Finite Group Databasebeta

← #8721158

Subgroups — #8721158

Order 512.

6655 conjugacy classes of subgroups.

The subgroup lattice has 1740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59945C211yesmaximal, characteristic, complemented
2#59944C212yesmaximal, complemented
3#59419C212yesmaximal, complemented
4#59414C212yesmaximal, complemented
5#59412C212yesmaximal, complemented
6#54942C214yesmaximal, complemented
7#53961C214yesmaximal, complemented
8#53938C214yesmaximal, complemented
9#53422C212yesmaximal, complemented
10#53055C212yesmaximal, complemented
11#52957C211yesmaximal, characteristic, complemented
12#52307C211yesmaximal, characteristic, complemented
13#47689C214yesmaximal, complemented
14#46971C212yesmaximal, complemented
15#44886C212yesmaximal, complemented
16#44870C211yesmaximal, characteristic, complemented
17#44242C212yesmaximal, complemented
18#43894C214yesmaximal, complemented
19#42909C211yesmaximal, characteristic, complemented
20#42420C212yesmaximal, complemented
21#42091C212yesmaximal, complemented
22#41932C214yesmaximal, complemented
23#40164C212yesmaximal, complemented
24#40129C212yesmaximal, complemented
25#39745C211yesmaximal, characteristic, complemented
26#39396C212yesmaximal, complemented
27#39361C212yesmaximal, complemented
28#36091C211yesmaximal, characteristic, complemented
29#35680C212yesmaximal, complemented
30C22×H(5,𝔽2)C2211yescharacteristic
31C2×#559C2211yescharacteristic, complemented
32C2×#550C2212yescomplemented
33C2×#550C2212yescomplemented
34C2×#550C2211yescharacteristic, complemented
35C2×#546C2214yescomplemented
36C2×#546C2212yescomplemented
37C2×D42C2212yes—
38C2×D42C2212yescomplemented
39C2×#538C2214yescomplemented
40C2×#537C2211yescharacteristic, complemented
41C2×#535C2212yescomplemented
42C2×#535C2214yescomplemented
43#2867C2211yescharacteristic, complemented
44#2860C2212yescomplemented
45#2828C2214yescomplemented
46#2828C2212yescomplemented
47#2824C2214yescomplemented
48#2824C2212yescomplemented
49#2818C2214yescomplemented
50#2816C2212yescomplemented
51#2815C2214yescomplemented
52#2813C2214yescomplemented
53#2812C2214yescomplemented
54#2811C2211yescharacteristic, complemented
55#2803C2214yescomplemented
56#2785C2211yescharacteristic, complemented
57#2785C2211yescharacteristic, complemented
58#2785C2212yescomplemented
59#2785C2212yescomplemented
60#2784C2212yescomplemented
61#2782C2212yescomplemented
62#2781C2214yescomplemented
63#2756C2214yescomplemented
64#2753C2214yescomplemented
65#2744C2214yescomplemented
66#2737C2214yescomplemented
67#2733C2212yescomplemented
68#2733C2212yescomplemented
69#2733C2212yescomplemented
70#2733C2211yescharacteristic, complemented
71#2733C2212yescomplemented
72#2733C2214yescomplemented
73#2730C2214yescomplemented
74#2730C2214yescomplemented
75#2714C2214yescomplemented
76#2714C2214yescomplemented
77#2706C2214yescomplemented
78#2703C2214yescomplemented
79#2703C2214yescomplemented
80#2699C2214yescomplemented
81#2699C2214yescomplemented
82#2686C2214yescomplemented
83#2685C2214yescomplemented
84#2685C2214yescomplemented
85#2684C2212yescomplemented
86#2684C2214yescomplemented
87#2679C2212yescomplemented
88#2678C2214yescomplemented
89#2678C2214yescomplemented
90#2678C2214yescomplemented
91#2676C2214yescomplemented
92#2675C2212yescomplemented
93#2673C2214yescomplemented
94#2673C2214yescomplemented
95#2673C2214yescomplemented
96#2673C2214yescomplemented
97#2673C2214yescomplemented
98#2673C2214yescomplemented
99#2673C2214yescomplemented
100#2671C2214yescomplemented
101#2670C2214yescomplemented
102#2670C2212yescomplemented
103#2670C2214yescomplemented
104#2669C2214yescomplemented
105#2669C2214yescomplemented
106#2669C2214yescomplemented
107#2669C2214yescomplemented
108#2669C2214yescomplemented
109#2669C2214yescomplemented
110#2669C2214yescomplemented
111#2669C2214yescomplemented
112#2661C2214yescomplemented
113#2657C2212yescomplemented
114#2656C2212yescomplemented
115#2636C2214yescomplemented
116#2635C2212yescomplemented
117#2635C2214yescomplemented
118#2619C2214yescomplemented
119#2617C2214yescomplemented
120#2615C2211yescharacteristic, complemented
121#2615C2212yescomplemented
122#2615C2211yescharacteristic, complemented
123#2615C2212yescomplemented
124#2613C2214yescomplemented
125#2613C2214yescomplemented
126#2601C2214yescomplemented
127#2598C2214yescomplemented
128#2582C2212yescomplemented
129#2580C2212yescomplemented
130#2572C2212yescomplemented
131#2564C2212yescomplemented
132#2559C2214yescomplemented
133#2557C2214yescomplemented
134#2555C2212yescomplemented
135#2554C2214yescomplemented
136#2554C2214yescomplemented
137#2548C2211yescharacteristic, complemented
138#2548C2212yescomplemented
139#2544C2212yescomplemented
140#2543C2214yescomplemented
141#2543C2214yescomplemented
142#2541C2212yescomplemented
143#2541C2211yescharacteristic, complemented
144#2541C2212yescomplemented
145#2541C2214yescomplemented
146#2539C2214yescomplemented
147#2538C2212yescomplemented
148#2537C2212yescomplemented
149#2537C2212yescomplemented
150#2535C2214yescomplemented
151#2535C2212yescomplemented
152#2531C2214yescomplemented
153#2526C2214yescomplemented
154#2501C2211yescharacteristic, complemented
155#2500C2212yescomplemented
156#2498C2214yescomplemented
157#2497C2212yescomplemented
158#2496C2212yescomplemented
159#2495C2212yescomplemented
160#2487C2211yescharacteristic, complemented
161#2485C2212yescomplemented
162#2482C2214yescomplemented
163#2464C2214yescomplemented
164#2461C2214yescomplemented
165#2459C2214yescomplemented
166#2456C2214yescomplemented
167#2456C2214yescomplemented
168#2433C2211yescharacteristic
169#2433C2212yes—
170#2433C2212yescomplemented
171#2433C2212yescomplemented
172#2433C2214yescomplemented
173#2433C2212yescomplemented
174#2433C2214yescomplemented
175#2433C2214yescomplemented
176#2433C2212yescomplemented
177#2431C2212yes—
178#2431C2212yescomplemented
179#2431C2214yescomplemented
180#2431C2212yescomplemented
181#2431C2214yescomplemented
182#2430C2214yescomplemented
183#2428C2212yescomplemented
184#2428C2212yescomplemented
185#2428C2212yescomplemented
186#2428C2212yescomplemented
187#2428C2212yescomplemented
188#2428C2214yescomplemented
189#2428C2212yescomplemented
190#2428C2212yescomplemented
191#2428C2212yescomplemented
192#2426C2212yescomplemented
193#2424C2214yescomplemented
194#2424C2214yescomplemented
195#2424C2214yescomplemented
196#2424C2214yescomplemented
197#2424C2214yescomplemented
198#2423C2212yescomplemented
199#2422C2212yescomplemented
200#2422C2212yescomplemented
201#2422C2212yescomplemented
202#2420C2212yescomplemented
203#2420C2212yescomplemented
204#2420C2214yescomplemented
205#2418C2214yescomplemented
206#2418C2214yescomplemented
207#2416C2212yescomplemented
208#2414C2212yescomplemented
209#2414C2212yescomplemented
210#2410C2214yescomplemented
211#2410C2214yescomplemented
212#2410C2214yescomplemented
213#2408C2211yescharacteristic
214#2408C2212yes—
215#2408C2214yescomplemented
216#2408C2212yescomplemented
217#2408C2214yescomplemented
218#2408C2212yescomplemented
219#2407C2212yes—
220#2407C2214yescomplemented
221#2407C2212yescomplemented
222#2404C2214yescomplemented
223#2403C2212yescomplemented
224#2403C2214yescomplemented
225#2403C2214yescomplemented
226#2388C2212yescomplemented
227#2388C2211yescharacteristic, complemented
228#2388C2212yescomplemented
229#2388C2211yescharacteristic, complemented
230#2388C2212yescomplemented
231C2×#392C2214yescomplemented
232#2368C2214yescomplemented
233#2363C2212yescomplemented
234#2362C2212yescomplemented
235#2361C2212yescomplemented
236#2358C2214yescomplemented
237#2358C2212yescomplemented
238#2341C2212yescomplemented
239#2341C2211yescharacteristic, complemented
240#2339C2211yescharacteristic, complemented
241#2339C2212yescomplemented
242#2339C2214yescomplemented
243D4×C22⋊C4C2212yes—
244D4×C22⋊C4C2212yescomplemented
245D4×C22⋊C4C2212yescomplemented
246#2337C2214yescomplemented
247#2328C2212yescomplemented
248#2321C2214yescomplemented
249C4×#127C2212yescomplemented
250C4×#127C2212yescomplemented
251C4×#124C2212yescomplemented
252C4×#124C2212yescomplemented
253C4×#124C2212yescomplemented
254C4×#124C2212yescomplemented
255C4×#124C2212yescomplemented
256C4×#124C2211yescharacteristic, complemented
257#2295C2211yescharacteristic, complemented
258#2293C2212yescomplemented
259C2×H(5,𝔽2)—48no—
260C2×H(5,𝔽2)—44no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2314yes—
265C22×#41C2311yescharacteristic
266C22×#41C2312yes—
267C22×#41C2311yescharacteristic
268C23×D4C2311yescharacteristic
269C23×D4C2312yes—
270C23×D4C2312yes—
271C23×D4C2314yes—
272C23×D4C2312yes—
273C23×D4C2314yes—
274C23×D4C2314yes—
275#559—44no—
276#550—48no—
277#550—44no—
278#550—48no—
279#546—48no—
280#546—416no—
281D42—48no—
282D42—48no—
283#538—416no—
284#537—44no—
285#535—48no—
286#535—416no—
287C2×#127C2312yes—
288C2×#127C2312yes—
289C2×#127C2314yes—
290C2×#127C2312yes—
291C2×#127C2314yes—
292C2×#127C2312yes—
293C2×#127C2312yes—
294C2×#127C2311yescharacteristic
295C2×#127C2311yescharacteristic
296C2×#127C2312yes—
297C2×#127C2314yes—
298C2×#127C2314yes—
299C2×#127C2312yes—
300C2×#127C2312yes—
301C2×#126C2314yes—
302C2×#126C2314yes—
303C2×#124C2314yes—
304C2×#124C2312yes—
305C2×#124C2312yes—
306C2×#124C2312yes—
307C2×#124C2312yes—
308C2×#124C2311yescharacteristic
309C2×#124C2312yes—
310C2×#124C2312yes—
311C2×#124C2314yes—
312C2×#124C2312yes—
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2311yescharacteristic
327C2×#121C2312yes—
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2312yes—
331C2×#121C2314yes—
332C2×#121C2312yes—
333C2×#121C2311yescharacteristic
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2312yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2314yes—
341C2×#121C2314yes—
342C2×#121C2314yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2314yes—
355C2×#121C2314yes—
356C2×#121C2314yes—
357C2×#120C2314yes—
358C2×#120C2314yes—
359C2×#120C2314yes—
360C2×#120C2314yes—
361C2×#120C2312yes—
362C2×#120C2314yes—
363C2×#120C2314yes—
364C2×#120C2314yes—
365C2×#120C2314yes—
366C2×#120C2314yes—
367C2×#120C2314yes—
368C2×#120C2314yes—
369C2×#120C2314yes—
370C2×#120C2314yes—
371C2×#120C2314yes—
372C2×#120C2314yes—
373C2×#120C2314yes—
374C2×#120C2314yes—
375C2×#120C2314yes—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2314yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2314yes—
387C2×C4×D4C2314yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2314yes—
392C2×C4×D4C2314yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2312yes—
398C2×C4×D4C2314yes—
399C2×#117C2314yes—
400C2×#117C2312yes—
401C22×C4⋊C4C2311yescharacteristic
402C22×C22⋊C4C2314yes—
403C22×C22⋊C4C2314yes—
404C22×C22⋊C4C2314yes—
405C22×C22⋊C4C2314yes—
406#400C2312yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#399C2312yes—
411#399C2312yes—
412#399C2312yes—
413#399C2314yes—
414#399C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#395C2311yescharacteristic
433#395C2311yescharacteristic
434#395C2312yes—
435#395C2312yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2312yes—
450#394C2312yes—
451#394C2311yescharacteristic
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2312yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2311yescharacteristic
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#393C2311yescharacteristic
479#393C2312yes—
480#393C2312yes—
481#393C2311yescharacteristic
482#393C2314yes—
483#393C2312yes—
484#393C2314yes—
485#393C2312yes—
486#392C2312yes—
487#392C2312yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#392C2312yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2312yes—
500#392C2312yes—
501#392C2312yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2312yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2312yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2311yescharacteristic
523#392C2312yes—
524#392C2312yes—
525#392C2312yes—
526#392C2312yes—
527#392C2314yes—
528#392C2312yes—
529#392C2312yes—
530#392C2311yescharacteristic
531#392C2314yes—
532#392C2314yes—
533#392C2314yes—
534#392C2312yes—
535#392C2314yes—
536#392C2314yes—
537#392C2314yes—
538#392C2314yes—
539#391C2311yescharacteristic
540#391C2314yes—
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#391C2312yes—
545#391C2312yes—
546#391C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2314yes—
550#390C2312yes—
551#390C2314yes—
552#390C2314yes—
553#390C2312yes—
554#390C2314yes—
555#390C2312yes—
556#390C2314yes—
557#390C2312yes—
558#390C2314yes—
559#390C2312yes—
560#390C2312yes—
561#390C2312yes—
562#390C2312yes—
563#390C2314yes—
564#390C2312yes—
565#390C2314yes—
566#390C2314yes—
567#390C2311yescharacteristic
568#390C2314yes—
569#390C2314yes—
570#390C2314yes—
571#390C2314yes—
572#390C2312yes—
573#390C2312yes—
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2314yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2312yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2312yes—
596#388C2314yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2312yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2312yes—
606#388C2314yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2314yes—
611#388C2312yes—
612#388C2312yes—
613#388C2314yes—
614#388C2312yes—
615#388C2312yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2312yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#385C2314yes—
662#385C2312yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#384C2312yes—
671#384C2312yes—
672#383C2314yes—
673#382C2312yes—
674#382C2311yescharacteristic
675#382C2312yes—
676#382C2312yes—
677#382C2312yes—
678#382C2312yes—
679#381C2312yes—
680#381C2314yes—
681#381C2314yes—
682#381C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688#380C2311yescharacteristic
689#380C2314yes—
690#380C2311yescharacteristic
691#380C2314yes—
692#380C2312yes—
693#380C2312yes—
694#380C2314yes—
695#379C2314yes—
696#379C2314yes—
697#379C2314yes—
698#379C2314yes—
699#379C2314yes—
700#379C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2311yescharacteristic
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721#376C2312yes—
722C2×#95C2312yes—
723C2×#95C2314yes—
724C43C2312yes—
725C43C2311yescharacteristic
726C25C2412yes—
727C25C2414yes—
728C25C2414yes—
729H(5,𝔽2)—464no—
730C2×#41—28no—
731C2×#41—24no—
732C2×#41—24no—
733C2×#41—216no—
734C2×#41—28no—
735C2×#41—44no—
736C2×#41—44no—
737C2×#41—42no—
738C2×#41—44no—
739C2×#41—42no—
740C2×#41—48no—
741C2×#41—48no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—84no—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2411yescharacteristic
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×D4—28no—
752C22×D4—28no—
753C22×D4—28no—
754C22×D4—48no—
755C22×D4—44no—
756C22×D4—42no—
757C22×D4—44no—
758C22×D4—44no—
759C22×D4—48no—
760C22×D4—44no—
761C22×D4—44no—
762C22×D4—48no—
763C22×D4—48no—
764C22×D4—48no—
765C22×D4—48no—
766C22×D4—48no—
767C22×D4—48no—
768C22×D4—84no—
769C22×D4—84no—
770C22×D4C2412yes—
771C22×D4C2411yescharacteristic
772C22×D4C2411yescharacteristic
773C22×D4C2414yes—
774C22×D4C2414yes—
775C22×D4C2412yes—
776C22×D4C2414yes—
777C22×D4C2412yes—
778C22×D4C2414yes—
779C22×D4C2414yes—
780C22×D4C2414yes—
781C22×D4C2412yes—
782C22×D4C2411yescharacteristic
783C22×D4C2412yes—
784C22×D4C2412yes—
785C22×D4C2412yes—
786C22×D4C2412yes—
787C22×D4C2414yes—
788C22×D4C2414yes—
789C22×D4C2414yes—
790C22×D4C2414yes—
791C22×D4C2414yes—
792C22×D4C2412yes—
793C22×D4C2412yes—
794C22×D4C2412yes—
795C22×D4C2411yescharacteristic
796C22×D4C2414yes—
797C22×D4C2414yes—
798C22×D4C2414yes—
799C22×D4C2412yes—
800C22×D4C2414yes—
801C22×D4C2412yes—
802C22×D4C2412yes—
803C22×D4C2414yes—
804C22×D4C2414yes—
805C22×D4C2412yes—
806C22×D4C2412yes—
807C22×D4C2414yes—
808C22×D4C2414yes—
809C22×D4C2414yes—
810C22×D4C2414yes—
811C22×D4C2412yes—
812C22×D4C2411yescharacteristic
813C23×C4C2411yescharacteristic
814C23×C4C2412yes—
815C23×C4C2411yescharacteristic
816C23×C4C2412yes—
817C23×C4C2414yes—
818C23×C4C2414yes—
819C23×C4C2414yes—
820C23×C4C2414yes—
821C23×C4C2412yes—
822C23×C4C2414yes—
823C23×C4C2412yes—
824C23×C4C2414yes—
825C23×C4C2414yes—
826C23×C4C2412yes—
827#127—28no—
828#127—28no—
829#127—44no—
830#127—48no—
831#127—48no—
832#127—44no—
833#127—44no—
834#127—44no—
835#127—42no—
836#127—42no—
837#127—48no—
838#127—48no—
839#127—82no—
840#127—82no—
841#126—48no—
842#126—48no—
843#124—28no—
844#124—28no—
845#124—216no—
846#124—28no—
847#124—28no—
848#124—44no—
849#124—42no—
850#124—48no—
851#124—44no—
852#124—82no—
853#123—48no—
854#123—48no—
855#123—48no—
856#123—48no—
857#123—48no—
858#123—48no—
859C22⋊Q8—28no—
860C22⋊Q8—216no—
861C22⋊Q8—44no—
862#121—28no—
863#121—28no—
864#121—48no—
865#121—48no—
866#121—48no—
867#121—48no—
868#121—44no—
869#121—48no—
870#121—48no—
871#121—48no—
872#121—48no—
873#121—48no—
874#121—48no—
875#121—48no—
876#121—48no—
877#121—48no—
878#121—48no—
879#121—48no—
880#121—44no—
881#121—44no—
882#121—44no—
883#121—44no—
884#121—44no—
885#121—44no—
886#121—44no—
887#121—48no—
888#121—44no—
889#121—42no—
890#121—42no—
891#121—44no—
892#121—44no—
893#121—48no—
894#121—48no—
895#121—48no—
896#121—84no—
897#120—44no—
898#120—48no—
899#120—48no—
900#120—48no—
901#120—48no—
902#120—48no—
903#120—48no—
904#120—48no—
905#120—48no—
906#120—48no—
907#120—48no—
908#120—48no—
909#120—48no—
910#120—48no—
911#120—48no—
912#120—48no—
913#120—48no—
914#120—48no—
915#120—84no—
916C4×Q8—24no—
917C4×Q8—44no—
918C4×Q8—42no—
919C4×Q8—44no—
920C4×D4—28no—
921C4×D4—48no—
922C4×D4—48no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—48no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—44no—
932C4×D4—48no—
933C4×D4—44no—
934C4×D4—44no—
935C4×D4—44no—
936C4×D4—42no—
937C4×D4—48no—
938C4×D4—84no—
939#117—48no—
940#117—44no—
941C2×C4⋊C4—42no—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2414yes—
971C2×C22⋊C4—48no—
972C2×C22⋊C4—48no—
973C2×C22⋊C4—48no—
974C2×C22⋊C4—48no—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2414yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2412yes—
991C2×C22⋊C4C2412yes—
992C2×C22⋊C4C2412yes—
993C2×C22⋊C4C2414yes—
994C2×C22⋊C4C2412yes—
995C2×C22⋊C4C2412yes—
996C2×C22⋊C4C2412yes—
997C2×C22⋊C4C2412yes—
998C2×C22⋊C4C2412yes—
999C2×C22⋊C4C2414yes—
1000C2×C22⋊C4C2414yes—
1001C2×C22⋊C4C2412yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2412yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2414yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2414yes—
1009C2×C22⋊C4C2414yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2411yescharacteristic
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C42C2412yes—
1053C2×C42C2414yes—
1054C2×C42C2412yes—
1055C2×C42C2412yes—
1056C2×C42C2412yes—
1057C2×C42C2412yes—
1058C2×C42C2412yes—
1059C2×C42C2412yes—
1060C2×C42C2412yes—
1061C2×C42C2411yescharacteristic
1062C2×C42C2411yescharacteristic
1063C2×C42C2414yes—
1064C2×C42C2412yes—
1065C2×C42C2414yes—
1066C2×C42C2412yes—
1067C2×C42C2412yes—
1068C2×C42C2411yescharacteristic
1069#95C2414yes—
1070#95C2411yescharacteristic
1071#95C2412yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2411yescharacteristic
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2411yescharacteristic
1083#95C2412yes—
1084#95C2414yes—
1085#95C2412yes—
1086#95C2411yescharacteristic
1087#95C2414yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2414yes—
1100#95C2412yes—
1101#95C2414yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2412yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110C24—28no—
1111C24—28no—
1112C24—28no—
1113C24—42no—
1114C24—44no—
1115C24—44no—
1116C24—44no—
1117C24—44no—
1118C24—44no—
1119C24—44no—
1120C24—44no—
1121C24—42no—
1122C24—44no—
1123C24—42no—
1124C24—44no—
1125C24—44no—
1126C24—44no—
1127C24—44no—
1128C24—44no—
1129C24C2512yes—
1130C24C2511yescharacteristic
1131C24C2512yes—
1132C24C2512yes—
1133C24C2514yes—
1134C24C2511yescharacteristic
1135C24C2512yes—
1136C24C2514yes—
1137#41—432no—
1138#41—416no—
1139#41—432no—
1140#41—416no—
1141#41—88no—
1142#41—832no—
1143#41—88no—
1144C2×Q8—24no—
1145C2×Q8—22no—
1146C2×Q8—42no—
1147C2×Q8—41no—
1148C2×Q8—42no—
1149C2×Q8—42no—
1150C2×Q8—41no—
1151C2×Q8—41no—
1152C2×Q8—42no—
1153C2×Q8—41no—
1154C2×Q8H(5,𝔽2)14yes—
1155C2×Q8H(5,𝔽2)18yescomplemented
1156C2×D4—28no—
1157C2×D4—28no—
1158C2×D4—28no—
1159C2×D4—28no—
1160C2×D4—28no—
1161C2×D4—28no—
1162C2×D4—28no—
1163C2×D4—28no—
1164C2×D4—28no—
1165C2×D4—28no—
1166C2×D4—24no—
1167C2×D4—24no—
1168C2×D4—28no—
1169C2×D4—24no—
1170C2×D4—24no—
1171C2×D4—24no—
1172C2×D4—28no—
1173C2×D4—28no—
1174C2×D4—24no—
1175C2×D4—22no—
1176C2×D4—24no—
1177C2×D4—24no—
1178C2×D4—24no—
1179C2×D4—22no—
1180C2×D4—24no—
1181C2×D4—24no—
1182C2×D4—28no—
1183C2×D4—28no—
1184C2×D4—24no—
1185C2×D4—22no—
1186C2×D4—24no—
1187C2×D4—24no—
1188C2×D4—42no—
1189C2×D4—42no—
1190C2×D4—44no—
1191C2×D4—44no—
1192C2×D4—44no—
1193C2×D4—42no—
1194C2×D4—44no—
1195C2×D4—44no—
1196C2×D4—42no—
1197C2×D4—41no—
1198C2×D4—42no—
1199C2×D4—42no—
1200C2×D4—42no—
1201C2×D4—42no—
1202C2×D4—42no—
1203C2×D4—44no—
1204C2×D4—44no—
1205C2×D4—42no—
1206C2×D4—44no—
1207C2×D4—44no—
1208C2×D4—42no—
1209C2×D4—42no—
1210C2×D4—41no—
1211C2×D4—42no—
1212C2×D4—42no—
1213C2×D4—42no—
1214C2×D4—44no—
1215C2×D4—44no—
1216C2×D4—44no—
1217C2×D4—44no—
1218C2×D4—44no—
1219C2×D4—44no—
1220C2×D4—44no—
1221C2×D4—42no—
1222C2×D4—44no—
1223C2×D4—44no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4—42no—
1227C2×D4—41no—
1228C2×D4—44no—
1229C2×D4—44no—
1230C2×D4—44no—
1231C2×D4—44no—
1232C2×D4—44no—
1233C2×D4—44no—
1234C2×D4—42no—
1235C2×D4—44no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—41no—
1240C2×D4—42no—
1241C2×D4—44no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—44no—
1248C2×D4—44no—
1249C2×D4—44no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—44no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—44no—
1269C2×D4—44no—
1270C2×D4—42no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—416no—
1274C2×D4—432no—
1275C2×D4—464no—
1276C2×D4—432no—
1277C2×D4—816no—
1278C2×D4—832no—
1279C2×D4—832no—
1280C2×D4H(5,𝔽2)18yes—
1281C22×C4—28no—
1282C22×C4—28no—
1283C22×C4—28no—
1284C22×C4—28no—
1285C22×C4—22no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—24no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—24no—
1294C22×C4—22no—
1295C22×C4—24no—
1296C22×C4—28no—
1297C22×C4—28no—
1298C22×C4—28no—
1299C22×C4—24no—
1300C22×C4—44no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4—42no—
1315C22×C4—44no—
1316C22×C4—44no—
1317C22×C4—44no—
1318C22×C4C2512yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2514yes—
1322C22×C4C2512yes—
1323C22×C4C2514yes—
1324C22×C4C2514yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2511yescharacteristic
1331C22×C4C2514yes—
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2511yescharacteristic
1338C22×C4C2511yescharacteristic
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—22no—
1344C4⋊C4—28no—
1345C4⋊C4—24no—
1346C4⋊C4—28no—
1347C4⋊C4—28no—
1348C4⋊C4—28no—
1349C4⋊C4—42no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—41no—
1353C4⋊C4—42no—
1354C4⋊C4—41no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—44no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C22⋊C4—28no—
1369C22⋊C4—28no—
1370C22⋊C4—28no—
1371C22⋊C4—24no—
1372C22⋊C4—24no—
1373C22⋊C4—24no—
1374C22⋊C4—28no—
1375C22⋊C4—28no—
1376C22⋊C4—28no—
1377C22⋊C4—28no—
1378C22⋊C4—28no—
1379C22⋊C4—24no—
1380C22⋊C4—28no—
1381C22⋊C4—24no—
1382C22⋊C4—24no—
1383C22⋊C4—24no—
1384C22⋊C4—24no—
1385C22⋊C4—28no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—28no—
1390C22⋊C4—28no—
1391C22⋊C4—24no—
1392C22⋊C4—28no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—44no—
1396C22⋊C4—42no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—44no—
1400C22⋊C4—44no—
1401C22⋊C4—44no—
1402C22⋊C4—44no—
1403C22⋊C4—44no—
1404C22⋊C4—44no—
1405C22⋊C4—42no—
1406C22⋊C4—42no—
1407C22⋊C4—44no—
1408C22⋊C4—42no—
1409C22⋊C4—42no—
1410C22⋊C4—44no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—42no—
1415C22⋊C4—44no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—44no—
1420C22⋊C4—42no—
1421C22⋊C4—41no—
1422C22⋊C4—41no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—44no—
1429C22⋊C4—42no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C42—24no—
1446C42—28no—
1447C42—24no—
1448C42—24no—
1449C42—24no—
1450C42—24no—
1451C42—24no—
1452C42—24no—
1453C42—24no—
1454C42—22no—
1455C42—22no—
1456C42—44no—
1457C42—44no—
1458C42—42no—
1459C42—42no—
1460C42—42no—
1461C42—41no—
1462C23—24no—
1463C23—24no—
1464C23—24no—
1465C23—24no—
1466C23—24no—
1467C23—24no—
1468C23—22no—
1469C23—24no—
1470C23—24no—
1471C23—22no—
1472C23—22no—
1473C23—22no—
1474C23—22no—
1475C23—24no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—24no—
1481C23—24no—
1482C23—24no—
1483C23—21no—
1484C23—24no—
1485C23—22no—
1486C23—24no—
1487C23—22no—
1488C23—22no—
1489C23—22no—
1490C23—21no—
1491C23—22no—
1492C23—22no—
1493C23—22no—
1494C23—24no—
1495C23—22no—
1496C23—22no—
1497C23—21no—
1498C23—21no—
1499C23—22no—
1500C23—24no—
1501C23—22no—
1502C23—22no—
1503C23—21no—
1504C23—22no—
1505C23—22no—
1506C23—24no—
1507C23—22no—
1508C23—21no—
1509C23—48no—
1510C23—416no—
1511C23—88no—
1512C23—88no—
1513C23—88no—
1514C23—88no—
1515C23—88no—
1516C23—88no—
1517C23—88no—
1518C23—88no—
1519C23—88no—
1520C23—164no—
1521C23—164no—
1522C23—162no—
1523C23—164no—
1524C23—164no—
1525C23—164no—
1526C23—162no—
1527C23—164no—
1528C23C2×H(5,𝔽2)18yes—
1529C23C2611yescharacteristic
1530Q8—28no—
1531Q8—48no—
1532Q8—44no—
1533Q8—82no—
1534Q8—82no—
1535D4—216no—
1536D4—416no—
1537D4—416no—
1538D4—416no—
1539D4—48no—
1540D4—48no—
1541D4—48no—
1542D4—48no—
1543D4—416no—
1544D4—48no—
1545D4—44no—
1546D4—44no—
1547D4—48no—
1548D4—44no—
1549D4—84no—
1550D4—82no—
1551D4—84no—
1552D4—84no—
1553D4—88no—
1554D4—88no—
1555D4—84no—
1556D4—88no—
1557D4—88no—
1558D4—88no—
1559D4—88no—
1560D4—88no—
1561D4—84no—
1562D4—88no—
1563D4—88no—
1564D4—88no—
1565D4—82no—
1566D4—84no—
1567D4—164no—
1568D4—164no—
1569D4—164no—
1570D4—164no—
1571D4—162no—
1572D4—164no—
1573D4—162no—
1574D4—164no—
1575D4—162no—
1576D4—162no—
1577D4—164no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—24no—
1603C2×C4—22no—
1604C2×C4—24no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—24no—
1609C2×C4—24no—
1610C2×C4—24no—
1611C2×C4—24no—
1612C2×C4—22no—
1613C2×C4—24no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—24no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—24no—
1628C2×C4—416no—
1629C2×C4—416no—
1630C2×C4—48no—
1631C2×C4—44no—
1632C2×C4—48no—
1633C2×C4—48no—
1634C2×C4—44no—
1635C2×C4—88no—
1636C2×C4—88no—
1637C2×C4—88no—
1638C2×C4—84no—
1639C2×C4—164no—
1640C2×C4—164no—
1641C2×C4—162no—
1642C2×C4C2×H(5,𝔽2)14yes—
1643C2×C4C2×H(5,𝔽2)14yes—
1644C2×C4C2×H(5,𝔽2)14yes—
1645C2×C4C2×H(5,𝔽2)14yes—
1646C2×C4C2×H(5,𝔽2)12yes—
1647C2×C4C2×H(5,𝔽2)14yes—
1648C2×C4#58512yes—
1649C22—28no—
1650C22—28no—
1651C22—28no—
1652C22—44no—
1653C22—44no—
1654C22—44no—
1655C22—44no—
1656C22—42no—
1657C22—44no—
1658C22—44no—
1659C22—44no—
1660C22—42no—
1661C22—42no—
1662C22—44no—
1663C22—42no—
1664C22—42no—
1665C22—42no—
1666C22—41no—
1667C22—44no—
1668C22—42no—
1669C22—42no—
1670C22—42no—
1671C22—41no—
1672C22—42no—
1673C22—44no—
1674C22—44no—
1675C22—42no—
1676C22—42no—
1677C22—42no—
1678C22—42no—
1679C22—44no—
1680C22—44no—
1681C22—42no—
1682C22—42no—
1683C22—42no—
1684C22—41no—
1685C22—44no—
1686C22—42no—
1687C22—41no—
1688C22—42no—
1689C22—42no—
1690C22—42no—
1691C22—42no—
1692C22—41no—
1693C22—41no—
1694C22—42no—
1695C22—42no—
1696C22—44no—
1697C22—168no—
1698C22—1616no—
1699C22—1616no—
1700C22C22×H(5,𝔽2)12yes—
1701C22C22×H(5,𝔽2)12yes—
1702C22C22×H(5,𝔽2)11yescharacteristic
1703C22C2×#58511yescharacteristic
1704C22H(7,𝔽2)11yescharacteristic
1705C4—24no—
1706C4—24no—
1707C4—24no—
1708C4—22no—
1709C4—24no—
1710C4—42no—
1711C4—42no—
1712C4—44no—
1713C4—42no—
1714C4—42no—
1715C4—44no—
1716C4—42no—
1717C4—41no—
1718C4—44no—
1719C4—44no—
1720C4—42no—
1721C4—42no—
1722C4—41no—
1723C4—41no—
1724C4—42no—
1725C4#353214yes—
1726C2—48no—
1727C2—81no—
1728C2—82no—
1729C2—84no—
1730C2—82no—
1731C2—82no—
1732C2—82no—
1733C2—81no—
1734C2C2×#353211yescharacteristic
1735C2#6289212yes—
1736C2#6289911yescharacteristic
1737C2#6301412yes—
1738C2#6304011yescharacteristic
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. #59945C2semidirect
2. #59944C2semidirect
3. #59419C2semidirect
4. #59414C2semidirect
5. #59412C2semidirect
6. #54942C2semidirect
7. #53961C2semidirect
8. #53938C2semidirect
9. #53422C2semidirect
10. #53055C2semidirect
11. #52957C2semidirect
12. #52307C2semidirect
13. #47689C2semidirect
14. #46971C2semidirect
15. #44886C2semidirect
16. #44870C2semidirect
17. #44242C2semidirect
18. #43894C2semidirect
19. #42909C2semidirect
20. #42420C2semidirect
21. #42091C2semidirect
22. #41932C2semidirect
23. #40164C2semidirect
24. #40129C2semidirect
25. #39745C2semidirect
26. #39396C2semidirect
27. #39361C2semidirect
28. #36091C2semidirect
29. #35680C2semidirect
31. C2×#559C22semidirect
32. C2×#550C22semidirect
33. C2×#550C22semidirect
34. C2×#550C22semidirect
35. C2×#546C22semidirect
36. C2×#546C22semidirect
38. C2×D42C22semidirect
39. C2×#538C22semidirect
40. C2×#537C22semidirect
41. C2×#535C22semidirect
42. C2×#535C22semidirect
43. #2867C22semidirect
44. #2860C22semidirect
45. #2828C22semidirect
46. #2828C22semidirect
47. #2824C22semidirect
48. #2824C22semidirect
49. #2818C22semidirect
50. #2816C22semidirect
51. #2815C22semidirect
52. #2813C22semidirect
53. #2812C22semidirect
54. #2811C22semidirect
55. #2803C22semidirect
56. #2785C22semidirect
57. #2785C22semidirect
58. #2785C22semidirect
59. #2785C22semidirect
60. #2784C22semidirect
61. #2782C22semidirect
62. #2781C22semidirect
63. #2756C22semidirect
64. #2753C22semidirect
65. #2744C22semidirect
66. #2737C22semidirect
67. #2733C22semidirect
68. #2733C22semidirect
69. #2733C22semidirect
70. #2733C22semidirect
71. #2733C22semidirect
72. #2733C22semidirect
73. #2730C22semidirect
74. #2730C22semidirect
75. #2714C22semidirect
76. #2714C22semidirect
77. #2706C22semidirect
78. #2703C22semidirect
79. #2703C22semidirect
80. #2699C22semidirect
81. #2699C22semidirect
82. #2686C22semidirect
83. #2685C22semidirect
84. #2685C22semidirect
85. #2684C22semidirect
86. #2684C22semidirect
87. #2679C22semidirect
88. #2678C22semidirect
89. #2678C22semidirect
90. #2678C22semidirect
91. #2676C22semidirect
92. #2675C22semidirect
93. #2673C22semidirect
94. #2673C22semidirect
95. #2673C22semidirect
96. #2673C22semidirect
97. #2673C22semidirect
98. #2673C22semidirect
99. #2673C22semidirect
100. #2671C22semidirect
101. #2670C22semidirect
102. #2670C22semidirect
103. #2670C22semidirect
104. #2669C22semidirect
105. #2669C22semidirect
106. #2669C22semidirect
107. #2669C22semidirect
108. #2669C22semidirect
109. #2669C22semidirect
110. #2669C22semidirect
111. #2669C22semidirect
112. #2661C22semidirect
113. #2657C22semidirect
114. #2656C22semidirect
115. #2636C22semidirect
116. #2635C22semidirect
117. #2635C22semidirect
118. #2619C22semidirect
119. #2617C22semidirect
120. #2615C22semidirect
121. #2615C22semidirect
122. #2615C22semidirect
123. #2615C22semidirect
124. #2613C22semidirect
125. #2613C22semidirect
126. #2601C22semidirect
127. #2598C22semidirect
128. #2582C22semidirect
129. #2580C22semidirect
130. #2572C22semidirect
131. #2564C22semidirect
132. #2559C22semidirect
133. #2557C22semidirect
134. #2555C22semidirect
135. #2554C22semidirect
136. #2554C22semidirect
137. #2548C22semidirect
138. #2548C22semidirect
139. #2544C22semidirect
140. #2543C22semidirect
141. #2543C22semidirect
142. #2541C22semidirect
143. #2541C22semidirect
144. #2541C22semidirect
145. #2541C22semidirect
146. #2539C22semidirect
147. #2538C22semidirect
148. #2537C22semidirect
149. #2537C22semidirect
150. #2535C22semidirect
151. #2535C22semidirect
152. #2531C22semidirect
153. #2526C22semidirect
154. #2501C22semidirect
155. #2500C22semidirect
156. #2498C22semidirect
157. #2497C22semidirect
158. #2496C22semidirect
159. #2495C22semidirect
160. #2487C22semidirect
161. #2485C22semidirect
162. #2482C22semidirect
163. #2464C22semidirect
164. #2461C22semidirect
165. #2459C22semidirect
166. #2456C22semidirect
167. #2456C22semidirect
170. #2433C22semidirect
171. #2433C22semidirect
172. #2433C22semidirect
173. #2433C22semidirect
174. #2433C22semidirect
175. #2433C22semidirect
176. #2433C22semidirect
178. #2431C22semidirect
179. #2431C22semidirect
180. #2431C22semidirect
181. #2431C22semidirect
182. #2430C22semidirect
183. #2428C22semidirect
184. #2428C22semidirect
185. #2428C22semidirect
186. #2428C22semidirect
187. #2428C22semidirect
188. #2428C22semidirect
189. #2428C22semidirect
190. #2428C22semidirect
191. #2428C22semidirect
192. #2426C22semidirect
193. #2424C22semidirect
194. #2424C22semidirect
195. #2424C22semidirect
196. #2424C22semidirect
197. #2424C22semidirect
198. #2423C22semidirect
199. #2422C22semidirect
200. #2422C22semidirect
201. #2422C22semidirect
202. #2420C22semidirect
203. #2420C22semidirect
204. #2420C22semidirect
205. #2418C22semidirect
206. #2418C22semidirect
207. #2416C22semidirect
208. #2414C22semidirect
209. #2414C22semidirect
210. #2410C22semidirect
211. #2410C22semidirect
212. #2410C22semidirect
215. #2408C22semidirect
216. #2408C22semidirect
217. #2408C22semidirect
218. #2408C22semidirect
220. #2407C22semidirect
221. #2407C22semidirect
222. #2404C22semidirect
223. #2403C22semidirect
224. #2403C22semidirect
225. #2403C22semidirect
226. #2388C22semidirect
227. #2388C22semidirect
228. #2388C22semidirect
229. #2388C22semidirect
230. #2388C22semidirect
231. C2×#392C22semidirect
232. #2368C22semidirect
233. #2363C22semidirect
234. #2362C22semidirect
235. #2361C22semidirect
236. #2358C22semidirect
237. #2358C22semidirect
238. #2341C22semidirect
239. #2341C22semidirect
240. #2339C22semidirect
241. #2339C22semidirect
242. #2339C22semidirect
244. D4×C22⋊C4C22semidirect
245. D4×C22⋊C4C22semidirect
246. #2337C22semidirect
247. #2328C22semidirect
248. #2321C22semidirect
249. C4×#127C22semidirect
250. C4×#127C22semidirect
251. C4×#124C22semidirect
252. C4×#124C22semidirect
253. C4×#124C22semidirect
254. C4×#124C22semidirect
255. C4×#124C22semidirect
256. C4×#124C22semidirect
257. #2295C22semidirect
258. #2293C22semidirect
1155. C2×Q8H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
#599452
#599442
#594192
#594142
#594122
#549422
#539612
#539382
#534222
#530552
#529572
#523072
#476892
#469712
#448862
#448702
#442422
#438942
#429092
#424202
#420912
#419322
#401642
#401292
#397452
#393962
#393612
#360912
#356802