Finite Group Databasebeta

← #7709171

Subgroups — #7709171

Order 512.

5218 conjugacy classes of subgroups.

The subgroup lattice has 1774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59638C212yesmaximal, complemented
2#59455C212yesmaximal, complemented
3#59259C211yesmaximal, characteristic, complemented
4#59245C211yesmaximal, characteristic, complemented
5#59078C211yesmaximal, characteristic, complemented
6#59064C211yesmaximal, characteristic, complemented
7#45745C214yesmaximal, complemented
8#45662C212yesmaximal, complemented
9#45619C212yesmaximal, complemented
10#40423C214yesmaximal, complemented
11#40119C212yesmaximal, complemented
12#40047C212yesmaximal, complemented
13#40031C212yesmaximal, complemented
14#39980C212yesmaximal, complemented
15#39726C211yesmaximal, characteristic, complemented
16#39599C211yesmaximal, characteristic, complemented
17#39478C211yesmaximal, characteristic, complemented
18#39351C211yesmaximal, characteristic, complemented
19#38609C214yesmaximal, complemented
20#37851C212yesmaximal, complemented
21#37665C212yesmaximal, complemented
22#37524C212yesmaximal, complemented
23#36954C214yesmaximal, complemented
24#36625C211yesmaximal, characteristic, complemented
25#36624C211yesmaximal, characteristic
26#36580C211yesmaximal, characteristic, complemented
27#36577C211yesmaximal, characteristic, complemented
28#36148C212yesmaximal, complemented
29#36143C212yesmaximal, complemented
30#36133C211yesmaximal, characteristic, complemented
31#36117C211yesmaximal, characteristic, complemented
32#35241C212yesmaximal, complemented
33#35083C212yesmaximal, complemented
34#34419C212yesmaximal, complemented
35C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic, complemented
37C2×#557C2211yescharacteristic, complemented
38C2×#542C2212yes—
39C2×#533C2211yescharacteristic
40C2×#533C2212yes—
41C2×#532C2211yescharacteristic
42C2×#529C2212yes—
43C2×#525C2212yes—
44C22×C22⋊Q8C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46C23×C42C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2856C2211yescharacteristic
55#2856C2211yescharacteristic
56#2855C2212yes—
57#2855C2211yescharacteristic
58#2855C2211yescharacteristic
59#2855C2212yes—
60#2854C2212yes—
61#2854C2212yes—
62#2854C2212yes—
63#2851C2212yes—
64#2851C2212yes—
65#2850C2212yes—
66#2850C2212yes—
67#2850C2212yes—
68#2848C2211yescharacteristic
69#2848C2211yescharacteristic
70#2848C2212yes—
71#2847C2212yes—
72#2847C2212yes—
73#2827C2214yes—
74#2827C2214yes—
75#2798C2214yescomplemented
76#2798C2214yescomplemented
77#2788C2214yes—
78#2788C2214yescomplemented
79#2783C2214yescomplemented
80#2781C2214yes—
81#2779C2214yes—
82#2768C2214yes—
83#2768C2214yescomplemented
84#2767C2214yescomplemented
85#2754C2214yescomplemented
86#2748C2214yes—
87#2747C2214yes—
88#2747C2214yescomplemented
89#2744C2214yescomplemented
90#2743C2214yes—
91#2741C2214yes—
92#2740C2214yes—
93#2732C2214yes—
94#2726C2214yescomplemented
95#2723C2214yescomplemented
96#2711C2214yes—
97#2708C2214yes—
98#2707C2214yescomplemented
99#2704C2214yes—
100#2702C2214yes—
101#2700C2214yes—
102#2692C2214yes—
103#2692C2214yes—
104#2687C2214yes—
105#2681C2214yes—
106#2672C2214yes—
107#2667C2214yescomplemented
108#2664C2214yescomplemented
109#2664C2214yescomplemented
110#2654C2214yescomplemented
111#2652C2214yescomplemented
112#2650C2214yescomplemented
113#2629C2212yes—
114#2625C2212yes—
115#2624C2212yes—
116#2620C2212yes—
117#2607C2214yescomplemented
118#2592C2212yescomplemented
119#2592C2212yescomplemented
120#2589C2214yescomplemented
121#2588C2214yescomplemented
122#2587C2214yescomplemented
123#2585C2214yescomplemented
124#2584C2212yescomplemented
125#2582C2212yescomplemented
126#2582C2211yescharacteristic, complemented
127#2582C2211yescharacteristic, complemented
128#2582C2212yescomplemented
129#2580C2212yescomplemented
130#2568C2212yescomplemented
131#2568C2212yescomplemented
132#2568C2211yescharacteristic, complemented
133#2565C2212yescomplemented
134#2565C2212yescomplemented
135#2558C2214yes—
136#2553C2214yes—
137#2552C2211yescharacteristic, complemented
138#2551C2211yescharacteristic, complemented
139#2549C2214yescomplemented
140#2548C2211yescharacteristic, complemented
141#2548C2211yescharacteristic, complemented
142#2547C2212yescomplemented
143#2546C2211yescharacteristic, complemented
144#2546C2212yescomplemented
145#2545C2212yescomplemented
146#2545C2212yescomplemented
147#2542C2212yescomplemented
148#2538C2212yescomplemented
149#2534C2214yes—
150#2512C2212yescomplemented
151#2512C2212yescomplemented
152#2511C2212yescomplemented
153#2511C2212yescomplemented
154#2511C2212yescomplemented
155#2509C2212yescomplemented
156#2508C2212yescomplemented
157#2508C2212yescomplemented
158#2507C2212yescomplemented
159#2506C2212yescomplemented
160#2501C2212yes—
161#2498C2214yes—
162#2498C2214yes—
163#2497C2212yes—
164#2497C2212yes—
165#2492C2212yes—
166#2491C2212yes—
167#2490C2212yes—
168#2489C2212yes—
169#2488C2214yes—
170#2481C2214yes—
171#2479C2214yescomplemented
172#2472C2214yes—
173#2470C2214yes—
174#2466C2214yes—
175#2462C2214yescomplemented
176#2460C2214yes—
177#2460C2214yescomplemented
178#2458C2214yes—
179#2458C2214yescomplemented
180#2454C2212yescomplemented
181#2454C2212yescomplemented
182#2453C2214yescomplemented
183#2453C2212yescomplemented
184#2452C2212yescomplemented
185#2452C2212yescomplemented
186#2451C2212yescomplemented
187#2451C2212yescomplemented
188#2450C2214yes—
189#2449C2214yes—
190#2448C2212yescomplemented
191#2448C2212yescomplemented
192#2448C2212yescomplemented
193#2448C2212yescomplemented
194#2447C2212yescomplemented
195#2447C2212yescomplemented
196#2446C2212yescomplemented
197#2443C2214yes—
198#2442C2212yes—
199#2442C2214yes—
200#2441C2212yes—
201#2440C2212yes—
202#2439C2212yes—
203#2438C2214yes—
204#2436C2212yes—
205#2432C2212yes—
206#2432C2212yes—
207#2429C2212yes—
208#2429C2212yes—
209#2427C2212yes—
210#2427C2212yes—
211#2426C2212yes—
212#2426C2212yes—
213#2425C2214yes—
214#2423C2212yes—
215#2422C2212yes—
216#2421C2212yes—
217#2420C2212yes—
218#2419C2214yes—
219#2419C2214yes—
220#2419C2214yescomplemented
221#2418C2214yes—
222#2417C2214yes—
223#2417C2214yes—
224#2411C2214yes—
225#2379C2214yes—
226#2376C2214yes—
227#2369C2212yescomplemented
228#2367C2214yes—
229#2367C2212yescomplemented
230#2367C2212yescomplemented
231#2366C2211yescharacteristic, complemented
232#2365C2211yescharacteristic, complemented
233#2365C2212yescomplemented
234#2362C2212yes—
235#2362C2212yes—
236#2361C2212yes—
237#2361C2212yes—
238#2359C2214yes—
239#2359C2214yes—
240#2355C2211yescharacteristic, complemented
241#2355C2212yescomplemented
242#2354C2212yescomplemented
243#2351C2212yescomplemented
244Q8×C4⋊C4C2211yescharacteristic, complemented
245Q8×C4⋊C4C2211yescharacteristic, complemented
246Q8×C4⋊C4C2211yescharacteristic, complemented
247#2349C2214yes—
248#2349C2212yescomplemented
249#2344C2212yes—
250#2341C2212yes—
251Q8×C22⋊C4C2212yes—
252#2339C2212yes—
253#2334C2214yescomplemented
254#2334C2214yescomplemented
255#2332C2214yescomplemented
256#2329C2214yescomplemented
257#2324C2212yes—
258#2323C2212yes—
259#2323C2214yescomplemented
260#2323C2214yescomplemented
261#2314C2212yes—
262C4×C22⋊Q8C2212yes—
263C4×C22⋊Q8C2211yescharacteristic
264C4×C22⋊Q8C2211yescharacteristic
265C4×C22⋊Q8C2212yes—
266C4×C22⋊Q8C2211yescharacteristic
267C4×C22⋊Q8C2212yes—
268C4×C22⋊Q8C2211yescharacteristic
269C4×C22⋊Q8C2212yes—
270C4×C22⋊Q8C2211yescharacteristic
271C4×C22⋊Q8C2212yes—
272C4×C22⋊Q8C2212yes—
273C4×C22⋊Q8C2211yescharacteristic
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2211yescharacteristic
277C4×C22⋊Q8C2211yescharacteristic
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2211yescharacteristic
280C4×C22⋊Q8C2212yes—
281C4×#121C2212yes—
282C4×#121C2212yes—
283C4×#121C2212yes—
284C4×#121C2212yes—
285C4×#121C2212yes—
286#2297C2212yes—
287#2296C2212yes—
288C2×#391C2211yescharacteristic
289C2×#389C2211yescharacteristic
290C2×#387C2212yes—
291C2×#385C2212yes—
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic
294#2280C2212yes—
295C2×#380C2211yescharacteristic
296C2×C4×C4⋊C4C2212yes—
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C22⋊C4C2212yes—
299C22×#41C2312yes—
300C23×Q8C2311yescharacteristic
301C24×C4C2311yescharacteristic
302C24×C4C2311yescharacteristic
303C24×C4C2311yescharacteristic
304#559—44no—
305#557—44no—
306#542—216no—
307#533—44no—
308#533—48no—
309#532—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×#127C2311yescharacteristic
318#529—48no—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2312yes—
324C2×#125C2314yes—
325C2×#125C2314yes—
326C2×#124C2314yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332#525—48no—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×C22⋊Q8—28no—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2311yescharacteristic
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2314yes—
359C2×C22⋊Q8C2311yescharacteristic
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#120C2314yes—
369C2×C4×Q8—44no—
370C2×C4×Q8C2311yescharacteristic
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2312yes—
380C2×C4×Q8C2314yes—
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2311yescharacteristic
384C2×C4×Q8C2311yescharacteristic
385C2×C4×Q8C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2314yes—
392C2×C4×D4C2314yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2314yes—
395C2×C4×D4C2312yes—
396C2×#117C2312yes—
397C2×#117C2312yes—
398C2×#117C2314yes—
399C2×#117C2314yes—
400C2×#117C2312yes—
401C22×C4⋊C4C2311yescharacteristic
402C22×C4⋊C4C2311yescharacteristic
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2311yescharacteristic
405C22×C4⋊C4C2312yes—
406C22×C4⋊C4C2312yes—
407C22×C22⋊C4C2312yes—
408C22×C22⋊C4C2312yes—
409C22×C42—44no—
410C22×C42C2312yes—
411C22×C42C2311yescharacteristic
412C22×C42C2311yescharacteristic
413C22×C42C2311yescharacteristic
414C22×C42C2311yescharacteristic
415C22×C42C2311yescharacteristic
416C22×C42C2312yes—
417C22×C42C2311yescharacteristic
418C22×C42C2311yescharacteristic
419C22×C42C2311yescharacteristic
420C22×C42C2311yescharacteristic
421C22×C42C2311yescharacteristic
422C22×C42C2311yescharacteristic
423C22×C42C2311yescharacteristic
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2314yes—
441#399C2314yes—
442#399C2314yes—
443#399C2314yes—
444#398C2314yes—
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#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#395C2314yes—
487#395C2314yes—
488#395C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#391C2311yescharacteristic
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2311yescharacteristic
510#391C2311yescharacteristic
511#391C2312yes—
512#391C2314yes—
513#391C2314yes—
514#391C2312yes—
515#391C2314yes—
516#391C2312yes—
517#391C2312yes—
518#391C2311yescharacteristic
519#391C2314yes—
520#391C2312yes—
521#391C2314yes—
522#391C2314yes—
523#391C2314yes—
524#391C2312yes—
525#391C2312yes—
526#391C2311yescharacteristic
527#391C2311yescharacteristic
528#391C2312yes—
529#391C2312yes—
530#391C2312yes—
531#391C2311yescharacteristic
532#391C2312yes—
533#391C2311yescharacteristic
534#391C2312yes—
535#390C2312yes—
536#390C2314yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2314yes—
544#390C2314yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#389C2314yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2311yescharacteristic
561#389C2312yes—
562#389C2311yescharacteristic
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#389C2314yes—
569#389C2311yescharacteristic
570#389C2314yes—
571#389C2312yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2312yes—
579#389C2312yes—
580#389C2314yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2311yescharacteristic
587#389C2311yescharacteristic
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2311yescharacteristic
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2311yescharacteristic
597#389C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2312yes—
635#387C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2312yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#385C2312yes—
681#385C2312yes—
682#385C2312yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2312yes—
693#385C2312yes—
694#385C2312yes—
695#385C2312yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2312yes—
705#385C2314yes—
706#385C2312yes—
707#385C2312yes—
708#385C2312yes—
709#385C2312yes—
710#385C2312yes—
711#385C2312yes—
712#384C2311yescharacteristic
713#384C2312yes—
714#384C2312yes—
715#384C2311yescharacteristic
716#384C2311yescharacteristic
717#384C2312yes—
718#384C2311yescharacteristic
719#384C2312yes—
720#382C2312yes—
721#382C2312yes—
722#382C2312yes—
723#382C2314yes—
724#382C2314yes—
725#382C2312yes—
726#382C2314yes—
727#381C2314yes—
728#381C2314yes—
729#381C2312yes—
730#381C2312yes—
731#381C2314yes—
732#380C2311yescharacteristic
733#380C2312yes—
734#380C2314yes—
735#380C2314yes—
736#380C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746#380C2312yes—
747#380C2311yescharacteristic
748#380C2311yescharacteristic
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2312yes—
755#380C2314yes—
756#380C2314yes—
757#380C2314yes—
758#380C2314yes—
759#380C2311yescharacteristic
760#380C2311yescharacteristic
761#380C2312yes—
762#380C2312yes—
763#380C2311yescharacteristic
764#379C2312yes—
765#379C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2314yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C2×#95C2314yes—
816C2×#95C2312yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C2×#95C2312yes—
820C2×#95C2312yes—
821C25C2411yescharacteristic
822C2×#41—28no—
823C2×#41—44no—
824C2×#41—44no—
825C22×Q8—24no—
826C22×Q8—24no—
827C22×Q8—42no—
828C22×Q8C2411yescharacteristic
829C22×Q8C2411yescharacteristic
830C22×Q8C2411yescharacteristic
831C22×Q8C2412yes—
832C22×Q8C2412yes—
833C22×Q8C2411yescharacteristic
834C22×Q8C2412yes—
835C22×Q8C2414yes—
836C22×D4C2414yes—
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2414yes—
840C22×D4C2412yes—
841C22×D4C2414yes—
842C23×C4—24no—
843C23×C4—24no—
844C23×C4—24no—
845C23×C4—24no—
846C23×C4—42no—
847C23×C4—42no—
848C23×C4—42no—
849C23×C4—42no—
850C23×C4—42no—
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2411yescharacteristic
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2412yes—
870C23×C4C2414yes—
871C23×C4C2414yes—
872C23×C4C2411yescharacteristic
873C23×C4C2411yescharacteristic
874C23×C4C2414yes—
875C23×C4C2411yescharacteristic
876C4⋊Q8—28no—
877C4⋊Q8—24no—
878C4⋊Q8—42no—
879C4⋊Q8—44no—
880C4⋊Q8—42no—
881C4⋊Q8—44no—
882C4⋊Q8—44no—
883#127—24no—
884#126—216no—
885#126—48no—
886#125—44no—
887#125—44no—
888#125—48no—
889#125—44no—
890#125—48no—
891#124—28no—
892#124—216no—
893#124—44no—
894#124—44no—
895#124—44no—
896#124—44no—
897#123—216no—
898#123—48no—
899#123—48no—
900#123—48no—
901#123—48no—
902C22⋊Q8—24no—
903C22⋊Q8—24no—
904C22⋊Q8—28no—
905C22⋊Q8—24no—
906C22⋊Q8—24no—
907C22⋊Q8—24no—
908C22⋊Q8—24no—
909C22⋊Q8—24no—
910C22⋊Q8—28no—
911C22⋊Q8—216no—
912C22⋊Q8—28no—
913C22⋊Q8—44no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—48no—
917C22⋊Q8—44no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—42no—
921C22⋊Q8—42no—
922C22⋊Q8#4118yescomplemented
923#121—28no—
924#121—28no—
925#121—28no—
926#121—44no—
927#121—44no—
928#121—44no—
929#121—44no—
930#121—44no—
931#120—48no—
932C4×Q8—28no—
933C4×Q8—24no—
934C4×Q8—24no—
935C4×Q8—24no—
936C4×Q8—24no—
937C4×Q8—44no—
938C4×Q8—44no—
939C4×Q8—44no—
940C4×Q8—48no—
941C4×Q8—42no—
942C4×Q8—42no—
943C4×Q8—44no—
944C4×Q8—44no—
945C4×Q8—44no—
946C4×Q8—44no—
947C4×Q8—44no—
948C4×D4—28no—
949C4×D4—44no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—48no—
955C4×D4—48no—
956C4×D4—48no—
957C4×D4—48no—
958#117—28no—
959#117—44no—
960#117—48no—
961#117—48no—
962#117—44no—
963C2×C4⋊C4—24no—
964C2×C4⋊C4—24no—
965C2×C4⋊C4—28no—
966C2×C4⋊C4—44no—
967C2×C4⋊C4—42no—
968C2×C4⋊C4—44no—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2411yescharacteristic
1043C2×C4⋊C4C2412yes—
1044C2×C22⋊C4—28no—
1045C2×C22⋊C4—44no—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2412yes—
1091C2×C42—28no—
1092C2×C42—24no—
1093C2×C42—24no—
1094C2×C42—24no—
1095C2×C42—44no—
1096C2×C42—42no—
1097C2×C42—42no—
1098C2×C42—42no—
1099C2×C42—42no—
1100C2×C42—42no—
1101C2×C42—42no—
1102C2×C42—42no—
1103C2×C42—42no—
1104C2×C42—42no—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2414yes—
1121C2×C42C2411yescharacteristic
1122C2×C42C2412yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2414yes—
1126C2×C42C2414yes—
1127C2×C42C2414yes—
1128C2×C42C2414yes—
1129C2×C42C2414yes—
1130C2×C42C2414yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2411yescharacteristic
1138C2×C42C2411yescharacteristic
1139C2×C42C2411yescharacteristic
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#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208C24—22no—
1209C24—22no—
1210C24—22no—
1211C24—22no—
1212C24—22no—
1213C24—41no—
1214C24—41no—
1215C24C2514yes—
1216C24C2511yescharacteristic
1217C24C2511yescharacteristic
1218C24C2511yescharacteristic
1219#41—816no—
1220C2×Q8—24no—
1221C2×Q8—22no—
1222C2×Q8—28no—
1223C2×Q8—22no—
1224C2×Q8—22no—
1225C2×Q8—22no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—24no—
1230C2×Q8—24no—
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—24no—
1235C2×Q8—22no—
1236C2×Q8—24no—
1237C2×Q8—24no—
1238C2×Q8—42no—
1239C2×Q8—42no—
1240C2×Q8—44no—
1241C2×Q8—44no—
1242C2×Q8—42no—
1243C2×Q8—416no—
1244C2×Q8C2×#4114yes—
1245C2×D4—28no—
1246C2×D4—28no—
1247C2×D4—28no—
1248C2×D4—28no—
1249C2×D4—28no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—44no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—42no—
1261C2×D4—42no—
1262C2×D4—44no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—22no—
1275C22×C4—24no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—24no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—28no—
1306C22×C4—28no—
1307C22×C4—41no—
1308C22×C4—41no—
1309C22×C4—41no—
1310C22×C4—41no—
1311C22×C4—41no—
1312C22×C4—41no—
1313C22×C4—41no—
1314C22×C4—41no—
1315C22×C4—41no—
1316C22×C4—42no—
1317C22×C4—42no—
1318C22×C4—41no—
1319C22×C4—41no—
1320C22×C4—41no—
1321C22×C4—41no—
1322C22×C4—41no—
1323C22×C4—41no—
1324C22×C4—41no—
1325C22×C4—416no—
1326C22×C4—416no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—44no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—44no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4—44no—
1336C22×C4—416no—
1337C22×C4C2×#4114yes—
1338C22×C4H(5,𝔽2)14yes—
1339C22×C42−1+414yes—
1340C22×C42−1+414yes—
1341C22×C4C2511yescharacteristic
1342C22×C4C2512yes—
1343C22×C4C2512yes—
1344C22×C4C2512yes—
1345C22×C4C2512yes—
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2511yescharacteristic
1349C22×C4C2512yes—
1350C22×C4C2514yes—
1351C22×C4C2512yes—
1352C22×C4C2514yes—
1353C22×C4C2512yes—
1354C22×C4C2512yes—
1355C22×C4C2514yes—
1356C22×C4C2512yes—
1357C22×C4C2512yes—
1358C22×C4C2512yes—
1359C22×C4C2512yes—
1360C22×C4C2512yes—
1361C22×C4C2512yes—
1362C22×C4C2512yes—
1363C22×C4C2511yescharacteristic
1364C22×C4C2512yes—
1365C22×C4C2511yescharacteristic
1366C22×C4C2511yescharacteristic
1367C22×C4C2511yescharacteristic
1368C22×C4C2511yescharacteristic
1369C22×C4C2511yescharacteristic
1370C22×C4C2511yescharacteristic
1371C22×C4C2511yescharacteristic
1372C4⋊C4—24no—
1373C4⋊C4—22no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—24no—
1379C4⋊C4—24no—
1380C4⋊C4—28no—
1381C4⋊C4—28no—
1382C4⋊C4—22no—
1383C4⋊C4—24no—
1384C4⋊C4—24no—
1385C4⋊C4—22no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—24no—
1392C4⋊C4—28no—
1393C4⋊C4—24no—
1394C4⋊C4—22no—
1395C4⋊C4—24no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—22no—
1399C4⋊C4—24no—
1400C4⋊C4—22no—
1401C4⋊C4—22no—
1402C4⋊C4—24no—
1403C4⋊C4—22no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—24no—
1408C4⋊C4—24no—
1409C4⋊C4—24no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—44no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4—44no—
1420C4⋊C4—44no—
1421C4⋊C4—44no—
1422C4⋊C4—44no—
1423C4⋊C4—42no—
1424C4⋊C4—42no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—42no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—42no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—42no—
1441C4⋊C4—42no—
1442C4⋊C4—44no—
1443C4⋊C4—44no—
1444C4⋊C4—44no—
1445C4⋊C4C2×#4114yes—
1446C4⋊C4C2×#4118yes—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—28no—
1452C22⋊C4—24no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—24no—
1459C22⋊C4—28no—
1460C22⋊C4—28no—
1461C22⋊C4—28no—
1462C22⋊C4—28no—
1463C22⋊C4—28no—
1464C22⋊C4—28no—
1465C22⋊C4—28no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—42no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—42no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—44no—
1491C22⋊C4C2×#4118yes—
1492C42—24no—
1493C42—24no—
1494C42—28no—
1495C42—22no—
1496C42—22no—
1497C42—22no—
1498C42—22no—
1499C42—22no—
1500C42—22no—
1501C42—22no—
1502C42—22no—
1503C42—22no—
1504C42—24no—
1505C42—24no—
1506C42—24no—
1507C42—24no—
1508C42—24no—
1509C42—24no—
1510C42—24no—
1511C42—24no—
1512C42—41no—
1513C42—41no—
1514C42—41no—
1515C42—41no—
1516C42—41no—
1517C42—41no—
1518C42—42no—
1519C42—42no—
1520C42—44no—
1521C42—44no—
1522C42—44no—
1523C42—44no—
1524C42—44no—
1525C42—44no—
1526C42H(5,𝔽2)14yes—
1527C23—21no—
1528C23—21no—
1529C23—21no—
1530C23—21no—
1531C23—28no—
1532C23—21no—
1533C23—21no—
1534C23—21no—
1535C23—21no—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—24no—
1545C23—24no—
1546C23—24no—
1547C23—24no—
1548C23—24no—
1549C23—24no—
1550C23—24no—
1551C23—44no—
1552C23—44no—
1553C23—44no—
1554C23—44no—
1555C23—44no—
1556C23—44no—
1557C23C22×#4112yes—
1558C23C2×H(5,𝔽2)12yes—
1559C23C2×2−1+412yes—
1560C23C2×2−1+412yes—
1561C23#58512yes—
1562C23C2611yescharacteristic
1563Q8—28no—
1564Q8—48no—
1565Q8—44no—
1566Q8—44no—
1567Q8—44no—
1568Q8—48no—
1569Q8—88no—
1570Q8—84no—
1571D4—416no—
1572D4—48no—
1573D4—48no—
1574D4—84no—
1575D4—88no—
1576D4—88no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—28no—
1594C2×C4—28no—
1595C2×C4—28no—
1596C2×C4—28no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—24no—
1621C2×C4—24no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—24no—
1625C2×C4—24no—
1626C2×C4—22no—
1627C2×C4—21no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—24no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—24no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—24no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—22no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—44no—
1661C2×C4—44no—
1662C2×C4—44no—
1663C2×C4—48no—
1664C2×C4—44no—
1665C2×C4—44no—
1666C2×C4—44no—
1667C2×C4—44no—
1668C2×C4—44no—
1669C2×C4—44no—
1670C2×C4—48no—
1671C2×C4—44no—
1672C2×C4—44no—
1673C2×C4—44no—
1674C2×C4—48no—
1675C2×C4—44no—
1676C2×C4—44no—
1677C2×C4—88no—
1678C2×C4—88no—
1679C2×C4—84no—
1680C2×C4—164no—
1681C2×C4C22×#4114yes—
1682C2×C4C22×#4112yes—
1683C2×C4C22×#4114yes—
1684C2×C4C22×#4112yes—
1685C2×C4C2×H(5,𝔽2)12yes—
1686C2×C4C2×H(5,𝔽2)12yes—
1687C2×C4C2×H(5,𝔽2)12yes—
1688C2×C4C2×H(5,𝔽2)12yes—
1689C2×C4C2×H(5,𝔽2)12yes—
1690C2×C4C2×2−1+412yes—
1691C2×C4C2×2−1+412yes—
1692C2×C4C2×2−1+412yes—
1693C2×C4C2×2−1+412yes—
1694C2×C4#58512yes—
1695C22—22no—
1696C22—22no—
1697C22—22no—
1698C22—22no—
1699C22—22no—
1700C22—22no—
1701C22—22no—
1702C22—22no—
1703C22—22no—
1704C22—22no—
1705C22—22no—
1706C22—22no—
1707C22—416no—
1708C22—41no—
1709C22—41no—
1710C22—41no—
1711C22—41no—
1712C22—41no—
1713C22—41no—
1714C22—41no—
1715C22—41no—
1716C22—44no—
1717C22—44no—
1718C22—44no—
1719C22—44no—
1720C22—44no—
1721C22—44no—
1722C22—44no—
1723C22#355414yes—
1724C22C23×#4111yescharacteristic
1725C22C22×H(5,𝔽2)11yescharacteristic
1726C22C22×H(5,𝔽2)11yescharacteristic
1727C22C22×2−1+411yescharacteristic
1728C22C22×2−1+411yescharacteristic
1729C22C2×#58511yescharacteristic
1730C22C2×#58511yescharacteristic
1731C4—22no—
1732C4—22no—
1733C4—22no—
1734C4—22no—
1735C4—24no—
1736C4—24no—
1737C4—22no—
1738C4—22no—
1739C4—41no—
1740C4—44no—
1741C4—42no—
1742C4—42no—
1743C4—42no—
1744C4—42no—
1745C4—44no—
1746C4—41no—
1747C4—42no—
1748C4—42no—
1749C4—42no—
1750C4—42no—
1751C4—42no—
1752C4—44no—
1753C4—42no—
1754C4—41no—
1755C4—41no—
1756C4—42no—
1757C4—42no—
1758C4—42no—
1759C4—42no—
1760C4#352014yes—
1761C4#353614yes—
1762C2—24no—
1763C2—42no—
1764C2—42no—
1765C2—84no—
1766C2C2×#353611yescharacteristic
1767C2C2×#355411yescharacteristic
1768C2C2×#352011yescharacteristic
1769C2#6278811yescharacteristic
1770C2#6280011yescharacteristic
1771C2#6282111yescharacteristic
1772C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59638C2semidirect
2. #59455C2semidirect
3. #59259C2semidirect
4. #59245C2semidirect
5. #59078C2semidirect
6. #59064C2semidirect
7. #45745C2semidirect
8. #45662C2semidirect
9. #45619C2semidirect
10. #40423C2semidirect
11. #40119C2semidirect
12. #40047C2semidirect
13. #40031C2semidirect
14. #39980C2semidirect
15. #39726C2semidirect
16. #39599C2semidirect
17. #39478C2semidirect
18. #39351C2semidirect
19. #38609C2semidirect
20. #37851C2semidirect
21. #37665C2semidirect
22. #37524C2semidirect
23. #36954C2semidirect
24. #36625C2semidirect
26. #36580C2semidirect
27. #36577C2semidirect
28. #36148C2semidirect
29. #36143C2semidirect
30. #36133C2semidirect
31. #36117C2semidirect
32. #35241C2semidirect
33. #35083C2semidirect
34. #34419C2semidirect
35. C2×C4×C22⋊Q8C2semidirect
36. C2×#559C22semidirect
37. C2×#557C22semidirect
75. #2798C22semidirect
76. #2798C22semidirect
78. #2788C22semidirect
79. #2783C22semidirect
83. #2768C22semidirect
84. #2767C22semidirect
85. #2754C22semidirect
88. #2747C22semidirect
89. #2744C22semidirect
94. #2726C22semidirect
95. #2723C22semidirect
98. #2707C22semidirect
107. #2667C22semidirect
108. #2664C22semidirect
109. #2664C22semidirect
110. #2654C22semidirect
111. #2652C22semidirect
112. #2650C22semidirect
117. #2607C22semidirect
118. #2592C22semidirect
119. #2592C22semidirect
120. #2589C22semidirect
121. #2588C22semidirect
122. #2587C22semidirect
123. #2585C22semidirect
124. #2584C22semidirect
125. #2582C22semidirect
126. #2582C22semidirect
127. #2582C22semidirect
128. #2582C22semidirect
129. #2580C22semidirect
130. #2568C22semidirect
131. #2568C22semidirect
132. #2568C22semidirect
133. #2565C22semidirect
134. #2565C22semidirect
137. #2552C22semidirect
138. #2551C22semidirect
139. #2549C22semidirect
140. #2548C22semidirect
141. #2548C22semidirect
142. #2547C22semidirect
143. #2546C22semidirect
144. #2546C22semidirect
145. #2545C22semidirect
146. #2545C22semidirect
147. #2542C22semidirect
148. #2538C22semidirect
150. #2512C22semidirect
151. #2512C22semidirect
152. #2511C22semidirect
153. #2511C22semidirect
154. #2511C22semidirect
155. #2509C22semidirect
156. #2508C22semidirect
157. #2508C22semidirect
158. #2507C22semidirect
159. #2506C22semidirect
171. #2479C22semidirect
175. #2462C22semidirect
177. #2460C22semidirect
179. #2458C22semidirect
180. #2454C22semidirect
181. #2454C22semidirect
182. #2453C22semidirect
183. #2453C22semidirect
184. #2452C22semidirect
185. #2452C22semidirect
186. #2451C22semidirect
187. #2451C22semidirect
190. #2448C22semidirect
191. #2448C22semidirect
192. #2448C22semidirect
193. #2448C22semidirect
194. #2447C22semidirect
195. #2447C22semidirect
196. #2446C22semidirect
220. #2419C22semidirect
227. #2369C22semidirect
229. #2367C22semidirect
230. #2367C22semidirect
231. #2366C22semidirect
232. #2365C22semidirect
233. #2365C22semidirect
240. #2355C22semidirect
241. #2355C22semidirect
242. #2354C22semidirect
243. #2351C22semidirect
244. Q8×C4⋊C4C22semidirect
245. Q8×C4⋊C4C22semidirect
246. Q8×C4⋊C4C22semidirect
248. #2349C22semidirect
253. #2334C22semidirect
254. #2334C22semidirect
255. #2332C22semidirect
256. #2329C22semidirect
259. #2323C22semidirect
260. #2323C22semidirect
922. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#596382
#594552
#592592
#592452
#590782
#590642
#457452
#456622
#456192
#404232
#401192
#400472
#400312
#399802
#397262
#395992
#394782
#393512
#386092
#378512
#376652
#375242
#369542
#366252
#366242
#365802
#365772
#361482
#361432
#361332
#361172
#352412
#350832
#344192
C2×C4×C22⋊Q82