Finite Group Databasebeta

← #7652171

Subgroups — #7652171

Order 512.

4849 conjugacy classes of subgroups.

The subgroup lattice has 1762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42713C212yesmaximal, complemented
2#42671C212yesmaximal, complemented
3#42660C212yesmaximal, complemented
4#42632C212yesmaximal, complemented
5#42594C212yesmaximal, complemented
6#42585C212yesmaximal, complemented
7#42473C212yesmaximal, complemented
8#42456C212yesmaximal, complemented
9#40891C214yesmaximal, complemented
10#40789C214yesmaximal, complemented
11#40174C212yesmaximal, complemented
12#40047C212yesmaximal, complemented
13#39924C212yesmaximal, complemented
14#39924C212yesmaximal, complemented
15#39737C212yesmaximal, complemented
16#39665C212yesmaximal, complemented
17#39608C212yesmaximal, complemented
18#39247C212yesmaximal, complemented
19#38578C214yesmaximal, complemented
20#38538C214yesmaximal, complemented
21#35575C211yesmaximal, characteristic, complemented
22#35566C211yesmaximal, characteristic, complemented
23#35557C211yesmaximal, characteristic, complemented
24#35542C211yesmaximal, characteristic, complemented
25#35542C211yesmaximal, characteristic, complemented
26#35517C211yesmaximal, characteristic, complemented
27#35263C211yesmaximal, characteristic, complemented
28#35257C211yesmaximal, characteristic, complemented
29#35180C211yesmaximal, characteristic, complemented
30C2×#2497C211yesmaximal, characteristic, complemented
31#34743C211yesmaximal, characteristic
32#34739C211yesmaximal, characteristic, complemented
33#34271C211yesmaximal, characteristic, complemented
34#34202C211yesmaximal, characteristic, complemented
35#34188C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#544C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C2×#532C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C2×#525C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2857C2212yescomplemented
46#2855C2212yes—
47#2854C2212yes—
48#2851C2212yescomplemented
49#2850C2214yes—
50#2839C2214yescomplemented
51#2837C2214yes—
52#2832C2214yescomplemented
53#2830C2214yes—
54#2800C2214yescomplemented
55#2799C2214yescomplemented
56#2798C2214yescomplemented
57#2790C2214yes—
58#2779C2214yes—
59#2774C2214yescomplemented
60#2774C2214yescomplemented
61#2772C2214yes—
62#2772C2214yes—
63#2772C2214yescomplemented
64#2767C2214yescomplemented
65#2763C2214yes—
66#2763C2214yescomplemented
67#2761C2214yes—
68#2761C2214yes—
69#2754C2214yescomplemented
70#2751C2214yes—
71#2747C2214yescomplemented
72#2747C2214yescomplemented
73#2741C2214yes—
74#2741C2214yescomplemented
75#2739C2214yescomplemented
76#2731C2214yes—
77#2718C2214yescomplemented
78#2716C2214yescomplemented
79#2715C2214yes—
80#2712C2214yes—
81#2705C2214yes—
82#2692C2214yes—
83#2692C2214yescomplemented
84#2672C2214yes—
85#2672C2214yes—
86#2665C2214yes—
87#2662C2214yes—
88#2654C2214yes—
89#2654C2214yescomplemented
90#2654C2214yescomplemented
91#2652C2214yescomplemented
92#2650C2214yes—
93#2650C2214yescomplemented
94#2639C2214yes—
95#2637C2214yescomplemented
96#2630C2214yes—
97#2629C2212yescomplemented
98#2628C2214yescomplemented
99#2628C2212yescomplemented
100#2625C2212yes—
101#2624C2212yes—
102#2620C2214yes—
103#2592C2212yescomplemented
104#2592C2212yescomplemented
105#2584C2212yescomplemented
106#2584C2212yescomplemented
107#2568C2212yescomplemented
108#2567C2212yescomplemented
109#2564C2214yes—
110#2563C2212yes—
111#2563C2212yes—
112#2563C2212yescomplemented
113#2562C2212yes—
114#2562C2212yes—
115#2562C2212yes—
116#2562C2212yes—
117#2562C2212yescomplemented
118#2562C2212yescomplemented
119#2552C2212yescomplemented
120#2551C2212yescomplemented
121#2550C2212yescomplemented
122#2550C2212yescomplemented
123#2549C2214yes—
124#2548C2212yescomplemented
125#2547C2212yes—
126#2547C2212yes—
127#2547C2212yescomplemented
128#2546C2212yescomplemented
129#2521C2214yescomplemented
130#2520C2214yescomplemented
131#2512C2212yescomplemented
132#2512C2212yescomplemented
133#2511C2214yescomplemented
134#2511C2212yescomplemented
135#2511C2212yescomplemented
136#2508C2214yescomplemented
137#2498C2214yes—
138#2497C2212yes—
139#2497C2212yes—
140#2497C2212yes—
141#2497C2212yes—
142#2497C2212yes—
143#2497C2212yes—
144#2497C2212yes—
145#2497C2212yes—
146#2497C2212yescomplemented
147#2497C2212yescomplemented
148#2496C2212yescomplemented
149#2496C2212yescomplemented
150#2492C2212yes—
151#2492C2212yes—
152#2491C2212yes—
153#2491C2212yes—
154#2490C2212yes—
155#2490C2212yes—
156#2489C2212yes—
157#2489C2212yes—
158#2488C2214yes—
159#2488C2214yes—
160#2487C2212yes—
161#2487C2212yescomplemented
162#2486C2212yes—
163#2486C2212yescomplemented
164#2485C2212yes—
165#2485C2212yes—
166#2485C2212yescomplemented
167#2485C2212yescomplemented
168#2481C2214yes—
169#2481C2214yes—
170#2474C2214yes—
171#2474C2214yescomplemented
172#2472C2214yes—
173#2472C2214yes—
174#2470C2214yes—
175#2470C2214yescomplemented
176#2468C2214yes—
177#2458C2214yes—
178#2454C2212yescomplemented
179#2454C2212yescomplemented
180#2453C2212yescomplemented
181#2453C2212yescomplemented
182#2452C2214yes—
183#2452C2212yescomplemented
184#2452C2212yescomplemented
185#2451C2212yescomplemented
186#2451C2212yescomplemented
187#2450C2214yes—
188#2449C2214yes—
189#2448C2214yes—
190#2448C2212yescomplemented
191#2447C2212yescomplemented
192#2446C2212yescomplemented
193#2445C2212yescomplemented
194#2444C2214yes—
195#2443C2214yes—
196#2442C2211yescharacteristic
197#2442C2211yescharacteristic
198#2442C2212yescomplemented
199#2441C2211yescharacteristic
200#2441C2211yescharacteristic
201#2441C2212yescomplemented
202#2440C2214yes—
203#2440C2211yescharacteristic
204#2440C2211yescharacteristic
205#2440C2212yescomplemented
206#2439C2211yescharacteristic
207#2439C2211yescharacteristic
208#2439C2212yescomplemented
209#2438C2212yes—
210#2438C2212yes—
211#2437C2212yes—
212#2437C2212yes—
213#2429C2211yescharacteristic
214#2429C2211yescharacteristic
215#2428C2211yescharacteristic
216#2428C2211yescharacteristic
217#2427C2211yescharacteristic
218#2427C2211yescharacteristic
219#2426C2211yescharacteristic
220#2426C2211yescharacteristic
221#2425C2212yes—
222#2425C2212yes—
223#2424C2212yes—
224#2424C2212yes—
225#2417C2214yes—
226#2412C2214yes—
227#2396C2212yes—
228#2396C2212yes—
229C2×#400C2212yes—
230#2392C2212yes—
231#2392C2212yes—
232C2×#396C2212yes—
233#2370C2212yescomplemented
234#2370C2212yescomplemented
235#2370C2212yescomplemented
236#2370C2212yescomplemented
237#2369C2212yescomplemented
238#2369C2212yescomplemented
239#2365C2212yescomplemented
240#2365C2212yescomplemented
241#2359C2214yes—
242#2358C2214yes—
243#2355C2212yescomplemented
244#2355C2212yescomplemented
245#2354C2212yes—
246#2354C2212yescomplemented
247#2354C2212yescomplemented
248#2352C2214yes—
249#2352C2214yes—
250#2352C2212yes—
251#2352C2212yes—
252D4×C4⋊C4C2212yes—
253#2332C2214yes—
254#2332C2214yescomplemented
255#2329C2214yes—
256#2324C2212yes—
257#2324C2214yes—
258#2323C2212yes—
259#2323C2214yescomplemented
260#2317C2211yescharacteristic
261#2316C2211yescharacteristic
262#2316C2211yescharacteristic
263#2314C2212yescomplemented
264#2314C2212yescomplemented
265#2311C2211yescharacteristic
266#2311C2211yescharacteristic
267#2311C2211yescharacteristic
268#2311C2211yescharacteristic
269#2311C2211yescharacteristic
270#2311C2211yescharacteristic
271#2311C2211yescharacteristic
272C4×C22⋊Q8C2212yes—
273C4×C22⋊Q8C2212yes—
274C4×C22⋊Q8C2214yes—
275C4×C22⋊Q8C2212yes—
276C4×#121C2212yes—
277C4×#121C2212yes—
278C4×#121C2212yes—
279#2297C2211yescharacteristic
280#2296C2211yescharacteristic
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283C2×#389C2211yescharacteristic
284C2×#389C2211yescharacteristic
285C2×#388C2212yes—
286C2×#387C2212yes—
287#2285C2211yescharacteristic
288#2285C2212yescomplemented
289#2285C2212yescomplemented
290C2×#384C2211yescharacteristic
291#2280C2211yescharacteristic
292C2×#380C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296#2274C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C24×C4C2311yescharacteristic
302#544—28no—
303#544—44no—
304#533—44no—
305#532—44no—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2314yes—
314C2×#127C2311yescharacteristic
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2311yescharacteristic
321C2×#125C2311yescharacteristic
322C2×#125C2312yes—
323C2×#124C2311yescharacteristic
324C2×#124C2311yescharacteristic
325C2×#124C2314yes—
326C2×#124C2314yes—
327C2×#124C2314yes—
328#525—28no—
329#525—44no—
330C2×#123C2312yes—
331C2×#123C2312yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×#121C2311yescharacteristic
347C2×#121C2312yes—
348C2×#121C2311yescharacteristic
349C2×#121C2312yes—
350C2×#121C2311yescharacteristic
351C2×#121C2312yes—
352C2×#121C2311yescharacteristic
353C2×#121C2312yes—
354C2×#120C2312yes—
355C2×#120C2312yes—
356#520—44no—
357C4×#41—28no—
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2314yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2314yes—
377C2×#117—44no—
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2311yescharacteristic
382C2×#117C2312yes—
383C2×#117C2311yescharacteristic
384C2×#117C2312yes—
385C2×#117C2311yescharacteristic
386C2×#117C2312yes—
387C2×#117C2311yescharacteristic
388C2×#117C2312yes—
389C2×#117C2314yes—
390C2×#117C2314yes—
391C2×#117C2311yescharacteristic
392C22×C4⋊C4C2311yescharacteristic
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2311yescharacteristic
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2311yescharacteristic
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C22⋊C4C2311yescharacteristic
404C22×C22⋊C4C2312yes—
405C22×C22⋊C4C2311yescharacteristic
406C22×C22⋊C4C2312yes—
407C22×C22⋊C4C2312yes—
408C22×C42C2312yes—
409C22×C42C2311yescharacteristic
410C22×C42C2311yescharacteristic
411C22×C42C2312yes—
412C22×C42C2312yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2312yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2312yes—
432#400C2314yes—
433#399C2314yes—
434#399C2314yes—
435#399C2314yes—
436#399C2314yes—
437#399C2312yes—
438#399C2312yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2312yes—
443#398C2312yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2312yes—
450#398C2312yes—
451#398C2312yes—
452#398C2312yes—
453#398C2314yes—
454#398C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2312yes—
467#397C2312yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2312yes—
474#396C2312yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2312yes—
482#396C2314yes—
483#396C2312yes—
484#396C2312yes—
485#396C2312yes—
486#396C2312yes—
487#396C2312yes—
488#396C2314yes—
489#395C2314yes—
490#395C2314yes—
491#395C2314yes—
492#395C2314yes—
493#395C2314yes—
494#395C2312yes—
495#395C2314yes—
496#395C2312yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2312yes—
504#394C2312yes—
505#394C2314yes—
506#394C2312yes—
507#394C2314yes—
508#394C2314yes—
509#394C2312yes—
510#394C2312yes—
511#394C2312yes—
512#394C2314yes—
513#393C2314yes—
514#393C2314yes—
515#393C2314yes—
516#393C2314yes—
517#393C2314yes—
518#393C2314yes—
519#393C2314yes—
520#393C2312yes—
521#393C2314yes—
522#393C2312yes—
523#392C2312yes—
524#392C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2312yes—
528#391C2312yes—
529#391C2312yes—
530#391C2312yes—
531#391C2312yes—
532#391C2314yes—
533#391C2314yes—
534#391C2314yes—
535#391C2314yes—
536#391C2314yes—
537#391C2314yes—
538#391C2314yes—
539#391C2314yes—
540#391C2314yes—
541#391C2312yes—
542#391C2314yes—
543#391C2311yescharacteristic
544#391C2311yescharacteristic
545#391C2312yes—
546#390C2314yes—
547#390C2314yes—
548#390C2314yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2312yes—
555#390C2312yes—
556#390C2314yes—
557#390C2312yes—
558#390C2312yes—
559#390C2311yescharacteristic
560#390C2311yescharacteristic
561#389C2311yescharacteristic
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2312yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2311yescharacteristic
580#389C2311yescharacteristic
581#389C2314yes—
582#389C2314yes—
583#389C2312yes—
584#389C2314yes—
585#389C2311yescharacteristic
586#389C2312yes—
587#389C2311yescharacteristic
588#389C2314yes—
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2314yes—
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2311yescharacteristic
596#389C2312yes—
597#389C2311yescharacteristic
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2312yes—
629#388C2312yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2312yes—
636#388C2312yes—
637#388C2314yes—
638#388C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2312yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2312yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2312yes—
669#387C2312yes—
670#387C2314yes—
671#386C2312yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2312yes—
684#386C2312yes—
685#386C2312yes—
686#386C2312yes—
687#386C2312yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2314yes—
693#385C2312yes—
694#385C2312yes—
695#385C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2312yes—
700#385C2314yes—
701#385C2312yes—
702#385C2312yes—
703#385C2312yes—
704#385C2312yes—
705#385C2312yes—
706#385C2312yes—
707#384C2314yes—
708#384C2312yes—
709#384C2312yes—
710#384C2312yes—
711#384C2312yes—
712#384C2311yescharacteristic
713#384C2311yescharacteristic
714#384C2312yes—
715#382C2314yes—
716#382C2314yes—
717#382C2314yes—
718#382C2311yescharacteristic
719#382C2311yescharacteristic
720#382C2312yes—
721#382C2314yes—
722#382C2314yes—
723#381C2314yes—
724#381C2314yes—
725#381C2312yes—
726#380C2311yescharacteristic
727#380C2312yes—
728#380C2312yes—
729#380C2311yescharacteristic
730#380C2311yescharacteristic
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2311yescharacteristic
745#380C2312yes—
746#380C2312yes—
747#380C2314yes—
748#380C2312yes—
749#380C2312yes—
750#380C2314yes—
751#380C2312yes—
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2312yes—
756#380C2314yes—
757#380C2314yes—
758#380C2312yes—
759#380C2312yes—
760#380C2314yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#379C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2314yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2314yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2312yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2312yes—
815C2×#95C2311yescharacteristic
816C2×#95C2312yes—
817C2×#95C2311yescharacteristic
818C2×#95C2312yes—
819C25C2411yescharacteristic
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C22×Q8C2411yescharacteristic
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2414yes—
830C22×Q8C2412yes—
831C22×Q8C2414yes—
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C22×D4C2412yes—
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C23×C4—24no—
843C23×C4—24no—
844C23×C4—24no—
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2414yes—
865C23×C4C2411yescharacteristic
866C4⋊Q8—28no—
867C4⋊Q8—28no—
868C4⋊Q8—42no—
869C4⋊Q8—42no—
870C4⋊Q8—44no—
871C4⋊Q8—44no—
872C4⋊Q8—42no—
873C4⋊Q8—84no—
874#127—42no—
875#126—84no—
876#126—84no—
877#125—28no—
878#125—28no—
879#125—42no—
880#125—42no—
881#125—44no—
882#125—44no—
883#124—42no—
884#124—42no—
885#124—84no—
886#124—84no—
887#124—84no—
888#123—28no—
889#123—44no—
890#123—84no—
891#123—84no—
892C22⋊Q8—24no—
893C22⋊Q8—24no—
894C22⋊Q8—216no—
895C22⋊Q8—28no—
896C22⋊Q8—44no—
897C22⋊Q8—44no—
898C22⋊Q8—48no—
899C22⋊Q8—44no—
900C22⋊Q8—48no—
901C22⋊Q8—48no—
902C22⋊Q8—42no—
903C22⋊Q8—42no—
904#121—24no—
905#121—24no—
906#121—28no—
907#121—44no—
908#121—42no—
909#121—42no—
910#121—44no—
911#121—44no—
912#120—28no—
913#120—44no—
914C4×Q8—24no—
915C4×Q8—24no—
916C4×Q8—44no—
917C4×Q8—44no—
918C4×Q8—44no—
919C4×Q8—84no—
920C4×D4—24no—
921C4×D4—24no—
922C4×D4—28no—
923C4×D4—28no—
924C4×D4—28no—
925C4×D4—28no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—48no—
932C4×D4—84no—
933#117—24no—
934#117—24no—
935#117—24no—
936#117—24no—
937#117—24no—
938#117—28no—
939#117—44no—
940#117—44no—
941#117—42no—
942#117—42no—
943#117—44no—
944#117—84no—
945#117—84no—
946#117#4118yes—
947C2×C4⋊C4—24no—
948C2×C4⋊C4—24no—
949C2×C4⋊C4—24no—
950C2×C4⋊C4—24no—
951C2×C4⋊C4—44no—
952C2×C4⋊C4—42no—
953C2×C4⋊C4—42no—
954C2×C4⋊C4—44no—
955C2×C4⋊C4—82no—
956C2×C4⋊C4—82no—
957C2×C4⋊C4—82no—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2411yescharacteristic
1031C2×C22⋊C4—24no—
1032C2×C22⋊C4—42no—
1033C2×C22⋊C4—44no—
1034C2×C22⋊C4—82no—
1035C2×C22⋊C4—82no—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2411yescharacteristic
1039C2×C22⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2411yescharacteristic
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2411yescharacteristic
1093C2×C42—24no—
1094C2×C42—24no—
1095C2×C42—28no—
1096C2×C42—44no—
1097C2×C42—82no—
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2414yes—
1119C2×C42C2414yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2414yes—
1124C2×C42C2412yes—
1125#95C2411yescharacteristic
1126#95C2411yescharacteristic
1127#95C2411yescharacteristic
1128#95C2411yescharacteristic
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2411yescharacteristic
1132#95C2411yescharacteristic
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193C24—22no—
1194C24—22no—
1195C24—22no—
1196C24—22no—
1197C24—41no—
1198C24—41no—
1199C24—41no—
1200C24C2511yescharacteristic
1201C24C2512yes—
1202C24C2512yes—
1203C24C2511yescharacteristic
1204C24C2511yescharacteristic
1205#41—416no—
1206#41—416no—
1207C2×Q8—22no—
1208C2×Q8—22no—
1209C2×Q8—28no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—22no—
1214C2×Q8—24no—
1215C2×Q8—42no—
1216C2×Q8—42no—
1217C2×Q8—44no—
1218C2×Q8—44no—
1219C2×Q8—42no—
1220C2×Q8—42no—
1221C2×Q8—42no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8—44no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—24no—
1235C2×D4—22no—
1236C2×D4—24no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—24no—
1242C2×D4—42no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—24no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—24no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—24no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—22no—
1291C22×C4—24no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—41no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—42no—
1307C22×C4—42no—
1308C22×C4—41no—
1309C22×C4—42no—
1310C22×C4—42no—
1311C22×C4—42no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4—44no—
1315C22×C4—416no—
1316C22×C4C2×#4114yes—
1317C22×C4H(5,𝔽2)14yes—
1318C22×C42−1+414yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2514yes—
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2514yes—
1328C22×C4C2514yes—
1329C22×C4C2512yes—
1330C22×C4C2511yescharacteristic
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2511yescharacteristic
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C22×C4C2514yes—
1341C22×C4C2512yes—
1342C22×C4C2512yes—
1343C22×C4C2512yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2511yescharacteristic
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2511yescharacteristic
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—28no—
1358C4⋊C4—28no—
1359C4⋊C4—28no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—22no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—28no—
1379C4⋊C4—24no—
1380C4⋊C4—24no—
1381C4⋊C4—44no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—42no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—44no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—44no—
1407C4⋊C4—42no—
1408C4⋊C4—44no—
1409C4⋊C4—42no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—42no—
1415C4⋊C4—44no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4—42no—
1420C4⋊C4C2×#4114yes—
1421C4⋊C4C2×#4114yes—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—24no—
1425C22⋊C4—24no—
1426C22⋊C4—24no—
1427C22⋊C4—22no—
1428C22⋊C4—24no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—24no—
1435C22⋊C4—22no—
1436C22⋊C4—22no—
1437C22⋊C4—24no—
1438C22⋊C4—22no—
1439C22⋊C4—22no—
1440C22⋊C4—24no—
1441C22⋊C4—41no—
1442C22⋊C4—41no—
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⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—42no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—44no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—44no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4C2×#4118yes—
1478C22⋊C42−1+414yes—
1479C42—22no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—24no—
1484C42—24no—
1485C42—24no—
1486C42—22no—
1487C42—22no—
1488C42—22no—
1489C42—22no—
1490C42—24no—
1491C42—24no—
1492C42—24no—
1493C42—24no—
1494C42—42no—
1495C42—42no—
1496C42—44no—
1497C42—44no—
1498C42—44no—
1499C42—44no—
1500C42—44no—
1501C42—44no—
1502C42—44no—
1503C42—44no—
1504C42—44no—
1505C42C2×#4118yes—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—22no—
1517C23—21no—
1518C23—22no—
1519C23—21no—
1520C23—22no—
1521C23—22no—
1522C23—21no—
1523C23—22no—
1524C23—21no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—22no—
1529C23—21no—
1530C23—22no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—21no—
1535C23—21no—
1536C23—22no—
1537C23—44no—
1538C23—44no—
1539C23—44no—
1540C23—44no—
1541C23—82no—
1542C23—82no—
1543C23—82no—
1544C23C22×#4112yes—
1545C23C2×H(5,𝔽2)12yes—
1546C23C2×2−1+412yes—
1547C23C2×2−1+412yes—
1548C23C2611yescharacteristic
1549Q8—44no—
1550Q8—44no—
1551Q8—88no—
1552Q8—84no—
1553Q8—84no—
1554Q8—164no—
1555D4—48no—
1556D4—48no—
1557D4—48no—
1558D4—44no—
1559D4—44no—
1560D4—84no—
1561D4—84no—
1562D4—84no—
1563D4—84no—
1564D4—84no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—22no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—24no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—24no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—24no—
1622C2×C4—22no—
1623C2×C4—24no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—24no—
1636C2×C4—24no—
1637C2×C4—22no—
1638C2×C4—24no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—48no—
1645C2×C4—48no—
1646C2×C4—44no—
1647C2×C4—44no—
1648C2×C4—44no—
1649C2×C4—44no—
1650C2×C4—44no—
1651C2×C4—44no—
1652C2×C4—44no—
1653C2×C4—44no—
1654C2×C4—48no—
1655C2×C4—48no—
1656C2×C4—84no—
1657C2×C4—84no—
1658C2×C4—84no—
1659C2×C4—84no—
1660C2×C4—82no—
1661C2×C4—84no—
1662C2×C4—84no—
1663C2×C4—164no—
1664C2×C4#542116yes—
1665C2×C4C22×#4114yes—
1666C2×C4C22×#4114yes—
1667C2×C4C22×#4112yes—
1668C2×C4C22×#4112yes—
1669C2×C4C2×H(5,𝔽2)12yes—
1670C2×C4C2×H(5,𝔽2)12yes—
1671C2×C4C2×2−1+412yes—
1672C2×C4C2×2−1+412yes—
1673C2×C4C2×2−1+412yes—
1674C2×C4C2×2−1+412yes—
1675C2×C4#58512yes—
1676C22—22no—
1677C22—22no—
1678C22—22no—
1679C22—22no—
1680C22—22no—
1681C22—22no—
1682C22—22no—
1683C22—22no—
1684C22—22no—
1685C22—41no—
1686C22—41no—
1687C22—41no—
1688C22—41no—
1689C22—42no—
1690C22—42no—
1691C22—41no—
1692C22—42no—
1693C22—41no—
1694C22—42no—
1695C22—42no—
1696C22—42no—
1697C22—41no—
1698C22—42no—
1699C22—42no—
1700C22—41no—
1701C22—42no—
1702C22—42no—
1703C22—41no—
1704C22—41no—
1705C22—42no—
1706C22—42no—
1707C22—42no—
1708C22—42no—
1709C22—41no—
1710C22—88no—
1711C22C2×#54214yes—
1712C22C23×#4111yescharacteristic
1713C22C22×H(5,𝔽2)11yescharacteristic
1714C22C22×2−1+411yescharacteristic
1715C22C22×2−1+411yescharacteristic
1716C22C2×#58511yescharacteristic
1717C22H(7,𝔽2)11yescharacteristic
1718C22H(7,𝔽2)11yescharacteristic
1719C4—22no—
1720C4—24no—
1721C4—22no—
1722C4—24no—
1723C4—22no—
1724C4—42no—
1725C4—41no—
1726C4—41no—
1727C4—44no—
1728C4—42no—
1729C4—44no—
1730C4—44no—
1731C4—42no—
1732C4—44no—
1733C4—41no—
1734C4—42no—
1735C4—41no—
1736C4—42no—
1737C4—42no—
1738C4—41no—
1739C4—41no—
1740C4—42no—
1741C4—42no—
1742C4—41no—
1743C4—42no—
1744C4—42no—
1745C4—42no—
1746C4—42no—
1747C4C2×#54214yes—
1748C4C2×#54214yes—
1749C2—24no—
1750C2—42no—
1751C2—82no—
1752C2—82no—
1753C2—81no—
1754C2C22×#54211yescharacteristic
1755C2#6283711yescharacteristic
1756C2#6288111yescharacteristic
1757C2#6293011yescharacteristic
1758C2#6294411yescharacteristic
1759C2#6300011yescharacteristic
1760C2#6300811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34743C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42713C2semidirect
2. #42671C2semidirect
3. #42660C2semidirect
4. #42632C2semidirect
5. #42594C2semidirect
6. #42585C2semidirect
7. #42473C2semidirect
8. #42456C2semidirect
9. #40891C2semidirect
10. #40789C2semidirect
11. #40174C2semidirect
12. #40047C2semidirect
13. #39924C2semidirect
14. #39924C2semidirect
15. #39737C2semidirect
16. #39665C2semidirect
17. #39608C2semidirect
18. #39247C2semidirect
19. #38578C2semidirect
20. #38538C2semidirect
21. #35575C2semidirect
22. #35566C2semidirect
23. #35557C2semidirect
24. #35542C2semidirect
25. #35542C2semidirect
26. #35517C2semidirect
27. #35263C2semidirect
28. #35257C2semidirect
29. #35180C2semidirect
30. C2×#2497C2semidirect
32. #34739C2semidirect
33. #34271C2semidirect
34. #34202C2semidirect
35. #34188C2semidirect
45. #2857C22semidirect
48. #2851C22semidirect
50. #2839C22semidirect
52. #2832C22semidirect
54. #2800C22semidirect
55. #2799C22semidirect
56. #2798C22semidirect
59. #2774C22semidirect
60. #2774C22semidirect
63. #2772C22semidirect
64. #2767C22semidirect
66. #2763C22semidirect
69. #2754C22semidirect
71. #2747C22semidirect
72. #2747C22semidirect
74. #2741C22semidirect
75. #2739C22semidirect
77. #2718C22semidirect
78. #2716C22semidirect
83. #2692C22semidirect
89. #2654C22semidirect
90. #2654C22semidirect
91. #2652C22semidirect
93. #2650C22semidirect
95. #2637C22semidirect
97. #2629C22semidirect
98. #2628C22semidirect
99. #2628C22semidirect
103. #2592C22semidirect
104. #2592C22semidirect
105. #2584C22semidirect
106. #2584C22semidirect
107. #2568C22semidirect
108. #2567C22semidirect
112. #2563C22semidirect
117. #2562C22semidirect
118. #2562C22semidirect
119. #2552C22semidirect
120. #2551C22semidirect
121. #2550C22semidirect
122. #2550C22semidirect
124. #2548C22semidirect
127. #2547C22semidirect
128. #2546C22semidirect
129. #2521C22semidirect
130. #2520C22semidirect
131. #2512C22semidirect
132. #2512C22semidirect
133. #2511C22semidirect
134. #2511C22semidirect
135. #2511C22semidirect
136. #2508C22semidirect
146. #2497C22semidirect
147. #2497C22semidirect
148. #2496C22semidirect
149. #2496C22semidirect
161. #2487C22semidirect
163. #2486C22semidirect
166. #2485C22semidirect
167. #2485C22semidirect
171. #2474C22semidirect
175. #2470C22semidirect
178. #2454C22semidirect
179. #2454C22semidirect
180. #2453C22semidirect
181. #2453C22semidirect
183. #2452C22semidirect
184. #2452C22semidirect
185. #2451C22semidirect
186. #2451C22semidirect
190. #2448C22semidirect
191. #2447C22semidirect
192. #2446C22semidirect
193. #2445C22semidirect
198. #2442C22semidirect
201. #2441C22semidirect
205. #2440C22semidirect
208. #2439C22semidirect
233. #2370C22semidirect
234. #2370C22semidirect
235. #2370C22semidirect
236. #2370C22semidirect
237. #2369C22semidirect
238. #2369C22semidirect
239. #2365C22semidirect
240. #2365C22semidirect
243. #2355C22semidirect
244. #2355C22semidirect
246. #2354C22semidirect
247. #2354C22semidirect
254. #2332C22semidirect
259. #2323C22semidirect
263. #2314C22semidirect
264. #2314C22semidirect
288. #2285C22semidirect
289. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#427132
#426712
#426602
#426322
#425942
#425852
#424732
#424562
#408912
#407892
#401742
#400472
#399242
#397372
#396652
#396082
#392472
#385782
#385382
#355752
#355662
#355572
#355422
#355172
#352632
#352572
#351802
C2×#24972
#347432
#347392
#342712
#342022
#341882