Finite Group Databasebeta

← #7712243

Subgroups — #7712243

Order 512.

4872 conjugacy classes of subgroups.

The subgroup lattice has 1716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59331C212yesmaximal, complemented
2#59323C212yesmaximal, complemented
3#59264C212yesmaximal, complemented
4#59250C212yesmaximal, complemented
5#45781C214yesmaximal, complemented
6#45470C214yesmaximal, complemented
7#39736C211yesmaximal, characteristic, complemented
8#39734C211yesmaximal, characteristic, complemented
9#39353C211yesmaximal, characteristic, complemented
10#39351C211yesmaximal, characteristic, complemented
11#38005C214yesmaximal, complemented
12#37983C212yesmaximal, complemented
13#37980C212yesmaximal, complemented
14#37924C214yesmaximal, complemented
15#37858C212yesmaximal, complemented
16#37857C212yesmaximal, complemented
17#37671C212yesmaximal, complemented
18#37668C212yesmaximal, complemented
19#37624C211yesmaximal, characteristic, complemented
20#37619C211yesmaximal, characteristic, complemented
21#37384C212yesmaximal, complemented
22#37293C212yesmaximal, complemented
23#36625C211yesmaximal, characteristic, complemented
24#36624C211yesmaximal, characteristic
25#36481C211yesmaximal, characteristic, complemented
26#36460C211yesmaximal, characteristic, complemented
27#36390C212yesmaximal, complemented
28#36379C212yesmaximal, complemented
29#36302C211yesmaximal, characteristic, complemented
30#36288C211yesmaximal, characteristic, complemented
31#35318C212yesmaximal, complemented
32#35299C212yesmaximal, complemented
33#34393C211yesmaximal, characteristic, complemented
34#34373C211yesmaximal, characteristic, complemented
35#34012C211yesmaximal, characteristic, complemented
36C2×#542C2212yes—
37C2×#541C2212yes—
38C2×#533C2211yescharacteristic
39C2×#532C2211yescharacteristic
40C2×#525C2212yes—
41C23×C42C2211yescharacteristic
42#2863C2212yescomplemented
43#2862C2212yescomplemented
44#2861C2212yescomplemented
45#2860C2212yescomplemented
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2857C2211yescharacteristic
52#2856C2211yescharacteristic
53#2856C2211yescharacteristic
54#2855C2211yescharacteristic
55#2855C2211yescharacteristic
56#2855C2212yes—
57#2854C2212yes—
58#2854C2212yes—
59#2851C2212yes—
60#2851C2212yes—
61#2850C2212yes—
62#2850C2212yes—
63#2848C2211yescharacteristic
64#2848C2211yescharacteristic
65#2848C2212yes—
66#2847C2212yes—
67#2847C2212yes—
68#2841C2214yes—
69#2816C2214yes—
70#2777C2214yescomplemented
71#2773C2214yescomplemented
72#2772C2214yescomplemented
73#2768C2214yescomplemented
74#2766C2214yescomplemented
75#2764C2214yescomplemented
76#2761C2214yescomplemented
77#2759C2214yescomplemented
78#2748C2214yes—
79#2747C2214yes—
80#2746C2214yes—
81#2743C2214yes—
82#2741C2214yes—
83#2740C2214yes—
84#2738C2214yescomplemented
85#2737C2214yes—
86#2723C2214yescomplemented
87#2722C2214yes—
88#2719C2214yescomplemented
89#2707C2214yes—
90#2702C2214yes—
91#2698C2214yescomplemented
92#2697C2214yes—
93#2695C2214yes—
94#2694C2214yes—
95#2692C2214yes—
96#2691C2214yes—
97#2687C2214yes—
98#2685C2214yes—
99#2685C2214yes—
100#2684C2214yes—
101#2672C2214yes—
102#2666C2214yescomplemented
103#2660C2212yescomplemented
104#2658C2212yescomplemented
105#2647C2212yescomplemented
106#2640C2212yescomplemented
107#2633C2214yescomplemented
108#2629C2212yes—
109#2628C2212yes—
110#2625C2212yes—
111#2624C2212yes—
112#2624C2212yes—
113#2624C2212yes—
114#2621C2212yes—
115#2620C2212yes—
116#2612C2214yescomplemented
117#2609C2214yes—
118#2606C2214yescomplemented
119#2601C2214yes—
120#2596C2214yescomplemented
121#2589C2214yescomplemented
122#2580C2212yescomplemented
123#2580C2212yescomplemented
124#2578C2214yes—
125#2576C2214yes—
126#2574C2214yes—
127#2572C2214yes—
128#2571C2211yescharacteristic, complemented
129#2570C2212yescomplemented
130#2570C2212yescomplemented
131#2566C2212yescomplemented
132#2560C2214yes—
133#2559C2214yes—
134#2556C2214yescomplemented
135#2556C2214yescomplemented
136#2553C2214yes—
137#2553C2214yes—
138#2552C2211yescharacteristic, complemented
139#2552C2212yescomplemented
140#2552C2211yescharacteristic, complemented
141#2551C2211yescharacteristic, complemented
142#2550C2212yescomplemented
143#2548C2211yescharacteristic, complemented
144#2548C2211yescharacteristic, complemented
145#2546C2211yescharacteristic, complemented
146#2546C2211yescharacteristic, complemented
147#2542C2212yescomplemented
148#2532C2214yescomplemented
149#2531C2214yes—
150#2531C2214yescomplemented
151#2530C2214yescomplemented
152#2527C2214yescomplemented
153#2526C2214yes—
154#2526C2214yescomplemented
155#2522C2214yes—
156#2522C2214yescomplemented
157#2521C2214yes—
158#2521C2214yes—
159#2519C2214yescomplemented
160#2519C2214yescomplemented
161#2516C2214yes—
162#2515C2214yescomplemented
163#2514C2212yescomplemented
164#2513C2212yescomplemented
165#2512C2212yescomplemented
166#2512C2212yescomplemented
167#2512C2212yescomplemented
168#2512C2212yescomplemented
169#2508C2212yescomplemented
170#2507C2212yescomplemented
171#2507C2212yescomplemented
172#2506C2212yescomplemented
173#2500C2212yes—
174#2500C2212yes—
175#2496C2212yes—
176#2496C2212yes—
177#2495C2212yes—
178#2494C2212yes—
179#2492C2212yes—
180#2491C2212yes—
181#2490C2212yes—
182#2490C2212yes—
183#2479C2214yes—
184#2478C2214yescomplemented
185#2477C2214yes—
186#2477C2214yes—
187#2476C2214yes—
188#2468C2214yes—
189#2468C2214yes—
190#2466C2214yes—
191#2460C2214yes—
192#2454C2214yes—
193#2453C2212yescomplemented
194#2452C2212yescomplemented
195#2450C2214yes—
196#2448C2212yescomplemented
197#2447C2214yes—
198#2447C2212yescomplemented
199#2446C2212yescomplemented
200#2446C2212yescomplemented
201#2441C2212yes—
202#2441C2212yes—
203#2439C2212yes—
204#2439C2212yes—
205#2432C2212yes—
206#2432C2212yes—
207#2429C2212yes—
208#2429C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2423C2212yes—
212#2422C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2419C2214yes—
216#2378C2214yes—
217#2377C2214yes—
218#2373C2214yescomplemented
219#2373C2214yescomplemented
220#2370C2212yescomplemented
221#2369C2212yescomplemented
222#2368C2214yescomplemented
223#2366C2211yescharacteristic, complemented
224#2366C2211yescharacteristic, complemented
225#2365C2211yescharacteristic, complemented
226#2365C2211yescharacteristic, complemented
227#2363C2212yes—
228#2363C2212yes—
229#2362C2212yes—
230#2362C2212yes—
231#2357C2212yescomplemented
232#2357C2212yescomplemented
233#2355C2211yescharacteristic, complemented
234#2355C2211yescharacteristic, complemented
235#2355C2212yescomplemented
236#2355C2212yescomplemented
237#2354C2212yescomplemented
238Q8×C4⋊C4C2211yescharacteristic, complemented
239Q8×C4⋊C4C2211yescharacteristic, complemented
240#2349C2212yescomplemented
241#2347C2212yes—
242#2346C2212yes—
243#2343C2214yescomplemented
244#2341C2212yes—
245#2339C2212yes—
246#2336C2214yescomplemented
247#2331C2212yescomplemented
248#2327C2212yescomplemented
249#2326C2212yescomplemented
250#2326C2212yescomplemented
251#2324C2212yes—
252#2324C2212yes—
253#2324C2212yes—
254#2323C2212yes—
255#2318C2214yescomplemented
256#2314C2212yes—
257#2314C2212yes—
258C4×C4⋊Q8C2212yescomplemented
259C4×#124C2212yescomplemented
260C4×C22⋊Q8C2211yescharacteristic
261C4×C22⋊Q8C2211yescharacteristic
262C4×C22⋊Q8C2211yescharacteristic
263C4×C22⋊Q8C2212yes—
264C4×C22⋊Q8C2211yescharacteristic
265C4×C22⋊Q8C2212yes—
266C4×#121C2212yes—
267C4×#121C2212yes—
268C4×#121C2212yes—
269C4×#121C2212yes—
270#2297C2212yes—
271#2296C2212yes—
272#2295C2212yescomplemented
273#2293C2212yescomplemented
274#2285C2211yescharacteristic
275#2285C2211yescharacteristic
276#2285C2211yescharacteristic
277#2285C2211yescharacteristic
278#2285C2211yescharacteristic
279#2285C2211yescharacteristic
280#2285C2211yescharacteristic
281#2285C2211yescharacteristic
282#2283C2212yes—
283#2283C2212yes—
284#2283C2211yescharacteristic
285#2283C2211yescharacteristic
286#2283C2212yes—
287#2283C2211yescharacteristic
288#2283C2212yes—
289#2283C2211yescharacteristic
290#2280C2212yes—
291#2280C2212yes—
292#2280C2212yes—
293#2280C2211yescharacteristic
294#2280C2211yescharacteristic
295C4×#117C2212yes—
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C4×#117C2212yes—
299C22×#41C2312yes—
300C24×C4C2311yescharacteristic
301C24×C4C2311yescharacteristic
302C24×C4C2311yescharacteristic
303#542—48no—
304#541—48no—
305#533—28no—
306#532—28no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×#127C2311yescharacteristic
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2314yes—
324C2×#125C2314yes—
325C2×#124C2312yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2314yes—
329#525—48no—
330C2×#123C2314yes—
331C2×#123C2314yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#120C2314yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×#117C2312yes—
370C2×#117C2311yescharacteristic
371C2×#117C2311yescharacteristic
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2314yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2312yes—
381C22×C42—28no—
382C22×C42C2311yescharacteristic
383C22×C42C2311yescharacteristic
384C22×C42C2311yescharacteristic
385C22×C42C2311yescharacteristic
386C22×C42C2311yescharacteristic
387C22×C42C2311yescharacteristic
388C22×C42C2311yescharacteristic
389C22×C42C2311yescharacteristic
390C22×C42C2311yescharacteristic
391C22×C42C2311yescharacteristic
392C22×C42C2311yescharacteristic
393C22×C42C2311yescharacteristic
394#401C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#399C2314yes—
405#399C2314yes—
406#399C2314yes—
407#399C2314yes—
408#399C2314yes—
409#399C2314yes—
410#399C2314yes—
411#399C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#391C2314yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2311yescharacteristic
488#391C2311yescharacteristic
489#391C2311yescharacteristic
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2312yes—
497#390C2314yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2312yes—
512#390C2314yes—
513#390C2314yes—
514#390C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2311yescharacteristic
544#389C2311yescharacteristic
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2312yes—
650#385C2312yes—
651#385C2312yes—
652#385C2312yes—
653#385C2312yes—
654#385C2312yes—
655#385C2312yes—
656#385C2312yes—
657#385C2312yes—
658#385C2312yes—
659#385C2312yes—
660#384C2312yes—
661#384C2311yescharacteristic
662#384C2312yes—
663#384C2312yes—
664#384C2311yescharacteristic
665#384C2312yes—
666#384C2311yescharacteristic
667#384C2311yescharacteristic
668#384C2311yescharacteristic
669#384C2311yescharacteristic
670#384C2311yescharacteristic
671#384C2311yescharacteristic
672#383C2314yes—
673#383C2314yes—
674#383C2312yes—
675#383C2312yes—
676#383C2312yes—
677#383C2312yes—
678#382C2312yes—
679#382C2312yes—
680#382C2312yes—
681#382C2311yescharacteristic
682#382C2312yes—
683#382C2312yes—
684#382C2314yes—
685#382C2314yes—
686#382C2311yescharacteristic
687#382C2312yes—
688#382C2311yescharacteristic
689#382C2311yescharacteristic
690#382C2312yes—
691#382C2312yes—
692#382C2312yes—
693#382C2312yes—
694#381C2312yes—
695#381C2312yes—
696#381C2314yes—
697#381C2314yes—
698#381C2312yes—
699#381C2314yes—
700#381C2312yes—
701#381C2312yes—
702#381C2312yes—
703#381C2312yes—
704#381C2312yes—
705#380C2311yescharacteristic
706#380C2311yescharacteristic
707#380C2312yes—
708#380C2314yes—
709#380C2312yes—
710#380C2312yes—
711#380C2311yescharacteristic
712#380C2311yescharacteristic
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2311yescharacteristic
719#380C2311yescharacteristic
720#380C2311yescharacteristic
721#380C2311yescharacteristic
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2314yes—
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730#380C2312yes—
731#380C2311yescharacteristic
732#380C2311yescharacteristic
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2311yescharacteristic
742#379C2312yes—
743#379C2312yes—
744#379C2312yes—
745#379C2312yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806#376C2312yes—
807#376C2312yes—
808#376C2314yes—
809#376C2312yes—
810#376C2312yes—
811#376C2312yes—
812#376C2312yes—
813C2×#95C2314yes—
814C43C2312yes—
815C43C2312yes—
816C25C2411yescharacteristic
817C2×#41—28no—
818C2×#41—44no—
819C2×#41—44no—
820C22×Q8C2411yescharacteristic
821C22×Q8C2411yescharacteristic
822C22×Q8C2412yes—
823C22×Q8C2412yes—
824C22×Q8C2414yes—
825C22×D4C2412yes—
826C22×D4C2412yes—
827C22×D4C2414yes—
828C22×D4C2414yes—
829C22×D4C2412yes—
830C22×D4C2414yes—
831C23×C4—24no—
832C23×C4—24no—
833C23×C4—24no—
834C23×C4—24no—
835C23×C4—24no—
836C23×C4—42no—
837C23×C4—42no—
838C23×C4—42no—
839C23×C4—42no—
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2414yes—
858C23×C4C2414yes—
859C23×C4C2414yes—
860C23×C4C2411yescharacteristic
861C4⋊Q8—24no—
862C4⋊Q8—24no—
863C4⋊Q8—24no—
864C4⋊Q8—44no—
865C4⋊Q8—44no—
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868#127—24no—
869#126—48no—
870#126—48no—
871#126—48no—
872#126—48no—
873#126—48no—
874#125—28no—
875#125—44no—
876#125—44no—
877#125—48no—
878#125—48no—
879#124—28no—
880#124—44no—
881#124—44no—
882#124—48no—
883#123—48no—
884#123—48no—
885C22⋊Q8—24no—
886C22⋊Q8—24no—
887C22⋊Q8—28no—
888C22⋊Q8—28no—
889C22⋊Q8—24no—
890C22⋊Q8—24no—
891C22⋊Q8—48no—
892C22⋊Q8—48no—
893C22⋊Q8—44no—
894C22⋊Q8—44no—
895C22⋊Q8—42no—
896C22⋊Q8—42no—
897C22⋊Q8—44no—
898#121—28no—
899#121—28no—
900#121—28no—
901#121—28no—
902#121—44no—
903#121—44no—
904#121—44no—
905#121—44no—
906#120—48no—
907C4×Q8—28no—
908C4×Q8—24no—
909C4×Q8—24no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×Q8—44no—
914C4×D4—28no—
915C4×D4—28no—
916C4×D4—44no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—44no—
920C4×D4—48no—
921C4×D4—48no—
922#117—28no—
923#117—28no—
924#117—24no—
925#117—24no—
926#117—44no—
927#117—44no—
928#117—44no—
929#117—48no—
930#117—42no—
931#117—42no—
932#117—44no—
933#117—44no—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2411yescharacteristic
936C2×C4⋊C4C2411yescharacteristic
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2411yescharacteristic
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2412yes—
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2414yes—
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⋊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⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C42—24no—
1054C2×C42—24no—
1055C2×C42—24no—
1056C2×C42—24no—
1057C2×C42—24no—
1058C2×C42—24no—
1059C2×C42—24no—
1060C2×C42—24no—
1061C2×C42—24no—
1062C2×C42—24no—
1063C2×C42—24no—
1064C2×C42#4118yes—
1065C2×C42C2412yes—
1066C2×C42C2412yes—
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2414yes—
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2414yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2414yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104#95C2412yes—
1105#95C2412yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176C24—22no—
1177C24—22no—
1178C24—22no—
1179C24—41no—
1180C24—41no—
1181C24—41no—
1182C24—41no—
1183C24C2514yes—
1184C24C2511yescharacteristic
1185C24C2511yescharacteristic
1186C24C2511yescharacteristic
1187#41—816no—
1188C2×Q8—22no—
1189C2×Q8—22no—
1190C2×Q8—24no—
1191C2×Q8—24no—
1192C2×Q8—22no—
1193C2×Q8—22no—
1194C2×Q8—24no—
1195C2×Q8—24no—
1196C2×Q8—22no—
1197C2×Q8—22no—
1198C2×Q8—42no—
1199C2×Q8—42no—
1200C2×Q8—44no—
1201C2×Q8—44no—
1202C2×Q8—44no—
1203C2×D4—28no—
1204C2×D4—28no—
1205C2×D4—28no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—24no—
1211C2×D4—24no—
1212C2×D4—24no—
1213C2×D4—44no—
1214C2×D4—44no—
1215C2×D4—42no—
1216C2×D4—42no—
1217C2×D4—44no—
1218C2×D4—44no—
1219C2×D4—44no—
1220C2×D4—44no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
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—22no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—22no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—28no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—416no—
1272C22×C4—416no—
1273C22×C4—44no—
1274C22×C4—44no—
1275C22×C4—44no—
1276C22×C4—44no—
1277C22×C4—44no—
1278C22×C4—44no—
1279C22×C4—44no—
1280C22×C4—44no—
1281C22×C4—416no—
1282C22×C4C2×#4114yes—
1283C22×C4C2×#4114yes—
1284C22×C4C2×#4114yes—
1285C22×C4H(5,𝔽2)14yes—
1286C22×C42−1+414yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2512yes—
1291C22×C4C2512yes—
1292C22×C4C2512yes—
1293C22×C4C2511yescharacteristic
1294C22×C4C2512yes—
1295C22×C4C2512yes—
1296C22×C4C2514yes—
1297C22×C4C2514yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2514yes—
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2511yescharacteristic
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2511yescharacteristic
1317C22×C4C2511yescharacteristic
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—24no—
1327C4⋊C4—22no—
1328C4⋊C4—22no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—22no—
1334C4⋊C4—28no—
1335C4⋊C4—22no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—42no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—28no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—24no—
1397C22⋊C4—28no—
1398C22⋊C4—28no—
1399C22⋊C4—28no—
1400C22⋊C4—28no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—42no—
1404C22⋊C4—42no—
1405C22⋊C4—42no—
1406C22⋊C4—42no—
1407C22⋊C4—42no—
1408C22⋊C4—44no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
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—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C42—22no—
1438C42—22no—
1439C42—22no—
1440C42—22no—
1441C42—22no—
1442C42—22no—
1443C42—22no—
1444C42—22no—
1445C42—22no—
1446C42—22no—
1447C42—22no—
1448C42—22no—
1449C42—24no—
1450C42—24no—
1451C42—24no—
1452C42—24no—
1453C42—24no—
1454C42—24no—
1455C42—24no—
1456C42—24no—
1457C42—24no—
1458C42—24no—
1459C42—24no—
1460C42—24no—
1461C42—42no—
1462C42—42no—
1463C42—42no—
1464C42—42no—
1465C42—44no—
1466C42—44no—
1467C42—44no—
1468C42—44no—
1469C42—44no—
1470C42—44no—
1471C42—44no—
1472C42C2×#4114yes—
1473C42C2×#4114yes—
1474C42C2×#4114yes—
1475C42C2×#4114yes—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—24no—
1495C23—24no—
1496C23—24no—
1497C23—24no—
1498C23—24no—
1499C23—24no—
1500C23—24no—
1501C23—44no—
1502C23—44no—
1503C23—44no—
1504C23—44no—
1505C23—44no—
1506C23—44no—
1507C23—44no—
1508C23C22×#4112yes—
1509C23C2×H(5,𝔽2)12yes—
1510C23C2×2−1+412yes—
1511C23C2611yescharacteristic
1512Q8—44no—
1513Q8—44no—
1514Q8—48no—
1515Q8—84no—
1516Q8—164no—
1517D4—48no—
1518D4—48no—
1519D4—84no—
1520D4—88no—
1521D4—88no—
1522D4—88no—
1523C2×C4—28no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—28no—
1541C2×C4—28no—
1542C2×C4—28no—
1543C2×C4—28no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—24no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—24no—
1557C2×C4—24no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—22no—
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—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—24no—
1586C2×C4—24no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—24no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—44no—
1608C2×C4—44no—
1609C2×C4—44no—
1610C2×C4—44no—
1611C2×C4—44no—
1612C2×C4—44no—
1613C2×C4—44no—
1614C2×C4—44no—
1615C2×C4—44no—
1616C2×C4—44no—
1617C2×C4—44no—
1618C2×C4—44no—
1619C2×C4—44no—
1620C2×C4—88no—
1621C2×C4—88no—
1622C2×C4—164no—
1623C2×C4C22×#4112yes—
1624C2×C4C22×#4112yes—
1625C2×C4C22×#4112yes—
1626C2×C4C22×#4112yes—
1627C2×C4C22×#4112yes—
1628C2×C4C22×#4112yes—
1629C2×C4C2×H(5,𝔽2)12yes—
1630C2×C4C2×H(5,𝔽2)12yes—
1631C2×C4C2×2−1+412yes—
1632C2×C4C2×2−1+412yes—
1633C2×C4#58512yes—
1634C2×C4#58512yes—
1635C2×C4#58512yes—
1636C2×C4#58512yes—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—22no—
1646C22—416no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—41no—
1658C22—41no—
1659C22—44no—
1660C22—44no—
1661C22—44no—
1662C22—44no—
1663C22—44no—
1664C22—44no—
1665C22—44no—
1666C22C23×#4111yescharacteristic
1667C22C22×H(5,𝔽2)11yescharacteristic
1668C22C22×2−1+411yescharacteristic
1669C22C2×#58511yescharacteristic
1670C22C2×#58511yescharacteristic
1671C22C2×#58511yescharacteristic
1672C22C2×#58511yescharacteristic
1673C4—22no—
1674C4—22no—
1675C4—22no—
1676C4—22no—
1677C4—22no—
1678C4—22no—
1679C4—22no—
1680C4—22no—
1681C4—42no—
1682C4—42no—
1683C4—42no—
1684C4—42no—
1685C4—42no—
1686C4—42no—
1687C4—41no—
1688C4—44no—
1689C4—42no—
1690C4—42no—
1691C4—41no—
1692C4—42no—
1693C4—42no—
1694C4—42no—
1695C4—42no—
1696C4—44no—
1697C4—42no—
1698C4—42no—
1699C4—42no—
1700C4—44no—
1701C4—42no—
1702C4#349414yes—
1703C4#349514yes—
1704C2—42no—
1705C2—42no—
1706C2—42no—
1707C2—84no—
1708C2#6276111yescharacteristic
1709C2#6276211yescharacteristic
1710C2C2×#349411yescharacteristic
1711C2C2×#349511yescharacteristic
1712C2#6281411yescharacteristic
1713C2#6283511yescharacteristic
1714C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59331C2semidirect
2. #59323C2semidirect
3. #59264C2semidirect
4. #59250C2semidirect
5. #45781C2semidirect
6. #45470C2semidirect
7. #39736C2semidirect
8. #39734C2semidirect
9. #39353C2semidirect
10. #39351C2semidirect
11. #38005C2semidirect
12. #37983C2semidirect
13. #37980C2semidirect
14. #37924C2semidirect
15. #37858C2semidirect
16. #37857C2semidirect
17. #37671C2semidirect
18. #37668C2semidirect
19. #37624C2semidirect
20. #37619C2semidirect
21. #37384C2semidirect
22. #37293C2semidirect
23. #36625C2semidirect
25. #36481C2semidirect
26. #36460C2semidirect
27. #36390C2semidirect
28. #36379C2semidirect
29. #36302C2semidirect
30. #36288C2semidirect
31. #35318C2semidirect
32. #35299C2semidirect
33. #34393C2semidirect
34. #34373C2semidirect
35. #34012C2semidirect
42. #2863C22semidirect
43. #2862C22semidirect
44. #2861C22semidirect
45. #2860C22semidirect
70. #2777C22semidirect
71. #2773C22semidirect
72. #2772C22semidirect
73. #2768C22semidirect
74. #2766C22semidirect
75. #2764C22semidirect
76. #2761C22semidirect
77. #2759C22semidirect
84. #2738C22semidirect
86. #2723C22semidirect
88. #2719C22semidirect
91. #2698C22semidirect
102. #2666C22semidirect
103. #2660C22semidirect
104. #2658C22semidirect
105. #2647C22semidirect
106. #2640C22semidirect
107. #2633C22semidirect
116. #2612C22semidirect
118. #2606C22semidirect
120. #2596C22semidirect
121. #2589C22semidirect
122. #2580C22semidirect
123. #2580C22semidirect
128. #2571C22semidirect
129. #2570C22semidirect
130. #2570C22semidirect
131. #2566C22semidirect
134. #2556C22semidirect
135. #2556C22semidirect
138. #2552C22semidirect
139. #2552C22semidirect
140. #2552C22semidirect
141. #2551C22semidirect
142. #2550C22semidirect
143. #2548C22semidirect
144. #2548C22semidirect
145. #2546C22semidirect
146. #2546C22semidirect
147. #2542C22semidirect
148. #2532C22semidirect
150. #2531C22semidirect
151. #2530C22semidirect
152. #2527C22semidirect
154. #2526C22semidirect
156. #2522C22semidirect
159. #2519C22semidirect
160. #2519C22semidirect
162. #2515C22semidirect
163. #2514C22semidirect
164. #2513C22semidirect
165. #2512C22semidirect
166. #2512C22semidirect
167. #2512C22semidirect
168. #2512C22semidirect
169. #2508C22semidirect
170. #2507C22semidirect
171. #2507C22semidirect
172. #2506C22semidirect
184. #2478C22semidirect
193. #2453C22semidirect
194. #2452C22semidirect
196. #2448C22semidirect
198. #2447C22semidirect
199. #2446C22semidirect
200. #2446C22semidirect
218. #2373C22semidirect
219. #2373C22semidirect
220. #2370C22semidirect
221. #2369C22semidirect
222. #2368C22semidirect
223. #2366C22semidirect
224. #2366C22semidirect
225. #2365C22semidirect
226. #2365C22semidirect
231. #2357C22semidirect
232. #2357C22semidirect
233. #2355C22semidirect
234. #2355C22semidirect
235. #2355C22semidirect
236. #2355C22semidirect
237. #2354C22semidirect
238. Q8×C4⋊C4C22semidirect
239. Q8×C4⋊C4C22semidirect
240. #2349C22semidirect
243. #2343C22semidirect
246. #2336C22semidirect
247. #2331C22semidirect
248. #2327C22semidirect
249. #2326C22semidirect
250. #2326C22semidirect
255. #2318C22semidirect
258. C4×C4⋊Q8C22semidirect
259. C4×#124C22semidirect
272. #2295C22semidirect
273. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#593312
#593232
#592642
#592502
#457812
#454702
#397362
#397342
#393532
#393512
#380052
#379832
#379802
#379242
#378582
#378572
#376712
#376682
#376242
#376192
#373842
#372932
#366252
#366242
#364812
#364602
#363902
#363792
#363022
#362882
#353182
#352992
#343932
#343732
#340122