Finite Group Databasebeta

← #7968156

Subgroups — #7968156

Order 512.

4918 conjugacy classes of subgroups.

The subgroup lattice has 1757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59771C212yesmaximal, complemented
2#59659C211yesmaximal, characteristic, complemented
3#59593C212yesmaximal, complemented
4#59244C211yesmaximal, characteristic, complemented
5#59234C211yesmaximal, characteristic, complemented
6#51635C214yesmaximal, complemented
7#48332C214yesmaximal, complemented
8#45721C212yesmaximal, complemented
9#45601C212yesmaximal, complemented
10#45404C212yesmaximal, complemented
11#45401C212yesmaximal, complemented
12#44072C214yesmaximal, complemented
13#42734C212yesmaximal, complemented
14#42686C212yesmaximal, complemented
15#41360C214yesmaximal, complemented
16#40127C212yesmaximal, complemented
17#39932C212yesmaximal, complemented
18#39794C212yesmaximal, complemented
19#39597C211yesmaximal, characteristic, complemented
20#39042C212yesmaximal, complemented
21#38978C211yesmaximal, characteristic, complemented
22#38940C212yesmaximal, complemented
23#36456C211yesmaximal, characteristic, complemented
24#36411C211yesmaximal, characteristic, complemented
25#36210C211yesmaximal, characteristic, complemented
26#36204C212yesmaximal, complemented
27#36174C211yesmaximal, characteristic, complemented
28#36160C211yesmaximal, characteristic, complemented
29#35177C211yesmaximal, characteristic, complemented
30#35172C211yesmaximal, characteristic, complemented
31#35080C212yesmaximal, complemented
32#34976C211yesmaximal, characteristic, complemented
33#34720C211yesmaximal, characteristic, complemented
34#34463C212yesmaximal, complemented
35C4×#546C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic, complemented
37C2×#556C2212yes—
38C2×#555C2211yescharacteristic
39C2×#546C2211yescharacteristic
40C2×#533C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic, complemented
43C22×C4×D4C2211yescharacteristic
44#2859C2211yescharacteristic, complemented
45#2857C2211yescharacteristic
46#2857C2212yescomplemented
47#2857C2211yescharacteristic, complemented
48#2857C2212yescomplemented
49#2855C2212yescomplemented
50#2854C2212yes—
51#2850C2212yescomplemented
52#2848C2212yes—
53#2848C2212yes—
54#2847C2212yes—
55#2829C2214yescomplemented
56#2824C2214yes—
57#2804C2214yescomplemented
58#2796C2214yescomplemented
59#2795C2214yescomplemented
60#2794C2214yescomplemented
61#2782C2214yescomplemented
62#2780C2214yescomplemented
63#2777C2214yescomplemented
64#2775C2214yescomplemented
65#2775C2214yescomplemented
66#2775C2214yescomplemented
67#2775C2214yescomplemented
68#2772C2214yescomplemented
69#2771C2214yescomplemented
70#2761C2214yescomplemented
71#2754C2214yescomplemented
72#2753C2214yescomplemented
73#2752C2214yescomplemented
74#2749C2214yes—
75#2737C2214yes—
76#2737C2214yescomplemented
77#2737C2214yescomplemented
78#2735C2214yes—
79#2731C2214yescomplemented
80#2731C2214yescomplemented
81#2715C2214yes—
82#2714C2214yes—
83#2713C2214yescomplemented
84#2712C2214yescomplemented
85#2705C2214yes—
86#2685C2214yes—
87#2684C2214yes—
88#2677C2214yes—
89#2670C2214yes—
90#2665C2214yescomplemented
91#2663C2214yescomplemented
92#2653C2214yescomplemented
93#2649C2214yes—
94#2649C2214yes—
95#2644C2212yes—
96#2640C2214yescomplemented
97#2628C2212yes—
98#2626C2214yes—
99#2609C2214yescomplemented
100#2597C2214yes—
101#2596C2214yescomplemented
102#2595C2214yescomplemented
103#2589C2214yescomplemented
104#2587C2214yescomplemented
105#2582C2211yescharacteristic, complemented
106#2581C2212yescomplemented
107#2580C2212yes—
108#2580C2212yes—
109#2575C2214yescomplemented
110#2573C2214yescomplemented
111#2567C2211yescharacteristic, complemented
112#2566C2214yes—
113#2563C2212yes—
114#2563C2211yescharacteristic
115#2563C2212yescomplemented
116#2562C2212yes—
117#2561C2214yes—
118#2551C2212yescomplemented
119#2551C2211yescharacteristic, complemented
120#2547C2212yescomplemented
121#2546C2212yescomplemented
122#2545C2214yescomplemented
123#2542C2212yes—
124#2538C2211yescharacteristic
125#2538C2211yescharacteristic
126#2538C2211yescharacteristic
127#2538C2211yescharacteristic
128#2538C2211yescharacteristic, complemented
129#2538C2212yescomplemented
130#2537C2211yescharacteristic
131#2527C2214yescomplemented
132#2526C2214yescomplemented
133#2523C2214yes—
134#2518C2214yescomplemented
135#2514C2212yescomplemented
136#2513C2212yes—
137#2512C2212yescomplemented
138#2510C2214yescomplemented
139#2509C2212yescomplemented
140#2509C2212yescomplemented
141#2509C2212yescomplemented
142#2499C2212yescomplemented
143#2497C2212yescomplemented
144#2496C2212yes—
145#2495C2212yescomplemented
146#2495C2212yescomplemented
147#2495C2212yescomplemented
148#2495C2212yescomplemented
149#2494C2212yes—
150#2494C2212yescomplemented
151#2493C2214yescomplemented
152#2492C2212yes—
153#2492C2212yescomplemented
154#2492C2214yescomplemented
155#2492C2212yescomplemented
156#2491C2212yes—
157#2491C2212yes—
158#2491C2212yes—
159#2491C2212yescomplemented
160#2490C2212yescomplemented
161#2489C2212yescomplemented
162#2489C2212yescomplemented
163#2485C2212yes—
164#2485C2212yes—
165#2485C2212yes—
166#2485C2212yescomplemented
167#2485C2212yescomplemented
168#2485C2212yescomplemented
169#2480C2214yes—
170#2477C2212yes—
171#2475C2212yescomplemented
172#2474C2214yescomplemented
173#2474C2214yescomplemented
174#2472C2214yes—
175#2472C2214yes—
176#2469C2214yescomplemented
177#2465C2214yescomplemented
178#2463C2212yes—
179#2461C2214yes—
180#2461C2214yescomplemented
181#2460C2212yescomplemented
182#2459C2214yes—
183#2458C2214yes—
184#2452C2212yes—
185#2452C2212yes—
186#2452C2214yescomplemented
187#2452C2214yescomplemented
188#2452C2211yescharacteristic, complemented
189#2450C2214yescomplemented
190#2448C2212yes—
191#2446C2212yescomplemented
192#2446C2211yescharacteristic, complemented
193#2441C2212yescomplemented
194#2439C2212yescomplemented
195#2439C2212yescomplemented
196#2439C2211yescharacteristic, complemented
197#2439C2214yescomplemented
198#2439C2212yescomplemented
199#2439C2212yescomplemented
200#2432C2211yescharacteristic, complemented
201#2427C2211yescharacteristic
202#2426C2212yes—
203#2426C2214yes—
204#2426C2212yescomplemented
205#2423C2212yes—
206#2422C2212yescomplemented
207#2421C2211yescharacteristic
208#2421C2212yes—
209#2421C2212yescomplemented
210#2420C2212yes—
211#2420C2212yes—
212#2418C2214yes—
213#2415C2212yes—
214#2415C2211yescharacteristic
215#2415C2212yescomplemented
216#2414C2212yes—
217#2414C2212yes—
218#2408C2212yes—
219#2407C2211yescharacteristic
220#2407C2212yes—
221#2407C2212yescomplemented
222#2407C2212yescomplemented
223#2398C2212yescomplemented
224#2392C2212yes—
225#2392C2214yescomplemented
226#2383C2214yescomplemented
227#2379C2214yes—
228#2373C2214yes—
229#2370C2212yescomplemented
230#2369C2212yescomplemented
231#2368C2214yescomplemented
232#2367C2211yescharacteristic
233#2365C2212yescomplemented
234#2364C2212yes—
235#2363C2212yes—
236#2363C2212yes—
237#2363C2211yescharacteristic
238#2362C2212yescomplemented
239#2362C2212yescomplemented
240#2362C2212yescomplemented
241#2362C2212yescomplemented
242#2360C2211yescharacteristic
243#2359C2212yes—
244#2358C2212yes—
245#2355C2214yescomplemented
246#2355C2211yescharacteristic, complemented
247#2354C2211yescharacteristic
248#2354C2212yescomplemented
249#2354C2211yescharacteristic, complemented
250#2352C2212yes—
251#2352C2211yescharacteristic
252#2351C2212yescomplemented
253Q8×C4⋊C4C2211yescharacteristic, complemented
254#2349C2211yescharacteristic
255#2347C2212yes—
256#2347C2212yescomplemented
257#2346C2212yescomplemented
258#2342C2212yes—
259#2341C2212yes—
260#2339C2211yescharacteristic
261D4×C22⋊C4C2211yescharacteristic
262#2337C2214yes—
263#2335C2214yescomplemented
264#2334C2214yes—
265#2334C2214yescomplemented
266#2331C2212yescomplemented
267#2323C2212yes—
268#2320C2214yescomplemented
269#2320C2212yescomplemented
270#2319C2212yes—
271#2317C2212yes—
272#2309C2212yes—
273C4×C4⋊Q8C2211yescharacteristic, complemented
274C4×#124C2211yescharacteristic
275C4×#124C2211yescharacteristic, complemented
276C4×C22⋊Q8C2211yescharacteristic
277C4×C22⋊Q8C2212yescomplemented
278C4×C22⋊Q8C2211yescharacteristic, complemented
279C4×C22⋊Q8C2212yescomplemented
280C4×C22⋊Q8C2212yescomplemented
281C4×C22⋊Q8C2212yescomplemented
282C4×#123C2212yes—
283C4×#121C2212yes—
284C4×#121C2211yescharacteristic
285C4×#121C2211yescharacteristic
286C4×#121C2212yes—
287C4×#121C2212yescomplemented
288C4×#120C2212yes—
289#2296C2212yescomplemented
290#2295C2211yescharacteristic, complemented
291#2290C2212yes—
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic, complemented
294#2283C2212yescomplemented
295#2280C2212yes—
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C22⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303Q82—44no—
304#556—216no—
305#555—44no—
306#546—28no—
307#533—44no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2314yes—
316C2×C4⋊Q8C2314yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#125C2312yes—
320C2×#125C2312yes—
321C2×#124C2314yes—
322C2×#124C2311yescharacteristic
323C2×#124C2311yescharacteristic
324C2×#124C2314yes—
325C2×#124C2314yes—
326C2×#124C2314yes—
327C2×#123C2312yes—
328C2×#123C2314yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2311yescharacteristic
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×#121C2312yes—
345C2×#121C2311yescharacteristic
346C2×#121C2312yes—
347C2×#121C2311yescharacteristic
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#120C2312yes—
352C2×#120C2314yes—
353C4×#41—44no—
354C4×#41—44no—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2314yes—
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×D4—44no—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2312yes—
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2314yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2311yescharacteristic
395C2×#117C2312yes—
396C2×#117C2311yescharacteristic
397C2×#117C2312yes—
398C2×#117C2312yes—
399C22×C4⋊C4C2311yescharacteristic
400C22×C22⋊C4C2312yes—
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2312yes—
403C22×C42C2311yescharacteristic
404C22×C42C2311yescharacteristic
405C22×C42C2312yes—
406C22×C42C2312yes—
407C22×C42C2312yes—
408#401C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2312yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2312yes—
421#400C2314yes—
422#399C2314yes—
423#399C2314yes—
424#399C2314yes—
425#399C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2312yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2312yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2312yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2312yes—
461#396C2312yes—
462#396C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2312yes—
479#394C2312yes—
480#394C2312yes—
481#394C2314yes—
482#394C2312yes—
483#394C2314yes—
484#394C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2314yes—
489#393C2314yes—
490#393C2314yes—
491#393C2314yes—
492#393C2314yes—
493#393C2314yes—
494#393C2312yes—
495#393C2314yes—
496#393C2314yes—
497#393C2312yes—
498#392C2312yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2311yescharacteristic
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2311yescharacteristic
509#391C2312yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2311yescharacteristic
515#391C2312yes—
516#391C2312yes—
517#391C2314yes—
518#391C2311yescharacteristic
519#391C2314yes—
520#391C2314yes—
521#391C2311yescharacteristic
522#391C2311yescharacteristic
523#391C2312yes—
524#390C2314yes—
525#390C2312yes—
526#390C2314yes—
527#390C2314yes—
528#390C2312yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2312yes—
533#390C2314yes—
534#390C2311yescharacteristic
535#390C2311yescharacteristic
536#390C2312yes—
537#390C2314yes—
538#390C2312yes—
539#390C2314yes—
540#390C2314yes—
541#390C2314yes—
542#390C2311yescharacteristic
543#390C2312yes—
544#390C2311yescharacteristic
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2311yescharacteristic
571#389C2312yes—
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2311yescharacteristic
577#389C2311yescharacteristic
578#389C2312yes—
579#389C2314yes—
580#389C2312yes—
581#389C2311yescharacteristic
582#389C2311yescharacteristic
583#388C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2312yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2312yes—
616#388C2314yes—
617#388C2314yes—
618#388C2312yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2312yes—
623#388C2314yes—
624#388C2314yes—
625#388C2312yes—
626#388C2312yes—
627#388C2314yes—
628#388C2312yes—
629#387C2312yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2312yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2312yes—
649#387C2312yes—
650#387C2312yes—
651#387C2314yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2312yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#386C2312yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2312yes—
667#386C2312yes—
668#386C2312yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2312yes—
677#386C2312yes—
678#386C2312yes—
679#386C2312yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2312yes—
688#385C2312yes—
689#385C2314yes—
690#385C2312yes—
691#385C2312yes—
692#385C2314yes—
693#385C2312yes—
694#385C2314yes—
695#385C2314yes—
696#385C2312yes—
697#385C2314yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#384C2311yescharacteristic
703#384C2314yes—
704#384C2312yes—
705#384C2311yescharacteristic
706#384C2311yescharacteristic
707#384C2312yes—
708#383C2314yes—
709#383C2314yes—
710#383C2314yes—
711#383C2314yes—
712#382C2314yes—
713#382C2312yes—
714#382C2314yes—
715#382C2314yes—
716#382C2312yes—
717#382C2312yes—
718#382C2314yes—
719#382C2312yes—
720#382C2311yescharacteristic
721#382C2312yes—
722#382C2311yescharacteristic
723#381C2314yes—
724#381C2314yes—
725#381C2314yes—
726#381C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2311yescharacteristic
738#380C2314yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2314yes—
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2311yescharacteristic
752#380C2312yes—
753#380C2312yes—
754#379C2314yes—
755#379C2314yes—
756#379C2314yes—
757#379C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813#376C2312yes—
814#376C2314yes—
815C2×#95C2312yes—
816C2×#95C2312yes—
817C43C2311yescharacteristic
818C25C2412yes—
819C2×#41—24no—
820C2×#41—24no—
821C2×#41—42no—
822C2×#41—42no—
823C2×#41—42no—
824C2×#41—42no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2411yescharacteristic
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2414yes—
830C22×Q8C2412yes—
831C22×Q8C2414yes—
832C22×D4—24no—
833C22×D4—24no—
834C22×D4—42no—
835C22×D4C2411yescharacteristic
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2414yes—
846C23×C4—44no—
847C23×C4—44no—
848C23×C4—44no—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C4⋊Q8—28no—
868C4⋊Q8—24no—
869C4⋊Q8—44no—
870C4⋊Q8—42no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—42no—
874C4⋊Q8—48no—
875C4⋊Q8—84no—
876#126—216no—
877#126—216no—
878#125—44no—
879#125—44no—
880#124—24no—
881#124—216no—
882#124—42no—
883#124—48no—
884#124—84no—
885#124—84no—
886#123—28no—
887#123—48no—
888C22⋊Q8—28no—
889C22⋊Q8—44no—
890C22⋊Q8—48no—
891C22⋊Q8—44no—
892C22⋊Q8—44no—
893C22⋊Q8—42no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—44no—
897C22⋊Q8—44no—
898C22⋊Q8—42no—
899C22⋊Q8—42no—
900C22⋊Q8—84no—
901C22⋊Q8—82no—
902C22⋊Q8#4118yescomplemented
903#121—28no—
904#121—24no—
905#121—28no—
906#121—44no—
907#121—42no—
908#121—44no—
909#121—44no—
910#120—28no—
911#120—84no—
912C4×Q8—28no—
913C4×Q8—216no—
914C4×Q8—24no—
915C4×Q8—24no—
916C4×Q8—24no—
917C4×Q8—44no—
918C4×Q8—42no—
919C4×Q8—42no—
920C4×Q8—44no—
921C4×Q8—44no—
922C4×Q8—82no—
923C4×D4—24no—
924C4×D4—24no—
925C4×D4—28no—
926C4×D4—24no—
927C4×D4—24no—
928C4×D4—24no—
929C4×D4—24no—
930C4×D4—44no—
931C4×D4—42no—
932C4×D4—42no—
933C4×D4—42no—
934C4×D4—42no—
935C4×D4—44no—
936C4×D4—44no—
937C4×D4—42no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—42no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—84no—
944#117—28no—
945#117—28no—
946#117—44no—
947#117—44no—
948#117—44no—
949#117—44no—
950#117—42no—
951#117—42no—
952#117—44no—
953#117—44no—
954#117—82no—
955C2×C4⋊C4—42no—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2412yes—
1018C2×C22⋊C4—28no—
1019C2×C22⋊C4—44no—
1020C2×C22⋊C4—44no—
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C42—24no—
1085C2×C42—24no—
1086C2×C42—44no—
1087C2×C42—44no—
1088C2×C42—44no—
1089C2×C42C2411yescharacteristic
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2414yes—
1093C2×C42C2414yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2412yes—
1104C2×C42C2411yescharacteristic
1105C2×C42C2414yes—
1106C2×C42C2411yescharacteristic
1107C2×C42C2414yes—
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2414yes—
1116C2×C42C2411yescharacteristic
1117C2×C42C2414yes—
1118C2×C42C2414yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2411yescharacteristic
1122#95C2411yescharacteristic
1123#95C2411yescharacteristic
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2414yes—
1132#95C2412yes—
1133#95C2414yes—
1134#95C2412yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2411yescharacteristic
1144#95C2412yes—
1145#95C2411yescharacteristic
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190C24—24no—
1191C24—24no—
1192C24—42no—
1193C24—42no—
1194C24—42no—
1195C24—42no—
1196C24—42no—
1197C24C2512yes—
1198C24C2512yes—
1199C24C2511yescharacteristic
1200C24C2511yescharacteristic
1201C24C2512yes—
1202#41—416no—
1203#41—416no—
1204C2×Q8—28no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—22no—
1208C2×Q8—24no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—22no—
1214C2×Q8—42no—
1215C2×Q8—42no—
1216C2×Q8—42no—
1217C2×Q8—42no—
1218C2×Q8—44no—
1219C2×Q8—44no—
1220C2×Q8—42no—
1221C2×Q8—44no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8C2×#4114yes—
1225C2×D4—22no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—28no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—24no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—416no—
1242C2×D4—42no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—42no—
1252C2×D4—44no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C2×D4—44no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C2×D42−1+414yes—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—22no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—24no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—24no—
1283C22×C4—22no—
1284C22×C4—24no—
1285C22×C4—22no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—41no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—41no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—41no—
1306C22×C4—42no—
1307C22×C4—42no—
1308C22×C4—42no—
1309C22×C4—42no—
1310C22×C4—42no—
1311C22×C4—42no—
1312C22×C4—816no—
1313C22×C4C2×#4114yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2511yescharacteristic
1318C22×C4C2514yes—
1319C22×C4C2512yes—
1320C22×C4C2511yescharacteristic
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2512yes—
1328C22×C4C2514yes—
1329C22×C4C2512yes—
1330C22×C4C2514yes—
1331C22×C4C2512yes—
1332C22×C4C2514yes—
1333C22×C4C2511yescharacteristic
1334C22×C4C2512yes—
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C22×C4C2511yescharacteristic
1343C22×C4C2511yescharacteristic
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—28no—
1349C4⋊C4—28no—
1350C4⋊C4—28no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—22no—
1354C4⋊C4—24no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—22no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—24no—
1369C4⋊C4—28no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—41no—
1381C4⋊C4—44no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—42no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—42no—
1404C4⋊C4C2×#4114yes—
1405C4⋊C4C2×#4118yes—
1406C22⋊C4—22no—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—28no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—28no—
1414C22⋊C4—24no—
1415C22⋊C4—22no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—28no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—22no—
1423C22⋊C4—24no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—41no—
1441C22⋊C4—41no—
1442C22⋊C4—41no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—42no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—42no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—42no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4C2×#4118yes—
1469C42—28no—
1470C42—28no—
1471C42—22no—
1472C42—24no—
1473C42—28no—
1474C42—22no—
1475C42—22no—
1476C42—22no—
1477C42—22no—
1478C42—22no—
1479C42—22no—
1480C42—24no—
1481C42—24no—
1482C42—24no—
1483C42—22no—
1484C42—22no—
1485C42—24no—
1486C42—22no—
1487C42—42no—
1488C42—42no—
1489C42—42no—
1490C42—42no—
1491C42—42no—
1492C42—42no—
1493C42—44no—
1494C42—44no—
1495C42—44no—
1496C42—41no—
1497C42—44no—
1498C42—41no—
1499C42—44no—
1500C42—44no—
1501C42H(5,𝔽2)14yes—
1502C23—22no—
1503C23—22no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23—21no—
1511C23—21no—
1512C23—22no—
1513C23—21no—
1514C23—22no—
1515C23—22no—
1516C23—21no—
1517C23—22no—
1518C23—22no—
1519C23—21no—
1520C23—21no—
1521C23—22no—
1522C23—22no—
1523C23—22no—
1524C23—21no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—21no—
1529C23—22no—
1530C23—21no—
1531C23—22no—
1532C23—21no—
1533C23—22no—
1534C23—22no—
1535C23—48no—
1536C23—48no—
1537C23—84no—
1538C23—84no—
1539C23—84no—
1540C23—84no—
1541C23—84no—
1542C23C22×#4112yes—
1543C23C2×2−1+414yes—
1544C23C2611yescharacteristic
1545Q8—28no—
1546Q8—44no—
1547Q8—44no—
1548Q8—88no—
1549Q8—84no—
1550Q8—84no—
1551Q8—164no—
1552D4—28no—
1553D4—48no—
1554D4—48no—
1555D4—44no—
1556D4—48no—
1557D4—44no—
1558D4—44no—
1559D4—84no—
1560D4—84no—
1561D4—88no—
1562D4—164no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—28no—
1574C2×C4—24no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—24no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—24no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—24no—
1612C2×C4—22no—
1613C2×C4—24no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—24no—
1620C2×C4—24no—
1621C2×C4—24no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—24no—
1635C2×C4—22no—
1636C2×C4—24no—
1637C2×C4—24no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—44no—
1644C2×C4—48no—
1645C2×C4—48no—
1646C2×C4—48no—
1647C2×C4—44no—
1648C2×C4—48no—
1649C2×C4—48no—
1650C2×C4—44no—
1651C2×C4—44no—
1652C2×C4—84no—
1653C2×C4—84no—
1654C2×C4—84no—
1655C2×C4—82no—
1656C2×C4—84no—
1657C2×C4—84no—
1658C2×C4—84no—
1659C2×C4—84no—
1660C2×C4C22×#4112yes—
1661C2×C4C22×#4114yes—
1662C2×C4C22×#4114yes—
1663C2×C4C22×#4112yes—
1664C2×C4C2×H(5,𝔽2)12yes—
1665C2×C4C2×H(5,𝔽2)12yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4C2×2−1+412yes—
1668C2×C4#58512yes—
1669C2×C4#58512yes—
1670C2×C4#58512yes—
1671C22—22no—
1672C22—24no—
1673C22—22no—
1674C22—24no—
1675C22—22no—
1676C22—24no—
1677C22—41no—
1678C22—42no—
1679C22—42no—
1680C22—41no—
1681C22—42no—
1682C22—41no—
1683C22—42no—
1684C22—41no—
1685C22—42no—
1686C22—42no—
1687C22—41no—
1688C22—41no—
1689C22—42no—
1690C22—42no—
1691C22—41no—
1692C22—42no—
1693C22—42no—
1694C22—41no—
1695C22—42no—
1696C22—42no—
1697C22—41no—
1698C22—42no—
1699C22—42no—
1700C22—42no—
1701C22—41no—
1702C22—42no—
1703C22—41no—
1704C22—42no—
1705C22—42no—
1706C22—816no—
1707C22C23×#4111yescharacteristic
1708C22C22×H(5,𝔽2)11yescharacteristic
1709C22C22×2−1+411yescharacteristic
1710C22C2×#58511yescharacteristic
1711C22C2×#58511yescharacteristic
1712C22C2×#58511yescharacteristic
1713C22H(7,𝔽2)11yescharacteristic
1714C4—24no—
1715C4—22no—
1716C4—24no—
1717C4—22no—
1718C4—22no—
1719C4—41no—
1720C4—42no—
1721C4—42no—
1722C4—41no—
1723C4—42no—
1724C4—42no—
1725C4—41no—
1726C4—42no—
1727C4—44no—
1728C4—42no—
1729C4—41no—
1730C4—42no—
1731C4—41no—
1732C4—44no—
1733C4—42no—
1734C4—41no—
1735C4—41no—
1736C4—44no—
1737C4—42no—
1738C4—41no—
1739C4—42no—
1740C4—44no—
1741C4—42no—
1742C4#352014yes—
1743C4#354014yes—
1744C2—44no—
1745C2—42no—
1746C2—81no—
1747C2—82no—
1748C2—82no—
1749C2C2×#354011yescharacteristic
1750C2C2×#352011yescharacteristic
1751C2#6279311yescharacteristic
1752C2#6295111yescharacteristic
1753C2#6295711yescharacteristic
1754C2#6299411yescharacteristic
1755C2#6302511yescharacteristic
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. #59771C2semidirect
2. #59659C2semidirect
3. #59593C2semidirect
4. #59244C2semidirect
5. #59234C2semidirect
6. #51635C2semidirect
7. #48332C2semidirect
8. #45721C2semidirect
9. #45601C2semidirect
10. #45404C2semidirect
11. #45401C2semidirect
12. #44072C2semidirect
13. #42734C2semidirect
14. #42686C2semidirect
15. #41360C2semidirect
16. #40127C2semidirect
17. #39932C2semidirect
18. #39794C2semidirect
19. #39597C2semidirect
20. #39042C2semidirect
21. #38978C2semidirect
22. #38940C2semidirect
23. #36456C2semidirect
24. #36411C2semidirect
25. #36210C2semidirect
26. #36204C2semidirect
27. #36174C2semidirect
28. #36160C2semidirect
29. #35177C2semidirect
30. #35172C2semidirect
31. #35080C2semidirect
32. #34976C2semidirect
33. #34720C2semidirect
34. #34463C2semidirect
35. C4×#546C2semidirect
36. C2×Q82C22semidirect
42. C2×C4×#41C22semidirect
44. #2859C22semidirect
46. #2857C22semidirect
47. #2857C22semidirect
48. #2857C22semidirect
49. #2855C22semidirect
51. #2850C22semidirect
55. #2829C22semidirect
57. #2804C22semidirect
58. #2796C22semidirect
59. #2795C22semidirect
60. #2794C22semidirect
61. #2782C22semidirect
62. #2780C22semidirect
63. #2777C22semidirect
64. #2775C22semidirect
65. #2775C22semidirect
66. #2775C22semidirect
67. #2775C22semidirect
68. #2772C22semidirect
69. #2771C22semidirect
70. #2761C22semidirect
71. #2754C22semidirect
72. #2753C22semidirect
73. #2752C22semidirect
76. #2737C22semidirect
77. #2737C22semidirect
79. #2731C22semidirect
80. #2731C22semidirect
83. #2713C22semidirect
84. #2712C22semidirect
90. #2665C22semidirect
91. #2663C22semidirect
92. #2653C22semidirect
96. #2640C22semidirect
99. #2609C22semidirect
101. #2596C22semidirect
102. #2595C22semidirect
103. #2589C22semidirect
104. #2587C22semidirect
105. #2582C22semidirect
106. #2581C22semidirect
109. #2575C22semidirect
110. #2573C22semidirect
111. #2567C22semidirect
115. #2563C22semidirect
118. #2551C22semidirect
119. #2551C22semidirect
120. #2547C22semidirect
121. #2546C22semidirect
122. #2545C22semidirect
128. #2538C22semidirect
129. #2538C22semidirect
131. #2527C22semidirect
132. #2526C22semidirect
134. #2518C22semidirect
135. #2514C22semidirect
137. #2512C22semidirect
138. #2510C22semidirect
139. #2509C22semidirect
140. #2509C22semidirect
141. #2509C22semidirect
142. #2499C22semidirect
143. #2497C22semidirect
145. #2495C22semidirect
146. #2495C22semidirect
147. #2495C22semidirect
148. #2495C22semidirect
150. #2494C22semidirect
151. #2493C22semidirect
153. #2492C22semidirect
154. #2492C22semidirect
155. #2492C22semidirect
159. #2491C22semidirect
160. #2490C22semidirect
161. #2489C22semidirect
162. #2489C22semidirect
166. #2485C22semidirect
167. #2485C22semidirect
168. #2485C22semidirect
171. #2475C22semidirect
172. #2474C22semidirect
173. #2474C22semidirect
176. #2469C22semidirect
177. #2465C22semidirect
180. #2461C22semidirect
181. #2460C22semidirect
186. #2452C22semidirect
187. #2452C22semidirect
188. #2452C22semidirect
189. #2450C22semidirect
191. #2446C22semidirect
192. #2446C22semidirect
193. #2441C22semidirect
194. #2439C22semidirect
195. #2439C22semidirect
196. #2439C22semidirect
197. #2439C22semidirect
198. #2439C22semidirect
199. #2439C22semidirect
200. #2432C22semidirect
204. #2426C22semidirect
206. #2422C22semidirect
209. #2421C22semidirect
215. #2415C22semidirect
221. #2407C22semidirect
222. #2407C22semidirect
223. #2398C22semidirect
225. #2392C22semidirect
226. #2383C22semidirect
229. #2370C22semidirect
230. #2369C22semidirect
231. #2368C22semidirect
233. #2365C22semidirect
238. #2362C22semidirect
239. #2362C22semidirect
240. #2362C22semidirect
241. #2362C22semidirect
245. #2355C22semidirect
246. #2355C22semidirect
248. #2354C22semidirect
249. #2354C22semidirect
252. #2351C22semidirect
253. Q8×C4⋊C4C22semidirect
256. #2347C22semidirect
257. #2346C22semidirect
263. #2335C22semidirect
265. #2334C22semidirect
266. #2331C22semidirect
268. #2320C22semidirect
269. #2320C22semidirect
273. C4×C4⋊Q8C22semidirect
275. C4×#124C22semidirect
277. C4×C22⋊Q8C22semidirect
278. C4×C22⋊Q8C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
281. C4×C22⋊Q8C22semidirect
287. C4×#121C22semidirect
289. #2296C22semidirect
290. #2295C22semidirect
293. #2285C22semidirect
294. #2283C22semidirect
902. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#597712
#596592
#595932
#592442
#592342
#516352
#483322
#457212
#456012
#454042
#454012
#440722
#427342
#426862
#413602
#401272
#399322
#397942
#395972
#390422
#389782
#389402
#364562
#364112
#362102
#362042
#361742
#361602
#351772
#351722
#350802
#349762
#347202
#344632
C4×#5462