Finite Group Databasebeta

← #8657133

Subgroups — #8657133

Order 512.

6638 conjugacy classes of subgroups.

The subgroup lattice has 1745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59015C212yesmaximal, complemented
2#57981C214yesmaximal, complemented
3#57970C214yesmaximal, complemented
4#57146C212yesmaximal, complemented
5#52988C211yesmaximal, characteristic, complemented
6#52031C214yesmaximal, complemented
7#48487C214yesmaximal, complemented
8#47934C214yesmaximal, complemented
9#47118C214yesmaximal, complemented
10#47063C212yesmaximal, complemented
11#45645C211yesmaximal, characteristic, complemented
12#45483C212yesmaximal, complemented
13#45352C212yesmaximal, complemented
14#44914C211yesmaximal, characteristic, complemented
15#43098C212yesmaximal, complemented
16#42504C212yesmaximal, complemented
17#42478C211yesmaximal, characteristic, complemented
18#40638C212yesmaximal, complemented
19#40148C212yesmaximal, complemented
20#39862C212yesmaximal, complemented
21#39046C212yesmaximal, complemented
22#38916C211yesmaximal, characteristic, complemented
23#37836C212yesmaximal, complemented
24#37346C212yesmaximal, complemented
25D4×#121C212yesmaximal, complemented
26#35680C211yesmaximal, characteristic, complemented
27#35512C212yesmaximal, complemented
28#35077C212yesmaximal, complemented
29#34655C211yesmaximal, characteristic, complemented
30C22×H(5,𝔽2)C2211yescharacteristic, complemented
31C2×#560C2214yescomplemented
32C2×#553C2212yescomplemented
33C2×#547C2211yescharacteristic, complemented
34C2×#546C2211yescharacteristic, complemented
35C2×#546C2214yescomplemented
36C2×D42C2212yescomplemented
37C2×D42C2214yescomplemented
38C2×#525C2212yescomplemented
39C2×#525C2212yescomplemented
40C22×#121C2211yescharacteristic, complemented
41C22×#121C2212yescomplemented
42C22×C4×D4C2212yescomplemented
43#2856C2212yescomplemented
44#2855C2212yescomplemented
45#2854C2212yescomplemented
46#2848C2211yescharacteristic, complemented
47#2847C2212yescomplemented
48#2847C2212yescomplemented
49#2842C2212yescomplemented
50#2827C2214yescomplemented
51#2826C2214yescomplemented
52#2826C2212yescomplemented
53#2824C2212yescomplemented
54#2816C2212yescomplemented
55#2813C2214yescomplemented
56#2797C2214yescomplemented
57#2786C2214yescomplemented
58#2784C2214yescomplemented
59#2782C2212yescomplemented
60#2780C2214yescomplemented
61#2768C2214yescomplemented
62#2763C2212yescomplemented
63#2761C2214yescomplemented
64#2753C2214yescomplemented
65#2750C2214yescomplemented
66#2743C2214yescomplemented
67#2741C2214yescomplemented
68#2735C2214yescomplemented
69#2723C2214yescomplemented
70#2708C2214yescomplemented
71#2708C2214yescomplemented
72#2708C2214yescomplemented
73#2706C2214yescomplemented
74#2706C2214yescomplemented
75#2706C2214yescomplemented
76#2705C2214yescomplemented
77#2705C2214yescomplemented
78#2703C2214yescomplemented
79#2703C2214yescomplemented
80#2702C2214yescomplemented
81#2697C2214yescomplemented
82#2697C2214yescomplemented
83#2696C2214yescomplemented
84#2695C2214yescomplemented
85#2693C2214yescomplemented
86#2691C2214yescomplemented
87#2688C2214yescomplemented
88#2688C2214yescomplemented
89#2686C2214yescomplemented
90#2685C2214yescomplemented
91#2685C2214yescomplemented
92#2684C2214yescomplemented
93#2679C2212yescomplemented
94#2678C2214yescomplemented
95#2678C2214yescomplemented
96#2678C2214yescomplemented
97#2676C2214yescomplemented
98#2675C2212yescomplemented
99#2673C2214yescomplemented
100#2672C2214yescomplemented
101#2671C2214yescomplemented
102#2671C2214yescomplemented
103#2671C2214yescomplemented
104#2670C2212yescomplemented
105#2669C2214yescomplemented
106#2668C2214yescomplemented
107#2668C2212yescomplemented
108#2668C2214yescomplemented
109#2668C2214yescomplemented
110#2644C2212yescomplemented
111#2640C2211yescharacteristic, complemented
112#2636C2214yescomplemented
113#2636C2214yescomplemented
114#2636C2214yescomplemented
115#2630C2214yescomplemented
116#2630C2214yescomplemented
117#2630C2214yescomplemented
118#2629C2212yescomplemented
119#2626C2212yescomplemented
120#2622C2212yescomplemented
121#2615C2212yescomplemented
122#2615C2211yescharacteristic, complemented
123#2613C2212yescomplemented
124#2612C2212yescomplemented
125#2603C2214yescomplemented
126#2603C2214yescomplemented
127#2603C2214yescomplemented
128#2579C2214yescomplemented
129#2563C2211yescharacteristic, complemented
130#2562C2212yescomplemented
131#2543C2214yescomplemented
132#2541C2212yescomplemented
133#2540C2211yescharacteristic, complemented
134#2537C2212yescomplemented
135#2537C2212yescomplemented
136#2535C2214yescomplemented
137#2534C2214yescomplemented
138#2534C2214yescomplemented
139#2531C2214yescomplemented
140#2512C2212yescomplemented
141#2511C2212yescomplemented
142#2505C2214yescomplemented
143#2502C2211yescharacteristic, complemented
144#2501C2212yescomplemented
145#2496C2212yescomplemented
146#2491C2212yescomplemented
147#2490C2212yescomplemented
148#2490C2212yescomplemented
149#2489C2212yescomplemented
150#2487C2211yescharacteristic, complemented
151#2487C2212yescomplemented
152#2485C2212yescomplemented
153#2485C2212yescomplemented
154#2480C2214yescomplemented
155#2467C2214yescomplemented
156#2463C2212yescomplemented
157#2463C2211yescharacteristic, complemented
158#2456C2214yescomplemented
159#2456C2214yescomplemented
160#2456C2212yescomplemented
161#2455C2211yescharacteristic, complemented
162#2454C2212yescomplemented
163#2450C2214yescomplemented
164#2449C2212yescomplemented
165#2445C2212yescomplemented
166#2443C2212yescomplemented
167#2440C2212yescomplemented
168#2437C2211yescharacteristic, complemented
169#2437C2214yescomplemented
170#2433C2211yescharacteristic, complemented
171#2431C2212yescomplemented
172#2430C2212yescomplemented
173#2430C2214yescomplemented
174#2428C2214yescomplemented
175#2428C2212yescomplemented
176#2427C2212yescomplemented
177#2425C2214yescomplemented
178#2424C2214yescomplemented
179#2424C2212yescomplemented
180#2424C2214yescomplemented
181#2424C2214yescomplemented
182#2424C2214yescomplemented
183#2424C2214yescomplemented
184#2422C2212yescomplemented
185#2418C2212yescomplemented
186#2418C2214yescomplemented
187#2417C2212yescomplemented
188#2417C2212yescomplemented
189#2416C2212yescomplemented
190#2416C2212yescomplemented
191#2416C2212yescomplemented
192#2416C2214yescomplemented
193#2416C2212yescomplemented
194#2416C2212yescomplemented
195#2416C2212yescomplemented
196#2412C2214yescomplemented
197#2410C2212yescomplemented
198#2410C2214yescomplemented
199#2410C2214yescomplemented
200#2410C2214yescomplemented
201#2410C2214yescomplemented
202#2410C2212yescomplemented
203#2408C2212yes—
204#2408C2214yescomplemented
205#2408C2212yescomplemented
206#2408C2212yescomplemented
207#2408C2214yescomplemented
208#2408C2214yescomplemented
209#2408C2211yescharacteristic, complemented
210#2408C2212yescomplemented
211#2408C2212yescomplemented
212#2407C2212yescomplemented
213#2407C2212yescomplemented
214#2407C2212yescomplemented
215#2407C2212yescomplemented
216#2407C2214yescomplemented
217#2407C2214yescomplemented
218#2407C2212yescomplemented
219#2405C2212yescomplemented
220#2405C2214yescomplemented
221#2405C2214yescomplemented
222#2405C2214yescomplemented
223#2405C2214yescomplemented
224#2404C2212yescomplemented
225#2404C2212yescomplemented
226#2403C2214yescomplemented
227#2403C2214yescomplemented
228#2403C2211yescharacteristic, complemented
229#2403C2214yescomplemented
230#2397C2211yescharacteristic, complemented
231#2392C2212yescomplemented
232#2388C2211yescharacteristic
233C2×#392C2212yes—
234#2375C2212yescomplemented
235#2361C2212yescomplemented
236D4×C4⋊C4C2212yescomplemented
237D4×C4⋊C4C2212yescomplemented
238#2346C2212yescomplemented
239#2339C2211yescharacteristic, complemented
240D4×C22⋊C4C2211yescharacteristic, complemented
241D4×C22⋊C4C2212yescomplemented
242D4×C22⋊C4C2214yescomplemented
243#2328C2214yescomplemented
244#2325C2214yescomplemented
245#2325C2214yescomplemented
246#2325C2214yescomplemented
247#2324C2212yescomplemented
248#2319C2211yescharacteristic, complemented
249#2315C2212yescomplemented
250#2311C2212yescomplemented
251#2311C2212yescomplemented
252#2309C2212yescomplemented
253C4×#121C2212yescomplemented
254C4×#121C2212yescomplemented
255C4×#120C2211yescharacteristic, complemented
256C4×#120C2212yescomplemented
257#2290C2212yescomplemented
258C2×#380C2212yescomplemented
259C2×H(5,𝔽2)—44no—
260C2×H(5,𝔽2)—48no—
261C22×#41C2311yescharacteristic
262C22×#41C2312yes—
263C22×#41C2311yescharacteristic
264C22×#41C2312yes—
265C22×#41C2312yes—
266C23×D4C2312yes—
267C23×D4C2311yescharacteristic
268C23×D4C2312yes—
269C23×D4C2312yes—
270C23×D4C2314yes—
271C23×D4C2311yescharacteristic
272C23×D4C2314yes—
273C23×D4C2314yes—
274C23×D4C2312yes—
275C24×C4C2312yes—
276C24×C4C2311yescharacteristic
277#560—416no—
278#553—48no—
279#547—44no—
280#546—44no—
281#546—416no—
282D42—48no—
283D42—416no—
284C2×C4⋊Q8C2311yescharacteristic
285C2×#127C2314yes—
286C2×#127C2312yes—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#125C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2314yes—
293#525—48no—
294#525—48no—
295C2×#123C2314yes—
296C2×#123C2312yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2312yes—
300C2×#123C2312yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2311yescharacteristic
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2314yes—
313C2×#121—44no—
314C2×#121—48no—
315C2×#121C2312yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2314yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2311yescharacteristic
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2314yes—
341C2×#121C2314yes—
342C2×#121C2314yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×#120C2312yes—
347C2×#120C2314yes—
348C2×#120C2314yes—
349C2×#120C2314yes—
350C2×#120C2312yes—
351C2×#120C2312yes—
352C2×#120C2312yes—
353C2×#120C2314yes—
354C2×#120C2312yes—
355C2×#120C2314yes—
356C2×#120C2314yes—
357C2×#120C2314yes—
358C2×#120C2314yes—
359C2×#120C2314yes—
360C2×#120C2314yes—
361C2×#120C2314yes—
362C2×#120C2311yescharacteristic
363C2×C4×D4—48no—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2314yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2314yes—
381C2×C4×D4C2314yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C22⋊C4C2312yes—
395C22×C22⋊C4C2312yes—
396C22×C22⋊C4C2312yes—
397C22×C22⋊C4C2314yes—
398C22×C22⋊C4C2314yes—
399C22×C22⋊C4C2312yes—
400C22×C22⋊C4C2312yes—
401C22×C22⋊C4C2314yes—
402C22×C42C2312yes—
403#400C2314yes—
404#400C2312yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#399C2311yescharacteristic
411#399C2312yes—
412#399C2311yescharacteristic
413#399C2312yes—
414#399C2314yes—
415#399C2314yes—
416#399C2312yes—
417#399C2314yes—
418#399C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2312yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2312yes—
453#396C2312yes—
454#396C2314yes—
455#395C2311yescharacteristic
456#395C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2312yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2311yescharacteristic
473#394C2314yes—
474#394C2314yes—
475#394C2312yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2312yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2312yes—
485#394C2312yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#393C2312yes—
495#393C2312yes—
496#393C2312yes—
497#393C2314yes—
498#393C2312yes—
499#393C2312yes—
500#393C2311yescharacteristic
501#392C2312yes—
502#392C2314yes—
503#392C2312yes—
504#392C2314yes—
505#392C2314yes—
506#392C2312yes—
507#392C2314yes—
508#392C2312yes—
509#392C2311yescharacteristic
510#392C2314yes—
511#392C2314yes—
512#392C2312yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2311yescharacteristic
520#392C2314yes—
521#392C2312yes—
522#392C2312yes—
523#392C2311yescharacteristic
524#392C2312yes—
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#391C2312yes—
529#391C2314yes—
530#391C2312yes—
531#391C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2314yes—
537#390C2312yes—
538#390C2314yes—
539#390C2312yes—
540#390C2314yes—
541#390C2312yes—
542#390C2312yes—
543#390C2314yes—
544#390C2314yes—
545#390C2314yes—
546#390C2312yes—
547#390C2314yes—
548#390C2314yes—
549#390C2312yes—
550#390C2314yes—
551#390C2314yes—
552#390C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
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#388C2312yes—
579#388C2312yes—
580#388C2314yes—
581#388C2312yes—
582#388C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2312yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2312yes—
626#386C2314yes—
627#386C2311yescharacteristic
628#386C2312yes—
629#386C2314yes—
630#386C2312yes—
631#386C2314yes—
632#386C2314yes—
633#386C2312yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#385C2311yescharacteristic
640#385C2312yes—
641#385C2314yes—
642#385C2312yes—
643#385C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2312yes—
654#385C2312yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2312yes—
662#385C2314yes—
663#385C2312yes—
664#385C2312yes—
665#385C2312yes—
666#385C2312yes—
667#384C2312yes—
668#384C2312yes—
669#382C2312yes—
670#382C2314yes—
671#382C2314yes—
672#381C2312yes—
673#381C2312yes—
674#381C2314yes—
675#380C2311yescharacteristic
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2312yes—
681#380C2312yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2314yes—
686#380C2314yes—
687#380C2312yes—
688#380C2314yes—
689#380C2314yes—
690#380C2314yes—
691#380C2314yes—
692#380C2312yes—
693#380C2311yescharacteristic
694#380C2312yes—
695#380C2312yes—
696#380C2314yes—
697#380C2314yes—
698#380C2312yes—
699#379C2314yes—
700#379C2314yes—
701#379C2314yes—
702#379C2312yes—
703#379C2312yes—
704#379C2314yes—
705#379C2312yes—
706#379C2314yes—
707#379C2314yes—
708#379C2314yes—
709#379C2311yescharacteristic
710#379C2314yes—
711#379C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2311yescharacteristic
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2311yescharacteristic
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2311yescharacteristic
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722#376C2311yescharacteristic
723#376C2314yes—
724C2×#95C2312yes—
725C2×#95C2314yes—
726C25C2412yes—
727C25C2411yescharacteristic
728C25C2412yes—
729C25C2414yes—
730C25C2412yes—
731H(5,𝔽2)—464no—
732C2×#41—24no—
733C2×#41—28no—
734C2×#41—28no—
735C2×#41—42no—
736C2×#41—44no—
737C2×#41—48no—
738C2×#41—44no—
739C2×#41—44no—
740C2×#41—44no—
741C2×#41—44no—
742C2×#41—48no—
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×D4—28no—
747C22×D4—28no—
748C22×D4—24no—
749C22×D4—28no—
750C22×D4—44no—
751C22×D4—48no—
752C22×D4—44no—
753C22×D4—42no—
754C22×D4—44no—
755C22×D4—48no—
756C22×D4—44no—
757C22×D4—44no—
758C22×D4—44no—
759C22×D4—48no—
760C22×D4—48no—
761C22×D4—48no—
762C22×D4—44no—
763C22×D4—48no—
764C22×D4—48no—
765C22×D4—48no—
766C22×D4—48no—
767C22×D4—48no—
768C22×D4—48no—
769C22×D4C2412yes—
770C22×D4C2411yescharacteristic
771C22×D4C2412yes—
772C22×D4C2412yes—
773C22×D4C2412yes—
774C22×D4C2412yes—
775C22×D4C2411yescharacteristic
776C22×D4C2414yes—
777C22×D4C2414yes—
778C22×D4C2411yescharacteristic
779C22×D4C2414yes—
780C22×D4C2412yes—
781C22×D4C2411yescharacteristic
782C22×D4C2411yescharacteristic
783C22×D4C2412yes—
784C22×D4C2414yes—
785C22×D4C2414yes—
786C22×D4C2412yes—
787C22×D4C2414yes—
788C22×D4C2414yes—
789C22×D4C2412yes—
790C22×D4C2414yes—
791C22×D4C2414yes—
792C22×D4C2414yes—
793C22×D4C2414yes—
794C22×D4C2414yes—
795C22×D4C2412yes—
796C22×D4C2414yes—
797C22×D4C2412yes—
798C22×D4C2414yes—
799C22×D4C2412yes—
800C22×D4C2412yes—
801C23×C4—28no—
802C23×C4—44no—
803C23×C4—44no—
804C23×C4—42no—
805C23×C4—44no—
806C23×C4C2412yes—
807C23×C4C2411yescharacteristic
808C23×C4C2411yescharacteristic
809C23×C4C2412yes—
810C23×C4C2412yes—
811C23×C4C2412yes—
812C23×C4C2412yes—
813C23×C4C2412yes—
814C23×C4C2412yes—
815C23×C4C2414yes—
816C23×C4C2414yes—
817C23×C4C2412yes—
818C23×C4C2412yes—
819C23×C4C2412yes—
820C23×C4C2414yes—
821C23×C4C2411yescharacteristic
822C23×C4C2414yes—
823C23×C4C2412yes—
824C23×C4C2412yes—
825C23×C4C2414yes—
826C23×C4C2414yes—
827C4⋊Q8—42no—
828#127—216no—
829#127—44no—
830#126—48no—
831#126—48no—
832#126—48no—
833#125—44no—
834#124—42no—
835#124—48no—
836#123—48no—
837#123—44no—
838#123—48no—
839#123—48no—
840#123—48no—
841#123—48no—
842#123—44no—
843#123—48no—
844#123—48no—
845#123—44no—
846#123—48no—
847C22⋊Q8—44no—
848C22⋊Q8—48no—
849C22⋊Q8—44no—
850C22⋊Q8—44no—
851C22⋊Q8—44no—
852C22⋊Q8—44no—
853C22⋊Q8—42no—
854#121—28no—
855#121—28no—
856#121—216no—
857#121—216no—
858#121—28no—
859#121—28no—
860#121—48no—
861#121—48no—
862#121—48no—
863#121—48no—
864#121—48no—
865#121—44no—
866#121—44no—
867#121—48no—
868#121—48no—
869#121—48no—
870#121—48no—
871#121—48no—
872#121—48no—
873#121—44no—
874#121—44no—
875#121—44no—
876#121—44no—
877#121—44no—
878#121—44no—
879#121—48no—
880#121—42no—
881#121—44no—
882#121—44no—
883#121—48no—
884#121—48no—
885#120—28no—
886#120—44no—
887#120—48no—
888#120—48no—
889#120—42no—
890#120—48no—
891#120—48no—
892#120—48no—
893#120—48no—
894#120—44no—
895#120—44no—
896#120—44no—
897#120—48no—
898#120—48no—
899#120—48no—
900#120—48no—
901#120—48no—
902C4×D4—24no—
903C4×D4—28no—
904C4×D4—28no—
905C4×D4—28no—
906C4×D4—48no—
907C4×D4—44no—
908C4×D4—48no—
909C4×D4—44no—
910C4×D4—44no—
911C4×D4—44no—
912C4×D4—44no—
913C4×D4—48no—
914C4×D4—48no—
915C4×D4—44no—
916C4×D4—48no—
917C4×D4—42no—
918C4×D4—42no—
919C4×D4—44no—
920C4×D4—44no—
921C4×D4—48no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—48no—
925#117—28no—
926#117—44no—
927C2×C4⋊C4—44no—
928C2×C4⋊C4—42no—
929C2×C4⋊C4—44no—
930C2×C4⋊C4—44no—
931C2×C4⋊C4—44no—
932C2×C4⋊C4C2411yescharacteristic
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C22⋊C4—44no—
972C2×C22⋊C4—48no—
973C2×C22⋊C4—44no—
974C2×C22⋊C4—44no—
975C2×C22⋊C4—44no—
976C2×C22⋊C4—48no—
977C2×C22⋊C4—48no—
978C2×C22⋊C4—44no—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2411yescharacteristic
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2414yes—
989C2×C22⋊C4C2414yes—
990C2×C22⋊C4C2412yes—
991C2×C22⋊C4C2414yes—
992C2×C22⋊C4C2412yes—
993C2×C22⋊C4C2412yes—
994C2×C22⋊C4C2414yes—
995C2×C22⋊C4C2414yes—
996C2×C22⋊C4C2412yes—
997C2×C22⋊C4C2412yes—
998C2×C22⋊C4C2412yes—
999C2×C22⋊C4C2412yes—
1000C2×C22⋊C4C2412yes—
1001C2×C22⋊C4C2414yes—
1002C2×C22⋊C4C2411yescharacteristic
1003C2×C22⋊C4C2412yes—
1004C2×C22⋊C4C2412yes—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2414yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2411yescharacteristic
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2414yes—
1057C2×C42—44no—
1058C2×C42C2412yes—
1059C2×C42C2414yes—
1060C2×C42C2412yes—
1061C2×C42C2411yescharacteristic
1062C2×C42C2412yes—
1063C2×C42C2414yes—
1064C2×C42C2414yes—
1065C2×C42C2412yes—
1066C2×C42C2412yes—
1067C2×C42C2412yes—
1068#95C2411yescharacteristic
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2414yes—
1075#95C2412yes—
1076#95C2411yescharacteristic
1077#95C2414yes—
1078#95C2414yes—
1079#95C2411yescharacteristic
1080#95C2414yes—
1081#95C2412yes—
1082#95C2411yescharacteristic
1083#95C2412yes—
1084#95C2414yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2412yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109C24—24no—
1110C24—24no—
1111C24—24no—
1112C24—24no—
1113C24—22no—
1114C24—24no—
1115C24—28no—
1116C24—28no—
1117C24—24no—
1118C24—42no—
1119C24—41no—
1120C24—42no—
1121C24—42no—
1122C24—42no—
1123C24—44no—
1124C24—44no—
1125C24—42no—
1126C24—42no—
1127C24—42no—
1128C24—41no—
1129C24—44no—
1130C24—44no—
1131C24—44no—
1132C24—44no—
1133C24—44no—
1134C24—44no—
1135C24—44no—
1136C24—42no—
1137C24—42no—
1138C24C2511yescharacteristic
1139C24C2514yes—
1140C24C2512yes—
1141C24C2512yes—
1142C24C2512yes—
1143C24C2512yes—
1144C24C2512yes—
1145C24C2511yescharacteristic
1146#41—416no—
1147#41—432no—
1148#41—416no—
1149#41—432no—
1150#41—816no—
1151C2×Q8—24no—
1152C2×Q8—24no—
1153C2×Q8—22no—
1154C2×Q8—41no—
1155C2×Q8—44no—
1156C2×Q8—42no—
1157C2×D4—24no—
1158C2×D4—24no—
1159C2×D4—24no—
1160C2×D4—24no—
1161C2×D4—24no—
1162C2×D4—24no—
1163C2×D4—28no—
1164C2×D4—24no—
1165C2×D4—24no—
1166C2×D4—28no—
1167C2×D4—24no—
1168C2×D4—24no—
1169C2×D4—28no—
1170C2×D4—28no—
1171C2×D4—28no—
1172C2×D4—28no—
1173C2×D4—24no—
1174C2×D4—24no—
1175C2×D4—28no—
1176C2×D4—24no—
1177C2×D4—28no—
1178C2×D4—24no—
1179C2×D4—28no—
1180C2×D4—28no—
1181C2×D4—28no—
1182C2×D4—28no—
1183C2×D4—24no—
1184C2×D4—28no—
1185C2×D4—22no—
1186C2×D4—28no—
1187C2×D4—24no—
1188C2×D4—24no—
1189C2×D4—24no—
1190C2×D4—28no—
1191C2×D4—24no—
1192C2×D4—22no—
1193C2×D4—24no—
1194C2×D4—24no—
1195C2×D4—24no—
1196C2×D4—28no—
1197C2×D4—432no—
1198C2×D4—42no—
1199C2×D4—42no—
1200C2×D4—44no—
1201C2×D4—44no—
1202C2×D4—41no—
1203C2×D4—42no—
1204C2×D4—44no—
1205C2×D4—41no—
1206C2×D4—42no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—44no—
1210C2×D4—44no—
1211C2×D4—42no—
1212C2×D4—42no—
1213C2×D4—42no—
1214C2×D4—41no—
1215C2×D4—42no—
1216C2×D4—42no—
1217C2×D4—44no—
1218C2×D4—44no—
1219C2×D4—44no—
1220C2×D4—44no—
1221C2×D4—44no—
1222C2×D4—44no—
1223C2×D4—44no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4—42no—
1227C2×D4—44no—
1228C2×D4—44no—
1229C2×D4—44no—
1230C2×D4—44no—
1231C2×D4—44no—
1232C2×D4—44no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—41no—
1236C2×D4—44no—
1237C2×D4—44no—
1238C2×D4—42no—
1239C2×D4—44no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—42no—
1243C2×D4—44no—
1244C2×D4—432no—
1245C2×D4—464no—
1246C2×D4—432no—
1247C2×D4—416no—
1248C2×D4—88no—
1249C2×D4—832no—
1250C2×D4—816no—
1251C2×D4—832no—
1252C2×D4H(5,𝔽2)14yes—
1253C2×D4H(5,𝔽2)18yescomplemented
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—28no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—24no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—28no—
1270C22×C4—24no—
1271C22×C4—22no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—28no—
1275C22×C4—24no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—44no—
1279C22×C4—44no—
1280C22×C4—44no—
1281C22×C4—42no—
1282C22×C4—41no—
1283C22×C4—42no—
1284C22×C4—42no—
1285C22×C4—42no—
1286C22×C4—44no—
1287C22×C4—44no—
1288C22×C4—44no—
1289C22×C4—44no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—816no—
1311C22×C4—88no—
1312C22×C4H(5,𝔽2)18yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2512yes—
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2514yes—
1318C22×C4C2514yes—
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2514yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2514yes—
1326C22×C4C2514yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2511yescharacteristic
1334C4⋊C4—22no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—28no—
1344C4⋊C4—28no—
1345C4⋊C4—24no—
1346C4⋊C4—42no—
1347C4⋊C4—42no—
1348C4⋊C4—44no—
1349C4⋊C4—42no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—44no—
1356C4⋊C4—41no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—41no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—42no—
1373C22⋊C4—28no—
1374C22⋊C4—24no—
1375C22⋊C4—24no—
1376C22⋊C4—28no—
1377C22⋊C4—28no—
1378C22⋊C4—28no—
1379C22⋊C4—28no—
1380C22⋊C4—24no—
1381C22⋊C4—24no—
1382C22⋊C4—28no—
1383C22⋊C4—24no—
1384C22⋊C4—24no—
1385C22⋊C4—22no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—28no—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—28no—
1394C22⋊C4—24no—
1395C22⋊C4—41no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—42no—
1399C22⋊C4—42no—
1400C22⋊C4—42no—
1401C22⋊C4—42no—
1402C22⋊C4—44no—
1403C22⋊C4—42no—
1404C22⋊C4—44no—
1405C22⋊C4—44no—
1406C22⋊C4—44no—
1407C22⋊C4—42no—
1408C22⋊C4—42no—
1409C22⋊C4—44no—
1410C22⋊C4—42no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4—41no—
1414C22⋊C4—42no—
1415C22⋊C4—42no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—42no—
1425C22⋊C4—44no—
1426C22⋊C4—41no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—42no—
1431C22⋊C4—44no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—42no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C42—24no—
1452C42—24no—
1453C42—28no—
1454C42—24no—
1455C42—22no—
1456C42—28no—
1457C42—42no—
1458C42—42no—
1459C42—42no—
1460C42—44no—
1461C23—22no—
1462C23—22no—
1463C23—22no—
1464C23—22no—
1465C23—22no—
1466C23—22no—
1467C23—21no—
1468C23—22no—
1469C23—24no—
1470C23—22no—
1471C23—22no—
1472C23—22no—
1473C23—22no—
1474C23—22no—
1475C23—24no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—22no—
1482C23—22no—
1483C23—21no—
1484C23—22no—
1485C23—22no—
1486C23—22no—
1487C23—24no—
1488C23—22no—
1489C23—24no—
1490C23—22no—
1491C23—24no—
1492C23—24no—
1493C23—22no—
1494C23—24no—
1495C23—24no—
1496C23—21no—
1497C23—24no—
1498C23—24no—
1499C23—21no—
1500C23—22no—
1501C23—24no—
1502C23—22no—
1503C23—21no—
1504C23—48no—
1505C23—48no—
1506C23—48no—
1507C23—44no—
1508C23—48no—
1509C23—416no—
1510C23—48no—
1511C23—48no—
1512C23—84no—
1513C23—84no—
1514C23—82no—
1515C23—84no—
1516C23—84no—
1517C23—84no—
1518C23—88no—
1519C23—88no—
1520C23—88no—
1521C23—84no—
1522C23—88no—
1523C23—88no—
1524C23—82no—
1525C23—84no—
1526C23—164no—
1527C23—164no—
1528C23—164no—
1529C23—162no—
1530C23—164no—
1531C23—162no—
1532C23—164no—
1533C23C2×H(5,𝔽2)14yes—
1534C23C2×H(5,𝔽2)14yes—
1535C23C2×H(5,𝔽2)14yes—
1536C23C2×H(5,𝔽2)14yes—
1537C23#58512yes—
1538C23C2611yescharacteristic
1539Q8—44no—
1540Q8—44no—
1541Q8—84no—
1542D4—216no—
1543D4—28no—
1544D4—48no—
1545D4—48no—
1546D4—416no—
1547D4—48no—
1548D4—48no—
1549D4—48no—
1550D4—44no—
1551D4—416no—
1552D4—416no—
1553D4—44no—
1554D4—416no—
1555D4—48no—
1556D4—48no—
1557D4—48no—
1558D4—44no—
1559D4—88no—
1560D4—88no—
1561D4—84no—
1562D4—82no—
1563D4—84no—
1564D4—88no—
1565D4—88no—
1566D4—88no—
1567D4—88no—
1568D4—88no—
1569D4—88no—
1570D4—88no—
1571D4—84no—
1572D4—162no—
1573D4—164no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—216no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—22no—
1584C2×C4—24no—
1585C2×C4—24no—
1586C2×C4—24no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—24no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—24no—
1600C2×C4—22no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—24no—
1609C2×C4—24no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—24no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—24no—
1620C2×C4—21no—
1621C2×C4—22no—
1622C2×C4—24no—
1623C2×C4—21no—
1624C2×C4—24no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—48no—
1629C2×C4—416no—
1630C2×C4—48no—
1631C2×C4—48no—
1632C2×C4—48no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—84no—
1636C2×C4—84no—
1637C2×C4—88no—
1638C2×C4—84no—
1639C2×C4—84no—
1640C2×C4—88no—
1641C2×C4—84no—
1642C2×C4—82no—
1643C2×C4—84no—
1644C2×C4—84no—
1645C2×C4—88no—
1646C2×C4—164no—
1647C2×C4—164no—
1648C2×C4C2×H(5,𝔽2)14yes—
1649C2×C4C2×H(5,𝔽2)14yes—
1650C2×C4C2×H(5,𝔽2)14yes—
1651C2×C4C2×H(5,𝔽2)12yes—
1652C22—24no—
1653C22—24no—
1654C22—24no—
1655C22—24no—
1656C22—24no—
1657C22—24no—
1658C22—24no—
1659C22—22no—
1660C22—24no—
1661C22—24no—
1662C22—24no—
1663C22—24no—
1664C22—24no—
1665C22—24no—
1666C22—42no—
1667C22—41no—
1668C22—42no—
1669C22—44no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—42no—
1674C22—42no—
1675C22—42no—
1676C22—42no—
1677C22—42no—
1678C22—42no—
1679C22—44no—
1680C22—42no—
1681C22—42no—
1682C22—41no—
1683C22—42no—
1684C22—44no—
1685C22—41no—
1686C22—44no—
1687C22—44no—
1688C22—44no—
1689C22—42no—
1690C22—41no—
1691C22—42no—
1692C22—44no—
1693C22—44no—
1694C22—42no—
1695C22—44no—
1696C22—44no—
1697C22—44no—
1698C22—41no—
1699C22—42no—
1700C22—816no—
1701C22—88no—
1702C22—168no—
1703C22—1616no—
1704C22—168no—
1705C22C22×H(5,𝔽2)12yes—
1706C22C22×H(5,𝔽2)11yescharacteristic
1707C22C22×H(5,𝔽2)12yes—
1708C22C2×#58511yescharacteristic
1709C222−1+611yescharacteristic
1710C4—24no—
1711C4—24no—
1712C4—42no—
1713C4—44no—
1714C4—44no—
1715C4—41no—
1716C4—42no—
1717C4—44no—
1718C4—42no—
1719C4—44no—
1720C4—41no—
1721C4—42no—
1722C4—42no—
1723C4—42no—
1724C4—44no—
1725C4—41no—
1726C4—42no—
1727C4—42no—
1728C4—42no—
1729C4—41no—
1730C4#353214yes—
1731C2—44no—
1732C2—44no—
1733C2—44no—
1734C2—42no—
1735C2—44no—
1736C2—82no—
1737C2—84no—
1738C2—81no—
1739C2C2×#353211yescharacteristic
1740C2#6281812yes—
1741C2#6289811yescharacteristic
1742C2#6291412yes—
1743C2#6301111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59015C2semidirect
2. #57981C2semidirect
3. #57970C2semidirect
4. #57146C2semidirect
5. #52988C2semidirect
6. #52031C2semidirect
7. #48487C2semidirect
8. #47934C2semidirect
9. #47118C2semidirect
10. #47063C2semidirect
11. #45645C2semidirect
12. #45483C2semidirect
13. #45352C2semidirect
14. #44914C2semidirect
15. #43098C2semidirect
16. #42504C2semidirect
17. #42478C2semidirect
18. #40638C2semidirect
19. #40148C2semidirect
20. #39862C2semidirect
21. #39046C2semidirect
22. #38916C2semidirect
23. #37836C2semidirect
24. #37346C2semidirect
25. D4×#121C2semidirect
26. #35680C2semidirect
27. #35512C2semidirect
28. #35077C2semidirect
29. #34655C2semidirect
30. C22×H(5,𝔽2)C22semidirect
31. C2×#560C22semidirect
32. C2×#553C22semidirect
33. C2×#547C22semidirect
34. C2×#546C22semidirect
35. C2×#546C22semidirect
36. C2×D42C22semidirect
37. C2×D42C22semidirect
38. C2×#525C22semidirect
39. C2×#525C22semidirect
40. C22×#121C22semidirect
41. C22×#121C22semidirect
42. C22×C4×D4C22semidirect
43. #2856C22semidirect
44. #2855C22semidirect
45. #2854C22semidirect
46. #2848C22semidirect
47. #2847C22semidirect
48. #2847C22semidirect
49. #2842C22semidirect
50. #2827C22semidirect
51. #2826C22semidirect
52. #2826C22semidirect
53. #2824C22semidirect
54. #2816C22semidirect
55. #2813C22semidirect
56. #2797C22semidirect
57. #2786C22semidirect
58. #2784C22semidirect
59. #2782C22semidirect
60. #2780C22semidirect
61. #2768C22semidirect
62. #2763C22semidirect
63. #2761C22semidirect
64. #2753C22semidirect
65. #2750C22semidirect
66. #2743C22semidirect
67. #2741C22semidirect
68. #2735C22semidirect
69. #2723C22semidirect
70. #2708C22semidirect
71. #2708C22semidirect
72. #2708C22semidirect
73. #2706C22semidirect
74. #2706C22semidirect
75. #2706C22semidirect
76. #2705C22semidirect
77. #2705C22semidirect
78. #2703C22semidirect
79. #2703C22semidirect
80. #2702C22semidirect
81. #2697C22semidirect
82. #2697C22semidirect
83. #2696C22semidirect
84. #2695C22semidirect
85. #2693C22semidirect
86. #2691C22semidirect
87. #2688C22semidirect
88. #2688C22semidirect
89. #2686C22semidirect
90. #2685C22semidirect
91. #2685C22semidirect
92. #2684C22semidirect
93. #2679C22semidirect
94. #2678C22semidirect
95. #2678C22semidirect
96. #2678C22semidirect
97. #2676C22semidirect
98. #2675C22semidirect
99. #2673C22semidirect
100. #2672C22semidirect
101. #2671C22semidirect
102. #2671C22semidirect
103. #2671C22semidirect
104. #2670C22semidirect
105. #2669C22semidirect
106. #2668C22semidirect
107. #2668C22semidirect
108. #2668C22semidirect
109. #2668C22semidirect
110. #2644C22semidirect
111. #2640C22semidirect
112. #2636C22semidirect
113. #2636C22semidirect
114. #2636C22semidirect
115. #2630C22semidirect
116. #2630C22semidirect
117. #2630C22semidirect
118. #2629C22semidirect
119. #2626C22semidirect
120. #2622C22semidirect
121. #2615C22semidirect
122. #2615C22semidirect
123. #2613C22semidirect
124. #2612C22semidirect
125. #2603C22semidirect
126. #2603C22semidirect
127. #2603C22semidirect
128. #2579C22semidirect
129. #2563C22semidirect
130. #2562C22semidirect
131. #2543C22semidirect
132. #2541C22semidirect
133. #2540C22semidirect
134. #2537C22semidirect
135. #2537C22semidirect
136. #2535C22semidirect
137. #2534C22semidirect
138. #2534C22semidirect
139. #2531C22semidirect
140. #2512C22semidirect
141. #2511C22semidirect
142. #2505C22semidirect
143. #2502C22semidirect
144. #2501C22semidirect
145. #2496C22semidirect
146. #2491C22semidirect
147. #2490C22semidirect
148. #2490C22semidirect
149. #2489C22semidirect
150. #2487C22semidirect
151. #2487C22semidirect
152. #2485C22semidirect
153. #2485C22semidirect
154. #2480C22semidirect
155. #2467C22semidirect
156. #2463C22semidirect
157. #2463C22semidirect
158. #2456C22semidirect
159. #2456C22semidirect
160. #2456C22semidirect
161. #2455C22semidirect
162. #2454C22semidirect
163. #2450C22semidirect
164. #2449C22semidirect
165. #2445C22semidirect
166. #2443C22semidirect
167. #2440C22semidirect
168. #2437C22semidirect
169. #2437C22semidirect
170. #2433C22semidirect
171. #2431C22semidirect
172. #2430C22semidirect
173. #2430C22semidirect
174. #2428C22semidirect
175. #2428C22semidirect
176. #2427C22semidirect
177. #2425C22semidirect
178. #2424C22semidirect
179. #2424C22semidirect
180. #2424C22semidirect
181. #2424C22semidirect
182. #2424C22semidirect
183. #2424C22semidirect
184. #2422C22semidirect
185. #2418C22semidirect
186. #2418C22semidirect
187. #2417C22semidirect
188. #2417C22semidirect
189. #2416C22semidirect
190. #2416C22semidirect
191. #2416C22semidirect
192. #2416C22semidirect
193. #2416C22semidirect
194. #2416C22semidirect
195. #2416C22semidirect
196. #2412C22semidirect
197. #2410C22semidirect
198. #2410C22semidirect
199. #2410C22semidirect
200. #2410C22semidirect
201. #2410C22semidirect
202. #2410C22semidirect
204. #2408C22semidirect
205. #2408C22semidirect
206. #2408C22semidirect
207. #2408C22semidirect
208. #2408C22semidirect
209. #2408C22semidirect
210. #2408C22semidirect
211. #2408C22semidirect
212. #2407C22semidirect
213. #2407C22semidirect
214. #2407C22semidirect
215. #2407C22semidirect
216. #2407C22semidirect
217. #2407C22semidirect
218. #2407C22semidirect
219. #2405C22semidirect
220. #2405C22semidirect
221. #2405C22semidirect
222. #2405C22semidirect
223. #2405C22semidirect
224. #2404C22semidirect
225. #2404C22semidirect
226. #2403C22semidirect
227. #2403C22semidirect
228. #2403C22semidirect
229. #2403C22semidirect
230. #2397C22semidirect
231. #2392C22semidirect
234. #2375C22semidirect
235. #2361C22semidirect
236. D4×C4⋊C4C22semidirect
237. D4×C4⋊C4C22semidirect
238. #2346C22semidirect
239. #2339C22semidirect
240. D4×C22⋊C4C22semidirect
241. D4×C22⋊C4C22semidirect
242. D4×C22⋊C4C22semidirect
243. #2328C22semidirect
244. #2325C22semidirect
245. #2325C22semidirect
246. #2325C22semidirect
247. #2324C22semidirect
248. #2319C22semidirect
249. #2315C22semidirect
250. #2311C22semidirect
251. #2311C22semidirect
252. #2309C22semidirect
253. C4×#121C22semidirect
254. C4×#121C22semidirect
255. C4×#120C22semidirect
256. C4×#120C22semidirect
257. #2290C22semidirect
258. C2×#380C22semidirect
1253. C2×D4H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
#590152
#579812
#579702
#571462
#529882
#520312
#484872
#479342
#471182
#470632
#456452
#454832
#453522
#449142
#430982
#425042
#424782
#406382
#401482
#398622
#390462
#389162
#378362
#373462
D4×#1212
#356802
#355122
#350772
#346552