Finite Group Databasebeta

← #8425217

Subgroups — #8425217

Order 512.

4830 conjugacy classes of subgroups.

The subgroup lattice has 1753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59638C212yesmaximal, complemented
2#59421C211yesmaximal, characteristic, complemented
3#59245C211yesmaximal, characteristic, complemented
4#59229C211yesmaximal, characteristic, complemented
5#59018C212yesmaximal, complemented
6#56491C214yesmaximal, complemented
7#54354C214yesmaximal, complemented
8#53070C212yesmaximal, complemented
9#53054C212yesmaximal, complemented
10#52990C212yesmaximal, complemented
11#52981C212yesmaximal, complemented
12#52501C214yesmaximal, complemented
13#42862C212yesmaximal, complemented
14#42757C212yesmaximal, complemented
15#42650C212yesmaximal, complemented
16#42568C212yesmaximal, complemented
17#41336C214yesmaximal, complemented
18#40093C212yesmaximal, complemented
19#39911C212yesmaximal, complemented
20#39761C211yesmaximal, characteristic, complemented
21#39727C211yesmaximal, characteristic, complemented
22#39377C211yesmaximal, characteristic, complemented
23#39268C212yesmaximal, complemented
24#39124C211yesmaximal, characteristic, complemented
25#37668C212yesmaximal, complemented
26#37631C211yesmaximal, characteristic, complemented
27#37622C211yesmaximal, characteristic, complemented
28#37494C212yesmaximal, complemented
29#37480C212yesmaximal, complemented
30#36274C211yesmaximal, characteristic, complemented
31#36194C211yesmaximal, characteristic, complemented
32#36161C211yesmaximal, characteristic, complemented
33#34935C211yesmaximal, characteristic, complemented
34#34720C211yesmaximal, characteristic, complemented
35#34700C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×#555C2212yescomplemented
38C2×D4×Q8C2211yescharacteristic, complemented
39C2×#542C2212yescomplemented
40C2×#533C2211yescharacteristic, complemented
41C2×#529C2211yescharacteristic
42C2×#525C2212yes—
43C2×C4×#41C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45#2868C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic, complemented
48#2855C2212yescomplemented
49#2848C2212yes—
50#2842C2214yes—
51#2840C2214yes—
52#2839C2214yescomplemented
53#2838C2214yescomplemented
54#2837C2214yes—
55#2832C2214yes—
56#2832C2214yes—
57#2832C2214yescomplemented
58#2831C2214yescomplemented
59#2831C2214yescomplemented
60#2829C2214yes—
61#2824C2214yes—
62#2814C2214yescomplemented
63#2813C2214yes—
64#2808C2214yescomplemented
65#2806C2214yescomplemented
66#2798C2214yescomplemented
67#2798C2214yescomplemented
68#2796C2214yescomplemented
69#2793C2214yescomplemented
70#2788C2214yes—
71#2772C2214yescomplemented
72#2765C2214yes—
73#2755C2214yescomplemented
74#2754C2214yescomplemented
75#2754C2214yescomplemented
76#2751C2214yes—
77#2745C2214yescomplemented
78#2736C2214yes—
79#2725C2214yescomplemented
80#2723C2214yescomplemented
81#2723C2214yescomplemented
82#2718C2214yescomplemented
83#2716C2214yescomplemented
84#2715C2214yescomplemented
85#2715C2214yescomplemented
86#2712C2214yes—
87#2712C2214yescomplemented
88#2705C2214yes—
89#2702C2214yescomplemented
90#2702C2214yescomplemented
91#2697C2214yes—
92#2696C2214yescomplemented
93#2695C2214yes—
94#2687C2214yes—
95#2686C2214yescomplemented
96#2685C2214yes—
97#2684C2214yes—
98#2684C2214yes—
99#2678C2214yes—
100#2674C2214yescomplemented
101#2665C2214yes—
102#2665C2214yes—
103#2665C2214yescomplemented
104#2665C2214yescomplemented
105#2664C2214yescomplemented
106#2653C2214yescomplemented
107#2652C2214yescomplemented
108#2650C2214yescomplemented
109#2645C2212yescomplemented
110#2643C2214yescomplemented
111#2640C2212yes—
112#2640C2212yes—
113#2639C2214yescomplemented
114#2628C2212yescomplemented
115#2628C2212yescomplemented
116#2628C2212yescomplemented
117#2628C2212yescomplemented
118#2625C2212yescomplemented
119#2625C2214yescomplemented
120#2625C2212yescomplemented
121#2624C2212yes—
122#2621C2212yescomplemented
123#2620C2212yes—
124#2607C2214yescomplemented
125#2607C2214yescomplemented
126#2597C2214yescomplemented
127#2592C2212yes—
128#2592C2212yes—
129#2589C2214yescomplemented
130#2588C2214yescomplemented
131#2584C2212yescomplemented
132#2582C2211yescharacteristic, complemented
133#2582C2212yescomplemented
134#2582C2211yescharacteristic, complemented
135#2571C2212yescomplemented
136#2568C2211yescharacteristic, complemented
137#2568C2212yescomplemented
138#2563C2212yes—
139#2563C2212yescomplemented
140#2560C2214yescomplemented
141#2557C2214yes—
142#2551C2211yescharacteristic, complemented
143#2547C2211yescharacteristic
144#2547C2212yescomplemented
145#2540C2212yes—
146#2538C2211yescharacteristic
147#2538C2211yescharacteristic
148#2538C2212yes—
149#2538C2211yescharacteristic
150#2537C2211yescharacteristic
151#2537C2211yescharacteristic
152#2536C2212yes—
153#2536C2212yescomplemented
154#2535C2212yes—
155#2535C2212yescomplemented
156#2534C2214yes—
157#2512C2212yes—
158#2511C2212yescomplemented
159#2511C2212yescomplemented
160#2509C2212yescomplemented
161#2501C2212yes—
162#2499C2212yescomplemented
163#2498C2214yescomplemented
164#2497C2212yes—
165#2497C2212yes—
166#2497C2212yescomplemented
167#2496C2212yescomplemented
168#2496C2212yescomplemented
169#2494C2212yescomplemented
170#2492C2212yes—
171#2492C2212yes—
172#2492C2212yescomplemented
173#2492C2212yescomplemented
174#2492C2212yescomplemented
175#2492C2212yescomplemented
176#2491C2212yes—
177#2491C2212yes—
178#2489C2212yescomplemented
179#2488C2214yescomplemented
180#2486C2212yes—
181#2485C2212yes—
182#2485C2212yescomplemented
183#2480C2214yes—
184#2480C2212yes—
185#2477C2212yescomplemented
186#2475C2212yescomplemented
187#2474C2214yescomplemented
188#2470C2214yes—
189#2468C2212yes—
190#2468C2214yescomplemented
191#2466C2214yes—
192#2463C2212yes—
193#2460C2212yes—
194#2459C2214yescomplemented
195#2457C2212yes—
196#2454C2211yescharacteristic
197#2452C2211yescharacteristic, complemented
198#2451C2212yescomplemented
199#2451C2212yescomplemented
200#2450C2214yes—
201#2450C2214yescomplemented
202#2448C2212yes—
203#2447C2212yes—
204#2447C2211yescharacteristic
205#2447C2214yescomplemented
206#2447C2214yescomplemented
207#2446C2211yescharacteristic, complemented
208#2444C2214yescomplemented
209#2442C2211yescharacteristic
210#2440C2212yescomplemented
211#2439C2212yes—
212#2439C2211yescharacteristic
213#2439C2212yes—
214#2439C2212yes—
215#2439C2212yescomplemented
216#2439C2212yescomplemented
217#2439C2212yescomplemented
218#2439C2212yescomplemented
219#2439C2212yescomplemented
220#2438C2214yescomplemented
221#2436C2212yes—
222#2436C2212yes—
223#2435C2212yes—
224#2435C2211yescharacteristic
225#2432C2211yescharacteristic
226#2429C2212yescomplemented
227#2427C2211yescharacteristic
228#2427C2212yescomplemented
229#2427C2211yescharacteristic, complemented
230#2426C2212yes—
231#2423C2212yescomplemented
232#2422C2212yescomplemented
233#2421C2212yescomplemented
234#2421C2211yescharacteristic, complemented
235#2420C2211yescharacteristic
236#2420C2212yescomplemented
237#2419C2214yescomplemented
238#2418C2212yes—
239#2417C2212yes—
240#2417C2211yescharacteristic
241#2416C2212yes—
242#2415C2212yes—
243#2415C2211yescharacteristic
244#2415C2212yescomplemented
245#2415C2212yescomplemented
246#2415C2212yescomplemented
247#2409C2212yes—
248#2409C2212yescomplemented
249#2408C2212yes—
250#2408C2211yescharacteristic
251#2407C2211yescharacteristic
252#2398C2212yes—
253#2395C2212yes—
254#2392C2214yes—
255#2392C2212yes—
256#2392C2212yes—
257#2369C2212yescomplemented
258#2369C2212yescomplemented
259#2367C2212yes—
260#2363C2212yescomplemented
261#2362C2212yes—
262#2360C2212yes—
263#2359C2214yescomplemented
264#2355C2211yescharacteristic, complemented
265#2355C2212yescomplemented
266#2354C2211yescharacteristic
267#2354C2212yes—
268Q8×C4⋊C4C2211yescharacteristic, complemented
269#2349C2212yescomplemented
270D4×C4⋊C4C2211yescharacteristic, complemented
271#2344C2212yescomplemented
272Q8×C22⋊C4C2212yescomplemented
273#2339C2212yes—
274#2334C2214yescomplemented
275#2331C2212yescomplemented
276#2324C2212yescomplemented
277#2323C2212yescomplemented
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×#124C2211yescharacteristic
280C4×#124C2211yescharacteristic, complemented
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2212yescomplemented
284C4×#121C2211yescharacteristic
285C4×#121C2212yes—
286C4×#121C2212yes—
287C4×#121C2211yescharacteristic, complemented
288C4×#120C2212yes—
289#2295C2211yescharacteristic, complemented
290C2×#391C2212yescomplemented
291#2293C2211yescharacteristic
292#2290C2212yescomplemented
293#2285C2211yescharacteristic
294#2285C2211yescharacteristic, complemented
295#2280C2212yes—
296#2280C2212yes—
297#2280C2212yes—
298C42×D4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×Q8C2312yes—
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303#556—44no—
304#555—48no—
305D4×Q8—44no—
306#542—48no—
307#533—44no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2311yescharacteristic
317#529—44no—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#126C2312yes—
321C2×#126C2314yes—
322C2×#125C2311yescharacteristic
323C2×#125C2312yes—
324C2×#124C2311yescharacteristic
325C2×#124C2311yescharacteristic
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2311yescharacteristic
329C2×#124C2314yes—
330C2×#124C2314yes—
331C2×#124C2314yes—
332#525—48no—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2312yes—
336C2×#123C2314yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2311yescharacteristic
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2311yescharacteristic
356C2×#121C2311yescharacteristic
357C2×#121C2311yescharacteristic
358C2×#121C2314yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#120C2314yes—
362C2×#120C2312yes—
363C4×#41—44no—
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2311yescharacteristic
372C2×C4×D4—44no—
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2314yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2314yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×#117C2312yes—
394C2×#117C2312yes—
395C2×#117C2314yes—
396C2×#117C2312yes—
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2312yes—
400C2×#117C2312yes—
401C2×#117C2312yes—
402C2×#117C2311yescharacteristic
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2311yescharacteristic
405C22×C22⋊C4C2312yes—
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2312yes—
409#401C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2312yes—
420#400C2312yes—
421#400C2314yes—
422#400C2314yes—
423#400C2312yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#399C2314yes—
434#399C2312yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2312yes—
447#398C2312yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2312yes—
452#397C2314yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2312yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2312yes—
470#397C2312yes—
471#397C2312yes—
472#397C2314yes—
473#397C2314yes—
474#397C2312yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2312yes—
482#396C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2312yes—
488#396C2314yes—
489#396C2312yes—
490#396C2314yes—
491#395C2314yes—
492#395C2314yes—
493#395C2314yes—
494#395C2314yes—
495#395C2314yes—
496#395C2314yes—
497#394C2314yes—
498#394C2312yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2312yes—
507#394C2314yes—
508#394C2312yes—
509#394C2312yes—
510#394C2314yes—
511#394C2314yes—
512#394C2312yes—
513#394C2312yes—
514#394C2314yes—
515#394C2312yes—
516#394C2312yes—
517#394C2312yes—
518#394C2312yes—
519#394C2314yes—
520#393C2314yes—
521#393C2314yes—
522#393C2314yes—
523#393C2314yes—
524#393C2314yes—
525#393C2312yes—
526#393C2314yes—
527#393C2314yes—
528#393C2314yes—
529#393C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2312yes—
535#393C2314yes—
536#393C2314yes—
537#393C2314yes—
538#393C2314yes—
539#392C2314yes—
540#392C2312yes—
541#392C2312yes—
542#392C2314yes—
543#391C2314yes—
544#391C2312yes—
545#391C2311yescharacteristic
546#391C2314yes—
547#391C2312yes—
548#391C2312yes—
549#391C2312yes—
550#391C2312yes—
551#391C2314yes—
552#391C2314yes—
553#391C2314yes—
554#391C2314yes—
555#391C2312yes—
556#391C2312yes—
557#391C2312yes—
558#391C2312yes—
559#391C2314yes—
560#391C2314yes—
561#391C2314yes—
562#391C2314yes—
563#391C2314yes—
564#391C2311yescharacteristic
565#391C2312yes—
566#391C2312yes—
567#391C2314yes—
568#391C2314yes—
569#391C2312yes—
570#391C2312yes—
571#391C2311yescharacteristic
572#391C2314yes—
573#391C2311yescharacteristic
574#391C2311yescharacteristic
575#391C2311yescharacteristic
576#390C2314yes—
577#390C2314yes—
578#390C2314yes—
579#390C2311yescharacteristic
580#390C2314yes—
581#390C2311yescharacteristic
582#390C2312yes—
583#390C2312yes—
584#390C2312yes—
585#390C2312yes—
586#390C2311yescharacteristic
587#390C2311yescharacteristic
588#390C2311yescharacteristic
589#390C2311yescharacteristic
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2314yes—
594#389C2312yes—
595#389C2312yes—
596#389C2314yes—
597#389C2311yescharacteristic
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2314yes—
602#389C2312yes—
603#389C2314yes—
604#389C2314yes—
605#389C2312yes—
606#389C2312yes—
607#389C2314yes—
608#389C2314yes—
609#389C2312yes—
610#389C2311yescharacteristic
611#389C2312yes—
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2312yes—
617#389C2314yes—
618#389C2311yescharacteristic
619#389C2311yescharacteristic
620#389C2311yescharacteristic
621#389C2311yescharacteristic
622#389C2311yescharacteristic
623#389C2311yescharacteristic
624#388C2312yes—
625#388C2312yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2312yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2312yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2312yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2312yes—
652#388C2312yes—
653#388C2312yes—
654#388C2312yes—
655#388C2312yes—
656#388C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2312yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2312yes—
682#387C2312yes—
683#387C2312yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2312yes—
690#386C2314yes—
691#386C2312yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2312yes—
696#386C2312yes—
697#386C2312yes—
698#386C2312yes—
699#386C2312yes—
700#386C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2312yes—
704#385C2314yes—
705#385C2312yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2312yes—
711#385C2312yes—
712#385C2314yes—
713#385C2312yes—
714#385C2312yes—
715#385C2312yes—
716#385C2312yes—
717#385C2312yes—
718#384C2311yescharacteristic
719#384C2312yes—
720#384C2311yescharacteristic
721#384C2312yes—
722#384C2311yescharacteristic
723#384C2312yes—
724#384C2312yes—
725#382C2314yes—
726#382C2314yes—
727#382C2312yes—
728#382C2312yes—
729#382C2312yes—
730#382C2312yes—
731#382C2311yescharacteristic
732#382C2311yescharacteristic
733#381C2314yes—
734#381C2314yes—
735#381C2312yes—
736#381C2312yes—
737#381C2314yes—
738#381C2314yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2311yescharacteristic
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2314yes—
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2311yescharacteristic
759#380C2311yescharacteristic
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#379C2312yes—
770#379C2314yes—
771#379C2314yes—
772#379C2312yes—
773#379C2314yes—
774#379C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2311yescharacteristic
814C4×C22⋊C4C2311yescharacteristic
815#376C2312yes—
816C2×#95C2314yes—
817C2×#95C2314yes—
818C43C2311yescharacteristic
819C25C2412yes—
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—42no—
823C22×Q8—44no—
824C22×Q8—44no—
825C22×Q8—44no—
826C22×Q8C2411yescharacteristic
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2411yescharacteristic
830C22×Q8C2412yes—
831C22×Q8C2414yes—
832C22×Q8C2414yes—
833C22×Q8C2414yes—
834C22×D4—42no—
835C22×D4—42no—
836C22×D4—42no—
837C22×D4C2411yescharacteristic
838C22×D4C2411yescharacteristic
839C22×D4C2411yescharacteristic
840C22×D4C2412yes—
841C22×D4C2411yescharacteristic
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C23×C4—28no—
849C23×C4—44no—
850C23×C4—44no—
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2414yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2414yes—
867C4⋊Q8—24no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871C4⋊Q8—42no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874C4⋊Q8—44no—
875C4⋊Q8—42no—
876#126—44no—
877#126—48no—
878#126—48no—
879#126—48no—
880#125—42no—
881#125—44no—
882#124—24no—
883#124—44no—
884#124—42no—
885#124—42no—
886#124—44no—
887#124—48no—
888#124—48no—
889#124—48no—
890#123—48no—
891#123—48no—
892#123—44no—
893#123—48no—
894C22⋊Q8—24no—
895C22⋊Q8—48no—
896C22⋊Q8—44no—
897C22⋊Q8—48no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900C22⋊Q8—44no—
901C22⋊Q8—42no—
902C22⋊Q8—44no—
903C22⋊Q8—44no—
904C22⋊Q8—42no—
905C22⋊Q8—42no—
906C22⋊Q8—42no—
907C22⋊Q8—44no—
908C22⋊Q8—44no—
909C22⋊Q8—44no—
910#121—28no—
911#121—28no—
912#121—24no—
913#121—42no—
914#121—44no—
915#121—44no—
916#121—42no—
917#121—48no—
918#120—44no—
919#120—48no—
920C4×Q8—24no—
921C4×Q8—24no—
922C4×Q8—24no—
923C4×Q8—44no—
924C4×Q8—44no—
925C4×Q8—42no—
926C4×Q8—44no—
927C4×Q8—44no—
928C4×D4—28no—
929C4×D4—24no—
930C4×D4—24no—
931C4×D4—24no—
932C4×D4—24no—
933C4×D4—44no—
934C4×D4—42no—
935C4×D4—42no—
936C4×D4—42no—
937C4×D4—42no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—42no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—48no—
947C4×D4—48no—
948#117—44no—
949#117—44no—
950#117—44no—
951#117—44no—
952#117—48no—
953#117—42no—
954#117—44no—
955#117—44no—
956#117—44no—
957#117—44no—
958C2×C4⋊C4—44no—
959C2×C4⋊C4—42no—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C22⋊C4—44no—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C22⋊C4C2411yescharacteristic
1065C2×C22⋊C4C2411yescharacteristic
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C42—24no—
1092C2×C42—24no—
1093C2×C42—44no—
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2412yes—
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2412yes—
1113C2×C42C2414yes—
1114C2×C42C2414yes—
1115C2×C42C2412yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2414yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121#95C2412yes—
1122#95C2412yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2411yescharacteristic
1135#95C2411yescharacteristic
1136#95C2411yescharacteristic
1137#95C2412yes—
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2411yescharacteristic
1141#95C2412yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191C24—24no—
1192C24—42no—
1193C24—42no—
1194C24—42no—
1195C24—42no—
1196C24—42no—
1197C24—42no—
1198C24C2512yes—
1199C24C2512yes—
1200C24C2511yescharacteristic
1201C24C2512yes—
1202C24C2511yescharacteristic
1203#41—416no—
1204C2×Q8—22no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—22no—
1208C2×Q8—24no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—24no—
1214C2×Q8—22no—
1215C2×Q8—22no—
1216C2×Q8—42no—
1217C2×Q8—44no—
1218C2×Q8—42no—
1219C2×Q8—44no—
1220C2×Q8—44no—
1221C2×Q8—42no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8—44no—
1225C2×Q8—44no—
1226C2×Q8—44no—
1227C2×Q8—44no—
1228C2×Q8—816no—
1229C2×D4—24no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—28no—
1233C2×D4—28no—
1234C2×D4—24no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—41no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—42no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—42no—
1257C2×D4—44no—
1258C2×D4—42no—
1259C2×D4—44no—
1260C2×D4—42no—
1261C2×D4—416no—
1262C2×D4H(5,𝔽2)14yes—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—28no—
1267C22×C4—24no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—24no—
1272C22×C4—22no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—22no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—24no—
1290C22×C4—24no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—44no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—44no—
1300C22×C4—41no—
1301C22×C4—41no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—44no—
1305C22×C4—41no—
1306C22×C4—41no—
1307C22×C4—42no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—816no—
1311C22×C42−1+414yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2512yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2512yes—
1316C22×C4C2511yescharacteristic
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2514yes—
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2514yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2514yes—
1332C22×C4C2514yes—
1333C22×C4C2511yescharacteristic
1334C22×C4C2511yescharacteristic
1335C22×C4C2512yes—
1336C22×C4C2511yescharacteristic
1337C22×C4C2511yescharacteristic
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C4⋊C4—22no—
1343C4⋊C4—22no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—24no—
1350C4⋊C4—22no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—22no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—28no—
1368C4⋊C4—44no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—44no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—41no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—42no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—44no—
1393C4⋊C4—42no—
1394C4⋊C4—42no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—42no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C22⋊C4—24no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—28no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—22no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—22no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
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—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—41no—
1445C22⋊C4—41no—
1446C22⋊C4—41no—
1447C22⋊C4—41no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—42no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—44no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—44no—
1472C42—22no—
1473C42—22no—
1474C42—22no—
1475C42—22no—
1476C42—22no—
1477C42—22no—
1478C42—24no—
1479C42—22no—
1480C42—24no—
1481C42—24no—
1482C42—24no—
1483C42—22no—
1484C42—22no—
1485C42—24no—
1486C42—22no—
1487C42—22no—
1488C42—42no—
1489C42—42no—
1490C42—41no—
1491C42—44no—
1492C42—44no—
1493C42—44no—
1494C42—44no—
1495C42—44no—
1496C42—44no—
1497C42—44no—
1498C42H(5,𝔽2)14yes—
1499C23—22no—
1500C23—21no—
1501C23—21no—
1502C23—22no—
1503C23—22no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—22no—
1508C23—22no—
1509C23—21no—
1510C23—22no—
1511C23—22no—
1512C23—22no—
1513C23—21no—
1514C23—22no—
1515C23—21no—
1516C23—22no—
1517C23—21no—
1518C23—22no—
1519C23—22no—
1520C23—22no—
1521C23—22no—
1522C23—21no—
1523C23—22no—
1524C23—21no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—21no—
1529C23—22no—
1530C23—22no—
1531C23—21no—
1532C23—48no—
1533C23—84no—
1534C23—84no—
1535C23—84no—
1536C23—84no—
1537C23—84no—
1538C23—84no—
1539C23C2×H(5,𝔽2)14yes—
1540C23C2×2−1+412yes—
1541C23C2611yescharacteristic
1542Q8—44no—
1543Q8—44no—
1544Q8—48no—
1545Q8—44no—
1546Q8—84no—
1547Q8—88no—
1548Q8—164no—
1549Q8—164no—
1550D4—28no—
1551D4—44no—
1552D4—48no—
1553D4—48no—
1554D4—44no—
1555D4—44no—
1556D4—88no—
1557D4—88no—
1558D4—84no—
1559D4—84no—
1560D4—84no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—28no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—24no—
1588C2×C4—24no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—24no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—24no—
1612C2×C4—24no—
1613C2×C4—24no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—24no—
1620C2×C4—22no—
1621C2×C4—24no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—24no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—24no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—48no—
1644C2×C4—44no—
1645C2×C4—48no—
1646C2×C4—48no—
1647C2×C4—44no—
1648C2×C4—44no—
1649C2×C4—48no—
1650C2×C4—82no—
1651C2×C4—82no—
1652C2×C4—84no—
1653C2×C4—84no—
1654C2×C4—88no—
1655C2×C4—84no—
1656C2×C4—84no—
1657C2×C4—88no—
1658C2×C4C2×H(5,𝔽2)12yes—
1659C2×C4C2×H(5,𝔽2)12yes—
1660C2×C4C2×H(5,𝔽2)12yes—
1661C2×C4C2×H(5,𝔽2)12yes—
1662C2×C4C2×2−1+412yes—
1663C2×C4C2×2−1+412yes—
1664C2×C4#58512yes—
1665C2×C4#58512yes—
1666C2×C4#58512yes—
1667C22—22no—
1668C22—24no—
1669C22—22no—
1670C22—24no—
1671C22—24no—
1672C22—22no—
1673C22—42no—
1674C22—41no—
1675C22—42no—
1676C22—41no—
1677C22—41no—
1678C22—42no—
1679C22—42no—
1680C22—41no—
1681C22—42no—
1682C22—42no—
1683C22—41no—
1684C22—41no—
1685C22—42no—
1686C22—42no—
1687C22—41no—
1688C22—42no—
1689C22—42no—
1690C22—41no—
1691C22—42no—
1692C22—42no—
1693C22—41no—
1694C22—42no—
1695C22—42no—
1696C22—41no—
1697C22—42no—
1698C22—42no—
1699C22—41no—
1700C22—42no—
1701C22—42no—
1702C22—816no—
1703C22C22×H(5,𝔽2)11yescharacteristic
1704C22C22×H(5,𝔽2)11yescharacteristic
1705C22C22×2−1+411yescharacteristic
1706C22C2×#58511yescharacteristic
1707C22C2×#58511yescharacteristic
1708C22C2×#58511yescharacteristic
1709C222−1+611yescharacteristic
1710C4—22no—
1711C4—22no—
1712C4—22no—
1713C4—41no—
1714C4—42no—
1715C4—42no—
1716C4—42no—
1717C4—42no—
1718C4—41no—
1719C4—41no—
1720C4—42no—
1721C4—42no—
1722C4—44no—
1723C4—42no—
1724C4—42no—
1725C4—44no—
1726C4—44no—
1727C4—41no—
1728C4—41no—
1729C4—44no—
1730C4—42no—
1731C4—42no—
1732C4—41no—
1733C4—41no—
1734C4—42no—
1735C4—41no—
1736C4—42no—
1737C4—42no—
1738C4#353614yes—
1739C4#354014yes—
1740C2—44no—
1741C2—42no—
1742C2—81no—
1743C2—82no—
1744C2—82no—
1745C2C2×#353611yescharacteristic
1746C2C2×#354011yescharacteristic
1747C2#6275211yescharacteristic
1748C2#6292111yescharacteristic
1749C2#6295911yescharacteristic
1750C2#6296011yescharacteristic
1751C2#6302111yescharacteristic
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. #59638C2semidirect
2. #59421C2semidirect
3. #59245C2semidirect
4. #59229C2semidirect
5. #59018C2semidirect
6. #56491C2semidirect
7. #54354C2semidirect
8. #53070C2semidirect
9. #53054C2semidirect
10. #52990C2semidirect
11. #52981C2semidirect
12. #52501C2semidirect
13. #42862C2semidirect
14. #42757C2semidirect
15. #42650C2semidirect
16. #42568C2semidirect
17. #41336C2semidirect
18. #40093C2semidirect
19. #39911C2semidirect
20. #39761C2semidirect
21. #39727C2semidirect
22. #39377C2semidirect
23. #39268C2semidirect
24. #39124C2semidirect
25. #37668C2semidirect
26. #37631C2semidirect
27. #37622C2semidirect
28. #37494C2semidirect
29. #37480C2semidirect
30. #36274C2semidirect
31. #36194C2semidirect
32. #36161C2semidirect
33. #34935C2semidirect
34. #34720C2semidirect
35. #34700C2semidirect
37. C2×#555C22semidirect
38. C2×D4×Q8C22semidirect
39. C2×#542C22semidirect
40. C2×#533C22semidirect
45. #2868C22semidirect
47. #2857C22semidirect
48. #2855C22semidirect
52. #2839C22semidirect
53. #2838C22semidirect
57. #2832C22semidirect
58. #2831C22semidirect
59. #2831C22semidirect
62. #2814C22semidirect
64. #2808C22semidirect
65. #2806C22semidirect
66. #2798C22semidirect
67. #2798C22semidirect
68. #2796C22semidirect
69. #2793C22semidirect
71. #2772C22semidirect
73. #2755C22semidirect
74. #2754C22semidirect
75. #2754C22semidirect
77. #2745C22semidirect
79. #2725C22semidirect
80. #2723C22semidirect
81. #2723C22semidirect
82. #2718C22semidirect
83. #2716C22semidirect
84. #2715C22semidirect
85. #2715C22semidirect
87. #2712C22semidirect
89. #2702C22semidirect
90. #2702C22semidirect
92. #2696C22semidirect
95. #2686C22semidirect
100. #2674C22semidirect
103. #2665C22semidirect
104. #2665C22semidirect
105. #2664C22semidirect
106. #2653C22semidirect
107. #2652C22semidirect
108. #2650C22semidirect
109. #2645C22semidirect
110. #2643C22semidirect
113. #2639C22semidirect
114. #2628C22semidirect
115. #2628C22semidirect
116. #2628C22semidirect
117. #2628C22semidirect
118. #2625C22semidirect
119. #2625C22semidirect
120. #2625C22semidirect
122. #2621C22semidirect
124. #2607C22semidirect
125. #2607C22semidirect
126. #2597C22semidirect
129. #2589C22semidirect
130. #2588C22semidirect
131. #2584C22semidirect
132. #2582C22semidirect
133. #2582C22semidirect
134. #2582C22semidirect
135. #2571C22semidirect
136. #2568C22semidirect
137. #2568C22semidirect
139. #2563C22semidirect
140. #2560C22semidirect
142. #2551C22semidirect
144. #2547C22semidirect
153. #2536C22semidirect
155. #2535C22semidirect
158. #2511C22semidirect
159. #2511C22semidirect
160. #2509C22semidirect
162. #2499C22semidirect
163. #2498C22semidirect
166. #2497C22semidirect
167. #2496C22semidirect
168. #2496C22semidirect
169. #2494C22semidirect
172. #2492C22semidirect
173. #2492C22semidirect
174. #2492C22semidirect
175. #2492C22semidirect
178. #2489C22semidirect
179. #2488C22semidirect
182. #2485C22semidirect
185. #2477C22semidirect
186. #2475C22semidirect
187. #2474C22semidirect
190. #2468C22semidirect
194. #2459C22semidirect
197. #2452C22semidirect
198. #2451C22semidirect
199. #2451C22semidirect
201. #2450C22semidirect
205. #2447C22semidirect
206. #2447C22semidirect
207. #2446C22semidirect
208. #2444C22semidirect
210. #2440C22semidirect
215. #2439C22semidirect
216. #2439C22semidirect
217. #2439C22semidirect
218. #2439C22semidirect
219. #2439C22semidirect
220. #2438C22semidirect
226. #2429C22semidirect
228. #2427C22semidirect
229. #2427C22semidirect
231. #2423C22semidirect
232. #2422C22semidirect
233. #2421C22semidirect
234. #2421C22semidirect
236. #2420C22semidirect
237. #2419C22semidirect
244. #2415C22semidirect
245. #2415C22semidirect
246. #2415C22semidirect
248. #2409C22semidirect
257. #2369C22semidirect
258. #2369C22semidirect
260. #2363C22semidirect
263. #2359C22semidirect
264. #2355C22semidirect
265. #2355C22semidirect
268. Q8×C4⋊C4C22semidirect
269. #2349C22semidirect
270. D4×C4⋊C4C22semidirect
271. #2344C22semidirect
272. Q8×C22⋊C4C22semidirect
274. #2334C22semidirect
275. #2331C22semidirect
276. #2324C22semidirect
277. #2323C22semidirect
278. C4×C4⋊Q8C22semidirect
280. C4×#124C22semidirect
283. C4×C22⋊Q8C22semidirect
287. C4×#121C22semidirect
289. #2295C22semidirect
290. C2×#391C22semidirect
292. #2290C22semidirect
294. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#596382
#594212
#592452
#592292
#590182
#564912
#543542
#530702
#530542
#529902
#529812
#525012
#428622
#427572
#426502
#425682
#413362
#400932
#399112
#397612
#397272
#393772
#392682
#391242
#376682
#376312
#376222
#374942
#374802
#362742
#361942
#361612
#349352
#347202
#347002