Finite Group Databasebeta

← #7654426

Subgroups — #7654426

Order 512.

5688 conjugacy classes of subgroups.

The subgroup lattice has 1807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42751C212yesmaximal, complemented
2#42617C212yesmaximal, complemented
3#42109C214yesmaximal, complemented
4#42101C214yesmaximal, complemented
5#40378C214yesmaximal, complemented
6#40122C212yesmaximal, complemented
7#39818C212yesmaximal, complemented
8#39745C211yesmaximal, characteristic, complemented
9#39256C212yesmaximal, complemented
10#39218C212yesmaximal, complemented
11#39181C211yesmaximal, characteristic, complemented
12#39138C211yesmaximal, characteristic, complemented
13#39137C211yesmaximal, characteristic, complemented
14#37822C214yesmaximal, complemented
15#37794C212yesmaximal, complemented
16#37772C212yesmaximal, complemented
17#37626C211yesmaximal, characteristic, complemented
18#37587C212yesmaximal, complemented
19#36587C211yesmaximal, characteristic, complemented
20#36495C212yesmaximal, complemented
21#36453C211yesmaximal, characteristic, complemented
22#36128C211yesmaximal, characteristic, complemented
23#36126C211yesmaximal, characteristic, complemented
24#36125C212yesmaximal, complemented
25#35715C212yesmaximal, complemented
26#35704C212yesmaximal, complemented
27#35278C211yesmaximal, characteristic, complemented
28#35198C211yesmaximal, characteristic, complemented
29#35193C212yesmaximal, complemented
30#35109C212yesmaximal, complemented
31#34974C211yesmaximal, characteristic, complemented
32#34925C212yesmaximal, complemented
33#34313C211yesmaximal, characteristic, complemented
34C4×#559C211yesmaximal, characteristic, complemented
35#34153C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#550C2212yes—
39C2×#547C2212yes—
40C2×#542C2212yes—
41C2×#540C2212yes—
42C2×#532C2214yes—
43C2×#532C2212yes—
44C2×#532C2212yes—
45C2×#529C2211yescharacteristic
46C2×#520C2212yes—
47#2867C2211yescharacteristic
48#2860C2212yes—
49#2859C2211yescharacteristic
50#2858C2212yes—
51#2856C2211yescharacteristic
52#2856C2212yes—
53#2856C2211yescharacteristic
54#2855C2212yes—
55#2854C2212yes—
56#2853C2214yes—
57#2850C2214yes—
58#2850C2212yes—
59#2829C2214yes—
60#2828C2214yes—
61#2828C2214yes—
62#2803C2214yes—
63#2778C2214yes—
64#2774C2214yes—
65#2756C2214yes—
66#2746C2214yes—
67#2733C2214yes—
68#2730C2214yes—
69#2715C2214yes—
70#2714C2214yes—
71#2714C2214yes—
72#2714C2214yes—
73#2713C2214yes—
74#2705C2214yes—
75#2701C2214yes—
76#2701C2214yes—
77#2688C2214yes—
78#2688C2214yes—
79#2686C2214yes—
80#2682C2214yes—
81#2674C2214yes—
82#2673C2214yes—
83#2673C2214yes—
84#2673C2214yes—
85#2673C2214yes—
86#2662C2214yes—
87#2661C2214yes—
88#2657C2212yes—
89#2653C2214yes—
90#2651C2214yes—
91#2648C2214yes—
92#2648C2214yes—
93#2647C2212yes—
94#2641C2212yes—
95#2635C2214yes—
96#2635C2214yes—
97#2635C2214yes—
98#2630C2214yes—
99#2624C2212yes—
100#2624C2212yes—
101#2620C2212yes—
102#2619C2212yes—
103#2619C2212yes—
104#2619C2212yes—
105#2619C2212yes—
106#2602C2214yes—
107#2597C2214yes—
108#2591C2214yes—
109#2581C2212yes—
110#2578C2214yes—
111#2576C2214yes—
112#2576C2214yes—
113#2571C2211yescharacteristic
114#2570C2212yes—
115#2559C2214yes—
116#2557C2214yes—
117#2555C2214yes—
118#2555C2214yes—
119#2551C2211yescharacteristic
120#2551C2212yes—
121#2548C2212yes—
122#2548C2211yescharacteristic
123#2548C2212yes—
124#2546C2212yes—
125#2544C2212yes—
126#2541C2212yes—
127#2541C2211yescharacteristic
128#2541C2212yes—
129#2541C2211yescharacteristic
130#2541C2211yescharacteristic
131#2541C2212yes—
132#2541C2212yes—
133#2540C2212yes—
134#2538C2211yescharacteristic
135#2537C2212yes—
136#2537C2211yescharacteristic
137#2535C2212yes—
138#2532C2212yes—
139#2529C2212yes—
140#2516C2214yes—
141#2513C2212yes—
142#2513C2212yes—
143#2512C2211yescharacteristic
144#2509C2212yes—
145#2508C2211yescharacteristic
146#2504C2212yes—
147#2495C2211yescharacteristic
148#2494C2212yes—
149#2494C2212yes—
150#2491C2212yes—
151#2491C2211yescharacteristic
152#2491C2212yes—
153#2491C2214yes—
154#2490C2212yes—
155#2479C2212yes—
156#2477C2214yes—
157#2476C2214yes—
158#2476C2214yes—
159#2474C2212yes—
160#2471C2214yes—
161#2467C2214yes—
162#2466C2214yes—
163#2464C2214yes—
164#2464C2214yes—
165#2464C2214yes—
166#2464C2214yes—
167#2461C2214yes—
168#2461C2214yes—
169#2460C2214yes—
170#2457C2214yes—
171#2456C2214yes—
172#2456C2214yes—
173#2454C2212yes—
174#2452C2212yes—
175#2452C2212yes—
176#2451C2212yes—
177#2451C2211yescharacteristic
178#2449C2214yes—
179#2448C2211yescharacteristic
180#2447C2212yes—
181#2445C2212yes—
182#2445C2212yes—
183#2445C2212yes—
184#2445C2212yes—
185#2445C2212yes—
186#2445C2212yes—
187#2444C2214yes—
188#2443C2214yes—
189#2432C2214yes—
190#2431C2214yes—
191#2431C2214yes—
192#2431C2212yes—
193#2431C2212yes—
194#2431C2212yes—
195#2430C2214yes—
196#2428C2212yes—
197#2428C2212yes—
198#2428C2212yes—
199#2428C2212yes—
200#2428C2212yes—
201#2428C2214yes—
202#2428C2212yes—
203#2428C2212yes—
204#2428C2212yes—
205#2428C2212yes—
206#2428C2214yes—
207#2428C2212yes—
208#2428C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2426C2212yes—
212#2426C2211yescharacteristic
213#2423C2211yescharacteristic
214#2420C2212yes—
215#2420C2212yes—
216#2420C2212yes—
217#2416C2212yes—
218#2407C2212yes—
219#2407C2214yes—
220#2406C2214yes—
221#2396C2212yes—
222#2395C2212yes—
223#2388C2214yes—
224#2388C2214yes—
225#2374C2214yes—
226#2373C2212yes—
227#2373C2212yes—
228#2370C2211yescharacteristic
229#2370C2211yescharacteristic
230#2367C2211yescharacteristic
231#2367C2211yescharacteristic
232#2367C2212yes—
233#2367C2212yes—
234#2366C2211yescharacteristic
235#2366C2212yes—
236#2366C2211yescharacteristic
237#2366C2212yes—
238#2361C2212yes—
239#2361C2214yes—
240#2361C2211yescharacteristic
241#2361C2212yes—
242#2361C2212yes—
243#2361C2212yes—
244#2361C2211yescharacteristic
245#2360C2211yescharacteristic
246#2360C2211yescharacteristic
247#2359C2212yes—
248#2359C2212yes—
249#2357C2212yes—
250#2357C2212yes—
251#2357C2212yes—
252#2355C2211yescharacteristic
253#2355C2211yescharacteristic
254Q8×C4⋊C4C2211yescharacteristic
255D4×C4⋊C4C2211yescharacteristic
256D4×C4⋊C4C2212yes—
257#2345C2212yes—
258#2341C2212yes—
259#2333C2214yes—
260#2333C2214yes—
261#2331C2212yes—
262#2328C2212yes—
263#2328C2212yes—
264#2324C2214yes—
265#2324C2212yes—
266#2324C2212yes—
267#2324C2212yes—
268#2324C2212yes—
269C4×C4⋊Q8C2211yescharacteristic
270C4×#127C2212yes—
271C4×#127C2211yescharacteristic
272C4×#127C2211yescharacteristic
273C4×#126C2212yes—
274C4×#124C2212yes—
275C4×#124C2212yes—
276C4×#124C2212yes—
277C4×#124C2211yescharacteristic
278C4×C22⋊Q8C2211yescharacteristic
279C4×#123C2214yes—
280C4×#121C2211yescharacteristic
281C4×#121C2212yes—
282C4×#121C2212yes—
283C4×#121C2214yes—
284#2298C2212yes—
285#2296C2212yes—
286#2295C2211yescharacteristic
287#2293C2212yes—
288#2293C2211yescharacteristic
289#2293C2211yescharacteristic
290#2290C2212yes—
291C42×Q8C2211yescharacteristic
292C42×Q8C2211yescharacteristic
293C42×D4C2212yes—
294C42×D4C2211yescharacteristic
295C42×D4C2212yes—
296C42×D4C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2314yes—
301C22×#41C2314yes—
302#559—28no—
303#550—28no—
304#550—48no—
305#547—48no—
306#542—48no—
307#540—48no—
308#532—416no—
309#532—48no—
310#532—48no—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2314yes—
315C2×#127C2311yescharacteristic
316C2×#127C2311yescharacteristic
317C2×#127C2312yes—
318C2×#127C2312yes—
319C2×#127C2312yes—
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2312yes—
326C2×#127C2312yes—
327C2×#127C2314yes—
328#529—28no—
329C2×#126C2312yes—
330C2×#126C2312yes—
331C2×#126C2314yes—
332C2×#125C2311yescharacteristic
333C2×#125C2312yes—
334C2×#124C2312yes—
335C2×#124C2311yescharacteristic
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2314yes—
339C2×#124C2312yes—
340C2×#124C2314yes—
341C2×#124C2311yescharacteristic
342C2×#124C2314yes—
343C2×#124C2314yes—
344C2×#123C2312yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2314yes—
356C2×#121C2314yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2311yescharacteristic
361C2×#121C2311yescharacteristic
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365C2×#121C2314yes—
366C2×#121C2312yes—
367C2×#121C2314yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2314yes—
374C2×#121C2312yes—
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2312yes—
378C2×#121C2312yes—
379C2×#121C2314yes—
380C2×#121C2314yes—
381C2×#121C2314yes—
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C2×#121C2314yes—
386#520—48no—
387C2×C4×Q8C2311yescharacteristic
388C2×C4×Q8C2311yescharacteristic
389C2×C4×Q8C2311yescharacteristic
390C2×C4×Q8C2312yes—
391C2×C4×Q8C2312yes—
392C2×C4×Q8C2311yescharacteristic
393C2×C4×Q8C2311yescharacteristic
394C2×C4×Q8C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2312yes—
407C2×C4×D4C2314yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2314yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2311yescharacteristic
419C2×C4×D4C2314yes—
420C2×C4×D4C2314yes—
421C2×C4×D4C2314yes—
422C2×C4×D4C2314yes—
423C2×C4×D4C2312yes—
424C2×#117C2312yes—
425C2×#117C2311yescharacteristic
426C2×#117C2312yes—
427C2×#117C2312yes—
428C2×#117C2314yes—
429C2×#117C2311yescharacteristic
430C22×C4⋊C4C2312yes—
431C22×C4⋊C4C2311yescharacteristic
432C22×C4⋊C4C2314yes—
433C22×C4⋊C4C2311yescharacteristic
434C22×C42C2311yescharacteristic
435C22×C42C2314yes—
436C22×C42C2312yes—
437C22×C42C2312yes—
438#401C2314yes—
439#400C2314yes—
440#400C2314yes—
441#400C2314yes—
442#400C2314yes—
443#400C2312yes—
444#400C2312yes—
445#399C2312yes—
446#399C2314yes—
447#399C2312yes—
448#399C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2312yes—
453#398C2312yes—
454#398C2312yes—
455#397C2312yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2312yes—
466#397C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2312yes—
473#396C2312yes—
474#395C2314yes—
475#395C2314yes—
476#395C2312yes—
477#395C2314yes—
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#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2312yes—
505#394C2314yes—
506#394C2314yes—
507#394C2312yes—
508#394C2314yes—
509#393C2312yes—
510#393C2314yes—
511#393C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#392C2314yes—
524#392C2314yes—
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#392C2314yes—
531#392C2314yes—
532#392C2314yes—
533#392C2314yes—
534#391C2312yes—
535#391C2311yescharacteristic
536#391C2312yes—
537#391C2314yes—
538#391C2314yes—
539#391C2312yes—
540#391C2311yescharacteristic
541#391C2311yescharacteristic
542#391C2311yescharacteristic
543#391C2312yes—
544#390C2312yes—
545#390C2311yescharacteristic
546#390C2312yes—
547#390C2314yes—
548#390C2312yes—
549#390C2312yes—
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2314yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2314yes—
560#390C2314yes—
561#390C2312yes—
562#390C2312yes—
563#390C2312yes—
564#390C2314yes—
565#390C2314yes—
566#390C2314yes—
567#390C2314yes—
568#390C2312yes—
569#390C2312yes—
570#390C2314yes—
571#390C2312yes—
572#390C2312yes—
573#390C2311yescharacteristic
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#390C2312yes—
578#390C2312yes—
579#390C2311yescharacteristic
580#390C2311yescharacteristic
581#390C2311yescharacteristic
582#390C2312yes—
583#390C2312yes—
584#390C2314yes—
585#390C2311yescharacteristic
586#389C2311yescharacteristic
587#389C2311yescharacteristic
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2314yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2311yescharacteristic
605#389C2311yescharacteristic
606#389C2312yes—
607#389C2312yes—
608#389C2311yescharacteristic
609#389C2312yes—
610#389C2311yescharacteristic
611#389C2311yescharacteristic
612#389C2311yescharacteristic
613#389C2314yes—
614#388C2312yes—
615#388C2312yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2314yes—
621#388C2312yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2312yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2312yes—
634#388C2314yes—
635#388C2312yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2312yes—
644#388C2312yes—
645#388C2312yes—
646#388C2312yes—
647#388C2312yes—
648#388C2314yes—
649#388C2314yes—
650#388C2312yes—
651#388C2312yes—
652#388C2314yes—
653#388C2312yes—
654#388C2312yes—
655#388C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2314yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2312yes—
671#387C2312yes—
672#387C2314yes—
673#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#387C2312yes—
677#386C2314yes—
678#386C2314yes—
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#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2312yes—
704#386C2312yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2312yes—
709#386C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2312yes—
720#385C2312yes—
721#385C2312yes—
722#385C2312yes—
723#385C2312yes—
724#385C2312yes—
725#385C2314yes—
726#385C2312yes—
727#384C2311yescharacteristic
728#384C2311yescharacteristic
729#384C2312yes—
730#384C2311yescharacteristic
731#383C2312yes—
732#382C2312yes—
733#382C2312yes—
734#382C2312yes—
735#382C2312yes—
736#382C2312yes—
737#382C2311yescharacteristic
738#382C2312yes—
739#381C2314yes—
740#381C2314yes—
741#381C2314yes—
742#381C2314yes—
743#380C2314yes—
744#380C2312yes—
745#380C2312yes—
746#380C2314yes—
747#380C2312yes—
748#380C2311yescharacteristic
749#380C2312yes—
750#380C2314yes—
751#380C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2314yes—
813#376C2311yescharacteristic
814#376C2312yes—
815#376C2311yescharacteristic
816C2×#95C2312yes—
817C43C2312yes—
818C43C2311yescharacteristic
819C43C2312yes—
820C43C2311yescharacteristic
821C2×#41—28no—
822C2×#41—48no—
823C2×#41—48no—
824C2×#41—48no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—48no—
828C2×#41—48no—
829C2×#41—48no—
830C22×Q8C2411yescharacteristic
831C22×Q8C2412yes—
832C22×Q8C2411yescharacteristic
833C22×Q8C2414yes—
834C22×D4C2411yescharacteristic
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2412yes—
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2411yescharacteristic
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2414yes—
867C23×C4C2414yes—
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2414yes—
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2414yes—
874C23×C4C2412yes—
875C4⋊Q8—24no—
876C4⋊Q8—28no—
877C4⋊Q8—44no—
878C4⋊Q8—48no—
879#127—24no—
880#127—28no—
881#127—24no—
882#127—44no—
883#127—44no—
884#127—44no—
885#127—44no—
886#127—44no—
887#127—44no—
888#127—44no—
889#127—44no—
890#127—44no—
891#127—48no—
892#126—28no—
893#126—48no—
894#126—44no—
895#125—24no—
896#125—44no—
897#124—24no—
898#124—28no—
899#124—28no—
900#124—28no—
901#124—48no—
902#124—42no—
903#124—44no—
904#124—48no—
905#124—48no—
906#124—48no—
907#123—28no—
908#123—216no—
909#123—48no—
910#123—48no—
911#123—48no—
912#123—48no—
913#123—48no—
914C22⋊Q8—24no—
915C22⋊Q8—48no—
916C22⋊Q8—48no—
917C22⋊Q8—42no—
918C22⋊Q8—44no—
919#121—24no—
920#121—28no—
921#121—216no—
922#121—24no—
923#121—28no—
924#121—216no—
925#121—48no—
926#121—48no—
927#121—48no—
928#121—48no—
929#121—48no—
930#121—48no—
931#121—48no—
932#121—48no—
933#121—48no—
934#121—48no—
935#121—44no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—44no—
940#121—44no—
941#121—44no—
942#121—48no—
943#121—44no—
944#121—44no—
945#121—44no—
946#121—44no—
947#121—44no—
948#121—44no—
949C4×Q8—24no—
950C4×Q8—24no—
951C4×Q8—24no—
952C4×Q8—44no—
953C4×Q8—42no—
954C4×Q8—42no—
955C4×Q8—44no—
956C4×Q8#4118yescomplemented
957C4×D4—28no—
958C4×D4—28no—
959C4×D4—28no—
960C4×D4—28no—
961C4×D4—24no—
962C4×D4—28no—
963C4×D4—24no—
964C4×D4—28no—
965C4×D4—24no—
966C4×D4—28no—
967C4×D4—28no—
968C4×D4—48no—
969C4×D4—44no—
970C4×D4—44no—
971C4×D4—44no—
972C4×D4—42no—
973C4×D4—44no—
974C4×D4—44no—
975C4×D4—44no—
976C4×D4—44no—
977C4×D4—48no—
978C4×D4—44no—
979C4×D4—44no—
980C4×D4—44no—
981C4×D4—48no—
982C4×D4—48no—
983C4×D4—48no—
984C4×D4—48no—
985C4×D4—48no—
986#117—24no—
987#117—28no—
988#117—44no—
989#117—44no—
990#117—42no—
991#117—48no—
992C2×C4⋊C4—28no—
993C2×C4⋊C4—24no—
994C2×C4⋊C4—42no—
995C2×C4⋊C4—48no—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2411yescharacteristic
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2411yescharacteristic
1051C2×C4⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2411yescharacteristic
1054C2×C22⋊C4C2411yescharacteristic
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2411yescharacteristic
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2411yescharacteristic
1119C2×C42—24no—
1120C2×C42—48no—
1121C2×C42—44no—
1122C2×C42—44no—
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2412yes—
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2411yescharacteristic
1138C2×C42C2412yes—
1139C2×C42C2411yescharacteristic
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2414yes—
1147C2×C42C2411yescharacteristic
1148C2×C42C2414yes—
1149C2×C42C2412yes—
1150C2×C42C2412yes—
1151C2×C42C2412yes—
1152C2×C42C2412yes—
1153C2×C42C2412yes—
1154C2×C42C2412yes—
1155C2×C42C2412yes—
1156C2×C42C2412yes—
1157C2×C42C2414yes—
1158C2×C42C2412yes—
1159C2×C42C2411yescharacteristic
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2411yescharacteristic
1165#95C2411yescharacteristic
1166#95C2411yescharacteristic
1167#95C2411yescharacteristic
1168#95C2411yescharacteristic
1169#95C2411yescharacteristic
1170#95C2411yescharacteristic
1171#95C2411yescharacteristic
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2414yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2414yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2412yes—
1210#95C2414yes—
1211#95C2412yes—
1212#95C2412yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218C24C2512yes—
1219C24C2514yes—
1220C24C2512yes—
1221C24C2514yes—
1222C24C2511yescharacteristic
1223#41—432no—
1224#41—832no—
1225#41—832no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—24no—
1230C2×Q8—24no—
1231C2×Q8—28no—
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—42no—
1235C2×Q8—44no—
1236C2×Q8—44no—
1237C2×Q8C2×#4114yes—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—28no—
1241C2×D4—28no—
1242C2×D4—24no—
1243C2×D4—22no—
1244C2×D4—24no—
1245C2×D4—24no—
1246C2×D4—24no—
1247C2×D4—22no—
1248C2×D4—28no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—28no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—22no—
1257C2×D4—24no—
1258C2×D4—22no—
1259C2×D4—24no—
1260C2×D4—28no—
1261C2×D4—28no—
1262C2×D4—22no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—22no—
1266C2×D4—24no—
1267C2×D4—24no—
1268C2×D4—28no—
1269C2×D4—44no—
1270C2×D4—42no—
1271C2×D4—42no—
1272C2×D4—44no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C2×D4—44no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—42no—
1299C2×D4—42no—
1300C2×D4—44no—
1301C2×D4—44no—
1302C2×D4—44no—
1303C2×D4—44no—
1304C2×D4—44no—
1305C2×D4—44no—
1306C2×D4—44no—
1307C2×D4—44no—
1308C2×D4—44no—
1309C2×D4—44no—
1310C2×D4—44no—
1311C2×D4—44no—
1312C2×D4—44no—
1313C22×C4—22no—
1314C22×C4—24no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—22no—
1318C22×C4—24no—
1319C22×C4—28no—
1320C22×C4—24no—
1321C22×C4—22no—
1322C22×C4—24no—
1323C22×C4—24no—
1324C22×C4—22no—
1325C22×C4—24no—
1326C22×C4—28no—
1327C22×C4—24no—
1328C22×C4—24no—
1329C22×C4—28no—
1330C22×C4—22no—
1331C22×C4—24no—
1332C22×C4—22no—
1333C22×C4—24no—
1334C22×C4—28no—
1335C22×C4—28no—
1336C22×C4—28no—
1337C22×C4—28no—
1338C22×C4—24no—
1339C22×C4—44no—
1340C22×C4—42no—
1341C22×C4—42no—
1342C22×C4—44no—
1343C22×C4—41no—
1344C22×C4—44no—
1345C22×C4—42no—
1346C22×C4—44no—
1347C22×C4—42no—
1348C22×C4—42no—
1349C22×C4—44no—
1350C22×C4—44no—
1351C22×C4—44no—
1352C22×C4—44no—
1353C22×C4—44no—
1354C22×C4—44no—
1355C22×C4—42no—
1356C22×C4—42no—
1357C22×C4—44no—
1358C22×C4—44no—
1359C22×C4—44no—
1360C22×C4—44no—
1361C22×C4C2511yescharacteristic
1362C22×C4C2511yescharacteristic
1363C22×C4C2512yes—
1364C22×C4C2514yes—
1365C22×C4C2512yes—
1366C22×C4C2512yes—
1367C22×C4C2512yes—
1368C22×C4C2512yes—
1369C22×C4C2512yes—
1370C22×C4C2511yescharacteristic
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2511yescharacteristic
1374C22×C4C2512yes—
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2511yescharacteristic
1378C22×C4C2511yescharacteristic
1379C22×C4C2511yescharacteristic
1380C22×C4C2514yes—
1381C22×C4C2511yescharacteristic
1382C22×C4C2512yes—
1383C22×C4C2512yes—
1384C22×C4C2511yescharacteristic
1385C22×C4C2512yes—
1386C22×C4C2512yes—
1387C22×C4C2511yescharacteristic
1388C22×C4C2511yescharacteristic
1389C22×C4C2511yescharacteristic
1390C22×C4C2511yescharacteristic
1391C4⋊C4—24no—
1392C4⋊C4—24no—
1393C4⋊C4—22no—
1394C4⋊C4—22no—
1395C4⋊C4—22no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—28no—
1399C4⋊C4—24no—
1400C4⋊C4—22no—
1401C4⋊C4—24no—
1402C4⋊C4—24no—
1403C4⋊C4—22no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—22no—
1408C4⋊C4—24no—
1409C4⋊C4—28no—
1410C4⋊C4—28no—
1411C4⋊C4—24no—
1412C4⋊C4—22no—
1413C4⋊C4—22no—
1414C4⋊C4—22no—
1415C4⋊C4—24no—
1416C4⋊C4—24no—
1417C4⋊C4—24no—
1418C4⋊C4—22no—
1419C4⋊C4—22no—
1420C4⋊C4—24no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—41no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—42no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—42no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—44no—
1439C4⋊C4—42no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—42no—
1443C4⋊C4C2×#4114yes—
1444C4⋊C4C2×#4118yes—
1445C4⋊C4H(5,𝔽2)14yes—
1446C4⋊C4H(5,𝔽2)14yes—
1447C22⋊C4—22no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—28no—
1453C22⋊C4—24no—
1454C22⋊C4—28no—
1455C22⋊C4—28no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—28no—
1459C22⋊C4—28no—
1460C22⋊C4—24no—
1461C22⋊C4—28no—
1462C22⋊C4—28no—
1463C22⋊C4—24no—
1464C22⋊C4—28no—
1465C22⋊C4—24no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—28no—
1469C22⋊C4—22no—
1470C22⋊C4—24no—
1471C22⋊C4—41no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—42no—
1489C22⋊C4—42no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—42no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—42no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C22⋊C4—42no—
1513C22⋊C4H(5,𝔽2)14yes—
1514C42—22no—
1515C42—22no—
1516C42—22no—
1517C42—24no—
1518C42—24no—
1519C42—24no—
1520C42—24no—
1521C42—22no—
1522C42—24no—
1523C42—22no—
1524C42—22no—
1525C42—24no—
1526C42—22no—
1527C42—22no—
1528C42—24no—
1529C42—24no—
1530C42—22no—
1531C42—24no—
1532C42—22no—
1533C42—22no—
1534C42—22no—
1535C42—22no—
1536C42—22no—
1537C42—42no—
1538C42—44no—
1539C42—42no—
1540C42—42no—
1541C42—42no—
1542C42—44no—
1543C42—41no—
1544C42—44no—
1545C42—42no—
1546C42—42no—
1547C42—42no—
1548C42—42no—
1549C42C2×#4114yes—
1550C42C2×#4118yes—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—22no—
1558C23—24no—
1559C23—24no—
1560C23—22no—
1561C23—22no—
1562C23—24no—
1563C23—24no—
1564C23—22no—
1565C23—24no—
1566C23—22no—
1567C23—24no—
1568C23—24no—
1569C23—22no—
1570C23—22no—
1571C23—22no—
1572C23—24no—
1573C23—22no—
1574C23—22no—
1575C23—22no—
1576C23—24no—
1577C23—24no—
1578C23—24no—
1579C23—24no—
1580C23—22no—
1581C23—24no—
1582C23—24no—
1583C23—22no—
1584C23—22no—
1585C23C2×H(5,𝔽2)12yes—
1586C23C2611yescharacteristic
1587Q8—28no—
1588Q8—48no—
1589Q8—44no—
1590Q8—88no—
1591D4—48no—
1592D4—48no—
1593D4—416no—
1594D4—44no—
1595D4—48no—
1596D4—48no—
1597D4—48no—
1598D4—48no—
1599D4—44no—
1600D4—88no—
1601D4—84no—
1602D4—84no—
1603D4—88no—
1604D4—88no—
1605D4—88no—
1606D4—88no—
1607D4—88no—
1608D4—88no—
1609D4—88no—
1610D4—88no—
1611D4—88no—
1612D4—164no—
1613D4—164no—
1614D4—164no—
1615D4—164no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—22no—
1654C2×C4—21no—
1655C2×C4—22no—
1656C2×C4—24no—
1657C2×C4—24no—
1658C2×C4—22no—
1659C2×C4—24no—
1660C2×C4—22no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—24no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—21no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—22no—
1682C2×C4—21no—
1683C2×C4—21no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—24no—
1689C2×C4—24no—
1690C2×C4—21no—
1691C2×C4—22no—
1692C2×C4—416no—
1693C2×C4—48no—
1694C2×C4—44no—
1695C2×C4—48no—
1696C2×C4—416no—
1697C2×C4—44no—
1698C2×C4—48no—
1699C2×C4—44no—
1700C2×C4—48no—
1701C2×C4—84no—
1702C2×C4—88no—
1703C2×C4—88no—
1704C2×C4—88no—
1705C2×C4—88no—
1706C2×C4—84no—
1707C2×C4—164no—
1708C2×C4C22×#4112yes—
1709C2×C4C22×#4114yes—
1710C2×C4C22×#4114yes—
1711C2×C4C22×#4112yes—
1712C2×C4C22×#4112yes—
1713C2×C4C2×H(5,𝔽2)12yes—
1714C2×C4C2×H(5,𝔽2)14yes—
1715C2×C4C2×H(5,𝔽2)14yes—
1716C2×C4C2×H(5,𝔽2)12yes—
1717C2×C4C2×H(5,𝔽2)12yes—
1718C2×C4C2×H(5,𝔽2)12yes—
1719C2×C4#58512yes—
1720C2×C4#58512yes—
1721C2×C4#58512yes—
1722C22—22no—
1723C22—22no—
1724C22—22no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—42no—
1730C22—44no—
1731C22—42no—
1732C22—44no—
1733C22—42no—
1734C22—44no—
1735C22—42no—
1736C22—44no—
1737C22—44no—
1738C22—42no—
1739C22—42no—
1740C22—44no—
1741C22—42no—
1742C22—44no—
1743C22—44no—
1744C22—42no—
1745C22—42no—
1746C22—44no—
1747C22—44no—
1748C22—42no—
1749C22—44no—
1750C22—42no—
1751C22—42no—
1752C22—44no—
1753C22—44no—
1754C22—42no—
1755C22—42no—
1756C22—44no—
1757C22C23×#4111yescharacteristic
1758C22C22×H(5,𝔽2)11yescharacteristic
1759C22C22×H(5,𝔽2)11yescharacteristic
1760C22C22×H(5,𝔽2)11yescharacteristic
1761C22C2×#58511yescharacteristic
1762C22C2×#58511yescharacteristic
1763C22C2×#58511yescharacteristic
1764C4—24no—
1765C4—24no—
1766C4—22no—
1767C4—22no—
1768C4—22no—
1769C4—22no—
1770C4—24no—
1771C4—24no—
1772C4—42no—
1773C4—42no—
1774C4—44no—
1775C4—41no—
1776C4—41no—
1777C4—42no—
1778C4—42no—
1779C4—44no—
1780C4—41no—
1781C4—41no—
1782C4—42no—
1783C4—42no—
1784C4—41no—
1785C4—41no—
1786C4—42no—
1787C4—42no—
1788C4—41no—
1789C4—42no—
1790C4—41no—
1791C4—42no—
1792C4#346014yes—
1793C4#351714yes—
1794C2—42no—
1795C2—82no—
1796C2—84no—
1797C2—82no—
1798C2—84no—
1799C2C2×#346011yescharacteristic
1800C2C2×#351711yescharacteristic
1801C2#6280011yescharacteristic
1802C2#6301111yescharacteristic
1803C2#6301911yescharacteristic
1804C2#6302111yescharacteristic
1805C2#6303511yescharacteristic
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. #42751C2semidirect
2. #42617C2semidirect
3. #42109C2semidirect
4. #42101C2semidirect
5. #40378C2semidirect
6. #40122C2semidirect
7. #39818C2semidirect
8. #39745C2semidirect
9. #39256C2semidirect
10. #39218C2semidirect
11. #39181C2semidirect
12. #39138C2semidirect
13. #39137C2semidirect
14. #37822C2semidirect
15. #37794C2semidirect
16. #37772C2semidirect
17. #37626C2semidirect
18. #37587C2semidirect
19. #36587C2semidirect
20. #36495C2semidirect
21. #36453C2semidirect
22. #36128C2semidirect
23. #36126C2semidirect
24. #36125C2semidirect
25. #35715C2semidirect
26. #35704C2semidirect
27. #35278C2semidirect
28. #35198C2semidirect
29. #35193C2semidirect
30. #35109C2semidirect
31. #34974C2semidirect
32. #34925C2semidirect
33. #34313C2semidirect
34. C4×#559C2semidirect
35. #34153C2semidirect
956. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#427512
#426172
#421092
#421012
#403782
#401222
#398182
#397452
#392562
#392182
#391812
#391382
#391372
#378222
#377942
#377722
#376262
#375872
#365872
#364952
#364532
#361282
#361262
#361252
#357152
#357042
#352782
#351982
#351932
#351092
#349742
#349252
#343132
C4×#5592
#341532