Finite Group Databasebeta

← #7680467

Subgroups — #7680467

Order 512.

5719 conjugacy classes of subgroups.

The subgroup lattice has 1810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59952C212yesmaximal, complemented
2#59903C212yesmaximal, complemented
3#59696C212yesmaximal, complemented
4#59487C212yesmaximal, complemented
5#59419C212yesmaximal, complemented
6#59403C212yesmaximal, complemented
7#59097C212yesmaximal, complemented
8#59039C212yesmaximal, complemented
9#44345C214yesmaximal, complemented
10#44158C214yesmaximal, complemented
11#43481C214yesmaximal, complemented
12#43425C214yesmaximal, complemented
13#39745C211yesmaximal, characteristic, complemented
14#39626C211yesmaximal, characteristic, complemented
15#38942C211yesmaximal, characteristic, complemented
16#38942C212yesmaximal, complemented
17#38941C211yesmaximal, characteristic, complemented
18#38936C212yesmaximal, complemented
19#37954C212yesmaximal, complemented
20#37772C212yesmaximal, complemented
21#36493C211yesmaximal, characteristic, complemented
22#36455C211yesmaximal, characteristic, complemented
23#36174C211yesmaximal, characteristic, complemented
24#36128C211yesmaximal, characteristic, complemented
25#35571C212yesmaximal, complemented
26#35570C212yesmaximal, complemented
27#35303C212yesmaximal, complemented
28#35278C211yesmaximal, characteristic, complemented
29#34934C211yesmaximal, characteristic, complemented
30#34925C211yesmaximal, characteristic, complemented
31#34331C211yesmaximal, characteristic, complemented
32#34330C211yesmaximal, characteristic, complemented
33#34222C212yesmaximal, complemented
34#34123C211yesmaximal, characteristic, complemented
35C4×#542C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#550C2212yes—
39C2×#550C2212yes—
40C2×#542C2211yescharacteristic
41C2×#540C2212yes—
42C2×#532C2212yes—
43C2×#532C2212yes—
44C2×#532C2212yes—
45C2×#529C2212yes—
46C2×C4×#41C2211yescharacteristic
47#2867C2211yescharacteristic
48#2859C2211yescharacteristic
49#2856C2211yescharacteristic
50#2856C2212yes—
51#2856C2211yescharacteristic
52#2856C2212yes—
53#2850C2212yes—
54#2850C2212yes—
55#2806C2214yes—
56#2792C2214yes—
57#2785C2214yes—
58#2781C2214yes—
59#2756C2214yes—
60#2756C2214yes—
61#2756C2214yes—
62#2756C2214yes—
63#2756C2214yes—
64#2737C2214yes—
65#2737C2214yes—
66#2733C2214yes—
67#2730C2214yes—
68#2714C2214yes—
69#2699C2214yes—
70#2699C2214yes—
71#2699C2214yes—
72#2699C2214yes—
73#2686C2214yes—
74#2686C2214yes—
75#2686C2214yes—
76#2673C2214yes—
77#2673C2214yes—
78#2673C2214yes—
79#2660C2212yes—
80#2657C2212yes—
81#2641C2212yes—
82#2641C2212yes—
83#2640C2212yes—
84#2619C2212yes—
85#2610C2214yes—
86#2610C2214yes—
87#2610C2214yes—
88#2603C2214yes—
89#2603C2214yes—
90#2602C2214yes—
91#2602C2214yes—
92#2582C2212yes—
93#2572C2214yes—
94#2567C2212yes—
95#2563C2212yes—
96#2559C2214yes—
97#2557C2214yes—
98#2555C2214yes—
99#2555C2214yes—
100#2555C2214yes—
101#2554C2214yes—
102#2553C2214yes—
103#2552C2211yescharacteristic
104#2552C2212yes—
105#2551C2211yescharacteristic
106#2550C2212yes—
107#2548C2211yescharacteristic
108#2548C2212yes—
109#2544C2212yes—
110#2543C2214yes—
111#2543C2214yes—
112#2543C2214yes—
113#2543C2214yes—
114#2541C2211yescharacteristic
115#2541C2212yes—
116#2541C2212yes—
117#2541C2211yescharacteristic
118#2541C2211yescharacteristic
119#2541C2212yes—
120#2540C2212yes—
121#2538C2211yescharacteristic
122#2537C2212yes—
123#2537C2214yes—
124#2537C2212yes—
125#2537C2211yescharacteristic
126#2535C2212yes—
127#2531C2214yes—
128#2526C2214yes—
129#2518C2214yes—
130#2518C2214yes—
131#2513C2212yes—
132#2512C2212yes—
133#2507C2212yes—
134#2500C2212yes—
135#2500C2214yes—
136#2500C2214yes—
137#2498C2214yes—
138#2495C2212yes—
139#2491C2212yes—
140#2491C2212yes—
141#2491C2212yes—
142#2491C2212yes—
143#2490C2212yes—
144#2490C2212yes—
145#2490C2212yes—
146#2489C2212yes—
147#2476C2214yes—
148#2471C2214yes—
149#2467C2214yes—
150#2464C2214yes—
151#2464C2214yes—
152#2459C2214yes—
153#2456C2214yes—
154#2456C2214yes—
155#2451C2212yes—
156#2448C2212yes—
157#2445C2212yes—
158#2445C2212yes—
159#2445C2212yes—
160#2445C2212yes—
161#2445C2212yes—
162#2431C2212yes—
163#2431C2214yes—
164#2431C2212yes—
165#2431C2214yes—
166#2431C2212yes—
167#2431C2214yes—
168#2430C2214yes—
169#2430C2214yes—
170#2430C2214yes—
171#2428C2212yes—
172#2428C2212yes—
173#2428C2212yes—
174#2428C2212yes—
175#2428C2212yes—
176#2428C2214yes—
177#2428C2212yes—
178#2428C2212yes—
179#2428C2212yes—
180#2428C2214yes—
181#2428C2212yes—
182#2428C2212yes—
183#2428C2214yes—
184#2428C2212yes—
185#2428C2212yes—
186#2427C2212yes—
187#2426C2212yes—
188#2422C2214yes—
189#2420C2212yes—
190#2420C2214yes—
191#2420C2214yes—
192#2420C2212yes—
193#2420C2212yes—
194#2414C2212yes—
195#2414C2214yes—
196#2414C2212yes—
197#2414C2214yes—
198#2407C2214yes—
199#2392C2214yes—
200#2388C2214yes—
201#2372C2214yes—
202#2372C2214yes—
203#2367C2212yes—
204#2367C2212yes—
205#2366C2212yes—
206#2366C2211yescharacteristic
207#2366C2212yes—
208#2366C2211yescharacteristic
209#2366C2212yes—
210#2364C2214yes—
211#2364C2214yes—
212#2364C2214yes—
213#2363C2212yes—
214#2363C2212yes—
215#2363C2212yes—
216#2359C2214yes—
217#2357C2212yes—
218#2356C2211yescharacteristic
219#2356C2211yescharacteristic
220#2355C2211yescharacteristic
221#2355C2211yescharacteristic
222#2354C2211yescharacteristic
223#2354C2212yes—
224#2353C2214yes—
225#2353C2212yes—
226#2353C2212yes—
227#2353C2214yes—
228Q8×C4⋊C4C2211yescharacteristic
229#2349C2212yes—
230#2349C2211yescharacteristic
231#2349C2211yescharacteristic
232#2346C2211yescharacteristic
233#2346C2211yescharacteristic
234#2346C2212yes—
235#2343C2212yes—
236#2343C2212yes—
237#2341C2212yes—
238#2339C2212yes—
239#2339C2211yescharacteristic
240#2339C2214yes—
241#2339C2211yescharacteristic
242#2339C2214yes—
243#2337C2212yes—
244#2335C2214yes—
245#2335C2212yes—
246#2334C2212yes—
247#2333C2214yes—
248#2332C2212yes—
249#2331C2211yescharacteristic
250#2331C2212yes—
251#2328C2212yes—
252#2328C2212yes—
253#2328C2212yes—
254#2326C2212yes—
255#2326C2211yescharacteristic
256#2324C2211yescharacteristic
257#2323C2211yescharacteristic
258#2320C2211yescharacteristic
259#2319C2212yes—
260#2319C2212yes—
261#2319C2211yescharacteristic
262#2314C2211yescharacteristic
263C4×C4⋊Q8C2211yescharacteristic
264C4×#127C2211yescharacteristic
265C4×#127C2211yescharacteristic
266C4×#127C2212yes—
267C4×#126C2212yes—
268C4×#124C2212yes—
269C4×#124C2212yes—
270C4×#124C2211yescharacteristic
271C4×C22⋊Q8C2211yescharacteristic
272C4×C22⋊Q8C2212yes—
273C4×#123C2212yes—
274C4×#121C2212yes—
275C4×#121C2212yes—
276C4×#121C2212yes—
277C4×#121C2211yescharacteristic
278C4×#121C2212yes—
279C4×#121C2212yes—
280C4×#121C2212yes—
281#2297C2212yes—
282#2295C2211yescharacteristic
283#2295C2211yescharacteristic
284#2293C2212yes—
285#2293C2212yes—
286#2290C2212yes—
287#2290C2212yes—
288#2283C2212yes—
289#2283C2211yescharacteristic
290#2283C2212yes—
291#2275C2212yes—
292#2275C2212yes—
293C42×Q8C2211yescharacteristic
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×#376C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2314yes—
302C22×#41C2314yes—
303#559—28no—
304#550—28no—
305#550—48no—
306#550—48no—
307#542—28no—
308#540—48no—
309#532—216no—
310#532—48no—
311#532—48no—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×#127C2311yescharacteristic
316C2×#127C2311yescharacteristic
317C2×#127C2312yes—
318C2×#127C2312yes—
319C2×#127C2312yes—
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2314yes—
326C2×#127C2312yes—
327C2×#127C2312yes—
328#529—48no—
329C2×#126C2312yes—
330C2×#126C2314yes—
331C2×#125C2312yes—
332C2×#125C2312yes—
333C2×#124C2311yescharacteristic
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#124C2314yes—
339C2×#124C2312yes—
340C2×#124C2314yes—
341C2×#124C2314yes—
342C2×#123C2314yes—
343C2×#123C2312yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×#121C2311yescharacteristic
351C2×#121C2314yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2314yes—
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365C2×#121C2314yes—
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2314yes—
369C2×#121C2314yes—
370C2×#121C2314yes—
371C2×#121C2314yes—
372C2×#121C2314yes—
373C2×#121C2312yes—
374C2×#121C2314yes—
375C2×#121C2314yes—
376C2×#121C2312yes—
377C2×#121C2312yes—
378C2×#121C2314yes—
379C2×#121C2314yes—
380C2×#121C2314yes—
381C2×#121C2314yes—
382C4×#41—28no—
383C2×C4×Q8C2311yescharacteristic
384C2×C4×Q8C2311yescharacteristic
385C2×C4×Q8C2311yescharacteristic
386C2×C4×Q8C2311yescharacteristic
387C2×C4×Q8C2312yes—
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2311yescharacteristic
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2312yes—
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2312yes—
402C2×C4×D4C2314yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2311yescharacteristic
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2312yes—
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2312yes—
409C2×C4×D4C2314yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2311yescharacteristic
413C2×C4×D4C2314yes—
414C2×C4×D4C2314yes—
415C2×C4×D4C2314yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2314yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2312yes—
421C2×C4×D4C2314yes—
422C2×C4×D4C2314yes—
423C2×#117C2311yescharacteristic
424C2×#117C2311yescharacteristic
425C2×#117C2312yes—
426C2×#117C2311yescharacteristic
427C2×#117C2312yes—
428C2×#117C2314yes—
429C2×#117C2314yes—
430C22×C42C2312yes—
431C22×C42C2312yes—
432C22×C42C2311yescharacteristic
433C22×C42C2312yes—
434C22×C42C2312yes—
435#400C2314yes—
436#399C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#396C2314yes—
452#396C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2311yescharacteristic
514#391C2314yes—
515#391C2312yes—
516#391C2312yes—
517#391C2312yes—
518#391C2311yescharacteristic
519#391C2311yescharacteristic
520#391C2311yescharacteristic
521#390C2312yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2314yes—
527#390C2314yes—
528#390C2312yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2312yes—
533#390C2311yescharacteristic
534#390C2311yescharacteristic
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2314yes—
544#390C2314yes—
545#390C2314yes—
546#390C2312yes—
547#390C2314yes—
548#390C2314yes—
549#390C2314yes—
550#390C2312yes—
551#390C2312yes—
552#390C2312yes—
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2312yes—
557#390C2314yes—
558#390C2314yes—
559#390C2312yes—
560#389C2311yescharacteristic
561#389C2311yescharacteristic
562#389C2312yes—
563#389C2311yescharacteristic
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2311yescharacteristic
568#389C2311yescharacteristic
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2314yes—
575#389C2311yescharacteristic
576#389C2311yescharacteristic
577#389C2311yescharacteristic
578#389C2312yes—
579#389C2314yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2312yes—
601#388C2312yes—
602#388C2314yes—
603#388C2314yes—
604#388C2312yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#387C2312yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2314yes—
639#387C2312yes—
640#387C2314yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#386C2314yes—
648#386C2314yes—
649#386C2312yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2312yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#385C2312yes—
687#385C2312yes—
688#385C2312yes—
689#385C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2314yes—
693#385C2312yes—
694#385C2312yes—
695#385C2312yes—
696#385C2312yes—
697#384C2312yes—
698#384C2311yescharacteristic
699#384C2311yescharacteristic
700#384C2311yescharacteristic
701#384C2314yes—
702#384C2312yes—
703#383C2312yes—
704#383C2312yes—
705#383C2312yes—
706#383C2314yes—
707#383C2312yes—
708#382C2311yescharacteristic
709#382C2312yes—
710#382C2311yescharacteristic
711#382C2312yes—
712#382C2312yes—
713#382C2312yes—
714#382C2312yes—
715#382C2312yes—
716#382C2314yes—
717#382C2311yescharacteristic
718#381C2314yes—
719#381C2314yes—
720#381C2312yes—
721#381C2314yes—
722#381C2314yes—
723#381C2312yes—
724#381C2312yes—
725#381C2312yes—
726#380C2314yes—
727#380C2314yes—
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730#380C2312yes—
731#380C2314yes—
732#380C2314yes—
733#380C2311yescharacteristic
734#380C2311yescharacteristic
735#380C2312yes—
736#380C2312yes—
737#380C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C22⋊C4C2312yes—
772C4×C22⋊C4C2312yes—
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2314yes—
775C4×C22⋊C4C2314yes—
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2311yescharacteristic
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2311yescharacteristic
784C4×C22⋊C4C2311yescharacteristic
785C4×C22⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802#376C2312yes—
803#376C2311yescharacteristic
804#376C2311yescharacteristic
805#376C2312yes—
806#376C2312yes—
807#376C2312yes—
808#376C2312yes—
809#376C2314yes—
810#376C2312yes—
811#376C2312yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2314yes—
815C2×#95C2312yes—
816C2×#95C2314yes—
817C2×#95C2312yes—
818C43C2312yes—
819C43C2311yescharacteristic
820C43C2311yescharacteristic
821C2×#41—24no—
822C2×#41—216no—
823C2×#41—28no—
824C2×#41—24no—
825C2×#41—48no—
826C2×#41—48no—
827C2×#41—48no—
828C2×#41—42no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—84no—
832C2×#41—84no—
833C22×Q8C2411yescharacteristic
834C22×Q8C2411yescharacteristic
835C22×Q8C2414yes—
836C22×Q8C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2411yescharacteristic
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C22×D4C2414yes—
861C22×D4C2414yes—
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2412yes—
869C23×C4C2414yes—
870C23×C4C2414yes—
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2412yes—
874C23×C4C2414yes—
875C23×C4C2412yes—
876C23×C4C2414yes—
877C23×C4C2412yes—
878C23×C4C2411yescharacteristic
879C23×C4C2414yes—
880C23×C4C2412yes—
881C4⋊Q8—44no—
882C4⋊Q8—44no—
883C4⋊Q8#4118yescomplemented
884#127—28no—
885#127—28no—
886#127—28no—
887#127—28no—
888#127—24no—
889#127—24no—
890#127—44no—
891#127—44no—
892#127—44no—
893#127—44no—
894#127—48no—
895#127—82no—
896#127—82no—
897#126—28no—
898#126—48no—
899#125—44no—
900#125—44no—
901#124—216no—
902#124—28no—
903#124—28no—
904#124—24no—
905#124—28no—
906#124—48no—
907#124—44no—
908#124—48no—
909#124—84no—
910#123—28no—
911#123—216no—
912#123—48no—
913#123—48no—
914#123—48no—
915C22⋊Q8—28no—
916C22⋊Q8—24no—
917C22⋊Q8—44no—
918#121—28no—
919#121—28no—
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—44no—
933#121—44no—
934#121—44no—
935#121—44no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—44no—
940#121—44no—
941#121—48no—
942#121—48no—
943#121—84no—
944#121—82no—
945#121—84no—
946#121—84no—
947#121—84no—
948#121—82no—
949#121—84no—
950C4×Q8—24no—
951C4×Q8—24no—
952C4×Q8—24no—
953C4×Q8—24no—
954C4×Q8—44no—
955C4×Q8—44no—
956C4×Q8#4118yescomplemented
957C4×D4—24no—
958C4×D4—24no—
959C4×D4—24no—
960C4×D4—28no—
961C4×D4—28no—
962C4×D4—28no—
963C4×D4—216no—
964C4×D4—24no—
965C4×D4—28no—
966C4×D4—28no—
967C4×D4—24no—
968C4×D4—28no—
969C4×D4—24no—
970C4×D4—28no—
971C4×D4—28no—
972C4×D4—24no—
973C4×D4—28no—
974C4×D4—44no—
975C4×D4—42no—
976C4×D4—42no—
977C4×D4—44no—
978C4×D4—44no—
979C4×D4—44no—
980C4×D4—48no—
981C4×D4—48no—
982C4×D4—44no—
983C4×D4—48no—
984C4×D4—48no—
985C4×D4—82no—
986C4×D4—82no—
987C4×D4—84no—
988C4×D4—84no—
989C4×D4—84no—
990#117—24no—
991#117—28no—
992#117—24no—
993#117—24no—
994#117—48no—
995#117—44no—
996#117—84no—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2411yescharacteristic
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2411yescharacteristic
1044C2×C4⋊C4C2411yescharacteristic
1045C2×C4⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C42—28no—
1111C2×C42—24no—
1112C2×C42—28no—
1113C2×C42—28no—
1114C2×C42—44no—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2412yes—
1127C2×C42C2411yescharacteristic
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2412yes—
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2412yes—
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2414yes—
1139C2×C42C2414yes—
1140C2×C42C2412yes—
1141C2×C42C2411yescharacteristic
1142C2×C42C2411yescharacteristic
1143C2×C42C2412yes—
1144C2×C42C2414yes—
1145C2×C42C2414yes—
1146C2×C42C2412yes—
1147C2×C42C2411yescharacteristic
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150C2×C42C2412yes—
1151C2×C42C2411yescharacteristic
1152C2×C42C2411yescharacteristic
1153#95C2412yes—
1154#95C2412yes—
1155#95C2411yescharacteristic
1156#95C2411yescharacteristic
1157#95C2411yescharacteristic
1158#95C2411yescharacteristic
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2411yescharacteristic
1179#95C2411yescharacteristic
1180#95C2411yescharacteristic
1181#95C2411yescharacteristic
1182#95C2414yes—
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#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2414yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2412yes—
1212#95C2412yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2412yes—
1216#95C2412yes—
1217C24C2511yescharacteristic
1218C24C2512yes—
1219C24C2514yes—
1220C24C2514yes—
1221C24C2512yes—
1222#41—416no—
1223#41—832no—
1224#41—832no—
1225#41—816no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—22no—
1231C2×Q8—42no—
1232C2×Q8—42no—
1233C2×Q8—44no—
1234C2×Q8—44no—
1235C2×Q8—44no—
1236C2×Q8C2×#4114yes—
1237C2×Q8C2×#4118yes—
1238C2×D4—28no—
1239C2×D4—28no—
1240C2×D4—24no—
1241C2×D4—28no—
1242C2×D4—28no—
1243C2×D4—28no—
1244C2×D4—22no—
1245C2×D4—24no—
1246C2×D4—22no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—22no—
1252C2×D4—24no—
1253C2×D4—28no—
1254C2×D4—28no—
1255C2×D4—24no—
1256C2×D4—28no—
1257C2×D4—28no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—28no—
1261C2×D4—24no—
1262C2×D4—28no—
1263C2×D4—24no—
1264C2×D4—22no—
1265C2×D4—24no—
1266C2×D4—24no—
1267C2×D4—24no—
1268C2×D4—22no—
1269C2×D4—24no—
1270C2×D4—24no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—42no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—42no—
1277C2×D4—44no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C2×D4—42no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—42no—
1291C2×D4—42no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—44no—
1299C2×D4—44no—
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×D4H(5,𝔽2)14yes—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—24no—
1317C22×C4—22no—
1318C22×C4—24no—
1319C22×C4—22no—
1320C22×C4—24no—
1321C22×C4—24no—
1322C22×C4—22no—
1323C22×C4—24no—
1324C22×C4—24no—
1325C22×C4—24no—
1326C22×C4—24no—
1327C22×C4—22no—
1328C22×C4—24no—
1329C22×C4—22no—
1330C22×C4—24no—
1331C22×C4—22no—
1332C22×C4—24no—
1333C22×C4—22no—
1334C22×C4—24no—
1335C22×C4—28no—
1336C22×C4—28no—
1337C22×C4—28no—
1338C22×C4—28no—
1339C22×C4—24no—
1340C22×C4—24no—
1341C22×C4—28no—
1342C22×C4—28no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—42no—
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—42no—
1359C22×C4—42no—
1360C22×C4—42no—
1361C22×C4—44no—
1362C22×C4—44no—
1363C22×C4—44no—
1364C22×C4—41no—
1365C22×C4—41no—
1366C22×C4—42no—
1367C22×C4—42no—
1368C22×C4—44no—
1369C22×C4—44no—
1370C22×C4C2512yes—
1371C22×C4C2511yescharacteristic
1372C22×C4C2511yescharacteristic
1373C22×C4C2512yes—
1374C22×C4C2511yescharacteristic
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2512yes—
1378C22×C4C2512yes—
1379C22×C4C2512yes—
1380C22×C4C2511yescharacteristic
1381C22×C4C2512yes—
1382C22×C4C2511yescharacteristic
1383C22×C4C2512yes—
1384C22×C4C2511yescharacteristic
1385C22×C4C2511yescharacteristic
1386C22×C4C2514yes—
1387C22×C4C2514yes—
1388C22×C4C2512yes—
1389C22×C4C2511yescharacteristic
1390C22×C4C2511yescharacteristic
1391C22×C4C2512yes—
1392C22×C4C2511yescharacteristic
1393C22×C4C2512yes—
1394C22×C4C2512yes—
1395C22×C4C2512yes—
1396C22×C4C2511yescharacteristic
1397C22×C4C2511yescharacteristic
1398C22×C4C2511yescharacteristic
1399C22×C4C2511yescharacteristic
1400C4⋊C4—24no—
1401C4⋊C4—22no—
1402C4⋊C4—22no—
1403C4⋊C4—22no—
1404C4⋊C4—22no—
1405C4⋊C4—22no—
1406C4⋊C4—24no—
1407C4⋊C4—24no—
1408C4⋊C4—24no—
1409C4⋊C4—22no—
1410C4⋊C4—22no—
1411C4⋊C4—22no—
1412C4⋊C4—24no—
1413C4⋊C4—22no—
1414C4⋊C4—22no—
1415C4⋊C4—24no—
1416C4⋊C4—24no—
1417C4⋊C4—22no—
1418C4⋊C4—24no—
1419C4⋊C4—22no—
1420C4⋊C4—24no—
1421C4⋊C4—22no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—42no—
1425C4⋊C4—44no—
1426C4⋊C4—42no—
1427C4⋊C4—44no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—42no—
1431C4⋊C4—42no—
1432C4⋊C4—42no—
1433C4⋊C4—42no—
1434C4⋊C4—44no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—42no—
1442C4⋊C4—42no—
1443C4⋊C4—42no—
1444C4⋊C4C2×#4114yes—
1445C4⋊C4C2×#4118yes—
1446C4⋊C4C2×#4114yes—
1447C4⋊C4C2×#4114yes—
1448C4⋊C4C2×#4118yes—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—28no—
1452C22⋊C4—24no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—22no—
1456C22⋊C4—22no—
1457C22⋊C4—28no—
1458C22⋊C4—24no—
1459C22⋊C4—28no—
1460C22⋊C4—28no—
1461C22⋊C4—28no—
1462C22⋊C4—28no—
1463C22⋊C4—28no—
1464C22⋊C4—28no—
1465C22⋊C4—24no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—28no—
1470C22⋊C4—24no—
1471C22⋊C4—22no—
1472C22⋊C4—22no—
1473C22⋊C4—28no—
1474C22⋊C4—24no—
1475C22⋊C4—28no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—42no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—42no—
1486C22⋊C4—44no—
1487C22⋊C4—42no—
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—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—42no—
1505C22⋊C4—42no—
1506C22⋊C4—42no—
1507C22⋊C4—44no—
1508C22⋊C4—42no—
1509C22⋊C4—44no—
1510C22⋊C4—44no—
1511C22⋊C4—42no—
1512C22⋊C4—42no—
1513C42—22no—
1514C42—24no—
1515C42—22no—
1516C42—24no—
1517C42—24no—
1518C42—24no—
1519C42—22no—
1520C42—24no—
1521C42—22no—
1522C42—24no—
1523C42—24no—
1524C42—24no—
1525C42—24no—
1526C42—24no—
1527C42—22no—
1528C42—24no—
1529C42—22no—
1530C42—24no—
1531C42—22no—
1532C42—24no—
1533C42—22no—
1534C42—22no—
1535C42—42no—
1536C42—42no—
1537C42—44no—
1538C42—42no—
1539C42—44no—
1540C42—44no—
1541C42—41no—
1542C42—42no—
1543C42—44no—
1544C42—41no—
1545C42—41no—
1546C42—41no—
1547C42C2×#4114yes—
1548C42C2×#4118yes—
1549C42C2×#4114yes—
1550C42H(5,𝔽2)14yes—
1551C23—22no—
1552C23—22no—
1553C23—22no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—21no—
1559C23—24no—
1560C23—21no—
1561C23—24no—
1562C23—24no—
1563C23—22no—
1564C23—24no—
1565C23—21no—
1566C23—24no—
1567C23—22no—
1568C23—24no—
1569C23—24no—
1570C23—21no—
1571C23—24no—
1572C23—22no—
1573C23—22no—
1574C23—24no—
1575C23—24no—
1576C23—21no—
1577C23—21no—
1578C23—22no—
1579C23—24no—
1580C23—24no—
1581C23—24no—
1582C23—21no—
1583C23—22no—
1584C23—24no—
1585C23C2×H(5,𝔽2)14yes—
1586C23C2611yescharacteristic
1587Q8—28no—
1588Q8—48no—
1589Q8—44no—
1590Q8—88no—
1591D4—28no—
1592D4—48no—
1593D4—416no—
1594D4—416no—
1595D4—44no—
1596D4—48no—
1597D4—48no—
1598D4—48no—
1599D4—48no—
1600D4—84no—
1601D4—88no—
1602D4—88no—
1603D4—84no—
1604D4—84no—
1605D4—88no—
1606D4—88no—
1607D4—88no—
1608D4—88no—
1609D4—88no—
1610D4—88no—
1611D4—88no—
1612D4—164no—
1613D4—164no—
1614D4—164no—
1615D4—164no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—22no—
1629C2×C4—21no—
1630C2×C4—22no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—21no—
1646C2×C4—22no—
1647C2×C4—21no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—22no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—24no—
1661C2×C4—22no—
1662C2×C4—24no—
1663C2×C4—24no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—24no—
1673C2×C4—21no—
1674C2×C4—22no—
1675C2×C4—21no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—22no—
1679C2×C4—21no—
1680C2×C4—24no—
1681C2×C4—22no—
1682C2×C4—24no—
1683C2×C4—21no—
1684C2×C4—21no—
1685C2×C4—21no—
1686C2×C4—21no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—22no—
1690C2×C4—22no—
1691C2×C4—48no—
1692C2×C4—48no—
1693C2×C4—48no—
1694C2×C4—48no—
1695C2×C4—48no—
1696C2×C4—44no—
1697C2×C4—44no—
1698C2×C4—48no—
1699C2×C4—84no—
1700C2×C4—84no—
1701C2×C4—88no—
1702C2×C4—84no—
1703C2×C4—82no—
1704C2×C4—84no—
1705C2×C4—88no—
1706C2×C4—88no—
1707C2×C4—88no—
1708C2×C4—88no—
1709C2×C4—88no—
1710C2×C4C22×#4112yes—
1711C2×C4C22×#4112yes—
1712C2×C4C22×#4114yes—
1713C2×C4C22×#4112yes—
1714C2×C4C22×#4114yes—
1715C2×C4C22×#4114yes—
1716C2×C4C22×#4114yes—
1717C2×C4C22×#4112yes—
1718C2×C4C22×#4112yes—
1719C2×C4C22×#4112yes—
1720C2×C4C2×H(5,𝔽2)12yes—
1721C2×C4C2×H(5,𝔽2)12yes—
1722C2×C4C2×H(5,𝔽2)12yes—
1723C2×C4C2×H(5,𝔽2)12yes—
1724C2×C4#58512yes—
1725C22—24no—
1726C22—24no—
1727C22—24no—
1728C22—42no—
1729C22—42no—
1730C22—42no—
1731C22—42no—
1732C22—44no—
1733C22—44no—
1734C22—42no—
1735C22—41no—
1736C22—44no—
1737C22—44no—
1738C22—42no—
1739C22—41no—
1740C22—41no—
1741C22—42no—
1742C22—44no—
1743C22—44no—
1744C22—44no—
1745C22—41no—
1746C22—42no—
1747C22—44no—
1748C22—42no—
1749C22—44no—
1750C22—44no—
1751C22—41no—
1752C22—44no—
1753C22—42no—
1754C22—44no—
1755C22—41no—
1756C22—41no—
1757C22—42no—
1758C22—44no—
1759C22—44no—
1760C22C23×#4111yescharacteristic
1761C22C23×#4111yescharacteristic
1762C22C22×H(5,𝔽2)11yescharacteristic
1763C22C22×H(5,𝔽2)11yescharacteristic
1764C22C2×#58511yescharacteristic
1765C22H(7,𝔽2)11yescharacteristic
1766C22H(7,𝔽2)11yescharacteristic
1767C4—22no—
1768C4—24no—
1769C4—24no—
1770C4—22no—
1771C4—24no—
1772C4—24no—
1773C4—22no—
1774C4—22no—
1775C4—22no—
1776C4—42no—
1777C4—41no—
1778C4—41no—
1779C4—42no—
1780C4—41no—
1781C4—42no—
1782C4—42no—
1783C4—41no—
1784C4—42no—
1785C4—42no—
1786C4—44no—
1787C4—42no—
1788C4—41no—
1789C4—42no—
1790C4—44no—
1791C4—41no—
1792C4—42no—
1793C4—41no—
1794C4—42no—
1795C4#348314yes—
1796C4#349414yes—
1797C2—44no—
1798C2—84no—
1799C2—84no—
1800C2—82no—
1801C2—81no—
1802C2C2×#348311yescharacteristic
1803C2C2×#349411yescharacteristic
1804C2#6285811yescharacteristic
1805C2#6291211yescharacteristic
1806C2#6295511yescharacteristic
1807C2#6298311yescharacteristic
1808C2#6300611yescharacteristic
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. #59952C2semidirect
2. #59903C2semidirect
3. #59696C2semidirect
4. #59487C2semidirect
5. #59419C2semidirect
6. #59403C2semidirect
7. #59097C2semidirect
8. #59039C2semidirect
9. #44345C2semidirect
10. #44158C2semidirect
11. #43481C2semidirect
12. #43425C2semidirect
13. #39745C2semidirect
14. #39626C2semidirect
15. #38942C2semidirect
16. #38942C2semidirect
17. #38941C2semidirect
18. #38936C2semidirect
19. #37954C2semidirect
20. #37772C2semidirect
21. #36493C2semidirect
22. #36455C2semidirect
23. #36174C2semidirect
24. #36128C2semidirect
25. #35571C2semidirect
26. #35570C2semidirect
27. #35303C2semidirect
28. #35278C2semidirect
29. #34934C2semidirect
30. #34925C2semidirect
31. #34331C2semidirect
32. #34330C2semidirect
33. #34222C2semidirect
34. #34123C2semidirect
35. C4×#542C2semidirect
883. C4⋊Q8#41semidirect
956. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599522
#599032
#596962
#594872
#594192
#594032
#590972
#590392
#443452
#441582
#434812
#434252
#397452
#396262
#389422
#389412
#389362
#379542
#377722
#364932
#364552
#361742
#361282
#355712
#355702
#353032
#352782
#349342
#349252
#343312
#343302
#342222
#341232
C4×#5422