Finite Group Databasebeta

← #8094422

Subgroups — #8094422

Order 512.

5678 conjugacy classes of subgroups.

The subgroup lattice has 1891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53151C212yesmaximal, complemented
2#53128C212yesmaximal, complemented
3#53090C212yesmaximal, complemented
4#53087C212yesmaximal, complemented
5#53060C212yesmaximal, complemented
6#53041C212yesmaximal, complemented
7#53004C212yesmaximal, complemented
8#52962C212yesmaximal, complemented
9#52369C214yesmaximal, complemented
10#52369C214yesmaximal, complemented
11#46050C212yesmaximal, complemented
12#46050C212yesmaximal, complemented
13#46048C212yesmaximal, complemented
14#46048C212yesmaximal, complemented
15#45743C214yesmaximal, complemented
16#45687C212yesmaximal, complemented
17#45663C212yesmaximal, complemented
18#45608C212yesmaximal, complemented
19#45518C212yesmaximal, complemented
20#45473C214yesmaximal, complemented
21#35676C211yesmaximal, characteristic, complemented
22#35660C211yesmaximal, characteristic, complemented
23#35660C211yesmaximal, characteristic, complemented
24#35619C211yesmaximal, characteristic, complemented
25#35564C211yesmaximal, characteristic, complemented
26#35533C211yesmaximal, characteristic, complemented
27#35329C211yesmaximal, characteristic, complemented
28#35307C211yesmaximal, characteristic, complemented
29#35267C211yesmaximal, characteristic, complemented
30#35256C211yesmaximal, characteristic, complemented
31#35168C211yesmaximal, characteristic, complemented
32#35165C211yesmaximal, characteristic, complemented
33#34937C211yesmaximal, characteristic, complemented
34#34816C211yesmaximal, characteristic, complemented
35C2×#2447C211yesmaximal, characteristic, complemented
36C22×2−1+4C2211yescharacteristic
37C2×#537C2211yescharacteristic
38C2×#537C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2211yescharacteristic
41C2×#535C2211yescharacteristic
42C2×#535C2211yescharacteristic
43C2×#535C2211yescharacteristic
44C2×#535C2211yescharacteristic
45C2×#532C2211yescharacteristic
46C2×#532C2211yescharacteristic
47C2×#532C2211yescharacteristic
48C22×#124C2211yescharacteristic
49C2×#520C2211yescharacteristic
50C2×C4×#41C2211yescharacteristic
51C22×C4×D4C2211yescharacteristic
52#2863C2212yescomplemented
53#2860C2212yescomplemented
54#2858C2212yes—
55#2858C2212yes—
56#2856C2212yes—
57#2855C2212yescomplemented
58#2855C2212yescomplemented
59#2850C2212yes—
60#2847C2214yes—
61#2847C2214yes—
62#2841C2214yescomplemented
63#2838C2214yescomplemented
64#2838C2214yescomplemented
65#2830C2214yescomplemented
66#2830C2214yescomplemented
67#2829C2214yescomplemented
68#2829C2214yescomplemented
69#2828C2214yescomplemented
70#2828C2214yescomplemented
71#2827C2214yescomplemented
72#2827C2214yescomplemented
73#2826C2214yescomplemented
74#2825C2214yescomplemented
75#2825C2214yescomplemented
76#2824C2214yescomplemented
77#2824C2214yescomplemented
78#2824C2214yescomplemented
79#2815C2214yescomplemented
80#2815C2214yescomplemented
81#2815C2214yescomplemented
82#2797C2214yescomplemented
83#2797C2214yescomplemented
84#2797C2214yescomplemented
85#2797C2214yescomplemented
86#2796C2214yescomplemented
87#2796C2214yescomplemented
88#2784C2214yescomplemented
89#2784C2214yescomplemented
90#2780C2214yescomplemented
91#2780C2214yescomplemented
92#2760C2214yescomplemented
93#2752C2214yescomplemented
94#2749C2214yescomplemented
95#2749C2214yescomplemented
96#2749C2214yescomplemented
97#2749C2214yescomplemented
98#2746C2214yescomplemented
99#2746C2214yescomplemented
100#2742C2214yescomplemented
101#2737C2214yescomplemented
102#2737C2214yescomplemented
103#2737C2214yescomplemented
104#2737C2214yescomplemented
105#2714C2214yescomplemented
106#2714C2214yescomplemented
107#2714C2214yescomplemented
108#2714C2214yescomplemented
109#2699C2214yescomplemented
110#2699C2214yescomplemented
111#2691C2214yescomplemented
112#2691C2214yescomplemented
113#2691C2214yescomplemented
114#2691C2214yescomplemented
115#2688C2214yescomplemented
116#2688C2214yescomplemented
117#2688C2214yescomplemented
118#2688C2214yescomplemented
119#2688C2214yescomplemented
120#2688C2214yescomplemented
121#2675C2214yescomplemented
122#2658C2212yes—
123#2657C2212yes—
124#2645C2212yescomplemented
125#2644C2212yescomplemented
126#2625C2212yescomplemented
127#2625C2212yescomplemented
128#2620C2212yes—
129#2619C2212yes—
130#2617C2214yes—
131#2617C2214yes—
132#2548C2212yes—
133#2548C2211yescharacteristic, complemented
134#2547C2212yes—
135#2547C2211yescharacteristic, complemented
136#2546C2211yescharacteristic, complemented
137#2545C2212yes—
138#2545C2211yescharacteristic, complemented
139#2545C2211yescharacteristic, complemented
140#2544C2212yes—
141#2544C2212yes—
142#2544C2212yes—
143#2544C2211yescharacteristic, complemented
144#2544C2211yescharacteristic, complemented
145#2543C2212yes—
146#2543C2212yes—
147#2543C2214yes—
148#2541C2212yes—
149#2541C2212yes—
150#2541C2211yescharacteristic, complemented
151#2540C2212yes—
152#2540C2212yes—
153#2540C2212yes—
154#2540C2212yes—
155#2539C2214yes—
156#2539C2214yes—
157#2537C2212yes—
158#2537C2212yes—
159#2535C2212yes—
160#2535C2212yes—
161#2514C2211yescharacteristic, complemented
162#2514C2211yescharacteristic, complemented
163#2513C2211yescharacteristic, complemented
164#2513C2211yescharacteristic, complemented
165#2512C2211yescharacteristic, complemented
166#2512C2211yescharacteristic, complemented
167#2511C2211yescharacteristic, complemented
168#2511C2211yescharacteristic, complemented
169#2510C2212yes—
170#2510C2212yes—
171#2510C2214yes—
172#2503C2212yescomplemented
173#2502C2212yescomplemented
174#2499C2212yescomplemented
175#2499C2212yescomplemented
176#2497C2212yescomplemented
177#2496C2212yescomplemented
178#2495C2212yescomplemented
179#2494C2212yescomplemented
180#2481C2212yes—
181#2481C2212yes—
182#2481C2214yes—
183#2447C2212yes—
184#2447C2212yes—
185#2447C2212yes—
186#2447C2212yes—
187#2447C2212yes—
188#2447C2212yes—
189#2447C2212yes—
190#2447C2212yes—
191#2447C2212yescomplemented
192#2447C2212yescomplemented
193#2447C2212yescomplemented
194#2447C2212yescomplemented
195#2446C2212yescomplemented
196#2446C2212yescomplemented
197#2446C2212yescomplemented
198#2446C2212yescomplemented
199#2436C2212yes—
200#2436C2212yes—
201#2436C2212yes—
202#2436C2212yes—
203#2436C2212yescomplemented
204#2436C2212yescomplemented
205#2434C2212yescomplemented
206#2434C2212yescomplemented
207#2432C2212yescomplemented
208#2432C2212yescomplemented
209#2431C2212yes—
210#2431C2212yes—
211#2431C2212yes—
212#2431C2212yes—
213#2431C2212yescomplemented
214#2431C2212yescomplemented
215#2430C2214yes—
216#2430C2214yes—
217#2430C2214yes—
218#2430C2214yes—
219#2429C2212yescomplemented
220#2428C2212yes—
221#2428C2212yes—
222#2428C2212yes—
223#2428C2212yes—
224#2428C2212yes—
225#2428C2212yes—
226#2428C2212yescomplemented
227#2427C2212yes—
228#2427C2212yes—
229#2427C2212yes—
230#2427C2212yes—
231#2427C2212yescomplemented
232#2426C2212yes—
233#2426C2212yes—
234#2426C2212yescomplemented
235#2424C2214yes—
236#2424C2214yes—
237#2424C2214yes—
238#2424C2214yes—
239#2419C2214yes—
240#2419C2214yes—
241#2419C2214yes—
242#2419C2214yes—
243#2417C2212yescomplemented
244#2416C2212yes—
245#2416C2212yes—
246#2416C2212yes—
247#2416C2212yes—
248#2416C2214yes—
249#2416C2212yescomplemented
250#2415C2212yescomplemented
251#2414C2212yes—
252#2414C2212yes—
253#2414C2212yescomplemented
254#2409C2212yescomplemented
255#2409C2212yescomplemented
256#2409C2212yescomplemented
257#2409C2212yescomplemented
258#2407C2212yescomplemented
259#2407C2212yescomplemented
260#2407C2212yescomplemented
261#2407C2212yescomplemented
262#2404C2214yes—
263#2404C2214yes—
264#2401C2212yescomplemented
265#2401C2212yescomplemented
266#2392C2212yescomplemented
267#2392C2212yescomplemented
268C2×#397C2212yes—
269C2×#397C2212yes—
270#2377C2214yescomplemented
271#2377C2214yescomplemented
272#2377C2214yescomplemented
273#2377C2214yescomplemented
274#2317C2211yescharacteristic
275#2316C2211yescharacteristic
276#2311C2211yescharacteristic
277#2311C2211yescharacteristic
278#2311C2211yescharacteristic
279#2310C2211yescharacteristic
280C4×#126C2212yescomplemented
281C4×#126C2212yescomplemented
282C4×#121C2212yescomplemented
283C4×#121C2212yescomplemented
284#2297C2211yescharacteristic
285#2297C2211yescharacteristic
286#2297C2211yescharacteristic
287#2297C2211yescharacteristic
288#2297C2211yescharacteristic
289#2296C2211yescharacteristic
290C2×#391C2211yescharacteristic
291C2×#391C2211yescharacteristic
292C2×#390C2211yescharacteristic
293C2×#389C2211yescharacteristic
294C2×#385C2212yes—
295#2285C2211yescharacteristic
296C2×#381C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C2×2−1+4—44no—
300C2×2−1+4—44no—
301C2×2−1+4—44no—
302C22×#41C2311yescharacteristic
303C22×#41C2311yescharacteristic
304C22×#41C2311yescharacteristic
305C22×#41C2311yescharacteristic
306C22×#41C2314yes—
307C22×#41C2312yes—
308C22×#41C2312yes—
309C23×Q8C2311yescharacteristic
310C23×Q8C2312yes—
311C23×Q8C2312yes—
312C23×D4C2311yescharacteristic
313C24×C4C2312yes—
314#537—44no—
315#537—44no—
316#536—44no—
317#536—44no—
318#535—44no—
319#535—44no—
320#535—44no—
321#535—44no—
322#532—44no—
323#532—44no—
324#532—44no—
325C2×C4⋊Q8C2312yes—
326C2×C4⋊Q8C2312yes—
327C2×C4⋊Q8C2311yescharacteristic
328C2×C4⋊Q8C2311yescharacteristic
329C2×C4⋊Q8C2311yescharacteristic
330C2×#127C2312yes—
331C2×#127C2312yes—
332C2×#127C2312yes—
333C2×#127C2311yescharacteristic
334C2×#127C2311yescharacteristic
335C2×#127C2311yescharacteristic
336C2×#127C2312yes—
337C2×#126C2312yes—
338C2×#126C2312yes—
339C2×#126C2314yes—
340C2×#124—44no—
341C2×#124C2312yes—
342C2×#124C2312yes—
343C2×#124C2311yescharacteristic
344C2×#124C2311yescharacteristic
345C2×#124C2312yes—
346C2×#124C2312yes—
347C2×#124C2312yes—
348C2×#124C2312yes—
349C2×#124C2312yes—
350C2×#124C2312yes—
351C2×#124C2312yes—
352C2×#124C2311yescharacteristic
353C2×#124C2311yescharacteristic
354C2×#124C2311yescharacteristic
355C2×#124C2311yescharacteristic
356C2×#124C2312yes—
357C2×#123C2314yes—
358C2×#123C2314yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2312yes—
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2312yes—
364C2×C22⋊Q8C2312yes—
365C2×C22⋊Q8C2312yes—
366C2×C22⋊Q8C2312yes—
367C2×#121C2312yes—
368C2×#121C2314yes—
369C2×#121C2314yes—
370C2×#121C2314yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2312yes—
374C2×#121C2314yes—
375C2×#121C2312yes—
376C2×#121C2314yes—
377C2×#121C2312yes—
378C2×#121C2312yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×#121C2312yes—
383C2×#121C2312yes—
384C2×#121C2312yes—
385C2×#121C2312yes—
386C2×#121C2314yes—
387C2×#121C2312yes—
388C2×#121C2312yes—
389C2×#121C2312yes—
390C2×#121C2312yes—
391C2×#121C2312yes—
392C2×#121C2312yes—
393C2×#121C2314yes—
394C2×#121C2314yes—
395C2×#121C2314yes—
396C2×#121C2314yes—
397C2×#121C2314yes—
398C2×#120C2314yes—
399C2×#120C2314yes—
400C2×#120C2314yes—
401C2×#120C2314yes—
402#520—44no—
403C4×#41—44no—
404C2×C4×Q8C2311yescharacteristic
405C2×C4×Q8C2311yescharacteristic
406C2×C4×Q8C2312yes—
407C2×C4×D4—44no—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2311yescharacteristic
420C2×C4×D4C2311yescharacteristic
421C2×C4×D4C2314yes—
422C2×C4×D4C2312yes—
423C2×C4×D4C2312yes—
424C2×#117C2311yescharacteristic
425C2×#117C2311yescharacteristic
426C2×#117C2311yescharacteristic
427C2×#117C2311yescharacteristic
428C2×#117C2312yes—
429C2×#117C2312yes—
430C22×C4⋊C4C2311yescharacteristic
431C22×C4⋊C4C2311yescharacteristic
432C22×C4⋊C4C2311yescharacteristic
433C22×C4⋊C4C2312yes—
434C22×C4⋊C4C2311yescharacteristic
435C22×C4⋊C4C2312yes—
436C22×C22⋊C4C2312yes—
437C22×C22⋊C4C2312yes—
438C22×C22⋊C4C2312yes—
439C22×C22⋊C4C2312yes—
440C22×C22⋊C4C2312yes—
441C22×C42C2311yescharacteristic
442C22×C42C2311yescharacteristic
443C22×C42C2311yescharacteristic
444C22×C42C2312yes—
445#401C2312yes—
446#401C2314yes—
447#401C2312yes—
448#400C2312yes—
449#400C2312yes—
450#400C2312yes—
451#400C2314yes—
452#400C2314yes—
453#400C2314yes—
454#400C2314yes—
455#400C2314yes—
456#400C2314yes—
457#400C2314yes—
458#400C2312yes—
459#400C2312yes—
460#400C2312yes—
461#399C2314yes—
462#399C2314yes—
463#399C2314yes—
464#399C2314yes—
465#398C2312yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2314yes—
470#398C2312yes—
471#398C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2312yes—
482#397C2314yes—
483#397C2312yes—
484#397C2314yes—
485#397C2314yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2312yes—
490#397C2314yes—
491#397C2312yes—
492#397C2314yes—
493#397C2314yes—
494#397C2314yes—
495#397C2314yes—
496#397C2314yes—
497#397C2314yes—
498#397C2314yes—
499#397C2312yes—
500#397C2312yes—
501#397C2312yes—
502#397C2312yes—
503#397C2314yes—
504#396C2312yes—
505#396C2314yes—
506#396C2312yes—
507#396C2314yes—
508#396C2312yes—
509#396C2314yes—
510#396C2314yes—
511#396C2312yes—
512#396C2314yes—
513#396C2314yes—
514#396C2314yes—
515#396C2312yes—
516#396C2312yes—
517#395C2314yes—
518#395C2314yes—
519#395C2314yes—
520#395C2314yes—
521#394C2312yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2312yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2314yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2312yes—
540#394C2312yes—
541#394C2314yes—
542#394C2314yes—
543#394C2314yes—
544#394C2314yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2312yes—
549#394C2312yes—
550#393C2314yes—
551#393C2314yes—
552#393C2314yes—
553#393C2314yes—
554#393C2314yes—
555#393C2314yes—
556#393C2314yes—
557#393C2314yes—
558#392C2314yes—
559#392C2314yes—
560#392C2314yes—
561#392C2312yes—
562#392C2314yes—
563#392C2314yes—
564#392C2314yes—
565#392C2314yes—
566#392C2314yes—
567#392C2314yes—
568#392C2314yes—
569#392C2314yes—
570#392C2314yes—
571#392C2314yes—
572#392C2314yes—
573#392C2314yes—
574#392C2314yes—
575#392C2314yes—
576#392C2314yes—
577#392C2312yes—
578#392C2314yes—
579#392C2314yes—
580#392C2314yes—
581#391C2312yes—
582#391C2312yes—
583#391C2312yes—
584#391C2312yes—
585#391C2312yes—
586#391C2312yes—
587#391C2312yes—
588#391C2311yescharacteristic
589#391C2312yes—
590#391C2311yescharacteristic
591#391C2311yescharacteristic
592#391C2312yes—
593#391C2311yescharacteristic
594#391C2312yes—
595#391C2312yes—
596#391C2311yescharacteristic
597#391C2311yescharacteristic
598#391C2311yescharacteristic
599#391C2311yescharacteristic
600#391C2311yescharacteristic
601#391C2311yescharacteristic
602#391C2312yes—
603#391C2312yes—
604#391C2312yes—
605#391C2312yes—
606#390C2312yes—
607#390C2312yes—
608#390C2312yes—
609#390C2314yes—
610#390C2314yes—
611#390C2314yes—
612#390C2314yes—
613#390C2314yes—
614#390C2314yes—
615#390C2312yes—
616#390C2311yescharacteristic
617#390C2314yes—
618#390C2314yes—
619#390C2314yes—
620#390C2314yes—
621#390C2314yes—
622#390C2311yescharacteristic
623#390C2311yescharacteristic
624#390C2312yes—
625#390C2312yes—
626#390C2314yes—
627#390C2314yes—
628#390C2311yescharacteristic
629#390C2311yescharacteristic
630#390C2311yescharacteristic
631#390C2311yescharacteristic
632#390C2312yes—
633#390C2311yescharacteristic
634#390C2312yes—
635#390C2312yes—
636#390C2311yescharacteristic
637#390C2311yescharacteristic
638#389C2312yes—
639#389C2312yes—
640#389C2312yes—
641#389C2312yes—
642#389C2312yes—
643#389C2312yes—
644#389C2312yes—
645#389C2314yes—
646#389C2311yescharacteristic
647#389C2311yescharacteristic
648#389C2312yes—
649#389C2311yescharacteristic
650#389C2311yescharacteristic
651#389C2312yes—
652#389C2312yes—
653#389C2312yes—
654#389C2312yes—
655#388C2312yes—
656#388C2312yes—
657#388C2312yes—
658#388C2312yes—
659#388C2312yes—
660#388C2312yes—
661#388C2314yes—
662#388C2314yes—
663#388C2312yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#388C2314yes—
668#388C2314yes—
669#388C2312yes—
670#388C2314yes—
671#388C2314yes—
672#388C2312yes—
673#388C2312yes—
674#387C2312yes—
675#387C2312yes—
676#387C2312yes—
677#387C2312yes—
678#387C2312yes—
679#387C2312yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2312yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2312yes—
711#386C2312yes—
712#386C2314yes—
713#386C2314yes—
714#386C2314yes—
715#386C2314yes—
716#386C2314yes—
717#386C2312yes—
718#386C2312yes—
719#386C2312yes—
720#386C2314yes—
721#386C2314yes—
722#386C2314yes—
723#386C2314yes—
724#386C2314yes—
725#386C2314yes—
726#386C2314yes—
727#386C2314yes—
728#386C2314yes—
729#386C2314yes—
730#386C2312yes—
731#386C2312yes—
732#386C2312yes—
733#386C2312yes—
734#386C2312yes—
735#386C2312yes—
736#386C2312yes—
737#386C2312yes—
738#385C2314yes—
739#385C2314yes—
740#385C2314yes—
741#385C2314yes—
742#385C2314yes—
743#385C2314yes—
744#385C2314yes—
745#385C2314yes—
746#385C2314yes—
747#385C2314yes—
748#385C2314yes—
749#385C2314yes—
750#385C2314yes—
751#385C2314yes—
752#385C2314yes—
753#385C2312yes—
754#385C2312yes—
755#385C2314yes—
756#385C2314yes—
757#384C2312yes—
758#384C2311yescharacteristic
759#384C2311yescharacteristic
760#383C2312yes—
761#383C2312yes—
762#383C2314yes—
763#382C2312yes—
764#382C2311yescharacteristic
765#382C2311yescharacteristic
766#381C2314yes—
767#381C2314yes—
768#381C2314yes—
769#381C2314yes—
770#381C2314yes—
771#381C2314yes—
772#381C2314yes—
773#381C2314yes—
774#381C2314yes—
775#380C2312yes—
776#380C2312yes—
777#380C2312yes—
778#380C2312yes—
779#380C2312yes—
780#380C2312yes—
781#380C2314yes—
782#380C2314yes—
783#380C2314yes—
784#380C2312yes—
785#380C2314yes—
786#380C2314yes—
787#380C2312yes—
788#380C2312yes—
789#380C2314yes—
790#380C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2311yescharacteristic
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2311yescharacteristic
803C4×C4⋊C4C2311yescharacteristic
804C4×C4⋊C4C2311yescharacteristic
805C4×C4⋊C4C2311yescharacteristic
806C4×C4⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2312yes—
818C4×C22⋊C4C2312yes—
819#376C2312yes—
820C2×#95C2312yes—
821C2×#95C2311yescharacteristic
822C2×#95C2312yes—
823C2×#95C2312yes—
824C2×#95C2312yes—
825C2×#95C2312yes—
826C2×#95C2311yescharacteristic
827C43C2312yes—
828C25C2412yes—
8292−1+4—464no—
830C2×#41—24no—
831C2×#41—24no—
832C2×#41—24no—
833C2×#41—24no—
834C2×#41—24no—
835C2×#41—24no—
836C2×#41—24no—
837C2×#41—24no—
838C2×#41—24no—
839C2×#41—24no—
840C2×#41—24no—
841C2×#41—24no—
842C2×#41—48no—
843C2×#41—48no—
844C2×#41—48no—
845C2×#41—44no—
846C2×#41—44no—
847C2×#41—44no—
848C2×#41—44no—
849C2×#41—44no—
850C2×#41—44no—
851C22×Q8—24no—
852C22×Q8—24no—
853C22×Q8—24no—
854C22×Q8—44no—
855C22×Q8—44no—
856C22×Q8—44no—
857C22×Q8—44no—
858C22×Q8—44no—
859C22×Q8—44no—
860C22×Q8C2411yescharacteristic
861C22×Q8C2411yescharacteristic
862C22×Q8C2412yes—
863C22×Q8C2411yescharacteristic
864C22×Q8C2412yes—
865C22×Q8C2411yescharacteristic
866C22×Q8C2414yes—
867C22×D4—24no—
868C22×D4—24no—
869C22×D4—24no—
870C22×D4C2412yes—
871C22×D4C2412yes—
872C22×D4C2412yes—
873C22×D4C2412yes—
874C22×D4C2411yescharacteristic
875C22×D4C2411yescharacteristic
876C22×D4C2412yes—
877C22×D4C2412yes—
878C22×D4C2411yescharacteristic
879C22×D4C2411yescharacteristic
880C22×D4C2412yes—
881C22×D4C2412yes—
882C22×D4C2412yes—
883C22×D4C2412yes—
884C22×D4C2412yes—
885C22×D4C2412yes—
886C22×D4C2414yes—
887C22×D4C2414yes—
888C22×D4C2414yes—
889C22×D4C2414yes—
890C22×D4C2414yes—
891C22×D4C2414yes—
892C22×D4C2414yes—
893C22×D4C2414yes—
894C22×D4C2414yes—
895C22×D4C2414yes—
896C22×D4C2414yes—
897C23×C4—44no—
898C23×C4—44no—
899C23×C4—82no—
900C23×C4C2412yes—
901C23×C4C2412yes—
902C23×C4C2412yes—
903C23×C4C2412yes—
904C23×C4C2412yes—
905C23×C4C2411yescharacteristic
906C23×C4C2411yescharacteristic
907C23×C4C2411yescharacteristic
908C23×C4C2412yes—
909C23×C4C2411yescharacteristic
910C23×C4C2411yescharacteristic
911C23×C4C2411yescharacteristic
912C23×C4C2412yes—
913C23×C4C2412yes—
914C23×C4C2414yes—
915C23×C4C2414yes—
916C23×C4C2412yes—
917C23×C4C2414yes—
918C23×C4C2414yes—
919C23×C4C2414yes—
920C23×C4C2411yescharacteristic
921C4⋊Q8—42no—
922C4⋊Q8—42no—
923C4⋊Q8—42no—
924C4⋊Q8—44no—
925C4⋊Q8—44no—
926#127—42no—
927#127—42no—
928#127—42no—
929#127—44no—
930#127—44no—
931#127—44no—
932#127—44no—
933#126—44no—
934#126—44no—
935#126—84no—
936#124—44no—
937#124—44no—
938#124—44no—
939#124—44no—
940#124—42no—
941#124—42no—
942#124—42no—
943#124—42no—
944#124—42no—
945#124—42no—
946#124—44no—
947#124—44no—
948#124—44no—
949#124—44no—
950#124—44no—
951#124—44no—
952#123—48no—
953#123—48no—
954C22⋊Q8—44no—
955C22⋊Q8—44no—
956C22⋊Q8—44no—
957C22⋊Q8—44no—
958C22⋊Q8—44no—
959C22⋊Q8—44no—
960C22⋊Q8—44no—
961C22⋊Q8—44no—
962#121—48no—
963#121—48no—
964#121—48no—
965#121—44no—
966#121—44no—
967#121—48no—
968#121—44no—
969#121—44no—
970#121—44no—
971#121—44no—
972#121—44no—
973#121—44no—
974#121—44no—
975#121—44no—
976#121—44no—
977#121—44no—
978#121—44no—
979#121—44no—
980#121—44no—
981#121—44no—
982#121—44no—
983#121—44no—
984#121—44no—
985#121—44no—
986#121—48no—
987#121—48no—
988#121—84no—
989#121—84no—
990#121—84no—
991#121—84no—
992#121—84no—
993#120—48no—
994#120—48no—
995#120—48no—
996#120—48no—
997C4×Q8—42no—
998C4×Q8—42no—
999C4×Q8—44no—
1000C4×D4—44no—
1001C4×D4—44no—
1002C4×D4—44no—
1003C4×D4—44no—
1004C4×D4—42no—
1005C4×D4—42no—
1006C4×D4—44no—
1007C4×D4—44no—
1008C4×D4—44no—
1009C4×D4—44no—
1010C4×D4—44no—
1011C4×D4—44no—
1012C4×D4—44no—
1013C4×D4—44no—
1014C4×D4—44no—
1015C4×D4—48no—
1016#117—24no—
1017#117—24no—
1018#117—24no—
1019#117—24no—
1020#117—44no—
1021#117—44no—
1022C2×C4⋊C4—24no—
1023C2×C4⋊C4—24no—
1024C2×C4⋊C4—42no—
1025C2×C4⋊C4—42no—
1026C2×C4⋊C4—44no—
1027C2×C4⋊C4—82no—
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2411yescharacteristic
1034C2×C4⋊C4C2411yescharacteristic
1035C2×C4⋊C4C2411yescharacteristic
1036C2×C4⋊C4C2411yescharacteristic
1037C2×C4⋊C4C2411yescharacteristic
1038C2×C4⋊C4C2411yescharacteristic
1039C2×C4⋊C4C2411yescharacteristic
1040C2×C4⋊C4C2411yescharacteristic
1041C2×C4⋊C4C2411yescharacteristic
1042C2×C4⋊C4C2411yescharacteristic
1043C2×C4⋊C4C2411yescharacteristic
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2411yescharacteristic
1050C2×C4⋊C4C2411yescharacteristic
1051C2×C4⋊C4C2411yescharacteristic
1052C2×C4⋊C4C2411yescharacteristic
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2412yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2414yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2414yes—
1066C2×C4⋊C4C2414yes—
1067C2×C4⋊C4C2414yes—
1068C2×C4⋊C4C2414yes—
1069C2×C4⋊C4C2414yes—
1070C2×C4⋊C4C2414yes—
1071C2×C4⋊C4C2414yes—
1072C2×C4⋊C4C2414yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2412yes—
1075C2×C4⋊C4C2412yes—
1076C2×C4⋊C4C2412yes—
1077C2×C22⋊C4—44no—
1078C2×C22⋊C4—44no—
1079C2×C22⋊C4—44no—
1080C2×C22⋊C4—44no—
1081C2×C22⋊C4—82no—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2412yes—
1127C2×C22⋊C4C2412yes—
1128C2×C22⋊C4C2412yes—
1129C2×C22⋊C4C2412yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2412yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2412yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2414yes—
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2414yes—
1142C2×C22⋊C4C2414yes—
1143C2×C22⋊C4C2412yes—
1144C2×C22⋊C4C2412yes—
1145C2×C22⋊C4C2412yes—
1146C2×C22⋊C4C2412yes—
1147C2×C22⋊C4C2412yes—
1148C2×C22⋊C4C2412yes—
1149C2×C22⋊C4C2412yes—
1150C2×C22⋊C4C2412yes—
1151C2×C22⋊C4C2412yes—
1152C2×C22⋊C4C2412yes—
1153C2×C42—24no—
1154C2×C42—24no—
1155C2×C42—24no—
1156C2×C42—44no—
1157C2×C42C2411yescharacteristic
1158C2×C42C2412yes—
1159C2×C42C2412yes—
1160C2×C42C2412yes—
1161C2×C42C2412yes—
1162C2×C42C2411yescharacteristic
1163C2×C42C2411yescharacteristic
1164C2×C42C2411yescharacteristic
1165C2×C42C2411yescharacteristic
1166C2×C42C2411yescharacteristic
1167C2×C42C2411yescharacteristic
1168C2×C42C2411yescharacteristic
1169C2×C42C2411yescharacteristic
1170C2×C42C2411yescharacteristic
1171C2×C42C2411yescharacteristic
1172C2×C42C2411yescharacteristic
1173C2×C42C2414yes—
1174C2×C42C2412yes—
1175C2×C42C2412yes—
1176C2×C42C2412yes—
1177C2×C42C2412yes—
1178C2×C42C2412yes—
1179C2×C42C2412yes—
1180#95C2411yescharacteristic
1181#95C2411yescharacteristic
1182#95C2411yescharacteristic
1183#95C2411yescharacteristic
1184#95C2411yescharacteristic
1185#95C2411yescharacteristic
1186#95C2411yescharacteristic
1187#95C2411yescharacteristic
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2412yes—
1212#95C2412yes—
1213#95C2412yes—
1214#95C2412yes—
1215#95C2412yes—
1216#95C2412yes—
1217#95C2412yes—
1218#95C2412yes—
1219#95C2412yes—
1220#95C2412yes—
1221#95C2412yes—
1222#95C2412yes—
1223#95C2412yes—
1224#95C2412yes—
1225#95C2412yes—
1226#95C2412yes—
1227#95C2412yes—
1228#95C2412yes—
1229#95C2412yes—
1230#95C2414yes—
1231#95C2414yes—
1232#95C2414yes—
1233#95C2414yes—
1234#95C2414yes—
1235#95C2414yes—
1236#95C2414yes—
1237#95C2414yes—
1238#95C2414yes—
1239#95C2414yes—
1240#95C2414yes—
1241#95C2414yes—
1242#95C2414yes—
1243#95C2414yes—
1244C24—24no—
1245C24—24no—
1246C24—24no—
1247C24—42no—
1248C24—42no—
1249C24—42no—
1250C24—42no—
1251C24C2514yes—
1252C24C2512yes—
1253C24C2512yes—
1254C24C2512yes—
1255C24C2512yes—
1256C24C2511yescharacteristic
1257#41—464no—
1258#41—432no—
1259#41—432no—
1260#41—416no—
1261#41—416no—
1262#41—416no—
1263#41—416no—
1264C2×Q8—22no—
1265C2×Q8—22no—
1266C2×Q8—22no—
1267C2×Q8—22no—
1268C2×Q8—24no—
1269C2×Q8—24no—
1270C2×Q8—22no—
1271C2×Q8—22no—
1272C2×Q8—22no—
1273C2×Q8—22no—
1274C2×Q8—24no—
1275C2×Q8—24no—
1276C2×Q8—22no—
1277C2×Q8—22no—
1278C2×Q8—24no—
1279C2×Q8—24no—
1280C2×Q8—22no—
1281C2×Q8—22no—
1282C2×Q8—44no—
1283C2×Q8—44no—
1284C2×Q8—44no—
1285C2×Q8—432no—
1286C2×Q8—432no—
1287C2×Q8—416no—
1288C2×D4—24no—
1289C2×D4—24no—
1290C2×D4—24no—
1291C2×D4—24no—
1292C2×D4—24no—
1293C2×D4—24no—
1294C2×D4—24no—
1295C2×D4—24no—
1296C2×D4—24no—
1297C2×D4—24no—
1298C2×D4—24no—
1299C2×D4—24no—
1300C2×D4—24no—
1301C2×D4—24no—
1302C2×D4—22no—
1303C2×D4—22no—
1304C2×D4—24no—
1305C2×D4—24no—
1306C2×D4—24no—
1307C2×D4—22no—
1308C2×D4—22no—
1309C2×D4—22no—
1310C2×D4—22no—
1311C2×D4—24no—
1312C2×D4—22no—
1313C2×D4—22no—
1314C2×D4—22no—
1315C2×D4—22no—
1316C2×D4—22no—
1317C2×D4—22no—
1318C2×D4—24no—
1319C2×D4—24no—
1320C2×D4—44no—
1321C2×D4—44no—
1322C2×D4—44no—
1323C2×D4—42no—
1324C2×D4—42no—
1325C2×D4—42no—
1326C2×D4—42no—
1327C2×D4—42no—
1328C2×D4—42no—
1329C2×D4—42no—
1330C2×D4—42no—
1331C2×D4—42no—
1332C2×D4—42no—
1333C2×D4—42no—
1334C2×D4—42no—
1335C2×D4—42no—
1336C2×D4—42no—
1337C2×D4—42no—
1338C2×D4—42no—
1339C2×D4—44no—
1340C2×D4—44no—
1341C2×D4—44no—
1342C2×D4—44no—
1343C2×D4—44no—
1344C2×D4—44no—
1345C2×D4—44no—
1346C2×D4—44no—
1347C2×D4—44no—
1348C2×D4—44no—
1349C2×D4—44no—
1350C2×D4—44no—
1351C2×D4—44no—
1352C2×D4—44no—
1353C2×D4—44no—
1354C2×D4—44no—
1355C2×D4—44no—
1356C2×D4—44no—
1357C2×D4—44no—
1358C2×D4—44no—
1359C2×D4—44no—
1360C2×D4—44no—
1361C2×D4—44no—
1362C2×D4—44no—
1363C2×D4—44no—
1364C2×D4—44no—
1365C2×D4—44no—
1366C2×D4—44no—
1367C2×D4—44no—
1368C2×D4—44no—
1369C2×D4—416no—
1370C22×C4—22no—
1371C22×C4—22no—
1372C22×C4—24no—
1373C22×C4—24no—
1374C22×C4—24no—
1375C22×C4—22no—
1376C22×C4—22no—
1377C22×C4—22no—
1378C22×C4—22no—
1379C22×C4—24no—
1380C22×C4—24no—
1381C22×C4—24no—
1382C22×C4—24no—
1383C22×C4—24no—
1384C22×C4—24no—
1385C22×C4—24no—
1386C22×C4—24no—
1387C22×C4—24no—
1388C22×C4—24no—
1389C22×C4—24no—
1390C22×C4—24no—
1391C22×C4—24no—
1392C22×C4—24no—
1393C22×C4—22no—
1394C22×C4—22no—
1395C22×C4—24no—
1396C22×C4—28no—
1397C22×C4—41no—
1398C22×C4—41no—
1399C22×C4—44no—
1400C22×C4—44no—
1401C22×C4—44no—
1402C22×C4—44no—
1403C22×C4—44no—
1404C22×C4—44no—
1405C22×C4—42no—
1406C22×C4—42no—
1407C22×C4—42no—
1408C22×C4—41no—
1409C22×C4—42no—
1410C22×C4—41no—
1411C22×C4—41no—
1412C22×C4—41no—
1413C22×C4—41no—
1414C22×C4—42no—
1415C22×C4—44no—
1416C22×C4—44no—
1417C22×C4—42no—
1418C22×C4—42no—
1419C22×C4—44no—
1420C22×C4—44no—
1421C22×C4—42no—
1422C22×C4—44no—
1423C22×C4—41no—
1424C22×C4—41no—
1425C22×C4—41no—
1426C22×C4—42no—
1427C22×C4—44no—
1428C22×C4—44no—
1429C22×C4—44no—
1430C22×C4—816no—
1431C22×C4H(5,𝔽2)14yes—
1432C22×C4H(5,𝔽2)14yes—
1433C22×C4H(5,𝔽2)14yes—
1434C22×C4C2511yescharacteristic
1435C22×C4C2511yescharacteristic
1436C22×C4C2511yescharacteristic
1437C22×C4C2511yescharacteristic
1438C22×C4C2512yes—
1439C22×C4C2512yes—
1440C22×C4C2511yescharacteristic
1441C22×C4C2512yes—
1442C22×C4C2512yes—
1443C22×C4C2512yes—
1444C22×C4C2514yes—
1445C22×C4C2512yes—
1446C22×C4C2512yes—
1447C22×C4C2514yes—
1448C22×C4C2511yescharacteristic
1449C22×C4C2512yes—
1450C22×C4C2512yes—
1451C22×C4C2511yescharacteristic
1452C22×C4C2511yescharacteristic
1453C22×C4C2514yes—
1454C22×C4C2512yes—
1455C22×C4C2511yescharacteristic
1456C22×C4C2511yescharacteristic
1457C22×C4C2512yes—
1458C22×C4C2512yes—
1459C22×C4C2511yescharacteristic
1460C22×C4C2511yescharacteristic
1461C22×C4C2511yescharacteristic
1462C22×C4C2511yescharacteristic
1463C4⋊C4—24no—
1464C4⋊C4—24no—
1465C4⋊C4—24no—
1466C4⋊C4—24no—
1467C4⋊C4—22no—
1468C4⋊C4—22no—
1469C4⋊C4—22no—
1470C4⋊C4—22no—
1471C4⋊C4—22no—
1472C4⋊C4—22no—
1473C4⋊C4—22no—
1474C4⋊C4—22no—
1475C4⋊C4—22no—
1476C4⋊C4—22no—
1477C4⋊C4—22no—
1478C4⋊C4—22no—
1479C4⋊C4—24no—
1480C4⋊C4—24no—
1481C4⋊C4—41no—
1482C4⋊C4—41no—
1483C4⋊C4—41no—
1484C4⋊C4—41no—
1485C4⋊C4—44no—
1486C4⋊C4—44no—
1487C4⋊C4—44no—
1488C4⋊C4—42no—
1489C4⋊C4—42no—
1490C4⋊C4—42no—
1491C4⋊C4—42no—
1492C4⋊C4—42no—
1493C4⋊C4—42no—
1494C4⋊C4—42no—
1495C4⋊C4—42no—
1496C4⋊C4—42no—
1497C4⋊C4—42no—
1498C4⋊C4—44no—
1499C4⋊C4—44no—
1500C4⋊C4—44no—
1501C4⋊C4—44no—
1502C4⋊C4—42no—
1503C4⋊C4—42no—
1504C4⋊C4—44no—
1505C4⋊C4—44no—
1506C4⋊C4—44no—
1507C4⋊C4—44no—
1508C4⋊C4—44no—
1509C4⋊C4—44no—
1510C4⋊C4—42no—
1511C4⋊C4—42no—
1512C22⋊C4—24no—
1513C22⋊C4—24no—
1514C22⋊C4—24no—
1515C22⋊C4—24no—
1516C22⋊C4—28no—
1517C22⋊C4—24no—
1518C22⋊C4—24no—
1519C22⋊C4—24no—
1520C22⋊C4—44no—
1521C22⋊C4—44no—
1522C22⋊C4—44no—
1523C22⋊C4—44no—
1524C22⋊C4—44no—
1525C22⋊C4—44no—
1526C22⋊C4—44no—
1527C22⋊C4—44no—
1528C22⋊C4—44no—
1529C22⋊C4—42no—
1530C22⋊C4—42no—
1531C22⋊C4—42no—
1532C22⋊C4—42no—
1533C22⋊C4—42no—
1534C22⋊C4—42no—
1535C22⋊C4—42no—
1536C22⋊C4—44no—
1537C22⋊C4—42no—
1538C22⋊C4—42no—
1539C22⋊C4—42no—
1540C22⋊C4—42no—
1541C22⋊C4—42no—
1542C22⋊C4—42no—
1543C22⋊C4—42no—
1544C22⋊C4—42no—
1545C22⋊C4—42no—
1546C22⋊C4—42no—
1547C22⋊C4—42no—
1548C22⋊C4—42no—
1549C22⋊C4—44no—
1550C22⋊C4—44no—
1551C22⋊C4—44no—
1552C22⋊C4—44no—
1553C22⋊C4—44no—
1554C22⋊C4—44no—
1555C22⋊C4—44no—
1556C22⋊C4—44no—
1557C22⋊C4—44no—
1558C22⋊C4—44no—
1559C22⋊C4—42no—
1560C22⋊C4—44no—
1561C22⋊C4—42no—
1562C22⋊C4—42no—
1563C22⋊C4—44no—
1564C22⋊C4—44no—
1565C22⋊C4—44no—
1566C22⋊C4—44no—
1567C22⋊C4—42no—
1568C22⋊C4—42no—
1569C22⋊C4—42no—
1570C22⋊C4—42no—
1571C22⋊C4—44no—
1572C22⋊C4—44no—
1573C22⋊C4—44no—
1574C22⋊C4—44no—
1575C22⋊C4—44no—
1576C22⋊C4—44no—
1577C22⋊C4—44no—
1578C22⋊C4—42no—
1579C22⋊C4—42no—
1580C22⋊C4—42no—
1581C22⋊C4—42no—
1582C22⋊C4—42no—
1583C42—22no—
1584C42—22no—
1585C42—22no—
1586C42—22no—
1587C42—22no—
1588C42—22no—
1589C42—22no—
1590C42—22no—
1591C42—22no—
1592C42—22no—
1593C42—22no—
1594C42—22no—
1595C42—24no—
1596C42—24no—
1597C42—24no—
1598C42—24no—
1599C42—42no—
1600C42—42no—
1601C42—42no—
1602C42—44no—
1603C42—42no—
1604C42—42no—
1605C42—42no—
1606C23—21no—
1607C23—21no—
1608C23—21no—
1609C23—21no—
1610C23—22no—
1611C23—22no—
1612C23—24no—
1613C23—22no—
1614C23—22no—
1615C23—24no—
1616C23—24no—
1617C23—22no—
1618C23—22no—
1619C23—22no—
1620C23—22no—
1621C23—22no—
1622C23—22no—
1623C23—22no—
1624C23—22no—
1625C23—22no—
1626C23—22no—
1627C23—24no—
1628C23—22no—
1629C23—22no—
1630C23—22no—
1631C23—22no—
1632C23—22no—
1633C23—24no—
1634C23—22no—
1635C23—22no—
1636C23—22no—
1637C23—24no—
1638C23—22no—
1639C23—22no—
1640C23—22no—
1641C23—22no—
1642C23—22no—
1643C23—22no—
1644C23—24no—
1645C23—48no—
1646C23—48no—
1647C23—48no—
1648C23—84no—
1649C23—84no—
1650C23—84no—
1651C23—84no—
1652C23C2×H(5,𝔽2)12yes—
1653C23C2×H(5,𝔽2)12yes—
1654C23C2×H(5,𝔽2)12yes—
1655C23C2611yescharacteristic
1656Q8—416no—
1657Q8—48no—
1658Q8—44no—
1659Q8—48no—
1660Q8—44no—
1661Q8—44no—
1662Q8—44no—
1663D4—416no—
1664D4—48no—
1665D4—48no—
1666D4—48no—
1667D4—48no—
1668D4—48no—
1669D4—48no—
1670D4—44no—
1671D4—44no—
1672D4—44no—
1673D4—44no—
1674D4—84no—
1675D4—84no—
1676D4—84no—
1677D4—84no—
1678D4—84no—
1679D4—84no—
1680D4—164no—
1681D4—164no—
1682D4—164no—
1683D4—164no—
1684D4—164no—
1685D4—164no—
1686D4—164no—
1687D4—164no—
1688D4—164no—
1689D4—164no—
1690C2×C4—21no—
1691C2×C4—21no—
1692C2×C4—21no—
1693C2×C4—21no—
1694C2×C4—21no—
1695C2×C4—21no—
1696C2×C4—21no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—21no—
1702C2×C4—21no—
1703C2×C4—21no—
1704C2×C4—22no—
1705C2×C4—22no—
1706C2×C4—22no—
1707C2×C4—22no—
1708C2×C4—22no—
1709C2×C4—22no—
1710C2×C4—22no—
1711C2×C4—22no—
1712C2×C4—22no—
1713C2×C4—22no—
1714C2×C4—24no—
1715C2×C4—22no—
1716C2×C4—22no—
1717C2×C4—24no—
1718C2×C4—22no—
1719C2×C4—22no—
1720C2×C4—22no—
1721C2×C4—22no—
1722C2×C4—24no—
1723C2×C4—22no—
1724C2×C4—22no—
1725C2×C4—22no—
1726C2×C4—22no—
1727C2×C4—24no—
1728C2×C4—24no—
1729C2×C4—21no—
1730C2×C4—21no—
1731C2×C4—22no—
1732C2×C4—22no—
1733C2×C4—22no—
1734C2×C4—22no—
1735C2×C4—24no—
1736C2×C4—22no—
1737C2×C4—21no—
1738C2×C4—22no—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—22no—
1745C2×C4—24no—
1746C2×C4—22no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—22no—
1750C2×C4—22no—
1751C2×C4—21no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—24no—
1755C2×C4—22no—
1756C2×C4—22no—
1757C2×C4—21no—
1758C2×C4—24no—
1759C2×C4—21no—
1760C2×C4—22no—
1761C2×C4—22no—
1762C2×C4—21no—
1763C2×C4—21no—
1764C2×C4—22no—
1765C2×C4—21no—
1766C2×C4—21no—
1767C2×C4—22no—
1768C2×C4—21no—
1769C2×C4—44no—
1770C2×C4—44no—
1771C2×C4—416no—
1772C2×C4—416no—
1773C2×C4—48no—
1774C2×C4—48no—
1775C2×C4—48no—
1776C2×C4—48no—
1777C2×C4—48no—
1778C2×C4—84no—
1779C2×C4—88no—
1780C2×C4—82no—
1781C2×C4—82no—
1782C2×C4—82no—
1783C2×C4—82no—
1784C2×C4—84no—
1785C2×C4—84no—
1786C2×C4—84no—
1787C2×C4—88no—
1788C2×C4—164no—
1789C2×C4#560116yes—
1790C2×C4C2×H(5,𝔽2)12yes—
1791C2×C4C2×H(5,𝔽2)12yes—
1792C2×C4C2×H(5,𝔽2)12yes—
1793C2×C4C2×H(5,𝔽2)12yes—
1794C2×C4C2×H(5,𝔽2)12yes—
1795C2×C4C2×H(5,𝔽2)12yes—
1796C2×C4#58512yes—
1797C2×C4#58512yes—
1798C22—22no—
1799C22—22no—
1800C22—22no—
1801C22—22no—
1802C22—22no—
1803C22—22no—
1804C22—42no—
1805C22—42no—
1806C22—42no—
1807C22—42no—
1808C22—44no—
1809C22—42no—
1810C22—42no—
1811C22—42no—
1812C22—42no—
1813C22—44no—
1814C22—44no—
1815C22—42no—
1816C22—42no—
1817C22—42no—
1818C22—42no—
1819C22—42no—
1820C22—42no—
1821C22—42no—
1822C22—42no—
1823C22—44no—
1824C22—42no—
1825C22—42no—
1826C22—44no—
1827C22—42no—
1828C22—42no—
1829C22—42no—
1830C22—42no—
1831C22—42no—
1832C22—42no—
1833C22—44no—
1834C22—42no—
1835C22—42no—
1836C22—42no—
1837C22—42no—
1838C22—44no—
1839C22—816no—
1840C22C2×#56014yes—
1841C22C22×H(5,𝔽2)11yescharacteristic
1842C22C22×H(5,𝔽2)11yescharacteristic
1843C22C22×H(5,𝔽2)11yescharacteristic
1844C22C2×#58511yescharacteristic
1845C22C2×#58511yescharacteristic
1846C22H(7,𝔽2)11yescharacteristic
1847C222−1+611yescharacteristic
1848C4—22no—
1849C4—22no—
1850C4—41no—
1851C4—42no—
1852C4—42no—
1853C4—41no—
1854C4—41no—
1855C4—42no—
1856C4—42no—
1857C4—41no—
1858C4—41no—
1859C4—44no—
1860C4—41no—
1861C4—41no—
1862C4—41no—
1863C4—41no—
1864C4—41no—
1865C4—42no—
1866C4—42no—
1867C4—42no—
1868C4—42no—
1869C4—44no—
1870C4—42no—
1871C4—42no—
1872C4—44no—
1873C4—42no—
1874C4—42no—
1875C4C2×#56014yes—
1876C4C2×#56014yes—
1877C2—24no—
1878C2—82no—
1879C2—82no—
1880C2—82no—
1881C2—82no—
1882C2—84no—
1883C2C22×#56011yescharacteristic
1884C2#6283011yescharacteristic
1885C2#6287811yescharacteristic
1886C2#6292411yescharacteristic
1887C2#6292511yescharacteristic
1888C2#6293111yescharacteristic
1889C2#6296111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53151C2semidirect
2. #53128C2semidirect
3. #53090C2semidirect
4. #53087C2semidirect
5. #53060C2semidirect
6. #53041C2semidirect
7. #53004C2semidirect
8. #52962C2semidirect
9. #52369C2semidirect
10. #52369C2semidirect
11. #46050C2semidirect
12. #46050C2semidirect
13. #46048C2semidirect
14. #46048C2semidirect
15. #45743C2semidirect
16. #45687C2semidirect
17. #45663C2semidirect
18. #45608C2semidirect
19. #45518C2semidirect
20. #45473C2semidirect
21. #35676C2semidirect
22. #35660C2semidirect
23. #35660C2semidirect
24. #35619C2semidirect
25. #35564C2semidirect
26. #35533C2semidirect
27. #35329C2semidirect
28. #35307C2semidirect
29. #35267C2semidirect
30. #35256C2semidirect
31. #35168C2semidirect
32. #35165C2semidirect
33. #34937C2semidirect
34. #34816C2semidirect
35. C2×#2447C2semidirect
52. #2863C22semidirect
53. #2860C22semidirect
57. #2855C22semidirect
58. #2855C22semidirect
62. #2841C22semidirect
63. #2838C22semidirect
64. #2838C22semidirect
65. #2830C22semidirect
66. #2830C22semidirect
67. #2829C22semidirect
68. #2829C22semidirect
69. #2828C22semidirect
70. #2828C22semidirect
71. #2827C22semidirect
72. #2827C22semidirect
73. #2826C22semidirect
74. #2825C22semidirect
75. #2825C22semidirect
76. #2824C22semidirect
77. #2824C22semidirect
78. #2824C22semidirect
79. #2815C22semidirect
80. #2815C22semidirect
81. #2815C22semidirect
82. #2797C22semidirect
83. #2797C22semidirect
84. #2797C22semidirect
85. #2797C22semidirect
86. #2796C22semidirect
87. #2796C22semidirect
88. #2784C22semidirect
89. #2784C22semidirect
90. #2780C22semidirect
91. #2780C22semidirect
92. #2760C22semidirect
93. #2752C22semidirect
94. #2749C22semidirect
95. #2749C22semidirect
96. #2749C22semidirect
97. #2749C22semidirect
98. #2746C22semidirect
99. #2746C22semidirect
100. #2742C22semidirect
101. #2737C22semidirect
102. #2737C22semidirect
103. #2737C22semidirect
104. #2737C22semidirect
105. #2714C22semidirect
106. #2714C22semidirect
107. #2714C22semidirect
108. #2714C22semidirect
109. #2699C22semidirect
110. #2699C22semidirect
111. #2691C22semidirect
112. #2691C22semidirect
113. #2691C22semidirect
114. #2691C22semidirect
115. #2688C22semidirect
116. #2688C22semidirect
117. #2688C22semidirect
118. #2688C22semidirect
119. #2688C22semidirect
120. #2688C22semidirect
121. #2675C22semidirect
124. #2645C22semidirect
125. #2644C22semidirect
126. #2625C22semidirect
127. #2625C22semidirect
133. #2548C22semidirect
135. #2547C22semidirect
136. #2546C22semidirect
138. #2545C22semidirect
139. #2545C22semidirect
143. #2544C22semidirect
144. #2544C22semidirect
150. #2541C22semidirect
161. #2514C22semidirect
162. #2514C22semidirect
163. #2513C22semidirect
164. #2513C22semidirect
165. #2512C22semidirect
166. #2512C22semidirect
167. #2511C22semidirect
168. #2511C22semidirect
172. #2503C22semidirect
173. #2502C22semidirect
174. #2499C22semidirect
175. #2499C22semidirect
176. #2497C22semidirect
177. #2496C22semidirect
178. #2495C22semidirect
179. #2494C22semidirect
191. #2447C22semidirect
192. #2447C22semidirect
193. #2447C22semidirect
194. #2447C22semidirect
195. #2446C22semidirect
196. #2446C22semidirect
197. #2446C22semidirect
198. #2446C22semidirect
203. #2436C22semidirect
204. #2436C22semidirect
205. #2434C22semidirect
206. #2434C22semidirect
207. #2432C22semidirect
208. #2432C22semidirect
213. #2431C22semidirect
214. #2431C22semidirect
219. #2429C22semidirect
226. #2428C22semidirect
231. #2427C22semidirect
234. #2426C22semidirect
243. #2417C22semidirect
249. #2416C22semidirect
250. #2415C22semidirect
253. #2414C22semidirect
254. #2409C22semidirect
255. #2409C22semidirect
256. #2409C22semidirect
257. #2409C22semidirect
258. #2407C22semidirect
259. #2407C22semidirect
260. #2407C22semidirect
261. #2407C22semidirect
264. #2401C22semidirect
265. #2401C22semidirect
266. #2392C22semidirect
267. #2392C22semidirect
270. #2377C22semidirect
271. #2377C22semidirect
272. #2377C22semidirect
273. #2377C22semidirect
280. C4×#126C22semidirect
281. C4×#126C22semidirect
282. C4×#121C22semidirect
283. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#531512
#531282
#530902
#530872
#530602
#530412
#530042
#529622
#523692
#460502
#460482
#457432
#456872
#456632
#456082
#455182
#454732
#356762
#356602
#356192
#355642
#355332
#353292
#353072
#352672
#352562
#351682
#351652
#349372
#348162
C2×#24472