Finite Group Databasebeta

← #8094829

Subgroups — #8094829

Order 512.

4688 conjugacy classes of subgroups.

The subgroup lattice has 1669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53132C212yesmaximal, complemented
2#53118C212yesmaximal, complemented
3#53089C212yesmaximal, complemented
4#53083C212yesmaximal, complemented
5#53039C212yesmaximal, complemented
6#53035C212yesmaximal, complemented
7#53001C212yesmaximal, complemented
8#52997C212yesmaximal, complemented
9#52473C214yesmaximal, complemented
10#52470C214yesmaximal, complemented
11#46124C214yesmaximal, complemented
12#46113C212yesmaximal, complemented
13#46082C212yesmaximal, complemented
14#46078C212yesmaximal, complemented
15#46068C212yesmaximal, complemented
16#46056C212yesmaximal, complemented
17#46019C212yesmaximal, complemented
18#45998C212yesmaximal, complemented
19#45993C212yesmaximal, complemented
20#45971C214yesmaximal, complemented
21#35575C211yesmaximal, characteristic, complemented
22#35541C211yesmaximal, characteristic
23#35532C211yesmaximal, characteristic, complemented
24#35531C211yesmaximal, characteristic
25#35529C211yesmaximal, characteristic, complemented
26#35529C211yesmaximal, characteristic, complemented
27#35275C211yesmaximal, characteristic, complemented
28#35266C211yesmaximal, characteristic, complemented
29#35265C211yesmaximal, characteristic, complemented
30#35264C211yesmaximal, characteristic
31#35167C211yesmaximal, characteristic, complemented
32#35160C211yesmaximal, characteristic, complemented
33#34948C211yesmaximal, characteristic, complemented
34#34816C211yesmaximal, characteristic, complemented
35C2×#2512C211yesmaximal, characteristic, complemented
36C2×#563C2214yescomplemented
37C2×#544C2211yescharacteristic
38C2×#544C2211yescharacteristic
39C2×#544C2211yescharacteristic
40C2×#535C2211yescharacteristic
41C22×#126C2212yes—
42C2×#520C2211yescharacteristic
43C2×#518C2211yescharacteristic
44#2868C2212yescomplemented
45#2864C2212yescomplemented
46#2861C2212yes—
47#2860C2212yes—
48#2860C2212yes—
49#2859C2212yescomplemented
50#2859C2212yescomplemented
51#2858C2212yes—
52#2857C2214yes—
53#2852C2214yes—
54#2841C2214yescomplemented
55#2838C2214yescomplemented
56#2838C2214yescomplemented
57#2838C2214yescomplemented
58#2838C2214yescomplemented
59#2837C2214yescomplemented
60#2837C2214yescomplemented
61#2836C2214yescomplemented
62#2831C2214yescomplemented
63#2830C2214yescomplemented
64#2827C2214yescomplemented
65#2827C2214yescomplemented
66#2827C2214yescomplemented
67#2823C2214yescomplemented
68#2823C2214yescomplemented
69#2821C2214yescomplemented
70#2821C2214yescomplemented
71#2820C2214yescomplemented
72#2817C2214yescomplemented
73#2814C2214yescomplemented
74#2793C2214yescomplemented
75#2793C2214yescomplemented
76#2787C2214yescomplemented
77#2777C2214yescomplemented
78#2775C2214yescomplemented
79#2770C2214yescomplemented
80#2765C2214yescomplemented
81#2765C2214yescomplemented
82#2745C2214yescomplemented
83#2738C2214yescomplemented
84#2731C2214yescomplemented
85#2729C2214yescomplemented
86#2728C2214yescomplemented
87#2727C2214yescomplemented
88#2725C2214yescomplemented
89#2725C2214yescomplemented
90#2723C2214yescomplemented
91#2723C2214yescomplemented
92#2723C2214yescomplemented
93#2722C2214yescomplemented
94#2721C2214yescomplemented
95#2720C2214yescomplemented
96#2718C2214yescomplemented
97#2718C2214yescomplemented
98#2718C2214yescomplemented
99#2717C2214yescomplemented
100#2716C2214yescomplemented
101#2715C2214yescomplemented
102#2707C2214yescomplemented
103#2702C2214yescomplemented
104#2698C2214yescomplemented
105#2695C2214yescomplemented
106#2695C2214yescomplemented
107#2689C2214yescomplemented
108#2683C2214yescomplemented
109#2680C2214yescomplemented
110#2677C2214yescomplemented
111#2674C2214yescomplemented
112#2674C2214yescomplemented
113#2674C2214yescomplemented
114#2660C2212yescomplemented
115#2660C2212yescomplemented
116#2659C2214yes—
117#2647C2212yescomplemented
118#2647C2212yescomplemented
119#2644C2212yes—
120#2644C2212yes—
121#2643C2214yes—
122#2641C2212yes—
123#2640C2212yes—
124#2571C2211yescharacteristic, complemented
125#2571C2211yescharacteristic, complemented
126#2570C2211yescharacteristic, complemented
127#2570C2211yescharacteristic, complemented
128#2570C2211yescharacteristic, complemented
129#2570C2211yescharacteristic, complemented
130#2569C2212yes—
131#2569C2212yes—
132#2567C2212yescomplemented
133#2566C2212yes—
134#2566C2212yes—
135#2566C2212yes—
136#2566C2212yes—
137#2566C2212yescomplemented
138#2565C2212yescomplemented
139#2564C2214yes—
140#2563C2212yes—
141#2563C2212yes—
142#2552C2212yescomplemented
143#2552C2212yescomplemented
144#2552C2212yescomplemented
145#2552C2212yescomplemented
146#2552C2211yescharacteristic, complemented
147#2552C2211yescharacteristic, complemented
148#2551C2212yescomplemented
149#2551C2212yescomplemented
150#2551C2212yescomplemented
151#2551C2212yescomplemented
152#2550C2212yescomplemented
153#2550C2212yescomplemented
154#2550C2212yescomplemented
155#2550C2212yescomplemented
156#2542C2212yes—
157#2542C2212yes—
158#2542C2212yescomplemented
159#2514C2211yescharacteristic, complemented
160#2514C2211yescharacteristic, complemented
161#2514C2212yescomplemented
162#2513C2212yes—
163#2513C2212yes—
164#2513C2211yescharacteristic, complemented
165#2513C2211yescharacteristic, complemented
166#2513C2212yescomplemented
167#2512C2212yes—
168#2512C2212yes—
169#2512C2212yes—
170#2512C2212yes—
171#2512C2212yes—
172#2512C2212yes—
173#2512C2212yes—
174#2512C2212yes—
175#2512C2212yes—
176#2512C2212yes—
177#2512C2211yescharacteristic, complemented
178#2512C2211yescharacteristic, complemented
179#2512C2212yescomplemented
180#2511C2211yescharacteristic, complemented
181#2511C2211yescharacteristic, complemented
182#2511C2212yescomplemented
183#2510C2212yes—
184#2510C2212yes—
185#2509C2212yescomplemented
186#2508C2212yescomplemented
187#2507C2212yescomplemented
188#2506C2212yescomplemented
189#2505C2214yes—
190#2504C2212yes—
191#2501C2212yes—
192#2500C2212yes—
193#2500C2212yes—
194#2497C2212yescomplemented
195#2496C2212yescomplemented
196#2495C2212yescomplemented
197#2494C2212yescomplemented
198#2491C2212yes—
199#2491C2212yes—
200#2490C2212yes—
201#2490C2212yes—
202#2481C2212yes—
203#2481C2212yes—
204#2480C2214yes—
205#2480C2214yes—
206#2473C2214yes—
207#2472C2214yes—
208#2472C2214yes—
209#2454C2212yes—
210#2454C2212yes—
211#2454C2212yes—
212#2454C2212yes—
213#2454C2212yescomplemented
214#2453C2212yescomplemented
215#2452C2212yes—
216#2452C2212yes—
217#2452C2212yes—
218#2452C2212yes—
219#2452C2212yescomplemented
220#2451C2212yescomplemented
221#2449C2214yes—
222#2449C2214yes—
223#2448C2212yes—
224#2448C2212yes—
225#2447C2212yes—
226#2447C2212yes—
227#2445C2212yes—
228#2445C2212yes—
229#2445C2212yes—
230#2445C2212yes—
231#2442C2212yes—
232#2442C2212yes—
233#2442C2212yescomplemented
234#2441C2212yescomplemented
235#2441C2212yescomplemented
236#2441C2212yescomplemented
237#2440C2214yes—
238#2440C2214yes—
239#2440C2212yescomplemented
240#2440C2212yescomplemented
241#2440C2212yescomplemented
242#2439C2212yescomplemented
243#2437C2214yes—
244#2437C2214yes—
245#2437C2214yes—
246#2437C2214yes—
247#2422C2212yes—
248#2422C2212yes—
249#2420C2212yes—
250#2420C2212yes—
251#2418C2214yes—
252#2418C2214yes—
253#2417C2214yes—
254#2412C2214yes—
255#2412C2214yes—
256#2402C2212yescomplemented
257#2402C2212yescomplemented
258#2401C2212yescomplemented
259#2401C2212yescomplemented
260C2×#397C2212yes—
261C2×#396C2212yes—
262#2383C2214yescomplemented
263#2383C2214yescomplemented
264#2376C2214yescomplemented
265#2317C2211yescharacteristic
266#2317C2211yescharacteristic
267#2317C2211yescharacteristic
268#2317C2211yescharacteristic
269#2316C2211yescharacteristic
270#2316C2211yescharacteristic
271#2311C2211yescharacteristic
272#2311C2211yescharacteristic
273#2309C2211yescharacteristic
274#2309C2211yescharacteristic
275C4×#125C2212yescomplemented
276C4×#125C2212yescomplemented
277C4×#126C2212yescomplemented
278C4×#126C2212yescomplemented
279#2297C2211yescharacteristic
280#2297C2211yescharacteristic
281#2297C2211yescharacteristic
282#2296C2211yescharacteristic
283#2296C2211yescharacteristic
284#2296C2211yescharacteristic
285C2×#390C2211yescharacteristic
286C2×#390C2211yescharacteristic
287C2×#390C2211yescharacteristic
288C2×#389C2211yescharacteristic
289C2×#388C2212yes—
290#2285C2211yescharacteristic
291#2285C2211yescharacteristic
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic
294C2×#384C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×D4C2311yescharacteristic
301#563—416no—
302#544—44no—
303#544—44no—
304#544—44no—
305#535—44no—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2314yes—
309C2×C4⋊Q8C2314yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2314yes—
315C2×#127C2312yes—
316C2×#126—48no—
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#126C2312yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#126C2314yes—
325C2×#126C2314yes—
326C2×#125C2312yes—
327C2×#125C2312yes—
328C2×#125C2314yes—
329C2×#125C2312yes—
330C2×#125C2312yes—
331C2×#125C2312yes—
332C2×#125C2312yes—
333C2×#125C2312yes—
334C2×#125C2312yes—
335C2×#124C2314yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#120C2314yes—
355#520—44no—
356#518—44no—
357C2×C4×Q8C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×#117C2311yescharacteristic
365C2×#117C2311yescharacteristic
366C2×#117C2311yescharacteristic
367C2×#117C2311yescharacteristic
368C2×#117C2311yescharacteristic
369C2×#117C2311yescharacteristic
370C2×#117C2311yescharacteristic
371C2×#117C2312yes—
372C22×C4⋊C4C2311yescharacteristic
373C22×C4⋊C4C2311yescharacteristic
374C22×C4⋊C4C2311yescharacteristic
375C22×C4⋊C4C2311yescharacteristic
376C22×C4⋊C4C2311yescharacteristic
377C22×C4⋊C4C2312yes—
378C22×C4⋊C4C2312yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C22⋊C4C2312yes—
382C22×C22⋊C4C2312yes—
383C22×C22⋊C4C2312yes—
384C22×C22⋊C4C2314yes—
385C22×C22⋊C4C2312yes—
386C22×C22⋊C4C2312yes—
387C22×C22⋊C4C2312yes—
388C22×C42C2311yescharacteristic
389C22×C42C2311yescharacteristic
390C22×C42C2311yescharacteristic
391C22×C42C2312yes—
392#401C2314yes—
393#401C2312yes—
394#401C2312yes—
395#400C2312yes—
396#400C2312yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2312yes—
401#400C2312yes—
402#400C2314yes—
403#400C2314yes—
404#400C2312yes—
405#400C2312yes—
406#400C2312yes—
407#400C2312yes—
408#400C2312yes—
409#400C2312yes—
410#400C2314yes—
411#400C2314yes—
412#400C2312yes—
413#400C2312yes—
414#400C2314yes—
415#400C2312yes—
416#400C2312yes—
417#399C2314yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2314yes—
424#399C2314yes—
425#399C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#398C2312yes—
432#398C2312yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2312yes—
438#398C2312yes—
439#398C2312yes—
440#398C2312yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2312yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2312yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2312yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2312yes—
476#397C2312yes—
477#396C2312yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2312yes—
492#396C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#395C2314yes—
499#395C2314yes—
500#395C2314yes—
501#395C2314yes—
502#395C2314yes—
503#395C2314yes—
504#395C2314yes—
505#395C2314yes—
506#395C2314yes—
507#395C2314yes—
508#395C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#393C2314yes—
522#393C2314yes—
523#393C2314yes—
524#393C2314yes—
525#393C2314yes—
526#393C2314yes—
527#393C2314yes—
528#391C2311yescharacteristic
529#391C2312yes—
530#391C2312yes—
531#391C2311yescharacteristic
532#391C2314yes—
533#391C2314yes—
534#391C2314yes—
535#391C2311yescharacteristic
536#391C2311yescharacteristic
537#391C2311yescharacteristic
538#391C2311yescharacteristic
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2311yescharacteristic
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2311yescharacteristic
556#390C2312yes—
557#390C2314yes—
558#390C2312yes—
559#390C2312yes—
560#390C2311yescharacteristic
561#390C2312yes—
562#390C2311yescharacteristic
563#390C2311yescharacteristic
564#390C2311yescharacteristic
565#390C2312yes—
566#390C2312yes—
567#390C2312yes—
568#390C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2314yes—
575#389C2311yescharacteristic
576#389C2311yescharacteristic
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2311yescharacteristic
580#389C2311yescharacteristic
581#389C2311yescharacteristic
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2314yes—
600#389C2314yes—
601#389C2314yes—
602#389C2314yes—
603#389C2314yes—
604#389C2314yes—
605#389C2314yes—
606#389C2311yescharacteristic
607#389C2312yes—
608#389C2314yes—
609#389C2314yes—
610#389C2314yes—
611#389C2311yescharacteristic
612#389C2314yes—
613#389C2312yes—
614#389C2311yescharacteristic
615#389C2311yescharacteristic
616#389C2312yes—
617#389C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
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#387C2312yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
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#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2312yes—
677#386C2314yes—
678#386C2312yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2312yes—
695#385C2312yes—
696#385C2312yes—
697#385C2312yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2312yes—
705#385C2312yes—
706#384C2312yes—
707#384C2311yescharacteristic
708#384C2311yescharacteristic
709#384C2312yes—
710#384C2312yes—
711#384C2312yes—
712#384C2314yes—
713#384C2314yes—
714#384C2311yescharacteristic
715#384C2311yescharacteristic
716#384C2311yescharacteristic
717#384C2311yescharacteristic
718#384C2311yescharacteristic
719#384C2312yes—
720#384C2312yes—
721#384C2312yes—
722#384C2314yes—
723#384C2312yes—
724#384C2311yescharacteristic
725#383C2312yes—
726#383C2312yes—
727#383C2314yes—
728#382C2312yes—
729#382C2312yes—
730#382C2311yescharacteristic
731#382C2311yescharacteristic
732#382C2312yes—
733#382C2312yes—
734#382C2311yescharacteristic
735#382C2311yescharacteristic
736#382C2311yescharacteristic
737#382C2311yescharacteristic
738#382C2311yescharacteristic
739#382C2311yescharacteristic
740#382C2312yes—
741#382C2312yes—
742#382C2314yes—
743#381C2314yes—
744#381C2314yes—
745#380C2314yes—
746#380C2314yes—
747#380C2314yes—
748#380C2314yes—
749#380C2312yes—
750#380C2314yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2314yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2314yes—
764#379C2314yes—
765#379C2314yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810#376C2312yes—
811#376C2312yes—
812C2×#95C2312yes—
813C2×#95C2311yescharacteristic
814C2×#95C2311yescharacteristic
815C2×#95C2312yes—
816C43C2312yes—
817C43C2312yes—
818C25C2412yes—
819C2×#41—24no—
820C2×#41—24no—
821C2×#41—24no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2414yes—
824C22×Q8C2414yes—
825C22×Q8C2414yes—
826C22×D4—24no—
827C22×D4—24no—
828C22×D4—24no—
829C22×D4C2412yes—
830C22×D4C2412yes—
831C22×D4C2412yes—
832C22×D4C2411yescharacteristic
833C22×D4C2414yes—
834C22×D4C2414yes—
835C23×C4C2412yes—
836C23×C4C2411yescharacteristic
837C23×C4C2411yescharacteristic
838C23×C4C2411yescharacteristic
839C23×C4C2411yescharacteristic
840C23×C4C2412yes—
841C23×C4C2412yes—
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2414yes—
846C23×C4C2414yes—
847C23×C4C2414yes—
848C23×C4C2411yescharacteristic
849C4⋊Q8—44no—
850C4⋊Q8—44no—
851C4⋊Q8—44no—
852C4⋊Q8—44no—
853C4⋊Q8—44no—
854C4⋊Q8—44no—
855C4⋊Q8—48no—
856C4⋊Q8—48no—
857C4⋊Q8—84no—
858#127—44no—
859#126—216no—
860#126—28no—
861#126—48no—
862#126—48no—
863#126—44no—
864#126—48no—
865#126—48no—
866#126—48no—
867#126—48no—
868#125—28no—
869#125—44no—
870#125—44no—
871#125—44no—
872#125—44no—
873#125—44no—
874#125—44no—
875#125—48no—
876#125—44no—
877#124—48no—
878#124—44no—
879#124—84no—
880#123—48no—
881#123—48no—
882#123—48no—
883#123—84no—
884C22⋊Q8—48no—
885C22⋊Q8—48no—
886C22⋊Q8—48no—
887C22⋊Q8—48no—
888C22⋊Q8—48no—
889C22⋊Q8—48no—
890C22⋊Q8—48no—
891C22⋊Q8—84no—
892C22⋊Q8—84no—
893C22⋊Q8—84no—
894#121—44no—
895#121—44no—
896#120—48no—
897C4×Q8—44no—
898C4×D4—44no—
899C4×D4—44no—
900C4×D4—44no—
901C4×D4—44no—
902C4×D4—44no—
903C4×D4—48no—
904#117—24no—
905#117—24no—
906#117—24no—
907#117—24no—
908#117—24no—
909#117—24no—
910#117—24no—
911#117—44no—
912C2×C4⋊C4—24no—
913C2×C4⋊C4—24no—
914C2×C4⋊C4—24no—
915C2×C4⋊C4—24no—
916C2×C4⋊C4—42no—
917C2×C4⋊C4—44no—
918C2×C4⋊C4—44no—
919C2×C4⋊C4—44no—
920C2×C4⋊C4—82no—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2411yescharacteristic
929C2×C4⋊C4C2411yescharacteristic
930C2×C4⋊C4C2411yescharacteristic
931C2×C4⋊C4C2411yescharacteristic
932C2×C4⋊C4C2411yescharacteristic
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2411yescharacteristic
936C2×C4⋊C4C2411yescharacteristic
937C2×C4⋊C4C2411yescharacteristic
938C2×C4⋊C4C2411yescharacteristic
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2411yescharacteristic
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2411yescharacteristic
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C22⋊C4—44no—
1006C2×C22⋊C4—44no—
1007C2×C22⋊C4—44no—
1008C2×C22⋊C4—44no—
1009C2×C22⋊C4—48no—
1010C2×C22⋊C4—82no—
1011C2×C22⋊C4—82no—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C42—24no—
1061C2×C42—24no—
1062C2×C42—24no—
1063C2×C42—44no—
1064C2×C42C2412yes—
1065C2×C42C2412yes—
1066C2×C42C2412yes—
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2414yes—
1074C2×C42C2412yes—
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2414yes—
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2414yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094#95C2411yescharacteristic
1095#95C2411yescharacteristic
1096#95C2411yescharacteristic
1097#95C2411yescharacteristic
1098#95C2411yescharacteristic
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2414yes—
1102#95C2414yes—
1103#95C2411yescharacteristic
1104#95C2414yes—
1105#95C2414yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170C24—24no—
1171C24—24no—
1172C24—24no—
1173C24—42no—
1174C24—42no—
1175C24—42no—
1176C24—42no—
1177C24C2514yes—
1178C24C2512yes—
1179C24C2511yescharacteristic
1180#41—416no—
1181C2×Q8—22no—
1182C2×Q8—22no—
1183C2×Q8—22no—
1184C2×Q8—44no—
1185C2×Q8—44no—
1186C2×Q8—44no—
1187C2×Q8—44no—
1188C2×Q8—44no—
1189C2×Q8—44no—
1190C2×Q8—44no—
1191C2×Q8—44no—
1192C2×Q8—44no—
1193C2×D4—24no—
1194C2×D4—24no—
1195C2×D4—24no—
1196C2×D4—24no—
1197C2×D4—24no—
1198C2×D4—22no—
1199C2×D4—24no—
1200C2×D4—24no—
1201C2×D4—24no—
1202C2×D4—24no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—44no—
1206C2×D4—44no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—44no—
1210C2×D4—44no—
1211C2×D4—416no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—24no—
1217C22×C4—24no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—24no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—24no—
1225C22×C4—24no—
1226C22×C4—24no—
1227C22×C4—22no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—42no—
1233C22×C4—42no—
1234C22×C4—42no—
1235C22×C4—42no—
1236C22×C4—41no—
1237C22×C4—41no—
1238C22×C4—42no—
1239C22×C4—42no—
1240C22×C4—41no—
1241C22×C4—41no—
1242C22×C4—44no—
1243C22×C4—44no—
1244C22×C4—44no—
1245C22×C4—44no—
1246C22×C4—44no—
1247C22×C4—44no—
1248C22×C4—44no—
1249C22×C4—44no—
1250C22×C4—44no—
1251C22×C4H(5,𝔽2)14yes—
1252C22×C42−1+414yes—
1253C22×C42−1+414yes—
1254C22×C4C2512yes—
1255C22×C4C2511yescharacteristic
1256C22×C4C2511yescharacteristic
1257C22×C4C2511yescharacteristic
1258C22×C4C2512yes—
1259C22×C4C2511yescharacteristic
1260C22×C4C2511yescharacteristic
1261C22×C4C2511yescharacteristic
1262C22×C4C2511yescharacteristic
1263C22×C4C2512yes—
1264C22×C4C2512yes—
1265C22×C4C2512yes—
1266C22×C4C2514yes—
1267C22×C4C2511yescharacteristic
1268C22×C4C2512yes—
1269C22×C4C2512yes—
1270C22×C4C2512yes—
1271C22×C4C2512yes—
1272C22×C4C2512yes—
1273C22×C4C2512yes—
1274C22×C4C2512yes—
1275C22×C4C2512yes—
1276C22×C4C2512yes—
1277C22×C4C2512yes—
1278C22×C4C2514yes—
1279C22×C4C2514yes—
1280C22×C4C2511yescharacteristic
1281C22×C4C2511yescharacteristic
1282C22×C4C2511yescharacteristic
1283C22×C4C2511yescharacteristic
1284C22×C4C2511yescharacteristic
1285C22×C4C2511yescharacteristic
1286C4⋊C4—24no—
1287C4⋊C4—24no—
1288C4⋊C4—24no—
1289C4⋊C4—24no—
1290C4⋊C4—22no—
1291C4⋊C4—22no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—28no—
1295C4⋊C4—28no—
1296C4⋊C4—22no—
1297C4⋊C4—22no—
1298C4⋊C4—22no—
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—22no—
1302C4⋊C4—22no—
1303C4⋊C4—22no—
1304C4⋊C4—22no—
1305C4⋊C4—24no—
1306C4⋊C4—24no—
1307C4⋊C4—24no—
1308C4⋊C4—24no—
1309C4⋊C4—24no—
1310C4⋊C4—24no—
1311C4⋊C4—24no—
1312C4⋊C4—24no—
1313C4⋊C4—24no—
1314C4⋊C4—22no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—22no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—41no—
1323C4⋊C4—41no—
1324C4⋊C4—44no—
1325C4⋊C4—44no—
1326C4⋊C4—44no—
1327C4⋊C4—44no—
1328C4⋊C4—44no—
1329C4⋊C4—42no—
1330C4⋊C4—42no—
1331C4⋊C4—42no—
1332C4⋊C4—42no—
1333C4⋊C4—42no—
1334C4⋊C4—42no—
1335C4⋊C4—42no—
1336C4⋊C4—44no—
1337C4⋊C4—44no—
1338C4⋊C4—44no—
1339C4⋊C4—44no—
1340C4⋊C4—44no—
1341C4⋊C4—44no—
1342C4⋊C4—44no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—44no—
1347C4⋊C4—44no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—44no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—44no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—42no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4H(5,𝔽2)14yes—
1370C22⋊C4—24no—
1371C22⋊C4—24no—
1372C22⋊C4—24no—
1373C22⋊C4—24no—
1374C22⋊C4—24no—
1375C22⋊C4—24no—
1376C22⋊C4—24no—
1377C22⋊C4—28no—
1378C22⋊C4—28no—
1379C22⋊C4—28no—
1380C22⋊C4—24no—
1381C22⋊C4—24no—
1382C22⋊C4—24no—
1383C22⋊C4—28no—
1384C22⋊C4—24no—
1385C22⋊C4—44no—
1386C22⋊C4—44no—
1387C22⋊C4—44no—
1388C22⋊C4—44no—
1389C22⋊C4—44no—
1390C22⋊C4—44no—
1391C22⋊C4—44no—
1392C22⋊C4—44no—
1393C22⋊C4—44no—
1394C22⋊C4—44no—
1395C22⋊C4—44no—
1396C22⋊C4—44no—
1397C22⋊C4—42no—
1398C22⋊C4—42no—
1399C22⋊C4—42no—
1400C22⋊C4—44no—
1401C22⋊C4—44no—
1402C22⋊C4—44no—
1403C22⋊C4—44no—
1404C22⋊C4—44no—
1405C22⋊C4—44no—
1406C22⋊C4—44no—
1407C22⋊C4—42no—
1408C22⋊C4—44no—
1409C22⋊C4—44no—
1410C22⋊C4—44no—
1411C22⋊C4—44no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C42—28no—
1419C42—24no—
1420C42—24no—
1421C42—24no—
1422C42—24no—
1423C42—24no—
1424C42—24no—
1425C42—24no—
1426C42—22no—
1427C42—22no—
1428C42—22no—
1429C42—22no—
1430C42—22no—
1431C42—22no—
1432C42—22no—
1433C42—22no—
1434C42—22no—
1435C42—22no—
1436C42—22no—
1437C42—22no—
1438C42—24no—
1439C42—24no—
1440C42—24no—
1441C42—44no—
1442C42—42no—
1443C42—42no—
1444C42—44no—
1445C42—42no—
1446C42—42no—
1447C42—42no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—24no—
1453C23—22no—
1454C23—24no—
1455C23—22no—
1456C23—22no—
1457C23—22no—
1458C23—24no—
1459C23—24no—
1460C23—22no—
1461C23—24no—
1462C23—24no—
1463C23—22no—
1464C23—22no—
1465C23—24no—
1466C23—48no—
1467C23—84no—
1468C23—84no—
1469C23—84no—
1470C23—84no—
1471C23—84no—
1472C23—84no—
1473C23C2×H(5,𝔽2)12yes—
1474C23C2×2−1+412yes—
1475C23C2×2−1+412yes—
1476C23C2611yescharacteristic
1477Q8—44no—
1478Q8—164no—
1479Q8—164no—
1480Q8—164no—
1481D4—48no—
1482D4—48no—
1483D4—48no—
1484D4—44no—
1485D4—164no—
1486D4—164no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—22no—
1496C2×C4—24no—
1497C2×C4—24no—
1498C2×C4—22no—
1499C2×C4—22no—
1500C2×C4—22no—
1501C2×C4—22no—
1502C2×C4—22no—
1503C2×C4—22no—
1504C2×C4—22no—
1505C2×C4—22no—
1506C2×C4—22no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—22no—
1510C2×C4—22no—
1511C2×C4—21no—
1512C2×C4—22no—
1513C2×C4—24no—
1514C2×C4—24no—
1515C2×C4—22no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—24no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—24no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—24no—
1541C2×C4—22no—
1542C2×C4—21no—
1543C2×C4—22no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—22no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—24no—
1557C2×C4—21no—
1558C2×C4—24no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—44no—
1574C2×C4—44no—
1575C2×C4—44no—
1576C2×C4—44no—
1577C2×C4—48no—
1578C2×C4—84no—
1579C2×C4—82no—
1580C2×C4—84no—
1581C2×C4—84no—
1582C2×C4—82no—
1583C2×C4—164no—
1584C2×C4—164no—
1585C2×C4—164no—
1586C2×C4#563116yescomplemented
1587C2×C4C2×H(5,𝔽2)12yes—
1588C2×C4C2×H(5,𝔽2)12yes—
1589C2×C4C2×H(5,𝔽2)12yes—
1590C2×C4C2×H(5,𝔽2)12yes—
1591C2×C4C2×H(5,𝔽2)12yes—
1592C2×C4C2×2−1+412yes—
1593C2×C4C2×2−1+412yes—
1594C2×C4C2×2−1+412yes—
1595C2×C4C2×2−1+412yes—
1596C2×C4#58512yes—
1597C22—22no—
1598C22—22no—
1599C22—22no—
1600C22—22no—
1601C22—22no—
1602C22—22no—
1603C22—42no—
1604C22—44no—
1605C22—42no—
1606C22—44no—
1607C22—42no—
1608C22—44no—
1609C22—42no—
1610C22—44no—
1611C22—44no—
1612C22—42no—
1613C22—42no—
1614C22—44no—
1615C22—42no—
1616C22—44no—
1617C22—168no—
1618C22C2×#56314yes—
1619C22C22×H(5,𝔽2)11yescharacteristic
1620C22C22×H(5,𝔽2)11yescharacteristic
1621C22C22×2−1+411yescharacteristic
1622C22C22×2−1+411yescharacteristic
1623C22C2×#58511yescharacteristic
1624C22H(7,𝔽2)11yescharacteristic
1625C222−1+611yescharacteristic
1626C4—22no—
1627C4—22no—
1628C4—22no—
1629C4—22no—
1630C4—42no—
1631C4—41no—
1632C4—44no—
1633C4—42no—
1634C4—41no—
1635C4—41no—
1636C4—42no—
1637C4—41no—
1638C4—41no—
1639C4—44no—
1640C4—44no—
1641C4—42no—
1642C4—42no—
1643C4—42no—
1644C4—42no—
1645C4—42no—
1646C4—42no—
1647C4—42no—
1648C4—42no—
1649C4—42no—
1650C4—42no—
1651C4—42no—
1652C4—42no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4C2×#56314yes—
1657C4C2×#56314yes—
1658C2—24no—
1659C2—82no—
1660C2—84no—
1661C2C22×#56311yescharacteristic
1662C2#6283511yescharacteristic
1663C2#6287911yescharacteristic
1664C2#6291511yescharacteristic
1665C2#6291611yescharacteristic
1666C2#6293111yescharacteristic
1667C2#6295811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53132C2semidirect
2. #53118C2semidirect
3. #53089C2semidirect
4. #53083C2semidirect
5. #53039C2semidirect
6. #53035C2semidirect
7. #53001C2semidirect
8. #52997C2semidirect
9. #52473C2semidirect
10. #52470C2semidirect
11. #46124C2semidirect
12. #46113C2semidirect
13. #46082C2semidirect
14. #46078C2semidirect
15. #46068C2semidirect
16. #46056C2semidirect
17. #46019C2semidirect
18. #45998C2semidirect
19. #45993C2semidirect
20. #45971C2semidirect
21. #35575C2semidirect
23. #35532C2semidirect
25. #35529C2semidirect
26. #35529C2semidirect
27. #35275C2semidirect
28. #35266C2semidirect
29. #35265C2semidirect
31. #35167C2semidirect
32. #35160C2semidirect
33. #34948C2semidirect
34. #34816C2semidirect
35. C2×#2512C2semidirect
36. C2×#563C22semidirect
44. #2868C22semidirect
45. #2864C22semidirect
49. #2859C22semidirect
50. #2859C22semidirect
54. #2841C22semidirect
55. #2838C22semidirect
56. #2838C22semidirect
57. #2838C22semidirect
58. #2838C22semidirect
59. #2837C22semidirect
60. #2837C22semidirect
61. #2836C22semidirect
62. #2831C22semidirect
63. #2830C22semidirect
64. #2827C22semidirect
65. #2827C22semidirect
66. #2827C22semidirect
67. #2823C22semidirect
68. #2823C22semidirect
69. #2821C22semidirect
70. #2821C22semidirect
71. #2820C22semidirect
72. #2817C22semidirect
73. #2814C22semidirect
74. #2793C22semidirect
75. #2793C22semidirect
76. #2787C22semidirect
77. #2777C22semidirect
78. #2775C22semidirect
79. #2770C22semidirect
80. #2765C22semidirect
81. #2765C22semidirect
82. #2745C22semidirect
83. #2738C22semidirect
84. #2731C22semidirect
85. #2729C22semidirect
86. #2728C22semidirect
87. #2727C22semidirect
88. #2725C22semidirect
89. #2725C22semidirect
90. #2723C22semidirect
91. #2723C22semidirect
92. #2723C22semidirect
93. #2722C22semidirect
94. #2721C22semidirect
95. #2720C22semidirect
96. #2718C22semidirect
97. #2718C22semidirect
98. #2718C22semidirect
99. #2717C22semidirect
100. #2716C22semidirect
101. #2715C22semidirect
102. #2707C22semidirect
103. #2702C22semidirect
104. #2698C22semidirect
105. #2695C22semidirect
106. #2695C22semidirect
107. #2689C22semidirect
108. #2683C22semidirect
109. #2680C22semidirect
110. #2677C22semidirect
111. #2674C22semidirect
112. #2674C22semidirect
113. #2674C22semidirect
114. #2660C22semidirect
115. #2660C22semidirect
117. #2647C22semidirect
118. #2647C22semidirect
124. #2571C22semidirect
125. #2571C22semidirect
126. #2570C22semidirect
127. #2570C22semidirect
128. #2570C22semidirect
129. #2570C22semidirect
132. #2567C22semidirect
137. #2566C22semidirect
138. #2565C22semidirect
142. #2552C22semidirect
143. #2552C22semidirect
144. #2552C22semidirect
145. #2552C22semidirect
146. #2552C22semidirect
147. #2552C22semidirect
148. #2551C22semidirect
149. #2551C22semidirect
150. #2551C22semidirect
151. #2551C22semidirect
152. #2550C22semidirect
153. #2550C22semidirect
154. #2550C22semidirect
155. #2550C22semidirect
158. #2542C22semidirect
159. #2514C22semidirect
160. #2514C22semidirect
161. #2514C22semidirect
164. #2513C22semidirect
165. #2513C22semidirect
166. #2513C22semidirect
177. #2512C22semidirect
178. #2512C22semidirect
179. #2512C22semidirect
180. #2511C22semidirect
181. #2511C22semidirect
182. #2511C22semidirect
185. #2509C22semidirect
186. #2508C22semidirect
187. #2507C22semidirect
188. #2506C22semidirect
194. #2497C22semidirect
195. #2496C22semidirect
196. #2495C22semidirect
197. #2494C22semidirect
213. #2454C22semidirect
214. #2453C22semidirect
219. #2452C22semidirect
220. #2451C22semidirect
233. #2442C22semidirect
234. #2441C22semidirect
235. #2441C22semidirect
236. #2441C22semidirect
239. #2440C22semidirect
240. #2440C22semidirect
241. #2440C22semidirect
242. #2439C22semidirect
256. #2402C22semidirect
257. #2402C22semidirect
258. #2401C22semidirect
259. #2401C22semidirect
262. #2383C22semidirect
263. #2383C22semidirect
264. #2376C22semidirect
275. C4×#125C22semidirect
276. C4×#125C22semidirect
277. C4×#126C22semidirect
278. C4×#126C22semidirect
1586. C2×C4#563semidirect

Maximal subgroups

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

subgroupindex
#531322
#531182
#530892
#530832
#530392
#530352
#530012
#529972
#524732
#524702
#461242
#461132
#460822
#460782
#460682
#460562
#460192
#459982
#459932
#459712
#355752
#355412
#355322
#355312
#355292
#352752
#352662
#352652
#352642
#351672
#351602
#349482
#348162
C2×#25122