Finite Group Databasebeta

← #7653569

Subgroups — #7653569

Order 512.

4842 conjugacy classes of subgroups.

The subgroup lattice has 1653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42546C212yesmaximal, complemented
2#42538C212yesmaximal, complemented
3#40815C214yesmaximal, complemented
4#40760C214yesmaximal, complemented
5#40202C212yesmaximal, complemented
6#39780C212yesmaximal, complemented
7#39379C211yesmaximal, characteristic, complemented
8#39203C211yesmaximal, characteristic, complemented
9#39149C211yesmaximal, characteristic, complemented
10#38931C211yesmaximal, characteristic, complemented
11#38579C214yesmaximal, complemented
12#38135C214yesmaximal, complemented
13#38113C212yesmaximal, complemented
14#37894C212yesmaximal, complemented
15#37850C212yesmaximal, complemented
16#37663C212yesmaximal, complemented
17#37628C211yesmaximal, characteristic, complemented
18#37504C212yesmaximal, complemented
19#36276C211yesmaximal, characteristic, complemented
20#36240C212yesmaximal
21#36239C212yesmaximal, complemented
22#36165C211yesmaximal, characteristic, complemented
23#36154C211yesmaximal, characteristic
24D4×C22⋊Q8C211yesmaximal, characteristic
25#35961C212yesmaximal, complemented
26#35873C212yesmaximal
27#35291C211yesmaximal, characteristic, complemented
28#35244C212yesmaximal, complemented
29#35185C211yesmaximal, characteristic, complemented
30#35086C212yesmaximal, complemented
31#34975C211yesmaximal, characteristic, complemented
32C2×#2421C212yesmaximal, complemented
33#34332C211yesmaximal, characteristic, complemented
34C4×D4×Q8C211yesmaximal, characteristic, complemented
35#34126C211yesmaximal, characteristic
36C2×#554C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#541C2212yescomplemented
39C22×C22⋊Q8C2212yes—
40C22×C4×Q8C2212yescomplemented
41C22×C4×D4C2211yescharacteristic
42#2864C2212yescomplemented
43#2862C2211yescharacteristic, complemented
44#2860C2212yes—
45#2859C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2212yescomplemented
49#2852C2214yes—
50#2851C2212yescomplemented
51#2851C2214yescomplemented
52#2848C2212yes—
53#2848C2212yes—
54#2839C2214yescomplemented
55#2836C2214yescomplemented
56#2836C2214yescomplemented
57#2798C2214yescomplemented
58#2798C2214yescomplemented
59#2789C2214yescomplemented
60#2776C2214yescomplemented
61#2772C2214yescomplemented
62#2772C2214yescomplemented
63#2766C2214yescomplemented
64#2766C2214yescomplemented
65#2758C2214yescomplemented
66#2758C2214yescomplemented
67#2754C2214yescomplemented
68#2754C2214yescomplemented
69#2747C2214yes—
70#2744C2214yescomplemented
71#2739C2214yes—
72#2739C2214yescomplemented
73#2725C2214yescomplemented
74#2725C2214yescomplemented
75#2722C2214yes—
76#2704C2214yes—
77#2698C2214yes—
78#2698C2214yescomplemented
79#2690C2214yes—
80#2689C2214yescomplemented
81#2664C2214yescomplemented
82#2655C2214yescomplemented
83#2654C2214yescomplemented
84#2652C2214yes—
85#2652C2214yescomplemented
86#2650C2214yescomplemented
87#2647C2212yescomplemented
88#2647C2212yescomplemented
89#2646C2214yescomplemented
90#2645C2212yescomplemented
91#2645C2212yescomplemented
92#2644C2212yes—
93#2643C2214yes—
94#2637C2214yescomplemented
95#2634C2214yescomplemented
96#2629C2212yescomplemented
97#2625C2212yes—
98#2625C2212yescomplemented
99#2625C2212yescomplemented
100#2621C2212yescomplemented
101#2571C2212yescomplemented
102#2571C2211yescharacteristic, complemented
103#2571C2211yescharacteristic, complemented
104#2570C2212yescomplemented
105#2570C2212yescomplemented
106#2570C2212yescomplemented
107#2569C2214yescomplemented
108#2569C2214yescomplemented
109#2569C2214yescomplemented
110#2567C2211yescharacteristic, complemented
111#2563C2211yescharacteristic
112#2550C2212yescomplemented
113#2550C2212yescomplemented
114#2549C2214yescomplemented
115#2549C2214yescomplemented
116#2546C2211yescharacteristic, complemented
117#2542C2211yescharacteristic
118#2538C2211yescharacteristic
119#2538C2211yescharacteristic
120#2533C2212yescomplemented
121#2528C2212yescomplemented
122#2514C2211yescharacteristic, complemented
123#2514C2212yescomplemented
124#2513C2212yes—
125#2513C2212yes—
126#2513C2212yes—
127#2513C2212yes—
128#2512C2212yes—
129#2512C2212yes—
130#2510C2214yes—
131#2510C2214yes—
132#2510C2214yes—
133#2510C2214yes—
134#2509C2212yescomplemented
135#2509C2212yescomplemented
136#2509C2212yescomplemented
137#2508C2212yescomplemented
138#2508C2212yescomplemented
139#2508C2212yescomplemented
140#2508C2212yescomplemented
141#2507C2212yescomplemented
142#2506C2212yescomplemented
143#2506C2212yescomplemented
144#2506C2211yescharacteristic, complemented
145#2505C2214yescomplemented
146#2505C2214yescomplemented
147#2505C2214yescomplemented
148#2505C2214yescomplemented
149#2505C2214yescomplemented
150#2505C2214yescomplemented
151#2505C2214yescomplemented
152#2502C2212yescomplemented
153#2497C2212yes—
154#2496C2212yes—
155#2496C2212yes—
156#2496C2211yescharacteristic
157#2496C2212yescomplemented
158#2495C2212yes—
159#2495C2212yes—
160#2494C2212yes—
161#2494C2212yes—
162#2489C2211yescharacteristic
163#2489C2212yes—
164#2489C2212yescomplemented
165#2487C2212yes—
166#2481C2214yes—
167#2481C2214yes—
168#2480C2214yes—
169#2480C2214yes—
170#2480C2214yes—
171#2480C2214yes—
172#2480C2214yes—
173#2480C2214yes—
174#2478C2212yes—
175#2475C2212yes—
176#2473C2214yescomplemented
177#2473C2214yescomplemented
178#2473C2214yescomplemented
179#2469C2214yescomplemented
180#2469C2214yescomplemented
181#2462C2214yescomplemented
182#2454C2212yes—
183#2453C2212yescomplemented
184#2453C2211yescharacteristic, complemented
185#2452C2212yes—
186#2450C2214yes—
187#2449C2214yes—
188#2446C2211yescharacteristic, complemented
189#2442C2212yes—
190#2442C2212yescomplemented
191#2442C2214yescomplemented
192#2442C2212yescomplemented
193#2440C2212yes—
194#2437C2214yes—
195#2437C2214yes—
196#2434C2212yescomplemented
197#2429C2212yes—
198#2429C2211yescharacteristic
199#2429C2212yescomplemented
200#2421C2214yes—
201#2421C2212yes—
202#2421C2212yes—
203#2421C2214yes—
204#2421C2211yescharacteristic
205#2421C2212yes—
206#2421C2212yescomplemented
207#2421C2212yescomplemented
208#2421C2214yescomplemented
209#2421C2214yescomplemented
210#2421C2212yescomplemented
211#2421C2212yescomplemented
212#2421C2212yescomplemented
213#2417C2212yes—
214#2417C2212yes—
215#2409C2212yes—
216#2402C2212yescomplemented
217#2401C2212yes—
218C2×#400C2214yescomplemented
219C2×#397C2214yes—
220#2370C2212yescomplemented
221#2369C2211yescharacteristic, complemented
222#2365C2211yescharacteristic, complemented
223#2365C2212yescomplemented
224#2360C2212yescomplemented
225#2360C2212yescomplemented
226#2360C2214yescomplemented
227#2360C2214yescomplemented
228#2357C2211yescharacteristic
229#2357C2211yescharacteristic
230#2353C2212yes—
231#2353C2212yes—
232Q8×C4⋊C4C2211yescharacteristic, complemented
233Q8×C4⋊C4C2211yescharacteristic, complemented
234#2349C2212yes—
235#2349C2212yes—
236#2349C2212yes—
237#2349C2212yes—
238#2349C2211yescharacteristic
239#2349C2211yescharacteristic
240#2349C2212yes—
241D4×C4⋊C4C2211yescharacteristic
242D4×C4⋊C4C2212yes—
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2211yescharacteristic
245D4×C4⋊C4C2212yes—
246#2345C2211yescharacteristic
247#2345C2211yescharacteristic
248#2345C2212yescomplemented
249#2342C2212yes—
250#2342C2212yes—
251Q8×C22⋊C4C2212yescomplemented
252D4×C22⋊C4C2211yescharacteristic
253D4×C22⋊C4C2212yes—
254D4×C22⋊C4C2212yes—
255D4×C22⋊C4C2211yescharacteristic
256#2334C2214yes—
257#2334C2214yescomplemented
258#2330C2212yescomplemented
259#2329C2214yescomplemented
260#2327C2212yescomplemented
261#2323C2212yes—
262#2323C2212yescomplemented
263#2323C2212yescomplemented
264#2320C2212yescomplemented
265#2320C2212yescomplemented
266#2314C2212yescomplemented
267C4×C4⋊Q8C2212yescomplemented
268C4×C4⋊Q8C2211yescharacteristic, complemented
269C4×C4⋊Q8C2211yescharacteristic, complemented
270C4×C4⋊Q8C2211yescharacteristic, complemented
271C4×#125C2211yescharacteristic, complemented
272C4×#125C2212yescomplemented
273C4×#126C2212yes—
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2212yescomplemented
277C4×C22⋊Q8C2212yescomplemented
278C4×C22⋊Q8C2214yescomplemented
279#2295C2211yescharacteristic, complemented
280C2×#391C2212yescomplemented
281#2293C2211yescharacteristic
282#2293C2211yescharacteristic
283C2×#389C2212yescomplemented
284#2290C2212yes—
285#2290C2212yes—
286C2×#388C2214yes—
287C2×#387C2214yescomplemented
288#2283C2211yescharacteristic
289C2×#382C2212yescomplemented
290#2280C2212yes—
291C2×#380C2212yes—
292#2275C2212yes—
293C42×Q8C2211yescharacteristic, complemented
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2212yes—
299C23×Q8C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#554—28no—
303D4×Q8—28no—
304#541—48no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×#126C2312yes—
311C2×#126C2314yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#125C2312yes—
316C2×#125C2311yescharacteristic
317C2×#125C2312yes—
318C2×#125C2314yes—
319C2×#125C2312yes—
320C2×#125C2314yes—
321C2×C22⋊Q8—48no—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2311yescharacteristic
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2311yescharacteristic
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C4×Q8—48no—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2314yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2314yes—
348C2×C4×D4—28no—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2312yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×#117C2312yes—
364C2×#117C2311yescharacteristic
365C2×#117C2312yes—
366C2×#117C2311yescharacteristic
367C22×C4⋊C4C2311yescharacteristic
368C22×C4⋊C4C2312yes—
369C22×C4⋊C4C2314yes—
370C22×C4⋊C4C2312yes—
371C22×C4⋊C4C2312yes—
372C22×C4⋊C4C2314yes—
373C22×C4⋊C4C2314yes—
374C22×C22⋊C4C2312yes—
375C22×C22⋊C4C2312yes—
376C22×C22⋊C4C2312yes—
377C22×C22⋊C4C2314yes—
378C22×C22⋊C4C2314yes—
379C22×C42C2311yescharacteristic
380C22×C42C2314yes—
381C22×C42C2312yes—
382C22×C42C2312yes—
383#401C2314yes—
384#401C2314yes—
385#401C2312yes—
386#400C2312yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2312yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2312yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2312yes—
414#400C2314yes—
415#400C2314yes—
416#400C2312yes—
417#400C2312yes—
418#400C2312yes—
419#399C2314yes—
420#399C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2312yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2312yes—
440#398C2314yes—
441#398C2312yes—
442#398C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2312yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2312yes—
473#395C2314yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#393C2314yes—
478#393C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2311yescharacteristic
483#391C2311yescharacteristic
484#391C2312yes—
485#391C2311yescharacteristic
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2311yescharacteristic
491#391C2312yes—
492#391C2314yes—
493#391C2312yes—
494#391C2314yes—
495#391C2312yes—
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2314yes—
499#391C2314yes—
500#391C2311yescharacteristic
501#390C2312yes—
502#390C2311yescharacteristic
503#390C2312yes—
504#390C2311yescharacteristic
505#390C2311yescharacteristic
506#390C2311yescharacteristic
507#390C2312yes—
508#390C2312yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2311yescharacteristic
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2311yescharacteristic
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2311yescharacteristic
550#389C2311yescharacteristic
551#389C2311yescharacteristic
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2314yes—
560#389C2312yes—
561#389C2314yes—
562#389C2311yescharacteristic
563#389C2311yescharacteristic
564#389C2311yescharacteristic
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2312yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2312yes—
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#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2312yes—
641#387C2312yes—
642#386C2312yes—
643#386C2314yes—
644#386C2314yes—
645#386C2312yes—
646#386C2312yes—
647#386C2312yes—
648#386C2314yes—
649#386C2314yes—
650#385C2312yes—
651#385C2312yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2312yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2312yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2312yes—
677#385C2312yes—
678#384C2312yes—
679#384C2311yescharacteristic
680#384C2311yescharacteristic
681#384C2311yescharacteristic
682#384C2312yes—
683#384C2312yes—
684#384C2312yes—
685#383C2312yes—
686#383C2314yes—
687#383C2314yes—
688#383C2312yes—
689#382C2312yes—
690#382C2311yescharacteristic
691#382C2312yes—
692#382C2312yes—
693#382C2311yescharacteristic
694#382C2311yescharacteristic
695#382C2312yes—
696#382C2312yes—
697#382C2312yes—
698#382C2314yes—
699#382C2312yes—
700#382C2312yes—
701#382C2314yes—
702#382C2314yes—
703#382C2312yes—
704#382C2314yes—
705#382C2314yes—
706#381C2312yes—
707#381C2312yes—
708#381C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2314yes—
712#380C2314yes—
713#380C2312yes—
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2314yes—
718#380C2312yes—
719#380C2312yes—
720#380C2311yescharacteristic
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2311yescharacteristic
725#380C2311yescharacteristic
726#380C2312yes—
727#380C2312yes—
728#380C2314yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2314yes—
733#380C2312yes—
734#380C2311yescharacteristic
735#380C2314yes—
736#380C2314yes—
737#379C2314yes—
738#379C2314yes—
739#379C2312yes—
740#379C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C22⋊C4C2311yescharacteristic
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801#376C2311yescharacteristic
802#376C2312yes—
803#376C2312yes—
804#376C2311yescharacteristic
805C2×#95C2314yes—
806C2×#95C2314yes—
807C2×#95C2314yes—
808C2×#95C2314yes—
809C2×#95C2312yes—
810C2×#95C2312yes—
811C2×#95C2314yes—
812C2×#95C2314yes—
813C43C2312yes—
814C43C2311yescharacteristic
815C43C2311yescharacteristic
816C25C2412yes—
817C22×Q8—28no—
818C22×Q8—28no—
819C22×Q8—44no—
820C22×Q8C2411yescharacteristic
821C22×Q8C2412yes—
822C22×Q8C2414yes—
823C22×Q8C2411yescharacteristic
824C22×Q8C2412yes—
825C22×D4—24no—
826C22×D4—24no—
827C22×D4—24no—
828C22×D4C2412yes—
829C22×D4C2411yescharacteristic
830C22×D4C2411yescharacteristic
831C23×C4—28no—
832C23×C4—44no—
833C23×C4—44no—
834C23×C4C2411yescharacteristic
835C23×C4C2412yes—
836C23×C4C2411yescharacteristic
837C23×C4C2411yescharacteristic
838C23×C4C2414yes—
839C23×C4C2412yes—
840C23×C4C2412yes—
841C23×C4C2414yes—
842C23×C4C2414yes—
843C23×C4C2412yes—
844C23×C4C2414yes—
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C4⋊Q8—24no—
851C4⋊Q8—28no—
852C4⋊Q8—24no—
853C4⋊Q8—24no—
854C4⋊Q8—44no—
855#126—48no—
856#126—48no—
857#126—44no—
858#126—48no—
859#126—48no—
860#125—28no—
861#125—42no—
862#125—44no—
863#125—48no—
864#125—44no—
865#125—48no—
866C22⋊Q8—24no—
867C22⋊Q8—28no—
868C22⋊Q8—28no—
869C22⋊Q8—28no—
870C22⋊Q8—216no—
871C22⋊Q8—216no—
872C22⋊Q8—44no—
873C22⋊Q8—48no—
874C22⋊Q8—48no—
875C22⋊Q8—44no—
876C22⋊Q8—44no—
877C22⋊Q8—42no—
878C22⋊Q8—44no—
879C22⋊Q8—44no—
880C4×Q8—24no—
881C4×Q8—28no—
882C4×Q8—24no—
883C4×Q8—24no—
884C4×Q8—44no—
885C4×Q8—44no—
886C4×Q8—48no—
887C4×Q8—44no—
888C4×Q8—48no—
889C4×Q8—42no—
890C4×Q8—44no—
891C4×D4—24no—
892C4×D4—28no—
893C4×D4—28no—
894C4×D4—24no—
895C4×D4—28no—
896C4×D4—28no—
897C4×D4—24no—
898C4×D4—24no—
899C4×D4—24no—
900C4×D4—28no—
901C4×D4—24no—
902C4×D4—28no—
903C4×D4—24no—
904C4×D4#4118yes—
905#117—44no—
906#117—44no—
907#117—42no—
908#117—42no—
909C2×C4⋊C4—28no—
910C2×C4⋊C4—24no—
911C2×C4⋊C4—48no—
912C2×C4⋊C4—44no—
913C2×C4⋊C4—48no—
914C2×C4⋊C4—44no—
915C2×C4⋊C4—48no—
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2411yescharacteristic
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2411yescharacteristic
936C2×C4⋊C4C2411yescharacteristic
937C2×C4⋊C4C2411yescharacteristic
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2411yescharacteristic
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C22⋊C4—28no—
993C2×C22⋊C4—44no—
994C2×C22⋊C4—48no—
995C2×C22⋊C4—44no—
996C2×C22⋊C4—48no—
997C2×C22⋊C4C2411yescharacteristic
998C2×C22⋊C4C2411yescharacteristic
999C2×C22⋊C4C2412yes—
1000C2×C22⋊C4C2412yes—
1001C2×C22⋊C4C2412yes—
1002C2×C22⋊C4C2412yes—
1003C2×C22⋊C4C2412yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2412yes—
1008C2×C22⋊C4C2411yescharacteristic
1009C2×C22⋊C4C2414yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2411yescharacteristic
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C42—24no—
1038C2×C42—44no—
1039C2×C42—48no—
1040C2×C42—44no—
1041C2×C42C2411yescharacteristic
1042C2×C42C2411yescharacteristic
1043C2×C42C2412yes—
1044C2×C42C2411yescharacteristic
1045C2×C42C2412yes—
1046C2×C42C2411yescharacteristic
1047C2×C42C2411yescharacteristic
1048C2×C42C2411yescharacteristic
1049C2×C42C2412yes—
1050C2×C42C2412yes—
1051C2×C42C2411yescharacteristic
1052C2×C42C2411yescharacteristic
1053C2×C42C2411yescharacteristic
1054C2×C42C2411yescharacteristic
1055C2×C42C2412yes—
1056C2×C42C2412yes—
1057C2×C42C2411yescharacteristic
1058C2×C42C2412yes—
1059C2×C42C2414yes—
1060C2×C42C2412yes—
1061C2×C42C2411yescharacteristic
1062C2×C42C2411yescharacteristic
1063C2×C42C2411yescharacteristic
1064C2×C42C2411yescharacteristic
1065C2×C42C2412yes—
1066C2×C42C2412yes—
1067C2×C42C2414yes—
1068C2×C42C2414yes—
1069C2×C42C2414yes—
1070C2×C42C2412yes—
1071C2×C42C2414yes—
1072C2×C42C2412yes—
1073C2×C42C2414yes—
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2411yescharacteristic
1077#95C2411yescharacteristic
1078#95C2411yescharacteristic
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2411yescharacteristic
1113#95C2411yescharacteristic
1114#95C2411yescharacteristic
1115#95C2411yescharacteristic
1116#95C2411yescharacteristic
1117#95C2411yescharacteristic
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163C24—24no—
1164C24—24no—
1165C24—24no—
1166C24—24no—
1167C24—42no—
1168C24—42no—
1169C24—42no—
1170C24C2512yes—
1171C24C2511yescharacteristic
1172C24C2512yes—
1173C2×Q8—22no—
1174C2×Q8—22no—
1175C2×Q8—28no—
1176C2×Q8—24no—
1177C2×Q8—24no—
1178C2×Q8—22no—
1179C2×Q8—28no—
1180C2×Q8—24no—
1181C2×Q8—22no—
1182C2×Q8—22no—
1183C2×Q8—24no—
1184C2×Q8—44no—
1185C2×Q8—42no—
1186C2×Q8—42no—
1187C2×Q8—432no—
1188C2×Q8H(5,𝔽2)14yes—
1189C2×D4—24no—
1190C2×D4—24no—
1191C2×D4—24no—
1192C2×D4—22no—
1193C2×D4—22no—
1194C2×D4—22no—
1195C2×D4—416no—
1196C2×D4C2×#4114yes—
1197C2×D42−1+414yes—
1198C2×D42−1+414yes—
1199C22×C4—24no—
1200C22×C4—24no—
1201C22×C4—28no—
1202C22×C4—24no—
1203C22×C4—22no—
1204C22×C4—28no—
1205C22×C4—24no—
1206C22×C4—28no—
1207C22×C4—24no—
1208C22×C4—28no—
1209C22×C4—24no—
1210C22×C4—24no—
1211C22×C4—22no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—24no—
1215C22×C4—28no—
1216C22×C4—24no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—24no—
1221C22×C4—24no—
1222C22×C4—22no—
1223C22×C4—24no—
1224C22×C4—24no—
1225C22×C4—42no—
1226C22×C4—41no—
1227C22×C4—44no—
1228C22×C4—42no—
1229C22×C4—44no—
1230C22×C4—42no—
1231C22×C4—42no—
1232C22×C4—44no—
1233C22×C4—42no—
1234C22×C4—42no—
1235C22×C4—44no—
1236C22×C4—42no—
1237C22×C4—44no—
1238C22×C4—42no—
1239C22×C4—44no—
1240C22×C4—44no—
1241C22×C4—42no—
1242C22×C4—42no—
1243C22×C4—42no—
1244C22×C4—42no—
1245C22×C4—42no—
1246C22×C4—816no—
1247C22×C4C2×#4118yes—
1248C22×C4C2511yescharacteristic
1249C22×C4C2511yescharacteristic
1250C22×C4C2511yescharacteristic
1251C22×C4C2512yes—
1252C22×C4C2512yes—
1253C22×C4C2511yescharacteristic
1254C22×C4C2511yescharacteristic
1255C22×C4C2511yescharacteristic
1256C22×C4C2511yescharacteristic
1257C22×C4C2512yes—
1258C22×C4C2512yes—
1259C22×C4C2512yes—
1260C22×C4C2514yes—
1261C22×C4C2512yes—
1262C22×C4C2512yes—
1263C22×C4C2512yes—
1264C22×C4C2512yes—
1265C22×C4C2511yescharacteristic
1266C22×C4C2514yes—
1267C22×C4C2514yes—
1268C22×C4C2514yes—
1269C22×C4C2512yes—
1270C22×C4C2512yes—
1271C22×C4C2511yescharacteristic
1272C22×C4C2511yescharacteristic
1273C22×C4C2512yes—
1274C22×C4C2511yescharacteristic
1275C22×C4C2512yes—
1276C22×C4C2512yes—
1277C22×C4C2511yescharacteristic
1278C22×C4C2511yescharacteristic
1279C22×C4C2511yescharacteristic
1280C4⋊C4—22no—
1281C4⋊C4—24no—
1282C4⋊C4—22no—
1283C4⋊C4—28no—
1284C4⋊C4—24no—
1285C4⋊C4—24no—
1286C4⋊C4—24no—
1287C4⋊C4—24no—
1288C4⋊C4—22no—
1289C4⋊C4—24no—
1290C4⋊C4—28no—
1291C4⋊C4—28no—
1292C4⋊C4—24no—
1293C4⋊C4—24no—
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—24no—
1297C4⋊C4—24no—
1298C4⋊C4—28no—
1299C4⋊C4—24no—
1300C4⋊C4—28no—
1301C4⋊C4—24no—
1302C4⋊C4—24no—
1303C4⋊C4—22no—
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—22no—
1307C4⋊C4—24no—
1308C4⋊C4—24no—
1309C4⋊C4—24no—
1310C4⋊C4—28no—
1311C4⋊C4—22no—
1312C4⋊C4—22no—
1313C4⋊C4—22no—
1314C4⋊C4—44no—
1315C4⋊C4—44no—
1316C4⋊C4—44no—
1317C4⋊C4—44no—
1318C4⋊C4—44no—
1319C4⋊C4—44no—
1320C4⋊C4—44no—
1321C4⋊C4—44no—
1322C4⋊C4—41no—
1323C4⋊C4—42no—
1324C4⋊C4—42no—
1325C4⋊C4—41no—
1326C4⋊C4—41no—
1327C4⋊C4—42no—
1328C4⋊C4—42no—
1329C4⋊C4—42no—
1330C4⋊C4—42no—
1331C4⋊C4—44no—
1332C4⋊C4—42no—
1333C4⋊C4—44no—
1334C4⋊C4—42no—
1335C4⋊C4—44no—
1336C4⋊C4—44no—
1337C4⋊C4—42no—
1338C4⋊C4—42no—
1339C4⋊C4—42no—
1340C4⋊C4—42no—
1341C4⋊C4—42no—
1342C4⋊C4—42no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—44no—
1347C4⋊C4—42no—
1348C4⋊C4—44no—
1349C4⋊C4—42no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—42no—
1353C4⋊C4—44no—
1354C4⋊C4—44no—
1355C4⋊C4C2×#4114yes—
1356C22⋊C4—24no—
1357C22⋊C4—28no—
1358C22⋊C4—28no—
1359C22⋊C4—24no—
1360C22⋊C4—24no—
1361C22⋊C4—24no—
1362C22⋊C4—24no—
1363C22⋊C4—28no—
1364C22⋊C4—28no—
1365C22⋊C4—22no—
1366C22⋊C4—24no—
1367C22⋊C4—28no—
1368C22⋊C4—24no—
1369C22⋊C4—22no—
1370C22⋊C4—24no—
1371C22⋊C4—24no—
1372C22⋊C4—24no—
1373C22⋊C4—24no—
1374C22⋊C4—28no—
1375C22⋊C4—22no—
1376C22⋊C4—24no—
1377C22⋊C4—42no—
1378C22⋊C4—44no—
1379C22⋊C4—42no—
1380C22⋊C4—42no—
1381C22⋊C4—44no—
1382C22⋊C4—42no—
1383C22⋊C4—44no—
1384C22⋊C4—44no—
1385C22⋊C4—41no—
1386C22⋊C4—42no—
1387C22⋊C4—42no—
1388C22⋊C4—42no—
1389C22⋊C4—42no—
1390C22⋊C4—42no—
1391C22⋊C4—44no—
1392C22⋊C4—44no—
1393C22⋊C4—44no—
1394C22⋊C4—44no—
1395C22⋊C4C2×#4118yes—
1396C42—22no—
1397C42—22no—
1398C42—22no—
1399C42—24no—
1400C42—24no—
1401C42—24no—
1402C42—22no—
1403C42—24no—
1404C42—28no—
1405C42—22no—
1406C42—22no—
1407C42—22no—
1408C42—22no—
1409C42—22no—
1410C42—24no—
1411C42—24no—
1412C42—22no—
1413C42—24no—
1414C42—22no—
1415C42—22no—
1416C42—24no—
1417C42—42no—
1418C42—42no—
1419C42—42no—
1420C42—44no—
1421C42—42no—
1422C42—44no—
1423C42—41no—
1424C42—41no—
1425C42—41no—
1426C42—42no—
1427C42—44no—
1428C42—44no—
1429C42—42no—
1430C42—44no—
1431C42C2×#4114yes—
1432C23—22no—
1433C23—22no—
1434C23—22no—
1435C23—22no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—22no—
1443C23—22no—
1444C23—22no—
1445C23—22no—
1446C23—22no—
1447C23—22no—
1448C23—22no—
1449C23—48no—
1450C23—48no—
1451C23—48no—
1452C23—48no—
1453C23—84no—
1454C23—84no—
1455C23—84no—
1456C23C22×#4114yes—
1457C23C2×2−1+414yes—
1458C23C2×2−1+414yes—
1459C23#58512yes—
1460C23C2611yescharacteristic
1461Q8—28no—
1462Q8—416no—
1463Q8—44no—
1464Q8—48no—
1465Q8—84no—
1466D4—48no—
1467D4—44no—
1468D4#541116yescomplemented
1469C2×C4—22no—
1470C2×C4—21no—
1471C2×C4—22no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—22no—
1476C2×C4—22no—
1477C2×C4—216no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—22no—
1482C2×C4—22no—
1483C2×C4—22no—
1484C2×C4—22no—
1485C2×C4—24no—
1486C2×C4—24no—
1487C2×C4—22no—
1488C2×C4—22no—
1489C2×C4—22no—
1490C2×C4—21no—
1491C2×C4—24no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—22no—
1495C2×C4—24no—
1496C2×C4—24no—
1497C2×C4—22no—
1498C2×C4—22no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—22no—
1504C2×C4—21no—
1505C2×C4—22no—
1506C2×C4—22no—
1507C2×C4—21no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—22no—
1512C2×C4—24no—
1513C2×C4—22no—
1514C2×C4—24no—
1515C2×C4—22no—
1516C2×C4—22no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—22no—
1526C2×C4—21no—
1527C2×C4—22no—
1528C2×C4—21no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—21no—
1532C2×C4—22no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—24no—
1536C2×C4—21no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—22no—
1540C2×C4—24no—
1541C2×C4—24no—
1542C2×C4—22no—
1543C2×C4—24no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—24no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—21no—
1556C2×C4—48no—
1557C2×C4—44no—
1558C2×C4—416no—
1559C2×C4—44no—
1560C2×C4—48no—
1561C2×C4—44no—
1562C2×C4—84no—
1563C2×C4—84no—
1564C2×C4—88no—
1565C2×C4—84no—
1566C2×C4—88no—
1567C2×C4—84no—
1568C2×C4—84no—
1569C2×C4—88no—
1570C2×C4—84no—
1571C2×C4C22×#4112yes—
1572C2×C4C22×#4114yes—
1573C2×C4C22×#4112yes—
1574C2×C4C22×#4112yes—
1575C2×C4C2×H(5,𝔽2)14yes—
1576C2×C4C2×H(5,𝔽2)12yes—
1577C2×C4C2×2−1+412yes—
1578C2×C4C2×2−1+412yes—
1579C2×C4#58512yes—
1580C2×C4#58512yes—
1581C22—24no—
1582C22—24no—
1583C22—24no—
1584C22—24no—
1585C22—24no—
1586C22—24no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—42no—
1595C22—42no—
1596C22—42no—
1597C22—42no—
1598C22—42no—
1599C22—42no—
1600C22—42no—
1601C22—816no—
1602C22C2×#54118yes—
1603C22C23×#4111yescharacteristic
1604C22C22×H(5,𝔽2)11yescharacteristic
1605C22C22×2−1+411yescharacteristic
1606C22C22×2−1+411yescharacteristic
1607C22C2×#58511yescharacteristic
1608C22C2×#58511yescharacteristic
1609C22C2×#58511yescharacteristic
1610C4—22no—
1611C4—24no—
1612C4—24no—
1613C4—22no—
1614C4—41no—
1615C4—41no—
1616C4—42no—
1617C4—44no—
1618C4—42no—
1619C4—44no—
1620C4—42no—
1621C4—41no—
1622C4—42no—
1623C4—41no—
1624C4—42no—
1625C4—42no—
1626C4—41no—
1627C4—41no—
1628C4—42no—
1629C4—42no—
1630C4—41no—
1631C4—42no—
1632C4—41no—
1633C4—44no—
1634C4—42no—
1635C4—42no—
1636C4—41no—
1637C4—42no—
1638C4—44no—
1639C4—41no—
1640C4C2×#54114yes—
1641C4#351314yes—
1642C2—28no—
1643C2—42no—
1644C2—82no—
1645C2C22×#54111yescharacteristic
1646C2C2×#351311yescharacteristic
1647C2#6281011yescharacteristic
1648C2#6301511yescharacteristic
1649C2#6301511yescharacteristic
1650C2#6302311yescharacteristic
1651C2#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. #42546C2semidirect
2. #42538C2semidirect
3. #40815C2semidirect
4. #40760C2semidirect
5. #40202C2semidirect
6. #39780C2semidirect
7. #39379C2semidirect
8. #39203C2semidirect
9. #39149C2semidirect
10. #38931C2semidirect
11. #38579C2semidirect
12. #38135C2semidirect
13. #38113C2semidirect
14. #37894C2semidirect
15. #37850C2semidirect
16. #37663C2semidirect
17. #37628C2semidirect
18. #37504C2semidirect
19. #36276C2semidirect
21. #36239C2semidirect
22. #36165C2semidirect
25. #35961C2semidirect
27. #35291C2semidirect
28. #35244C2semidirect
29. #35185C2semidirect
30. #35086C2semidirect
31. #34975C2semidirect
32. C2×#2421C2semidirect
33. #34332C2semidirect
34. C4×D4×Q8C2semidirect
38. C2×#541C22semidirect
40. C22×C4×Q8C22semidirect
42. #2864C22semidirect
43. #2862C22semidirect
45. #2859C22semidirect
48. #2857C22semidirect
50. #2851C22semidirect
51. #2851C22semidirect
54. #2839C22semidirect
55. #2836C22semidirect
56. #2836C22semidirect
57. #2798C22semidirect
58. #2798C22semidirect
59. #2789C22semidirect
60. #2776C22semidirect
61. #2772C22semidirect
62. #2772C22semidirect
63. #2766C22semidirect
64. #2766C22semidirect
65. #2758C22semidirect
66. #2758C22semidirect
67. #2754C22semidirect
68. #2754C22semidirect
70. #2744C22semidirect
72. #2739C22semidirect
73. #2725C22semidirect
74. #2725C22semidirect
78. #2698C22semidirect
80. #2689C22semidirect
81. #2664C22semidirect
82. #2655C22semidirect
83. #2654C22semidirect
85. #2652C22semidirect
86. #2650C22semidirect
87. #2647C22semidirect
88. #2647C22semidirect
89. #2646C22semidirect
90. #2645C22semidirect
91. #2645C22semidirect
94. #2637C22semidirect
95. #2634C22semidirect
96. #2629C22semidirect
98. #2625C22semidirect
99. #2625C22semidirect
100. #2621C22semidirect
101. #2571C22semidirect
102. #2571C22semidirect
103. #2571C22semidirect
104. #2570C22semidirect
105. #2570C22semidirect
106. #2570C22semidirect
107. #2569C22semidirect
108. #2569C22semidirect
109. #2569C22semidirect
110. #2567C22semidirect
112. #2550C22semidirect
113. #2550C22semidirect
114. #2549C22semidirect
115. #2549C22semidirect
116. #2546C22semidirect
120. #2533C22semidirect
121. #2528C22semidirect
122. #2514C22semidirect
123. #2514C22semidirect
134. #2509C22semidirect
135. #2509C22semidirect
136. #2509C22semidirect
137. #2508C22semidirect
138. #2508C22semidirect
139. #2508C22semidirect
140. #2508C22semidirect
141. #2507C22semidirect
142. #2506C22semidirect
143. #2506C22semidirect
144. #2506C22semidirect
145. #2505C22semidirect
146. #2505C22semidirect
147. #2505C22semidirect
148. #2505C22semidirect
149. #2505C22semidirect
150. #2505C22semidirect
151. #2505C22semidirect
152. #2502C22semidirect
157. #2496C22semidirect
164. #2489C22semidirect
176. #2473C22semidirect
177. #2473C22semidirect
178. #2473C22semidirect
179. #2469C22semidirect
180. #2469C22semidirect
181. #2462C22semidirect
183. #2453C22semidirect
184. #2453C22semidirect
188. #2446C22semidirect
190. #2442C22semidirect
191. #2442C22semidirect
192. #2442C22semidirect
196. #2434C22semidirect
199. #2429C22semidirect
206. #2421C22semidirect
207. #2421C22semidirect
208. #2421C22semidirect
209. #2421C22semidirect
210. #2421C22semidirect
211. #2421C22semidirect
212. #2421C22semidirect
216. #2402C22semidirect
218. C2×#400C22semidirect
220. #2370C22semidirect
221. #2369C22semidirect
222. #2365C22semidirect
223. #2365C22semidirect
224. #2360C22semidirect
225. #2360C22semidirect
226. #2360C22semidirect
227. #2360C22semidirect
232. Q8×C4⋊C4C22semidirect
233. Q8×C4⋊C4C22semidirect
248. #2345C22semidirect
251. Q8×C22⋊C4C22semidirect
257. #2334C22semidirect
258. #2330C22semidirect
259. #2329C22semidirect
260. #2327C22semidirect
262. #2323C22semidirect
263. #2323C22semidirect
264. #2320C22semidirect
265. #2320C22semidirect
266. #2314C22semidirect
267. C4×C4⋊Q8C22semidirect
268. C4×C4⋊Q8C22semidirect
269. C4×C4⋊Q8C22semidirect
270. C4×C4⋊Q8C22semidirect
271. C4×#125C22semidirect
272. C4×#125C22semidirect
276. C4×C22⋊Q8C22semidirect
277. C4×C22⋊Q8C22semidirect
278. C4×C22⋊Q8C22semidirect
279. #2295C22semidirect
280. C2×#391C22semidirect
283. C2×#389C22semidirect
287. C2×#387C22semidirect
289. C2×#382C22semidirect
293. C42×Q8C22semidirect
1468. D4#541semidirect

Maximal subgroups

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

subgroupindex
#425462
#425382
#408152
#407602
#402022
#397802
#393792
#392032
#391492
#389312
#385792
#381352
#381132
#378942
#378502
#376632
#376282
#375042
#362762
#362402
#362392
#361652
#361542
D4×C22⋊Q82
#359612
#358732
#352912
#352442
#351852
#350862
#349752
C2×#24212
#343322
C4×D4×Q82
#341262