Finite Group Databasebeta

← #7633118

Subgroups — #7633118

Order 512.

5576 conjugacy classes of subgroups.

The subgroup lattice has 1786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36564C211yesmaximal, characteristic, complemented
2#36551C211yesmaximal, characteristic, complemented
3#36480C211yesmaximal, characteristic, complemented
4#36459C211yesmaximal, characteristic, complemented
5#36393C212yesmaximal, complemented
6#36369C212yesmaximal, complemented
7#36302C211yesmaximal, characteristic, complemented
8#36273C211yesmaximal, characteristic, complemented
9#36150C212yesmaximal, complemented
10#36142C212yesmaximal, complemented
11#36126C211yesmaximal, characteristic, complemented
12#36117C211yesmaximal, characteristic, complemented
13#36087C212yesmaximal, complemented
14#36000C212yesmaximal, complemented
15#35989C212yesmaximal, complemented
16#35814C214yesmaximal, complemented
17#35744C214yesmaximal, complemented
18#35682C212yesmaximal, complemented
19#35598C212yesmaximal, complemented
20#35597C212yesmaximal, complemented
21#35436C214yesmaximal, complemented
22#35421C214yesmaximal, complemented
23#35292C211yesmaximal, characteristic, complemented
24#35238C211yesmaximal, characteristic, complemented
25#35114C212yesmaximal, complemented
26#35107C212yesmaximal, complemented
27#34938C211yesmaximal, characteristic, complemented
28#34911C211yesmaximal, characteristic, complemented
29#34893C212yesmaximal, complemented
30#34889C212yesmaximal, complemented
31#34321C212yesmaximal, complemented
32#34316C212yesmaximal, complemented
33#34242C211yesmaximal, characteristic, complemented
34#34155C211yesmaximal, characteristic, complemented
35C4×#520C211yesmaximal, characteristic, complemented
36C2×#555C2212yes—
37C2×#547C2212yes—
38C2×#533C2212yes—
39C2×#532C2211yescharacteristic
40C2×#532C2212yes—
41C2×#529C2211yescharacteristic
42C2×#529C2212yes—
43C2×#520C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46#2863C2212yes—
47#2861C2212yes—
48#2860C2212yes—
49#2858C2212yes—
50#2857C2212yes—
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2856C2212yes—
54#2856C2211yescharacteristic
55#2856C2211yescharacteristic
56#2854C2212yes—
57#2854C2212yes—
58#2851C2212yes—
59#2850C2212yes—
60#2662C2214yes—
61#2651C2214yes—
62#2650C2214yes—
63#2632C2214yes—
64#2630C2214yes—
65#2624C2212yes—
66#2615C2212yes—
67#2610C2214yes—
68#2605C2214yes—
69#2604C2212yes—
70#2603C2212yes—
71#2602C2214yes—
72#2602C2212yes—
73#2602C2212yes—
74#2598C2214yes—
75#2597C2214yes—
76#2596C2214yes—
77#2595C2214yes—
78#2593C2214yes—
79#2592C2211yescharacteristic
80#2592C2212yes—
81#2589C2214yes—
82#2589C2214yes—
83#2587C2214yes—
84#2586C2214yes—
85#2584C2211yescharacteristic
86#2580C2212yes—
87#2578C2214yes—
88#2567C2211yescharacteristic
89#2566C2212yes—
90#2563C2211yescharacteristic
91#2562C2211yescharacteristic
92#2560C2214yes—
93#2560C2214yes—
94#2559C2214yes—
95#2559C2214yes—
96#2557C2214yes—
97#2555C2214yes—
98#2554C2214yes—
99#2552C2211yescharacteristic
100#2552C2211yescharacteristic
101#2551C2211yescharacteristic
102#2551C2211yescharacteristic
103#2550C2212yes—
104#2550C2212yes—
105#2549C2214yes—
106#2549C2214yes—
107#2548C2211yescharacteristic
108#2544C2212yes—
109#2541C2211yescharacteristic
110#2540C2214yes—
111#2540C2211yescharacteristic
112#2540C2212yes—
113#2535C2212yes—
114#2532C2214yes—
115#2531C2214yes—
116#2525C2214yes—
117#2522C2214yes—
118#2521C2214yes—
119#2521C2214yes—
120#2513C2212yes—
121#2512C2212yes—
122#2509C2212yes—
123#2509C2212yes—
124#2507C2212yes—
125#2507C2212yes—
126#2501C2212yes—
127#2500C2212yes—
128#2497C2212yes—
129#2497C2212yes—
130#2496C2212yes—
131#2495C2212yes—
132#2492C2212yes—
133#2491C2212yes—
134#2491C2212yes—
135#2491C2212yes—
136#2490C2212yes—
137#2490C2212yes—
138#2487C2212yes—
139#2485C2212yes—
140#2479C2214yes—
141#2479C2214yes—
142#2477C2214yes—
143#2477C2214yes—
144#2476C2214yes—
145#2476C2214yes—
146#2474C2214yes—
147#2470C2214yes—
148#2469C2214yes—
149#2465C2214yes—
150#2465C2214yes—
151#2464C2214yes—
152#2464C2214yes—
153#2463C2214yes—
154#2461C2214yes—
155#2461C2214yes—
156#2461C2214yes—
157#2458C2214yes—
158#2458C2214yes—
159#2456C2214yes—
160#2454C2212yes—
161#2454C2212yes—
162#2452C2212yes—
163#2451C2212yes—
164#2450C2214yes—
165#2448C2214yes—
166#2448C2212yes—
167#2445C2212yes—
168#2440C2212yes—
169#2440C2212yes—
170#2440C2212yes—
171#2439C2212yes—
172#2430C2214yes—
173#2430C2214yes—
174#2428C2212yes—
175#2427C2212yes—
176#2427C2214yes—
177#2426C2214yes—
178#2426C2214yes—
179#2425C2214yes—
180#2416C2212yes—
181#2416C2212yes—
182#2416C2212yes—
183#2415C2211yescharacteristic
184#2415C2211yescharacteristic
185#2414C2212yes—
186#2414C2211yescharacteristic
187#2414C2212yes—
188#2414C2212yes—
189#2414C2211yescharacteristic
190#2407C2214yes—
191#2407C2212yes—
192#2407C2212yes—
193#2399C2214yes—
194#2396C2214yes—
195#2396C2214yes—
196#2395C2214yes—
197#2395C2212yes—
198#2388C2214yes—
199#2388C2212yes—
200#2374C2214yes—
201#2374C2214yes—
202#2373C2214yes—
203#2372C2214yes—
204#2369C2212yes—
205#2369C2211yescharacteristic
206#2369C2211yescharacteristic
207#2367C2214yes—
208#2367C2214yes—
209#2366C2211yescharacteristic
210#2366C2211yescharacteristic
211#2365C2212yes—
212#2363C2212yes—
213#2363C2212yes—
214#2363C2214yes—
215#2363C2212yes—
216#2363C2212yes—
217#2363C2212yes—
218#2363C2212yes—
219#2363C2212yes—
220#2362C2214yes—
221#2362C2212yes—
222#2361C2212yes—
223#2361C2212yes—
224#2355C2211yescharacteristic
225#2354C2212yes—
226#2354C2212yes—
227#2354C2212yes—
228#2354C2211yescharacteristic
229#2354C2212yes—
230#2352C2212yes—
231Q8×C4⋊C4C2211yescharacteristic
232D4×C4⋊C4C2212yes—
233D4×C4⋊C4C2211yescharacteristic
234#2347C2214yes—
235#2347C2212yes—
236#2347C2212yes—
237#2345C2212yes—
238#2345C2212yes—
239#2341C2214yes—
240#2337C2214yes—
241#2337C2214yes—
242#2335C2214yes—
243#2335C2214yes—
244#2335C2214yes—
245#2324C2212yes—
246#2324C2212yes—
247#2324C2212yes—
248#2324C2212yes—
249#2314C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×C4⋊Q8C2212yes—
252C4×C4⋊Q8C2212yes—
253C4×#125C2212yes—
254C4×#125C2212yes—
255C4×#124C2212yes—
256C4×C22⋊Q8C2214yes—
257C4×C22⋊Q8C2211yescharacteristic
258C4×C22⋊Q8C2212yes—
259C4×C22⋊Q8C2211yescharacteristic
260C4×#121C2214yes—
261C4×#121C2212yes—
262C4×#121C2211yescharacteristic
263C4×#121C2211yescharacteristic
264#2297C2214yes—
265#2297C2214yes—
266#2296C2214yes—
267#2296C2212yes—
268#2293C2212yes—
269#2293C2212yes—
270#2293C2212yes—
271#2293C2212yes—
272#2293C2212yes—
273#2293C2212yes—
274#2285C2211yescharacteristic
275#2276C2212yes—
276#2275C2212yes—
277#2275C2212yes—
278#2275C2212yes—
279#2274C2211yescharacteristic
280#2274C2212yes—
281#2274C2211yescharacteristic
282#2274C2211yescharacteristic
283#2274C2211yescharacteristic
284#2274C2211yescharacteristic
285#2274C2211yescharacteristic
286C42×Q8C2212yes—
287C42×D4C2212yes—
288C42×D4C2212yes—
289C42×D4C2212yes—
290C42×D4C2212yes—
291C42×D4C2212yes—
292C4×#117C2211yescharacteristic
293C4×#117C2211yescharacteristic
294C4×#117C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C2×C4×C4⋊C4C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2314yes—
301C22×#41C2312yes—
302#555—216no—
303#547—216no—
304#533—48no—
305#532—28no—
306#532—48no—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×#127C2311yescharacteristic
313C2×#127C2312yes—
314#529—28no—
315#529—48no—
316C2×#126C2312yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#125C2311yescharacteristic
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#124C2312yes—
323C2×#124C2311yescharacteristic
324C2×#124C2314yes—
325C2×#124C2314yes—
326C2×#124C2312yes—
327C2×#124C2314yes—
328C2×#124C2314yes—
329C2×#123C2312yes—
330C2×#123C2314yes—
331C2×#123C2314yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2314yes—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2311yescharacteristic
349C2×#121C2312yes—
350C2×#121C2314yes—
351C2×#121C2311yescharacteristic
352C2×#121C2311yescharacteristic
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2314yes—
356C2×#121C2314yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360#520—28no—
361#520—28no—
362C4×#41—28no—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2314yes—
369C2×C4×Q8C2314yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2314yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2314yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2314yes—
398C2×#117C2312yes—
399C2×#117C2311yescharacteristic
400C2×#117C2311yescharacteristic
401C2×#117C2314yes—
402C2×#117C2312yes—
403C2×#117C2311yescharacteristic
404C2×#117C2311yescharacteristic
405C2×#117C2311yescharacteristic
406C2×#117C2311yescharacteristic
407C2×#117C2311yescharacteristic
408C2×#117C2311yescharacteristic
409C2×#117C2311yescharacteristic
410C2×#117C2311yescharacteristic
411C2×#117C2314yes—
412C2×#117C2312yes—
413C2×#117C2314yes—
414C2×#117C2314yes—
415C2×#117C2311yescharacteristic
416C22×C4⋊C4C2312yes—
417C22×C4⋊C4C2311yescharacteristic
418C22×C4⋊C4C2311yescharacteristic
419C22×C4⋊C4C2311yescharacteristic
420C22×C4⋊C4C2311yescharacteristic
421C22×C4⋊C4C2311yescharacteristic
422C22×C4⋊C4C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2311yescharacteristic
425C22×C42C2312yes—
426C22×C42C2312yes—
427C22×C42C2312yes—
428C22×C42C2314yes—
429C22×C42C2311yescharacteristic
430#400C2312yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#399C2314yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2312yes—
441#398C2314yes—
442#398C2314yes—
443#398C2312yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#397C2312yes—
450#397C2314yes—
451#397C2312yes—
452#397C2314yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#395C2314yes—
465#395C2312yes—
466#395C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2312yes—
479#394C2312yes—
480#394C2312yes—
481#394C2312yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#393C2314yes—
489#393C2314yes—
490#393C2314yes—
491#393C2312yes—
492#393C2314yes—
493#393C2314yes—
494#392C2314yes—
495#392C2312yes—
496#392C2312yes—
497#392C2312yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#391C2312yes—
512#391C2311yescharacteristic
513#391C2311yescharacteristic
514#391C2314yes—
515#391C2312yes—
516#390C2314yes—
517#390C2314yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2314yes—
529#390C2312yes—
530#390C2312yes—
531#390C2314yes—
532#390C2314yes—
533#390C2314yes—
534#390C2312yes—
535#390C2312yes—
536#390C2311yescharacteristic
537#390C2311yescharacteristic
538#390C2312yes—
539#390C2314yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2314yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2311yescharacteristic
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2311yescharacteristic
569#389C2311yescharacteristic
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2312yes—
583#389C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2312yes—
591#388C2312yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2312yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2312yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2312yes—
621#388C2312yes—
622#388C2314yes—
623#388C2314yes—
624#388C2312yes—
625#388C2312yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2312yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2312yes—
650#386C2312yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2312yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2312yes—
681#385C2312yes—
682#385C2314yes—
683#385C2314yes—
684#384C2312yes—
685#384C2312yes—
686#384C2312yes—
687#384C2312yes—
688#384C2311yescharacteristic
689#384C2311yescharacteristic
690#383C2314yes—
691#383C2314yes—
692#382C2312yes—
693#382C2312yes—
694#382C2312yes—
695#380C2311yescharacteristic
696#380C2311yescharacteristic
697#380C2311yescharacteristic
698#380C2311yescharacteristic
699#380C2312yes—
700#380C2312yes—
701#380C2312yes—
702#380C2312yes—
703#380C2314yes—
704#380C2312yes—
705#380C2312yes—
706#380C2312yes—
707#380C2314yes—
708#380C2314yes—
709#380C2312yes—
710#380C2314yes—
711#380C2312yes—
712#380C2312yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2314yes—
719C4×C4⋊C4C2314yes—
720C4×C4⋊C4C2311yescharacteristic
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2311yescharacteristic
723C4×C4⋊C4C2311yescharacteristic
724C4×C4⋊C4C2314yes—
725C4×C4⋊C4C2314yes—
726C4×C4⋊C4C2314yes—
727C4×C4⋊C4C2311yescharacteristic
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2311yescharacteristic
730C4×C4⋊C4C2311yescharacteristic
731C4×C4⋊C4C2311yescharacteristic
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2314yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C22⋊C4C2312yes—
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2312yes—
775C4×C22⋊C4C2314yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2314yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809#376C2312yes—
810#376C2312yes—
811#376C2312yes—
812#376C2312yes—
813C2×#95C2312yes—
814C2×#95C2312yes—
815C2×#95C2312yes—
816C43C2312yes—
817C43C2312yes—
818C43C2312yes—
819C43C2312yes—
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—28no—
824C2×#41—216no—
825C2×#41—48no—
826C2×#41—82no—
827C2×#41—84no—
828C2×#41—82no—
829C22×Q8C2411yescharacteristic
830C22×Q8C2411yescharacteristic
831C22×Q8C2414yes—
832C22×Q8C2414yes—
833C22×Q8C2412yes—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2412yes—
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2414yes—
853C23×C4C2414yes—
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2412yes—
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2414yes—
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C4⋊Q8—28no—
870C4⋊Q8—28no—
871C4⋊Q8—28no—
872C4⋊Q8—24no—
873C4⋊Q8—44no—
874#127—24no—
875#127—44no—
876#126—28no—
877#126—48no—
878#126—84no—
879#125—28no—
880#125—24no—
881#125—44no—
882#124—216no—
883#124—24no—
884#124—28no—
885#124—216no—
886#124—44no—
887#124—48no—
888#124—84no—
889#123—28no—
890#123—216no—
891#123—216no—
892#123—48no—
893#123—84no—
894C22⋊Q8—24no—
895C22⋊Q8—216no—
896C22⋊Q8—24no—
897C22⋊Q8—24no—
898C22⋊Q8—48no—
899C22⋊Q8—48no—
900C22⋊Q8—82no—
901C22⋊Q8—84no—
902C22⋊Q8—82no—
903#121—24no—
904#121—28no—
905#121—28no—
906#121—28no—
907#121—28no—
908#121—28no—
909#121—28no—
910#121—24no—
911#121—24no—
912#121—216no—
913#121—48no—
914#121—44no—
915#121—44no—
916#121—82no—
917#121—84no—
918#121—84no—
919#121—82no—
920C4×Q8—28no—
921C4×Q8—24no—
922C4×Q8—24no—
923C4×Q8—28no—
924C4×Q8—24no—
925C4×Q8—48no—
926C4×Q8—44no—
927C4×Q8—48no—
928C4×Q8—84no—
929C4×D4—24no—
930C4×D4—24no—
931C4×D4—24no—
932C4×D4—24no—
933C4×D4—28no—
934C4×D4—28no—
935C4×D4—28no—
936C4×D4—28no—
937C4×D4—28no—
938C4×D4—28no—
939C4×D4—28no—
940C4×D4—28no—
941C4×D4—28no—
942C4×D4—28no—
943C4×D4—28no—
944C4×D4—28no—
945C4×D4—24no—
946C4×D4—24no—
947C4×D4—28no—
948C4×D4—24no—
949C4×D4—28no—
950C4×D4—28no—
951C4×D4—44no—
952C4×D4—48no—
953C4×D4—48no—
954C4×D4—84no—
955#117—24no—
956#117—24no—
957#117—24no—
958#117—24no—
959#117—24no—
960#117—24no—
961#117—28no—
962#117—24no—
963#117—24no—
964#117—24no—
965#117—24no—
966#117—28no—
967#117—216no—
968#117—48no—
969#117—44no—
970#117—84no—
971#117—84no—
972#117#4118yescomplemented
973C2×C4⋊C4—24no—
974C2×C4⋊C4—24no—
975C2×C4⋊C4—24no—
976C2×C4⋊C4—24no—
977C2×C4⋊C4—24no—
978C2×C4⋊C4—28no—
979C2×C4⋊C4#4118yescomplemented
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2411yescharacteristic
1037C2×C4⋊C4C2411yescharacteristic
1038C2×C4⋊C4C2411yescharacteristic
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2411yescharacteristic
1041C2×C4⋊C4C2411yescharacteristic
1042C2×C4⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2411yescharacteristic
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2411yescharacteristic
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C42—24no—
1103C2×C42—24no—
1104C2×C42—44no—
1105C2×C42—44no—
1106C2×C42—44no—
1107C2×C42—84no—
1108C2×C42#4118yescomplemented
1109C2×C42C2414yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2412yes—
1134C2×C42C2414yes—
1135C2×C42C2414yes—
1136C2×C42C2414yes—
1137C2×C42C2412yes—
1138C2×C42C2414yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2414yes—
1143C2×C42C2412yes—
1144C2×C42C2412yes—
1145C2×C42C2412yes—
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2412yes—
1149C2×C42C2411yescharacteristic
1150C2×C42C2412yes—
1151C2×C42C2411yescharacteristic
1152C2×C42C2411yescharacteristic
1153C2×C42C2411yescharacteristic
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2414yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2412yes—
1209#95C2412yes—
1210C24C2512yes—
1211C24C2514yes—
1212C24C2511yescharacteristic
1213C24C2511yescharacteristic
1214C24C2511yescharacteristic
1215#41—232no—
1216#41—816no—
1217#41—832no—
1218C2×Q8—22no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—28no—
1223C2×Q8—28no—
1224C2×Q8—24no—
1225C2×Q8—22no—
1226C2×Q8—28no—
1227C2×Q8—22no—
1228C2×Q8—44no—
1229C2×Q8—44no—
1230C2×Q8—44no—
1231C2×Q8—42no—
1232C2×Q8—42no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—28no—
1243C2×D4—28no—
1244C2×D4—28no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—22no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—28no—
1254C2×D4—28no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—22no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—44no—
1270C2×D4—44no—
1271C2×D4—44no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—24no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—24no—
1290C22×C4—24no—
1291C22×C4—28no—
1292C22×C4—24no—
1293C22×C4—28no—
1294C22×C4—28no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—28no—
1298C22×C4—28no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—28no—
1308C22×C4—42no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—41no—
1314C22×C4—41no—
1315C22×C4—42no—
1316C22×C4—42no—
1317C22×C4—42no—
1318C22×C4—42no—
1319C22×C4—42no—
1320C22×C4—42no—
1321C22×C4—44no—
1322C22×C4—42no—
1323C22×C4—44no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—41no—
1327C22×C4—41no—
1328C22×C4—42no—
1329C22×C4—41no—
1330C22×C4—41no—
1331C22×C4—42no—
1332C22×C4C2×#4114yes—
1333C22×C4C2×#4114yes—
1334C22×C4C2×#4114yes—
1335C22×C4C2×#4114yes—
1336C22×C4C2×#4114yes—
1337C22×C4C2×#4118yes—
1338C22×C4C2512yes—
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2512yes—
1342C22×C4C2512yes—
1343C22×C4C2512yes—
1344C22×C4C2514yes—
1345C22×C4C2514yes—
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2514yes—
1354C22×C4C2511yescharacteristic
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2512yes—
1358C22×C4C2511yescharacteristic
1359C22×C4C2511yescharacteristic
1360C22×C4C2511yescharacteristic
1361C22×C4C2512yes—
1362C22×C4C2512yes—
1363C22×C4C2511yescharacteristic
1364C22×C4C2512yes—
1365C22×C4C2512yes—
1366C22×C4C2511yescharacteristic
1367C22×C4C2511yescharacteristic
1368C4⋊C4—22no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—28no—
1378C4⋊C4—22no—
1379C4⋊C4—24no—
1380C4⋊C4—22no—
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—28no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—24no—
1390C4⋊C4—24no—
1391C4⋊C4—24no—
1392C4⋊C4—24no—
1393C4⋊C4—22no—
1394C4⋊C4—24no—
1395C4⋊C4—22no—
1396C4⋊C4—24no—
1397C4⋊C4—28no—
1398C4⋊C4—22no—
1399C4⋊C4—24no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—28no—
1403C4⋊C4—28no—
1404C4⋊C4—28no—
1405C4⋊C4—22no—
1406C4⋊C4—24no—
1407C4⋊C4—42no—
1408C4⋊C4—44no—
1409C4⋊C4—44no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—42no—
1416C4⋊C4—44no—
1417C4⋊C4—44no—
1418C4⋊C4—44no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—44no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4C2×#4114yes—
1425C4⋊C4C2×#4114yes—
1426C4⋊C4C2×#4114yes—
1427C4⋊C4C2×#4118yes—
1428C4⋊C4C2×#4114yes—
1429C4⋊C4H(5,𝔽2)14yes—
1430C4⋊C42−1+414yes—
1431C22⋊C4—24no—
1432C22⋊C4—22no—
1433C22⋊C4—22no—
1434C22⋊C4—24no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—24no—
1439C22⋊C4—22no—
1440C22⋊C4—22no—
1441C22⋊C4—22no—
1442C22⋊C4—22no—
1443C22⋊C4—24no—
1444C22⋊C4—24no—
1445C22⋊C4—28no—
1446C22⋊C4—28no—
1447C22⋊C4—28no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—28no—
1451C22⋊C4—28no—
1452C22⋊C4—24no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—28no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—28no—
1459C22⋊C4—28no—
1460C22⋊C4—24no—
1461C22⋊C4—28no—
1462C22⋊C4—24no—
1463C22⋊C4—24no—
1464C22⋊C4—24no—
1465C22⋊C4—28no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—44no—
1472C22⋊C4—44no—
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—42no—
1484C22⋊C4—44no—
1485C22⋊C4—42no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4—42no—
1489C22⋊C4C2×#4118yes—
1490C42—22no—
1491C42—22no—
1492C42—22no—
1493C42—22no—
1494C42—22no—
1495C42—22no—
1496C42—28no—
1497C42—24no—
1498C42—24no—
1499C42—24no—
1500C42—24no—
1501C42—24no—
1502C42—24no—
1503C42—24no—
1504C42—24no—
1505C42—24no—
1506C42—24no—
1507C42—24no—
1508C42—24no—
1509C42—24no—
1510C42—24no—
1511C42—42no—
1512C42—42no—
1513C42—42no—
1514C42—42no—
1515C42—42no—
1516C42—42no—
1517C42—42no—
1518C42—42no—
1519C42—44no—
1520C42—44no—
1521C42—44no—
1522C42—44no—
1523C42—42no—
1524C42—42no—
1525C42—42no—
1526C42—44no—
1527C42—42no—
1528C42—42no—
1529C42—42no—
1530C42C2×#4114yes—
1531C42C2×#4114yes—
1532C42C2×#4114yes—
1533C42C2×#4114yes—
1534C42C2×#4118yes—
1535C23—21no—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—22no—
1554C23—24no—
1555C23—24no—
1556C23—22no—
1557C23—24no—
1558C23—22no—
1559C23—24no—
1560C23—22no—
1561C23—24no—
1562C23—22no—
1563C23—22no—
1564C23—24no—
1565C23—24no—
1566C23—22no—
1567C23C22×#4112yes—
1568C23C22×#4112yes—
1569C23C22×#4112yes—
1570C23C2611yescharacteristic
1571Q8—28no—
1572Q8—416no—
1573Q8—44no—
1574Q8—88no—
1575Q8—84no—
1576D4—28no—
1577D4—28no—
1578D4—28no—
1579D4—48no—
1580D4—48no—
1581D4—48no—
1582D4—44no—
1583D4—48no—
1584D4—88no—
1585D4—88no—
1586D4—84no—
1587D4—88no—
1588D4—84no—
1589D4—88no—
1590D4—88no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—28no—
1616C2×C4—28no—
1617C2×C4—28no—
1618C2×C4—28no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—24no—
1636C2×C4—24no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—24no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—21no—
1649C2×C4—22no—
1650C2×C4—21no—
1651C2×C4—22no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—22no—
1656C2×C4—24no—
1657C2×C4—21no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—24no—
1664C2×C4—22no—
1665C2×C4—24no—
1666C2×C4—24no—
1667C2×C4—48no—
1668C2×C4—44no—
1669C2×C4—416no—
1670C2×C4—416no—
1671C2×C4—416no—
1672C2×C4—48no—
1673C2×C4—44no—
1674C2×C4—44no—
1675C2×C4—84no—
1676C2×C4—84no—
1677C2×C4—84no—
1678C2×C4—84no—
1679C2×C4—82no—
1680C2×C4—82no—
1681C2×C4—88no—
1682C2×C4—84no—
1683C2×C4C22×#4114yes—
1684C2×C4C22×#4112yes—
1685C2×C4C22×#4112yes—
1686C2×C4C22×#4114yes—
1687C2×C4C22×#4114yes—
1688C2×C4C22×#4112yes—
1689C2×C4C22×#4112yes—
1690C2×C4C22×#4112yes—
1691C2×C4C22×#4112yes—
1692C2×C4C22×#4114yes—
1693C2×C4C22×#4112yes—
1694C2×C4C22×#4112yes—
1695C2×C4C22×#4112yes—
1696C2×C4C22×#4112yes—
1697C2×C4C2×H(5,𝔽2)14yes—
1698C2×C4C2×H(5,𝔽2)12yes—
1699C2×C4C2×2−1+414yes—
1700C2×C4C2×2−1+412yes—
1701C22—22no—
1702C22—22no—
1703C22—22no—
1704C22—22no—
1705C22—22no—
1706C22—22no—
1707C22—22no—
1708C22—22no—
1709C22—22no—
1710C22—41no—
1711C22—41no—
1712C22—41no—
1713C22—41no—
1714C22—41no—
1715C22—41no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—41no—
1722C22—44no—
1723C22—42no—
1724C22—42no—
1725C22—44no—
1726C22—44no—
1727C22—42no—
1728C22—44no—
1729C22—42no—
1730C22—42no—
1731C22—44no—
1732C22—44no—
1733C22—42no—
1734C22—42no—
1735C22—44no—
1736C22C23×#4111yescharacteristic
1737C22C23×#4111yescharacteristic
1738C22C23×#4111yescharacteristic
1739C22C22×H(5,𝔽2)11yescharacteristic
1740C22C22×2−1+411yescharacteristic
1741C22H(7,𝔽2)11yescharacteristic
1742C22H(7,𝔽2)11yescharacteristic
1743C4—24no—
1744C4—24no—
1745C4—24no—
1746C4—24no—
1747C4—24no—
1748C4—24no—
1749C4—22no—
1750C4—22no—
1751C4—22no—
1752C4—22no—
1753C4—22no—
1754C4—22no—
1755C4—42no—
1756C4—44no—
1757C4—42no—
1758C4—42no—
1759C4—44no—
1760C4—42no—
1761C4—42no—
1762C4—42no—
1763C4—41no—
1764C4—41no—
1765C4—42no—
1766C4—44no—
1767C4—41no—
1768C4—41no—
1769C4—42no—
1770C4—42no—
1771C4#344414yes—
1772C4#351114yes—
1773C2—42no—
1774C2—42no—
1775C2—42no—
1776C2—84no—
1777C2—82no—
1778C2C2×#344411yescharacteristic
1779C2C2×#351111yescharacteristic
1780C2#6285511yescharacteristic
1781C2#6298311yescharacteristic
1782C2#6298611yescharacteristic
1783C2#6299911yescharacteristic
1784C2#6300011yescharacteristic
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. #36564C2semidirect
2. #36551C2semidirect
3. #36480C2semidirect
4. #36459C2semidirect
5. #36393C2semidirect
6. #36369C2semidirect
7. #36302C2semidirect
8. #36273C2semidirect
9. #36150C2semidirect
10. #36142C2semidirect
11. #36126C2semidirect
12. #36117C2semidirect
13. #36087C2semidirect
14. #36000C2semidirect
15. #35989C2semidirect
16. #35814C2semidirect
17. #35744C2semidirect
18. #35682C2semidirect
19. #35598C2semidirect
20. #35597C2semidirect
21. #35436C2semidirect
22. #35421C2semidirect
23. #35292C2semidirect
24. #35238C2semidirect
25. #35114C2semidirect
26. #35107C2semidirect
27. #34938C2semidirect
28. #34911C2semidirect
29. #34893C2semidirect
30. #34889C2semidirect
31. #34321C2semidirect
32. #34316C2semidirect
33. #34242C2semidirect
34. #34155C2semidirect
35. C4×#520C2semidirect
972. #117#41semidirect
979. C2×C4⋊C4#41semidirect
1108. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#365642
#365512
#364802
#364592
#363932
#363692
#363022
#362732
#361502
#361422
#361262
#361172
#360872
#360002
#359892
#358142
#357442
#356822
#355982
#355972
#354362
#354212
#352922
#352382
#351142
#351072
#349382
#349112
#348932
#348892
#343212
#343162
#342422
#341552
C4×#5202