Finite Group Databasebeta

← #8750354

Subgroups — #8750354

Order 512.

6255 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59816C211yesmaximal, characteristic, complemented
2#59476C212yesmaximal, complemented
3#57988C214yesmaximal, complemented
4#56343C214yesmaximal, complemented
5#56317C212yesmaximal, complemented
6#55423C214yesmaximal, complemented
7#54816C214yesmaximal, complemented
8#53044C212yesmaximal, complemented
9#53015C211yesmaximal, characteristic, complemented
10#52410C212yesmaximal, complemented
11#52316C214yesmaximal, complemented
12#47695C212yesmaximal, complemented
13#45088C211yesmaximal, characteristic, complemented
14#45079C212yesmaximal, complemented
15#44929C212yesmaximal, complemented
16#44877C212yesmaximal, complemented
17#44874C212yesmaximal, complemented
18#42967C211yesmaximal, characteristic, complemented
19#42712C212yesmaximal, complemented
20#42547C212yesmaximal, complemented
21#42474C212yesmaximal, complemented
22#42443C212yesmaximal, complemented
23#41983C212yesmaximal, complemented
24#40590C214yesmaximal, complemented
25#39532C212yesmaximal, complemented
26#39491C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#35750C211yesmaximal, characteristic, complemented
29#35680C212yesmaximal, complemented
30C22×H(5,𝔽2)C2211yescharacteristic, complemented
31C2×#555C2211yescharacteristic, complemented
32C2×#551C2214yescomplemented
33C2×#547C2211yescharacteristic, complemented
34C2×#546C2212yescomplemented
35C2×#546C2212yescomplemented
36C2×D42C2212yes—
37C2×D42C2212yescomplemented
38C2×D42C2212yescomplemented
39C2×D42C2212yescomplemented
40C2×#542C2212yescomplemented
41C2×#535C2211yescharacteristic, complemented
42#2862C2211yescharacteristic, complemented
43#2843C2211yescharacteristic, complemented
44#2840C2212yescomplemented
45#2830C2212yescomplemented
46#2830C2214yescomplemented
47#2830C2211yescharacteristic, complemented
48#2829C2214yescomplemented
49#2829C2212yescomplemented
50#2829C2212yescomplemented
51#2829C2212yescomplemented
52#2828C2212yescomplemented
53#2828C2214yescomplemented
54#2828C2211yescharacteristic, complemented
55#2826C2214yescomplemented
56#2824C2214yescomplemented
57#2823C2211yescharacteristic, complemented
58#2819C2214yescomplemented
59#2819C2212yescomplemented
60#2818C2212yescomplemented
61#2813C2214yescomplemented
62#2813C2214yescomplemented
63#2813C2212yescomplemented
64#2812C2214yescomplemented
65#2803C2214yescomplemented
66#2785C2212yescomplemented
67#2782C2212yescomplemented
68#2761C2214yescomplemented
69#2761C2214yescomplemented
70#2753C2214yescomplemented
71#2752C2214yescomplemented
72#2751C2214yescomplemented
73#2751C2214yescomplemented
74#2743C2214yescomplemented
75#2742C2214yescomplemented
76#2736C2212yescomplemented
77#2730C2214yescomplemented
78#2730C2214yescomplemented
79#2718C2214yescomplemented
80#2714C2214yescomplemented
81#2714C2214yescomplemented
82#2710C2214yescomplemented
83#2710C2214yescomplemented
84#2710C2214yescomplemented
85#2706C2214yescomplemented
86#2705C2214yescomplemented
87#2702C2214yescomplemented
88#2701C2214yescomplemented
89#2697C2214yescomplemented
90#2697C2214yescomplemented
91#2697C2214yescomplemented
92#2696C2214yescomplemented
93#2696C2214yescomplemented
94#2685C2214yescomplemented
95#2685C2214yescomplemented
96#2685C2214yescomplemented
97#2685C2214yescomplemented
98#2684C2214yescomplemented
99#2684C2214yescomplemented
100#2682C2214yescomplemented
101#2681C2214yescomplemented
102#2681C2214yescomplemented
103#2679C2214yescomplemented
104#2679C2212yescomplemented
105#2679C2212yescomplemented
106#2678C2214yescomplemented
107#2678C2214yescomplemented
108#2678C2214yescomplemented
109#2678C2214yescomplemented
110#2676C2214yescomplemented
111#2676C2214yescomplemented
112#2676C2214yescomplemented
113#2671C2214yescomplemented
114#2670C2212yescomplemented
115#2670C2214yescomplemented
116#2670C2214yescomplemented
117#2670C2214yescomplemented
118#2668C2214yescomplemented
119#2661C2212yescomplemented
120#2648C2214yescomplemented
121#2639C2214yescomplemented
122#2639C2214yescomplemented
123#2636C2214yescomplemented
124#2635C2214yescomplemented
125#2626C2214yescomplemented
126#2625C2211yescharacteristic, complemented
127#2622C2214yescomplemented
128#2620C2212yescomplemented
129#2620C2214yescomplemented
130#2619C2212yescomplemented
131#2618C2212yescomplemented
132#2616C2211yescharacteristic, complemented
133#2615C2212yescomplemented
134#2613C2212yescomplemented
135#2613C2214yescomplemented
136#2613C2214yescomplemented
137#2609C2212yescomplemented
138#2598C2214yescomplemented
139#2591C2212yescomplemented
140#2563C2212yescomplemented
141#2563C2211yescharacteristic, complemented
142#2559C2214yescomplemented
143#2553C2214yescomplemented
144#2545C2212yescomplemented
145#2544C2212yescomplemented
146#2542C2212yescomplemented
147#2542C2211yescharacteristic, complemented
148#2540C2212yescomplemented
149#2539C2214yescomplemented
150#2538C2212yescomplemented
151#2537C2212yescomplemented
152#2537C2212yescomplemented
153#2537C2212yescomplemented
154#2511C2212yescomplemented
155#2505C2214yescomplemented
156#2504C2212yescomplemented
157#2500C2212yescomplemented
158#2497C2212yescomplemented
159#2496C2212yescomplemented
160#2492C2212yescomplemented
161#2491C2212yescomplemented
162#2491C2212yescomplemented
163#2491C2212yescomplemented
164#2485C2212yescomplemented
165#2476C2214yescomplemented
166#2472C2214yescomplemented
167#2472C2214yescomplemented
168#2472C2214yescomplemented
169#2471C2214yescomplemented
170#2463C2214yescomplemented
171#2459C2214yescomplemented
172#2452C2212yescomplemented
173#2452C2212yescomplemented
174#2450C2214yescomplemented
175#2450C2214yescomplemented
176#2447C2212yescomplemented
177#2445C2212yescomplemented
178#2445C2212yescomplemented
179#2437C2214yescomplemented
180#2437C2212yescomplemented
181#2435C2214yescomplemented
182#2435C2211yescharacteristic, complemented
183#2435C2212yescomplemented
184#2435C2214yescomplemented
185#2435C2211yescharacteristic, complemented
186#2433C2212yes—
187#2432C2212yescomplemented
188#2431C2212yes—
189#2431C2212yescomplemented
190#2430C2212yescomplemented
191#2430C2214yescomplemented
192#2428C2212yescomplemented
193#2427C2212yescomplemented
194#2426C2212yescomplemented
195#2424C2214yescomplemented
196#2423C2212yescomplemented
197#2422C2212yescomplemented
198#2422C2212yescomplemented
199#2418C2214yescomplemented
200#2415C2212yescomplemented
201#2415C2212yescomplemented
202#2414C2212yescomplemented
203#2411C2214yescomplemented
204#2411C2214yescomplemented
205#2411C2214yescomplemented
206#2410C2214yescomplemented
207#2410C2214yescomplemented
208#2410C2214yescomplemented
209#2410C2214yescomplemented
210#2410C2214yescomplemented
211#2408C2211yescharacteristic
212#2408C2212yescomplemented
213#2408C2212yescomplemented
214#2408C2211yescharacteristic, complemented
215#2408C2214yescomplemented
216#2408C2214yescomplemented
217#2408C2214yescomplemented
218#2408C2212yescomplemented
219#2407C2212yescomplemented
220#2407C2212yescomplemented
221#2407C2212yescomplemented
222#2407C2212yescomplemented
223#2406C2212yescomplemented
224#2405C2214yescomplemented
225#2405C2214yescomplemented
226#2405C2214yescomplemented
227#2404C2214yescomplemented
228#2403C2214yescomplemented
229#2403C2214yescomplemented
230#2403C2214yescomplemented
231#2395C2211yescharacteristic, complemented
232#2395C2212yescomplemented
233#2392C2212yescomplemented
234#2392C2212yescomplemented
235#2392C2212yescomplemented
236#2388C2211yescharacteristic, complemented
237#2388C2212yescomplemented
238C2×#394C2212yescomplemented
239C2×#392C2214yescomplemented
240#2367C2212yescomplemented
241#2366C2212yescomplemented
242#2363C2212yescomplemented
243#2354C2212yescomplemented
244#2341C2211yescharacteristic, complemented
245#2339C2211yescharacteristic, complemented
246#2339C2212yescomplemented
247D4×C22⋊C4C2212yescomplemented
248D4×C22⋊C4C2212yescomplemented
249D4×C22⋊C4C2212yescomplemented
250#2324C2212yescomplemented
251#2324C2212yescomplemented
252#2318C2214yescomplemented
253#2317C2212yescomplemented
254#2309C2212yescomplemented
255C4×#127C2211yescharacteristic, complemented
256C4×#127C2212yescomplemented
257C4×#126C2212yescomplemented
258#2293C2211yescharacteristic, complemented
259C2×H(5,𝔽2)—44no—
260C2×H(5,𝔽2)—48no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2311yescharacteristic
265C22×#41C2312yes—
266C23×D4C2311yescharacteristic
267C23×D4C2312yes—
268C23×D4C2312yes—
269C23×D4C2314yes—
270C23×D4C2312yes—
271C23×D4C2311yescharacteristic
272C23×D4C2314yes—
273C23×D4C2314yes—
274C23×D4C2314yes—
275#555—44no—
276#551—416no—
277#547—44no—
278#546—48no—
279#546—48no—
280D42—48no—
281D42—48no—
282D42—48no—
283D42—48no—
284#542—48no—
285#535—44no—
286C2×C4⋊Q8C2311yescharacteristic
287C2×C4⋊Q8C2312yes—
288C2×C4⋊Q8C2311yescharacteristic
289C2×#127C2311yescharacteristic
290C2×#127C2312yes—
291C2×#127C2312yes—
292C2×#126C2312yes—
293C2×#126C2314yes—
294C2×#126C2314yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#124C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2312yes—
306C2×#123C2314yes—
307C2×#123C2312yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2311yescharacteristic
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2314yes—
341C2×#120C2314yes—
342C2×#120C2314yes—
343C2×#120C2314yes—
344C2×#120C2314yes—
345C2×#120C2314yes—
346C2×#120C2314yes—
347C2×#120C2314yes—
348C2×#120C2314yes—
349C2×#120C2314yes—
350C2×#120C2312yes—
351C2×#120C2314yes—
352C2×#120C2314yes—
353C2×#120C2312yes—
354C2×#120C2314yes—
355C2×#120C2314yes—
356C2×#120C2314yes—
357C2×C4×Q8C2312yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2314yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2311yescharacteristic
379C2×#117C2314yes—
380C22×C4⋊C4C2312yes—
381C22×C22⋊C4C2314yes—
382C22×C22⋊C4C2314yes—
383C22×C22⋊C4C2314yes—
384C22×C22⋊C4C2314yes—
385C22×C22⋊C4C2314yes—
386#400C2312yes—
387#400C2314yes—
388#400C2314yes—
389#400C2311yescharacteristic
390#400C2312yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#399C2314yes—
395#399C2312yes—
396#399C2311yescharacteristic
397#399C2314yes—
398#399C2314yes—
399#399C2314yes—
400#399C2314yes—
401#398C2311yescharacteristic
402#398C2312yes—
403#398C2314yes—
404#398C2312yes—
405#398C2312yes—
406#398C2312yes—
407#398C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2314yes—
412#397C2312yes—
413#397C2312yes—
414#397C2312yes—
415#397C2314yes—
416#397C2311yescharacteristic
417#397C2312yes—
418#397C2314yes—
419#397C2312yes—
420#397C2312yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2312yes—
429#396C2314yes—
430#396C2314yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#395C2312yes—
443#395C2311yescharacteristic
444#395C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2312yes—
451#394C2311yescharacteristic
452#394C2312yes—
453#394C2314yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2312yes—
459#394C2312yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2312yes—
467#394C2312yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2312yes—
476#394C2312yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2312yes—
481#394C2314yes—
482#394C2312yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2312yes—
488#394C2314yes—
489#394C2314yes—
490#394C2312yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2312yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#393C2314yes—
506#393C2312yes—
507#393C2314yes—
508#393C2312yes—
509#393C2314yes—
510#393C2314yes—
511#393C2314yes—
512#393C2314yes—
513#393C2314yes—
514#393C2312yes—
515#393C2311yescharacteristic
516#393C2314yes—
517#393C2314yes—
518#392C2312yes—
519#392C2312yes—
520#392C2312yes—
521#392C2312yes—
522#392C2312yes—
523#392C2312yes—
524#392C2312yes—
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#392C2314yes—
531#392C2312yes—
532#392C2311yescharacteristic
533#392C2314yes—
534#392C2314yes—
535#392C2314yes—
536#392C2314yes—
537#392C2314yes—
538#392C2314yes—
539#392C2314yes—
540#392C2314yes—
541#392C2312yes—
542#392C2314yes—
543#392C2314yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#391C2312yes—
548#391C2312yes—
549#391C2312yes—
550#391C2312yes—
551#391C2314yes—
552#391C2314yes—
553#390C2312yes—
554#390C2311yescharacteristic
555#390C2312yes—
556#390C2311yescharacteristic
557#390C2312yes—
558#390C2314yes—
559#390C2312yes—
560#390C2314yes—
561#390C2312yes—
562#390C2314yes—
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2314yes—
567#390C2312yes—
568#390C2314yes—
569#390C2314yes—
570#390C2314yes—
571#390C2314yes—
572#390C2312yes—
573#390C2312yes—
574#390C2314yes—
575#390C2314yes—
576#390C2312yes—
577#390C2314yes—
578#390C2314yes—
579#390C2312yes—
580#390C2312yes—
581#390C2314yes—
582#390C2314yes—
583#390C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2314yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
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#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#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#384C2311yescharacteristic
667#384C2312yes—
668#384C2312yes—
669#384C2312yes—
670#383C2312yes—
671#382C2312yes—
672#382C2314yes—
673#382C2312yes—
674#382C2312yes—
675#381C2314yes—
676#381C2314yes—
677#381C2312yes—
678#380C2312yes—
679#380C2311yescharacteristic
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683#380C2314yes—
684#380C2312yes—
685#380C2312yes—
686#380C2311yescharacteristic
687#380C2312yes—
688#380C2314yes—
689#380C2314yes—
690#380C2314yes—
691#379C2314yes—
692#379C2314yes—
693#379C2314yes—
694#379C2312yes—
695#379C2314yes—
696#379C2314yes—
697#379C2314yes—
698#379C2314yes—
699#379C2314yes—
700#379C2314yes—
701#379C2314yes—
702#379C2312yes—
703#379C2314yes—
704#379C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2311yescharacteristic
718C4×C22⋊C4C2311yescharacteristic
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C2×#95C2314yes—
723C2×#95C2312yes—
724C43C2311yescharacteristic
725C25C2414yes—
726C25C2412yes—
727C25C2414yes—
728C25C2412yes—
729H(5,𝔽2)—464no—
730C2×#41—28no—
731C2×#41—24no—
732C2×#41—24no—
733C2×#41—42no—
734C2×#41—44no—
735C2×#41—48no—
736C2×#41—44no—
737C2×#41—44no—
738C2×#41—44no—
739C2×#41—44no—
740C2×#41—44no—
741C22×Q8C2411yescharacteristic
742C22×Q8C2411yescharacteristic
743C22×Q8C2414yes—
744C22×Q8C2412yes—
745C22×Q8C2411yescharacteristic
746C22×D4—28no—
747C22×D4—28no—
748C22×D4—28no—
749C22×D4—28no—
750C22×D4—44no—
751C22×D4—42no—
752C22×D4—42no—
753C22×D4—44no—
754C22×D4—44no—
755C22×D4—44no—
756C22×D4—48no—
757C22×D4—48no—
758C22×D4—48no—
759C22×D4—44no—
760C22×D4—48no—
761C22×D4—48no—
762C22×D4—48no—
763C22×D4—48no—
764C22×D4—48no—
765C22×D4—48no—
766C22×D4—84no—
767C22×D4—84no—
768C22×D4—84no—
769C22×D4—84no—
770C22×D4C2412yes—
771C22×D4C2414yes—
772C22×D4C2412yes—
773C22×D4C2414yes—
774C22×D4C2412yes—
775C22×D4C2411yescharacteristic
776C22×D4C2414yes—
777C22×D4C2411yescharacteristic
778C22×D4C2411yescharacteristic
779C22×D4C2414yes—
780C22×D4C2412yes—
781C22×D4C2412yes—
782C22×D4C2412yes—
783C22×D4C2414yes—
784C22×D4C2414yes—
785C22×D4C2414yes—
786C22×D4C2414yes—
787C22×D4C2414yes—
788C22×D4C2414yes—
789C22×D4C2412yes—
790C22×D4C2412yes—
791C22×D4C2412yes—
792C22×D4C2412yes—
793C22×D4C2414yes—
794C22×D4C2412yes—
795C22×D4C2414yes—
796C22×D4C2414yes—
797C22×D4C2414yes—
798C22×D4C2412yes—
799C22×D4C2411yescharacteristic
800C23×C4C2412yes—
801C23×C4C2411yescharacteristic
802C23×C4C2411yescharacteristic
803C23×C4C2412yes—
804C23×C4C2412yes—
805C23×C4C2414yes—
806C23×C4C2412yes—
807C23×C4C2414yes—
808C23×C4C2414yes—
809C23×C4C2412yes—
810C23×C4C2414yes—
811C23×C4C2414yes—
812C23×C4C2414yes—
813C4⋊Q8—44no—
814C4⋊Q8—42no—
815C4⋊Q8—42no—
816#127—28no—
817#127—28no—
818#127—24no—
819#126—28no—
820#126—48no—
821#126—48no—
822#124—28no—
823#124—48no—
824#124—44no—
825#124—44no—
826#124—48no—
827#124—48no—
828#124—84no—
829#124—84no—
830#123—48no—
831#123—48no—
832#123—48no—
833#123—48no—
834#123—48no—
835#123—44no—
836#123—44no—
837#123—48no—
838#123—84no—
839C22⋊Q8—48no—
840C22⋊Q8—48no—
841C22⋊Q8—48no—
842C22⋊Q8—44no—
843C22⋊Q8—44no—
844C22⋊Q8—44no—
845C22⋊Q8—42no—
846C22⋊Q8—42no—
847C22⋊Q8—84no—
848C22⋊Q8—84no—
849#121—28no—
850#121—28no—
851#121—28no—
852#121—48no—
853#121—48no—
854#121—48no—
855#121—48no—
856#121—44no—
857#121—48no—
858#121—48no—
859#121—44no—
860#121—44no—
861#121—44no—
862#121—44no—
863#121—44no—
864#121—48no—
865#121—44no—
866#121—44no—
867#121—84no—
868#120—44no—
869#120—48no—
870#120—44no—
871#120—48no—
872#120—48no—
873#120—48no—
874#120—48no—
875#120—48no—
876#120—48no—
877#120—48no—
878#120—48no—
879#120—48no—
880#120—48no—
881#120—84no—
882#120—84no—
883#120—84no—
884C4×Q8—44no—
885C4×D4—28no—
886C4×D4—24no—
887C4×D4—216no—
888C4×D4—44no—
889C4×D4—44no—
890C4×D4—44no—
891C4×D4—44no—
892C4×D4—44no—
893C4×D4—44no—
894C4×D4—44no—
895C4×D4—44no—
896C4×D4—44no—
897C4×D4—42no—
898C4×D4—42no—
899C4×D4—48no—
900C4×D4—84no—
901#117—28no—
902#117—42no—
903#117—44no—
904#117—48no—
905#117—44no—
906#117—44no—
907C2×C4⋊C4—44no—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2411yescharacteristic
924C2×C4⋊C4C2411yescharacteristic
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2412yes—
948C2×C22⋊C4—48no—
949C2×C22⋊C4—48no—
950C2×C22⋊C4—48no—
951C2×C22⋊C4—48no—
952C2×C22⋊C4—84no—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2414yes—
991C2×C22⋊C4C2412yes—
992C2×C22⋊C4C2412yes—
993C2×C22⋊C4C2412yes—
994C2×C22⋊C4C2414yes—
995C2×C22⋊C4C2412yes—
996C2×C22⋊C4C2412yes—
997C2×C22⋊C4C2414yes—
998C2×C22⋊C4C2411yescharacteristic
999C2×C22⋊C4C2411yescharacteristic
1000C2×C22⋊C4C2414yes—
1001C2×C22⋊C4C2412yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2412yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2414yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C42C2412yes—
1035C2×C42C2412yes—
1036C2×C42C2412yes—
1037C2×C42C2412yes—
1038C2×C42C2412yes—
1039C2×C42C2411yescharacteristic
1040C2×C42C2414yes—
1041C2×C42C2414yes—
1042C2×C42C2412yes—
1043C2×C42C2414yes—
1044C2×C42C2414yes—
1045C2×C42C2411yescharacteristic
1046C2×C42C2411yescharacteristic
1047#95C2412yes—
1048#95C2411yescharacteristic
1049#95C2412yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2411yescharacteristic
1056#95C2412yes—
1057#95C2412yes—
1058#95C2411yescharacteristic
1059#95C2414yes—
1060#95C2412yes—
1061#95C2411yescharacteristic
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2414yes—
1071#95C2412yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090C24—28no—
1091C24—28no—
1092C24—28no—
1093C24—28no—
1094C24—44no—
1095C24—42no—
1096C24—44no—
1097C24—44no—
1098C24—44no—
1099C24—42no—
1100C24—44no—
1101C24—44no—
1102C24—44no—
1103C24—42no—
1104C24—44no—
1105C24—44no—
1106C24—44no—
1107C24—44no—
1108C24—42no—
1109C24—44no—
1110C24—42no—
1111C24—44no—
1112C24—44no—
1113C24—42no—
1114C24C2512yes—
1115C24C2514yes—
1116C24C2512yes—
1117C24C2511yescharacteristic
1118C24C2511yescharacteristic
1119C24C2514yes—
1120C24C2512yes—
1121#41—432no—
1122#41—416no—
1123#41—432no—
1124#41—416no—
1125#41—88no—
1126C2×Q8—24no—
1127C2×Q8—22no—
1128C2×Q8—24no—
1129C2×Q8—22no—
1130C2×Q8—42no—
1131C2×Q8—41no—
1132C2×Q8—44no—
1133C2×Q8—44no—
1134C2×Q8—44no—
1135C2×Q8—44no—
1136C2×Q8—42no—
1137C2×D4—28no—
1138C2×D4—28no—
1139C2×D4—28no—
1140C2×D4—28no—
1141C2×D4—28no—
1142C2×D4—24no—
1143C2×D4—28no—
1144C2×D4—28no—
1145C2×D4—28no—
1146C2×D4—24no—
1147C2×D4—28no—
1148C2×D4—28no—
1149C2×D4—28no—
1150C2×D4—28no—
1151C2×D4—24no—
1152C2×D4—24no—
1153C2×D4—24no—
1154C2×D4—28no—
1155C2×D4—24no—
1156C2×D4—24no—
1157C2×D4—24no—
1158C2×D4—24no—
1159C2×D4—24no—
1160C2×D4—22no—
1161C2×D4—22no—
1162C2×D4—42no—
1163C2×D4—42no—
1164C2×D4—42no—
1165C2×D4—44no—
1166C2×D4—42no—
1167C2×D4—42no—
1168C2×D4—42no—
1169C2×D4—44no—
1170C2×D4—44no—
1171C2×D4—42no—
1172C2×D4—41no—
1173C2×D4—42no—
1174C2×D4—44no—
1175C2×D4—44no—
1176C2×D4—42no—
1177C2×D4—42no—
1178C2×D4—42no—
1179C2×D4—42no—
1180C2×D4—42no—
1181C2×D4—42no—
1182C2×D4—44no—
1183C2×D4—41no—
1184C2×D4—41no—
1185C2×D4—44no—
1186C2×D4—44no—
1187C2×D4—44no—
1188C2×D4—44no—
1189C2×D4—44no—
1190C2×D4—44no—
1191C2×D4—44no—
1192C2×D4—44no—
1193C2×D4—44no—
1194C2×D4—44no—
1195C2×D4—44no—
1196C2×D4—44no—
1197C2×D4—42no—
1198C2×D4—42no—
1199C2×D4—44no—
1200C2×D4—44no—
1201C2×D4—44no—
1202C2×D4—44no—
1203C2×D4—42no—
1204C2×D4—44no—
1205C2×D4—44no—
1206C2×D4—44no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—44no—
1210C2×D4—41no—
1211C2×D4—41no—
1212C2×D4—44no—
1213C2×D4—42no—
1214C2×D4—42no—
1215C2×D4—44no—
1216C2×D4—44no—
1217C2×D4—44no—
1218C2×D4—44no—
1219C2×D4—416no—
1220C2×D4—432no—
1221C2×D4—432no—
1222C2×D4—464no—
1223C2×D4—816no—
1224C2×D4—88no—
1225C2×D4—832no—
1226C2×D4—832no—
1227C2×D4—832no—
1228C2×D4H(5,𝔽2)18yes—
1229C2×D4H(5,𝔽2)14yes—
1230C22×C4—28no—
1231C22×C4—24no—
1232C22×C4—24no—
1233C22×C4—28no—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—24no—
1237C22×C4—24no—
1238C22×C4—22no—
1239C22×C4—24no—
1240C22×C4—24no—
1241C22×C4—24no—
1242C22×C4—24no—
1243C22×C4—24no—
1244C22×C4—24no—
1245C22×C4—22no—
1246C22×C4—28no—
1247C22×C4—28no—
1248C22×C4—42no—
1249C22×C4—44no—
1250C22×C4—44no—
1251C22×C4—44no—
1252C22×C4—44no—
1253C22×C4—44no—
1254C22×C4—44no—
1255C22×C4—44no—
1256C22×C4—44no—
1257C22×C4—44no—
1258C22×C4—44no—
1259C22×C4—44no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—44no—
1263C22×C4—44no—
1264C22×C4—44no—
1265C22×C4C2512yes—
1266C22×C4C2512yes—
1267C22×C4C2511yescharacteristic
1268C22×C4C2512yes—
1269C22×C4C2512yes—
1270C22×C4C2514yes—
1271C22×C4C2512yes—
1272C22×C4C2512yes—
1273C22×C4C2512yes—
1274C22×C4C2514yes—
1275C22×C4C2512yes—
1276C22×C4C2514yes—
1277C22×C4C2511yescharacteristic
1278C22×C4C2511yescharacteristic
1279C22×C4C2512yes—
1280C22×C4C2514yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2511yescharacteristic
1286C22×C4C2511yescharacteristic
1287C4⋊C4—28no—
1288C4⋊C4—22no—
1289C4⋊C4—24no—
1290C4⋊C4—24no—
1291C4⋊C4—28no—
1292C4⋊C4—24no—
1293C4⋊C4—24no—
1294C4⋊C4—24no—
1295C4⋊C4—24no—
1296C4⋊C4—24no—
1297C4⋊C4—41no—
1298C4⋊C4—42no—
1299C4⋊C4—42no—
1300C4⋊C4—42no—
1301C4⋊C4—42no—
1302C4⋊C4—41no—
1303C4⋊C4—41no—
1304C4⋊C4—41no—
1305C4⋊C4—42no—
1306C4⋊C4—42no—
1307C4⋊C4—44no—
1308C4⋊C4—42no—
1309C4⋊C4—42no—
1310C4⋊C4—42no—
1311C4⋊C4—42no—
1312C4⋊C4—42no—
1313C4⋊C4—42no—
1314C4⋊C4—44no—
1315C4⋊C4—44no—
1316C4⋊C4—44no—
1317C4⋊C4—44no—
1318C4⋊C4—44no—
1319C4⋊C4—44no—
1320C4⋊C4—44no—
1321C4⋊C4—42no—
1322C4⋊C4—42no—
1323C4⋊C4—44no—
1324C4⋊C4—44no—
1325C4⋊C4—42no—
1326C4⋊C4—44no—
1327C22⋊C4—28no—
1328C22⋊C4—28no—
1329C22⋊C4—28no—
1330C22⋊C4—28no—
1331C22⋊C4—24no—
1332C22⋊C4—28no—
1333C22⋊C4—28no—
1334C22⋊C4—24no—
1335C22⋊C4—24no—
1336C22⋊C4—28no—
1337C22⋊C4—28no—
1338C22⋊C4—28no—
1339C22⋊C4—24no—
1340C22⋊C4—42no—
1341C22⋊C4—42no—
1342C22⋊C4—44no—
1343C22⋊C4—44no—
1344C22⋊C4—44no—
1345C22⋊C4—44no—
1346C22⋊C4—44no—
1347C22⋊C4—44no—
1348C22⋊C4—44no—
1349C22⋊C4—44no—
1350C22⋊C4—42no—
1351C22⋊C4—44no—
1352C22⋊C4—44no—
1353C22⋊C4—44no—
1354C22⋊C4—42no—
1355C22⋊C4—44no—
1356C22⋊C4—44no—
1357C22⋊C4—42no—
1358C22⋊C4—42no—
1359C22⋊C4—42no—
1360C22⋊C4—44no—
1361C22⋊C4—44no—
1362C22⋊C4—42no—
1363C22⋊C4—42no—
1364C22⋊C4—44no—
1365C22⋊C4—42no—
1366C22⋊C4—42no—
1367C22⋊C4—44no—
1368C22⋊C4—42no—
1369C22⋊C4—42no—
1370C22⋊C4—42no—
1371C22⋊C4—44no—
1372C22⋊C4—42no—
1373C22⋊C4—44no—
1374C22⋊C4—42no—
1375C22⋊C4—42no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—44no—
1379C22⋊C4—42no—
1380C22⋊C4—44no—
1381C22⋊C4—44no—
1382C22⋊C4—42no—
1383C22⋊C4—44no—
1384C22⋊C4—44no—
1385C22⋊C4—44no—
1386C22⋊C4—42no—
1387C22⋊C4—44no—
1388C22⋊C4—44no—
1389C22⋊C4—44no—
1390C22⋊C4—44no—
1391C22⋊C4—42no—
1392C22⋊C4—44no—
1393C22⋊C4—44no—
1394C22⋊C4—44no—
1395C22⋊C4—44no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—42no—
1400C22⋊C4—42no—
1401C22⋊C4—42no—
1402C22⋊C4—44no—
1403C22⋊C4—44no—
1404C22⋊C4—44no—
1405C22⋊C4—42no—
1406C22⋊C4—42no—
1407C22⋊C4—42no—
1408C42—24no—
1409C42—24no—
1410C42—24no—
1411C42—24no—
1412C42—22no—
1413C42—24no—
1414C42—41no—
1415C42—44no—
1416C42—44no—
1417C42—42no—
1418C42—44no—
1419C42—44no—
1420C42H(5,𝔽2)14yescomplemented
1421C23—22no—
1422C23—24no—
1423C23—24no—
1424C23—24no—
1425C23—24no—
1426C23—24no—
1427C23—24no—
1428C23—24no—
1429C23—24no—
1430C23—22no—
1431C23—22no—
1432C23—24no—
1433C23—21no—
1434C23—22no—
1435C23—22no—
1436C23—22no—
1437C23—24no—
1438C23—21no—
1439C23—22no—
1440C23—24no—
1441C23—22no—
1442C23—24no—
1443C23—22no—
1444C23—21no—
1445C23—21no—
1446C23—22no—
1447C23—22no—
1448C23—22no—
1449C23—22no—
1450C23—22no—
1451C23—22no—
1452C23—24no—
1453C23—24no—
1454C23—22no—
1455C23—22no—
1456C23—22no—
1457C23—21no—
1458C23—22no—
1459C23—22no—
1460C23—24no—
1461C23—21no—
1462C23—416no—
1463C23—48no—
1464C23—88no—
1465C23—88no—
1466C23—88no—
1467C23—88no—
1468C23—88no—
1469C23—88no—
1470C23—88no—
1471C23—88no—
1472C23—88no—
1473C23—88no—
1474C23—88no—
1475C23—88no—
1476C23—84no—
1477C23—162no—
1478C23—164no—
1479C23—164no—
1480C23—164no—
1481C23—162no—
1482C23—164no—
1483C23—162no—
1484C23—164no—
1485C23—162no—
1486C23C2×H(5,𝔽2)18yes—
1487C23C2×H(5,𝔽2)14yes—
1488C23C2611yescharacteristic
1489Q8—44no—
1490Q8—44no—
1491Q8—44no—
1492Q8—162no—
1493Q8—164no—
1494D4—216no—
1495D4—28no—
1496D4—416no—
1497D4—48no—
1498D4—48no—
1499D4—416no—
1500D4—48no—
1501D4—48no—
1502D4—416no—
1503D4—48no—
1504D4—44no—
1505D4—48no—
1506D4—48no—
1507D4—82no—
1508D4—82no—
1509D4—88no—
1510D4—88no—
1511D4—88no—
1512D4—88no—
1513D4—88no—
1514D4—88no—
1515D4—88no—
1516D4—84no—
1517D4—84no—
1518D4—84no—
1519D4—88no—
1520D4—88no—
1521D4—88no—
1522D4—84no—
1523D4—164no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—21no—
1528C2×C4—22no—
1529C2×C4—24no—
1530C2×C4—21no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—24no—
1541C2×C4—24no—
1542C2×C4—24no—
1543C2×C4—24no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—24no—
1549C2×C4—24no—
1550C2×C4—24no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—24no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—24no—
1566C2×C4—24no—
1567C2×C4—22no—
1568C2×C4—24no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—24no—
1572C2×C4—22no—
1573C2×C4—24no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—48no—
1581C2×C4—48no—
1582C2×C4—416no—
1583C2×C4—44no—
1584C2×C4—48no—
1585C2×C4—48no—
1586C2×C4—44no—
1587C2×C4—88no—
1588C2×C4—88no—
1589C2×C4—88no—
1590C2×C4—84no—
1591C2×C4—88no—
1592C2×C4—164no—
1593C2×C4C2×H(5,𝔽2)12yes—
1594C2×C4C2×H(5,𝔽2)14yes—
1595C2×C4C2×H(5,𝔽2)12yes—
1596C2×C4C2×H(5,𝔽2)14yes—
1597C22—24no—
1598C22—28no—
1599C22—28no—
1600C22—24no—
1601C22—24no—
1602C22—28no—
1603C22—44no—
1604C22—44no—
1605C22—44no—
1606C22—44no—
1607C22—44no—
1608C22—44no—
1609C22—42no—
1610C22—42no—
1611C22—44no—
1612C22—41no—
1613C22—41no—
1614C22—42no—
1615C22—42no—
1616C22—44no—
1617C22—42no—
1618C22—42no—
1619C22—42no—
1620C22—44no—
1621C22—42no—
1622C22—44no—
1623C22—44no—
1624C22—42no—
1625C22—42no—
1626C22—42no—
1627C22—42no—
1628C22—42no—
1629C22—42no—
1630C22—41no—
1631C22—42no—
1632C22—41no—
1633C22—44no—
1634C22—42no—
1635C22—41no—
1636C22—42no—
1637C22—41no—
1638C22—42no—
1639C22—44no—
1640C22—1616no—
1641C22—168no—
1642C22—1616no—
1643C22—168no—
1644C22C22×H(5,𝔽2)11yescharacteristic
1645C22C22×H(5,𝔽2)12yes—
1646C22C22×H(5,𝔽2)11yescharacteristic
1647C22H(7,𝔽2)12yes—
1648C222−1+611yescharacteristic
1649C4—24no—
1650C4—22no—
1651C4—42no—
1652C4—44no—
1653C4—41no—
1654C4—42no—
1655C4—42no—
1656C4—42no—
1657C4—42no—
1658C4—44no—
1659C4—44no—
1660C4—44no—
1661C4—42no—
1662C4—42no—
1663C4—42no—
1664C4—42no—
1665C4—41no—
1666C4—42no—
1667C4—41no—
1668C4—42no—
1669C4—42no—
1670C4#353214yes—
1671C2—44no—
1672C2—48no—
1673C2—82no—
1674C2—82no—
1675C2—84no—
1676C2—81no—
1677C2—81no—
1678C2C2×#353211yescharacteristic
1679C2#6291212yes—
1680C2#6291411yescharacteristic
1681C2#6304511yescharacteristic
1682C2#6304912yes—
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. #59816C2semidirect
2. #59476C2semidirect
3. #57988C2semidirect
4. #56343C2semidirect
5. #56317C2semidirect
6. #55423C2semidirect
7. #54816C2semidirect
8. #53044C2semidirect
9. #53015C2semidirect
10. #52410C2semidirect
11. #52316C2semidirect
12. #47695C2semidirect
13. #45088C2semidirect
14. #45079C2semidirect
15. #44929C2semidirect
16. #44877C2semidirect
17. #44874C2semidirect
18. #42967C2semidirect
19. #42712C2semidirect
20. #42547C2semidirect
21. #42474C2semidirect
22. #42443C2semidirect
23. #41983C2semidirect
24. #40590C2semidirect
25. #39532C2semidirect
26. #39491C2semidirect
27. #36696C2semidirect
28. #35750C2semidirect
29. #35680C2semidirect
30. C22×H(5,𝔽2)C22semidirect
31. C2×#555C22semidirect
32. C2×#551C22semidirect
33. C2×#547C22semidirect
34. C2×#546C22semidirect
35. C2×#546C22semidirect
37. C2×D42C22semidirect
38. C2×D42C22semidirect
39. C2×D42C22semidirect
40. C2×#542C22semidirect
41. C2×#535C22semidirect
42. #2862C22semidirect
43. #2843C22semidirect
44. #2840C22semidirect
45. #2830C22semidirect
46. #2830C22semidirect
47. #2830C22semidirect
48. #2829C22semidirect
49. #2829C22semidirect
50. #2829C22semidirect
51. #2829C22semidirect
52. #2828C22semidirect
53. #2828C22semidirect
54. #2828C22semidirect
55. #2826C22semidirect
56. #2824C22semidirect
57. #2823C22semidirect
58. #2819C22semidirect
59. #2819C22semidirect
60. #2818C22semidirect
61. #2813C22semidirect
62. #2813C22semidirect
63. #2813C22semidirect
64. #2812C22semidirect
65. #2803C22semidirect
66. #2785C22semidirect
67. #2782C22semidirect
68. #2761C22semidirect
69. #2761C22semidirect
70. #2753C22semidirect
71. #2752C22semidirect
72. #2751C22semidirect
73. #2751C22semidirect
74. #2743C22semidirect
75. #2742C22semidirect
76. #2736C22semidirect
77. #2730C22semidirect
78. #2730C22semidirect
79. #2718C22semidirect
80. #2714C22semidirect
81. #2714C22semidirect
82. #2710C22semidirect
83. #2710C22semidirect
84. #2710C22semidirect
85. #2706C22semidirect
86. #2705C22semidirect
87. #2702C22semidirect
88. #2701C22semidirect
89. #2697C22semidirect
90. #2697C22semidirect
91. #2697C22semidirect
92. #2696C22semidirect
93. #2696C22semidirect
94. #2685C22semidirect
95. #2685C22semidirect
96. #2685C22semidirect
97. #2685C22semidirect
98. #2684C22semidirect
99. #2684C22semidirect
100. #2682C22semidirect
101. #2681C22semidirect
102. #2681C22semidirect
103. #2679C22semidirect
104. #2679C22semidirect
105. #2679C22semidirect
106. #2678C22semidirect
107. #2678C22semidirect
108. #2678C22semidirect
109. #2678C22semidirect
110. #2676C22semidirect
111. #2676C22semidirect
112. #2676C22semidirect
113. #2671C22semidirect
114. #2670C22semidirect
115. #2670C22semidirect
116. #2670C22semidirect
117. #2670C22semidirect
118. #2668C22semidirect
119. #2661C22semidirect
120. #2648C22semidirect
121. #2639C22semidirect
122. #2639C22semidirect
123. #2636C22semidirect
124. #2635C22semidirect
125. #2626C22semidirect
126. #2625C22semidirect
127. #2622C22semidirect
128. #2620C22semidirect
129. #2620C22semidirect
130. #2619C22semidirect
131. #2618C22semidirect
132. #2616C22semidirect
133. #2615C22semidirect
134. #2613C22semidirect
135. #2613C22semidirect
136. #2613C22semidirect
137. #2609C22semidirect
138. #2598C22semidirect
139. #2591C22semidirect
140. #2563C22semidirect
141. #2563C22semidirect
142. #2559C22semidirect
143. #2553C22semidirect
144. #2545C22semidirect
145. #2544C22semidirect
146. #2542C22semidirect
147. #2542C22semidirect
148. #2540C22semidirect
149. #2539C22semidirect
150. #2538C22semidirect
151. #2537C22semidirect
152. #2537C22semidirect
153. #2537C22semidirect
154. #2511C22semidirect
155. #2505C22semidirect
156. #2504C22semidirect
157. #2500C22semidirect
158. #2497C22semidirect
159. #2496C22semidirect
160. #2492C22semidirect
161. #2491C22semidirect
162. #2491C22semidirect
163. #2491C22semidirect
164. #2485C22semidirect
165. #2476C22semidirect
166. #2472C22semidirect
167. #2472C22semidirect
168. #2472C22semidirect
169. #2471C22semidirect
170. #2463C22semidirect
171. #2459C22semidirect
172. #2452C22semidirect
173. #2452C22semidirect
174. #2450C22semidirect
175. #2450C22semidirect
176. #2447C22semidirect
177. #2445C22semidirect
178. #2445C22semidirect
179. #2437C22semidirect
180. #2437C22semidirect
181. #2435C22semidirect
182. #2435C22semidirect
183. #2435C22semidirect
184. #2435C22semidirect
185. #2435C22semidirect
187. #2432C22semidirect
189. #2431C22semidirect
190. #2430C22semidirect
191. #2430C22semidirect
192. #2428C22semidirect
193. #2427C22semidirect
194. #2426C22semidirect
195. #2424C22semidirect
196. #2423C22semidirect
197. #2422C22semidirect
198. #2422C22semidirect
199. #2418C22semidirect
200. #2415C22semidirect
201. #2415C22semidirect
202. #2414C22semidirect
203. #2411C22semidirect
204. #2411C22semidirect
205. #2411C22semidirect
206. #2410C22semidirect
207. #2410C22semidirect
208. #2410C22semidirect
209. #2410C22semidirect
210. #2410C22semidirect
212. #2408C22semidirect
213. #2408C22semidirect
214. #2408C22semidirect
215. #2408C22semidirect
216. #2408C22semidirect
217. #2408C22semidirect
218. #2408C22semidirect
219. #2407C22semidirect
220. #2407C22semidirect
221. #2407C22semidirect
222. #2407C22semidirect
223. #2406C22semidirect
224. #2405C22semidirect
225. #2405C22semidirect
226. #2405C22semidirect
227. #2404C22semidirect
228. #2403C22semidirect
229. #2403C22semidirect
230. #2403C22semidirect
231. #2395C22semidirect
232. #2395C22semidirect
233. #2392C22semidirect
234. #2392C22semidirect
235. #2392C22semidirect
236. #2388C22semidirect
237. #2388C22semidirect
238. C2×#394C22semidirect
239. C2×#392C22semidirect
240. #2367C22semidirect
241. #2366C22semidirect
242. #2363C22semidirect
243. #2354C22semidirect
244. #2341C22semidirect
245. #2339C22semidirect
246. #2339C22semidirect
247. D4×C22⋊C4C22semidirect
248. D4×C22⋊C4C22semidirect
249. D4×C22⋊C4C22semidirect
250. #2324C22semidirect
251. #2324C22semidirect
252. #2318C22semidirect
253. #2317C22semidirect
254. #2309C22semidirect
255. C4×#127C22semidirect
256. C4×#127C22semidirect
257. C4×#126C22semidirect
258. #2293C22semidirect
1420. C42H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
#598162
#594762
#579882
#563432
#563172
#554232
#548162
#530442
#530152
#524102
#523162
#476952
#450882
#450792
#449292
#448772
#448742
#429672
#427122
#425472
#424742
#424432
#419832
#405902
#395322
#394912
#366962
#357502
#356802