Finite Group Databasebeta

← #7643159

Subgroups — #7643159

Order 512.

5538 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#40438C214yesmaximal, complemented
2#40125C212yesmaximal, complemented
3#40054C212yesmaximal, complemented
4#39808C212yesmaximal, complemented
5#39790C212yesmaximal, complemented
6#39770C211yesmaximal, characteristic, complemented
7#39745C211yesmaximal, characteristic, complemented
8#39726C211yesmaximal, characteristic, complemented
9#39725C211yesmaximal, characteristic, complemented
10#39672C212yesmaximal, complemented
11#39633C211yesmaximal, characteristic, complemented
12#39625C211yesmaximal, characteristic, complemented
13#39406C212yesmaximal, complemented
14#39352C211yesmaximal, characteristic, complemented
15#39351C211yesmaximal, characteristic, complemented
16#37810C214yesmaximal, complemented
17#37794C212yesmaximal, complemented
18#37792C212yesmaximal, complemented
19#37051C214yesmaximal, complemented
20#36911C214yesmaximal, complemented
21#36644C211yesmaximal, characteristic, complemented
22#36638C211yesmaximal, characteristic, complemented
23#35607C212yesmaximal, complemented
24#35600C212yesmaximal, complemented
25#35560C212yesmaximal, complemented
26#35535C212yesmaximal, complemented
27#35295C212yesmaximal, complemented
28#35276C212yesmaximal, complemented
29#35198C212yesmaximal, complemented
30#35198C211yesmaximal, characteristic, complemented
31#35186C211yesmaximal, characteristic, complemented
32#35114C212yesmaximal, complemented
33#34331C211yesmaximal, characteristic, complemented
34#34313C211yesmaximal, characteristic, complemented
35C4×#533C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#542C2212yes—
39C2×#542C2214yes—
40C2×#542C2212yes—
41C2×#540C2212yes—
42C2×#533C2211yescharacteristic
43C2×#532C2212yes—
44C2×#532C2212yes—
45C2×#532C2212yes—
46C2×#520C2212yes—
47#2868C2211yescharacteristic
48#2867C2211yescharacteristic
49#2866C2212yes—
50#2865C2212yes—
51#2864C2211yescharacteristic
52#2863C2211yescharacteristic
53#2861C2211yescharacteristic
54#2861C2212yes—
55#2860C2211yescharacteristic
56#2860C2212yes—
57#2860C2212yes—
58#2858C2212yes—
59#2858C2212yes—
60#2858C2212yes—
61#2858C2212yes—
62#2856C2211yescharacteristic
63#2856C2211yescharacteristic
64#2856C2212yes—
65#2856C2212yes—
66#2856C2212yes—
67#2855C2211yescharacteristic
68#2854C2211yescharacteristic
69#2853C2212yes—
70#2852C2212yes—
71#2851C2211yescharacteristic
72#2850C2211yescharacteristic
73#2803C2214yes—
74#2803C2214yes—
75#2797C2214yes—
76#2792C2214yes—
77#2790C2214yes—
78#2784C2214yes—
79#2780C2214yes—
80#2748C2214yes—
81#2734C2214yes—
82#2729C2214yes—
83#2723C2214yes—
84#2715C2214yes—
85#2711C2214yes—
86#2710C2214yes—
87#2710C2214yes—
88#2709C2214yes—
89#2709C2214yes—
90#2707C2214yes—
91#2706C2214yes—
92#2701C2214yes—
93#2692C2214yes—
94#2686C2214yes—
95#2682C2214yes—
96#2681C2214yes—
97#2676C2214yes—
98#2674C2214yes—
99#2673C2214yes—
100#2673C2214yes—
101#2672C2214yes—
102#2672C2214yes—
103#2671C2214yes—
104#2671C2214yes—
105#2662C2214yes—
106#2662C2214yes—
107#2662C2214yes—
108#2660C2212yes—
109#2657C2212yes—
110#2651C2214yes—
111#2651C2214yes—
112#2647C2212yes—
113#2641C2212yes—
114#2632C2214yes—
115#2624C2212yes—
116#2624C2212yes—
117#2620C2212yes—
118#2619C2212yes—
119#2602C2214yes—
120#2600C2214yes—
121#2597C2214yes—
122#2597C2214yes—
123#2592C2212yes—
124#2582C2211yescharacteristic
125#2580C2212yes—
126#2579C2214yes—
127#2567C2212yes—
128#2564C2214yes—
129#2559C2214yes—
130#2559C2214yes—
131#2555C2214yes—
132#2555C2214yes—
133#2554C2214yes—
134#2554C2214yes—
135#2552C2211yescharacteristic
136#2551C2212yes—
137#2551C2212yes—
138#2551C2211yescharacteristic
139#2550C2212yes—
140#2548C2211yescharacteristic
141#2548C2212yes—
142#2548C2211yescharacteristic
143#2548C2211yescharacteristic
144#2545C2212yes—
145#2544C2212yes—
146#2544C2212yes—
147#2544C2212yes—
148#2542C2212yes—
149#2541C2212yes—
150#2541C2211yescharacteristic
151#2540C2212yes—
152#2538C2211yescharacteristic
153#2538C2212yes—
154#2537C2212yes—
155#2521C2214yes—
156#2512C2212yes—
157#2512C2212yes—
158#2507C2212yes—
159#2502C2212yes—
160#2501C2212yes—
161#2497C2212yes—
162#2492C2212yes—
163#2491C2214yes—
164#2491C2212yes—
165#2491C2212yes—
166#2491C2212yes—
167#2479C2214yes—
168#2479C2214yes—
169#2479C2214yes—
170#2476C2214yes—
171#2476C2214yes—
172#2474C2214yes—
173#2468C2214yes—
174#2466C2214yes—
175#2464C2214yes—
176#2464C2214yes—
177#2461C2214yes—
178#2461C2214yes—
179#2461C2214yes—
180#2461C2214yes—
181#2461C2214yes—
182#2459C2214yes—
183#2458C2214yes—
184#2455C2214yes—
185#2455C2214yes—
186#2454C2212yes—
187#2454C2212yes—
188#2452C2212yes—
189#2452C2212yes—
190#2452C2212yes—
191#2452C2212yes—
192#2451C2212yes—
193#2451C2212yes—
194#2450C2214yes—
195#2449C2214yes—
196#2449C2214yes—
197#2448C2212yes—
198#2448C2212yes—
199#2447C2212yes—
200#2445C2212yes—
201#2445C2212yes—
202#2445C2212yes—
203#2445C2212yes—
204#2445C2212yes—
205#2445C2212yes—
206#2440C2212yes—
207#2432C2214yes—
208#2432C2212yes—
209#2431C2212yes—
210#2431C2212yes—
211#2430C2214yes—
212#2428C2212yes—
213#2428C2212yes—
214#2427C2212yes—
215#2426C2212yes—
216#2426C2214yes—
217#2426C2212yes—
218#2425C2214yes—
219#2422C2212yes—
220#2422C2212yes—
221#2416C2212yes—
222#2407C2212yes—
223#2407C2214yes—
224#2406C2214yes—
225#2367C2212yes—
226#2367C2212yes—
227#2366C2211yescharacteristic
228#2366C2212yes—
229#2366C2211yescharacteristic
230#2361C2212yes—
231#2361C2214yes—
232#2359C2214yes—
233#2355C2211yescharacteristic
234#2354C2212yes—
235Q8×C4⋊C4C2211yescharacteristic
236Q8×C4⋊C4C2211yescharacteristic
237#2349C2212yes—
238D4×C4⋊C4C2212yes—
239D4×C4⋊C4C2211yescharacteristic
240#2341C2212yes—
241#2337C2214yes—
242#2335C2214yes—
243#2335C2214yes—
244#2330C2212yes—
245#2328C2212yes—
246#2328C2212yes—
247#2326C2212yes—
248#2326C2212yes—
249#2326C2212yes—
250#2324C2212yes—
251#2324C2214yes—
252#2324C2212yes—
253#2324C2212yes—
254#2324C2212yes—
255#2324C2214yes—
256#2319C2212yes—
257C4×C4⋊Q8C2211yescharacteristic
258C4×C4⋊Q8C2211yescharacteristic
259C4×C4⋊Q8C2211yescharacteristic
260C4×C4⋊Q8C2211yescharacteristic
261C4×#127C2211yescharacteristic
262C4×#127C2212yes—
263C4×#127C2211yescharacteristic
264C4×#127C2212yes—
265C4×#127C2212yes—
266C4×#127C2212yes—
267C4×#125C2211yescharacteristic
268C4×#125C2212yes—
269C4×#125C2212yes—
270C4×#126C2212yes—
271C4×#124C2212yes—
272C4×#124C2211yescharacteristic
273C4×C22⋊Q8C2211yescharacteristic
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2212yes—
277C4×C22⋊Q8C2211yescharacteristic
278C4×C22⋊Q8C2212yes—
279C4×C22⋊Q8C2211yescharacteristic
280C4×#123C2212yes—
281C4×#121C2211yescharacteristic
282#2298C2212yes—
283#2296C2212yes—
284#2295C2211yescharacteristic
285#2295C2211yescharacteristic
286#2295C2211yescharacteristic
287#2295C2212yes—
288#2293C2211yescharacteristic
289#2293C2212yes—
290#2293C2212yes—
291#2290C2212yes—
292#2285C2211yescharacteristic
293#2275C2212yes—
294C42×Q8C2211yescharacteristic
295C42×Q8C2212yes—
296C42×Q8C2211yescharacteristic
297C4×#117C2212yes—
298C2×C43C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2314yes—
301#559—28no—
302#550—28no—
303#542—48no—
304#542—48no—
305#542—416no—
306#540—48no—
307#533—28no—
308#532—48no—
309#532—48no—
310#532—48no—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2314yes—
319C2×#127C2312yes—
320C2×#127C2311yescharacteristic
321C2×#127C2311yescharacteristic
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2312yes—
326C2×#127C2312yes—
327C2×#127C2312yes—
328C2×#127C2312yes—
329C2×#126C2312yes—
330C2×#126C2314yes—
331C2×#126C2314yes—
332C2×#126C2314yes—
333C2×#125C2312yes—
334C2×#125C2311yescharacteristic
335C2×#125C2312yes—
336C2×#124C2311yescharacteristic
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2314yes—
340C2×#124C2312yes—
341C2×#124C2314yes—
342C2×#124C2314yes—
343C2×#124C2314yes—
344C2×#124C2314yes—
345C2×#124C2312yes—
346C2×#124C2314yes—
347C2×#124C2314yes—
348C2×#124C2312yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×#123C2312yes—
352C2×#123C2314yes—
353C2×#123C2314yes—
354C2×#123C2314yes—
355C2×#123C2314yes—
356C2×#123C2314yes—
357C2×#123C2314yes—
358C2×C22⋊Q8C2311yescharacteristic
359C2×C22⋊Q8C2311yescharacteristic
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2311yescharacteristic
362C2×C22⋊Q8C2314yes—
363C2×C22⋊Q8C2314yes—
364C2×C22⋊Q8C2314yes—
365C2×C22⋊Q8C2314yes—
366C2×C22⋊Q8C2314yes—
367C2×C22⋊Q8C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2314yes—
371C2×#121C2312yes—
372C2×#121C2311yescharacteristic
373C2×#121C2314yes—
374C2×#121C2312yes—
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379C2×#121C2312yes—
380C2×#121C2314yes—
381C2×#121C2314yes—
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C2×#121C2312yes—
386#520—48no—
387C2×C4×Q8C2311yescharacteristic
388C2×C4×Q8C2311yescharacteristic
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2312yes—
391C2×C4×Q8C2311yescharacteristic
392C2×C4×Q8C2311yescharacteristic
393C2×C4×Q8C2311yescharacteristic
394C2×C4×Q8C2311yescharacteristic
395C2×C4×Q8C2312yes—
396C2×C4×Q8C2312yes—
397C2×C4×Q8C2312yes—
398C2×C4×Q8C2311yescharacteristic
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2314yes—
411C2×C4×D4C2314yes—
412C2×C4×D4C2314yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2314yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2312yes—
421C2×#117C2312yes—
422C2×#117C2312yes—
423C2×#117C2312yes—
424C2×#117C2314yes—
425C2×#117C2314yes—
426C22×C4⋊C4C2314yes—
427C22×C4⋊C4C2312yes—
428C22×C42C2311yescharacteristic
429C22×C42C2311yescharacteristic
430C22×C42C2311yescharacteristic
431C22×C42C2311yescharacteristic
432C22×C42C2311yescharacteristic
433C22×C42C2311yescharacteristic
434C22×C42C2311yescharacteristic
435#400C2314yes—
436#400C2314yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2314yes—
441#399C2314yes—
442#399C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#395C2314yes—
473#395C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#391C2311yescharacteristic
516#391C2311yescharacteristic
517#391C2312yes—
518#391C2312yes—
519#391C2311yescharacteristic
520#391C2311yescharacteristic
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2311yescharacteristic
525#391C2314yes—
526#391C2314yes—
527#391C2311yescharacteristic
528#391C2311yescharacteristic
529#391C2311yescharacteristic
530#390C2311yescharacteristic
531#390C2312yes—
532#390C2312yes—
533#390C2314yes—
534#390C2314yes—
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2314yes—
540#390C2314yes—
541#390C2314yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2314yes—
546#390C2312yes—
547#390C2314yes—
548#390C2312yes—
549#390C2312yes—
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2312yes—
556#390C2314yes—
557#390C2314yes—
558#390C2314yes—
559#390C2312yes—
560#390C2314yes—
561#390C2314yes—
562#390C2312yes—
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2312yes—
567#390C2312yes—
568#390C2312yes—
569#390C2312yes—
570#390C2311yescharacteristic
571#390C2311yescharacteristic
572#390C2311yescharacteristic
573#390C2312yes—
574#390C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2311yescharacteristic
580#389C2311yescharacteristic
581#389C2311yescharacteristic
582#389C2311yescharacteristic
583#389C2311yescharacteristic
584#389C2311yescharacteristic
585#389C2312yes—
586#389C2312yes—
587#389C2314yes—
588#389C2314yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2314yes—
594#389C2312yes—
595#389C2312yes—
596#389C2314yes—
597#389C2311yescharacteristic
598#389C2314yes—
599#389C2312yes—
600#389C2312yes—
601#389C2314yes—
602#389C2311yescharacteristic
603#389C2311yescharacteristic
604#389C2311yescharacteristic
605#389C2311yescharacteristic
606#389C2312yes—
607#389C2311yescharacteristic
608#389C2312yes—
609#388C2312yes—
610#388C2312yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2312yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2312yes—
638#388C2312yes—
639#388C2312yes—
640#388C2312yes—
641#388C2314yes—
642#388C2312yes—
643#388C2312yes—
644#388C2312yes—
645#388C2312yes—
646#388C2312yes—
647#388C2312yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#387C2312yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2314yes—
666#387C2314yes—
667#387C2312yes—
668#387C2312yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#387C2312yes—
677#387C2312yes—
678#387C2312yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2312yes—
700#386C2312yes—
701#386C2312yes—
702#386C2312yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2312yes—
722#385C2312yes—
723#385C2312yes—
724#385C2312yes—
725#385C2312yes—
726#385C2312yes—
727#385C2312yes—
728#385C2312yes—
729#384C2312yes—
730#384C2312yes—
731#384C2311yescharacteristic
732#384C2311yescharacteristic
733#384C2312yes—
734#384C2312yes—
735#384C2311yescharacteristic
736#384C2311yescharacteristic
737#384C2312yes—
738#384C2312yes—
739#383C2312yes—
740#382C2312yes—
741#382C2311yescharacteristic
742#382C2312yes—
743#382C2311yescharacteristic
744#381C2314yes—
745#381C2312yes—
746#380C2314yes—
747#380C2314yes—
748#380C2314yes—
749#380C2311yescharacteristic
750#380C2311yescharacteristic
751#380C2312yes—
752#380C2314yes—
753#380C2312yes—
754#380C2314yes—
755#380C2312yes—
756#380C2311yescharacteristic
757#380C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807#376C2312yes—
808#376C2312yes—
809#376C2312yes—
810C2×#95C2314yes—
811C43C2311yescharacteristic
812C43C2311yescharacteristic
813C43C2311yescharacteristic
814C43C2311yescharacteristic
815C43C2311yescharacteristic
816C43C2311yescharacteristic
817C43C2311yescharacteristic
818C43C2312yes—
819C43C2311yescharacteristic
820C43C2312yes—
821C2×#41—28no—
822C2×#41—48no—
823C2×#41—48no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—48no—
827C22×Q8C2411yescharacteristic
828C22×Q8C2411yescharacteristic
829C22×Q8C2412yes—
830C22×Q8C2411yescharacteristic
831C22×Q8C2414yes—
832C22×Q8C2414yes—
833C22×D4C2412yes—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2414yes—
839C22×D4C2412yes—
840C22×D4C2414yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2412yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2414yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2414yes—
866C4⋊Q8—24no—
867C4⋊Q8—24no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—48no—
874#127—24no—
875#127—28no—
876#127—24no—
877#127—28no—
878#127—44no—
879#127—44no—
880#127—44no—
881#127—44no—
882#127—44no—
883#127—44no—
884#126—28no—
885#126—48no—
886#126—48no—
887#126—48no—
888#125—28no—
889#125—24no—
890#125—44no—
891#124—28no—
892#124—28no—
893#124—216no—
894#124—24no—
895#124—48no—
896#124—48no—
897#124—48no—
898#124—48no—
899#124—44no—
900#124—44no—
901#124—44no—
902#124—48no—
903#124—48no—
904#123—216no—
905#123—48no—
906#123—48no—
907#123—48no—
908#123—48no—
909#123—44no—
910#123—48no—
911#123—48no—
912#123—48no—
913C22⋊Q8—24no—
914C22⋊Q8—24no—
915C22⋊Q8—24no—
916C22⋊Q8—28no—
917C22⋊Q8—48no—
918C22⋊Q8—48no—
919C22⋊Q8—48no—
920C22⋊Q8—48no—
921C22⋊Q8—48no—
922C22⋊Q8—44no—
923#121—28no—
924#121—28no—
925#121—24no—
926#121—28no—
927#121—216no—
928#121—48no—
929#121—48no—
930#121—44no—
931#121—44no—
932#121—48no—
933#121—48no—
934#121—48no—
935#121—48no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—44no—
940#121—48no—
941C4×Q8—28no—
942C4×Q8—24no—
943C4×Q8—24no—
944C4×Q8—24no—
945C4×Q8—28no—
946C4×Q8—24no—
947C4×Q8—44no—
948C4×Q8—42no—
949C4×Q8—42no—
950C4×Q8—44no—
951C4×Q8—44no—
952C4×Q8#4118yescomplemented
953C4×D4—28no—
954C4×D4—24no—
955C4×D4—28no—
956C4×D4—28no—
957C4×D4—28no—
958C4×D4—28no—
959C4×D4—48no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—48no—
963C4×D4—48no—
964C4×D4—48no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—44no—
971C4×D4—44no—
972C4×D4—44no—
973C4×D4—48no—
974C4×D4—48no—
975#117—28no—
976#117—28no—
977#117—28no—
978#117—48no—
979#117—48no—
980C2×C4⋊C4—48no—
981C2×C4⋊C4—44no—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2411yescharacteristic
1045C2×C4⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C42—24no—
1105C2×C42—24no—
1106C2×C42—24no—
1107C2×C42—24no—
1108C2×C42—24no—
1109C2×C42—42no—
1110C2×C42—42no—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2411yescharacteristic
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2411yescharacteristic
1138C2×C42C2411yescharacteristic
1139C2×C42C2411yescharacteristic
1140C2×C42C2411yescharacteristic
1141C2×C42C2414yes—
1142C2×C42C2414yes—
1143C2×C42C2414yes—
1144C2×C42C2412yes—
1145C2×C42C2412yes—
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150C2×C42C2411yescharacteristic
1151C2×C42C2411yescharacteristic
1152C2×C42C2412yes—
1153C2×C42C2411yescharacteristic
1154C2×C42C2411yescharacteristic
1155C2×C42C2411yescharacteristic
1156C2×C42C2411yescharacteristic
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
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#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213C24C2514yes—
1214C24C2512yes—
1215C24C2514yes—
1216C24C2511yescharacteristic
1217#41—432no—
1218#41—832no—
1219C2×Q8—24no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—24no—
1224C2×Q8—22no—
1225C2×Q8—22no—
1226C2×Q8—28no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—42no—
1231C2×Q8—44no—
1232C2×Q8—44no—
1233C2×Q8—44no—
1234C2×Q8—44no—
1235C2×Q8—44no—
1236C2×Q8C2×#4114yes—
1237C2×D4—24no—
1238C2×D4—28no—
1239C2×D4—28no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—22no—
1244C2×D4—28no—
1245C2×D4—24no—
1246C2×D4—24no—
1247C2×D4—28no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—22no—
1254C2×D4—28no—
1255C2×D4—22no—
1256C2×D4—24no—
1257C2×D4—24no—
1258C2×D4—28no—
1259C2×D4—28no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—28no—
1263C2×D4—44no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—44no—
1269C2×D4—44no—
1270C2×D4—44no—
1271C2×D4—42no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—42no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—42no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—42no—
1285C2×D4—44no—
1286C2×D4—44no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—44no—
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—28no—
1300C22×C4—24no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—24no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—24no—
1311C22×C4—28no—
1312C22×C4—28no—
1313C22×C4—28no—
1314C22×C4—41no—
1315C22×C4—41no—
1316C22×C4—41no—
1317C22×C4—41no—
1318C22×C4—44no—
1319C22×C4—44no—
1320C22×C4—44no—
1321C22×C4—44no—
1322C22×C4—44no—
1323C22×C4—44no—
1324C22×C4—44no—
1325C22×C4—44no—
1326C22×C4—44no—
1327C22×C4—44no—
1328C22×C4—44no—
1329C22×C4—44no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—44no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4H(5,𝔽2)14yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2512yes—
1341C22×C4C2512yes—
1342C22×C4C2512yes—
1343C22×C4C2512yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2511yescharacteristic
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2514yes—
1351C22×C4C2512yes—
1352C22×C4C2514yes—
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2511yescharacteristic
1360C22×C4C2511yescharacteristic
1361C22×C4C2511yescharacteristic
1362C22×C4C2511yescharacteristic
1363C22×C4C2511yescharacteristic
1364C22×C4C2511yescharacteristic
1365C22×C4C2511yescharacteristic
1366C22×C4C2511yescharacteristic
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—22no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—24no—
1379C4⋊C4—22no—
1380C4⋊C4—24no—
1381C4⋊C4—24no—
1382C4⋊C4—24no—
1383C4⋊C4—24no—
1384C4⋊C4—24no—
1385C4⋊C4—24no—
1386C4⋊C4—22no—
1387C4⋊C4—24no—
1388C4⋊C4—22no—
1389C4⋊C4—24no—
1390C4⋊C4—24no—
1391C4⋊C4—22no—
1392C4⋊C4—24no—
1393C4⋊C4—24no—
1394C4⋊C4—24no—
1395C4⋊C4—24no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—24no—
1400C4⋊C4—22no—
1401C4⋊C4—22no—
1402C4⋊C4—22no—
1403C4⋊C4—24no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—44no—
1408C4⋊C4—44no—
1409C4⋊C4—44no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—42no—
1416C4⋊C4—44no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—44no—
1421C4⋊C4—44no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—42no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C4⋊C4—44no—
1429C4⋊C4C2×#4114yes—
1430C4⋊C4C2×#4118yes—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—24no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—28no—
1438C22⋊C4—28no—
1439C22⋊C4—28no—
1440C22⋊C4—28no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—28no—
1444C22⋊C4—28no—
1445C22⋊C4—28no—
1446C22⋊C4—28no—
1447C22⋊C4—24no—
1448C22⋊C4—28no—
1449C22⋊C4—28no—
1450C22⋊C4—28no—
1451C22⋊C4—28no—
1452C22⋊C4—24no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—42no—
1461C22⋊C4—44no—
1462C22⋊C4—42no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
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—42no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C42—22no—
1490C42—22no—
1491C42—22no—
1492C42—24no—
1493C42—24no—
1494C42—22no—
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—22no—
1512C42—22no—
1513C42—22no—
1514C42—22no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—24no—
1519C42—41no—
1520C42—41no—
1521C42—41no—
1522C42—41no—
1523C42—44no—
1524C42—44no—
1525C42—42no—
1526C42—42no—
1527C42—42no—
1528C42—42no—
1529C42—44no—
1530C42C2×#4114yes—
1531C42C2×#4118yes—
1532C42H(5,𝔽2)14yes—
1533C42H(5,𝔽2)14yes—
1534C422−1+414yes—
1535C23—21no—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—24no—
1542C23—24no—
1543C23—22no—
1544C23—22no—
1545C23—22no—
1546C23—24no—
1547C23—24no—
1548C23—24no—
1549C23—24no—
1550C23—24no—
1551C23—24no—
1552C23—22no—
1553C23—22no—
1554C23—24no—
1555C23—24no—
1556C23—22no—
1557C23—24no—
1558C23—24no—
1559C23—24no—
1560C23—22no—
1561C23—24no—
1562C23C2×H(5,𝔽2)12yes—
1563C23C2611yescharacteristic
1564Q8—28no—
1565Q8—48no—
1566Q8—44no—
1567Q8—44no—
1568Q8—88no—
1569Q8—164no—
1570D4—416no—
1571D4—48no—
1572D4—48no—
1573D4—48no—
1574D4—48no—
1575D4—44no—
1576D4—84no—
1577D4—84no—
1578D4—88no—
1579D4—88no—
1580D4—88no—
1581D4—88no—
1582D4—88no—
1583D4—84no—
1584D4—88no—
1585D4—88no—
1586D4—164no—
1587D4—164no—
1588C2×C4—28no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—28no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—24no—
1637C2×C4—24no—
1638C2×C4—24no—
1639C2×C4—24no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—24no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—21no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—22no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—44no—
1666C2×C4—44no—
1667C2×C4—44no—
1668C2×C4—44no—
1669C2×C4—416no—
1670C2×C4—44no—
1671C2×C4—48no—
1672C2×C4—88no—
1673C2×C4—88no—
1674C2×C4—88no—
1675C2×C4—164no—
1676C2×C4—164no—
1677C2×C4—164no—
1678C2×C4C22×#4112yes—
1679C2×C4C22×#4114yes—
1680C2×C4C22×#4114yes—
1681C2×C4C22×#4112yes—
1682C2×C4C22×#4112yes—
1683C2×C4C2×H(5,𝔽2)12yes—
1684C2×C4C2×H(5,𝔽2)12yes—
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×H(5,𝔽2)12yes—
1691C2×C4C2×2−1+412yes—
1692C2×C4C2×2−1+412yes—
1693C2×C4C2×2−1+412yes—
1694C2×C4#58512yes—
1695C2×C4#58512yes—
1696C22—22no—
1697C22—22no—
1698C22—22no—
1699C22—41no—
1700C22—41no—
1701C22—41no—
1702C22—41no—
1703C22—44no—
1704C22—44no—
1705C22—42no—
1706C22—44no—
1707C22—42no—
1708C22—44no—
1709C22—44no—
1710C22—42no—
1711C22—44no—
1712C22—44no—
1713C22—44no—
1714C22—42no—
1715C22—44no—
1716C22—44no—
1717C22—44no—
1718C22—44no—
1719C22—42no—
1720C22—42no—
1721C22—44no—
1722C22—42no—
1723C22—44no—
1724C22C23×#4111yescharacteristic
1725C22C22×H(5,𝔽2)11yescharacteristic
1726C22C22×H(5,𝔽2)11yescharacteristic
1727C22C22×H(5,𝔽2)11yescharacteristic
1728C22C22×2−1+411yescharacteristic
1729C22C2×#58511yescharacteristic
1730C22C2×#58511yescharacteristic
1731C4—22no—
1732C4—22no—
1733C4—22no—
1734C4—24no—
1735C4—22no—
1736C4—22no—
1737C4—22no—
1738C4—22no—
1739C4—22no—
1740C4—22no—
1741C4—22no—
1742C4—24no—
1743C4—42no—
1744C4—42no—
1745C4—42no—
1746C4—41no—
1747C4—42no—
1748C4—42no—
1749C4—42no—
1750C4—44no—
1751C4—44no—
1752C4—42no—
1753C4—42no—
1754C4—42no—
1755C4—42no—
1756C4—42no—
1757C4—41no—
1758C4—42no—
1759C4—42no—
1760C4#346014yes—
1761C4#352214yes—
1762C2—42no—
1763C2—84no—
1764C2—82no—
1765C2—84no—
1766C2C2×#346011yescharacteristic
1767C2C2×#352211yescharacteristic
1768C2#6280011yescharacteristic
1769C2#6283011yescharacteristic
1770C2#6283211yescharacteristic
1771C2#6283511yescharacteristic
1772C2#6283511yescharacteristic
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. #40438C2semidirect
2. #40125C2semidirect
3. #40054C2semidirect
4. #39808C2semidirect
5. #39790C2semidirect
6. #39770C2semidirect
7. #39745C2semidirect
8. #39726C2semidirect
9. #39725C2semidirect
10. #39672C2semidirect
11. #39633C2semidirect
12. #39625C2semidirect
13. #39406C2semidirect
14. #39352C2semidirect
15. #39351C2semidirect
16. #37810C2semidirect
17. #37794C2semidirect
18. #37792C2semidirect
19. #37051C2semidirect
20. #36911C2semidirect
21. #36644C2semidirect
22. #36638C2semidirect
23. #35607C2semidirect
24. #35600C2semidirect
25. #35560C2semidirect
26. #35535C2semidirect
27. #35295C2semidirect
28. #35276C2semidirect
29. #35198C2semidirect
30. #35198C2semidirect
31. #35186C2semidirect
32. #35114C2semidirect
33. #34331C2semidirect
34. #34313C2semidirect
35. C4×#533C2semidirect
952. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#404382
#401252
#400542
#398082
#397902
#397702
#397452
#397262
#397252
#396722
#396332
#396252
#394062
#393522
#393512
#378102
#377942
#377922
#370512
#369112
#366442
#366382
#356072
#356002
#355602
#355352
#352952
#352762
#351982
#351862
#351142
#343312
#343132
C4×#5332