Finite Group Databasebeta

← #8424618

Subgroups — #8424618

Order 512.

4748 conjugacy classes of subgroups.

The subgroup lattice has 1709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59428C211yesmaximal, characteristic, complemented
2#59197C212yesmaximal, complemented
3#59148C212yesmaximal, complemented
4#59144C211yesmaximal, characteristic, complemented
5#59079C211yesmaximal, characteristic, complemented
6#58011C214yesmaximal, complemented
7#57267C214yesmaximal, complemented
8#53097C212yesmaximal, complemented
9#53037C212yesmaximal, complemented
10#53029C212yesmaximal, complemented
11#52961C212yesmaximal, complemented
12#52490C214yesmaximal, complemented
13#42721C212yesmaximal, complemented
14#42671C212yesmaximal, complemented
15#42649C212yesmaximal, complemented
16#42628C212yesmaximal, complemented
17#40760C214yesmaximal, complemented
18#39752C212yesmaximal, complemented
19#39515C211yesmaximal, characteristic, complemented
20#39350C211yesmaximal, characteristic, complemented
21#39173C211yesmaximal, characteristic, complemented
22#39154C212yesmaximal, complemented
23#39127C211yesmaximal, characteristic, complemented
24#37850C212yesmaximal, complemented
25#37696C212yesmaximal
26#37633C211yesmaximal, characteristic, complemented
27#37631C211yesmaximal, characteristic, complemented
28#37495C212yesmaximal, complemented
29#37477C212yesmaximal, complemented
30#36564C211yesmaximal, characteristic, complemented
31#36154C211yesmaximal, characteristic, complemented
32#36129C211yesmaximal, characteristic, complemented
33C2×#2547C211yesmaximal, characteristic, complemented
34#34772C211yesmaximal, characteristic, complemented
35#34700C211yesmaximal, characteristic
36C2×#557C2211yescharacteristic, complemented
37C2×#556C2212yes—
38C2×#554C2211yescharacteristic
39C2×#542C2212yes—
40C2×#533C2211yescharacteristic, complemented
41C22×C4⋊Q8C2211yescharacteristic
42C2×#529C2211yescharacteristic
43C22×#124C2212yes—
44C22×C4×D4C2211yescharacteristic
45#2862C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2212yes—
48#2857C2211yescharacteristic, complemented
49#2848C2212yes—
50#2841C2214yescomplemented
51#2841C2214yescomplemented
52#2838C2214yescomplemented
53#2837C2214yescomplemented
54#2836C2214yescomplemented
55#2836C2214yescomplemented
56#2836C2214yescomplemented
57#2834C2214yescomplemented
58#2833C2214yescomplemented
59#2831C2214yescomplemented
60#2831C2214yescomplemented
61#2830C2214yescomplemented
62#2814C2214yescomplemented
63#2814C2214yescomplemented
64#2809C2214yescomplemented
65#2806C2214yescomplemented
66#2799C2214yescomplemented
67#2799C2214yescomplemented
68#2798C2214yescomplemented
69#2798C2214yescomplemented
70#2788C2214yescomplemented
71#2787C2214yescomplemented
72#2786C2214yescomplemented
73#2772C2214yescomplemented
74#2759C2214yescomplemented
75#2747C2214yescomplemented
76#2747C2214yescomplemented
77#2744C2214yescomplemented
78#2741C2214yescomplemented
79#2739C2214yescomplemented
80#2739C2214yescomplemented
81#2738C2214yescomplemented
82#2728C2214yescomplemented
83#2725C2214yescomplemented
84#2722C2214yescomplemented
85#2722C2214yescomplemented
86#2717C2214yescomplemented
87#2715C2214yes—
88#2715C2214yes—
89#2715C2214yescomplemented
90#2715C2214yescomplemented
91#2713C2214yescomplemented
92#2712C2214yes—
93#2710C2214yes—
94#2707C2214yescomplemented
95#2700C2214yes—
96#2700C2214yes—
97#2698C2214yescomplemented
98#2690C2214yescomplemented
99#2690C2214yescomplemented
100#2689C2214yescomplemented
101#2666C2214yescomplemented
102#2659C2214yes—
103#2659C2214yescomplemented
104#2652C2214yescomplemented
105#2650C2214yescomplemented
106#2650C2214yescomplemented
107#2646C2214yes—
108#2646C2214yescomplemented
109#2645C2212yescomplemented
110#2643C2214yes—
111#2642C2212yescomplemented
112#2640C2212yes—
113#2637C2214yescomplemented
114#2629C2212yescomplemented
115#2629C2212yescomplemented
116#2629C2212yescomplemented
117#2628C2212yescomplemented
118#2628C2212yescomplemented
119#2625C2212yescomplemented
120#2625C2214yescomplemented
121#2625C2212yescomplemented
122#2621C2212yescomplemented
123#2620C2212yes—
124#2592C2212yes—
125#2586C2214yescomplemented
126#2581C2212yescomplemented
127#2581C2212yescomplemented
128#2569C2214yes—
129#2569C2214yes—
130#2568C2211yescharacteristic, complemented
131#2567C2211yescharacteristic, complemented
132#2565C2212yescomplemented
133#2565C2212yescomplemented
134#2563C2211yescharacteristic
135#2562C2212yescomplemented
136#2551C2211yescharacteristic, complemented
137#2550C2212yescomplemented
138#2550C2212yescomplemented
139#2549C2214yes—
140#2547C2211yescharacteristic
141#2547C2212yes—
142#2547C2211yescharacteristic
143#2547C2211yescharacteristic
144#2547C2212yes—
145#2547C2211yescharacteristic
146#2547C2212yes—
147#2547C2212yes—
148#2547C2212yes—
149#2547C2214yes—
150#2547C2212yescomplemented
151#2546C2211yescharacteristic, complemented
152#2546C2212yescomplemented
153#2545C2212yes—
154#2545C2212yes—
155#2538C2211yescharacteristic
156#2538C2212yescomplemented
157#2522C2212yescomplemented
158#2521C2214yes—
159#2520C2212yescomplemented
160#2514C2212yescomplemented
161#2511C2211yescharacteristic, complemented
162#2510C2214yes—
163#2507C2212yescomplemented
164#2507C2212yescomplemented
165#2507C2211yescharacteristic, complemented
166#2505C2212yes—
167#2505C2214yes—
168#2502C2211yescharacteristic
169#2498C2214yescomplemented
170#2497C2211yescharacteristic, complemented
171#2496C2212yescomplemented
172#2496C2212yescomplemented
173#2496C2212yescomplemented
174#2495C2212yescomplemented
175#2494C2212yescomplemented
176#2494C2212yescomplemented
177#2493C2214yescomplemented
178#2492C2212yescomplemented
179#2492C2211yescharacteristic, complemented
180#2492C2212yescomplemented
181#2489C2212yescomplemented
182#2489C2212yescomplemented
183#2487C2212yes—
184#2487C2211yescharacteristic
185#2486C2212yescomplemented
186#2485C2212yescomplemented
187#2485C2212yescomplemented
188#2480C2214yes—
189#2480C2214yes—
190#2480C2212yes—
191#2480C2214yes—
192#2478C2214yescomplemented
193#2474C2214yes—
194#2473C2214yes—
195#2472C2214yes—
196#2468C2212yes—
197#2457C2212yes—
198#2454C2212yes—
199#2454C2211yescharacteristic
200#2453C2212yescomplemented
201#2453C2212yescomplemented
202#2451C2212yescomplemented
203#2451C2212yescomplemented
204#2451C2212yescomplemented
205#2451C2212yescomplemented
206#2451C2212yescomplemented
207#2450C2212yes—
208#2450C2214yes—
209#2448C2212yes—
210#2448C2212yes—
211#2447C2212yes—
212#2447C2212yes—
213#2447C2211yescharacteristic
214#2446C2212yescomplemented
215#2446C2212yescomplemented
216#2446C2212yescomplemented
217#2442C2212yes—
218#2442C2212yes—
219#2442C2212yes—
220#2442C2211yescharacteristic
221#2442C2212yescomplemented
222#2442C2212yescomplemented
223#2442C2212yescomplemented
224#2440C2211yescharacteristic
225#2440C2212yes—
226#2440C2212yescomplemented
227#2440C2212yescomplemented
228#2439C2212yescomplemented
229#2437C2214yes—
230#2437C2214yes—
231#2437C2214yes—
232#2435C2211yescharacteristic
233#2434C2212yes—
234#2429C2212yescomplemented
235#2429C2212yescomplemented
236#2427C2212yes—
237#2427C2211yescharacteristic
238#2426C2212yes—
239#2421C2212yescomplemented
240#2421C2212yescomplemented
241#2421C2214yescomplemented
242#2420C2211yescharacteristic
243#2418C2212yes—
244#2417C2212yes—
245#2417C2212yes—
246#2417C2211yescharacteristic
247#2417C2211yescharacteristic
248#2415C2212yescomplemented
249#2412C2214yes—
250#2409C2212yes—
251#2408C2211yescharacteristic
252#2402C2212yescomplemented
253#2396C2212yescomplemented
254#2395C2212yes—
255#2392C2212yes—
256C2×#397C2214yes—
257#2369C2211yescharacteristic, complemented
258#2369C2212yescomplemented
259#2367C2212yes—
260#2365C2211yescharacteristic, complemented
261#2360C2212yes—
262#2360C2212yes—
263#2352C2212yes—
264#2352C2212yescomplemented
265Q8×C4⋊C4C2211yescharacteristic, complemented
266#2349C2212yes—
267D4×C4⋊C4C2211yescharacteristic
268#2345C2212yes—
269#2344C2212yescomplemented
270#2342C2214yes—
271Q8×C22⋊C4C2212yes—
272Q8×C22⋊C4C2212yes—
273D4×C22⋊C4C2212yes—
274#2329C2214yes—
275#2326C2212yes—
276#2323C2212yescomplemented
277#2314C2212yescomplemented
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×C4⋊Q8C2211yescharacteristic, complemented
280C4×#124C2211yescharacteristic
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2212yes—
284C4×C22⋊Q8C2212yes—
285C4×C22⋊Q8C2211yescharacteristic, complemented
286C4×#121C2211yescharacteristic
287C4×#120C2212yes—
288#2295C2211yescharacteristic, complemented
289C2×#391C2212yes—
290#2293C2211yescharacteristic
291#2290C2212yes—
292#2285C2211yescharacteristic, complemented
293#2280C2212yes—
294C2×#380C2212yes—
295C2×#380C2212yes—
296C2×#380C2212yes—
297C42×D4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C23×Q8C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#557—44no—
303#556—48no—
304#554—44no—
305#542—48no—
306#533—44no—
307C2×C4⋊Q8—44no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319#529—44no—
320C2×#126C2312yes—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#125C2312yes—
325C2×#125C2311yescharacteristic
326C2×#125C2312yes—
327C2×#125C2312yes—
328C2×#125C2314yes—
329C2×#124—48no—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2311yescharacteristic
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2314yes—
336C2×#124C2314yes—
337C2×#124C2311yescharacteristic
338C2×#124C2314yes—
339C2×#123C2314yes—
340C2×#123C2312yes—
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2311yescharacteristic
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2314yes—
356C2×#121C2311yescharacteristic
357C2×#121C2311yescharacteristic
358C2×#120C2312yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×D4—44no—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2312yes—
382C2×C4×D4C2311yescharacteristic
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2314yes—
386C2×#117C2312yes—
387C2×#117C2312yes—
388C22×C4⋊C4C2311yescharacteristic
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2311yescharacteristic
395C22×C22⋊C4C2314yes—
396C22×C22⋊C4C2314yes—
397C22×C22⋊C4C2312yes—
398C22×C22⋊C4C2314yes—
399C22×C42C2311yescharacteristic
400C22×C42C2311yescharacteristic
401C22×C42C2312yes—
402#401C2314yes—
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#400C2314yes—
418#400C2314yes—
419#400C2312yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2312yes—
425#400C2314yes—
426#400C2312yes—
427#400C2312yes—
428#400C2312yes—
429#399C2312yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#399C2312yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2312yes—
446#398C2314yes—
447#398C2314yes—
448#398C2312yes—
449#398C2314yes—
450#398C2314yes—
451#398C2312yes—
452#398C2314yes—
453#398C2314yes—
454#398C2312yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2312yes—
462#398C2312yes—
463#398C2312yes—
464#398C2312yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2312yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2312yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2312yes—
485#397C2314yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2314yes—
490#397C2314yes—
491#397C2314yes—
492#397C2314yes—
493#397C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2312yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2314yes—
504#396C2312yes—
505#396C2314yes—
506#396C2314yes—
507#396C2312yes—
508#396C2312yes—
509#395C2314yes—
510#395C2314yes—
511#395C2314yes—
512#395C2314yes—
513#395C2314yes—
514#395C2314yes—
515#395C2314yes—
516#395C2314yes—
517#395C2314yes—
518#395C2312yes—
519#395C2314yes—
520#394C2314yes—
521#394C2312yes—
522#394C2314yes—
523#394C2314yes—
524#394C2312yes—
525#394C2312yes—
526#394C2312yes—
527#394C2312yes—
528#394C2314yes—
529#393C2314yes—
530#393C2312yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#392C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#391C2312yes—
545#391C2312yes—
546#391C2314yes—
547#391C2314yes—
548#391C2311yescharacteristic
549#391C2312yes—
550#391C2312yes—
551#391C2312yes—
552#391C2314yes—
553#391C2314yes—
554#391C2312yes—
555#391C2314yes—
556#391C2314yes—
557#391C2312yes—
558#391C2312yes—
559#391C2314yes—
560#391C2314yes—
561#391C2314yes—
562#391C2314yes—
563#391C2312yes—
564#391C2312yes—
565#391C2311yescharacteristic
566#391C2311yescharacteristic
567#391C2314yes—
568#391C2311yescharacteristic
569#391C2311yescharacteristic
570#391C2311yescharacteristic
571#391C2312yes—
572#390C2312yes—
573#390C2314yes—
574#390C2311yescharacteristic
575#390C2311yescharacteristic
576#390C2312yes—
577#390C2311yescharacteristic
578#390C2311yescharacteristic
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2312yes—
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2314yes—
588#389C2314yes—
589#389C2314yes—
590#389C2314yes—
591#389C2311yescharacteristic
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2314yes—
596#389C2314yes—
597#389C2314yes—
598#389C2314yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2314yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2311yescharacteristic
611#389C2311yescharacteristic
612#389C2311yescharacteristic
613#389C2311yescharacteristic
614#389C2311yescharacteristic
615#389C2311yescharacteristic
616#389C2312yes—
617#389C2311yescharacteristic
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2312yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2312yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2312yes—
638#388C2312yes—
639#388C2314yes—
640#388C2312yes—
641#388C2312yes—
642#388C2312yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2312yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2312yes—
669#387C2314yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2312yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#386C2312yes—
683#386C2312yes—
684#386C2312yes—
685#385C2312yes—
686#385C2312yes—
687#385C2312yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2312yes—
701#385C2314yes—
702#385C2314yes—
703#385C2312yes—
704#385C2312yes—
705#385C2312yes—
706#385C2312yes—
707#385C2312yes—
708#385C2312yes—
709#384C2311yescharacteristic
710#384C2311yescharacteristic
711#384C2312yes—
712#384C2312yes—
713#384C2311yescharacteristic
714#384C2311yescharacteristic
715#383C2314yes—
716#382C2312yes—
717#382C2311yescharacteristic
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2312yes—
722#382C2314yes—
723#381C2312yes—
724#381C2312yes—
725#381C2314yes—
726#381C2314yes—
727#380C2311yescharacteristic
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2314yes—
734#380C2312yes—
735#380C2314yes—
736#380C2314yes—
737#380C2314yes—
738#380C2312yes—
739#380C2314yes—
740#380C2314yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2311yescharacteristic
745#380C2314yes—
746#380C2312yes—
747#380C2312yes—
748#380C2314yes—
749#380C2311yescharacteristic
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2312yes—
755#380C2314yes—
756#380C2312yes—
757#380C2314yes—
758#380C2314yes—
759#380C2312yes—
760#380C2311yescharacteristic
761#380C2312yes—
762#380C2312yes—
763#380C2311yescharacteristic
764#380C2312yes—
765#380C2314yes—
766#380C2314yes—
767#380C2311yescharacteristic
768#379C2314yes—
769#379C2312yes—
770#379C2312yes—
771#379C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2311yescharacteristic
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813#376C2312yes—
814C2×#95C2314yes—
815C2×#95C2314yes—
816C2×#95C2314yes—
817C2×#95C2312yes—
818C43C2311yescharacteristic
819C25C2412yes—
820C22×Q8—28no—
821C22×Q8—44no—
822C22×Q8—44no—
823C22×Q8C2411yescharacteristic
824C22×Q8C2411yescharacteristic
825C22×Q8C2412yes—
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2414yes—
829C22×Q8C2412yes—
830C22×Q8C2414yes—
831C22×D4—24no—
832C22×D4—24no—
833C22×D4—42no—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2412yes—
840C23×C4—28no—
841C23×C4—44no—
842C23×C4—44no—
843C23×C4C2412yes—
844C23×C4C2411yescharacteristic
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2414yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2414yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2411yescharacteristic
858C23×C4C2414yes—
859C4⋊Q8—24no—
860C4⋊Q8—24no—
861C4⋊Q8—24no—
862C4⋊Q8—44no—
863C4⋊Q8—44no—
864C4⋊Q8—42no—
865C4⋊Q8—44no—
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870#126—44no—
871#126—48no—
872#126—48no—
873#126—48no—
874#125—42no—
875#125—44no—
876#125—44no—
877#125—44no—
878#125—48no—
879#124—28no—
880#124—28no—
881#124—24no—
882#124—44no—
883#124—44no—
884#124—42no—
885#124—48no—
886#124—48no—
887#124—48no—
888#123—44no—
889#123—48no—
890C22⋊Q8—24no—
891C22⋊Q8—24no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894C22⋊Q8—48no—
895C22⋊Q8—48no—
896C22⋊Q8—48no—
897C22⋊Q8—48no—
898C22⋊Q8—44no—
899C22⋊Q8—42no—
900C22⋊Q8—42no—
901C22⋊Q8—44no—
902C22⋊Q8—44no—
903C22⋊Q8—44no—
904C22⋊Q8—44no—
905#121—24no—
906#121—42no—
907#120—44no—
908C4×Q8—24no—
909C4×Q8—24no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×Q8—44no—
914C4×Q8—44no—
915C4×Q8—44no—
916C4×Q8—44no—
917C4×Q8—44no—
918C4×D4—28no—
919C4×D4—24no—
920C4×D4—24no—
921C4×D4—24no—
922C4×D4—24no—
923C4×D4—44no—
924C4×D4—42no—
925C4×D4—42no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—42no—
931#117—44no—
932#117—44no—
933#117—44no—
934#117—48no—
935#117—44no—
936C2×C4⋊C4—24no—
937C2×C4⋊C4—44no—
938C2×C4⋊C4—42no—
939C2×C4⋊C4—42no—
940C2×C4⋊C4—44no—
941C2×C4⋊C4—44no—
942C2×C4⋊C4—44no—
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2411yescharacteristic
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C22⋊C4—44no—
1020C2×C22⋊C4—48no—
1021C2×C22⋊C4—48no—
1022C2×C22⋊C4—48no—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C42—24no—
1075C2×C42—24no—
1076C2×C42—44no—
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2412yes—
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2411yescharacteristic
1093C2×C42C2414yes—
1094C2×C42C2414yes—
1095C2×C42C2414yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2411yescharacteristic
1102C2×C42C2414yes—
1103C2×C42C2411yescharacteristic
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
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#95C2412yes—
1136#95C2412yes—
1137#95C2414yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182C24—24no—
1183C24—24no—
1184C24—24no—
1185C24—24no—
1186C24—42no—
1187C24—42no—
1188C24—42no—
1189C24C2512yes—
1190C24C2511yescharacteristic
1191C24C2512yes—
1192C24C2511yescharacteristic
1193C2×Q8—22no—
1194C2×Q8—22no—
1195C2×Q8—22no—
1196C2×Q8—24no—
1197C2×Q8—24no—
1198C2×Q8—24no—
1199C2×Q8—24no—
1200C2×Q8—24no—
1201C2×Q8—22no—
1202C2×Q8—22no—
1203C2×Q8—24no—
1204C2×Q8—24no—
1205C2×Q8—28no—
1206C2×Q8—22no—
1207C2×Q8—42no—
1208C2×Q8—42no—
1209C2×Q8—42no—
1210C2×Q8—44no—
1211C2×Q8—44no—
1212C2×Q8—42no—
1213C2×Q8—42no—
1214C2×Q8—44no—
1215C2×Q8—44no—
1216C2×Q8—44no—
1217C2×Q8—816no—
1218C2×D4—24no—
1219C2×D4—22no—
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—24no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—22no—
1229C2×D4—416no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—42no—
1234C2×D4—42no—
1235C2×D4—42no—
1236C2×D4H(5,𝔽2)14yes—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—28no—
1243C22×C4—24no—
1244C22×C4—24no—
1245C22×C4—28no—
1246C22×C4—24no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—24no—
1251C22×C4—22no—
1252C22×C4—24no—
1253C22×C4—22no—
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—41no—
1264C22×C4—42no—
1265C22×C4—42no—
1266C22×C4—44no—
1267C22×C4—42no—
1268C22×C4—44no—
1269C22×C4—44no—
1270C22×C4—44no—
1271C22×C4—42no—
1272C22×C4—42no—
1273C22×C4—42no—
1274C22×C4—41no—
1275C22×C4—42no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—41no—
1279C22×C4—42no—
1280C22×C4—44no—
1281C22×C4—44no—
1282C22×C4—44no—
1283C22×C4—816no—
1284C22×C42−1+414yes—
1285C22×C42−1+414yes—
1286C22×C4C2511yescharacteristic
1287C22×C4C2511yescharacteristic
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2512yes—
1291C22×C4C2512yes—
1292C22×C4C2512yes—
1293C22×C4C2511yescharacteristic
1294C22×C4C2511yescharacteristic
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2514yes—
1299C22×C4C2512yes—
1300C22×C4C2514yes—
1301C22×C4C2514yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2511yescharacteristic
1305C22×C4C2512yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2511yescharacteristic
1308C22×C4C2512yes—
1309C22×C4C2514yes—
1310C22×C4C2512yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2511yescharacteristic
1317C4⋊C4—22no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—22no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—24no—
1327C4⋊C4—22no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—22no—
1331C4⋊C4—24no—
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—24no—
1343C4⋊C4—22no—
1344C4⋊C4—42no—
1345C4⋊C4—44no—
1346C4⋊C4—42no—
1347C4⋊C4—44no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—42no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—44no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—44no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—41no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C22⋊C4—28no—
1394C22⋊C4—28no—
1395C22⋊C4—28no—
1396C22⋊C4—28no—
1397C22⋊C4—24no—
1398C22⋊C4—28no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—28no—
1407C22⋊C4—22no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—24no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—44no—
1414C22⋊C4—44no—
1415C22⋊C4—42no—
1416C22⋊C4—42no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—44no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—41no—
1436C22⋊C4—44no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C42—22no—
1445C42—22no—
1446C42—22no—
1447C42—22no—
1448C42—22no—
1449C42—22no—
1450C42—24no—
1451C42—24no—
1452C42—24no—
1453C42—24no—
1454C42—24no—
1455C42—22no—
1456C42—22no—
1457C42—22no—
1458C42—22no—
1459C42—24no—
1460C42—42no—
1461C42—42no—
1462C42—41no—
1463C42—44no—
1464C42—44no—
1465C42—44no—
1466C42—44no—
1467C42—41no—
1468C42—44no—
1469C42—44no—
1470C42H(5,𝔽2)14yes—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—22no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—22no—
1482C23—21no—
1483C23—22no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—22no—
1488C23—22no—
1489C23—22no—
1490C23—22no—
1491C23—21no—
1492C23—21no—
1493C23—22no—
1494C23—21no—
1495C23—48no—
1496C23—48no—
1497C23—48no—
1498C23—48no—
1499C23—84no—
1500C23—84no—
1501C23—84no—
1502C23C2×H(5,𝔽2)14yes—
1503C23C2×2−1+412yes—
1504C23C2×2−1+412yes—
1505C23#58512yes—
1506C23C2611yescharacteristic
1507Q8—44no—
1508Q8—48no—
1509Q8—48no—
1510Q8—44no—
1511Q8—84no—
1512Q8—88no—
1513Q8—84no—
1514Q8—164no—
1515D4—28no—
1516D4—48no—
1517D4—44no—
1518D4—44no—
1519D4—84no—
1520D4—84no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—28no—
1528C2×C4—28no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—21no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—24no—
1547C2×C4—22no—
1548C2×C4—24no—
1549C2×C4—24no—
1550C2×C4—24no—
1551C2×C4—24no—
1552C2×C4—24no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—24no—
1571C2×C4—24no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—24no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—24no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—24no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—44no—
1608C2×C4—44no—
1609C2×C4—44no—
1610C2×C4—48no—
1611C2×C4—48no—
1612C2×C4—82no—
1613C2×C4—84no—
1614C2×C4—84no—
1615C2×C4—88no—
1616C2×C4—84no—
1617C2×C4—84no—
1618C2×C4—84no—
1619C2×C4—88no—
1620C2×C4—164no—
1621C2×C4C2×H(5,𝔽2)12yes—
1622C2×C4C2×H(5,𝔽2)12yes—
1623C2×C4C2×H(5,𝔽2)12yes—
1624C2×C4C2×H(5,𝔽2)12yes—
1625C2×C4C2×2−1+412yes—
1626C2×C4C2×2−1+412yes—
1627C2×C4C2×2−1+412yes—
1628C2×C4C2×2−1+412yes—
1629C2×C4#58512yes—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—24no—
1637C22—24no—
1638C22—24no—
1639C22—42no—
1640C22—42no—
1641C22—42no—
1642C22—42no—
1643C22—41no—
1644C22—42no—
1645C22—42no—
1646C22—41no—
1647C22—41no—
1648C22—42no—
1649C22—41no—
1650C22—42no—
1651C22—41no—
1652C22—42no—
1653C22—41no—
1654C22—42no—
1655C22—41no—
1656C22—42no—
1657C22—816no—
1658C22#355514yes—
1659C22C22×H(5,𝔽2)11yescharacteristic
1660C22C22×H(5,𝔽2)11yescharacteristic
1661C22C22×2−1+411yescharacteristic
1662C22C22×2−1+411yescharacteristic
1663C22C2×#58511yescharacteristic
1664C22C2×#58511yescharacteristic
1665C222−1+611yescharacteristic
1666C4—22no—
1667C4—22no—
1668C4—22no—
1669C4—41no—
1670C4—44no—
1671C4—44no—
1672C4—42no—
1673C4—41no—
1674C4—42no—
1675C4—42no—
1676C4—42no—
1677C4—41no—
1678C4—42no—
1679C4—42no—
1680C4—44no—
1681C4—42no—
1682C4—42no—
1683C4—41no—
1684C4—41no—
1685C4—42no—
1686C4—42no—
1687C4—42no—
1688C4—41no—
1689C4—42no—
1690C4—41no—
1691C4—41no—
1692C4—42no—
1693C4—44no—
1694C4—42no—
1695C4#353614yes—
1696C4#356114yes—
1697C2—24no—
1698C2—44no—
1699C2—81no—
1700C2—82no—
1701C2C2×#353611yescharacteristic
1702C2C2×#356111yescharacteristic
1703C2C2×#355511yescharacteristic
1704C2#6291511yescharacteristic
1705C2#6293211yescharacteristic
1706C2#6295411yescharacteristic
1707C2#6301811yescharacteristic
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. #59428C2semidirect
2. #59197C2semidirect
3. #59148C2semidirect
4. #59144C2semidirect
5. #59079C2semidirect
6. #58011C2semidirect
7. #57267C2semidirect
8. #53097C2semidirect
9. #53037C2semidirect
10. #53029C2semidirect
11. #52961C2semidirect
12. #52490C2semidirect
13. #42721C2semidirect
14. #42671C2semidirect
15. #42649C2semidirect
16. #42628C2semidirect
17. #40760C2semidirect
18. #39752C2semidirect
19. #39515C2semidirect
20. #39350C2semidirect
21. #39173C2semidirect
22. #39154C2semidirect
23. #39127C2semidirect
24. #37850C2semidirect
26. #37633C2semidirect
27. #37631C2semidirect
28. #37495C2semidirect
29. #37477C2semidirect
30. #36564C2semidirect
31. #36154C2semidirect
32. #36129C2semidirect
33. C2×#2547C2semidirect
34. #34772C2semidirect
36. C2×#557C22semidirect
40. C2×#533C22semidirect
45. #2862C22semidirect
48. #2857C22semidirect
50. #2841C22semidirect
51. #2841C22semidirect
52. #2838C22semidirect
53. #2837C22semidirect
54. #2836C22semidirect
55. #2836C22semidirect
56. #2836C22semidirect
57. #2834C22semidirect
58. #2833C22semidirect
59. #2831C22semidirect
60. #2831C22semidirect
61. #2830C22semidirect
62. #2814C22semidirect
63. #2814C22semidirect
64. #2809C22semidirect
65. #2806C22semidirect
66. #2799C22semidirect
67. #2799C22semidirect
68. #2798C22semidirect
69. #2798C22semidirect
70. #2788C22semidirect
71. #2787C22semidirect
72. #2786C22semidirect
73. #2772C22semidirect
74. #2759C22semidirect
75. #2747C22semidirect
76. #2747C22semidirect
77. #2744C22semidirect
78. #2741C22semidirect
79. #2739C22semidirect
80. #2739C22semidirect
81. #2738C22semidirect
82. #2728C22semidirect
83. #2725C22semidirect
84. #2722C22semidirect
85. #2722C22semidirect
86. #2717C22semidirect
89. #2715C22semidirect
90. #2715C22semidirect
91. #2713C22semidirect
94. #2707C22semidirect
97. #2698C22semidirect
98. #2690C22semidirect
99. #2690C22semidirect
100. #2689C22semidirect
101. #2666C22semidirect
103. #2659C22semidirect
104. #2652C22semidirect
105. #2650C22semidirect
106. #2650C22semidirect
108. #2646C22semidirect
109. #2645C22semidirect
111. #2642C22semidirect
113. #2637C22semidirect
114. #2629C22semidirect
115. #2629C22semidirect
116. #2629C22semidirect
117. #2628C22semidirect
118. #2628C22semidirect
119. #2625C22semidirect
120. #2625C22semidirect
121. #2625C22semidirect
122. #2621C22semidirect
125. #2586C22semidirect
126. #2581C22semidirect
127. #2581C22semidirect
130. #2568C22semidirect
131. #2567C22semidirect
132. #2565C22semidirect
133. #2565C22semidirect
135. #2562C22semidirect
136. #2551C22semidirect
137. #2550C22semidirect
138. #2550C22semidirect
150. #2547C22semidirect
151. #2546C22semidirect
152. #2546C22semidirect
156. #2538C22semidirect
157. #2522C22semidirect
159. #2520C22semidirect
160. #2514C22semidirect
161. #2511C22semidirect
163. #2507C22semidirect
164. #2507C22semidirect
165. #2507C22semidirect
169. #2498C22semidirect
170. #2497C22semidirect
171. #2496C22semidirect
172. #2496C22semidirect
173. #2496C22semidirect
174. #2495C22semidirect
175. #2494C22semidirect
176. #2494C22semidirect
177. #2493C22semidirect
178. #2492C22semidirect
179. #2492C22semidirect
180. #2492C22semidirect
181. #2489C22semidirect
182. #2489C22semidirect
185. #2486C22semidirect
186. #2485C22semidirect
187. #2485C22semidirect
192. #2478C22semidirect
200. #2453C22semidirect
201. #2453C22semidirect
202. #2451C22semidirect
203. #2451C22semidirect
204. #2451C22semidirect
205. #2451C22semidirect
206. #2451C22semidirect
214. #2446C22semidirect
215. #2446C22semidirect
216. #2446C22semidirect
221. #2442C22semidirect
222. #2442C22semidirect
223. #2442C22semidirect
226. #2440C22semidirect
227. #2440C22semidirect
228. #2439C22semidirect
234. #2429C22semidirect
235. #2429C22semidirect
239. #2421C22semidirect
240. #2421C22semidirect
241. #2421C22semidirect
248. #2415C22semidirect
252. #2402C22semidirect
253. #2396C22semidirect
257. #2369C22semidirect
258. #2369C22semidirect
260. #2365C22semidirect
264. #2352C22semidirect
265. Q8×C4⋊C4C22semidirect
269. #2344C22semidirect
276. #2323C22semidirect
277. #2314C22semidirect
278. C4×C4⋊Q8C22semidirect
279. C4×C4⋊Q8C22semidirect
285. C4×C22⋊Q8C22semidirect
288. #2295C22semidirect
292. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#594282
#591972
#591482
#591442
#590792
#580112
#572672
#530972
#530372
#530292
#529612
#524902
#427212
#426712
#426492
#426282
#407602
#397522
#395152
#393502
#391732
#391542
#391272
#378502
#376962
#376332
#376312
#374952
#374772
#365642
#361542
#361292
C2×#25472
#347722
#347002