Finite Group Databasebeta

← #7650797

Subgroups — #7650797

Order 512.

4936 conjugacy classes of subgroups.

The subgroup lattice has 1731 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42751C212yesmaximal, complemented
2#42729C212yesmaximal, complemented
3#42725C212yesmaximal, complemented
4#42635C212yesmaximal, complemented
5#42632C212yesmaximal, complemented
6#42624C212yesmaximal, complemented
7#42571C212yesmaximal, complemented
8#42545C212yesmaximal, complemented
9#41390C214yesmaximal, complemented
10#40561C214yesmaximal, complemented
11#40174C212yesmaximal, complemented
12#40121C212yesmaximal, complemented
13#40117C212yesmaximal, complemented
14#40050C212yesmaximal, complemented
15#39792C212yesmaximal, complemented
16#39224C212yesmaximal, complemented
17#39033C212yesmaximal, complemented
18#39029C212yesmaximal, complemented
19#38391C214yesmaximal, complemented
20#37852C214yesmaximal, complemented
21#35649C211yesmaximal, characteristic, complemented
22#35575C211yesmaximal, characteristic, complemented
23#35566C211yesmaximal, characteristic, complemented
24#35556C211yesmaximal, characteristic, complemented
25#35545C211yesmaximal, characteristic, complemented
26#35531C211yesmaximal, characteristic, complemented
27#35264C211yesmaximal, characteristic, complemented
28#35254C211yesmaximal, characteristic, complemented
29#35168C211yesmaximal, characteristic
30#34947C211yesmaximal, characteristic, complemented
31#34816C211yesmaximal, characteristic, complemented
32C2×#2454C211yesmaximal, characteristic, complemented
33#34267C211yesmaximal, characteristic, complemented
34#34217C211yesmaximal, characteristic, complemented
35#34186C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#537C2211yescharacteristic
38C2×#535C2211yescharacteristic
39C2×#535C2211yescharacteristic
40C2×#533C2211yescharacteristic
41C22×#125C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45#2861C2212yes—
46#2858C2212yes—
47#2854C2212yes—
48#2854C2212yes—
49#2847C2214yes—
50#2838C2214yescomplemented
51#2837C2214yescomplemented
52#2837C2214yescomplemented
53#2829C2214yescomplemented
54#2801C2214yescomplemented
55#2800C2214yescomplemented
56#2795C2214yescomplemented
57#2779C2214yescomplemented
58#2773C2214yescomplemented
59#2773C2214yescomplemented
60#2757C2214yescomplemented
61#2754C2214yescomplemented
62#2754C2214yescomplemented
63#2747C2214yescomplemented
64#2746C2214yescomplemented
65#2746C2214yescomplemented
66#2745C2214yescomplemented
67#2742C2214yescomplemented
68#2741C2214yescomplemented
69#2741C2214yescomplemented
70#2738C2214yescomplemented
71#2737C2214yescomplemented
72#2737C2214yescomplemented
73#2731C2214yescomplemented
74#2730C2214yescomplemented
75#2730C2214yescomplemented
76#2718C2214yescomplemented
77#2717C2214yescomplemented
78#2717C2214yescomplemented
79#2705C2214yescomplemented
80#2705C2214yescomplemented
81#2701C2214yescomplemented
82#2691C2214yescomplemented
83#2686C2214yescomplemented
84#2674C2214yescomplemented
85#2672C2214yescomplemented
86#2663C2214yescomplemented
87#2663C2214yescomplemented
88#2662C2214yescomplemented
89#2654C2214yescomplemented
90#2653C2214yescomplemented
91#2651C2214yescomplemented
92#2651C2214yescomplemented
93#2650C2214yescomplemented
94#2649C2214yescomplemented
95#2641C2212yes—
96#2640C2212yes—
97#2630C2214yescomplemented
98#2628C2214yescomplemented
99#2624C2212yes—
100#2624C2212yes—
101#2624C2214yescomplemented
102#2617C2214yes—
103#2592C2212yes—
104#2592C2212yes—
105#2591C2214yes—
106#2584C2212yescomplemented
107#2584C2212yescomplemented
108#2568C2211yescharacteristic, complemented
109#2567C2212yescomplemented
110#2567C2211yescharacteristic, complemented
111#2566C2211yescharacteristic, complemented
112#2566C2211yescharacteristic, complemented
113#2565C2211yescharacteristic, complemented
114#2565C2211yescharacteristic, complemented
115#2564C2212yes—
116#2564C2212yes—
117#2564C2214yes—
118#2563C2211yescharacteristic, complemented
119#2552C2212yescomplemented
120#2551C2212yescomplemented
121#2550C2212yescomplemented
122#2550C2212yescomplemented
123#2549C2214yes—
124#2548C2212yes—
125#2548C2212yes—
126#2546C2212yescomplemented
127#2542C2211yescharacteristic, complemented
128#2525C2214yescomplemented
129#2521C2214yescomplemented
130#2521C2214yescomplemented
131#2514C2211yescharacteristic, complemented
132#2514C2211yescharacteristic, complemented
133#2514C2212yescomplemented
134#2513C2211yescharacteristic, complemented
135#2513C2211yescharacteristic, complemented
136#2513C2212yescomplemented
137#2512C2211yescharacteristic, complemented
138#2512C2211yescharacteristic, complemented
139#2512C2212yescomplemented
140#2511C2211yescharacteristic, complemented
141#2511C2211yescharacteristic, complemented
142#2511C2212yescomplemented
143#2510C2212yes—
144#2510C2212yes—
145#2510C2214yes—
146#2504C2212yes—
147#2504C2214yes—
148#2501C2212yes—
149#2500C2212yes—
150#2500C2212yes—
151#2497C2212yescomplemented
152#2496C2212yescomplemented
153#2495C2214yescomplemented
154#2495C2212yescomplemented
155#2494C2212yescomplemented
156#2494C2214yescomplemented
157#2491C2212yes—
158#2491C2212yes—
159#2491C2212yes—
160#2491C2212yes—
161#2491C2214yescomplemented
162#2490C2212yes—
163#2490C2212yes—
164#2490C2212yes—
165#2490C2212yes—
166#2490C2212yescomplemented
167#2490C2212yescomplemented
168#2490C2212yescomplemented
169#2490C2212yescomplemented
170#2489C2212yescomplemented
171#2489C2212yescomplemented
172#2489C2212yescomplemented
173#2489C2212yescomplemented
174#2481C2212yes—
175#2481C2212yes—
176#2481C2214yes—
177#2479C2214yescomplemented
178#2477C2214yescomplemented
179#2474C2214yescomplemented
180#2472C2214yes—
181#2472C2214yes—
182#2472C2214yes—
183#2472C2214yes—
184#2470C2214yescomplemented
185#2461C2214yescomplemented
186#2454C2212yes—
187#2454C2212yes—
188#2454C2212yes—
189#2454C2212yes—
190#2454C2212yes—
191#2454C2212yes—
192#2454C2212yes—
193#2454C2212yes—
194#2454C2212yescomplemented
195#2453C2212yescomplemented
196#2452C2212yescomplemented
197#2451C2212yescomplemented
198#2448C2212yes—
199#2448C2212yes—
200#2448C2212yes—
201#2448C2212yes—
202#2445C2212yes—
203#2445C2212yes—
204#2445C2212yes—
205#2445C2212yes—
206#2442C2212yescomplemented
207#2441C2212yescomplemented
208#2440C2214yes—
209#2440C2212yescomplemented
210#2439C2212yescomplemented
211#2428C2212yes—
212#2428C2212yes—
213#2428C2212yes—
214#2428C2212yes—
215#2427C2212yes—
216#2427C2212yes—
217#2427C2212yes—
218#2427C2212yes—
219#2422C2214yescomplemented
220#2418C2214yes—
221#2418C2214yes—
222#2418C2214yes—
223#2418C2214yes—
224#2417C2214yes—
225#2417C2212yes—
226#2417C2212yes—
227#2401C2212yescomplemented
228#2401C2212yescomplemented
229#2396C2212yescomplemented
230#2396C2212yescomplemented
231C2×#399C2212yes—
232C2×#396C2212yes—
233#2370C2212yescomplemented
234#2370C2212yescomplemented
235#2370C2212yescomplemented
236#2370C2212yescomplemented
237#2364C2214yes—
238#2363C2212yescomplemented
239#2362C2212yescomplemented
240#2361C2214yes—
241#2361C2212yescomplemented
242#2360C2212yescomplemented
243#2357C2212yes—
244#2357C2212yes—
245#2357C2212yes—
246#2357C2212yes—
247#2354C2212yes—
248#2354C2212yes—
249#2354C2212yes—
250#2354C2212yes—
251#2345C2214yes—
252#2345C2214yes—
253#2337C2214yescomplemented
254#2335C2214yescomplemented
255#2330C2212yescomplemented
256#2330C2212yescomplemented
257#2324C2212yescomplemented
258#2324C2214yescomplemented
259#2323C2212yescomplemented
260#2317C2211yescharacteristic
261#2316C2211yescharacteristic
262#2316C2211yescharacteristic
263#2314C2214yescomplemented
264#2312C2214yes—
265#2311C2211yescharacteristic
266#2311C2211yescharacteristic
267#2311C2211yescharacteristic
268#2309C2211yescharacteristic
269#2309C2211yescharacteristic
270C4×#125C2212yescomplemented
271C4×#125C2212yescomplemented
272C4×#126C2212yescomplemented
273C4×#126C2212yescomplemented
274C4×C22⋊Q8C2212yescomplemented
275C4×C22⋊Q8C2212yescomplemented
276C4×C22⋊Q8C2212yescomplemented
277C4×#121C2212yescomplemented
278#2297C2211yescharacteristic
279#2297C2211yescharacteristic
280#2297C2211yescharacteristic
281#2297C2211yescharacteristic
282#2297C2211yescharacteristic
283#2296C2211yescharacteristic
284C2×#390C2211yescharacteristic
285C2×#390C2211yescharacteristic
286C2×#389C2211yescharacteristic
287C2×#389C2211yescharacteristic
288C2×#385C2212yes—
289#2285C2211yescharacteristic
290#2285C2211yescharacteristic
291#2285C2211yescharacteristic
292#2280C2214yes—
293C2×#380C2212yes—
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296#2274C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303#544—44no—
304#537—28no—
305#535—44no—
306#535—44no—
307#533—44no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2314yes—
313C2×#127C2312yes—
314C2×#127C2312yes—
315C2×#126C2312yes—
316C2×#126C2312yes—
317C2×#126C2314yes—
318C2×#125—28no—
319C2×#125C2312yes—
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2311yescharacteristic
324C2×#125C2311yescharacteristic
325C2×#125C2312yes—
326C2×#125C2312yes—
327C2×#124C2312yes—
328C2×#124C2314yes—
329C2×#124C2312yes—
330C2×#124C2314yes—
331C2×#124C2314yes—
332C2×#124C2314yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2314yes—
345C2×#121C2312yes—
346C2×#121C2314yes—
347C2×#121C2312yes—
348C2×#121C2314yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2314yes—
354C2×#120C2314yes—
355C2×#120C2314yes—
356#520—44no—
357C4×#41—44no—
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×D4—28no—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2314yes—
375C2×#117C2311yescharacteristic
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2314yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2314yes—
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2311yescharacteristic
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2311yescharacteristic
395C22×C22⋊C4C2312yes—
396C22×C22⋊C4C2312yes—
397C22×C22⋊C4C2312yes—
398C22×C22⋊C4C2312yes—
399C22×C22⋊C4C2312yes—
400C22×C42C2311yescharacteristic
401C22×C42C2311yescharacteristic
402C22×C42C2311yescharacteristic
403C22×C42C2312yes—
404#401C2312yes—
405#401C2314yes—
406#401C2312yes—
407#400C2312yes—
408#400C2312yes—
409#400C2314yes—
410#400C2312yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2312yes—
416#400C2314yes—
417#400C2312yes—
418#400C2312yes—
419#400C2312yes—
420#400C2312yes—
421#399C2312yes—
422#399C2312yes—
423#399C2314yes—
424#399C2314yes—
425#399C2314yes—
426#399C2314yes—
427#399C2314yes—
428#399C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#398C2312yes—
433#398C2312yes—
434#398C2312yes—
435#398C2312yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2312yes—
455#397C2314yes—
456#397C2312yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2312yes—
462#397C2314yes—
463#397C2312yes—
464#397C2312yes—
465#396C2312yes—
466#396C2312yes—
467#396C2312yes—
468#396C2312yes—
469#396C2314yes—
470#396C2314yes—
471#396C2312yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#395C2312yes—
479#395C2312yes—
480#395C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2314yes—
484#395C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#393C2312yes—
508#393C2312yes—
509#393C2314yes—
510#393C2314yes—
511#393C2314yes—
512#393C2314yes—
513#393C2314yes—
514#392C2314yes—
515#392C2314yes—
516#391C2311yescharacteristic
517#391C2311yescharacteristic
518#391C2311yescharacteristic
519#391C2311yescharacteristic
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2314yes—
524#391C2312yes—
525#391C2312yes—
526#391C2311yescharacteristic
527#391C2311yescharacteristic
528#391C2314yes—
529#391C2314yes—
530#391C2311yescharacteristic
531#391C2311yescharacteristic
532#391C2311yescharacteristic
533#391C2311yescharacteristic
534#390C2311yescharacteristic
535#390C2311yescharacteristic
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2311yescharacteristic
545#390C2311yescharacteristic
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2314yes—
550#390C2311yescharacteristic
551#390C2314yes—
552#390C2314yes—
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2314yes—
559#390C2312yes—
560#390C2314yes—
561#390C2311yescharacteristic
562#390C2311yescharacteristic
563#390C2311yescharacteristic
564#390C2311yescharacteristic
565#390C2312yes—
566#390C2312yes—
567#390C2312yes—
568#390C2312yes—
569#390C2311yescharacteristic
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2311yescharacteristic
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2314yes—
592#389C2314yes—
593#389C2314yes—
594#389C2314yes—
595#389C2314yes—
596#389C2312yes—
597#389C2312yes—
598#389C2311yescharacteristic
599#389C2314yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
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#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2312yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#386C2312yes—
671#386C2314yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#386C2312yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2312yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2312yes—
689#386C2312yes—
690#386C2314yes—
691#386C2312yes—
692#386C2312yes—
693#385C2312yes—
694#385C2312yes—
695#385C2312yes—
696#385C2312yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2312yes—
706#385C2312yes—
707#385C2314yes—
708#384C2311yescharacteristic
709#384C2311yescharacteristic
710#384C2311yescharacteristic
711#384C2311yescharacteristic
712#384C2314yes—
713#384C2312yes—
714#384C2311yescharacteristic
715#384C2311yescharacteristic
716#383C2312yes—
717#383C2312yes—
718#383C2314yes—
719#382C2311yescharacteristic
720#382C2311yescharacteristic
721#382C2311yescharacteristic
722#382C2311yescharacteristic
723#382C2314yes—
724#382C2312yes—
725#382C2311yescharacteristic
726#382C2311yescharacteristic
727#382C2314yes—
728#381C2314yes—
729#381C2314yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2314yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2314yes—
745#380C2314yes—
746#380C2314yes—
747#380C2314yes—
748#380C2314yes—
749#380C2314yes—
750#380C2314yes—
751#380C2314yes—
752#380C2314yes—
753#380C2314yes—
754#380C2312yes—
755#379C2314yes—
756#379C2314yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813#376C2312yes—
814C2×#95C2311yescharacteristic
815C2×#95C2311yescharacteristic
816C2×#95C2312yes—
817C2×#95C2312yes—
818C43C2312yes—
819C25C2412yes—
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×Q8C2412yes—
830C22×Q8C2414yes—
831C22×D4—24no—
832C22×D4—24no—
833C22×D4—24no—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2412yes—
838C22×D4C2411yescharacteristic
839C22×D4C2411yescharacteristic
840C22×D4C2414yes—
841C22×D4C2414yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C23×C4—28no—
846C23×C4—44no—
847C23×C4—82no—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2414yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2414yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C4⋊Q8—42no—
866C4⋊Q8—42no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—84no—
870#127—44no—
871#127—44no—
872#126—44no—
873#126—44no—
874#126—84no—
875#125—28no—
876#125—28no—
877#125—28no—
878#125—28no—
879#125—42no—
880#125—42no—
881#125—44no—
882#125—44no—
883#124—44no—
884#124—44no—
885#124—48no—
886#124—84no—
887#124—84no—
888#124—84no—
889#123—48no—
890#123—84no—
891#123—84no—
892#123—84no—
893C22⋊Q8—28no—
894C22⋊Q8—28no—
895C22⋊Q8—44no—
896C22⋊Q8—44no—
897C22⋊Q8—48no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900C22⋊Q8—84no—
901#121—216no—
902#121—28no—
903#121—28no—
904#121—48no—
905#121—44no—
906#121—44no—
907#121—44no—
908#121—44no—
909#121—84no—
910#120—48no—
911#120—48no—
912C4×Q8—44no—
913C4×Q8—44no—
914C4×Q8—42no—
915C4×Q8—42no—
916C4×Q8—44no—
917C4×D4—28no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—28no—
921C4×D4—42no—
922C4×D4—42no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—44no—
926C4×D4—48no—
927C4×D4—84no—
928#117—24no—
929#117—24no—
930#117—24no—
931#117—24no—
932#117—24no—
933#117—24no—
934#117—44no—
935#117—48no—
936#117—44no—
937#117—84no—
938C2×C4⋊C4—28no—
939C2×C4⋊C4—28no—
940C2×C4⋊C4—24no—
941C2×C4⋊C4—24no—
942C2×C4⋊C4—42no—
943C2×C4⋊C4—42no—
944C2×C4⋊C4—44no—
945C2×C4⋊C4—82no—
946C2×C4⋊C4—82no—
947C2×C4⋊C4#4118yes—
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C22⋊C4—28no—
1018C2×C22⋊C4—44no—
1019C2×C22⋊C4—82no—
1020C2×C22⋊C4—82no—
1021C2×C22⋊C4—82no—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C42—24no—
1082C2×C42—24no—
1083C2×C42—24no—
1084C2×C42—44no—
1085C2×C42C2412yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2414yes—
1104C2×C42C2414yes—
1105C2×C42C2414yes—
1106C2×C42C2414yes—
1107C2×C42C2414yes—
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2414yes—
1113C2×C42C2414yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116#95C2414yes—
1117#95C2411yescharacteristic
1118#95C2411yescharacteristic
1119#95C2411yescharacteristic
1120#95C2411yescharacteristic
1121#95C2411yescharacteristic
1122#95C2411yescharacteristic
1123#95C2411yescharacteristic
1124#95C2411yescharacteristic
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186C24—24no—
1187C24—24no—
1188C24—24no—
1189C24—42no—
1190C24—42no—
1191C24—42no—
1192C24—42no—
1193C24C2514yes—
1194C24C2512yes—
1195C24C2512yes—
1196C24C2511yescharacteristic
1197#41—416no—
1198#41—416no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—22no—
1202C2×Q8—22no—
1203C2×Q8—22no—
1204C2×Q8—22no—
1205C2×Q8—24no—
1206C2×Q8—42no—
1207C2×Q8—42no—
1208C2×Q8—42no—
1209C2×Q8—42no—
1210C2×Q8—42no—
1211C2×Q8—44no—
1212C2×Q8—44no—
1213C2×Q8—44no—
1214C2×D4—24no—
1215C2×D4—24no—
1216C2×D4—24no—
1217C2×D4—24no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—28no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—22no—
1232C2×D4—22no—
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—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—416no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—24no—
1254C22×C4—22no—
1255C22×C4—24no—
1256C22×C4—28no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—24no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—28no—
1266C22×C4—28no—
1267C22×C4—24no—
1268C22×C4—41no—
1269C22×C4—42no—
1270C22×C4—44no—
1271C22×C4—42no—
1272C22×C4—41no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—42no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—42no—
1280C22×C4—42no—
1281C22×C4—42no—
1282C22×C4—41no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—42no—
1288C22×C4—44no—
1289C22×C4—42no—
1290C22×C4—42no—
1291C22×C4—44no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—816no—
1296C22×C4C2×#4118yes—
1297C22×C4C2×#4114yes—
1298C22×C4H(5,𝔽2)14yes—
1299C22×C42−1+414yes—
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2511yescharacteristic
1309C22×C4C2511yescharacteristic
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2514yes—
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2511yescharacteristic
1324C22×C4C2511yescharacteristic
1325C22×C4C2514yes—
1326C22×C4C2514yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C4⋊C4—28no—
1332C4⋊C4—28no—
1333C4⋊C4—28no—
1334C4⋊C4—28no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—28no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—22no—
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—41no—
1360C4⋊C4—41no—
1361C4⋊C4—41no—
1362C4⋊C4—41no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—42no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4C2×#4118yes—
1399C4⋊C4C2×#4118yes—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—28no—
1407C22⋊C4—28no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—28no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—44no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
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—42no—
1450C22⋊C4—44no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—44no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—22no—
1463C42—22no—
1464C42—22no—
1465C42—22no—
1466C42—22no—
1467C42—22no—
1468C42—22no—
1469C42—22no—
1470C42—22no—
1471C42—24no—
1472C42—24no—
1473C42—24no—
1474C42—24no—
1475C42—24no—
1476C42—24no—
1477C42—42no—
1478C42—42no—
1479C42—44no—
1480C42—44no—
1481C42—44no—
1482C42—44no—
1483C42—44no—
1484C42—44no—
1485C42—42no—
1486C42—42no—
1487C42—44no—
1488C42—42no—
1489C42—42no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—24no—
1495C23—22no—
1496C23—22no—
1497C23—24no—
1498C23—22no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—24no—
1503C23—22no—
1504C23—24no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—24no—
1509C23—22no—
1510C23—24no—
1511C23—22no—
1512C23—24no—
1513C23—22no—
1514C23—22no—
1515C23—48no—
1516C23—48no—
1517C23—48no—
1518C23—84no—
1519C23—84no—
1520C23—84no—
1521C23—84no—
1522C23C22×#4112yes—
1523C23C2×H(5,𝔽2)12yes—
1524C23C2×2−1+412yes—
1525C23C2611yescharacteristic
1526Q8—44no—
1527Q8—44no—
1528Q8—84no—
1529Q8—84no—
1530Q8—164no—
1531D4—48no—
1532D4—48no—
1533D4—48no—
1534D4—48no—
1535D4—44no—
1536D4—44no—
1537D4—88no—
1538D4—164no—
1539D4—164no—
1540D4—164no—
1541D4—164no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—24no—
1545C2×C4—21no—
1546C2×C4—24no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—24no—
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—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—24no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—24no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—24no—
1619C2×C4—24no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—21no—
1626C2×C4—48no—
1627C2×C4—416no—
1628C2×C4—44no—
1629C2×C4—44no—
1630C2×C4—48no—
1631C2×C4—48no—
1632C2×C4—84no—
1633C2×C4—88no—
1634C2×C4—82no—
1635C2×C4—82no—
1636C2×C4—82no—
1637C2×C4—84no—
1638C2×C4—82no—
1639C2×C4—84no—
1640C2×C4—84no—
1641C2×C4—164no—
1642C2×C4#542116yes—
1643C2×C4C22×#4118yes—
1644C2×C4C22×#4112yes—
1645C2×C4C22×#4112yes—
1646C2×C4C2×H(5,𝔽2)12yes—
1647C2×C4C2×H(5,𝔽2)12yes—
1648C2×C4C2×2−1+412yes—
1649C2×C4C2×2−1+412yes—
1650C2×C4#58512yes—
1651C2×C4#58512yes—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—22no—
1656C22—22no—
1657C22—22no—
1658C22—44no—
1659C22—42no—
1660C22—42no—
1661C22—42no—
1662C22—42no—
1663C22—44no—
1664C22—42no—
1665C22—42no—
1666C22—44no—
1667C22—42no—
1668C22—42no—
1669C22—44no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—42no—
1674C22—44no—
1675C22—44no—
1676C22—42no—
1677C22—42no—
1678C22—44no—
1679C22—816no—
1680C22C2×#54214yes—
1681C22C23×#4111yescharacteristic
1682C22C22×H(5,𝔽2)11yescharacteristic
1683C22C22×2−1+411yescharacteristic
1684C22C2×#58511yescharacteristic
1685C22C2×#58511yescharacteristic
1686C22H(7,𝔽2)11yescharacteristic
1687C22H(7,𝔽2)11yescharacteristic
1688C4—22no—
1689C4—28no—
1690C4—22no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—41no—
1696C4—41no—
1697C4—41no—
1698C4—44no—
1699C4—41no—
1700C4—42no—
1701C4—42no—
1702C4—42no—
1703C4—42no—
1704C4—41no—
1705C4—42no—
1706C4—44no—
1707C4—41no—
1708C4—42no—
1709C4—42no—
1710C4—42no—
1711C4—42no—
1712C4—42no—
1713C4—42no—
1714C4—42no—
1715C4—42no—
1716C4—42no—
1717C4C2×#54214yes—
1718C4C2×#54214yes—
1719C2—24no—
1720C2—82no—
1721C2—82no—
1722C2—84no—
1723C2C22×#54211yescharacteristic
1724C2#6283011yescharacteristic
1725C2#6288011yescharacteristic
1726C2#6292611yescharacteristic
1727C2#6292611yescharacteristic
1728C2#6299011yescharacteristic
1729C2#6300611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35168C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42751C2semidirect
2. #42729C2semidirect
3. #42725C2semidirect
4. #42635C2semidirect
5. #42632C2semidirect
6. #42624C2semidirect
7. #42571C2semidirect
8. #42545C2semidirect
9. #41390C2semidirect
10. #40561C2semidirect
11. #40174C2semidirect
12. #40121C2semidirect
13. #40117C2semidirect
14. #40050C2semidirect
15. #39792C2semidirect
16. #39224C2semidirect
17. #39033C2semidirect
18. #39029C2semidirect
19. #38391C2semidirect
20. #37852C2semidirect
21. #35649C2semidirect
22. #35575C2semidirect
23. #35566C2semidirect
24. #35556C2semidirect
25. #35545C2semidirect
26. #35531C2semidirect
27. #35264C2semidirect
28. #35254C2semidirect
30. #34947C2semidirect
31. #34816C2semidirect
32. C2×#2454C2semidirect
33. #34267C2semidirect
34. #34217C2semidirect
35. #34186C2semidirect
50. #2838C22semidirect
51. #2837C22semidirect
52. #2837C22semidirect
53. #2829C22semidirect
54. #2801C22semidirect
55. #2800C22semidirect
56. #2795C22semidirect
57. #2779C22semidirect
58. #2773C22semidirect
59. #2773C22semidirect
60. #2757C22semidirect
61. #2754C22semidirect
62. #2754C22semidirect
63. #2747C22semidirect
64. #2746C22semidirect
65. #2746C22semidirect
66. #2745C22semidirect
67. #2742C22semidirect
68. #2741C22semidirect
69. #2741C22semidirect
70. #2738C22semidirect
71. #2737C22semidirect
72. #2737C22semidirect
73. #2731C22semidirect
74. #2730C22semidirect
75. #2730C22semidirect
76. #2718C22semidirect
77. #2717C22semidirect
78. #2717C22semidirect
79. #2705C22semidirect
80. #2705C22semidirect
81. #2701C22semidirect
82. #2691C22semidirect
83. #2686C22semidirect
84. #2674C22semidirect
85. #2672C22semidirect
86. #2663C22semidirect
87. #2663C22semidirect
88. #2662C22semidirect
89. #2654C22semidirect
90. #2653C22semidirect
91. #2651C22semidirect
92. #2651C22semidirect
93. #2650C22semidirect
94. #2649C22semidirect
97. #2630C22semidirect
98. #2628C22semidirect
101. #2624C22semidirect
106. #2584C22semidirect
107. #2584C22semidirect
108. #2568C22semidirect
109. #2567C22semidirect
110. #2567C22semidirect
111. #2566C22semidirect
112. #2566C22semidirect
113. #2565C22semidirect
114. #2565C22semidirect
118. #2563C22semidirect
119. #2552C22semidirect
120. #2551C22semidirect
121. #2550C22semidirect
122. #2550C22semidirect
126. #2546C22semidirect
127. #2542C22semidirect
128. #2525C22semidirect
129. #2521C22semidirect
130. #2521C22semidirect
131. #2514C22semidirect
132. #2514C22semidirect
133. #2514C22semidirect
134. #2513C22semidirect
135. #2513C22semidirect
136. #2513C22semidirect
137. #2512C22semidirect
138. #2512C22semidirect
139. #2512C22semidirect
140. #2511C22semidirect
141. #2511C22semidirect
142. #2511C22semidirect
151. #2497C22semidirect
152. #2496C22semidirect
153. #2495C22semidirect
154. #2495C22semidirect
155. #2494C22semidirect
156. #2494C22semidirect
161. #2491C22semidirect
166. #2490C22semidirect
167. #2490C22semidirect
168. #2490C22semidirect
169. #2490C22semidirect
170. #2489C22semidirect
171. #2489C22semidirect
172. #2489C22semidirect
173. #2489C22semidirect
177. #2479C22semidirect
178. #2477C22semidirect
179. #2474C22semidirect
184. #2470C22semidirect
185. #2461C22semidirect
194. #2454C22semidirect
195. #2453C22semidirect
196. #2452C22semidirect
197. #2451C22semidirect
206. #2442C22semidirect
207. #2441C22semidirect
209. #2440C22semidirect
210. #2439C22semidirect
219. #2422C22semidirect
227. #2401C22semidirect
228. #2401C22semidirect
229. #2396C22semidirect
230. #2396C22semidirect
233. #2370C22semidirect
234. #2370C22semidirect
235. #2370C22semidirect
236. #2370C22semidirect
238. #2363C22semidirect
239. #2362C22semidirect
241. #2361C22semidirect
242. #2360C22semidirect
253. #2337C22semidirect
254. #2335C22semidirect
255. #2330C22semidirect
256. #2330C22semidirect
257. #2324C22semidirect
258. #2324C22semidirect
259. #2323C22semidirect
263. #2314C22semidirect
270. C4×#125C22semidirect
271. C4×#125C22semidirect
272. C4×#126C22semidirect
273. C4×#126C22semidirect
274. C4×C22⋊Q8C22semidirect
275. C4×C22⋊Q8C22semidirect
276. C4×C22⋊Q8C22semidirect
277. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#427512
#427292
#427252
#426352
#426322
#426242
#425712
#425452
#413902
#405612
#401742
#401212
#401172
#400502
#397922
#392242
#390332
#390292
#383912
#378522
#356492
#355752
#355662
#355562
#355452
#355312
#352642
#352542
#351682
#349472
#348162
C2×#24542
#342672
#342172
#341862