4—42no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—42no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—44no—
1354C4⋊C4—44no—
1355C4⋊C4—41no—
1356C4⋊C4—41no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—42no—
1362C4⋊C4—42no—
1363C4⋊C4—44no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4C2×#4114yes—
1380C22⋊C4—24no—
1381C22⋊C4—24no—
1382C22⋊C4—24no—
1383C22⋊C4—24no—
1384C22⋊C4—24no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—28no—
1388C22⋊C4—28no—
1389C22⋊C4—28no—
1390C22⋊C4—28no—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—28no—
1394C22⋊C4—22no—
1395C22⋊C4—42no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—42no—
1400C22⋊C4—42no—
1401C22⋊C4—44no—
1402C22⋊C4—44no—
1403C22⋊C4—42no—
1404C22⋊C4—42no—
1405C22⋊C4—44no—
1406C22⋊C4—42no—
1407C22⋊C4—42no—
1408C22⋊C4—44no—
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—42no—
1418C22⋊C4—42no—
1419C22⋊C4—44no—
1420C22⋊C4—41no—
1421C22⋊C4—41no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—41no—
1425C22⋊C4—41no—
1426C22⋊C4—41no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—42no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—44no—
1451C22⋊C4C2×#4118yes—
1452C42—22no—
1453C42—22no—
1454C42—24no—
1455C42—22no—
1456C42—24no—
1457C42—22no—
1458C42—24no—
1459C42—22no—
1460C42—22no—
1461C42—24no—
1462C42—24no—
1463C42—22no—
1464C42—24no—
1465C42—28no—
1466C42—22no—
1467C42—24no—
1468C42—22no—
1469C42—22no—
1470C42—24no—
1471C42—24no—
1472C42—44no—
1473C42—44no—
1474C42—44no—
1475C42—42no—
1476C42—42no—
1477C42—44no—
1478C42—44no—
1479C42—42no—
1480C42—41no—
1481C42—41no—
1482C42—44no—
1483C42—44no—
1484C42—44no—
1485C42C2×#4114yes—
1486C23—22no—
1487C23—22no—
1488C23—22no—
1489C23—22no—
1490C23—22no—
1491C23—22no—
1492C23—21no—
1493C23—21no—
1494C23—22no—
1495C23—24no—
1496C23—22no—
1497C23—21no—
1498C23—24no—
1499C23—21no—
1500C23—22no—
1501C23—24no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—22no—
1508C23—24no—
1509C23—21no—
1510C23—24no—
1511C23—24no—
1512C23—21no—
1513C23—21no—
1514C23—22no—
1515C23—22no—
1516C23—21no—
1517C23—22no—
1518C23—24no—
1519C23—21no—
1520C23—88no—
1521C23—88no—
1522C23—88no—
1523C23—88no—
1524C23—88no—
1525C23—164no—
1526C23—164no—
1527C23C22×#4114yes—
1528C23C2611yescharacteristic
1529Q8—28no—
1530Q8—44no—
1531Q8—164no—
1532D4—28no—
1533D4—48no—
1534D4—44no—
1535D4—48no—
1536D4—48no—
1537D4—44no—
1538D4—84no—
1539D4—88no—
1540D4—84no—
1541D4—88no—
1542D4—84no—
1543D4—84no—
1544D4—164no—
1545D4—164no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—216no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—24no—
1571C2×C4—22no—
1572C2×C4—24no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—21no—
1596C2×C4—24no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—24no—
1603C2×C4—24no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—24no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—24no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—44no—
1628C2×C4—48no—
1629C2×C4—48no—
1630C2×C4—44no—
1631C2×C4—48no—
1632C2×C4—44no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—82no—
1636C2×C4—164no—
1637C2×C4—164no—
1638C2×C4—164no—
1639C2×C4C22×#4112yes—
1640C2×C4C22×#4114yes—
1641C2×C4C22×#4112yes—
1642C2×C4C22×#4112yes—
1643C2×C4C2×H(5,𝔽2)14yes—
1644C2×C4C2×H(5,𝔽2)12yes—
1645C2×C4#58512yes—
1646C2×C4#58512yes—
1647C2×C4#58512yes—
1648C2×C4#58512yes—
1649C22—24no—
1650C22—24no—
1651C22—24no—
1652C22—42no—
1653C22—42no—
1654C22—42no—
1655C22—42no—
1656C22—41no—
1657C22—41no—
1658C22—44no—
1659C22—42no—
1660C22—41no—
1661C22—41no—
1662C22—44no—
1663C22—42no—
1664C22—41no—
1665C22—44no—
1666C22—41no—
1667C22—42no—
1668C22—41no—
1669C22—41no—
1670C22—42no—
1671C22—44no—
1672C22—41no—
1673C22—41no—
1674C22—42no—
1675C22—44no—
1676C22—44no—
1677C22—41no—
1678C22—42no—
1679C22—41no—
1680C22—44no—
1681C22—41no—
1682C22—42no—
1683C22—41no—
1684C22—1616no—
1685C22C23×#4111yescharacteristic
1686C22C22×H(5,𝔽2)11yescharacteristic
1687C22C2×#58511yescharacteristic
1688C22C2×#58511yescharacteristic
1689C22C2×#58511yescharacteristic
1690C22C2×#58511yescharacteristic
1691C22H(7,𝔽2)11yescharacteristic
1692C4—22no—
1693C4—22no—
1694C4—24no—
1695C4—24no—
1696C4—42no—
1697C4—41no—
1698C4—42no—
1699C4—42no—
1700C4—42no—
1701C4—41no—
1702C4—42no—
1703C4—41no—
1704C4—42no—
1705C4—44no—
1706C4—41no—
1707C4—41no—
1708C4—41no—
1709C4—41no—
1710C4—42no—
1711C4—42no—
1712C4—41no—
1713C4—42no—
1714C4—42no—
1715C4—42no—
1716C4—44no—
1717C4—44no—
1718C4—41no—
1719C4—42no—
1720C4#349414yes—
1721C4#352114yes—
1722C2—44no—
1723C2—81no—
1724C2—81no—
1725C2—84no—
1726C2—82no—
1727C2#6276211yescharacteristic
1728C2C2×#352111yescharacteristic
1729C2C2×#349411yescharacteristic
1730C2#6292311yescharacteristic
1731C2#6296611yescharacteristic
1732C2#6300811yescharacteristic
1733C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59679C2semidirect
2. #59484C2semidirect
3. #59272C2semidirect
4. #59234C2semidirect
5. #59211C2semidirect
6. #49292C2semidirect
7. #49180C2semidirect
8. #46087C2semidirect
9. #45398C2semidirect
10. #45187C2semidirect
11. #45049C2semidirect
12. #44903C2semidirect
13. #42975C2semidirect
14. #42947C2semidirect
15. #42778C2semidirect
16. #42740C2semidirect
17. #39379C2semidirect
18. #39351C2semidirect
19. #38967C2semidirect
20. #38910C2semidirect
21. #38589C2semidirect
22. #38202C2semidirect
23. #37980C2semidirect
24. #36589C2semidirect
25. #36461C2semidirect
26. #36460C2semidirect
27. #36258C2semidirect
28. #36211C2semidirect
29. #35266C2semidirect
30. #35220C2semidirect
31. #34797C2semidirect
32. #34724C2semidirect
33. #34493C2semidirect
34. #34383C2semidirect
35. #34129C2semidirect
38. C2×#542C22semidirect
39. C2×#541C22semidirect
42. #2861C22semidirect
43. #2860C22semidirect
44. #2860C22semidirect
45. #2860C22semidirect
46. #2859C22semidirect
50. #2837C22semidirect
51. #2828C22semidirect
52. #2803C22semidirect
53. #2800C22semidirect
54. #2788C22semidirect
55. #2779C22semidirect
56. #2775C22semidirect
57. #2773C22semidirect
58. #2761C22semidirect
59. #2757C22semidirect
60. #2757C22semidirect
61. #2756C22semidirect
62. #2753C22semidirect
63. #2752C22semidirect
64. #2750C22semidirect
65. #2742C22semidirect
66. #2736C22semidirect
67. #2735C22semidirect
68. #2730C22semidirect
69. #2725C22semidirect
70. #2725C22semidirect
71. #2723C22semidirect
72. #2711C22semidirect
73. #2703C22semidirect
74. #2698C22semidirect
75. #2694C22semidirect
76. #2691C22semidirect
77. #2687C22semidirect
79. #2685C22semidirect
80. #2685C22semidirect
81. #2685C22semidirect
83. #2672C22semidirect
84. #2670C22semidirect
85. #2664C22semidirect
86. #2662C22semidirect
87. #2662C22semidirect
88. #2649C22semidirect
89. #2644C22semidirect
90. #2644C22semidirect
91. #2629C22semidirect
92. #2628C22semidirect
94. #2624C22semidirect
95. #2597C22semidirect
96. #2596C22semidirect
97. #2593C22semidirect
98. #2578C22semidirect
99. #2573C22semidirect
100. #2572C22semidirect
101. #2571C22semidirect
102. #2570C22semidirect
103. #2566C22semidirect
105. #2561C22semidirect
106. #2560C22semidirect
107. #2559C22semidirect
108. #2558C22semidirect
109. #2558C22semidirect
110. #2557C22semidirect
111. #2556C22semidirect
112. #2554C22semidirect
113. #2554C22semidirect
114. #2551C22semidirect
115. #2550C22semidirect
118. #2547C22semidirect
119. #2545C22semidirect
120. #2542C22semidirect
124. #2536C22semidirect
125. #2535C22semidirect
126. #2532C22semidirect
127. #2531C22semidirect
128. #2529C22semidirect
129. #2526C22semidirect
130. #2526C22semidirect
131. #2525C22semidirect
132. #2525C22semidirect
133. #2518C22semidirect
134. #2516C22semidirect
137. #2513C22semidirect
138. #2513C22semidirect
139. #2513C22semidirect
143. #2512C22semidirect
144. #2512C22semidirect
145. #2512C22semidirect
146. #2512C22semidirect
147. #2509C22semidirect
148. #2507C22semidirect
149. #2506C22semidirect
150. #2506C22semidirect
153. #2500C22semidirect
154. #2495C22semidirect
155. #2495C22semidirect
156. #2495C22semidirect
157. #2492C22semidirect
159. #2491C22semidirect
162. #2490C22semidirect
163. #2490C22semidirect
164. #2490C22semidirect
165. #2485C22semidirect
166. #2485C22semidirect
167. #2480C22semidirect
168. #2480C22semidirect
169. #2480C22semidirect
170. #2480C22semidirect
171. #2480C22semidirect
172. #2479C22semidirect
173. #2478C22semidirect
174. #2477C22semidirect
175. #2474C22semidirect
176. #2472C22semidirect
177. #2470C22semidirect
178. #2467C22semidirect
179. #2466C22semidirect
180. #2466C22semidirect
181. #2455C22semidirect
183. #2453C22semidirect
184. #2452C22semidirect
185. #2448C22semidirect
187. #2447C22semidirect
188. #2442C22semidirect
189. #2441C22semidirect
190. #2441C22semidirect
191. #2439C22semidirect
194. #2429C22semidirect
196. #2426C22semidirect
199. #2422C22semidirect
200. #2421C22semidirect
201. #2421C22semidirect
202. #2420C22semidirect
203. #2420C22semidirect
204. #2420C22semidirect
206. #2415C22semidirect
207. #2415C22semidirect
211. #2414C22semidirect
212. #2414C22semidirect
213. #2412C22semidirect
215. #2411C22semidirect
220. #2395C22semidirect
221. #2395C22semidirect
222. #2392C22semidirect
223. #2392C22semidirect
224. #2376C22semidirect
226. #2370C22semidirect
227. #2369C22semidirect
229. #2367C22semidirect
233. #2363C22semidirect
234. #2363C22semidirect
235. #2363C22semidirect
236. #2362C22semidirect
237. #2357C22semidirect
238. #2357C22semidirect
239. #2357C22semidirect
240. #2355C22semidirect
244. #2354C22semidirect
245. #2354C22semidirect
246. #2354C22semidirect
247. #2352C22semidirect
248. Q8×C4⋊C4C22semidirect
249. Q8×C4⋊C4C22semidirect
250. Q8×C4⋊C4C22semidirect
252. #2347C22semidirect
253. #2347C22semidirect
254. #2346C22semidirect
255. #2346C22semidirect
256. #2342C22semidirect
261. #2334C22semidirect
265. #2323C22semidirect
267. #2317C22semidirect
268. #2316C22semidirect
269. #2314C22semidirect
273. C4×C4⋊Q8C22semidirect
275. C4×#125C22semidirect
276. C4×#126C22semidirect
277. C4×#126C22semidirect
278. C4×#124C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
281. C4×#123C22semidirect
284. #2296C22semidirect
288. #2293C22semidirect
289. #2293C22semidirect
291. #2285C22semidirect
292. #2285C22semidirect
293. #2285C22semidirect
294. #2285C22semidirect
295. C42×Q8C22semidirect
296. C42×D4C22semidirect
297. C4×#117C22semidirect
298. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#596792
#594842
#592722
#592342
#592112
#492922
#491802
#460872
#453982
#451872
#450492
#449032
#429752
#429472
#427782
#427402
#393792
#393512
#389672
#389102
#385892
#382022
#379802
#365892
#364612
#364602
#362582
#362112
#352662
#352202
#347972
#347242
#344932
#343832
#341292