Finite Group Databasebeta

← #8425003

Subgroups — #8425003

Order 512.

4869 conjugacy classes of subgroups.

The subgroup lattice has 1759 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59655C211yesmaximal, characteristic, complemented
2#59397C212yesmaximal, complemented
3#59314C211yesmaximal, characteristic, complemented
4#59245C211yesmaximal, characteristic, complemented
5#59024C212yesmaximal, complemented
6#56693C214yesmaximal, complemented
7#55908C214yesmaximal, complemented
8#53017C212yesmaximal, complemented
9#52982C212yesmaximal, complemented
10#52975C212yesmaximal, complemented
11#52963C212yesmaximal, complemented
12#52498C214yesmaximal, complemented
13#42827C212yesmaximal, complemented
14#42790C212yesmaximal, complemented
15#42642C212yesmaximal, complemented
16#42606C212yesmaximal, complemented
17#41189C214yesmaximal, complemented
18#40102C212yesmaximal, complemented
19#39908C212yesmaximal, complemented
20#39690C212yesmaximal, complemented
21#39379C211yesmaximal, characteristic, complemented
22#39193C211yesmaximal, characteristic, complemented
23#39126C211yesmaximal, characteristic, complemented
24#39125C211yesmaximal, characteristic, complemented
25#37671C212yesmaximal, complemented
26#37636C211yesmaximal, characteristic, complemented
27#37620C211yesmaximal, characteristic, complemented
28#37524C212yesmaximal, complemented
29#37476C212yesmaximal, complemented
30#36456C211yesmaximal, characteristic, complemented
31#36189C211yesmaximal, characteristic, complemented
32#36154C211yesmaximal, characteristic, complemented
33#34935C211yesmaximal, characteristic, complemented
34#34724C211yesmaximal, characteristic, complemented
35#34700C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic, complemented
37C2×#554C2211yescharacteristic
38C2×#554C2212yescomplemented
39C2×#541C2212yescomplemented
40C2×#529C2211yescharacteristic
41C2×#529C2211yescharacteristic, complemented
42C2×#525C2212yes—
43C2×C4×#41C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45#2859C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2212yescomplemented
48#2857C2211yescharacteristic, complemented
49#2848C2212yes—
50#2841C2214yes—
51#2841C2214yes—
52#2839C2214yescomplemented
53#2832C2214yescomplemented
54#2831C2214yescomplemented
55#2831C2214yescomplemented
56#2831C2214yescomplemented
57#2827C2214yescomplemented
58#2827C2214yescomplemented
59#2827C2214yescomplemented
60#2826C2214yes—
61#2824C2214yes—
62#2823C2214yescomplemented
63#2822C2214yescomplemented
64#2807C2214yescomplemented
65#2788C2214yes—
66#2781C2214yes—
67#2779C2214yescomplemented
68#2777C2214yescomplemented
69#2769C2214yescomplemented
70#2764C2214yes—
71#2757C2214yescomplemented
72#2750C2214yes—
73#2750C2214yescomplemented
74#2735C2214yes—
75#2732C2214yescomplemented
76#2730C2214yes—
77#2729C2214yescomplemented
78#2725C2214yescomplemented
79#2725C2214yescomplemented
80#2720C2214yescomplemented
81#2716C2214yescomplemented
82#2708C2214yescomplemented
83#2707C2214yes—
84#2707C2214yes—
85#2704C2214yescomplemented
86#2704C2214yescomplemented
87#2702C2214yes—
88#2702C2214yescomplemented
89#2702C2214yescomplemented
90#2700C2214yescomplemented
91#2696C2214yes—
92#2694C2214yes—
93#2692C2214yescomplemented
94#2685C2214yes—
95#2685C2214yes—
96#2684C2214yes—
97#2681C2214yescomplemented
98#2676C2214yes—
99#2674C2214yescomplemented
100#2672C2214yescomplemented
101#2667C2214yescomplemented
102#2665C2214yescomplemented
103#2664C2214yescomplemented
104#2654C2214yescomplemented
105#2652C2214yescomplemented
106#2649C2214yes—
107#2636C2214yes—
108#2632C2214yescomplemented
109#2629C2212yescomplemented
110#2629C2212yescomplemented
111#2629C2212yescomplemented
112#2629C2212yescomplemented
113#2628C2212yescomplemented
114#2628C2212yescomplemented
115#2628C2212yescomplemented
116#2626C2214yes—
117#2626C2214yes—
118#2625C2212yescomplemented
119#2624C2212yes—
120#2624C2212yescomplemented
121#2620C2212yes—
122#2620C2212yescomplemented
123#2618C2214yescomplemented
124#2589C2214yescomplemented
125#2588C2214yescomplemented
126#2582C2211yescharacteristic, complemented
127#2578C2214yescomplemented
128#2577C2214yescomplemented
129#2570C2212yescomplemented
130#2569C2214yescomplemented
131#2568C2212yescomplemented
132#2563C2211yescharacteristic
133#2563C2212yes—
134#2563C2211yescharacteristic, complemented
135#2562C2214yescomplemented
136#2562C2212yescomplemented
137#2551C2211yescharacteristic, complemented
138#2550C2212yescomplemented
139#2550C2212yescomplemented
140#2549C2214yescomplemented
141#2547C2212yescomplemented
142#2542C2212yes—
143#2538C2211yescharacteristic
144#2538C2211yescharacteristic
145#2538C2212yes—
146#2538C2211yescharacteristic
147#2538C2211yescharacteristic, complemented
148#2537C2211yescharacteristic
149#2537C2212yes—
150#2537C2211yescharacteristic
151#2536C2212yes—
152#2536C2212yescomplemented
153#2536C2212yescomplemented
154#2535C2212yes—
155#2534C2214yes—
156#2512C2212yes—
157#2512C2212yes—
158#2511C2212yescomplemented
159#2511C2212yescomplemented
160#2509C2212yescomplemented
161#2507C2212yescomplemented
162#2506C2212yescomplemented
163#2506C2212yescomplemented
164#2506C2212yescomplemented
165#2504C2212yescomplemented
166#2497C2212yes—
167#2497C2212yes—
168#2495C2212yescomplemented
169#2495C2212yescomplemented
170#2495C2212yescomplemented
171#2495C2212yescomplemented
172#2492C2212yes—
173#2492C2212yescomplemented
174#2491C2212yes—
175#2491C2212yes—
176#2491C2212yescomplemented
177#2490C2212yescomplemented
178#2487C2212yes—
179#2487C2212yes—
180#2487C2212yescomplemented
181#2486C2212yes—
182#2480C2212yes—
183#2478C2212yescomplemented
184#2472C2214yes—
185#2470C2212yescomplemented
186#2468C2212yes—
187#2468C2214yescomplemented
188#2466C2212yes—
189#2466C2214yescomplemented
190#2460C2214yescomplemented
191#2460C2214yescomplemented
192#2457C2212yes—
193#2455C2212yes—
194#2454C2211yescharacteristic
195#2454C2212yes—
196#2454C2214yescomplemented
197#2453C2212yescomplemented
198#2453C2211yescharacteristic, complemented
199#2452C2212yes—
200#2452C2214yes—
201#2452C2212yescomplemented
202#2450C2214yes—
203#2450C2214yescomplemented
204#2449C2214yescomplemented
205#2448C2212yes—
206#2447C2211yescharacteristic
207#2447C2211yescharacteristic, complemented
208#2442C2211yescharacteristic
209#2442C2212yes—
210#2442C2212yescomplemented
211#2442C2212yescomplemented
212#2442C2212yescomplemented
213#2441C2212yes—
214#2441C2211yescharacteristic
215#2440C2212yescomplemented
216#2440C2212yescomplemented
217#2440C2212yescomplemented
218#2439C2212yes—
219#2439C2212yes—
220#2439C2214yescomplemented
221#2437C2214yes—
222#2435C2211yescharacteristic
223#2432C2211yescharacteristic
224#2429C2212yescomplemented
225#2429C2214yescomplemented
226#2429C2211yescharacteristic, complemented
227#2427C2211yescharacteristic
228#2427C2212yes—
229#2427C2214yescomplemented
230#2426C2212yescomplemented
231#2424C2214yes—
232#2423C2212yes—
233#2423C2212yescomplemented
234#2422C2211yescharacteristic, complemented
235#2421C2212yescomplemented
236#2421C2212yescomplemented
237#2421C2212yescomplemented
238#2420C2211yescharacteristic
239#2418C2212yes—
240#2417C2212yes—
241#2417C2212yes—
242#2417C2211yescharacteristic
243#2417C2212yescomplemented
244#2417C2212yescomplemented
245#2416C2212yes—
246#2416C2212yescomplemented
247#2416C2212yescomplemented
248#2415C2211yescharacteristic
249#2408C2211yescharacteristic
250#2408C2212yes—
251#2407C2211yescharacteristic
252#2395C2212yes—
253#2395C2212yes—
254#2392C2214yes—
255#2392C2212yes—
256#2392C2212yes—
257#2369C2212yescomplemented
258#2367C2212yes—
259#2364C2214yescomplemented
260#2362C2212yes—
261#2361C2212yes—
262#2360C2212yescomplemented
263#2360C2212yescomplemented
264#2355C2211yescharacteristic, complemented
265#2352C2212yes—
266#2351C2212yescomplemented
267Q8×C4⋊C4C2211yescharacteristic, complemented
268Q8×C4⋊C4C2211yescharacteristic, complemented
269#2349C2212yes—
270D4×C4⋊C4C2211yescharacteristic
271#2345C2212yescomplemented
272#2341C2212yes—
273D4×C22⋊C4C2212yes—
274#2337C2214yescomplemented
275#2324C2212yes—
276#2324C2212yes—
277#2323C2212yescomplemented
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×C4⋊Q8C2211yescharacteristic, complemented
280C4×#124C2211yescharacteristic
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2212yescomplemented
284C4×C22⋊Q8C2211yescharacteristic, complemented
285C4×#123C2212yescomplemented
286C4×#121C2212yes—
287C4×#121C2212yes—
288C4×#121C2211yescharacteristic
289C4×#120C2212yes—
290#2296C2212yescomplemented
291#2293C2211yescharacteristic
292#2293C2211yescharacteristic, complemented
293#2285C2211yescharacteristic
294C2×#384C2211yescharacteristic, complemented
295#2280C2212yes—
296#2280C2212yes—
297C2×#380C2212yes—
298C42×D4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302Q82—44no—
303#554—44no—
304#554—48no—
305#541—48no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2314yes—
313#529—44no—
314#529—44no—
315C2×#126C2312yes—
316C2×#126C2312yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#125C2314yes—
320C2×#125C2312yes—
321C2×#125C2314yes—
322C2×#125C2312yes—
323C2×#125C2311yescharacteristic
324C2×#125C2311yescharacteristic
325C2×#125C2314yes—
326C2×#124C2311yescharacteristic
327C2×#124C2314yes—
328C2×#124C2311yescharacteristic
329C2×#124C2311yescharacteristic
330C2×#124C2314yes—
331#525—48no—
332C2×#123C2312yes—
333C2×#123C2312yes—
334C2×#123C2314yes—
335C2×#123C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2314yes—
354C2×#121C2312yes—
355C2×#121C2311yescharacteristic
356C2×#121C2314yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2311yescharacteristic
360C2×#121C2311yescharacteristic
361C2×#121C2312yes—
362C2×#121C2314yes—
363C2×#120C2314yes—
364C2×#120C2312yes—
365C4×#41—44no—
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×Q8C2311yescharacteristic
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×D4—44no—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2314yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2314yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2312yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2312yes—
400C2×#117C2312yes—
401C2×#117C2312yes—
402C2×#117C2312yes—
403C2×#117C2311yescharacteristic
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2312yes—
406C22×C4⋊C4C2312yes—
407C22×C4⋊C4C2312yes—
408C22×C4⋊C4C2311yescharacteristic
409C22×C4⋊C4C2312yes—
410C22×C22⋊C4C2312yes—
411C22×C22⋊C4C2314yes—
412C22×C42C2311yescharacteristic
413C22×C42C2311yescharacteristic
414C22×C42C2312yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2312yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2312yes—
434#399C2314yes—
435#399C2314yes—
436#399C2314yes—
437#399C2314yes—
438#399C2312yes—
439#399C2314yes—
440#399C2314yes—
441#399C2314yes—
442#399C2312yes—
443#398C2312yes—
444#398C2312yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2312yes—
460#398C2312yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#397C2312yes—
466#397C2314yes—
467#397C2312yes—
468#397C2314yes—
469#397C2314yes—
470#397C2312yes—
471#397C2312yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2312yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2312yes—
480#397C2314yes—
481#397C2314yes—
482#397C2312yes—
483#397C2312yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2312yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2312yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2312yes—
504#396C2314yes—
505#396C2314yes—
506#396C2314yes—
507#396C2312yes—
508#395C2314yes—
509#395C2314yes—
510#395C2314yes—
511#395C2314yes—
512#395C2314yes—
513#394C2312yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2312yes—
520#394C2314yes—
521#394C2314yes—
522#394C2312yes—
523#394C2314yes—
524#394C2314yes—
525#394C2312yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2312yes—
531#394C2312yes—
532#394C2314yes—
533#394C2312yes—
534#394C2312yes—
535#394C2312yes—
536#394C2312yes—
537#393C2314yes—
538#393C2314yes—
539#393C2314yes—
540#393C2314yes—
541#393C2314yes—
542#393C2314yes—
543#393C2314yes—
544#393C2314yes—
545#393C2314yes—
546#392C2314yes—
547#392C2312yes—
548#392C2312yes—
549#391C2312yes—
550#391C2311yescharacteristic
551#391C2311yescharacteristic
552#391C2311yescharacteristic
553#391C2314yes—
554#391C2312yes—
555#391C2314yes—
556#391C2314yes—
557#391C2314yes—
558#391C2311yescharacteristic
559#391C2312yes—
560#391C2314yes—
561#391C2314yes—
562#391C2312yes—
563#391C2312yes—
564#391C2312yes—
565#391C2311yescharacteristic
566#391C2311yescharacteristic
567#390C2312yes—
568#390C2314yes—
569#390C2312yes—
570#390C2311yescharacteristic
571#390C2311yescharacteristic
572#390C2314yes—
573#390C2314yes—
574#390C2312yes—
575#390C2312yes—
576#390C2314yes—
577#390C2312yes—
578#390C2311yescharacteristic
579#390C2311yescharacteristic
580#390C2311yescharacteristic
581#390C2312yes—
582#390C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2314yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2314yes—
595#389C2314yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2311yescharacteristic
600#389C2314yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2314yes—
608#389C2312yes—
609#389C2314yes—
610#389C2314yes—
611#389C2312yes—
612#389C2312yes—
613#389C2314yes—
614#389C2311yescharacteristic
615#389C2311yescharacteristic
616#389C2311yescharacteristic
617#389C2311yescharacteristic
618#389C2312yes—
619#389C2312yes—
620#389C2314yes—
621#389C2312yes—
622#389C2311yescharacteristic
623#389C2312yes—
624#389C2311yescharacteristic
625#389C2311yescharacteristic
626#389C2312yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2312yes—
636#388C2312yes—
637#388C2314yes—
638#388C2312yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2312yes—
650#388C2312yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2312yes—
655#388C2312yes—
656#388C2312yes—
657#387C2312yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2312yes—
671#387C2312yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2312yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2312yes—
683#386C2314yes—
684#386C2312yes—
685#386C2314yes—
686#386C2314yes—
687#386C2312yes—
688#386C2314yes—
689#386C2312yes—
690#386C2312yes—
691#386C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2312yes—
695#385C2312yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2312yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2312yes—
709#385C2312yes—
710#385C2312yes—
711#385C2312yes—
712#385C2312yes—
713#385C2312yes—
714#385C2312yes—
715#385C2312yes—
716#384C2311yescharacteristic
717#384C2311yescharacteristic
718#384C2312yes—
719#384C2312yes—
720#384C2311yescharacteristic
721#384C2311yescharacteristic
722#384C2312yes—
723#384C2312yes—
724#384C2312yes—
725#383C2314yes—
726#383C2314yes—
727#382C2314yes—
728#382C2312yes—
729#382C2312yes—
730#382C2312yes—
731#382C2312yes—
732#382C2312yes—
733#382C2311yescharacteristic
734#381C2314yes—
735#381C2312yes—
736#381C2312yes—
737#381C2312yes—
738#380C2311yescharacteristic
739#380C2312yes—
740#380C2314yes—
741#380C2314yes—
742#380C2312yes—
743#380C2314yes—
744#380C2314yes—
745#380C2312yes—
746#380C2311yescharacteristic
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2312yes—
756#380C2314yes—
757#380C2312yes—
758#380C2312yes—
759#380C2314yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2311yescharacteristic
766#380C2312yes—
767#380C2314yes—
768#380C2311yescharacteristic
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2312yes—
773#379C2314yes—
774#379C2314yes—
775#379C2312yes—
776#379C2312yes—
777#379C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2314yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2311yescharacteristic
817C2×#95C2314yes—
818C43C2311yescharacteristic
819C25C2412yes—
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—42no—
823C22×Q8C2411yescharacteristic
824C22×Q8C2411yescharacteristic
825C22×Q8C2411yescharacteristic
826C22×Q8C2412yes—
827C22×Q8C2414yes—
828C22×Q8C2414yes—
829C22×D4—24no—
830C22×D4—42no—
831C22×D4—42no—
832C22×D4C2411yescharacteristic
833C22×D4C2411yescharacteristic
834C22×D4C2411yescharacteristic
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2414yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C23×C4—28no—
844C23×C4—44no—
845C23×C4—44no—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2414yes—
862C23×C4C2412yes—
863C4⋊Q8—24no—
864C4⋊Q8—24no—
865C4⋊Q8—44no—
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—48no—
870#126—44no—
871#126—44no—
872#126—48no—
873#126—48no—
874#125—42no—
875#125—42no—
876#125—44no—
877#125—48no—
878#125—44no—
879#125—48no—
880#125—48no—
881#124—24no—
882#124—42no—
883#124—42no—
884#124—48no—
885#124—84no—
886#123—44no—
887#123—44no—
888#123—44no—
889#123—48no—
890C22⋊Q8—28no—
891C22⋊Q8—28no—
892C22⋊Q8—24no—
893C22⋊Q8—24no—
894C22⋊Q8—44no—
895C22⋊Q8—48no—
896C22⋊Q8—48no—
897C22⋊Q8—48no—
898C22⋊Q8—44no—
899C22⋊Q8—42no—
900C22⋊Q8—42no—
901C22⋊Q8—42no—
902C22⋊Q8—44no—
903C22⋊Q8—44no—
904C22⋊Q8—82no—
905C22⋊Q8—84no—
906C22⋊Q8—84no—
907C22⋊Q8—84no—
908#121—24no—
909#121—28no—
910#121—48no—
911#121—44no—
912#121—44no—
913#121—44no—
914#121—42no—
915#121—42no—
916#121—84no—
917#120—48no—
918#120—44no—
919C4×Q8—28no—
920C4×Q8—24no—
921C4×Q8—24no—
922C4×Q8—24no—
923C4×Q8—42no—
924C4×Q8—44no—
925C4×Q8—44no—
926C4×Q8—44no—
927C4×Q8—82no—
928C4×D4—24no—
929C4×D4—24no—
930C4×D4—24no—
931C4×D4—24no—
932C4×D4—44no—
933C4×D4—48no—
934C4×D4—42no—
935C4×D4—42no—
936C4×D4—44no—
937C4×D4—42no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—42no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—48no—
947C4×D4—48no—
948C4×D4—42no—
949#117—44no—
950#117—44no—
951#117—44no—
952#117—44no—
953#117—44no—
954#117—42no—
955#117—44no—
956C2×C4⋊C4—44no—
957C2×C4⋊C4—42no—
958C2×C4⋊C4—44no—
959C2×C4⋊C4—44no—
960C2×C4⋊C4—44no—
961C2×C4⋊C4—82no—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C22⋊C4—44no—
1037C2×C22⋊C4—84no—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2411yescharacteristic
1081C2×C22⋊C4C2411yescharacteristic
1082C2×C22⋊C4C2411yescharacteristic
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C42—24no—
1103C2×C42—24no—
1104C2×C42—44no—
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2414yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2414yes—
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2414yes—
1126C2×C42C2411yescharacteristic
1127C2×C42C2414yes—
1128C2×C42C2414yes—
1129C2×C42C2414yes—
1130C2×C42C2411yescharacteristic
1131#95C2412yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2412yes—
1136#95C2411yescharacteristic
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2412yes—
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195C24—24no—
1196C24—24no—
1197C24—42no—
1198C24—42no—
1199C24—42no—
1200C24—42no—
1201C24—42no—
1202C24C2512yes—
1203C24C2512yes—
1204C24C2511yescharacteristic
1205C24C2512yes—
1206C24C2511yescharacteristic
1207#41—416no—
1208C2×Q8—22no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—22no—
1214C2×Q8—22no—
1215C2×Q8—22no—
1216C2×Q8—22no—
1217C2×Q8—42no—
1218C2×Q8—42no—
1219C2×Q8—44no—
1220C2×Q8—44no—
1221C2×Q8—44no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8—44no—
1225C2×Q8H(5,𝔽2)14yes—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—28no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—24no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—41no—
1248C2×D4—42no—
1249C2×D4—44no—
1250C2×D4—44no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—42no—
1256C2×D4—42no—
1257C2×D4—44no—
1258C2×D4—416no—
1259C2×D42−1+414yes—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—22no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—24no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—22no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—42no—
1289C22×C4—41no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—816no—
1311C22×C42−1+414yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2512yes—
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2514yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2512yes—
1327C22×C4C2512yes—
1328C22×C4C2514yes—
1329C22×C4C2514yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2511yescharacteristic
1334C22×C4C2514yes—
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C22×C4C2512yes—
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—22no—
1345C4⋊C4—24no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—28no—
1355C4⋊C4—28no—
1356C4⋊C4—22no—
1357C4⋊C4—24no—
1358C4⋊C4—28no—
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—24no—
1370C4⋊C4—22no—
1371C4⋊C4—44no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—41no—
1389C4⋊C4—41no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—42no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—42no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—42no—
1408C4⋊C4—44no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—42no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C22⋊C4—22no—
1417C22⋊C4—24no—
1418C22⋊C4—28no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—22no—
1423C22⋊C4—28no—
1424C22⋊C4—24no—
1425C22⋊C4—24no—
1426C22⋊C4—24no—
1427C22⋊C4—24no—
1428C22⋊C4—28no—
1429C22⋊C4—24no—
1430C22⋊C4—28no—
1431C22⋊C4—22no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—42no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—42no—
1449C22⋊C4—41no—
1450C22⋊C4—41no—
1451C22⋊C4—44no—
1452C22⋊C4—41no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—44no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—42no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—42no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—22no—
1484C42—22no—
1485C42—22no—
1486C42—24no—
1487C42—22no—
1488C42—24no—
1489C42—24no—
1490C42—24no—
1491C42—28no—
1492C42—22no—
1493C42—22no—
1494C42—22no—
1495C42—24no—
1496C42—42no—
1497C42—42no—
1498C42—44no—
1499C42—41no—
1500C42—44no—
1501C42—44no—
1502C42—41no—
1503C42—44no—
1504C42—44no—
1505C42H(5,𝔽2)14yes—
1506C23—21no—
1507C23—22no—
1508C23—22no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—22no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—22no—
1519C23—21no—
1520C23—22no—
1521C23—21no—
1522C23—22no—
1523C23—21no—
1524C23—22no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—22no—
1529C23—22no—
1530C23—22no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—22no—
1535C23—22no—
1536C23—22no—
1537C23—22no—
1538C23—48no—
1539C23—48no—
1540C23—84no—
1541C23—84no—
1542C23—84no—
1543C23—84no—
1544C23—84no—
1545C23C2×2−1+414yes—
1546C23C2×2−1+412yes—
1547C23#58512yes—
1548C23C2611yescharacteristic
1549Q8—28no—
1550Q8—44no—
1551Q8—44no—
1552Q8—84no—
1553Q8—164no—
1554Q8—164no—
1555D4—28no—
1556D4—48no—
1557D4—44no—
1558D4—48no—
1559D4—48no—
1560D4—44no—
1561D4—44no—
1562D4—88no—
1563D4—84no—
1564D4—84no—
1565D4—88no—
1566C2×C4—21no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—28no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—24no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—24no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—24no—
1592C2×C4—24no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—24no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—24no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—24no—
1625C2×C4—21no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—24no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—21no—
1637C2×C4—24no—
1638C2×C4—21no—
1639C2×C4—24no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—24no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—21no—
1646C2×C4—22no—
1647C2×C4—21no—
1648C2×C4—48no—
1649C2×C4—44no—
1650C2×C4—44no—
1651C2×C4—48no—
1652C2×C4—48no—
1653C2×C4—44no—
1654C2×C4—48no—
1655C2×C4—44no—
1656C2×C4—82no—
1657C2×C4—84no—
1658C2×C4—84no—
1659C2×C4—84no—
1660C2×C4—84no—
1661C2×C4—164no—
1662C2×C4—164no—
1663C2×C4—164no—
1664C2×C4C2×H(5,𝔽2)12yes—
1665C2×C4C2×H(5,𝔽2)14yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4C2×H(5,𝔽2)12yes—
1668C2×C4C2×H(5,𝔽2)12yes—
1669C2×C4C2×2−1+412yes—
1670C2×C4C2×2−1+412yes—
1671C2×C4C2×2−1+412yes—
1672C2×C4#58512yes—
1673C22—24no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—24no—
1679C22—22no—
1680C22—24no—
1681C22—22no—
1682C22—41no—
1683C22—41no—
1684C22—42no—
1685C22—41no—
1686C22—42no—
1687C22—41no—
1688C22—41no—
1689C22—42no—
1690C22—41no—
1691C22—41no—
1692C22—41no—
1693C22—42no—
1694C22—42no—
1695C22—42no—
1696C22—42no—
1697C22—42no—
1698C22—42no—
1699C22—42no—
1700C22—42no—
1701C22—42no—
1702C22—42no—
1703C22—42no—
1704C22—42no—
1705C22—42no—
1706C22—42no—
1707C22—42no—
1708C22—816no—
1709C22C22×H(5,𝔽2)11yescharacteristic
1710C22C22×H(5,𝔽2)11yescharacteristic
1711C22C22×2−1+411yescharacteristic
1712C22C22×2−1+411yescharacteristic
1713C22C2×#58511yescharacteristic
1714C22C2×#58511yescharacteristic
1715C22H(7,𝔽2)11yescharacteristic
1716C4—22no—
1717C4—24no—
1718C4—22no—
1719C4—41no—
1720C4—42no—
1721C4—41no—
1722C4—42no—
1723C4—41no—
1724C4—42no—
1725C4—42no—
1726C4—42no—
1727C4—42no—
1728C4—41no—
1729C4—41no—
1730C4—42no—
1731C4—44no—
1732C4—41no—
1733C4—44no—
1734C4—42no—
1735C4—44no—
1736C4—42no—
1737C4—41no—
1738C4—41no—
1739C4—41no—
1740C4—42no—
1741C4—42no—
1742C4—44no—
1743C4—42no—
1744C4#353614yes—
1745C4#354114yes—
1746C2—42no—
1747C2—44no—
1748C2—42no—
1749C2—82no—
1750C2—82no—
1751C2C2×#354111yescharacteristic
1752C2C2×#353611yescharacteristic
1753C2#6275211yescharacteristic
1754C2#6292311yescharacteristic
1755C2#6294511yescharacteristic
1756C2#6295711yescharacteristic
1757C2#6301511yescharacteristic
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. #59655C2semidirect
2. #59397C2semidirect
3. #59314C2semidirect
4. #59245C2semidirect
5. #59024C2semidirect
6. #56693C2semidirect
7. #55908C2semidirect
8. #53017C2semidirect
9. #52982C2semidirect
10. #52975C2semidirect
11. #52963C2semidirect
12. #52498C2semidirect
13. #42827C2semidirect
14. #42790C2semidirect
15. #42642C2semidirect
16. #42606C2semidirect
17. #41189C2semidirect
18. #40102C2semidirect
19. #39908C2semidirect
20. #39690C2semidirect
21. #39379C2semidirect
22. #39193C2semidirect
23. #39126C2semidirect
24. #39125C2semidirect
25. #37671C2semidirect
26. #37636C2semidirect
27. #37620C2semidirect
28. #37524C2semidirect
29. #37476C2semidirect
30. #36456C2semidirect
31. #36189C2semidirect
32. #36154C2semidirect
33. #34935C2semidirect
34. #34724C2semidirect
35. #34700C2semidirect
36. C2×Q82C22semidirect
38. C2×#554C22semidirect
39. C2×#541C22semidirect
41. C2×#529C22semidirect
45. #2859C22semidirect
47. #2857C22semidirect
48. #2857C22semidirect
52. #2839C22semidirect
53. #2832C22semidirect
54. #2831C22semidirect
55. #2831C22semidirect
56. #2831C22semidirect
57. #2827C22semidirect
58. #2827C22semidirect
59. #2827C22semidirect
62. #2823C22semidirect
63. #2822C22semidirect
64. #2807C22semidirect
67. #2779C22semidirect
68. #2777C22semidirect
69. #2769C22semidirect
71. #2757C22semidirect
73. #2750C22semidirect
75. #2732C22semidirect
77. #2729C22semidirect
78. #2725C22semidirect
79. #2725C22semidirect
80. #2720C22semidirect
81. #2716C22semidirect
82. #2708C22semidirect
85. #2704C22semidirect
86. #2704C22semidirect
88. #2702C22semidirect
89. #2702C22semidirect
90. #2700C22semidirect
93. #2692C22semidirect
97. #2681C22semidirect
99. #2674C22semidirect
100. #2672C22semidirect
101. #2667C22semidirect
102. #2665C22semidirect
103. #2664C22semidirect
104. #2654C22semidirect
105. #2652C22semidirect
108. #2632C22semidirect
109. #2629C22semidirect
110. #2629C22semidirect
111. #2629C22semidirect
112. #2629C22semidirect
113. #2628C22semidirect
114. #2628C22semidirect
115. #2628C22semidirect
118. #2625C22semidirect
120. #2624C22semidirect
122. #2620C22semidirect
123. #2618C22semidirect
124. #2589C22semidirect
125. #2588C22semidirect
126. #2582C22semidirect
127. #2578C22semidirect
128. #2577C22semidirect
129. #2570C22semidirect
130. #2569C22semidirect
131. #2568C22semidirect
134. #2563C22semidirect
135. #2562C22semidirect
136. #2562C22semidirect
137. #2551C22semidirect
138. #2550C22semidirect
139. #2550C22semidirect
140. #2549C22semidirect
141. #2547C22semidirect
147. #2538C22semidirect
152. #2536C22semidirect
153. #2536C22semidirect
158. #2511C22semidirect
159. #2511C22semidirect
160. #2509C22semidirect
161. #2507C22semidirect
162. #2506C22semidirect
163. #2506C22semidirect
164. #2506C22semidirect
165. #2504C22semidirect
168. #2495C22semidirect
169. #2495C22semidirect
170. #2495C22semidirect
171. #2495C22semidirect
173. #2492C22semidirect
176. #2491C22semidirect
177. #2490C22semidirect
180. #2487C22semidirect
183. #2478C22semidirect
185. #2470C22semidirect
187. #2468C22semidirect
189. #2466C22semidirect
190. #2460C22semidirect
191. #2460C22semidirect
196. #2454C22semidirect
197. #2453C22semidirect
198. #2453C22semidirect
201. #2452C22semidirect
203. #2450C22semidirect
204. #2449C22semidirect
207. #2447C22semidirect
210. #2442C22semidirect
211. #2442C22semidirect
212. #2442C22semidirect
215. #2440C22semidirect
216. #2440C22semidirect
217. #2440C22semidirect
220. #2439C22semidirect
224. #2429C22semidirect
225. #2429C22semidirect
226. #2429C22semidirect
229. #2427C22semidirect
230. #2426C22semidirect
233. #2423C22semidirect
234. #2422C22semidirect
235. #2421C22semidirect
236. #2421C22semidirect
237. #2421C22semidirect
243. #2417C22semidirect
244. #2417C22semidirect
246. #2416C22semidirect
247. #2416C22semidirect
257. #2369C22semidirect
259. #2364C22semidirect
262. #2360C22semidirect
263. #2360C22semidirect
264. #2355C22semidirect
266. #2351C22semidirect
267. Q8×C4⋊C4C22semidirect
268. Q8×C4⋊C4C22semidirect
271. #2345C22semidirect
274. #2337C22semidirect
277. #2323C22semidirect
278. C4×C4⋊Q8C22semidirect
279. C4×C4⋊Q8C22semidirect
283. C4×C22⋊Q8C22semidirect
284. C4×C22⋊Q8C22semidirect
285. C4×#123C22semidirect
290. #2296C22semidirect
292. #2293C22semidirect
294. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#596552
#593972
#593142
#592452
#590242
#566932
#559082
#530172
#529822
#529752
#529632
#524982
#428272
#427902
#426422
#426062
#411892
#401022
#399082
#396902
#393792
#391932
#391262
#391252
#376712
#376362
#376202
#375242
#374762
#364562
#361892
#361542
#349352
#347242
#347002