Finite Group Databasebeta

← #7653659

Subgroups — #7653659

Order 512.

5150 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42614C212yesmaximal, complemented
2#42610C212yesmaximal, complemented
3#40735C214yesmaximal, complemented
4#40726C214yesmaximal, complemented
5#40213C212yesmaximal, complemented
6#39661C212yesmaximal, complemented
7#39385C211yesmaximal, characteristic, complemented
8#39192C211yesmaximal, characteristic, complemented
9#39149C211yesmaximal, characteristic, complemented
10#38943C211yesmaximal, characteristic, complemented
11#38599C214yesmaximal, complemented
12#38172C214yesmaximal, complemented
13#38122C212yesmaximal, complemented
14#37695C212yesmaximal, complemented
15#37663C212yesmaximal, complemented
16#37663C212yesmaximal, complemented
17#37628C211yesmaximal, characteristic, complemented
18#37495C212yesmaximal, complemented
19#36290C212yesmaximal, complemented
20#36290C211yesmaximal, characteristic, complemented
21#36240C212yesmaximal
22D4×C4⋊Q8C211yesmaximal, characteristic, complemented
23D4×C22⋊Q8C211yesmaximal, characteristic
24D4×C22⋊Q8C211yesmaximal, characteristic
25#35914C212yesmaximal
26#35858C212yesmaximal, complemented
27#35284C211yesmaximal, characteristic, complemented
28#35244C212yesmaximal, complemented
29#35209C211yesmaximal, characteristic, complemented
30#35086C212yesmaximal, complemented
31#34975C211yesmaximal, characteristic, complemented
32C2×#2429C212yesmaximal, complemented
33#34334C211yesmaximal, characteristic, complemented
34C4×D4×Q8C211yesmaximal, characteristic, complemented
35#34126C211yesmaximal, characteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#541C2212yescomplemented
39C2×#541C2212yescomplemented
40C22×C4⋊Q8C2212yescomplemented
41C22×C22⋊Q8C2212yes—
42C22×C22⋊Q8C2212yes—
43C22×C4×Q8C2212yescomplemented
44C22×C4×D4C2211yescharacteristic
45#2868C2211yescharacteristic, complemented
46#2860C2212yes—
47#2859C2211yescharacteristic, complemented
48#2859C2212yescomplemented
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2857C2212yescomplemented
52#2852C2214yes—
53#2851C2212yescomplemented
54#2851C2214yescomplemented
55#2848C2212yes—
56#2848C2212yes—
57#2836C2214yescomplemented
58#2833C2214yescomplemented
59#2831C2214yescomplemented
60#2802C2214yescomplemented
61#2783C2214yescomplemented
62#2776C2214yescomplemented
63#2776C2214yescomplemented
64#2772C2214yescomplemented
65#2769C2214yescomplemented
66#2744C2214yes—
67#2739C2214yes—
68#2725C2214yescomplemented
69#2725C2214yescomplemented
70#2721C2214yescomplemented
71#2721C2214yescomplemented
72#2716C2214yescomplemented
73#2716C2214yescomplemented
74#2713C2214yescomplemented
75#2713C2214yescomplemented
76#2704C2214yes—
77#2704C2214yes—
78#2698C2214yescomplemented
79#2698C2214yescomplemented
80#2690C2214yes—
81#2690C2214yes—
82#2689C2214yescomplemented
83#2689C2214yescomplemented
84#2666C2214yescomplemented
85#2664C2214yescomplemented
86#2654C2214yescomplemented
87#2652C2214yes—
88#2652C2214yescomplemented
89#2650C2214yescomplemented
90#2647C2212yescomplemented
91#2647C2212yescomplemented
92#2646C2214yescomplemented
93#2645C2212yescomplemented
94#2644C2212yes—
95#2643C2214yes—
96#2642C2212yescomplemented
97#2637C2214yescomplemented
98#2634C2214yescomplemented
99#2629C2212yes—
100#2625C2212yescomplemented
101#2625C2212yescomplemented
102#2621C2212yescomplemented
103#2621C2212yescomplemented
104#2571C2212yescomplemented
105#2571C2211yescharacteristic, complemented
106#2570C2212yescomplemented
107#2569C2214yescomplemented
108#2552C2212yescomplemented
109#2552C2211yescharacteristic, complemented
110#2552C2212yescomplemented
111#2551C2212yescomplemented
112#2551C2212yescomplemented
113#2546C2211yescharacteristic, complemented
114#2546C2211yescharacteristic, complemented
115#2542C2211yescharacteristic
116#2542C2211yescharacteristic
117#2538C2211yescharacteristic
118#2538C2211yescharacteristic
119#2533C2212yescomplemented
120#2528C2212yescomplemented
121#2519C2214yescomplemented
122#2514C2211yescharacteristic, complemented
123#2513C2212yes—
124#2513C2212yes—
125#2512C2212yes—
126#2512C2212yes—
127#2512C2212yes—
128#2512C2212yes—
129#2510C2214yes—
130#2510C2214yes—
131#2509C2212yescomplemented
132#2509C2212yescomplemented
133#2509C2212yescomplemented
134#2508C2212yescomplemented
135#2507C2212yescomplemented
136#2507C2212yescomplemented
137#2507C2212yescomplemented
138#2507C2212yescomplemented
139#2507C2212yescomplemented
140#2506C2212yescomplemented
141#2506C2211yescharacteristic, complemented
142#2505C2214yescomplemented
143#2505C2214yescomplemented
144#2505C2214yescomplemented
145#2505C2214yescomplemented
146#2497C2212yes—
147#2497C2212yes—
148#2497C2212yes—
149#2497C2212yes—
150#2496C2211yescharacteristic
151#2496C2212yescomplemented
152#2495C2212yes—
153#2494C2212yes—
154#2489C2212yes—
155#2489C2211yescharacteristic
156#2489C2212yescomplemented
157#2481C2214yes—
158#2481C2214yes—
159#2481C2214yes—
160#2481C2214yes—
161#2480C2214yes—
162#2480C2214yes—
163#2480C2214yes—
164#2480C2214yes—
165#2480C2214yes—
166#2480C2214yes—
167#2478C2212yes—
168#2475C2212yes—
169#2473C2214yescomplemented
170#2473C2214yescomplemented
171#2473C2214yescomplemented
172#2473C2214yescomplemented
173#2473C2214yescomplemented
174#2473C2214yescomplemented
175#2469C2214yescomplemented
176#2462C2214yescomplemented
177#2453C2211yescharacteristic, complemented
178#2452C2212yes—
179#2452C2212yes—
180#2449C2214yes—
181#2449C2214yes—
182#2446C2211yescharacteristic, complemented
183#2446C2212yescomplemented
184#2446C2212yescomplemented
185#2442C2214yescomplemented
186#2442C2214yescomplemented
187#2442C2212yescomplemented
188#2442C2212yescomplemented
189#2442C2214yescomplemented
190#2440C2212yes—
191#2440C2212yes—
192#2440C2214yescomplemented
193#2440C2214yescomplemented
194#2437C2214yes—
195#2437C2214yes—
196#2434C2212yescomplemented
197#2434C2212yescomplemented
198#2429C2212yes—
199#2429C2214yes—
200#2429C2212yes—
201#2429C2212yes—
202#2429C2212yes—
203#2429C2214yes—
204#2429C2211yescharacteristic
205#2429C2212yescomplemented
206#2429C2214yescomplemented
207#2429C2214yescomplemented
208#2429C2212yescomplemented
209#2429C2212yescomplemented
210#2429C2212yescomplemented
211#2429C2212yescomplemented
212#2421C2212yes—
213#2421C2211yescharacteristic
214#2421C2212yescomplemented
215#2417C2212yes—
216#2417C2212yes—
217#2409C2212yes—
218#2409C2212yes—
219#2402C2212yescomplemented
220#2401C2212yes—
221C2×#398C2214yescomplemented
222C2×#396C2214yes—
223#2369C2212yescomplemented
224#2368C2214yescomplemented
225#2365C2211yescharacteristic, complemented
226#2365C2211yescharacteristic, complemented
227#2365C2212yescomplemented
228#2360C2214yescomplemented
229#2360C2212yescomplemented
230#2360C2212yescomplemented
231#2357C2211yescharacteristic
232#2357C2211yescharacteristic
233#2355C2211yescharacteristic, complemented
234#2353C2212yes—
235#2353C2212yes—
236Q8×C4⋊C4C2211yescharacteristic, complemented
237#2349C2211yescharacteristic
238#2349C2212yes—
239#2349C2212yes—
240#2349C2211yescharacteristic
241D4×C4⋊C4C2212yes—
242D4×C4⋊C4C2212yes—
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yes—
245D4×C4⋊C4C2212yes—
246D4×C4⋊C4C2211yescharacteristic
247D4×C4⋊C4C2212yes—
248D4×C4⋊C4C2211yescharacteristic
249#2345C2211yescharacteristic
250#2345C2211yescharacteristic
251#2342C2212yes—
252#2342C2212yes—
253Q8×C22⋊C4C2212yescomplemented
254Q8×C22⋊C4C2212yescomplemented
255D4×C22⋊C4C2211yescharacteristic
256D4×C22⋊C4C2212yes—
257D4×C22⋊C4C2212yes—
258D4×C22⋊C4C2211yescharacteristic
259#2334C2214yes—
260#2334C2214yescomplemented
261#2331C2212yescomplemented
262#2330C2212yescomplemented
263#2329C2214yescomplemented
264#2327C2212yescomplemented
265#2323C2212yescomplemented
266#2323C2212yescomplemented
267#2320C2212yescomplemented
268#2314C2212yes—
269C4×C4⋊Q8C2212yescomplemented
270C4×C4⋊Q8C2211yescharacteristic, complemented
271C4×C4⋊Q8C2211yescharacteristic, complemented
272C4×C4⋊Q8C2211yescharacteristic, complemented
273C4×#125C2212yescomplemented
274C4×#125C2211yescharacteristic, complemented
275C4×#126C2212yes—
276C4×C22⋊Q8C2211yescharacteristic
277C4×C22⋊Q8C2211yescharacteristic
278C4×C22⋊Q8C2212yescomplemented
279C4×C22⋊Q8C2212yescomplemented
280C4×C22⋊Q8C2214yescomplemented
281#2295C2211yescharacteristic, complemented
282C2×#391C2212yescomplemented
283#2293C2211yescharacteristic
284#2293C2211yescharacteristic
285C2×#389C2214yescomplemented
286C2×#389C2212yescomplemented
287#2290C2212yes—
288#2290C2212yes—
289C2×#388C2214yes—
290#2283C2211yescharacteristic
291#2280C2212yes—
292#2275C2212yes—
293C42×Q8C2211yescharacteristic, complemented
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2212yes—
299C23×Q8C2312yes—
300C23×Q8C2312yes—
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303D4×Q8—28no—
304D4×Q8—28no—
305#541—48no—
306#541—48no—
307C2×C4⋊Q8—48no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2314yes—
318C2×C4⋊Q8C2314yes—
319C2×#126C2312yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#126C2314yes—
325C2×#125C2311yescharacteristic
326C2×#125C2312yes—
327C2×#125C2312yes—
328C2×#125C2314yes—
329C2×#125C2312yes—
330C2×#125C2314yes—
331C2×#125C2314yes—
332C2×#125C2314yes—
333C2×C22⋊Q8—48no—
334C2×C22⋊Q8—48no—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2314yes—
353C2×C4×Q8—48no—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2314yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2314yes—
365C2×C4×D4—28no—
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2312yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2311yescharacteristic
384C22×C4⋊C4C2311yescharacteristic
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2314yes—
389C22×C4⋊C4C2314yes—
390C22×C4⋊C4C2314yes—
391C22×C4⋊C4C2314yes—
392C22×C4⋊C4C2314yes—
393C22×C22⋊C4C2312yes—
394C22×C22⋊C4C2312yes—
395C22×C22⋊C4C2312yes—
396C22×C22⋊C4C2314yes—
397C22×C22⋊C4C2314yes—
398C22×C42C2311yescharacteristic
399C22×C42C2314yes—
400C22×C42C2312yes—
401C22×C42C2312yes—
402#401C2312yes—
403#401C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2312yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2312yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2312yes—
425#400C2314yes—
426#400C2312yes—
427#400C2312yes—
428#400C2312yes—
429#400C2312yes—
430#399C2314yes—
431#399C2314yes—
432#398C2312yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2312yes—
450#398C2314yes—
451#398C2312yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2312yes—
458#398C2314yes—
459#398C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2312yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2312yes—
475#397C2312yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2312yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#395C2314yes—
491#395C2314yes—
492#395C2314yes—
493#395C2314yes—
494#395C2314yes—
495#395C2314yes—
496#393C2314yes—
497#393C2314yes—
498#391C2311yescharacteristic
499#391C2312yes—
500#391C2314yes—
501#391C2311yescharacteristic
502#391C2312yes—
503#391C2314yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2311yescharacteristic
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2312yes—
514#391C2314yes—
515#391C2312yes—
516#391C2314yes—
517#391C2311yescharacteristic
518#391C2311yescharacteristic
519#390C2311yescharacteristic
520#390C2312yes—
521#390C2312yes—
522#390C2311yescharacteristic
523#390C2311yescharacteristic
524#390C2311yescharacteristic
525#390C2312yes—
526#390C2312yes—
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2311yescharacteristic
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2311yescharacteristic
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2312yes—
563#389C2314yes—
564#389C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2311yescharacteristic
567#389C2311yescharacteristic
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2314yes—
580#389C2311yescharacteristic
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2314yes—
590#388C2314yes—
591#388C2312yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2312yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2312yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#386C2312yes—
656#386C2314yes—
657#386C2314yes—
658#386C2312yes—
659#386C2312yes—
660#386C2312yes—
661#386C2314yes—
662#386C2314yes—
663#385C2312yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2312yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2312yes—
682#385C2312yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2312yes—
690#385C2312yes—
691#384C2312yes—
692#384C2311yescharacteristic
693#384C2311yescharacteristic
694#384C2311yescharacteristic
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#384C2312yes—
699#384C2312yes—
700#384C2312yes—
701#384C2312yes—
702#383C2312yes—
703#383C2314yes—
704#383C2312yes—
705#382C2311yescharacteristic
706#382C2312yes—
707#382C2312yes—
708#382C2311yescharacteristic
709#382C2312yes—
710#382C2311yescharacteristic
711#382C2314yes—
712#382C2312yes—
713#382C2312yes—
714#382C2314yes—
715#382C2314yes—
716#381C2312yes—
717#381C2312yes—
718#381C2312yes—
719#380C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2314yes—
727#380C2311yescharacteristic
728#380C2311yescharacteristic
729#380C2312yes—
730#380C2312yes—
731#380C2311yescharacteristic
732#380C2311yescharacteristic
733#380C2312yes—
734#380C2312yes—
735#380C2314yes—
736#380C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2314yes—
740#380C2312yes—
741#380C2312yes—
742#380C2314yes—
743#379C2314yes—
744#379C2314yes—
745#379C2312yes—
746#379C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C22⋊C4C2311yescharacteristic
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807#376C2312yes—
808#376C2311yescharacteristic
809#376C2312yes—
810#376C2311yescharacteristic
811C2×#95C2314yes—
812C2×#95C2314yes—
813C2×#95C2312yes—
814C2×#95C2312yes—
815C2×#95C2314yes—
816C43C2312yes—
817C43C2311yescharacteristic
818C43C2311yescharacteristic
819C25C2412yes—
820C22×Q8—28no—
821C22×Q8—28no—
822C22×Q8—28no—
823C22×Q8—44no—
824C22×Q8—44no—
825C22×Q8—44no—
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2411yescharacteristic
829C22×Q8C2414yes—
830C22×Q8C2411yescharacteristic
831C22×Q8C2414yes—
832C22×D4—24no—
833C22×D4—24no—
834C22×D4—24no—
835C22×D4C2412yes—
836C22×D4C2411yescharacteristic
837C22×D4C2411yescharacteristic
838C23×C4—28no—
839C23×C4—44no—
840C23×C4—44no—
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2414yes—
846C23×C4C2414yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2414yes—
852C23×C4C2414yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C4⋊Q8—24no—
858C4⋊Q8—28no—
859C4⋊Q8—28no—
860C4⋊Q8—28no—
861C4⋊Q8—24no—
862C4⋊Q8—24no—
863C4⋊Q8—44no—
864C4⋊Q8—44no—
865C4⋊Q8—44no—
866C4⋊Q8—48no—
867C4⋊Q8—48no—
868#126—28no—
869#126—48no—
870#126—48no—
871#126—48no—
872#126—48no—
873#126—48no—
874#125—24no—
875#125—44no—
876#125—44no—
877#125—48no—
878#125—48no—
879#125—44no—
880#125—48no—
881#125—48no—
882C22⋊Q8—24no—
883C22⋊Q8—28no—
884C22⋊Q8—28no—
885C22⋊Q8—28no—
886C22⋊Q8—24no—
887C22⋊Q8—28no—
888C22⋊Q8—216no—
889C22⋊Q8—216no—
890C22⋊Q8—48no—
891C22⋊Q8—48no—
892C22⋊Q8—48no—
893C22⋊Q8—48no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—44no—
897C22⋊Q8—44no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900C4×Q8—24no—
901C4×Q8—24no—
902C4×Q8—28no—
903C4×Q8—24no—
904C4×Q8—24no—
905C4×Q8—48no—
906C4×Q8—48no—
907C4×Q8—44no—
908C4×Q8—44no—
909C4×Q8—44no—
910C4×Q8—44no—
911C4×D4—24no—
912C4×D4—28no—
913C4×D4—28no—
914C4×D4—24no—
915C4×D4—28no—
916C4×D4—24no—
917C4×D4—24no—
918C4×D4—28no—
919C4×D4—24no—
920C4×D4—28no—
921C4×D4—24no—
922C4×D4—28no—
923C4×D4—24no—
924C4×D4#4118yes—
925#117—24no—
926#117—44no—
927#117—44no—
928#117—42no—
929C2×C4⋊C4—24no—
930C2×C4⋊C4—28no—
931C2×C4⋊C4—48no—
932C2×C4⋊C4—48no—
933C2×C4⋊C4—44no—
934C2×C4⋊C4—48no—
935C2×C4⋊C4—48no—
936C2×C4⋊C4—48no—
937C2×C4⋊C4—48no—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C22⋊C4—28no—
1020C2×C22⋊C4—28no—
1021C2×C22⋊C4—44no—
1022C2×C22⋊C4—48no—
1023C2×C22⋊C4—48no—
1024C2×C22⋊C4C2411yescharacteristic
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C42—24no—
1065C2×C42—44no—
1066C2×C42—48no—
1067C2×C42—44no—
1068C2×C42C2411yescharacteristic
1069C2×C42C2411yescharacteristic
1070C2×C42C2412yes—
1071C2×C42C2411yescharacteristic
1072C2×C42C2412yes—
1073C2×C42C2411yescharacteristic
1074C2×C42C2411yescharacteristic
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2412yes—
1079C2×C42C2412yes—
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2412yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2412yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2414yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2411yescharacteristic
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2412yes—
1100C2×C42C2414yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104#95C2411yescharacteristic
1105#95C2411yescharacteristic
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2411yescharacteristic
1128#95C2411yescharacteristic
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2411yescharacteristic
1132#95C2411yescharacteristic
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184C24—24no—
1185C24—24no—
1186C24—24no—
1187C24—24no—
1188C24—42no—
1189C24—42no—
1190C24—42no—
1191C24C2512yes—
1192C24C2511yescharacteristic
1193C24C2512yes—
1194C2×Q8—22no—
1195C2×Q8—22no—
1196C2×Q8—28no—
1197C2×Q8—24no—
1198C2×Q8—24no—
1199C2×Q8—28no—
1200C2×Q8—22no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—22no—
1205C2×Q8—28no—
1206C2×Q8—24no—
1207C2×Q8—22no—
1208C2×Q8—44no—
1209C2×Q8—44no—
1210C2×Q8—44no—
1211C2×Q8—432no—
1212C2×Q8—816no—
1213C2×Q8H(5,𝔽2)14yes—
1214C2×D4—24no—
1215C2×D4—24no—
1216C2×D4—24no—
1217C2×D4—22no—
1218C2×D4—22no—
1219C2×D4—22no—
1220C2×D4—416no—
1221C2×D4C2×#4114yes—
1222C2×D42−1+414yes—
1223C2×D42−1+414yes—
1224C22×C4—24no—
1225C22×C4—24no—
1226C22×C4—28no—
1227C22×C4—22no—
1228C22×C4—28no—
1229C22×C4—24no—
1230C22×C4—24no—
1231C22×C4—24no—
1232C22×C4—24no—
1233C22×C4—28no—
1234C22×C4—28no—
1235C22×C4—24no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—24no—
1240C22×C4—28no—
1241C22×C4—28no—
1242C22×C4—24no—
1243C22×C4—24no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—24no—
1247C22×C4—24no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—42no—
1254C22×C4—42no—
1255C22×C4—42no—
1256C22×C4—44no—
1257C22×C4—44no—
1258C22×C4—41no—
1259C22×C4—42no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—42no—
1263C22×C4—42no—
1264C22×C4—42no—
1265C22×C4—44no—
1266C22×C4—44no—
1267C22×C4—42no—
1268C22×C4—42no—
1269C22×C4—42no—
1270C22×C4—42no—
1271C22×C4—816no—
1272C22×C4C2×#4118yes—
1273C22×C4C2511yescharacteristic
1274C22×C4C2512yes—
1275C22×C4C2511yescharacteristic
1276C22×C4C2512yes—
1277C22×C4C2511yescharacteristic
1278C22×C4C2511yescharacteristic
1279C22×C4C2512yes—
1280C22×C4C2512yes—
1281C22×C4C2511yescharacteristic
1282C22×C4C2512yes—
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2514yes—
1288C22×C4C2514yes—
1289C22×C4C2511yescharacteristic
1290C22×C4C2512yes—
1291C22×C4C2511yescharacteristic
1292C22×C4C2511yescharacteristic
1293C22×C4C2514yes—
1294C22×C4C2514yes—
1295C22×C4C2512yes—
1296C22×C4C2511yescharacteristic
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2511yescharacteristic
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C4⋊C4—24no—
1306C4⋊C4—22no—
1307C4⋊C4—24no—
1308C4⋊C4—24no—
1309C4⋊C4—24no—
1310C4⋊C4—22no—
1311C4⋊C4—22no—
1312C4⋊C4—24no—
1313C4⋊C4—28no—
1314C4⋊C4—28no—
1315C4⋊C4—24no—
1316C4⋊C4—24no—
1317C4⋊C4—28no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—22no—
1321C4⋊C4—24no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—28no—
1326C4⋊C4—24no—
1327C4⋊C4—28no—
1328C4⋊C4—28no—
1329C4⋊C4—28no—
1330C4⋊C4—28no—
1331C4⋊C4—22no—
1332C4⋊C4—24no—
1333C4⋊C4—22no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—24no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—28no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
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—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—41no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4C2×#4114yes—
1385C4⋊C4H(5,𝔽2)14yes—
1386C22⋊C4—24no—
1387C22⋊C4—28no—
1388C22⋊C4—28no—
1389C22⋊C4—24no—
1390C22⋊C4—22no—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—28no—
1395C22⋊C4—24no—
1396C22⋊C4—28no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—28no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—22no—
1408C22⋊C4—24no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—44no—
1415C22⋊C4—41no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4C2×#4118yes—
1425C22⋊C42−1+414yes—
1426C42—22no—
1427C42—22no—
1428C42—22no—
1429C42—24no—
1430C42—24no—
1431C42—24no—
1432C42—22no—
1433C42—22no—
1434C42—24no—
1435C42—24no—
1436C42—28no—
1437C42—22no—
1438C42—22no—
1439C42—24no—
1440C42—22no—
1441C42—22no—
1442C42—22no—
1443C42—24no—
1444C42—22no—
1445C42—22no—
1446C42—22no—
1447C42—24no—
1448C42—24no—
1449C42—22no—
1450C42—42no—
1451C42—44no—
1452C42—44no—
1453C42—42no—
1454C42—42no—
1455C42—42no—
1456C42—41no—
1457C42—44no—
1458C42—44no—
1459C42—42no—
1460C42—44no—
1461C42C2×#4114yes—
1462C23—22no—
1463C23—22no—
1464C23—22no—
1465C23—22no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—22no—
1473C23—22no—
1474C23—22no—
1475C23—22no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—48no—
1480C23—48no—
1481C23—48no—
1482C23—48no—
1483C23—84no—
1484C23—84no—
1485C23—84no—
1486C23C22×#4114yes—
1487C23C2×2−1+412yes—
1488C23C2×2−1+414yes—
1489C23C2×2−1+414yes—
1490C23C2611yescharacteristic
1491Q8—28no—
1492Q8—416no—
1493Q8—48no—
1494Q8—48no—
1495Q8—44no—
1496Q8—88no—
1497D4—48no—
1498D4—44no—
1499D4#541116yescomplemented
1500C2×C4—22no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—22no—
1505C2×C4—22no—
1506C2×C4—22no—
1507C2×C4—21no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—22no—
1514C2×C4—216no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—24no—
1523C2×C4—24no—
1524C2×C4—22no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—22no—
1528C2×C4—21no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—24no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—24no—
1537C2×C4—24no—
1538C2×C4—24no—
1539C2×C4—24no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—24no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—24no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—24no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—21no—
1583C2×C4—22no—
1584C2×C4—416no—
1585C2×C4—48no—
1586C2×C4—48no—
1587C2×C4—48no—
1588C2×C4—44no—
1589C2×C4—416no—
1590C2×C4—44no—
1591C2×C4—48no—
1592C2×C4—44no—
1593C2×C4—84no—
1594C2×C4—84no—
1595C2×C4—84no—
1596C2×C4—88no—
1597C2×C4—84no—
1598C2×C4—88no—
1599C2×C4C22×#4112yes—
1600C2×C4C22×#4114yes—
1601C2×C4C22×#4112yes—
1602C2×C4C22×#4112yes—
1603C2×C4C2×H(5,𝔽2)14yes—
1604C2×C4C2×H(5,𝔽2)14yes—
1605C2×C4C2×H(5,𝔽2)12yes—
1606C2×C4C2×H(5,𝔽2)12yes—
1607C2×C4C2×2−1+412yes—
1608C2×C4C2×2−1+412yes—
1609C2×C4C2×2−1+412yes—
1610C2×C4C2×2−1+412yes—
1611C2×C4#58512yes—
1612C22—24no—
1613C22—24no—
1614C22—24no—
1615C22—24no—
1616C22—24no—
1617C22—24no—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—42no—
1626C22—42no—
1627C22—42no—
1628C22—42no—
1629C22—42no—
1630C22—42no—
1631C22—42no—
1632C22—816no—
1633C22C2×#54118yes—
1634C22C23×#4111yescharacteristic
1635C22C22×H(5,𝔽2)11yescharacteristic
1636C22C22×H(5,𝔽2)11yescharacteristic
1637C22C22×2−1+411yescharacteristic
1638C22C22×2−1+411yescharacteristic
1639C22C22×2−1+411yescharacteristic
1640C22C2×#58511yescharacteristic
1641C4—24no—
1642C4—22no—
1643C4—22no—
1644C4—22no—
1645C4—24no—
1646C4—24no—
1647C4—22no—
1648C4—41no—
1649C4—44no—
1650C4—42no—
1651C4—41no—
1652C4—41no—
1653C4—42no—
1654C4—44no—
1655C4—42no—
1656C4—41no—
1657C4—41no—
1658C4—42no—
1659C4—42no—
1660C4—42no—
1661C4—42no—
1662C4—42no—
1663C4—41no—
1664C4—44no—
1665C4—42no—
1666C4—44no—
1667C4—42no—
1668C4—42no—
1669C4—41no—
1670C4—41no—
1671C4C2×#54114yes—
1672C4#351914yes—
1673C2—28no—
1674C2—42no—
1675C2—82no—
1676C2C22×#54111yescharacteristic
1677C2C2×#351911yescharacteristic
1678C2#6280511yescharacteristic
1679C2#6301311yescharacteristic
1680C2#6301511yescharacteristic
1681C2#6301611yescharacteristic
1682C2#6301611yescharacteristic
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. #42614C2semidirect
2. #42610C2semidirect
3. #40735C2semidirect
4. #40726C2semidirect
5. #40213C2semidirect
6. #39661C2semidirect
7. #39385C2semidirect
8. #39192C2semidirect
9. #39149C2semidirect
10. #38943C2semidirect
11. #38599C2semidirect
12. #38172C2semidirect
13. #38122C2semidirect
14. #37695C2semidirect
15. #37663C2semidirect
16. #37663C2semidirect
17. #37628C2semidirect
18. #37495C2semidirect
19. #36290C2semidirect
20. #36290C2semidirect
22. D4×C4⋊Q8C2semidirect
26. #35858C2semidirect
27. #35284C2semidirect
28. #35244C2semidirect
29. #35209C2semidirect
30. #35086C2semidirect
31. #34975C2semidirect
32. C2×#2429C2semidirect
33. #34334C2semidirect
34. C4×D4×Q8C2semidirect
38. C2×#541C22semidirect
39. C2×#541C22semidirect
40. C22×C4⋊Q8C22semidirect
43. C22×C4×Q8C22semidirect
45. #2868C22semidirect
47. #2859C22semidirect
48. #2859C22semidirect
51. #2857C22semidirect
53. #2851C22semidirect
54. #2851C22semidirect
57. #2836C22semidirect
58. #2833C22semidirect
59. #2831C22semidirect
60. #2802C22semidirect
61. #2783C22semidirect
62. #2776C22semidirect
63. #2776C22semidirect
64. #2772C22semidirect
65. #2769C22semidirect
68. #2725C22semidirect
69. #2725C22semidirect
70. #2721C22semidirect
71. #2721C22semidirect
72. #2716C22semidirect
73. #2716C22semidirect
74. #2713C22semidirect
75. #2713C22semidirect
78. #2698C22semidirect
79. #2698C22semidirect
82. #2689C22semidirect
83. #2689C22semidirect
84. #2666C22semidirect
85. #2664C22semidirect
86. #2654C22semidirect
88. #2652C22semidirect
89. #2650C22semidirect
90. #2647C22semidirect
91. #2647C22semidirect
92. #2646C22semidirect
93. #2645C22semidirect
96. #2642C22semidirect
97. #2637C22semidirect
98. #2634C22semidirect
100. #2625C22semidirect
101. #2625C22semidirect
102. #2621C22semidirect
103. #2621C22semidirect
104. #2571C22semidirect
105. #2571C22semidirect
106. #2570C22semidirect
107. #2569C22semidirect
108. #2552C22semidirect
109. #2552C22semidirect
110. #2552C22semidirect
111. #2551C22semidirect
112. #2551C22semidirect
113. #2546C22semidirect
114. #2546C22semidirect
119. #2533C22semidirect
120. #2528C22semidirect
121. #2519C22semidirect
122. #2514C22semidirect
131. #2509C22semidirect
132. #2509C22semidirect
133. #2509C22semidirect
134. #2508C22semidirect
135. #2507C22semidirect
136. #2507C22semidirect
137. #2507C22semidirect
138. #2507C22semidirect
139. #2507C22semidirect
140. #2506C22semidirect
141. #2506C22semidirect
142. #2505C22semidirect
143. #2505C22semidirect
144. #2505C22semidirect
145. #2505C22semidirect
151. #2496C22semidirect
156. #2489C22semidirect
169. #2473C22semidirect
170. #2473C22semidirect
171. #2473C22semidirect
172. #2473C22semidirect
173. #2473C22semidirect
174. #2473C22semidirect
175. #2469C22semidirect
176. #2462C22semidirect
177. #2453C22semidirect
182. #2446C22semidirect
183. #2446C22semidirect
184. #2446C22semidirect
185. #2442C22semidirect
186. #2442C22semidirect
187. #2442C22semidirect
188. #2442C22semidirect
189. #2442C22semidirect
192. #2440C22semidirect
193. #2440C22semidirect
196. #2434C22semidirect
197. #2434C22semidirect
205. #2429C22semidirect
206. #2429C22semidirect
207. #2429C22semidirect
208. #2429C22semidirect
209. #2429C22semidirect
210. #2429C22semidirect
211. #2429C22semidirect
214. #2421C22semidirect
219. #2402C22semidirect
221. C2×#398C22semidirect
223. #2369C22semidirect
224. #2368C22semidirect
225. #2365C22semidirect
226. #2365C22semidirect
227. #2365C22semidirect
228. #2360C22semidirect
229. #2360C22semidirect
230. #2360C22semidirect
233. #2355C22semidirect
236. Q8×C4⋊C4C22semidirect
253. Q8×C22⋊C4C22semidirect
254. Q8×C22⋊C4C22semidirect
260. #2334C22semidirect
261. #2331C22semidirect
262. #2330C22semidirect
263. #2329C22semidirect
264. #2327C22semidirect
265. #2323C22semidirect
266. #2323C22semidirect
267. #2320C22semidirect
269. C4×C4⋊Q8C22semidirect
270. C4×C4⋊Q8C22semidirect
271. C4×C4⋊Q8C22semidirect
272. C4×C4⋊Q8C22semidirect
273. C4×#125C22semidirect
274. C4×#125C22semidirect
278. C4×C22⋊Q8C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
281. #2295C22semidirect
282. C2×#391C22semidirect
285. C2×#389C22semidirect
286. C2×#389C22semidirect
293. C42×Q8C22semidirect
1499. D4#541semidirect

Maximal subgroups

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

subgroupindex
#426142
#426102
#407352
#407262
#402132
#396612
#393852
#391922
#391492
#389432
#385992
#381722
#381222
#376952
#376632
#376282
#374952
#362902
#362402
D4×C4⋊Q82
D4×C22⋊Q82
#359142
#358582
#352842
#352442
#352092
#350862
#349752
C2×#24292
#343342
C4×D4×Q82
#341262