Finite Group Databasebeta

← #7654852

Subgroups — #7654852

Order 512.

4804 conjugacy classes of subgroups.

The subgroup lattice has 1663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42214C214yesmaximal, complemented
2#42040C214yesmaximal, complemented
3#42010C214yesmaximal, complemented
4#39800C212yesmaximal, complemented
5#39675C212yesmaximal, complemented
6#39263C212yesmaximal, complemented
7#39257C212yesmaximal, complemented
8#38231C212yesmaximal, complemented
9#38224C212yesmaximal, complemented
10#38066C212yesmaximal, complemented
11#38054C212yesmaximal
12#37955C212yesmaximal, complemented
13#37853C212yesmaximal, complemented
14#37765C212yesmaximal, complemented
15#37663C212yesmaximal, complemented
16#37631C211yesmaximal, characteristic, complemented
17#37628C211yesmaximal, characteristic, complemented
18#37623C211yesmaximal, characteristic, complemented
19#36293C212yesmaximal
20#36280C212yesmaximal, complemented
21#36167C212yesmaximal, complemented
22#36130C212yesmaximal, complemented
23#35824C214yesmaximal, complemented
24#35248C211yesmaximal, characteristic, complemented
25#35240C211yesmaximal, characteristic
26#35209C211yesmaximal, characteristic, complemented
27#35206C211yesmaximal, characteristic, complemented
28#35184C211yesmaximal, characteristic, complemented
29#35176C211yesmaximal, characteristic, complemented
30#34945C211yesmaximal, characteristic, complemented
31#34929C211yesmaximal, characteristic, complemented
32C2×#2538C211yesmaximal, characteristic
33#34214C211yesmaximal, characteristic, complemented
34#34128C211yesmaximal, characteristic, complemented
35#34126C211yesmaximal, characteristic
36C2×#541C2212yescomplemented
37C2×#533C2211yescharacteristic
38C2×#533C2212yescomplemented
39C22×C22⋊Q8C2212yes—
40C22×C4×Q8C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42#2863C2212yescomplemented
43#2861C2212yes—
44#2860C2212yes—
45#2859C2212yescomplemented
46#2857C2212yescomplemented
47#2855C2212yes—
48#2855C2212yes—
49#2855C2212yescomplemented
50#2855C2212yescomplemented
51#2851C2212yescomplemented
52#2848C2212yes—
53#2848C2212yes—
54#2843C2214yescomplemented
55#2838C2214yescomplemented
56#2836C2214yescomplemented
57#2793C2214yescomplemented
58#2790C2214yescomplemented
59#2783C2214yescomplemented
60#2776C2214yescomplemented
61#2775C2214yescomplemented
62#2769C2214yescomplemented
63#2766C2214yescomplemented
64#2765C2214yescomplemented
65#2761C2214yes—
66#2757C2214yes—
67#2747C2214yescomplemented
68#2745C2214yescomplemented
69#2744C2214yescomplemented
70#2742C2214yescomplemented
71#2738C2214yescomplemented
72#2737C2214yes—
73#2723C2214yes—
74#2721C2214yescomplemented
75#2720C2214yescomplemented
76#2719C2214yescomplemented
77#2704C2214yescomplemented
78#2698C2214yescomplemented
79#2690C2214yescomplemented
80#2689C2214yescomplemented
81#2667C2214yescomplemented
82#2664C2214yescomplemented
83#2660C2212yescomplemented
84#2660C2212yescomplemented
85#2654C2214yescomplemented
86#2654C2214yescomplemented
87#2652C2214yescomplemented
88#2650C2214yescomplemented
89#2647C2212yescomplemented
90#2647C2212yescomplemented
91#2647C2212yescomplemented
92#2645C2212yescomplemented
93#2644C2212yes—
94#2640C2212yes—
95#2634C2214yescomplemented
96#2633C2214yes—
97#2628C2212yescomplemented
98#2627C2214yes—
99#2625C2212yescomplemented
100#2625C2212yescomplemented
101#2621C2212yescomplemented
102#2612C2214yescomplemented
103#2606C2214yescomplemented
104#2597C2214yes—
105#2594C2214yescomplemented
106#2587C2214yescomplemented
107#2585C2214yescomplemented
108#2581C2212yescomplemented
109#2581C2212yescomplemented
110#2577C2214yescomplemented
111#2574C2214yescomplemented
112#2573C2214yescomplemented
113#2573C2214yescomplemented
114#2571C2211yescharacteristic, complemented
115#2568C2211yescharacteristic, complemented
116#2568C2211yescharacteristic, complemented
117#2561C2214yes—
118#2556C2214yescomplemented
119#2556C2214yescomplemented
120#2552C2211yescharacteristic, complemented
121#2552C2211yescharacteristic, complemented
122#2551C2211yescharacteristic, complemented
123#2549C2214yescomplemented
124#2547C2211yescharacteristic
125#2547C2211yescharacteristic
126#2546C2211yescharacteristic, complemented
127#2546C2211yescharacteristic, complemented
128#2542C2211yescharacteristic
129#2542C2211yescharacteristic
130#2538C2214yes—
131#2538C2212yes—
132#2538C2212yes—
133#2538C2212yes—
134#2538C2212yes—
135#2538C2211yescharacteristic
136#2538C2211yescharacteristic
137#2538C2211yescharacteristic
138#2538C2211yescharacteristic
139#2536C2212yes—
140#2536C2212yes—
141#2531C2214yes—
142#2530C2214yescomplemented
143#2529C2214yescomplemented
144#2526C2214yes—
145#2525C2214yescomplemented
146#2525C2214yescomplemented
147#2522C2214yescomplemented
148#2519C2214yescomplemented
149#2515C2214yescomplemented
150#2514C2212yescomplemented
151#2513C2212yes—
152#2512C2212yes—
153#2511C2212yescomplemented
154#2507C2212yescomplemented
155#2507C2212yescomplemented
156#2506C2212yescomplemented
157#2506C2212yescomplemented
158#2505C2214yescomplemented
159#2503C2212yes—
160#2502C2212yes—
161#2495C2212yescomplemented
162#2495C2212yescomplemented
163#2494C2212yescomplemented
164#2494C2212yescomplemented
165#2493C2214yes—
166#2493C2214yes—
167#2493C2214yescomplemented
168#2492C2212yescomplemented
169#2492C2212yescomplemented
170#2489C2212yescomplemented
171#2489C2212yescomplemented
172#2484C2214yes—
173#2483C2214yes—
174#2482C2214yes—
175#2482C2214yes—
176#2480C2214yes—
177#2480C2214yes—
178#2479C2214yes—
179#2475C2214yescomplemented
180#2473C2214yes—
181#2473C2214yes—
182#2469C2214yescomplemented
183#2465C2214yescomplemented
184#2462C2214yescomplemented
185#2454C2212yes—
186#2453C2212yescomplemented
187#2452C2212yes—
188#2451C2212yescomplemented
189#2448C2212yes—
190#2448C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2442C2212yes—
194#2442C2214yes—
195#2442C2212yes—
196#2440C2212yes—
197#2440C2212yes—
198#2438C2214yes—
199#2438C2214yescomplemented
200#2437C2214yes—
201#2435C2212yes—
202#2434C2212yes—
203#2429C2212yescomplemented
204#2429C2212yescomplemented
205#2429C2212yescomplemented
206#2429C2212yescomplemented
207#2423C2212yescomplemented
208#2423C2212yescomplemented
209#2421C2212yescomplemented
210#2421C2212yescomplemented
211#2401C2214yescomplemented
212#2396C2214yescomplemented
213C2×#396C2214yes—
214#2360C2212yes—
215#2360C2212yes—
216#2360C2214yes—
217#2360C2212yes—
218#2360C2212yes—
219#2357C2211yescharacteristic
220#2357C2211yescharacteristic
221#2356C2212yescomplemented
222#2356C2211yescharacteristic, complemented
223#2356C2211yescharacteristic, complemented
224#2356C2212yescomplemented
225#2355C2212yescomplemented
226#2355C2212yescomplemented
227#2353C2212yes—
228#2353C2212yes—
229#2351C2211yescharacteristic, complemented
230#2351C2211yescharacteristic, complemented
231Q8×C4⋊C4C2212yescomplemented
232Q8×C4⋊C4C2212yescomplemented
233#2349C2211yescharacteristic
234#2349C2211yescharacteristic
235#2345C2211yescharacteristic
236#2345C2211yescharacteristic
237#2344C2212yes—
238#2344C2211yescharacteristic
239#2344C2211yescharacteristic
240#2344C2212yes—
241#2343C2214yes—
242#2342C2212yes—
243#2342C2214yes—
244#2342C2214yes—
245#2342C2212yes—
246Q8×C22⋊C4C2211yescharacteristic
247Q8×C22⋊C4C2211yescharacteristic
248D4×C22⋊C4C2211yescharacteristic
249D4×C22⋊C4C2211yescharacteristic
250#2330C2212yescomplemented
251#2330C2212yescomplemented
252#2330C2212yescomplemented
253#2327C2212yescomplemented
254#2327C2212yescomplemented
255#2326C2212yes—
256#2326C2212yes—
257#2326C2212yes—
258#2323C2212yescomplemented
259#2323C2212yescomplemented
260#2320C2212yescomplemented
261#2319C2212yes—
262#2317C2212yes—
263#2314C2212yescomplemented
264C4×C4⋊Q8C2211yescharacteristic, complemented
265C4×C4⋊Q8C2211yescharacteristic, complemented
266C4×C4⋊Q8C2212yescomplemented
267C4×C4⋊Q8C2211yescharacteristic, complemented
268C4×C4⋊Q8C2211yescharacteristic, complemented
269C4×#124C2212yes—
270C4×C22⋊Q8C2212yescomplemented
271C4×C22⋊Q8C2212yescomplemented
272#2295C2212yescomplemented
273#2295C2212yescomplemented
274#2295C2211yescharacteristic, complemented
275#2295C2211yescharacteristic, complemented
276#2295C2212yescomplemented
277#2293C2211yescharacteristic
278#2293C2211yescharacteristic
279#2293C2212yes—
280C2×#390C2212yes—
281C2×#389C2212yes—
282#2290C2212yes—
283#2290C2212yes—
284C2×#384C2211yescharacteristic
285#2283C2211yescharacteristic
286#2283C2212yes—
287#2283C2211yescharacteristic
288#2283C2212yescomplemented
289#2280C2212yes—
290C2×#380C2212yes—
291#2274C2212yes—
292C42×Q8C2211yescharacteristic, complemented
293C42×Q8C2211yescharacteristic, complemented
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2212yes—
298C2×C4×C22⋊C4C2212yes—
299C23×Q8C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#541—48no—
303#533—28no—
304#533—48no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×#126C2314yes—
312C2×#126C2314yes—
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2314yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×#124C2312yes—
320C2×#124C2312yes—
321C2×C22⋊Q8—48no—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C4×Q8—28no—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2314yes—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×D4—28no—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2312yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2311yescharacteristic
365C2×#117C2312yes—
366C2×#117C2312yes—
367C2×#117C2311yescharacteristic
368C2×#117C2312yes—
369C2×#117C2311yescharacteristic
370C2×#117C2312yes—
371C2×#117C2314yes—
372C2×#117C2312yes—
373C22×C4⋊C4C2312yes—
374C22×C4⋊C4C2311yescharacteristic
375C22×C4⋊C4C2311yescharacteristic
376C22×C4⋊C4C2312yes—
377C22×C4⋊C4C2312yes—
378C22×C4⋊C4C2312yes—
379C22×C4⋊C4C2314yes—
380C22×C22⋊C4C2312yes—
381C22×C22⋊C4C2312yes—
382C22×C22⋊C4C2314yes—
383C22×C22⋊C4C2312yes—
384C22×C22⋊C4C2314yes—
385C22×C42C2312yes—
386C22×C42C2312yes—
387C22×C42C2312yes—
388C22×C42C2311yescharacteristic
389#401C2314yes—
390#401C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#399C2314yes—
411#399C2314yes—
412#399C2314yes—
413#399C2314yes—
414#399C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#394C2314yes—
473#394C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2311yescharacteristic
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2311yescharacteristic
505#390C2311yescharacteristic
506#390C2311yescharacteristic
507#390C2311yescharacteristic
508#390C2314yes—
509#390C2312yes—
510#390C2312yes—
511#390C2312yes—
512#390C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2311yescharacteristic
547#389C2311yescharacteristic
548#389C2311yescharacteristic
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2311yescharacteristic
554#389C2311yescharacteristic
555#389C2311yescharacteristic
556#389C2311yescharacteristic
557#389C2314yes—
558#389C2312yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2312yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2314yes—
596#388C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2312yes—
615#387C2314yes—
616#387C2314yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2314yes—
642#387C2314yes—
643#386C2312yes—
644#386C2312yes—
645#386C2312yes—
646#386C2312yes—
647#385C2314yes—
648#385C2314yes—
649#385C2312yes—
650#385C2314yes—
651#385C2312yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2312yes—
664#385C2312yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#384C2311yescharacteristic
670#384C2311yescharacteristic
671#384C2312yes—
672#384C2312yes—
673#384C2314yes—
674#384C2312yes—
675#384C2312yes—
676#384C2312yes—
677#384C2312yes—
678#384C2312yes—
679#383C2314yes—
680#383C2314yes—
681#383C2314yes—
682#383C2312yes—
683#383C2312yes—
684#383C2312yes—
685#383C2312yes—
686#382C2312yes—
687#382C2312yes—
688#382C2312yes—
689#382C2312yes—
690#382C2314yes—
691#382C2314yes—
692#382C2314yes—
693#382C2311yescharacteristic
694#382C2311yescharacteristic
695#382C2311yescharacteristic
696#382C2311yescharacteristic
697#382C2312yes—
698#382C2312yes—
699#381C2312yes—
700#381C2314yes—
701#381C2314yes—
702#381C2314yes—
703#381C2314yes—
704#381C2312yes—
705#381C2314yes—
706#381C2312yes—
707#381C2312yes—
708#381C2312yes—
709#381C2312yes—
710#380C2312yes—
711#380C2312yes—
712#380C2314yes—
713#380C2314yes—
714#380C2314yes—
715#380C2312yes—
716#380C2311yescharacteristic
717#380C2311yescharacteristic
718#380C2312yes—
719#380C2312yes—
720#380C2311yescharacteristic
721#380C2311yescharacteristic
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2314yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2312yes—
733#379C2312yes—
734#379C2314yes—
735#379C2314yes—
736#379C2312yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2314yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C22⋊C4C2314yes—
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2314yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2311yescharacteristic
782C4×C22⋊C4C2311yescharacteristic
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2311yescharacteristic
785C4×C22⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800#376C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2311yescharacteristic
805#376C2311yescharacteristic
806#376C2314yes—
807#376C2312yes—
808#376C2312yes—
809C2×#95C2314yes—
810C2×#95C2312yes—
811C2×#95C2312yes—
812C43C2311yescharacteristic
813C43C2311yescharacteristic
814C43C2312yes—
815C43C2312yes—
816C25C2412yes—
817C22×Q8—24no—
818C22×Q8—24no—
819C22×Q8—42no—
820C22×Q8C2412yes—
821C22×Q8C2412yes—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2411yescharacteristic
825C22×Q8C2414yes—
826C22×D4—24no—
827C22×D4—24no—
828C22×D4—42no—
829C22×D4C2411yescharacteristic
830C22×D4C2412yes—
831C22×D4C2411yescharacteristic
832C23×C4—28no—
833C23×C4—44no—
834C23×C4—44no—
835C23×C4C2412yes—
836C23×C4C2412yes—
837C23×C4C2412yes—
838C23×C4C2412yes—
839C23×C4C2412yes—
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2414yes—
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C4⋊Q8—28no—
851C4⋊Q8—24no—
852C4⋊Q8—24no—
853C4⋊Q8—44no—
854C4⋊Q8—44no—
855C4⋊Q8—44no—
856#126—48no—
857#126—48no—
858#125—28no—
859#125—44no—
860#125—44no—
861#125—48no—
862#125—48no—
863#125—48no—
864#124—28no—
865#124—44no—
866C22⋊Q8—28no—
867C22⋊Q8—28no—
868C22⋊Q8—28no—
869C22⋊Q8—28no—
870C22⋊Q8—48no—
871C22⋊Q8—48no—
872C22⋊Q8—48no—
873C22⋊Q8—48no—
874C22⋊Q8—44no—
875C22⋊Q8—44no—
876C22⋊Q8—44no—
877C22⋊Q8—44no—
878C22⋊Q8—44no—
879C22⋊Q8—44no—
880C4×Q8—24no—
881C4×Q8—24no—
882C4×Q8—24no—
883C4×Q8—28no—
884C4×Q8—24no—
885C4×Q8—28no—
886C4×Q8—24no—
887C4×Q8—24no—
888C4×Q8—28no—
889C4×Q8—28no—
890C4×Q8—48no—
891C4×Q8—42no—
892C4×Q8—42no—
893C4×Q8—44no—
894C4×Q8—44no—
895C4×Q8—44no—
896C4×Q8—44no—
897C4×D4—24no—
898C4×D4—24no—
899C4×D4—28no—
900C4×D4—24no—
901C4×D4—24no—
902C4×D4—28no—
903C4×D4—24no—
904C4×D4—24no—
905C4×D4—42no—
906C4×D4—42no—
907#117—28no—
908#117—24no—
909#117—28no—
910#117—44no—
911#117—44no—
912#117—48no—
913#117—42no—
914#117—44no—
915C2×C4⋊C4—24no—
916C2×C4⋊C4—24no—
917C2×C4⋊C4—28no—
918C2×C4⋊C4—44no—
919C2×C4⋊C4—44no—
920C2×C4⋊C4—48no—
921C2×C4⋊C4—44no—
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2411yescharacteristic
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2411yescharacteristic
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2411yescharacteristic
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2411yescharacteristic
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C22⋊C4—28no—
997C2×C22⋊C4—28no—
998C2×C22⋊C4—48no—
999C2×C22⋊C4—44no—
1000C2×C22⋊C4—48no—
1001C2×C22⋊C4C2411yescharacteristic
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2412yes—
1004C2×C22⋊C4C2412yes—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2411yescharacteristic
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2411yescharacteristic
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C42—28no—
1043C2×C42—44no—
1044C2×C42—44no—
1045C2×C42#4118yes—
1046C2×C42C2411yescharacteristic
1047C2×C42C2412yes—
1048C2×C42C2411yescharacteristic
1049C2×C42C2414yes—
1050C2×C42C2412yes—
1051C2×C42C2412yes—
1052C2×C42C2412yes—
1053C2×C42C2411yescharacteristic
1054C2×C42C2411yescharacteristic
1055C2×C42C2412yes—
1056C2×C42C2411yescharacteristic
1057C2×C42C2411yescharacteristic
1058C2×C42C2411yescharacteristic
1059C2×C42C2411yescharacteristic
1060C2×C42C2411yescharacteristic
1061C2×C42C2412yes—
1062C2×C42C2412yes—
1063C2×C42C2412yes—
1064C2×C42C2412yes—
1065C2×C42C2412yes—
1066C2×C42C2411yescharacteristic
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2414yes—
1070C2×C42C2411yescharacteristic
1071C2×C42C2411yescharacteristic
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2414yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2414yes—
1079C2×C42C2414yes—
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087#95C2411yescharacteristic
1088#95C2411yescharacteristic
1089#95C2414yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2411yescharacteristic
1102#95C2411yescharacteristic
1103#95C2412yes—
1104#95C2412yes—
1105#95C2411yescharacteristic
1106#95C2411yescharacteristic
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2414yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169C24—24no—
1170C24—24no—
1171C24—24no—
1172C24—24no—
1173C24—42no—
1174C24—42no—
1175C24—42no—
1176C24C2512yes—
1177C24C2512yes—
1178C24C2511yescharacteristic
1179C2×Q8—22no—
1180C2×Q8—24no—
1181C2×Q8—22no—
1182C2×Q8—24no—
1183C2×Q8—24no—
1184C2×Q8—24no—
1185C2×Q8—24no—
1186C2×Q8—22no—
1187C2×Q8—24no—
1188C2×Q8—22no—
1189C2×Q8—24no—
1190C2×Q8—24no—
1191C2×Q8—22no—
1192C2×Q8—42no—
1193C2×Q8—44no—
1194C2×Q8—44no—
1195C2×Q8—44no—
1196C2×Q8—416no—
1197C2×Q8H(5,𝔽2)14yes—
1198C2×D4—24no—
1199C2×D4—22no—
1200C2×D4—24no—
1201C2×D4—22no—
1202C2×D4—22no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—416no—
1206C2×D4—42no—
1207C2×D42−1+414yes—
1208C22×C4—22no—
1209C22×C4—22no—
1210C22×C4—22no—
1211C22×C4—22no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—24no—
1215C22×C4—24no—
1216C22×C4—24no—
1217C22×C4—24no—
1218C22×C4—24no—
1219C22×C4—24no—
1220C22×C4—24no—
1221C22×C4—28no—
1222C22×C4—24no—
1223C22×C4—24no—
1224C22×C4—24no—
1225C22×C4—24no—
1226C22×C4—24no—
1227C22×C4—24no—
1228C22×C4—24no—
1229C22×C4—24no—
1230C22×C4—24no—
1231C22×C4—24no—
1232C22×C4—24no—
1233C22×C4—42no—
1234C22×C4—42no—
1235C22×C4—42no—
1236C22×C4—42no—
1237C22×C4—42no—
1238C22×C4—44no—
1239C22×C4—42no—
1240C22×C4—42no—
1241C22×C4—42no—
1242C22×C4—44no—
1243C22×C4—42no—
1244C22×C4—42no—
1245C22×C4—42no—
1246C22×C4—42no—
1247C22×C4—42no—
1248C22×C4—42no—
1249C22×C4—42no—
1250C22×C4—816no—
1251C22×C4C2×#4114yes—
1252C22×C4C2×#4114yes—
1253C22×C4C2×#4114yes—
1254C22×C4C2511yescharacteristic
1255C22×C4C2512yes—
1256C22×C4C2514yes—
1257C22×C4C2512yes—
1258C22×C4C2512yes—
1259C22×C4C2512yes—
1260C22×C4C2512yes—
1261C22×C4C2511yescharacteristic
1262C22×C4C2511yescharacteristic
1263C22×C4C2511yescharacteristic
1264C22×C4C2512yes—
1265C22×C4C2512yes—
1266C22×C4C2512yes—
1267C22×C4C2512yes—
1268C22×C4C2512yes—
1269C22×C4C2512yes—
1270C22×C4C2512yes—
1271C22×C4C2511yescharacteristic
1272C22×C4C2512yes—
1273C22×C4C2514yes—
1274C22×C4C2514yes—
1275C22×C4C2514yes—
1276C22×C4C2511yescharacteristic
1277C22×C4C2511yescharacteristic
1278C22×C4C2511yescharacteristic
1279C22×C4C2511yescharacteristic
1280C22×C4C2511yescharacteristic
1281C22×C4C2512yes—
1282C22×C4C2511yescharacteristic
1283C22×C4C2511yescharacteristic
1284C22×C4C2511yescharacteristic
1285C22×C4C2511yescharacteristic
1286C4⋊C4—24no—
1287C4⋊C4—22no—
1288C4⋊C4—22no—
1289C4⋊C4—24no—
1290C4⋊C4—24no—
1291C4⋊C4—24no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—24no—
1295C4⋊C4—24no—
1296C4⋊C4—24no—
1297C4⋊C4—24no—
1298C4⋊C4—28no—
1299C4⋊C4—28no—
1300C4⋊C4—24no—
1301C4⋊C4—24no—
1302C4⋊C4—28no—
1303C4⋊C4—24no—
1304C4⋊C4—24no—
1305C4⋊C4—28no—
1306C4⋊C4—28no—
1307C4⋊C4—24no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—24no—
1311C4⋊C4—28no—
1312C4⋊C4—22no—
1313C4⋊C4—22no—
1314C4⋊C4—24no—
1315C4⋊C4—24no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—22no—
1321C4⋊C4—22no—
1322C4⋊C4—22no—
1323C4⋊C4—22no—
1324C4⋊C4—42no—
1325C4⋊C4—42no—
1326C4⋊C4—44no—
1327C4⋊C4—44no—
1328C4⋊C4—44no—
1329C4⋊C4—44no—
1330C4⋊C4—44no—
1331C4⋊C4—41no—
1332C4⋊C4—41no—
1333C4⋊C4—42no—
1334C4⋊C4—42no—
1335C4⋊C4—42no—
1336C4⋊C4—42no—
1337C4⋊C4—42no—
1338C4⋊C4—42no—
1339C4⋊C4—44no—
1340C4⋊C4—42no—
1341C4⋊C4—42no—
1342C4⋊C4—44no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—44no—
1347C4⋊C4—44no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—44no—
1353C4⋊C4—44no—
1354C4⋊C4—44no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C22⋊C4—28no—
1361C22⋊C4—24no—
1362C22⋊C4—22no—
1363C22⋊C4—24no—
1364C22⋊C4—24no—
1365C22⋊C4—24no—
1366C22⋊C4—28no—
1367C22⋊C4—28no—
1368C22⋊C4—22no—
1369C22⋊C4—24no—
1370C22⋊C4—22no—
1371C22⋊C4—24no—
1372C22⋊C4—24no—
1373C22⋊C4—24no—
1374C22⋊C4—24no—
1375C22⋊C4—24no—
1376C22⋊C4—28no—
1377C22⋊C4—28no—
1378C22⋊C4—24no—
1379C22⋊C4—24no—
1380C22⋊C4—44no—
1381C22⋊C4—44no—
1382C22⋊C4—42no—
1383C22⋊C4—42no—
1384C22⋊C4—44no—
1385C22⋊C4—44no—
1386C22⋊C4—44no—
1387C22⋊C4—44no—
1388C22⋊C4—42no—
1389C22⋊C4—42no—
1390C22⋊C4—44no—
1391C22⋊C4—42no—
1392C22⋊C4—42no—
1393C22⋊C4—42no—
1394C22⋊C4—42no—
1395C22⋊C4—44no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—44no—
1400C22⋊C42−1+414yes—
1401C42—24no—
1402C42—24no—
1403C42—24no—
1404C42—24no—
1405C42—28no—
1406C42—22no—
1407C42—24no—
1408C42—24no—
1409C42—22no—
1410C42—24no—
1411C42—22no—
1412C42—22no—
1413C42—24no—
1414C42—24no—
1415C42—22no—
1416C42—22no—
1417C42—24no—
1418C42—22no—
1419C42—24no—
1420C42—22no—
1421C42—22no—
1422C42—22no—
1423C42—24no—
1424C42—42no—
1425C42—42no—
1426C42—42no—
1427C42—42no—
1428C42—41no—
1429C42—41no—
1430C42—42no—
1431C42—42no—
1432C42—44no—
1433C42—42no—
1434C42—44no—
1435C42—42no—
1436C42—44no—
1437C42—44no—
1438C42C2×#4114yes—
1439C42C2×#4114yes—
1440C42C2×#4114yes—
1441C42C2×#4114yes—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—22no—
1447C23—22no—
1448C23—22no—
1449C23—22no—
1450C23—22no—
1451C23—22no—
1452C23—22no—
1453C23—22no—
1454C23—22no—
1455C23—22no—
1456C23—22no—
1457C23—22no—
1458C23—22no—
1459C23—48no—
1460C23—48no—
1461C23—48no—
1462C23—48no—
1463C23—84no—
1464C23—84no—
1465C23—84no—
1466C23C22×#4112yes—
1467C23C2×2−1+414yes—
1468C23C2×2−1+412yes—
1469C23#58512yes—
1470C23C2611yescharacteristic
1471Q8—28no—
1472Q8—48no—
1473Q8—48no—
1474Q8—44no—
1475Q8—48no—
1476Q8—88no—
1477D4—28no—
1478D4—48no—
1479D4—44no—
1480C2×C4—22no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—22no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—28no—
1495C2×C4—28no—
1496C2×C4—28no—
1497C2×C4—22no—
1498C2×C4—22no—
1499C2×C4—22no—
1500C2×C4—24no—
1501C2×C4—24no—
1502C2×C4—22no—
1503C2×C4—22no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—22no—
1510C2×C4—22no—
1511C2×C4—24no—
1512C2×C4—22no—
1513C2×C4—24no—
1514C2×C4—24no—
1515C2×C4—22no—
1516C2×C4—22no—
1517C2×C4—22no—
1518C2×C4—21no—
1519C2×C4—22no—
1520C2×C4—21no—
1521C2×C4—22no—
1522C2×C4—21no—
1523C2×C4—22no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—21no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—24no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—22no—
1540C2×C4—21no—
1541C2×C4—22no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—22no—
1546C2×C4—24no—
1547C2×C4—22no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—24no—
1555C2×C4—24no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—24no—
1560C2×C4—24no—
1561C2×C4—24no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—48no—
1567C2×C4—48no—
1568C2×C4—48no—
1569C2×C4—48no—
1570C2×C4—48no—
1571C2×C4—84no—
1572C2×C4—84no—
1573C2×C4—84no—
1574C2×C4—88no—
1575C2×C4—84no—
1576C2×C4—84no—
1577C2×C4—84no—
1578C2×C4C22×#4112yes—
1579C2×C4C22×#4112yes—
1580C2×C4C22×#4112yes—
1581C2×C4C22×#4112yes—
1582C2×C4C22×#4112yes—
1583C2×C4C22×#4112yes—
1584C2×C4C2×H(5,𝔽2)14yes—
1585C2×C4C2×H(5,𝔽2)12yes—
1586C2×C4C2×2−1+412yes—
1587C2×C4C2×2−1+412yes—
1588C2×C4C2×2−1+412yes—
1589C2×C4#58512yes—
1590C2×C4#58512yes—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—22no—
1595C22—22no—
1596C22—22no—
1597C22—24no—
1598C22—24no—
1599C22—24no—
1600C22—42no—
1601C22—42no—
1602C22—42no—
1603C22—42no—
1604C22—42no—
1605C22—42no—
1606C22—42no—
1607C22—42no—
1608C22—42no—
1609C22—42no—
1610C22—42no—
1611C22—816no—
1612C22#346114yes—
1613C22C23×#4111yescharacteristic
1614C22C22×H(5,𝔽2)11yescharacteristic
1615C22C22×2−1+411yescharacteristic
1616C22C22×2−1+411yescharacteristic
1617C22C2×#58511yescharacteristic
1618C22C2×#58511yescharacteristic
1619C22C2×#58511yescharacteristic
1620C4—22no—
1621C4—22no—
1622C4—22no—
1623C4—24no—
1624C4—22no—
1625C4—22no—
1626C4—22no—
1627C4—41no—
1628C4—42no—
1629C4—42no—
1630C4—41no—
1631C4—44no—
1632C4—41no—
1633C4—44no—
1634C4—42no—
1635C4—42no—
1636C4—41no—
1637C4—42no—
1638C4—42no—
1639C4—41no—
1640C4—41no—
1641C4—42no—
1642C4—42no—
1643C4—42no—
1644C4—42no—
1645C4—42no—
1646C4—44no—
1647C4—44no—
1648C4—42no—
1649C4—42no—
1650C4#349414yes—
1651C4#349514yes—
1652C2—24no—
1653C2—44no—
1654C2—82no—
1655C2C2×#346111yescharacteristic
1656C2C2×#349411yescharacteristic
1657C2C2×#349511yescharacteristic
1658C2#6301611yescharacteristic
1659C2#6301911yescharacteristic
1660C2#6302311yescharacteristic
1661C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42214C2semidirect
2. #42040C2semidirect
3. #42010C2semidirect
4. #39800C2semidirect
5. #39675C2semidirect
6. #39263C2semidirect
7. #39257C2semidirect
8. #38231C2semidirect
9. #38224C2semidirect
10. #38066C2semidirect
12. #37955C2semidirect
13. #37853C2semidirect
14. #37765C2semidirect
15. #37663C2semidirect
16. #37631C2semidirect
17. #37628C2semidirect
18. #37623C2semidirect
20. #36280C2semidirect
21. #36167C2semidirect
22. #36130C2semidirect
23. #35824C2semidirect
24. #35248C2semidirect
26. #35209C2semidirect
27. #35206C2semidirect
28. #35184C2semidirect
29. #35176C2semidirect
30. #34945C2semidirect
31. #34929C2semidirect
33. #34214C2semidirect
34. #34128C2semidirect
36. C2×#541C22semidirect
38. C2×#533C22semidirect
42. #2863C22semidirect
45. #2859C22semidirect
46. #2857C22semidirect
49. #2855C22semidirect
50. #2855C22semidirect
51. #2851C22semidirect
54. #2843C22semidirect
55. #2838C22semidirect
56. #2836C22semidirect
57. #2793C22semidirect
58. #2790C22semidirect
59. #2783C22semidirect
60. #2776C22semidirect
61. #2775C22semidirect
62. #2769C22semidirect
63. #2766C22semidirect
64. #2765C22semidirect
67. #2747C22semidirect
68. #2745C22semidirect
69. #2744C22semidirect
70. #2742C22semidirect
71. #2738C22semidirect
74. #2721C22semidirect
75. #2720C22semidirect
76. #2719C22semidirect
77. #2704C22semidirect
78. #2698C22semidirect
79. #2690C22semidirect
80. #2689C22semidirect
81. #2667C22semidirect
82. #2664C22semidirect
83. #2660C22semidirect
84. #2660C22semidirect
85. #2654C22semidirect
86. #2654C22semidirect
87. #2652C22semidirect
88. #2650C22semidirect
89. #2647C22semidirect
90. #2647C22semidirect
91. #2647C22semidirect
92. #2645C22semidirect
95. #2634C22semidirect
97. #2628C22semidirect
99. #2625C22semidirect
100. #2625C22semidirect
101. #2621C22semidirect
102. #2612C22semidirect
103. #2606C22semidirect
105. #2594C22semidirect
106. #2587C22semidirect
107. #2585C22semidirect
108. #2581C22semidirect
109. #2581C22semidirect
110. #2577C22semidirect
111. #2574C22semidirect
112. #2573C22semidirect
113. #2573C22semidirect
114. #2571C22semidirect
115. #2568C22semidirect
116. #2568C22semidirect
118. #2556C22semidirect
119. #2556C22semidirect
120. #2552C22semidirect
121. #2552C22semidirect
122. #2551C22semidirect
123. #2549C22semidirect
126. #2546C22semidirect
127. #2546C22semidirect
142. #2530C22semidirect
143. #2529C22semidirect
145. #2525C22semidirect
146. #2525C22semidirect
147. #2522C22semidirect
148. #2519C22semidirect
149. #2515C22semidirect
150. #2514C22semidirect
153. #2511C22semidirect
154. #2507C22semidirect
155. #2507C22semidirect
156. #2506C22semidirect
157. #2506C22semidirect
158. #2505C22semidirect
161. #2495C22semidirect
162. #2495C22semidirect
163. #2494C22semidirect
164. #2494C22semidirect
167. #2493C22semidirect
168. #2492C22semidirect
169. #2492C22semidirect
170. #2489C22semidirect
171. #2489C22semidirect
179. #2475C22semidirect
182. #2469C22semidirect
183. #2465C22semidirect
184. #2462C22semidirect
186. #2453C22semidirect
188. #2451C22semidirect
199. #2438C22semidirect
203. #2429C22semidirect
204. #2429C22semidirect
205. #2429C22semidirect
206. #2429C22semidirect
207. #2423C22semidirect
208. #2423C22semidirect
209. #2421C22semidirect
210. #2421C22semidirect
211. #2401C22semidirect
212. #2396C22semidirect
221. #2356C22semidirect
222. #2356C22semidirect
223. #2356C22semidirect
224. #2356C22semidirect
225. #2355C22semidirect
226. #2355C22semidirect
229. #2351C22semidirect
230. #2351C22semidirect
231. Q8×C4⋊C4C22semidirect
232. Q8×C4⋊C4C22semidirect
250. #2330C22semidirect
251. #2330C22semidirect
252. #2330C22semidirect
253. #2327C22semidirect
254. #2327C22semidirect
258. #2323C22semidirect
259. #2323C22semidirect
260. #2320C22semidirect
263. #2314C22semidirect
264. C4×C4⋊Q8C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×C4⋊Q8C22semidirect
267. C4×C4⋊Q8C22semidirect
268. C4×C4⋊Q8C22semidirect
270. C4×C22⋊Q8C22semidirect
271. C4×C22⋊Q8C22semidirect
272. #2295C22semidirect
273. #2295C22semidirect
274. #2295C22semidirect
275. #2295C22semidirect
276. #2295C22semidirect
288. #2283C22semidirect
292. C42×Q8C22semidirect
293. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#422142
#420402
#420102
#398002
#396752
#392632
#392572
#382312
#382242
#380662
#380542
#379552
#378532
#377652
#376632
#376312
#376282
#376232
#362932
#362802
#361672
#361302
#358242
#352482
#352402
#352092
#352062
#351842
#351762
#349452
#349292
C2×#25382
#342142
#341282
#341262