Finite Group Databasebeta

← #8424404

Subgroups — #8424404

Order 512.

4730 conjugacy classes of subgroups.

The subgroup lattice has 1715 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59663C212yesmaximal, complemented
2#59653C211yesmaximal, characteristic, complemented
3#59322C211yesmaximal, characteristic, complemented
4#59244C211yesmaximal, characteristic, complemented
5#59025C212yesmaximal, complemented
6#58315C214yesmaximal, complemented
7#56497C214yesmaximal, complemented
8#53052C212yesmaximal, complemented
9#53050C212yesmaximal, complemented
10#53021C212yesmaximal, complemented
11#52994C212yesmaximal, complemented
12#52371C214yesmaximal, complemented
13#42904C212yesmaximal, complemented
14#42896C212yesmaximal, complemented
15#42878C212yesmaximal, complemented
16#42526C212yesmaximal, complemented
17#40563C214yesmaximal, complemented
18#39727C211yesmaximal, characteristic, complemented
19#39511C212yesmaximal, complemented
20#39477C212yesmaximal, complemented
21#39379C211yesmaximal, characteristic, complemented
22#39127C211yesmaximal, characteristic, complemented
23#38978C211yesmaximal, characteristic, complemented
24#38122C212yesmaximal, complemented
25#37663C212yesmaximal, complemented
26#37631C211yesmaximal, characteristic, complemented
27#37622C211yesmaximal, characteristic, complemented
28#37492C212yesmaximal
29#37476C212yesmaximal, complemented
30#36577C211yesmaximal, characteristic, complemented
31#36189C211yesmaximal, characteristic, complemented
32#36161C211yesmaximal, characteristic, complemented
33C2×#2538C211yesmaximal, characteristic, complemented
34#34700C211yesmaximal, characteristic
35#34691C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic, complemented
37C2×#556C2211yescharacteristic
38C2×#556C2212yescomplemented
39C2×#541C2212yescomplemented
40C2×#533C2211yescharacteristic, complemented
41C2×#529C2211yescharacteristic
42C22×C22⋊Q8C2212yes—
43C22×C4×Q8C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45#2859C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2212yes—
48#2857C2211yescharacteristic, complemented
49#2848C2212yes—
50#2841C2214yescomplemented
51#2841C2214yescomplemented
52#2838C2214yescomplemented
53#2838C2214yescomplemented
54#2837C2214yescomplemented
55#2837C2214yescomplemented
56#2836C2214yescomplemented
57#2836C2214yescomplemented
58#2831C2214yescomplemented
59#2831C2214yescomplemented
60#2830C2214yes—
61#2829C2214yes—
62#2820C2214yescomplemented
63#2814C2214yescomplemented
64#2808C2214yes—
65#2802C2214yescomplemented
66#2802C2214yescomplemented
67#2800C2214yes—
68#2800C2214yes—
69#2792C2214yescomplemented
70#2787C2214yescomplemented
71#2783C2214yescomplemented
72#2783C2214yescomplemented
73#2783C2214yescomplemented
74#2781C2214yescomplemented
75#2779C2214yescomplemented
76#2777C2214yescomplemented
77#2776C2214yescomplemented
78#2775C2214yescomplemented
79#2772C2214yescomplemented
80#2772C2214yescomplemented
81#2770C2214yescomplemented
82#2755C2214yescomplemented
83#2727C2214yes—
84#2727C2214yescomplemented
85#2725C2214yescomplemented
86#2725C2214yescomplemented
87#2725C2214yescomplemented
88#2725C2214yescomplemented
89#2725C2214yescomplemented
90#2725C2214yescomplemented
91#2725C2214yescomplemented
92#2715C2214yescomplemented
93#2707C2214yescomplemented
94#2704C2214yescomplemented
95#2702C2214yescomplemented
96#2700C2214yescomplemented
97#2698C2214yescomplemented
98#2690C2214yescomplemented
99#2689C2214yescomplemented
100#2689C2214yescomplemented
101#2667C2214yescomplemented
102#2665C2214yescomplemented
103#2664C2214yescomplemented
104#2662C2214yes—
105#2654C2214yescomplemented
106#2651C2214yes—
107#2650C2214yescomplemented
108#2645C2212yescomplemented
109#2644C2212yes—
110#2640C2212yes—
111#2637C2214yescomplemented
112#2629C2212yescomplemented
113#2629C2212yescomplemented
114#2628C2212yescomplemented
115#2628C2212yescomplemented
116#2626C2214yes—
117#2626C2214yes—
118#2625C2212yescomplemented
119#2625C2212yescomplemented
120#2624C2212yes—
121#2622C2214yes—
122#2621C2212yescomplemented
123#2620C2212yes—
124#2592C2212yes—
125#2592C2212yes—
126#2588C2214yescomplemented
127#2584C2212yescomplemented
128#2584C2214yescomplemented
129#2583C2214yes—
130#2582C2212yescomplemented
131#2582C2211yescharacteristic, complemented
132#2582C2212yescomplemented
133#2582C2211yescharacteristic, complemented
134#2570C2212yescomplemented
135#2569C2214yes—
136#2568C2212yescomplemented
137#2568C2211yescharacteristic, complemented
138#2567C2212yescomplemented
139#2567C2212yescomplemented
140#2562C2212yescomplemented
141#2560C2214yescomplemented
142#2551C2211yescharacteristic, complemented
143#2549C2214yes—
144#2547C2211yescharacteristic
145#2545C2212yes—
146#2545C2212yes—
147#2538C2212yes—
148#2538C2211yescharacteristic
149#2538C2212yes—
150#2538C2211yescharacteristic
151#2538C2212yes—
152#2538C2211yescharacteristic
153#2538C2212yes—
154#2538C2214yes—
155#2538C2211yescharacteristic
156#2538C2211yescharacteristic
157#2538C2212yescomplemented
158#2536C2212yescomplemented
159#2519C2214yescomplemented
160#2512C2212yes—
161#2512C2212yes—
162#2512C2212yes—
163#2511C2212yescomplemented
164#2510C2214yes—
165#2509C2212yescomplemented
166#2507C2212yescomplemented
167#2507C2212yescomplemented
168#2507C2212yescomplemented
169#2506C2212yescomplemented
170#2506C2212yescomplemented
171#2505C2214yes—
172#2499C2212yescomplemented
173#2497C2212yescomplemented
174#2496C2212yescomplemented
175#2495C2212yescomplemented
176#2494C2212yescomplemented
177#2492C2212yescomplemented
178#2491C2212yes—
179#2489C2212yescomplemented
180#2489C2212yescomplemented
181#2487C2212yes—
182#2485C2212yes—
183#2485C2212yescomplemented
184#2481C2214yes—
185#2480C2214yes—
186#2480C2214yes—
187#2480C2214yes—
188#2480C2214yes—
189#2480C2212yes—
190#2473C2214yes—
191#2473C2212yes—
192#2472C2214yes—
193#2469C2214yescomplemented
194#2468C2212yes—
195#2466C2214yes—
196#2465C2214yescomplemented
197#2465C2212yescomplemented
198#2462C2212yescomplemented
199#2457C2212yes—
200#2454C2211yescharacteristic
201#2453C2212yescomplemented
202#2453C2212yescomplemented
203#2453C2214yescomplemented
204#2451C2212yescomplemented
205#2451C2211yescharacteristic, complemented
206#2449C2212yes—
207#2448C2212yes—
208#2448C2212yes—
209#2448C2212yes—
210#2447C2212yes—
211#2447C2211yescharacteristic
212#2446C2212yescomplemented
213#2446C2211yescharacteristic, complemented
214#2442C2211yescharacteristic
215#2442C2212yes—
216#2442C2214yes—
217#2442C2212yes—
218#2442C2214yes—
219#2441C2212yescomplemented
220#2441C2212yescomplemented
221#2441C2212yescomplemented
222#2440C2212yes—
223#2440C2211yescharacteristic
224#2440C2212yes—
225#2439C2212yescomplemented
226#2439C2212yescomplemented
227#2435C2212yes—
228#2435C2211yescharacteristic
229#2434C2211yescharacteristic
230#2429C2212yescomplemented
231#2429C2212yescomplemented
232#2429C2212yescomplemented
233#2429C2211yescharacteristic, complemented
234#2427C2211yescharacteristic
235#2426C2212yes—
236#2423C2212yescomplemented
237#2423C2211yescharacteristic, complemented
238#2421C2212yescomplemented
239#2421C2212yescomplemented
240#2421C2212yescomplemented
241#2420C2211yescharacteristic
242#2418C2212yes—
243#2417C2211yescharacteristic
244#2417C2212yes—
245#2417C2211yescharacteristic
246#2415C2212yes—
247#2415C2212yescomplemented
248#2415C2212yescomplemented
249#2415C2212yescomplemented
250#2409C2211yescharacteristic
251#2408C2211yescharacteristic
252#2399C2212yescomplemented
253#2396C2212yescomplemented
254#2395C2212yes—
255#2392C2212yes—
256C2×#396C2214yes—
257#2367C2212yes—
258#2365C2212yescomplemented
259#2362C2212yescomplemented
260#2360C2212yes—
261#2360C2212yes—
262#2360C2214yes—
263#2360C2212yes—
264#2360C2212yes—
265#2354C2211yescharacteristic
266#2352C2212yes—
267#2351C2212yescomplemented
268#2351C2212yescomplemented
269Q8×C4⋊C4C2211yescharacteristic, complemented
270Q8×C4⋊C4C2211yescharacteristic, complemented
271Q8×C4⋊C4C2211yescharacteristic, complemented
272#2345C2212yes—
273Q8×C22⋊C4C2212yes—
274#2323C2212yescomplemented
275#2323C2212yescomplemented
276#2320C2212yescomplemented
277#2312C2214yes—
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×C4⋊Q8C2211yescharacteristic, complemented
280C4×#124C2211yescharacteristic
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic, complemented
286C4×#121C2211yescharacteristic
287C4×#120C2212yes—
288#2295C2211yescharacteristic, complemented
289#2293C2211yescharacteristic
290C2×#390C2212yes—
291C2×#389C2212yes—
292#2290C2212yes—
293#2285C2211yescharacteristic, complemented
294C2×#384C2211yescharacteristic
295#2280C2212yes—
296#2280C2212yes—
297C2×#380C2212yes—
298C42×D4C2211yescharacteristic
299C23×Q8C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#557—44no—
303#556—44no—
304#556—48no—
305#541—48no—
306#533—44no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314#529—44no—
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#125C2312yes—
322C2×#125C2314yes—
323C2×#125C2311yescharacteristic
324C2×#125C2312yes—
325C2×#125C2312yes—
326C2×#125C2314yes—
327C2×#125C2314yes—
328C2×#124C2314yes—
329C2×#124C2311yescharacteristic
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2311yescharacteristic
333C2×#123C2312yes—
334C2×C22⋊Q8—48no—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2311yescharacteristic
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2312yes—
354C2×#121C2311yescharacteristic
355C2×#121C2311yescharacteristic
356C2×#120C2312yes—
357C2×C4×Q8—44no—
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2314yes—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2312yes—
375C2×C4×D4—44no—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2312yes—
397C22×C4⋊C4C2314yes—
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2311yescharacteristic
400C22×C22⋊C4C2314yes—
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2314yes—
403C22×C42C2311yescharacteristic
404C22×C42C2311yescharacteristic
405C22×C42C2312yes—
406#401C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2312yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2312yes—
423#400C2314yes—
424#400C2314yes—
425#399C2314yes—
426#399C2314yes—
427#399C2314yes—
428#399C2312yes—
429#399C2312yes—
430#399C2314yes—
431#399C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2312yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2312yes—
452#398C2312yes—
453#398C2314yes—
454#398C2312yes—
455#398C2314yes—
456#398C2312yes—
457#398C2312yes—
458#398C2312yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2312yes—
469#397C2312yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2312yes—
482#397C2312yes—
483#396C2312yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2312yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2314yes—
504#396C2314yes—
505#396C2314yes—
506#396C2312yes—
507#396C2312yes—
508#396C2314yes—
509#395C2314yes—
510#395C2314yes—
511#395C2314yes—
512#395C2314yes—
513#395C2312yes—
514#395C2314yes—
515#395C2314yes—
516#395C2312yes—
517#395C2312yes—
518#395C2312yes—
519#395C2312yes—
520#394C2314yes—
521#394C2314yes—
522#394C2312yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2312yes—
528#394C2314yes—
529#394C2312yes—
530#394C2314yes—
531#394C2312yes—
532#394C2312yes—
533#393C2312yes—
534#393C2314yes—
535#393C2314yes—
536#393C2314yes—
537#393C2314yes—
538#393C2314yes—
539#392C2312yes—
540#391C2314yes—
541#391C2311yescharacteristic
542#391C2312yes—
543#391C2311yescharacteristic
544#391C2311yescharacteristic
545#391C2311yescharacteristic
546#391C2312yes—
547#391C2312yes—
548#391C2312yes—
549#391C2312yes—
550#391C2312yes—
551#391C2312yes—
552#391C2312yes—
553#391C2314yes—
554#391C2314yes—
555#391C2314yes—
556#391C2311yescharacteristic
557#391C2311yescharacteristic
558#391C2314yes—
559#391C2312yes—
560#391C2312yes—
561#391C2312yes—
562#391C2312yes—
563#391C2311yescharacteristic
564#391C2311yescharacteristic
565#390C2314yes—
566#390C2314yes—
567#390C2311yescharacteristic
568#390C2312yes—
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2311yescharacteristic
573#390C2311yescharacteristic
574#390C2314yes—
575#390C2311yescharacteristic
576#390C2312yes—
577#390C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2314yes—
591#389C2314yes—
592#389C2314yes—
593#389C2314yes—
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2311yescharacteristic
597#389C2314yes—
598#389C2312yes—
599#389C2312yes—
600#389C2314yes—
601#389C2312yes—
602#389C2314yes—
603#389C2314yes—
604#389C2314yes—
605#389C2312yes—
606#389C2314yes—
607#389C2314yes—
608#389C2312yes—
609#389C2314yes—
610#389C2314yes—
611#389C2314yes—
612#389C2312yes—
613#389C2314yes—
614#389C2312yes—
615#389C2312yes—
616#389C2314yes—
617#389C2312yes—
618#389C2314yes—
619#389C2312yes—
620#389C2312yes—
621#389C2312yes—
622#389C2312yes—
623#389C2312yes—
624#389C2314yes—
625#389C2312yes—
626#389C2312yes—
627#389C2312yes—
628#389C2311yescharacteristic
629#389C2311yescharacteristic
630#389C2311yescharacteristic
631#389C2311yescharacteristic
632#389C2311yescharacteristic
633#389C2311yescharacteristic
634#389C2312yes—
635#389C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2312yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2312yes—
662#388C2314yes—
663#388C2314yes—
664#388C2312yes—
665#388C2314yes—
666#388C2312yes—
667#388C2312yes—
668#388C2312yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2312yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2312yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2314yes—
692#387C2312yes—
693#387C2312yes—
694#387C2312yes—
695#387C2312yes—
696#387C2312yes—
697#387C2312yes—
698#387C2312yes—
699#386C2312yes—
700#386C2314yes—
701#386C2312yes—
702#386C2312yes—
703#386C2312yes—
704#386C2312yes—
705#386C2312yes—
706#385C2312yes—
707#385C2314yes—
708#385C2312yes—
709#385C2312yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2312yes—
715#385C2312yes—
716#385C2314yes—
717#385C2314yes—
718#385C2312yes—
719#385C2312yes—
720#385C2312yes—
721#385C2312yes—
722#385C2312yes—
723#384C2311yescharacteristic
724#384C2311yescharacteristic
725#384C2312yes—
726#384C2312yes—
727#384C2312yes—
728#384C2312yes—
729#384C2311yescharacteristic
730#384C2312yes—
731#384C2311yescharacteristic
732#384C2312yes—
733#383C2314yes—
734#382C2314yes—
735#382C2312yes—
736#382C2312yes—
737#382C2312yes—
738#382C2314yes—
739#382C2311yescharacteristic
740#382C2314yes—
741#381C2314yes—
742#381C2312yes—
743#381C2312yes—
744#380C2311yescharacteristic
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2314yes—
750#380C2312yes—
751#380C2314yes—
752#380C2311yescharacteristic
753#380C2312yes—
754#380C2312yes—
755#380C2314yes—
756#380C2312yes—
757#380C2312yes—
758#380C2314yes—
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2311yescharacteristic
766#380C2311yescharacteristic
767#380C2314yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#379C2312yes—
773#379C2314yes—
774#379C2312yes—
775#379C2312yes—
776#379C2314yes—
777C4×C4⋊C4C2314yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2314yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816#376C2312yes—
817C2×#95C2314yes—
818C43C2311yescharacteristic
819C25C2412yes—
820C22×Q8—24no—
821C22×Q8—24no—
822C22×Q8—42no—
823C22×Q8C2411yescharacteristic
824C22×Q8C2411yescharacteristic
825C22×Q8C2412yes—
826C22×Q8C2411yescharacteristic
827C22×Q8C2412yes—
828C22×Q8C2411yescharacteristic
829C22×Q8C2412yes—
830C22×Q8C2414yes—
831C22×D4—24no—
832C22×D4—42no—
833C22×D4—42no—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C23×C4—28no—
841C23×C4—44no—
842C23×C4—44no—
843C23×C4C2411yescharacteristic
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2414yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C4⋊Q8—24no—
858C4⋊Q8—24no—
859C4⋊Q8—44no—
860C4⋊Q8—42no—
861C4⋊Q8—44no—
862C4⋊Q8—42no—
863C4⋊Q8—44no—
864#126—44no—
865#126—48no—
866#126—48no—
867#126—48no—
868#126—48no—
869#126—48no—
870#125—42no—
871#125—44no—
872#125—44no—
873#125—48no—
874#125—44no—
875#125—48no—
876#125—48no—
877#124—48no—
878#124—42no—
879#124—44no—
880#124—42no—
881#124—44no—
882#123—44no—
883C22⋊Q8—28no—
884C22⋊Q8—28no—
885C22⋊Q8—24no—
886C22⋊Q8—28no—
887C22⋊Q8—24no—
888C22⋊Q8—24no—
889C22⋊Q8—44no—
890C22⋊Q8—48no—
891C22⋊Q8—48no—
892C22⋊Q8—48no—
893C22⋊Q8—44no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—44no—
897C22⋊Q8—42no—
898C22⋊Q8—42no—
899C22⋊Q8—42no—
900C22⋊Q8—44no—
901C22⋊Q8—44no—
902#121—42no—
903#121—42no—
904#120—44no—
905C4×Q8—28no—
906C4×Q8—24no—
907C4×Q8—24no—
908C4×Q8—24no—
909C4×Q8—24no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×Q8—48no—
914C4×Q8—42no—
915C4×Q8—42no—
916C4×Q8—44no—
917C4×Q8—44no—
918C4×Q8—44no—
919C4×Q8—44no—
920C4×Q8—44no—
921C4×Q8—44no—
922C4×D4—24no—
923C4×D4—24no—
924C4×D4—24no—
925C4×D4—24no—
926C4×D4—44no—
927C4×D4—42no—
928C4×D4—42no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—44no—
932C4×D4—42no—
933#117—44no—
934#117—44no—
935#117—44no—
936#117—44no—
937#117—44no—
938#117—44no—
939C2×C4⋊C4—44no—
940C2×C4⋊C4—42no—
941C2×C4⋊C4—44no—
942C2×C4⋊C4—42no—
943C2×C4⋊C4—44no—
944C2×C4⋊C4—48no—
945C2×C4⋊C4—44no—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C22⋊C4—44no—
1029C2×C22⋊C4—48no—
1030C2×C22⋊C4—48no—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2411yescharacteristic
1039C2×C22⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2411yescharacteristic
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C42—24no—
1085C2×C42—24no—
1086C2×C42—44no—
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2414yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2414yes—
1105C2×C42C2414yes—
1106C2×C42C2414yes—
1107C2×C42C2411yescharacteristic
1108C2×C42C2414yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2414yes—
1112C2×C42C2414yes—
1113C2×C42C2414yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2411yescharacteristic
1125#95C2411yescharacteristic
1126#95C2412yes—
1127#95C2411yescharacteristic
1128#95C2411yescharacteristic
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186C24—24no—
1187C24—24no—
1188C24—24no—
1189C24—42no—
1190C24—42no—
1191C24—42no—
1192C24—42no—
1193C24C2512yes—
1194C24C2512yes—
1195C24C2511yescharacteristic
1196C24C2511yescharacteristic
1197C2×Q8—22no—
1198C2×Q8—22no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—22no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—22no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—22no—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—42no—
1214C2×Q8—42no—
1215C2×Q8—44no—
1216C2×Q8—44no—
1217C2×Q8—42no—
1218C2×Q8—44no—
1219C2×Q8—42no—
1220C2×Q8—416no—
1221C2×Q8H(5,𝔽2)14yes—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—42no—
1233C2×D4—42no—
1234C2×D4—416no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—42no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—24no—
1246C22×C4—22no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—28no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—24no—
1254C22×C4—22no—
1255C22×C4—24no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—42no—
1268C22×C4—41no—
1269C22×C4—42no—
1270C22×C4—44no—
1271C22×C4—42no—
1272C22×C4—42no—
1273C22×C4—44no—
1274C22×C4—42no—
1275C22×C4—42no—
1276C22×C4—41no—
1277C22×C4—42no—
1278C22×C4—42no—
1279C22×C4—41no—
1280C22×C4—42no—
1281C22×C4—816no—
1282C22×C42−1+414yes—
1283C22×C42−1+414yes—
1284C22×C4C2511yescharacteristic
1285C22×C4C2511yescharacteristic
1286C22×C4C2512yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2514yes—
1291C22×C4C2511yescharacteristic
1292C22×C4C2512yes—
1293C22×C4C2514yes—
1294C22×C4C2512yes—
1295C22×C4C2511yescharacteristic
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2511yescharacteristic
1303C22×C4C2512yes—
1304C22×C4C2514yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2514yes—
1308C22×C4C2511yescharacteristic
1309C22×C4C2512yes—
1310C22×C4C2511yescharacteristic
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C4⋊C4—24no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—28no—
1324C4⋊C4—28no—
1325C4⋊C4—24no—
1326C4⋊C4—22no—
1327C4⋊C4—22no—
1328C4⋊C4—24no—
1329C4⋊C4—22no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—28no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—28no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—42no—
1363C4⋊C4—44no—
1364C4⋊C4—42no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—41no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—44no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—42no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C22⋊C4—22no—
1398C22⋊C4—22no—
1399C22⋊C4—24no—
1400C22⋊C4—28no—
1401C22⋊C4—24no—
1402C22⋊C4—22no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—28no—
1408C22⋊C4—28no—
1409C22⋊C4—24no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—42no—
1424C22⋊C4—44no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—41no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—42no—
1447C22⋊C4—44no—
1448C22⋊C4—42no—
1449C22⋊C4—44no—
1450C42—22no—
1451C42—22no—
1452C42—22no—
1453C42—22no—
1454C42—22no—
1455C42—22no—
1456C42—24no—
1457C42—24no—
1458C42—22no—
1459C42—24no—
1460C42—24no—
1461C42—24no—
1462C42—28no—
1463C42—22no—
1464C42—22no—
1465C42—22no—
1466C42—24no—
1467C42—42no—
1468C42—42no—
1469C42—41no—
1470C42—44no—
1471C42—44no—
1472C42—44no—
1473C42—41no—
1474C42—44no—
1475C42—44no—
1476C42—44no—
1477C42—44no—
1478C42H(5,𝔽2)14yes—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—22no—
1484C23—21no—
1485C23—22no—
1486C23—22no—
1487C23—22no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—22no—
1492C23—22no—
1493C23—22no—
1494C23—22no—
1495C23—22no—
1496C23—22no—
1497C23—21no—
1498C23—22no—
1499C23—22no—
1500C23—21no—
1501C23—22no—
1502C23—22no—
1503C23—21no—
1504C23—48no—
1505C23—48no—
1506C23—48no—
1507C23—84no—
1508C23—84no—
1509C23—84no—
1510C23—84no—
1511C23C2×2−1+412yes—
1512C23C2×2−1+412yes—
1513C23#58512yes—
1514C23C2611yescharacteristic
1515Q8—28no—
1516Q8—48no—
1517Q8—44no—
1518Q8—44no—
1519Q8—44no—
1520Q8—48no—
1521Q8—88no—
1522Q8—84no—
1523D4—48no—
1524D4—44no—
1525D4—44no—
1526D4—44no—
1527D4—84no—
1528D4—84no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—22no—
1532C2×C4—21no—
1533C2×C4—22no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—28no—
1538C2×C4—28no—
1539C2×C4—22no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—22no—
1545C2×C4—24no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—24no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—24no—
1562C2×C4—24no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—24no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—24no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—24no—
1589C2×C4—24no—
1590C2×C4—24no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—24no—
1600C2×C4—24no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—44no—
1615C2×C4—48no—
1616C2×C4—44no—
1617C2×C4—48no—
1618C2×C4—48no—
1619C2×C4—44no—
1620C2×C4—82no—
1621C2×C4—84no—
1622C2×C4—84no—
1623C2×C4—88no—
1624C2×C4—84no—
1625C2×C4—84no—
1626C2×C4C2×H(5,𝔽2)12yes—
1627C2×C4C2×H(5,𝔽2)14yes—
1628C2×C4C2×H(5,𝔽2)12yes—
1629C2×C4C2×H(5,𝔽2)12yes—
1630C2×C4C2×H(5,𝔽2)12yes—
1631C2×C4C2×2−1+412yes—
1632C2×C4C2×2−1+412yes—
1633C2×C4C2×2−1+412yes—
1634C2×C4C2×2−1+412yes—
1635C2×C4#58512yes—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—41no—
1643C22—42no—
1644C22—42no—
1645C22—42no—
1646C22—42no—
1647C22—41no—
1648C22—41no—
1649C22—42no—
1650C22—42no—
1651C22—41no—
1652C22—42no—
1653C22—42no—
1654C22—41no—
1655C22—42no—
1656C22—42no—
1657C22—41no—
1658C22—42no—
1659C22—42no—
1660C22—41no—
1661C22—42no—
1662C22—42no—
1663C22—816no—
1664C22#355514yes—
1665C22C22×H(5,𝔽2)11yescharacteristic
1666C22C22×H(5,𝔽2)11yescharacteristic
1667C22C22×2−1+411yescharacteristic
1668C22C22×2−1+411yescharacteristic
1669C22C2×#58511yescharacteristic
1670C22C2×#58511yescharacteristic
1671C222−1+611yescharacteristic
1672C4—22no—
1673C4—22no—
1674C4—24no—
1675C4—22no—
1676C4—41no—
1677C4—42no—
1678C4—44no—
1679C4—41no—
1680C4—42no—
1681C4—42no—
1682C4—42no—
1683C4—42no—
1684C4—41no—
1685C4—41no—
1686C4—44no—
1687C4—44no—
1688C4—42no—
1689C4—42no—
1690C4—42no—
1691C4—44no—
1692C4—41no—
1693C4—41no—
1694C4—42no—
1695C4—42no—
1696C4—41no—
1697C4—42no—
1698C4—42no—
1699C4—41no—
1700C4—42no—
1701C4#353614yes—
1702C4#354114yes—
1703C2—24no—
1704C2—81no—
1705C2—82no—
1706C2—82no—
1707C2C2×#354111yescharacteristic
1708C2C2×#353611yescharacteristic
1709C2C2×#355511yescharacteristic
1710C2#6291311yescharacteristic
1711C2#6292711yescharacteristic
1712C2#6295911yescharacteristic
1713C2#6301911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2408C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59663C2semidirect
2. #59653C2semidirect
3. #59322C2semidirect
4. #59244C2semidirect
5. #59025C2semidirect
6. #58315C2semidirect
7. #56497C2semidirect
8. #53052C2semidirect
9. #53050C2semidirect
10. #53021C2semidirect
11. #52994C2semidirect
12. #52371C2semidirect
13. #42904C2semidirect
14. #42896C2semidirect
15. #42878C2semidirect
16. #42526C2semidirect
17. #40563C2semidirect
18. #39727C2semidirect
19. #39511C2semidirect
20. #39477C2semidirect
21. #39379C2semidirect
22. #39127C2semidirect
23. #38978C2semidirect
24. #38122C2semidirect
25. #37663C2semidirect
26. #37631C2semidirect
27. #37622C2semidirect
29. #37476C2semidirect
30. #36577C2semidirect
31. #36189C2semidirect
32. #36161C2semidirect
33. C2×#2538C2semidirect
35. #34691C2semidirect
36. C2×#557C22semidirect
38. C2×#556C22semidirect
39. C2×#541C22semidirect
40. C2×#533C22semidirect
45. #2859C22semidirect
48. #2857C22semidirect
50. #2841C22semidirect
51. #2841C22semidirect
52. #2838C22semidirect
53. #2838C22semidirect
54. #2837C22semidirect
55. #2837C22semidirect
56. #2836C22semidirect
57. #2836C22semidirect
58. #2831C22semidirect
59. #2831C22semidirect
62. #2820C22semidirect
63. #2814C22semidirect
65. #2802C22semidirect
66. #2802C22semidirect
69. #2792C22semidirect
70. #2787C22semidirect
71. #2783C22semidirect
72. #2783C22semidirect
73. #2783C22semidirect
74. #2781C22semidirect
75. #2779C22semidirect
76. #2777C22semidirect
77. #2776C22semidirect
78. #2775C22semidirect
79. #2772C22semidirect
80. #2772C22semidirect
81. #2770C22semidirect
82. #2755C22semidirect
84. #2727C22semidirect
85. #2725C22semidirect
86. #2725C22semidirect
87. #2725C22semidirect
88. #2725C22semidirect
89. #2725C22semidirect
90. #2725C22semidirect
91. #2725C22semidirect
92. #2715C22semidirect
93. #2707C22semidirect
94. #2704C22semidirect
95. #2702C22semidirect
96. #2700C22semidirect
97. #2698C22semidirect
98. #2690C22semidirect
99. #2689C22semidirect
100. #2689C22semidirect
101. #2667C22semidirect
102. #2665C22semidirect
103. #2664C22semidirect
105. #2654C22semidirect
107. #2650C22semidirect
108. #2645C22semidirect
111. #2637C22semidirect
112. #2629C22semidirect
113. #2629C22semidirect
114. #2628C22semidirect
115. #2628C22semidirect
118. #2625C22semidirect
119. #2625C22semidirect
122. #2621C22semidirect
126. #2588C22semidirect
127. #2584C22semidirect
128. #2584C22semidirect
130. #2582C22semidirect
131. #2582C22semidirect
132. #2582C22semidirect
133. #2582C22semidirect
134. #2570C22semidirect
136. #2568C22semidirect
137. #2568C22semidirect
138. #2567C22semidirect
139. #2567C22semidirect
140. #2562C22semidirect
141. #2560C22semidirect
142. #2551C22semidirect
157. #2538C22semidirect
158. #2536C22semidirect
159. #2519C22semidirect
163. #2511C22semidirect
165. #2509C22semidirect
166. #2507C22semidirect
167. #2507C22semidirect
168. #2507C22semidirect
169. #2506C22semidirect
170. #2506C22semidirect
172. #2499C22semidirect
173. #2497C22semidirect
174. #2496C22semidirect
175. #2495C22semidirect
176. #2494C22semidirect
177. #2492C22semidirect
179. #2489C22semidirect
180. #2489C22semidirect
183. #2485C22semidirect
193. #2469C22semidirect
196. #2465C22semidirect
197. #2465C22semidirect
198. #2462C22semidirect
201. #2453C22semidirect
202. #2453C22semidirect
203. #2453C22semidirect
204. #2451C22semidirect
205. #2451C22semidirect
212. #2446C22semidirect
213. #2446C22semidirect
219. #2441C22semidirect
220. #2441C22semidirect
221. #2441C22semidirect
225. #2439C22semidirect
226. #2439C22semidirect
230. #2429C22semidirect
231. #2429C22semidirect
232. #2429C22semidirect
233. #2429C22semidirect
236. #2423C22semidirect
237. #2423C22semidirect
238. #2421C22semidirect
239. #2421C22semidirect
240. #2421C22semidirect
247. #2415C22semidirect
248. #2415C22semidirect
249. #2415C22semidirect
252. #2399C22semidirect
253. #2396C22semidirect
258. #2365C22semidirect
259. #2362C22semidirect
267. #2351C22semidirect
268. #2351C22semidirect
269. Q8×C4⋊C4C22semidirect
270. Q8×C4⋊C4C22semidirect
271. Q8×C4⋊C4C22semidirect
274. #2323C22semidirect
275. #2323C22semidirect
276. #2320C22semidirect
278. C4×C4⋊Q8C22semidirect
279. C4×C4⋊Q8C22semidirect
285. C4×C22⋊Q8C22semidirect
288. #2295C22semidirect
293. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#596632
#596532
#593222
#592442
#590252
#583152
#564972
#530522
#530502
#530212
#529942
#523712
#429042
#428962
#428782
#425262
#405632
#397272
#395112
#394772
#393792
#391272
#389782
#381222
#376632
#376312
#376222
#374922
#374762
#365772
#361892
#361612
C2×#25382
#347002
#346912