Finite Group Databasebeta

← #7986748

Subgroups — #7986748

Order 512.

5601 conjugacy classes of subgroups.

The subgroup lattice has 1783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59465C211yesmaximal, characteristic, complemented
2#59459C211yesmaximal, characteristic, complemented
3#59457C211yesmaximal, characteristic, complemented
4#59072C212yesmaximal, complemented
5#59039C212yesmaximal, complemented
6#51948C214yesmaximal, complemented
7#50778C214yesmaximal, complemented
8#45718C212yesmaximal, complemented
9#45653C212yesmaximal, complemented
10#45034C212yesmaximal, complemented
11#44880C212yesmaximal, complemented
12#44151C214yesmaximal, complemented
13#42585C212yesmaximal, complemented
14#42467C212yesmaximal, complemented
15#42093C214yesmaximal, complemented
16#40174C212yesmaximal, complemented
17#39853C212yesmaximal, complemented
18#39853C212yesmaximal, complemented
19#39386C211yesmaximal, characteristic, complemented
20#39202C211yesmaximal, characteristic, complemented
21#39137C212yesmaximal, complemented
22#37792C212yesmaximal, complemented
23#36595C211yesmaximal, characteristic, complemented
24#36469C211yesmaximal, characteristic, complemented
25#36139C212yesmaximal, complemented
26#36128C211yesmaximal, characteristic, complemented
27#36115C211yesmaximal, characteristic, complemented
28#36115C211yesmaximal, characteristic, complemented
29#35238C212yesmaximal, complemented
30#35196C211yesmaximal, characteristic, complemented
31#35171C211yesmaximal, characteristic, complemented
32#34925C211yesmaximal, characteristic, complemented
33#34893C211yesmaximal, characteristic, complemented
34#34423C212yesmaximal, complemented
35C4×#554C211yesmaximal, characteristic, complemented
36C2×#559C2212yes—
37C2×#559C2212yes—
38C2×#554C2211yescharacteristic
39C2×#550C2212yes—
40C2×#540C2212yes—
41C2×#540C2212yes—
42C2×#532C2212yes—
43C2×#532C2212yes—
44C2×#532C2212yes—
45C2×#529C2212yes—
46C2×#529C2212yes—
47#2867C2211yescharacteristic
48#2858C2211yescharacteristic
49#2858C2211yescharacteristic
50#2856C2212yes—
51#2856C2212yes—
52#2855C2212yes—
53#2854C2212yes—
54#2854C2212yes—
55#2850C2212yes—
56#2850C2212yes—
57#2850C2212yes—
58#2832C2214yes—
59#2830C2214yes—
60#2800C2214yes—
61#2797C2214yes—
62#2792C2214yes—
63#2784C2214yes—
64#2780C2214yes—
65#2752C2214yes—
66#2751C2214yes—
67#2741C2214yes—
68#2718C2214yes—
69#2715C2214yes—
70#2712C2214yes—
71#2712C2214yes—
72#2710C2214yes—
73#2708C2214yes—
74#2705C2214yes—
75#2705C2214yes—
76#2701C2214yes—
77#2696C2214yes—
78#2692C2214yes—
79#2686C2214yes—
80#2686C2214yes—
81#2682C2214yes—
82#2682C2214yes—
83#2681C2214yes—
84#2676C2214yes—
85#2676C2214yes—
86#2673C2214yes—
87#2673C2214yes—
88#2672C2214yes—
89#2672C2214yes—
90#2672C2214yes—
91#2671C2214yes—
92#2671C2214yes—
93#2662C2214yes—
94#2662C2214yes—
95#2661C2214yes—
96#2649C2214yes—
97#2630C2214yes—
98#2630C2214yes—
99#2624C2212yes—
100#2620C2214yes—
101#2619C2212yes—
102#2602C2214yes—
103#2592C2212yes—
104#2589C2212yes—
105#2587C2212yes—
106#2586C2214yes—
107#2584C2212yes—
108#2584C2211yescharacteristic
109#2580C2212yes—
110#2580C2211yescharacteristic
111#2571C2211yescharacteristic
112#2567C2212yes—
113#2567C2212yes—
114#2566C2212yes—
115#2566C2212yes—
116#2566C2211yescharacteristic
117#2564C2214yes—
118#2563C2212yes—
119#2563C2212yes—
120#2557C2214yes—
121#2555C2214yes—
122#2552C2211yescharacteristic
123#2551C2211yescharacteristic
124#2550C2211yescharacteristic
125#2550C2212yes—
126#2548C2212yes—
127#2548C2212yes—
128#2548C2212yes—
129#2548C2212yes—
130#2548C2212yes—
131#2547C2211yescharacteristic
132#2544C2212yes—
133#2544C2212yes—
134#2544C2212yes—
135#2544C2212yes—
136#2542C2211yescharacteristic
137#2541C2211yescharacteristic
138#2541C2211yescharacteristic
139#2541C2212yes—
140#2541C2211yescharacteristic
141#2541C2211yescharacteristic
142#2541C2212yes—
143#2541C2212yes—
144#2540C2214yes—
145#2538C2212yes—
146#2537C2214yes—
147#2537C2211yescharacteristic
148#2522C2212yes—
149#2521C2214yes—
150#2516C2214yes—
151#2512C2212yes—
152#2512C2212yes—
153#2509C2211yescharacteristic
154#2507C2211yescharacteristic
155#2497C2212yes—
156#2491C2212yes—
157#2491C2212yes—
158#2491C2212yes—
159#2490C2212yes—
160#2490C2212yes—
161#2474C2214yes—
162#2471C2214yes—
163#2471C2214yes—
164#2470C2214yes—
165#2468C2214yes—
166#2467C2214yes—
167#2467C2214yes—
168#2465C2212yes—
169#2464C2214yes—
170#2461C2214yes—
171#2455C2214yes—
172#2454C2212yes—
173#2454C2212yes—
174#2454C2212yes—
175#2454C2211yescharacteristic
176#2452C2212yes—
177#2452C2212yes—
178#2452C2212yes—
179#2452C2211yescharacteristic
180#2451C2212yes—
181#2451C2212yes—
182#2450C2214yes—
183#2448C2212yes—
184#2447C2212yes—
185#2445C2212yes—
186#2445C2212yes—
187#2445C2212yes—
188#2445C2212yes—
189#2445C2212yes—
190#2445C2212yes—
191#2445C2212yes—
192#2445C2212yes—
193#2443C2214yes—
194#2431C2214yes—
195#2430C2214yes—
196#2430C2214yes—
197#2430C2214yes—
198#2430C2214yes—
199#2428C2214yes—
200#2428C2212yes—
201#2428C2212yes—
202#2428C2212yes—
203#2428C2212yes—
204#2428C2212yes—
205#2428C2212yes—
206#2428C2212yes—
207#2428C2212yes—
208#2427C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2426C2212yes—
212#2426C2212yes—
213#2425C2214yes—
214#2425C2214yes—
215#2422C2212yes—
216#2422C2212yes—
217#2422C2214yes—
218#2421C2212yes—
219#2420C2212yes—
220#2420C2212yes—
221#2416C2214yes—
222#2416C2214yes—
223#2407C2214yes—
224#2407C2214yes—
225#2406C2214yes—
226#2396C2212yes—
227#2396C2212yes—
228#2388C2214yes—
229#2376C2214yes—
230#2376C2214yes—
231#2370C2212yes—
232#2370C2211yescharacteristic
233#2370C2211yescharacteristic
234#2369C2211yescharacteristic
235#2368C2212yes—
236#2368C2212yes—
237#2367C2212yes—
238#2366C2211yescharacteristic
239#2366C2211yescharacteristic
240#2366C2212yes—
241#2366C2212yes—
242#2366C2211yescharacteristic
243#2366C2211yescharacteristic
244#2366C2212yes—
245#2366C2212yes—
246#2366C2212yes—
247#2365C2211yescharacteristic
248#2365C2211yescharacteristic
249#2360C2212yes—
250#2359C2214yes—
251#2359C2214yes—
252#2355C2211yescharacteristic
253#2354C2212yes—
254#2354C2212yes—
255Q8×C4⋊C4C2212yes—
256#2349C2212yes—
257#2349C2212yes—
258#2349C2212yes—
259#2349C2212yes—
260#2349C2211yescharacteristic
261#2349C2211yescharacteristic
262D4×C4⋊C4C2211yescharacteristic
263#2345C2212yes—
264#2339C2214yes—
265#2325C2214yes—
266#2325C2214yes—
267#2324C2212yes—
268#2324C2212yes—
269#2324C2214yes—
270#2324C2214yes—
271#2324C2214yes—
272#2324C2212yes—
273#2314C2212yes—
274C4×C4⋊Q8C2211yescharacteristic
275C4×C4⋊Q8C2211yescharacteristic
276C4×C4⋊Q8C2211yescharacteristic
277C4×#127C2211yescharacteristic
278C4×#127C2211yescharacteristic
279C4×#125C2211yescharacteristic
280C4×#125C2211yescharacteristic
281C4×#125C2211yescharacteristic
282C4×#125C2211yescharacteristic
283C4×C22⋊Q8C2212yes—
284C4×C22⋊Q8C2212yes—
285C4×C22⋊Q8C2212yes—
286C4×C22⋊Q8C2212yes—
287C4×#121C2212yes—
288C4×#121C2212yes—
289C4×#121C2212yes—
290#2296C2212yes—
291#2293C2211yescharacteristic
292#2293C2211yescharacteristic
293C42×Q8C2211yescharacteristic
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C4⋊C4C2212yes—
299C22×#41C2314yes—
300C22×#41C2314yes—
301#559—48no—
302#559—48no—
303#554—28no—
304#550—48no—
305#540—216no—
306#540—48no—
307#532—48no—
308#532—48no—
309#532—48no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×#127C2311yescharacteristic
316C2×#127C2311yescharacteristic
317C2×#127C2312yes—
318C2×#127C2312yes—
319C2×#127C2312yes—
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2312yes—
326C2×#127C2312yes—
327#529—48no—
328#529—48no—
329C2×#126C2314yes—
330C2×#126C2314yes—
331C2×#125C2311yescharacteristic
332C2×#125C2311yescharacteristic
333C2×#125C2311yescharacteristic
334C2×#125C2312yes—
335C2×#125C2311yescharacteristic
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2312yes—
340C2×#124C2312yes—
341C2×#124C2314yes—
342C2×#124C2314yes—
343C2×#124C2314yes—
344C2×#124C2314yes—
345C2×#124C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×#123C2314yes—
352C2×#123C2314yes—
353C2×#123C2314yes—
354C2×#123C2314yes—
355C2×#123C2314yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2312yes—
362C2×C22⋊Q8C2314yes—
363C2×C22⋊Q8C2314yes—
364C2×#121C2314yes—
365C2×#121C2314yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2314yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2312yes—
374C2×#121C2312yes—
375C2×#121C2312yes—
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379C2×#121C2314yes—
380C2×#121C2314yes—
381C2×#121C2314yes—
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C2×#121C2314yes—
386C2×#121C2314yes—
387C2×#121C2314yes—
388C2×C4×Q8C2311yescharacteristic
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2311yescharacteristic
391C2×C4×Q8C2312yes—
392C2×C4×Q8C2312yes—
393C2×C4×Q8C2312yes—
394C2×C4×Q8C2312yes—
395C2×C4×Q8C2311yescharacteristic
396C2×C4×D4C2312yes—
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2312yes—
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2311yescharacteristic
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2314yes—
417C2×C4×D4C2314yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2314yes—
420C2×C4×D4C2314yes—
421C2×C4×D4C2314yes—
422C2×C4×D4C2314yes—
423C2×C4×D4C2312yes—
424C2×C4×D4C2314yes—
425C2×C4×D4C2312yes—
426C2×C4×D4C2312yes—
427C2×#117C2312yes—
428C2×#117C2314yes—
429C2×#117C2312yes—
430C2×#117C2314yes—
431C22×C4⋊C4C2312yes—
432C22×C4⋊C4C2312yes—
433C22×C42C2312yes—
434C22×C42C2312yes—
435C22×C42C2312yes—
436C22×C42C2312yes—
437#400C2314yes—
438#400C2312yes—
439#400C2314yes—
440#400C2312yes—
441#399C2314yes—
442#399C2312yes—
443#399C2314yes—
444#399C2312yes—
445#399C2314yes—
446#399C2314yes—
447#398C2312yes—
448#398C2314yes—
449#398C2312yes—
450#398C2314yes—
451#398C2312yes—
452#398C2314yes—
453#398C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2312yes—
466#396C2312yes—
467#396C2314yes—
468#396C2314yes—
469#396C2312yes—
470#396C2312yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#395C2314yes—
477#395C2314yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#395C2312yes—
482#395C2312yes—
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#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#393C2314yes—
512#393C2314yes—
513#393C2314yes—
514#393C2314yes—
515#393C2314yes—
516#393C2314yes—
517#393C2312yes—
518#393C2312yes—
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#391C2312yes—
532#391C2312yes—
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2312yes—
537#391C2314yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2312yes—
542#391C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2311yescharacteristic
553#390C2311yescharacteristic
554#390C2312yes—
555#390C2312yes—
556#390C2314yes—
557#390C2314yes—
558#390C2314yes—
559#390C2314yes—
560#390C2314yes—
561#390C2312yes—
562#390C2312yes—
563#390C2312yes—
564#390C2314yes—
565#390C2314yes—
566#390C2314yes—
567#390C2311yescharacteristic
568#390C2311yescharacteristic
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2312yes—
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#390C2312yes—
578#390C2312yes—
579#390C2312yes—
580#390C2312yes—
581#390C2314yes—
582#390C2314yes—
583#390C2314yes—
584#390C2312yes—
585#389C2311yescharacteristic
586#389C2311yescharacteristic
587#389C2311yescharacteristic
588#389C2311yescharacteristic
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2312yes—
594#389C2311yescharacteristic
595#389C2311yescharacteristic
596#389C2312yes—
597#389C2311yescharacteristic
598#389C2312yes—
599#389C2311yescharacteristic
600#389C2312yes—
601#389C2314yes—
602#389C2312yes—
603#389C2314yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2312yes—
613#389C2314yes—
614#389C2311yescharacteristic
615#389C2311yescharacteristic
616#389C2314yes—
617#389C2312yes—
618#389C2311yescharacteristic
619#389C2311yescharacteristic
620#389C2312yes—
621#389C2312yes—
622#389C2312yes—
623#389C2312yes—
624#389C2312yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#388C2312yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#387C2312yes—
650#387C2312yes—
651#387C2312yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2314yes—
658#387C2314yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
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#385C2314yes—
701#385C2314yes—
702#385C2312yes—
703#385C2312yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2312yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2312yes—
714#385C2314yes—
715#385C2312yes—
716#385C2312yes—
717#385C2314yes—
718#385C2312yes—
719#385C2312yes—
720#385C2312yes—
721#385C2312yes—
722#385C2312yes—
723#385C2312yes—
724#385C2314yes—
725#385C2314yes—
726#384C2311yescharacteristic
727#384C2311yescharacteristic
728#384C2311yescharacteristic
729#384C2312yes—
730#384C2314yes—
731#384C2312yes—
732#382C2311yescharacteristic
733#382C2311yescharacteristic
734#382C2311yescharacteristic
735#382C2311yescharacteristic
736#382C2312yes—
737#382C2312yes—
738#381C2314yes—
739#381C2314yes—
740#380C2314yes—
741#380C2314yes—
742#380C2314yes—
743#380C2314yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2314yes—
748#380C2314yes—
749#380C2314yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2314yes—
755#380C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2314yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C2×#95C2314yes—
815C2×#95C2314yes—
816C2×#95C2312yes—
817C2×#95C2312yes—
818C43C2311yescharacteristic
819C43C2311yescharacteristic
820C43C2311yescharacteristic
821C2×#41—48no—
822C2×#41—48no—
823C2×#41—48no—
824C2×#41—48no—
825C2×#41—48no—
826C2×#41—84no—
827C22×Q8C2412yes—
828C22×Q8C2411yescharacteristic
829C22×Q8C2412yes—
830C22×Q8C2412yes—
831C22×Q8C2414yes—
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2414yes—
838C22×D4C2411yescharacteristic
839C22×D4C2414yes—
840C22×D4C2414yes—
841C22×D4C2414yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2414yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2414yes—
868C23×C4C2414yes—
869C4⋊Q8—24no—
870C4⋊Q8—24no—
871C4⋊Q8—24no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874#127—28no—
875#127—28no—
876#127—28no—
877#127—24no—
878#127—24no—
879#127—44no—
880#127—44no—
881#127—44no—
882#127—44no—
883#127—44no—
884#127—44no—
885#127—82no—
886#126—48no—
887#126—48no—
888#125—24no—
889#125—24no—
890#125—24no—
891#125—44no—
892#125#4118yescomplemented
893#124—28no—
894#124—48no—
895#124—48no—
896#124—44no—
897#124—44no—
898#124—44no—
899#124—44no—
900#124—48no—
901#124—48no—
902#124—48no—
903#123—216no—
904#123—216no—
905#123—48no—
906#123—48no—
907#123—48no—
908#123—48no—
909#123—48no—
910#123—48no—
911#123—48no—
912#123—48no—
913C22⋊Q8—28no—
914C22⋊Q8—28no—
915C22⋊Q8—28no—
916C22⋊Q8—44no—
917C22⋊Q8—44no—
918C22⋊Q8—44no—
919C22⋊Q8—84no—
920C22⋊Q8—84no—
921#121—28no—
922#121—216no—
923#121—216no—
924#121—28no—
925#121—28no—
926#121—28no—
927#121—48no—
928#121—48no—
929#121—48no—
930#121—48no—
931#121—48no—
932#121—48no—
933#121—48no—
934#121—44no—
935#121—44no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—44no—
940#121—48no—
941#121—48no—
942#121—84no—
943#121—84no—
944#121—84no—
945C4×Q8—28no—
946C4×Q8—24no—
947C4×Q8—24no—
948C4×Q8—44no—
949C4×Q8—44no—
950C4×Q8—42no—
951C4×Q8—44no—
952C4×Q8—44no—
953C4×D4—24no—
954C4×D4—24no—
955C4×D4—24no—
956C4×D4—28no—
957C4×D4—28no—
958C4×D4—24no—
959C4×D4—24no—
960C4×D4—28no—
961C4×D4—24no—
962C4×D4—24no—
963C4×D4—24no—
964C4×D4—28no—
965C4×D4—24no—
966C4×D4—24no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—48no—
970C4×D4—44no—
971C4×D4—44no—
972C4×D4—44no—
973C4×D4—44no—
974C4×D4—44no—
975C4×D4—44no—
976C4×D4—48no—
977C4×D4—48no—
978C4×D4—48no—
979C4×D4—48no—
980C4×D4—48no—
981C4×D4—48no—
982C4×D4—82no—
983C4×D4—82no—
984#117—28no—
985#117—44no—
986#117—48no—
987#117—48no—
988C2×C4⋊C4—28no—
989C2×C4⋊C4—44no—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2411yescharacteristic
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2411yescharacteristic
1056C2×C4⋊C4C2411yescharacteristic
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2411yescharacteristic
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
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⋊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⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C42—28no—
1118C2×C42—44no—
1119C2×C42—44no—
1120C2×C42—44no—
1121C2×C42C2411yescharacteristic
1122C2×C42C2412yes—
1123C2×C42C2414yes—
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2412yes—
1132C2×C42C2411yescharacteristic
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2411yescharacteristic
1138C2×C42C2411yescharacteristic
1139C2×C42C2412yes—
1140C2×C42C2411yescharacteristic
1141C2×C42C2412yes—
1142C2×C42C2414yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2412yes—
1146C2×C42C2412yes—
1147C2×C42C2414yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150C2×C42C2412yes—
1151C2×C42C2412yes—
1152C2×C42C2412yes—
1153C2×C42C2411yescharacteristic
1154C2×C42C2411yescharacteristic
1155C2×C42C2411yescharacteristic
1156C2×C42C2411yescharacteristic
1157#95C2412yes—
1158#95C2411yescharacteristic
1159#95C2411yescharacteristic
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2411yescharacteristic
1191#95C2411yescharacteristic
1192#95C2411yescharacteristic
1193#95C2411yescharacteristic
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2414yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2414yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215C24C2514yes—
1216C24C2512yes—
1217C24C2514yes—
1218C24C2512yes—
1219#41—832no—
1220#41—832no—
1221C2×Q8—22no—
1222C2×Q8—24no—
1223C2×Q8—24no—
1224C2×Q8—22no—
1225C2×Q8—24no—
1226C2×Q8—24no—
1227C2×Q8—24no—
1228C2×Q8—24no—
1229C2×Q8—41no—
1230C2×Q8—42no—
1231C2×Q8—42no—
1232C2×Q8—42no—
1233C2×Q8—44no—
1234C2×Q8—44no—
1235C2×Q8—44no—
1236C2×D4—28no—
1237C2×D4—28no—
1238C2×D4—28no—
1239C2×D4—28no—
1240C2×D4—28no—
1241C2×D4—22no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—28no—
1245C2×D4—28no—
1246C2×D4—28no—
1247C2×D4—28no—
1248C2×D4—22no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—22no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—28no—
1257C2×D4—22no—
1258C2×D4—22no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—28no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
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—
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—42no—
1289C2×D4—42no—
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×D4H(5,𝔽2)14yes—
1299C22×C4—24no—
1300C22×C4—24no—
1301C22×C4—24no—
1302C22×C4—24no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—28no—
1316C22×C4—28no—
1317C22×C4—24no—
1318C22×C4—28no—
1319C22×C4—28no—
1320C22×C4—42no—
1321C22×C4—42no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—42no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—44no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4—44no—
1336C22×C4—44no—
1337C22×C4—44no—
1338C22×C4—42no—
1339C22×C4—42no—
1340C22×C4—44no—
1341C22×C4—42no—
1342C22×C4—44no—
1343C22×C4—44no—
1344C22×C4—44no—
1345C22×C4—44no—
1346C22×C4—44no—
1347C22×C4C2512yes—
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2511yescharacteristic
1355C22×C4C2511yescharacteristic
1356C22×C4C2514yes—
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2511yescharacteristic
1360C22×C4C2512yes—
1361C22×C4C2512yes—
1362C22×C4C2512yes—
1363C22×C4C2514yes—
1364C22×C4C2511yescharacteristic
1365C22×C4C2511yescharacteristic
1366C22×C4C2512yes—
1367C22×C4C2511yescharacteristic
1368C22×C4C2511yescharacteristic
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2511yescharacteristic
1372C22×C4C2512yes—
1373C22×C4C2511yescharacteristic
1374C22×C4C2511yescharacteristic
1375C22×C4C2511yescharacteristic
1376C22×C4C2511yescharacteristic
1377C22×C4C2511yescharacteristic
1378C4⋊C4—22no—
1379C4⋊C4—24no—
1380C4⋊C4—24no—
1381C4⋊C4—24no—
1382C4⋊C4—24no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—22no—
1390C4⋊C4—24no—
1391C4⋊C4—22no—
1392C4⋊C4—22no—
1393C4⋊C4—22no—
1394C4⋊C4—22no—
1395C4⋊C4—24no—
1396C4⋊C4—24no—
1397C4⋊C4—22no—
1398C4⋊C4—22no—
1399C4⋊C4—22no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—22no—
1403C4⋊C4—22no—
1404C4⋊C4—28no—
1405C4⋊C4—22no—
1406C4⋊C4—22no—
1407C4⋊C4—22no—
1408C4⋊C4—24no—
1409C4⋊C4—24no—
1410C4⋊C4—22no—
1411C4⋊C4—24no—
1412C4⋊C4—22no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—44no—
1416C4⋊C4—44no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—44no—
1421C4⋊C4—44no—
1422C4⋊C4—42no—
1423C4⋊C4—41no—
1424C4⋊C4—42no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—44no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—42no—
1439C4⋊C4—42no—
1440C4⋊C4—42no—
1441C4⋊C4—44no—
1442C4⋊C4C2×#4118yes—
1443C4⋊C4C2×#4114yes—
1444C4⋊C4C2×#4114yes—
1445C4⋊C4C2×#4118yes—
1446C4⋊C4H(5,𝔽2)14yes—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—28no—
1451C22⋊C4—24no—
1452C22⋊C4—24no—
1453C22⋊C4—28no—
1454C22⋊C4—28no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—28no—
1459C22⋊C4—28no—
1460C22⋊C4—28no—
1461C22⋊C4—28no—
1462C22⋊C4—24no—
1463C22⋊C4—28no—
1464C22⋊C4—28no—
1465C22⋊C4—24no—
1466C22⋊C4—28no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—24no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
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—44no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—42no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C42—24no—
1506C42—22no—
1507C42—22no—
1508C42—24no—
1509C42—24no—
1510C42—24no—
1511C42—22no—
1512C42—22no—
1513C42—22no—
1514C42—24no—
1515C42—24no—
1516C42—24no—
1517C42—22no—
1518C42—28no—
1519C42—24no—
1520C42—22no—
1521C42—22no—
1522C42—22no—
1523C42—22no—
1524C42—22no—
1525C42—42no—
1526C42—42no—
1527C42—42no—
1528C42—42no—
1529C42—42no—
1530C42—42no—
1531C42—44no—
1532C42—44no—
1533C42—41no—
1534C42—41no—
1535C42—41no—
1536C42—41no—
1537C42—41no—
1538C42C2×#4114yes—
1539C42H(5,𝔽2)14yes—
1540C422−1+414yes—
1541C23—22no—
1542C23—22no—
1543C23—22no—
1544C23—22no—
1545C23—22no—
1546C23—22no—
1547C23—24no—
1548C23—22no—
1549C23—24no—
1550C23—24no—
1551C23—22no—
1552C23—24no—
1553C23—24no—
1554C23—24no—
1555C23—22no—
1556C23—24no—
1557C23—24no—
1558C23—22no—
1559C23—22no—
1560C23—24no—
1561C23—24no—
1562C23—22no—
1563C23—24no—
1564C23—24no—
1565C23—24no—
1566C23—24no—
1567C23—22no—
1568C23C2×H(5,𝔽2)14yes—
1569C23C2611yescharacteristic
1570Q8—44no—
1571Q8—48no—
1572Q8—48no—
1573Q8—84no—
1574Q8—88no—
1575D4—28no—
1576D4—416no—
1577D4—48no—
1578D4—48no—
1579D4—44no—
1580D4—48no—
1581D4—48no—
1582D4—88no—
1583D4—88no—
1584D4—88no—
1585D4—88no—
1586D4—84no—
1587D4—84no—
1588D4—88no—
1589D4—88no—
1590D4—88no—
1591D4—88no—
1592D4—88no—
1593D4—88no—
1594D4—164no—
1595D4—164no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—24no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—24no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—24no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—24no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—24no—
1672C2×C4—22no—
1673C2×C4—22no—
1674C2×C4—48no—
1675C2×C4—48no—
1676C2×C4—48no—
1677C2×C4—48no—
1678C2×C4—48no—
1679C2×C4—48no—
1680C2×C4—84no—
1681C2×C4—88no—
1682C2×C4—84no—
1683C2×C4—84no—
1684C2×C4—88no—
1685C2×C4—88no—
1686C2×C4—88no—
1687C2×C4—84no—
1688C2×C4—88no—
1689C2×C4—164no—
1690C2×C4C22×#4112yes—
1691C2×C4C22×#4112yes—
1692C2×C4C22×#4114yes—
1693C2×C4C22×#4114yes—
1694C2×C4C22×#4112yes—
1695C2×C4C2×H(5,𝔽2)12yes—
1696C2×C4C2×H(5,𝔽2)12yes—
1697C2×C4C2×H(5,𝔽2)14yes—
1698C2×C4C2×H(5,𝔽2)12yes—
1699C2×C4C2×H(5,𝔽2)12yes—
1700C2×C4C2×H(5,𝔽2)12yes—
1701C2×C4C2×2−1+412yes—
1702C2×C4C2×2−1+412yes—
1703C2×C4C2×2−1+412yes—
1704C2×C4#58512yes—
1705C22—24no—
1706C22—24no—
1707C22—24no—
1708C22—42no—
1709C22—42no—
1710C22—42no—
1711C22—42no—
1712C22—44no—
1713C22—42no—
1714C22—44no—
1715C22—44no—
1716C22—42no—
1717C22—44no—
1718C22—44no—
1719C22—44no—
1720C22—42no—
1721C22—42no—
1722C22—44no—
1723C22—44no—
1724C22—44no—
1725C22—44no—
1726C22—42no—
1727C22—42no—
1728C22—44no—
1729C22—44no—
1730C22—44no—
1731C22—44no—
1732C22—42no—
1733C22C23×#4111yescharacteristic
1734C22C22×H(5,𝔽2)11yescharacteristic
1735C22C22×H(5,𝔽2)11yescharacteristic
1736C22C22×H(5,𝔽2)11yescharacteristic
1737C22C22×2−1+411yescharacteristic
1738C22C2×#58511yescharacteristic
1739C22H(7,𝔽2)11yescharacteristic
1740C4—24no—
1741C4—22no—
1742C4—22no—
1743C4—24no—
1744C4—22no—
1745C4—24no—
1746C4—22no—
1747C4—22no—
1748C4—22no—
1749C4—42no—
1750C4—41no—
1751C4—42no—
1752C4—41no—
1753C4—42no—
1754C4—44no—
1755C4—42no—
1756C4—41no—
1757C4—41no—
1758C4—42no—
1759C4—42no—
1760C4—42no—
1761C4—42no—
1762C4—41no—
1763C4—42no—
1764C4—42no—
1765C4—44no—
1766C4—41no—
1767C4—42no—
1768C4—41no—
1769C4#352214yes—
1770C4#354814yes—
1771C2—44no—
1772C2—84no—
1773C2—84no—
1774C2—82no—
1775C2C2×#354811yescharacteristic
1776C2C2×#352211yescharacteristic
1777C2#6280011yescharacteristic
1778C2#6291211yescharacteristic
1779C2#6296211yescharacteristic
1780C2#6298611yescharacteristic
1781C2#6301211yescharacteristic
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. #59465C2semidirect
2. #59459C2semidirect
3. #59457C2semidirect
4. #59072C2semidirect
5. #59039C2semidirect
6. #51948C2semidirect
7. #50778C2semidirect
8. #45718C2semidirect
9. #45653C2semidirect
10. #45034C2semidirect
11. #44880C2semidirect
12. #44151C2semidirect
13. #42585C2semidirect
14. #42467C2semidirect
15. #42093C2semidirect
16. #40174C2semidirect
17. #39853C2semidirect
18. #39853C2semidirect
19. #39386C2semidirect
20. #39202C2semidirect
21. #39137C2semidirect
22. #37792C2semidirect
23. #36595C2semidirect
24. #36469C2semidirect
25. #36139C2semidirect
26. #36128C2semidirect
27. #36115C2semidirect
28. #36115C2semidirect
29. #35238C2semidirect
30. #35196C2semidirect
31. #35171C2semidirect
32. #34925C2semidirect
33. #34893C2semidirect
34. #34423C2semidirect
35. C4×#554C2semidirect
892. #125#41semidirect

Maximal subgroups

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

subgroupindex
#594652
#594592
#594572
#590722
#590392
#519482
#507782
#457182
#456532
#450342
#448802
#441512
#425852
#424672
#420932
#401742
#398532
#393862
#392022
#391372
#377922
#365952
#364692
#361392
#361282
#361152
#352382
#351962
#351712
#349252
#348932
#344232
C4×#5542