Finite Group Databasebeta

← #7710224

Subgroups — #7710224

Order 512.

4800 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#59655C211yesmaximal, characteristic, complemented
2#59653C211yesmaximal, characteristic, complemented
3#59428C211yesmaximal, characteristic, complemented
4#59426C211yesmaximal, characteristic, complemented
5#59325C212yesmaximal, complemented
6#59148C212yesmaximal
7#46174C212yesmaximal, complemented
8#46055C212yesmaximal, complemented
9#45579C214yesmaximal, complemented
10#40105C212yesmaximal, complemented
11#40080C212yesmaximal, complemented
12#39216C212yesmaximal, complemented
13#39173C211yesmaximal, characteristic, complemented
14#39172C211yesmaximal, characteristic, complemented
15#39026C212yesmaximal, complemented
16#38978C211yesmaximal, characteristic, complemented
17#38977C211yesmaximal, characteristic, complemented
18#38613C214yesmaximal, complemented
19#38172C214yesmaximal, complemented
20#38057C212yesmaximal, complemented
21#38054C212yesmaximal
22#37581C212yesmaximal, complemented
23#37101C214yesmaximal, complemented
24#36635C211yesmaximal, characteristic, complemented
25#36635C211yesmaximal, characteristic, complemented
26#36545C211yesmaximal, characteristic, complemented
27Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
28#36204C212yesmaximal, complemented
29#36167C212yesmaximal, complemented
30#36161C211yesmaximal, characteristic
31#36154C211yesmaximal, characteristic
32#35086C212yesmaximal, complemented
33#35079C212yesmaximal, complemented
34#34499C212yesmaximal, complemented
35C2×C4×#124C211yesmaximal, characteristic
36C2×Q82C2211yescharacteristic, complemented
37C2×#557C2211yescharacteristic, complemented
38C2×#556C2212yes—
39C2×#556C2211yescharacteristic
40C2×#554C2211yescharacteristic
41C22×#124C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44#2864C2212yescomplemented
45#2864C2212yescomplemented
46#2863C2211yescharacteristic, complemented
47#2863C2211yescharacteristic, complemented
48#2863C2212yescomplemented
49#2863C2212yescomplemented
50#2863C2212yescomplemented
51#2862C2211yescharacteristic, complemented
52#2862C2211yescharacteristic, complemented
53#2859C2211yescharacteristic, complemented
54#2859C2211yescharacteristic, complemented
55#2857C2211yescharacteristic
56#2857C2212yes—
57#2857C2211yescharacteristic
58#2857C2211yescharacteristic
59#2857C2211yescharacteristic
60#2855C2212yes—
61#2855C2212yes—
62#2855C2211yescharacteristic
63#2855C2211yescharacteristic
64#2855C2212yes—
65#2851C2212yes—
66#2851C2212yes—
67#2851C2212yes—
68#2848C2212yes—
69#2848C2212yes—
70#2838C2214yescomplemented
71#2831C2214yescomplemented
72#2793C2214yescomplemented
73#2783C2214yescomplemented
74#2777C2214yescomplemented
75#2774C2214yescomplemented
76#2773C2214yescomplemented
77#2772C2214yescomplemented
78#2770C2214yescomplemented
79#2765C2214yescomplemented
80#2762C2214yescomplemented
81#2762C2214yescomplemented
82#2761C2214yes—
83#2759C2214yescomplemented
84#2758C2214yescomplemented
85#2757C2214yes—
86#2755C2214yescomplemented
87#2755C2214yescomplemented
88#2745C2214yescomplemented
89#2744C2214yescomplemented
90#2739C2214yescomplemented
91#2737C2214yes—
92#2729C2214yescomplemented
93#2725C2214yescomplemented
94#2723C2214yes—
95#2721C2214yescomplemented
96#2716C2214yescomplemented
97#2716C2214yescomplemented
98#2715C2214yes—
99#2700C2214yes—
100#2690C2214yescomplemented
101#2690C2214yescomplemented
102#2690C2214yescomplemented
103#2689C2214yescomplemented
104#2667C2214yescomplemented
105#2665C2214yescomplemented
106#2654C2214yescomplemented
107#2652C2214yescomplemented
108#2652C2214yescomplemented
109#2650C2214yescomplemented
110#2645C2212yescomplemented
111#2644C2212yes—
112#2642C2212yescomplemented
113#2640C2212yes—
114#2592C2212yes—
115#2584C2212yescomplemented
116#2582C2211yescharacteristic, complemented
117#2582C2211yescharacteristic, complemented
118#2582C2212yescomplemented
119#2581C2212yescomplemented
120#2581C2212yescomplemented
121#2577C2214yescomplemented
122#2573C2214yescomplemented
123#2569C2214yes—
124#2568C2212yescomplemented
125#2567C2211yescharacteristic, complemented
126#2567C2212yescomplemented
127#2565C2212yescomplemented
128#2563C2211yescharacteristic
129#2561C2214yes—
130#2550C2212yescomplemented
131#2549C2214yes—
132#2547C2212yes—
133#2547C2211yescharacteristic
134#2546C2211yescharacteristic, complemented
135#2545C2212yes—
136#2545C2212yes—
137#2538C2211yescharacteristic
138#2538C2211yescharacteristic
139#2530C2214yescomplemented
140#2527C2214yescomplemented
141#2523C2214yescomplemented
142#2521C2214yes—
143#2520C2214yescomplemented
144#2519C2214yescomplemented
145#2514C2212yescomplemented
146#2512C2212yes—
147#2509C2212yescomplemented
148#2508C2214yescomplemented
149#2508C2212yescomplemented
150#2505C2214yes—
151#2505C2214yes—
152#2505C2214yes—
153#2503C2212yescomplemented
154#2499C2212yescomplemented
155#2496C2212yescomplemented
156#2496C2212yescomplemented
157#2496C2212yescomplemented
158#2495C2212yescomplemented
159#2494C2212yescomplemented
160#2494C2212yescomplemented
161#2493C2214yes—
162#2493C2214yes—
163#2493C2214yescomplemented
164#2492C2212yescomplemented
165#2489C2212yescomplemented
166#2489C2212yescomplemented
167#2489C2212yescomplemented
168#2487C2212yes—
169#2485C2212yes—
170#2483C2214yes—
171#2480C2214yes—
172#2480C2214yes—
173#2480C2214yes—
174#2480C2214yes—
175#2478C2214yescomplemented
176#2474C2214yes—
177#2473C2214yes—
178#2469C2214yescomplemented
179#2466C2214yes—
180#2462C2214yescomplemented
181#2454C2212yes—
182#2453C2212yescomplemented
183#2452C2212yes—
184#2451C2212yescomplemented
185#2451C2214yescomplemented
186#2450C2214yes—
187#2448C2212yes—
188#2448C2212yes—
189#2447C2212yes—
190#2447C2212yes—
191#2447C2212yes—
192#2446C2212yescomplemented
193#2446C2212yescomplemented
194#2446C2212yescomplemented
195#2442C2212yes—
196#2442C2212yescomplemented
197#2442C2212yescomplemented
198#2442C2212yescomplemented
199#2441C2212yescomplemented
200#2441C2212yescomplemented
201#2440C2214yes—
202#2440C2212yes—
203#2440C2212yescomplemented
204#2440C2212yescomplemented
205#2439C2212yescomplemented
206#2439C2212yescomplemented
207#2439C2212yescomplemented
208#2437C2214yes—
209#2437C2214yes—
210#2437C2214yes—
211#2435C2212yes—
212#2434C2212yes—
213#2429C2212yescomplemented
214#2429C2212yescomplemented
215#2429C2214yescomplemented
216#2421C2212yescomplemented
217#2421C2212yescomplemented
218#2421C2212yescomplemented
219#2421C2212yescomplemented
220#2417C2212yes—
221#2415C2212yes—
222#2383C2214yescomplemented
223#2378C2214yescomplemented
224#2373C2214yescomplemented
225#2368C2214yes—
226#2367C2212yes—
227#2367C2212yes—
228#2365C2212yescomplemented
229#2362C2212yescomplemented
230#2360C2212yes—
231#2360C2212yes—
232#2360C2212yescomplemented
233#2355C2211yescharacteristic, complemented
234#2355C2212yescomplemented
235#2354C2211yescharacteristic
236#2351C2212yescomplemented
237Q8×C4⋊C4C2211yescharacteristic, complemented
238Q8×C4⋊C4C2212yescomplemented
239#2349C2212yes—
240D4×C4⋊C4C2211yescharacteristic
241#2347C2212yescomplemented
242#2344C2212yescomplemented
243#2343C2214yescomplemented
244#2342C2214yes—
245Q8×C22⋊C4C2212yes—
246D4×C22⋊C4C2212yes—
247#2334C2214yescomplemented
248#2334C2214yescomplemented
249#2334C2214yescomplemented
250#2329C2214yescomplemented
251#2329C2214yescomplemented
252#2327C2212yescomplemented
253#2326C2212yes—
254#2320C2212yescomplemented
255#2319C2212yes—
256#2314C2214yescomplemented
257C4×C4⋊Q8C2211yescharacteristic, complemented
258C4×C4⋊Q8C2211yescharacteristic, complemented
259C4×C4⋊Q8C2211yescharacteristic, complemented
260C4×C4⋊Q8C2211yescharacteristic, complemented
261C4×#125C2212yescomplemented
262C4×#125C2212yescomplemented
263C4×#124C2211yescharacteristic
264C4×#124C2211yescharacteristic
265C4×#124C2211yescharacteristic
266C4×#124C2211yescharacteristic
267C4×#124C2212yes—
268C4×#124C2212yes—
269C4×#124C2211yescharacteristic
270C4×#124C2211yescharacteristic
271C4×#124C2211yescharacteristic
272C4×#124C2211yescharacteristic
273C4×#124C2212yes—
274C4×#124C2212yes—
275C4×C22⋊Q8C2212yes—
276C4×C22⋊Q8C2212yes—
277C4×C22⋊Q8C2212yes—
278C4×C22⋊Q8C2212yes—
279C4×C22⋊Q8C2212yes—
280C4×C22⋊Q8C2211yescharacteristic
281C4×C22⋊Q8C2211yescharacteristic
282#2295C2211yescharacteristic, complemented
283#2295C2211yescharacteristic, complemented
284#2295C2212yescomplemented
285#2295C2212yescomplemented
286#2295C2212yescomplemented
287C2×#391C2211yescharacteristic
288C2×#390C2211yescharacteristic
289C2×#388C2212yes—
290C2×#388C2212yes—
291#2283C2212yes—
292#2283C2212yes—
293C2×#382C2211yescharacteristic
294#2280C2212yes—
295C2×#380C2212yes—
296C2×C4×C22⋊C4C2212yes—
297C2×C4×C22⋊C4C2212yes—
298C2×C43C2211yescharacteristic
299C23×Q8C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302Q82—44no—
303#557—44no—
304#556—216no—
305#556—44no—
306#554—44no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2314yes—
316C2×#126C2314yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2312yes—
324C2×#125C2314yes—
325C2×#124—28no—
326C2×#124C2312yes—
327C2×#124C2311yescharacteristic
328C2×#124C2312yes—
329C2×#124C2311yescharacteristic
330C2×#124C2311yescharacteristic
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2311yescharacteristic
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2314yes—
347C2×C4×Q8—44no—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2312yes—
365C2×C4×D4—44no—
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×#117C2314yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C22×C4⋊C4C2312yes—
378C22×C4⋊C4C2311yescharacteristic
379C22×C4⋊C4C2311yescharacteristic
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C22⋊C4C2312yes—
383C22×C22⋊C4C2312yes—
384C22×C22⋊C4C2312yes—
385C22×C22⋊C4C2314yes—
386C22×C22⋊C4C2312yes—
387C22×C22⋊C4C2312yes—
388C22×C42C2311yescharacteristic
389C22×C42C2311yescharacteristic
390C22×C42C2311yescharacteristic
391C22×C42C2311yescharacteristic
392C22×C42C2311yescharacteristic
393C22×C42C2311yescharacteristic
394C22×C42C2312yes—
395C22×C42C2311yescharacteristic
396#401C2314yes—
397#401C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#399C2314yes—
418#399C2314yes—
419#399C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2314yes—
468#395C2314yes—
469#394C2314yes—
470#394C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#391C2311yescharacteristic
477#391C2311yescharacteristic
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2311yescharacteristic
490#391C2312yes—
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2312yes—
497#391C2314yes—
498#391C2312yes—
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#391C2311yescharacteristic
503#391C2311yescharacteristic
504#391C2312yes—
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2311yescharacteristic
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2314yes—
512#391C2311yescharacteristic
513#391C2311yescharacteristic
514#391C2311yescharacteristic
515#391C2312yes—
516#391C2312yes—
517#390C2312yes—
518#390C2311yescharacteristic
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#390C2311yescharacteristic
523#390C2311yescharacteristic
524#390C2311yescharacteristic
525#390C2312yes—
526#390C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2311yescharacteristic
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2312yes—
554#389C2312yes—
555#389C2311yescharacteristic
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2312yes—
567#389C2312yes—
568#389C2311yescharacteristic
569#389C2311yescharacteristic
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2314yes—
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2312yes—
601#388C2312yes—
602#388C2312yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#387C2312yes—
615#387C2312yes—
616#387C2314yes—
617#387C2312yes—
618#387C2314yes—
619#387C2312yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2312yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2314yes—
646#387C2314yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2312yes—
651#387C2312yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#386C2314yes—
667#386C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2312yes—
683#385C2312yes—
684#385C2312yes—
685#385C2314yes—
686#385C2312yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#384C2311yescharacteristic
693#384C2311yescharacteristic
694#384C2311yescharacteristic
695#384C2311yescharacteristic
696#384C2312yes—
697#384C2314yes—
698#384C2312yes—
699#383C2314yes—
700#383C2314yes—
701#383C2314yes—
702#383C2312yes—
703#383C2312yes—
704#382C2312yes—
705#382C2312yes—
706#382C2312yes—
707#382C2311yescharacteristic
708#382C2311yescharacteristic
709#382C2314yes—
710#382C2311yescharacteristic
711#382C2312yes—
712#382C2314yes—
713#382C2314yes—
714#382C2312yes—
715#382C2312yes—
716#382C2312yes—
717#382C2312yes—
718#382C2311yescharacteristic
719#382C2312yes—
720#382C2312yes—
721#381C2312yes—
722#381C2314yes—
723#381C2314yes—
724#381C2314yes—
725#381C2314yes—
726#381C2312yes—
727#381C2314yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2314yes—
733#380C2314yes—
734#380C2314yes—
735#380C2314yes—
736#380C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2314yes—
746#380C2311yescharacteristic
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#379C2314yes—
753#379C2314yes—
754#379C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2314yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2314yes—
805C2×#95C2312yes—
806C2×#95C2314yes—
807C2×#95C2312yes—
808C2×#95C2312yes—
809C2×#95C2312yes—
810C43C2311yescharacteristic
811C43C2311yescharacteristic
812C43C2311yescharacteristic
813C43C2311yescharacteristic
814C43C2311yescharacteristic
815C43C2311yescharacteristic
816C43C2311yescharacteristic
817C43C2311yescharacteristic
818C25C2412yes—
819C22×Q8—24no—
820C22×Q8—24no—
821C22×Q8—42no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2411yescharacteristic
824C22×Q8C2412yes—
825C22×Q8C2411yescharacteristic
826C22×Q8C2412yes—
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2412yes—
830C22×Q8C2414yes—
831C22×D4—24no—
832C22×D4—24no—
833C22×D4—42no—
834C22×D4C2411yescharacteristic
835C22×D4C2412yes—
836C22×D4C2411yescharacteristic
837C23×C4—28no—
838C23×C4—44no—
839C23×C4—44no—
840C23×C4C2411yescharacteristic
841C23×C4C2412yes—
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2412yes—
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2412yes—
851C23×C4C2414yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2414yes—
856C4⋊Q8—28no—
857C4⋊Q8—24no—
858C4⋊Q8—24no—
859C4⋊Q8—42no—
860C4⋊Q8—44no—
861C4⋊Q8—44no—
862C4⋊Q8—42no—
863C4⋊Q8—44no—
864C4⋊Q8—48no—
865#126—216no—
866#126—216no—
867#126—48no—
868#126—48no—
869#125—44no—
870#125—44no—
871#125—44no—
872#125—44no—
873#125—48no—
874#124—24no—
875#124—24no—
876#124—28no—
877#124—28no—
878#124—28no—
879#124—24no—
880#124—44no—
881#124#4118yes—
882C22⋊Q8—24no—
883C22⋊Q8—24no—
884C22⋊Q8—28no—
885C22⋊Q8—216no—
886C22⋊Q8—44no—
887C22⋊Q8—44no—
888C22⋊Q8—48no—
889C22⋊Q8—48no—
890C22⋊Q8—48no—
891C22⋊Q8—44no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894C22⋊Q8—44no—
895C4×Q8—28no—
896C4×Q8—28no—
897C4×Q8—28no—
898C4×Q8—24no—
899C4×Q8—24no—
900C4×Q8—24no—
901C4×Q8—24no—
902C4×Q8—44no—
903C4×Q8—44no—
904C4×Q8—44no—
905C4×Q8—42no—
906C4×Q8—42no—
907C4×Q8—44no—
908C4×Q8—44no—
909C4×Q8—44no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×D4—28no—
913C4×D4—24no—
914C4×D4—24no—
915C4×D4—44no—
916C4×D4—42no—
917C4×D4—42no—
918C4×D4—44no—
919C4×D4—44no—
920#117—216no—
921#117—44no—
922#117—44no—
923C2×C4⋊C4—44no—
924C2×C4⋊C4—42no—
925C2×C4⋊C4—42no—
926C2×C4⋊C4—44no—
927C2×C4⋊C4—44no—
928C2×C4⋊C4C2411yescharacteristic
929C2×C4⋊C4C2411yescharacteristic
930C2×C4⋊C4C2411yescharacteristic
931C2×C4⋊C4C2411yescharacteristic
932C2×C4⋊C4C2411yescharacteristic
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2411yescharacteristic
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C22⋊C4—28no—
999C2×C22⋊C4—28no—
1000C2×C22⋊C4—44no—
1001C2×C22⋊C4—44no—
1002C2×C22⋊C4—48no—
1003C2×C22⋊C4—44no—
1004C2×C22⋊C4C2412yes—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C42—24no—
1045C2×C42—24no—
1046C2×C42—24no—
1047C2×C42—24no—
1048C2×C42—44no—
1049C2×C42—42no—
1050C2×C42—42no—
1051C2×C42—42no—
1052C2×C42C2414yes—
1053C2×C42C2414yes—
1054C2×C42C2411yescharacteristic
1055C2×C42C2411yescharacteristic
1056C2×C42C2411yescharacteristic
1057C2×C42C2412yes—
1058C2×C42C2412yes—
1059C2×C42C2412yes—
1060C2×C42C2412yes—
1061C2×C42C2412yes—
1062C2×C42C2412yes—
1063C2×C42C2411yescharacteristic
1064C2×C42C2411yescharacteristic
1065C2×C42C2411yescharacteristic
1066C2×C42C2411yescharacteristic
1067C2×C42C2411yescharacteristic
1068C2×C42C2411yescharacteristic
1069C2×C42C2411yescharacteristic
1070C2×C42C2411yescharacteristic
1071C2×C42C2411yescharacteristic
1072C2×C42C2411yescharacteristic
1073C2×C42C2411yescharacteristic
1074C2×C42C2411yescharacteristic
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2414yes—
1079C2×C42C2414yes—
1080C2×C42C2414yes—
1081C2×C42C2414yes—
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2414yes—
1085C2×C42C2414yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2411yescharacteristic
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096#95C2412yes—
1097#95C2414yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2412yes—
1102#95C2412yes—
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2414yes—
1123#95C2412yes—
1124#95C2414yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176C24—24no—
1177C24—24no—
1178C24—24no—
1179C24—24no—
1180C24—42no—
1181C24—42no—
1182C24—42no—
1183C24C2512yes—
1184C24C2512yes—
1185C24C2511yescharacteristic
1186C2×Q8—24no—
1187C2×Q8—24no—
1188C2×Q8—22no—
1189C2×Q8—24no—
1190C2×Q8—22no—
1191C2×Q8—22no—
1192C2×Q8—22no—
1193C2×Q8—22no—
1194C2×Q8—24no—
1195C2×Q8—24no—
1196C2×Q8—22no—
1197C2×Q8—24no—
1198C2×Q8—22no—
1199C2×Q8—22no—
1200C2×Q8—24no—
1201C2×Q8—22no—
1202C2×Q8—22no—
1203C2×Q8—22no—
1204C2×Q8—42no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×Q8—42no—
1208C2×Q8—42no—
1209C2×Q8—44no—
1210C2×Q8—44no—
1211C2×Q8—44no—
1212C2×Q8—416no—
1213C2×Q8C2×#4114yes—
1214C2×D4—24no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—22no—
1219C2×D4—24no—
1220C2×D4—22no—
1221C2×D4—416no—
1222C2×D4—42no—
1223C2×D4C2×#4114yes—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—22no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—24no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—22no—
1236C22×C4—28no—
1237C22×C4—24no—
1238C22×C4—24no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—24no—
1242C22×C4—22no—
1243C22×C4—24no—
1244C22×C4—24no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—22no—
1248C22×C4—24no—
1249C22×C4—24no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—42no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—42no—
1258C22×C4—42no—
1259C22×C4—42no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—42no—
1263C22×C4—42no—
1264C22×C4—42no—
1265C22×C4—42no—
1266C22×C4—42no—
1267C22×C4—44no—
1268C22×C4—44no—
1269C22×C4—44no—
1270C22×C4—816no—
1271C22×C42−1+414yes—
1272C22×C42−1+414yes—
1273C22×C4C2511yescharacteristic
1274C22×C4C2511yescharacteristic
1275C22×C4C2511yescharacteristic
1276C22×C4C2511yescharacteristic
1277C22×C4C2512yes—
1278C22×C4C2512yes—
1279C22×C4C2512yes—
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2514yes—
1284C22×C4C2511yescharacteristic
1285C22×C4C2514yes—
1286C22×C4C2512yes—
1287C22×C4C2512yes—
1288C22×C4C2512yes—
1289C22×C4C2514yes—
1290C22×C4C2512yes—
1291C22×C4C2514yes—
1292C22×C4C2512yes—
1293C22×C4C2512yes—
1294C22×C4C2511yescharacteristic
1295C22×C4C2512yes—
1296C22×C4C2511yescharacteristic
1297C22×C4C2512yes—
1298C22×C4C2511yescharacteristic
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2511yescharacteristic
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C4⋊C4—24no—
1306C4⋊C4—28no—
1307C4⋊C4—24no—
1308C4⋊C4—28no—
1309C4⋊C4—28no—
1310C4⋊C4—24no—
1311C4⋊C4—24no—
1312C4⋊C4—28no—
1313C4⋊C4—22no—
1314C4⋊C4—22no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—24no—
1327C4⋊C4—24no—
1328C4⋊C4—22no—
1329C4⋊C4—22no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—28no—
1333C4⋊C4—22no—
1334C4⋊C4—24no—
1335C4⋊C4—22no—
1336C4⋊C4—24no—
1337C4⋊C4—28no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—44no—
1341C4⋊C4—42no—
1342C4⋊C4—42no—
1343C4⋊C4—42no—
1344C4⋊C4—42no—
1345C4⋊C4—44no—
1346C4⋊C4—42no—
1347C4⋊C4—44no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—44no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C22⋊C4—24no—
1376C22⋊C4—24no—
1377C22⋊C4—28no—
1378C22⋊C4—28no—
1379C22⋊C4—28no—
1380C22⋊C4—24no—
1381C22⋊C4—24no—
1382C22⋊C4—28no—
1383C22⋊C4—24no—
1384C22⋊C4—28no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—42no—
1395C22⋊C4—42no—
1396C22⋊C4—42no—
1397C22⋊C4—42no—
1398C22⋊C4—42no—
1399C22⋊C4—42no—
1400C22⋊C4—44no—
1401C22⋊C4—44no—
1402C22⋊C4—42no—
1403C22⋊C4—42no—
1404C22⋊C4—44no—
1405C22⋊C4—44no—
1406C22⋊C4—44no—
1407C22⋊C4—44no—
1408C22⋊C4—44no—
1409C22⋊C4—44no—
1410C22⋊C4—44no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4C2×#4118yes—
1414C22⋊C4C2×#4118yes—
1415C42—22no—
1416C42—22no—
1417C42—22no—
1418C42—28no—
1419C42—28no—
1420C42—24no—
1421C42—24no—
1422C42—22no—
1423C42—22no—
1424C42—22no—
1425C42—24no—
1426C42—24no—
1427C42—24no—
1428C42—24no—
1429C42—22no—
1430C42—22no—
1431C42—22no—
1432C42—22no—
1433C42—22no—
1434C42—22no—
1435C42—22no—
1436C42—22no—
1437C42—22no—
1438C42—22no—
1439C42—22no—
1440C42—22no—
1441C42—41no—
1442C42—41no—
1443C42—41no—
1444C42—41no—
1445C42—41no—
1446C42—41no—
1447C42—41no—
1448C42—41no—
1449C42—42no—
1450C42—42no—
1451C42—44no—
1452C42—44no—
1453C42—44no—
1454C42—44no—
1455C42—44no—
1456C42—44no—
1457C42C2×#4114yes—
1458C42H(5,𝔽2)14yes—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—22no—
1464C23—22no—
1465C23—22no—
1466C23—22no—
1467C23—22no—
1468C23—22no—
1469C23—22no—
1470C23—22no—
1471C23—22no—
1472C23—22no—
1473C23—22no—
1474C23—22no—
1475C23—22no—
1476C23—48no—
1477C23—48no—
1478C23—48no—
1479C23—48no—
1480C23—84no—
1481C23—84no—
1482C23—84no—
1483C23C22×#4114yes—
1484C23C2×2−1+412yes—
1485C23C2×2−1+412yes—
1486C23#58512yes—
1487C23C2611yescharacteristic
1488Q8—28no—
1489Q8—48no—
1490Q8—48no—
1491Q8—44no—
1492Q8—44no—
1493Q8—44no—
1494Q8—84no—
1495Q8—84no—
1496Q8—164no—
1497D4—28no—
1498D4—48no—
1499D4—44no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—22no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—22no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—28no—
1515C2×C4—28no—
1516C2×C4—22no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—24no—
1520C2×C4—22no—
1521C2×C4—24no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—21no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—24no—
1535C2×C4—24no—
1536C2×C4—22no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—24no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—24no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—22no—
1561C2×C4—24no—
1562C2×C4—22no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—24no—
1567C2×C4—24no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—24no—
1571C2×C4—22no—
1572C2×C4—24no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—44no—
1586C2×C4—44no—
1587C2×C4—44no—
1588C2×C4—44no—
1589C2×C4—48no—
1590C2×C4—44no—
1591C2×C4—48no—
1592C2×C4—48no—
1593C2×C4—84no—
1594C2×C4—84no—
1595C2×C4—88no—
1596C2×C4—84no—
1597C2×C4—84no—
1598C2×C4—164no—
1599C2×C4C22×#4112yes—
1600C2×C4C22×#4114yes—
1601C2×C4C22×#4112yes—
1602C2×C4C22×#4112yes—
1603C2×C4C2×H(5,𝔽2)12yes—
1604C2×C4C2×H(5,𝔽2)12yes—
1605C2×C4C2×H(5,𝔽2)12yes—
1606C2×C4C2×2−1+412yes—
1607C2×C4C2×2−1+412yes—
1608C2×C4C2×2−1+412yes—
1609C2×C4C2×2−1+412yes—
1610C2×C4#58512yes—
1611C2×C4#58512yes—
1612C22—22no—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—24no—
1619C22—24no—
1620C22—24no—
1621C22—42no—
1622C22—42no—
1623C22—42no—
1624C22—42no—
1625C22—42no—
1626C22—42no—
1627C22—42no—
1628C22—42no—
1629C22—42no—
1630C22—42no—
1631C22—42no—
1632C22—816no—
1633C22#355514yes—
1634C22C23×#4111yescharacteristic
1635C22C22×H(5,𝔽2)11yescharacteristic
1636C22C22×2−1+411yescharacteristic
1637C22C22×2−1+411yescharacteristic
1638C22C2×#58511yescharacteristic
1639C22C2×#58511yescharacteristic
1640C22C2×#58511yescharacteristic
1641C4—22no—
1642C4—22no—
1643C4—24no—
1644C4—22no—
1645C4—22no—
1646C4—22no—
1647C4—22no—
1648C4—42no—
1649C4—42no—
1650C4—42no—
1651C4—42no—
1652C4—41no—
1653C4—41no—
1654C4—42no—
1655C4—44no—
1656C4—42no—
1657C4—42no—
1658C4—41no—
1659C4—41no—
1660C4—44no—
1661C4—42no—
1662C4—42no—
1663C4—41no—
1664C4—42no—
1665C4—42no—
1666C4—42no—
1667C4—44no—
1668C4—42no—
1669C4—44no—
1670C4—41no—
1671C4#352014yes—
1672C4#356114yes—
1673C2—24no—
1674C2—44no—
1675C2—82no—
1676C2C2×#356111yescharacteristic
1677C2C2×#355511yescharacteristic
1678C2C2×#352011yescharacteristic
1679C2#6280511yescharacteristic
1680C2#6281611yescharacteristic
1681C2#6283011yescharacteristic
1682C2#6283111yescharacteristic
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. #59655C2semidirect
2. #59653C2semidirect
3. #59428C2semidirect
4. #59426C2semidirect
5. #59325C2semidirect
7. #46174C2semidirect
8. #46055C2semidirect
9. #45579C2semidirect
10. #40105C2semidirect
11. #40080C2semidirect
12. #39216C2semidirect
13. #39173C2semidirect
14. #39172C2semidirect
15. #39026C2semidirect
16. #38978C2semidirect
17. #38977C2semidirect
18. #38613C2semidirect
19. #38172C2semidirect
20. #38057C2semidirect
22. #37581C2semidirect
23. #37101C2semidirect
24. #36635C2semidirect
25. #36635C2semidirect
26. #36545C2semidirect
27. Q8×C22⋊Q8C2semidirect
28. #36204C2semidirect
29. #36167C2semidirect
32. #35086C2semidirect
33. #35079C2semidirect
34. #34499C2semidirect
36. C2×Q82C22semidirect
37. C2×#557C22semidirect
44. #2864C22semidirect
45. #2864C22semidirect
46. #2863C22semidirect
47. #2863C22semidirect
48. #2863C22semidirect
49. #2863C22semidirect
50. #2863C22semidirect
51. #2862C22semidirect
52. #2862C22semidirect
53. #2859C22semidirect
54. #2859C22semidirect
70. #2838C22semidirect
71. #2831C22semidirect
72. #2793C22semidirect
73. #2783C22semidirect
74. #2777C22semidirect
75. #2774C22semidirect
76. #2773C22semidirect
77. #2772C22semidirect
78. #2770C22semidirect
79. #2765C22semidirect
80. #2762C22semidirect
81. #2762C22semidirect
83. #2759C22semidirect
84. #2758C22semidirect
86. #2755C22semidirect
87. #2755C22semidirect
88. #2745C22semidirect
89. #2744C22semidirect
90. #2739C22semidirect
92. #2729C22semidirect
93. #2725C22semidirect
95. #2721C22semidirect
96. #2716C22semidirect
97. #2716C22semidirect
100. #2690C22semidirect
101. #2690C22semidirect
102. #2690C22semidirect
103. #2689C22semidirect
104. #2667C22semidirect
105. #2665C22semidirect
106. #2654C22semidirect
107. #2652C22semidirect
108. #2652C22semidirect
109. #2650C22semidirect
110. #2645C22semidirect
112. #2642C22semidirect
115. #2584C22semidirect
116. #2582C22semidirect
117. #2582C22semidirect
118. #2582C22semidirect
119. #2581C22semidirect
120. #2581C22semidirect
121. #2577C22semidirect
122. #2573C22semidirect
124. #2568C22semidirect
125. #2567C22semidirect
126. #2567C22semidirect
127. #2565C22semidirect
130. #2550C22semidirect
134. #2546C22semidirect
139. #2530C22semidirect
140. #2527C22semidirect
141. #2523C22semidirect
143. #2520C22semidirect
144. #2519C22semidirect
145. #2514C22semidirect
147. #2509C22semidirect
148. #2508C22semidirect
149. #2508C22semidirect
153. #2503C22semidirect
154. #2499C22semidirect
155. #2496C22semidirect
156. #2496C22semidirect
157. #2496C22semidirect
158. #2495C22semidirect
159. #2494C22semidirect
160. #2494C22semidirect
163. #2493C22semidirect
164. #2492C22semidirect
165. #2489C22semidirect
166. #2489C22semidirect
167. #2489C22semidirect
175. #2478C22semidirect
178. #2469C22semidirect
180. #2462C22semidirect
182. #2453C22semidirect
184. #2451C22semidirect
185. #2451C22semidirect
192. #2446C22semidirect
193. #2446C22semidirect
194. #2446C22semidirect
196. #2442C22semidirect
197. #2442C22semidirect
198. #2442C22semidirect
199. #2441C22semidirect
200. #2441C22semidirect
203. #2440C22semidirect
204. #2440C22semidirect
205. #2439C22semidirect
206. #2439C22semidirect
207. #2439C22semidirect
213. #2429C22semidirect
214. #2429C22semidirect
215. #2429C22semidirect
216. #2421C22semidirect
217. #2421C22semidirect
218. #2421C22semidirect
219. #2421C22semidirect
222. #2383C22semidirect
223. #2378C22semidirect
224. #2373C22semidirect
228. #2365C22semidirect
229. #2362C22semidirect
232. #2360C22semidirect
233. #2355C22semidirect
234. #2355C22semidirect
236. #2351C22semidirect
237. Q8×C4⋊C4C22semidirect
238. Q8×C4⋊C4C22semidirect
241. #2347C22semidirect
242. #2344C22semidirect
243. #2343C22semidirect
247. #2334C22semidirect
248. #2334C22semidirect
249. #2334C22semidirect
250. #2329C22semidirect
251. #2329C22semidirect
252. #2327C22semidirect
254. #2320C22semidirect
256. #2314C22semidirect
257. C4×C4⋊Q8C22semidirect
258. C4×C4⋊Q8C22semidirect
259. C4×C4⋊Q8C22semidirect
260. C4×C4⋊Q8C22semidirect
261. C4×#125C22semidirect
262. C4×#125C22semidirect
282. #2295C22semidirect
283. #2295C22semidirect
284. #2295C22semidirect
285. #2295C22semidirect
286. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#596552
#596532
#594282
#594262
#593252
#591482
#461742
#460552
#455792
#401052
#400802
#392162
#391732
#391722
#390262
#389782
#389772
#386132
#381722
#380572
#380542
#375812
#371012
#366352
#365452
Q8×C22⋊Q82
#362042
#361672
#361612
#361542
#350862
#350792
#344992
C2×C4×#1242