Finite Group Databasebeta

← #8581957

Subgroups — #8581957

Order 512.

6200 conjugacy classes of subgroups.

The subgroup lattice has 1673 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59095C212yesmaximal, complemented
2#57964C214yesmaximal, complemented
3#57272C214yesmaximal, complemented
4#57209C214yesmaximal, complemented
5#57149C214yesmaximal, complemented
6#56660C212yesmaximal, complemented
7#55430C214yesmaximal, complemented
8#53000C212yesmaximal, complemented
9#52990C211yesmaximal, characteristic, complemented
10#52398C212yesmaximal, complemented
11#52203C211yesmaximal, characteristic, complemented
12#47934C214yesmaximal, complemented
13#47063C212yesmaximal, complemented
14#45487C211yesmaximal, characteristic, complemented
15#45244C211yesmaximal, characteristic, complemented
16#44876C212yesmaximal, complemented
17#42560C212yesmaximal, complemented
18#42519C212yesmaximal, complemented
19#42483C211yesmaximal, characteristic, complemented
20#40586C212yesmaximal, complemented
21#39864C212yesmaximal, complemented
22#38918C211yesmaximal, characteristic, complemented
23#38054C212yesmaximal, complemented
24#37780C212yesmaximal, complemented
25#37677C212yesmaximal, complemented
26#37618C212yesmaximal, complemented
27#37346C212yesmaximal, complemented
28#35680C211yesmaximal, characteristic, complemented
29#35513C212yesmaximal, complemented
30C22×H(5,𝔽2)C2211yescharacteristic
31C2×#560C2212yescomplemented
32C2×#550C2211yescharacteristic, complemented
33C2×#548C2212yescomplemented
34C2×#546C2211yescharacteristic
35C2×#546C2214yescomplemented
36C2×D42C2212yes—
37C2×#537C2212yescomplemented
38C2×#535C2212yes—
39C2×#532C2212yescomplemented
40C2×#532C2212yescomplemented
41C22×#124C2211yescharacteristic, complemented
42#2856C2212yescomplemented
43#2855C2211yescharacteristic, complemented
44#2855C2212yescomplemented
45#2840C2212yescomplemented
46#2832C2214yescomplemented
47#2828C2214yescomplemented
48#2825C2214yescomplemented
49#2824C2214yescomplemented
50#2824C2214yescomplemented
51#2824C2212yescomplemented
52#2815C2212yescomplemented
53#2815C2214yescomplemented
54#2815C2212yescomplemented
55#2815C2214yescomplemented
56#2813C2214yescomplemented
57#2812C2214yescomplemented
58#2797C2214yescomplemented
59#2797C2214yescomplemented
60#2786C2214yescomplemented
61#2786C2214yescomplemented
62#2784C2214yescomplemented
63#2784C2214yescomplemented
64#2779C2214yescomplemented
65#2764C2211yescharacteristic, complemented
66#2763C2211yescharacteristic, complemented
67#2762C2212yescomplemented
68#2761C2212yescomplemented
69#2761C2214yescomplemented
70#2760C2211yescharacteristic, complemented
71#2757C2214yescomplemented
72#2751C2214yescomplemented
73#2750C2214yescomplemented
74#2749C2212yescomplemented
75#2743C2212yescomplemented
76#2737C2214yescomplemented
77#2737C2212yescomplemented
78#2736C2212yescomplemented
79#2723C2214yescomplemented
80#2717C2214yescomplemented
81#2714C2214yescomplemented
82#2712C2212yescomplemented
83#2708C2214yescomplemented
84#2706C2212yescomplemented
85#2703C2214yescomplemented
86#2703C2214yescomplemented
87#2700C2214yescomplemented
88#2699C2214yescomplemented
89#2699C2214yescomplemented
90#2696C2214yescomplemented
91#2696C2214yescomplemented
92#2695C2214yescomplemented
93#2693C2211yescharacteristic, complemented
94#2688C2214yescomplemented
95#2688C2214yescomplemented
96#2688C2214yescomplemented
97#2688C2214yescomplemented
98#2686C2214yescomplemented
99#2686C2214yescomplemented
100#2686C2214yescomplemented
101#2686C2214yescomplemented
102#2684C2214yescomplemented
103#2683C2212yescomplemented
104#2678C2214yescomplemented
105#2678C2214yescomplemented
106#2678C2214yescomplemented
107#2678C2214yescomplemented
108#2676C2214yescomplemented
109#2676C2214yescomplemented
110#2676C2214yescomplemented
111#2676C2214yescomplemented
112#2676C2214yescomplemented
113#2676C2214yescomplemented
114#2675C2212yescomplemented
115#2675C2212yescomplemented
116#2671C2214yescomplemented
117#2670C2214yescomplemented
118#2670C2214yescomplemented
119#2670C2214yescomplemented
120#2669C2214yescomplemented
121#2669C2212yescomplemented
122#2668C2214yescomplemented
123#2668C2214yescomplemented
124#2657C2212yescomplemented
125#2657C2211yescharacteristic, complemented
126#2648C2214yescomplemented
127#2644C2212yescomplemented
128#2643C2214yescomplemented
129#2640C2212yescomplemented
130#2640C2212yescomplemented
131#2638C2214yescomplemented
132#2631C2214yescomplemented
133#2631C2214yescomplemented
134#2630C2214yescomplemented
135#2630C2214yescomplemented
136#2622C2212yescomplemented
137#2620C2212yescomplemented
138#2617C2212yescomplemented
139#2615C2211yescharacteristic
140#2615C2214yescomplemented
141#2615C2212yescomplemented
142#2615C2214yescomplemented
143#2613C2212yes—
144#2600C2214yescomplemented
145#2592C2211yescharacteristic, complemented
146#2592C2212yescomplemented
147#2564C2214yescomplemented
148#2561C2214yescomplemented
149#2555C2212yescomplemented
150#2548C2212yescomplemented
151#2547C2212yescomplemented
152#2547C2212yescomplemented
153#2544C2212yescomplemented
154#2544C2212yescomplemented
155#2543C2214yescomplemented
156#2541C2212yescomplemented
157#2541C2212yescomplemented
158#2541C2211yescharacteristic, complemented
159#2535C2214yescomplemented
160#2535C2214yescomplemented
161#2512C2212yescomplemented
162#2511C2212yescomplemented
163#2492C2212yescomplemented
164#2491C2212yescomplemented
165#2483C2212yescomplemented
166#2483C2214yescomplemented
167#2480C2214yescomplemented
168#2467C2214yescomplemented
169#2463C2212yescomplemented
170#2456C2214yescomplemented
171#2456C2214yescomplemented
172#2452C2212yescomplemented
173#2450C2214yescomplemented
174#2450C2214yescomplemented
175#2448C2212yescomplemented
176#2447C2212yescomplemented
177#2446C2212yescomplemented
178#2445C2212yescomplemented
179#2445C2212yescomplemented
180#2440C2212yescomplemented
181#2437C2214yescomplemented
182#2436C2212yescomplemented
183#2435C2212yes—
184#2435C2212yescomplemented
185#2434C2211yescharacteristic, complemented
186#2433C2211yescharacteristic
187#2433C2212yes—
188#2433C2212yescomplemented
189#2433C2212yescomplemented
190#2432C2212yes—
191#2432C2212yescomplemented
192#2431C2212yes—
193#2431C2212yes—
194#2431C2212yescomplemented
195#2431C2212yescomplemented
196#2431C2212yescomplemented
197#2430C2212yes—
198#2430C2214yescomplemented
199#2430C2214yescomplemented
200#2428C2212yescomplemented
201#2428C2214yescomplemented
202#2428C2212yescomplemented
203#2427C2212yescomplemented
204#2427C2212yescomplemented
205#2426C2212yescomplemented
206#2424C2214yescomplemented
207#2424C2214yescomplemented
208#2424C2214yescomplemented
209#2424C2214yescomplemented
210#2424C2214yescomplemented
211#2422C2212yescomplemented
212#2416C2212yescomplemented
213#2412C2212yescomplemented
214#2410C2214yes—
215#2410C2214yescomplemented
216#2410C2214yescomplemented
217#2410C2214yescomplemented
218#2410C2214yescomplemented
219#2410C2214yescomplemented
220#2410C2214yescomplemented
221#2410C2214yescomplemented
222#2409C2211yescharacteristic, complemented
223#2408C2211yescharacteristic
224#2408C2214yescomplemented
225#2408C2214yescomplemented
226#2407C2212yes—
227#2407C2214yescomplemented
228#2407C2214yescomplemented
229#2407C2214yescomplemented
230#2404C2212yes—
231#2404C2214yescomplemented
232#2404C2214yescomplemented
233#2404C2212yescomplemented
234#2403C2214yes—
235#2401C2212yescomplemented
236#2398C2211yescharacteristic, complemented
237#2396C2212yescomplemented
238#2388C2211yescharacteristic
239C2×#392C2212yes—
240#2366C2212yescomplemented
241#2361C2212yescomplemented
242#2360C2212yescomplemented
243#2339C2211yescharacteristic
244#2339C2212yescomplemented
245D4×C22⋊C4C2212yes—
246D4×C22⋊C4C2211yescharacteristic, complemented
247#2326C2212yescomplemented
248#2325C2214yescomplemented
249#2324C2212yescomplemented
250#2319C2211yescharacteristic, complemented
251#2315C2212yescomplemented
252#2311C2212yescomplemented
253C4×#123C2211yescharacteristic, complemented
254C4×#123C2212yescomplemented
255#2297C2212yescomplemented
256C2×#390C2212yes—
257#2290C2212yescomplemented
258#2283C2212yescomplemented
259C2×H(5,𝔽2)—44no—
260C2×H(5,𝔽2)—48no—
261C22×#41C2311yescharacteristic
262C22×#41C2312yes—
263C22×#41C2311yescharacteristic
264C22×#41C2312yes—
265C22×#41C2312yes—
266C22×#41C2314yes—
267C22×#41C2312yes—
268C23×Q8C2311yescharacteristic
269C23×D4C2312yes—
270C23×D4C2311yescharacteristic
271C23×D4C2312yes—
272C23×D4C2314yes—
273C23×D4C2311yescharacteristic
274C23×D4C2314yes—
275#560—48no—
276#550—44no—
277#548—48no—
278#546—416no—
279#546—44no—
280D42—48no—
281#537—48no—
282#535—48no—
283#532—48no—
284#532—48no—
285C2×C4⋊Q8C2312yes—
286C2×C4⋊Q8C2312yes—
287C2×#127C2312yes—
288C2×#127C2312yes—
289C2×#127C2312yes—
290C2×#127C2312yes—
291C2×#127C2311yescharacteristic
292C2×#127C2312yes—
293C2×#127C2312yes—
294C2×#126C2314yes—
295C2×#124—44no—
296C2×#124C2312yes—
297C2×#124C2311yescharacteristic
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2314yes—
301C2×#124C2312yes—
302C2×#124C2312yes—
303C2×#124C2312yes—
304C2×#124C2314yes—
305C2×#124C2314yes—
306C2×#124C2314yes—
307C2×#123C2311yescharacteristic
308C2×#123C2312yes—
309C2×#123C2312yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2311yescharacteristic
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2314yes—
325C2×#121C2312yes—
326C2×#121C2311yescharacteristic
327C2×#121C2314yes—
328C2×#121C2312yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2314yes—
341C2×#121C2314yes—
342C2×#121C2314yes—
343C2×#121C2312yes—
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#120C2314yes—
349C2×#120C2314yes—
350C2×#120C2312yes—
351C2×#120C2312yes—
352C2×#120C2314yes—
353C2×#120C2314yes—
354C2×#120C2314yes—
355C2×#120C2314yes—
356C2×#120C2314yes—
357C2×#120C2314yes—
358C2×#120C2314yes—
359C2×#120C2314yes—
360C2×#120C2314yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2311yescharacteristic
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2312yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2314yes—
376C2×#117C2312yes—
377C22×C4⋊C4C2312yes—
378C22×C22⋊C4C2312yes—
379C22×C22⋊C4C2312yes—
380C22×C22⋊C4C2312yes—
381C22×C22⋊C4C2314yes—
382C22×C22⋊C4C2312yes—
383C22×C22⋊C4C2314yes—
384C22×C22⋊C4C2314yes—
385C22×C42C2312yes—
386C22×C42C2311yescharacteristic
387#401C2312yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2312yes—
393#400C2312yes—
394#400C2312yes—
395#400C2312yes—
396#400C2312yes—
397#399C2314yes—
398#399C2312yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2312yes—
417#397C2311yescharacteristic
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2311yescharacteristic
425#397C2312yes—
426#397C2312yes—
427#397C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2312yes—
432#396C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2312yes—
437#396C2314yes—
438#395C2314yes—
439#395C2312yes—
440#395C2311yescharacteristic
441#395C2312yes—
442#395C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2312yes—
459#394C2314yes—
460#394C2311yescharacteristic
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2312yes—
481#393C2312yes—
482#393C2311yescharacteristic
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2311yescharacteristic
488#393C2314yes—
489#393C2312yes—
490#393C2312yes—
491#393C2314yes—
492#393C2311yescharacteristic
493#392C2314yes—
494#392C2314yes—
495#392C2312yes—
496#392C2312yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2312yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2312yes—
505#392C2314yes—
506#392C2314yes—
507#392C2312yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2312yes—
518#392C2312yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2311yescharacteristic
523#392C2314yes—
524#392C2312yes—
525#392C2312yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#392C2314yes—
531#392C2314yes—
532#391C2312yes—
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2312yes—
546#390C2312yes—
547#390C2314yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2314yes—
553#390C2314yes—
554#390C2312yes—
555#390C2314yes—
556#390C2312yes—
557#390C2314yes—
558#390C2314yes—
559#390C2314yes—
560#390C2312yes—
561#390C2312yes—
562#390C2314yes—
563#390C2312yes—
564#390C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2311yescharacteristic
625#386C2312yes—
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#386C2312yes—
639#386C2312yes—
640#386C2312yes—
641#386C2312yes—
642#386C2312yes—
643#386C2312yes—
644#386C2312yes—
645#386C2314yes—
646#386C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2312yes—
650#385C2314yes—
651#385C2314yes—
652#385C2311yescharacteristic
653#385C2312yes—
654#385C2312yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2312yes—
667#385C2312yes—
668#385C2312yes—
669#385C2314yes—
670#384C2312yes—
671#383C2312yes—
672#383C2312yes—
673#382C2312yes—
674#382C2312yes—
675#381C2312yes—
676#381C2314yes—
677#381C2312yes—
678#381C2312yes—
679#381C2314yes—
680#381C2312yes—
681#381C2312yes—
682#381C2314yes—
683#381C2312yes—
684#381C2311yescharacteristic
685#380C2314yes—
686#380C2314yes—
687#380C2314yes—
688#380C2314yes—
689#380C2314yes—
690#380C2314yes—
691#380C2312yes—
692#380C2312yes—
693#380C2314yes—
694#380C2311yescharacteristic
695#380C2311yescharacteristic
696#380C2312yes—
697#380C2312yes—
698#380C2314yes—
699#379C2314yes—
700#379C2314yes—
701#379C2312yes—
702#379C2314yes—
703#379C2312yes—
704#379C2314yes—
705#379C2314yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2311yescharacteristic
715C4×C22⋊C4C2311yescharacteristic
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721#376C2311yescharacteristic
722#376C2312yes—
723C2×#95C2314yes—
724C2×#95C2312yes—
725C25C2412yes—
726C25C2414yes—
727C25C2412yes—
728H(5,𝔽2)—464no—
729C2×#41—24no—
730C2×#41—28no—
731C2×#41—28no—
732C2×#41—28no—
733C2×#41—42no—
734C2×#41—48no—
735C2×#41—44no—
736C2×#41—48no—
737C2×#41—44no—
738C2×#41—44no—
739C2×#41—44no—
740C2×#41—48no—
741C2×#41—44no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—84no—
745C2×#41—84no—
746C22×Q8—42no—
747C22×Q8—44no—
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2412yes—
753C22×Q8C2414yes—
754C22×D4—28no—
755C22×D4—24no—
756C22×D4—28no—
757C22×D4—44no—
758C22×D4—48no—
759C22×D4—42no—
760C22×D4—44no—
761C22×D4—44no—
762C22×D4—44no—
763C22×D4—48no—
764C22×D4—48no—
765C22×D4—48no—
766C22×D4—48no—
767C22×D4—48no—
768C22×D4—84no—
769C22×D4C2411yescharacteristic
770C22×D4C2412yes—
771C22×D4C2412yes—
772C22×D4C2412yes—
773C22×D4C2414yes—
774C22×D4C2411yescharacteristic
775C22×D4C2412yes—
776C22×D4C2411yescharacteristic
777C22×D4C2411yescharacteristic
778C22×D4C2414yes—
779C22×D4C2414yes—
780C22×D4C2414yes—
781C22×D4C2414yes—
782C22×D4C2414yes—
783C22×D4C2414yes—
784C22×D4C2414yes—
785C22×D4C2414yes—
786C22×D4C2412yes—
787C22×D4C2412yes—
788C22×D4C2414yes—
789C22×D4C2414yes—
790C22×D4C2414yes—
791C22×D4C2412yes—
792C22×D4C2414yes—
793C22×D4C2414yes—
794C22×D4C2414yes—
795C22×D4C2414yes—
796C22×D4C2414yes—
797C22×D4C2414yes—
798C22×D4C2412yes—
799C22×D4C2412yes—
800C22×D4C2412yes—
801C23×C4C2411yescharacteristic
802C23×C4C2411yescharacteristic
803C23×C4C2412yes—
804C23×C4C2412yes—
805C23×C4C2412yes—
806C23×C4C2411yescharacteristic
807C23×C4C2412yes—
808C23×C4C2414yes—
809C23×C4C2412yes—
810C23×C4C2414yes—
811C23×C4C2414yes—
812C23×C4C2414yes—
813C23×C4C2414yes—
814C23×C4C2412yes—
815C23×C4C2411yescharacteristic
816C23×C4C2414yes—
817C23×C4C2414yes—
818C4⋊Q8—44no—
819C4⋊Q8—44no—
820#127—28no—
821#127—44no—
822#127—44no—
823#127—44no—
824#127—44no—
825#127—42no—
826#127—44no—
827#126—48no—
828#124—28no—
829#124—48no—
830#124—44no—
831#124—44no—
832#124—44no—
833#124—44no—
834#124—42no—
835#124—44no—
836#124—48no—
837#124—48no—
838#124—48no—
839#123—28no—
840#123—24no—
841#123—48no—
842#123—48no—
843#123—44no—
844#123—84no—
845C22⋊Q8—28no—
846C22⋊Q8—48no—
847C22⋊Q8—48no—
848C22⋊Q8—48no—
849C22⋊Q8—44no—
850C22⋊Q8—42no—
851C22⋊Q8—84no—
852#121—28no—
853#121—28no—
854#121—216no—
855#121—48no—
856#121—48no—
857#121—48no—
858#121—48no—
859#121—48no—
860#121—48no—
861#121—48no—
862#121—48no—
863#121—48no—
864#121—44no—
865#121—44no—
866#121—42no—
867#121—48no—
868#121—44no—
869#121—48no—
870#121—48no—
871#121—48no—
872#121—48no—
873#121—44no—
874#121—44no—
875#121—48no—
876#121—84no—
877#121—84no—
878#121—84no—
879#121—84no—
880#120—48no—
881#120—48no—
882#120—48no—
883#120—48no—
884#120—48no—
885#120—48no—
886#120—44no—
887#120—48no—
888#120—44no—
889#120—84no—
890#120—84no—
891#120—84no—
892#120—84no—
893C4×Q8—42no—
894C4×Q8—44no—
895C4×D4—24no—
896C4×D4—28no—
897C4×D4—48no—
898C4×D4—44no—
899C4×D4—44no—
900C4×D4—44no—
901C4×D4—44no—
902C4×D4—48no—
903C4×D4—48no—
904C4×D4—42no—
905C4×D4—48no—
906C4×D4—48no—
907C4×D4—48no—
908#117—44no—
909C2×C4⋊C4—44no—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2411yescharacteristic
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2411yescharacteristic
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C22⋊C4—28no—
943C2×C22⋊C4—48no—
944C2×C22⋊C4—44no—
945C2×C22⋊C4—44no—
946C2×C22⋊C4—44no—
947C2×C22⋊C4—84no—
948C2×C22⋊C4—84no—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2411yescharacteristic
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2411yescharacteristic
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2414yes—
989C2×C22⋊C4C2414yes—
990C2×C22⋊C4C2414yes—
991C2×C22⋊C4C2414yes—
992C2×C22⋊C4C2414yes—
993C2×C22⋊C4C2412yes—
994C2×C22⋊C4C2412yes—
995C2×C22⋊C4C2412yes—
996C2×C22⋊C4C2412yes—
997C2×C22⋊C4C2414yes—
998C2×C22⋊C4C2414yes—
999C2×C22⋊C4C2414yes—
1000C2×C22⋊C4C2414yes—
1001C2×C22⋊C4C2414yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2414yes—
1004C2×C22⋊C4C2412yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2414yes—
1009C2×C22⋊C4C2414yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C42—28no—
1024C2×C42—42no—
1025C2×C42C2412yes—
1026C2×C42C2412yes—
1027C2×C42C2412yes—
1028C2×C42C2412yes—
1029C2×C42C2411yescharacteristic
1030C2×C42C2412yes—
1031C2×C42C2412yes—
1032C2×C42C2412yes—
1033C2×C42C2414yes—
1034C2×C42C2414yes—
1035C2×C42C2412yes—
1036C2×C42C2412yes—
1037#95C2412yes—
1038#95C2411yescharacteristic
1039#95C2414yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2411yescharacteristic
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2411yescharacteristic
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2411yescharacteristic
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2412yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090C24—24no—
1091C24—24no—
1092C24—28no—
1093C24—28no—
1094C24—44no—
1095C24—44no—
1096C24—42no—
1097C24—42no—
1098C24—44no—
1099C24—44no—
1100C24—44no—
1101C24—44no—
1102C24—44no—
1103C24—44no—
1104C24—42no—
1105C24—44no—
1106C24—42no—
1107C24C2511yescharacteristic
1108C24C2514yes—
1109C24C2512yes—
1110C24C2514yes—
1111C24C2512yes—
1112C24C2511yescharacteristic
1113C24C2512yes—
1114#41—416no—
1115#41—432no—
1116#41—416no—
1117#41—432no—
1118#41—816no—
1119#41—832no—
1120#41—816no—
1121C2×Q8—24no—
1122C2×Q8—24no—
1123C2×Q8—24no—
1124C2×Q8—22no—
1125C2×Q8—24no—
1126C2×Q8—24no—
1127C2×Q8—41no—
1128C2×Q8—41no—
1129C2×Q8—42no—
1130C2×Q8—44no—
1131C2×Q8—44no—
1132C2×Q8—44no—
1133C2×Q8—42no—
1134C2×Q8—44no—
1135C2×Q8—88no—
1136C2×D4—24no—
1137C2×D4—28no—
1138C2×D4—24no—
1139C2×D4—24no—
1140C2×D4—28no—
1141C2×D4—24no—
1142C2×D4—24no—
1143C2×D4—28no—
1144C2×D4—22no—
1145C2×D4—28no—
1146C2×D4—28no—
1147C2×D4—28no—
1148C2×D4—28no—
1149C2×D4—28no—
1150C2×D4—28no—
1151C2×D4—24no—
1152C2×D4—24no—
1153C2×D4—24no—
1154C2×D4—24no—
1155C2×D4—24no—
1156C2×D4—28no—
1157C2×D4—24no—
1158C2×D4—22no—
1159C2×D4—24no—
1160C2×D4—24no—
1161C2×D4—24no—
1162C2×D4—24no—
1163C2×D4—28no—
1164C2×D4—432no—
1165C2×D4—44no—
1166C2×D4—42no—
1167C2×D4—44no—
1168C2×D4—41no—
1169C2×D4—42no—
1170C2×D4—44no—
1171C2×D4—44no—
1172C2×D4—44no—
1173C2×D4—44no—
1174C2×D4—42no—
1175C2×D4—44no—
1176C2×D4—41no—
1177C2×D4—44no—
1178C2×D4—44no—
1179C2×D4—44no—
1180C2×D4—44no—
1181C2×D4—44no—
1182C2×D4—44no—
1183C2×D4—44no—
1184C2×D4—44no—
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—44no—
1199C2×D4—44no—
1200C2×D4—44no—
1201C2×D4—44no—
1202C2×D4—44no—
1203C2×D4—44no—
1204C2×D4—41no—
1205C2×D4—44no—
1206C2×D4—44no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—42no—
1210C2×D4—44no—
1211C2×D4—44no—
1212C2×D4—44no—
1213C2×D4—44no—
1214C2×D4—44no—
1215C2×D4—44no—
1216C2×D4—44no—
1217C2×D4—44no—
1218C2×D4—42no—
1219C2×D4—42no—
1220C2×D4—44no—
1221C2×D4—42no—
1222C2×D4—44no—
1223C2×D4—44no—
1224C2×D4—464no—
1225C2×D4—432no—
1226C2×D4—416no—
1227C2×D4—88no—
1228C2×D4—832no—
1229C2×D4H(5,𝔽2)14yes—
1230C22×C4—24no—
1231C22×C4—24no—
1232C22×C4—24no—
1233C22×C4—24no—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—28no—
1241C22×C4—22no—
1242C22×C4—24no—
1243C22×C4—28no—
1244C22×C4—28no—
1245C22×C4—28no—
1246C22×C4—44no—
1247C22×C4—44no—
1248C22×C4—44no—
1249C22×C4—42no—
1250C22×C4—41no—
1251C22×C4—41no—
1252C22×C4—42no—
1253C22×C4—42no—
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—42no—
1265C22×C4—44no—
1266C22×C4—44no—
1267C22×C4—44no—
1268C22×C4—44no—
1269C22×C4—42no—
1270C22×C4—41no—
1271C22×C4—44no—
1272C22×C4—44no—
1273C22×C4—44no—
1274C22×C4H(5,𝔽2)18yes—
1275C22×C4C2512yes—
1276C22×C4C2512yes—
1277C22×C4C2511yescharacteristic
1278C22×C4C2512yes—
1279C22×C4C2511yescharacteristic
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2511yescharacteristic
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2514yes—
1286C22×C4C2512yes—
1287C22×C4C2512yes—
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2511yescharacteristic
1291C22×C4C2514yes—
1292C22×C4C2514yes—
1293C22×C4C2514yes—
1294C22×C4C2512yes—
1295C22×C4C2512yes—
1296C22×C4C2511yescharacteristic
1297C4⋊C4—24no—
1298C4⋊C4—24no—
1299C4⋊C4—22no—
1300C4⋊C4—24no—
1301C4⋊C4—24no—
1302C4⋊C4—24no—
1303C4⋊C4—28no—
1304C4⋊C4—28no—
1305C4⋊C4—24no—
1306C4⋊C4—24no—
1307C4⋊C4—44no—
1308C4⋊C4—42no—
1309C4⋊C4—42no—
1310C4⋊C4—42no—
1311C4⋊C4—42no—
1312C4⋊C4—44no—
1313C4⋊C4—44no—
1314C4⋊C4—44no—
1315C4⋊C4—41no—
1316C4⋊C4—42no—
1317C4⋊C4—41no—
1318C4⋊C4—44no—
1319C4⋊C4—44no—
1320C4⋊C4—42no—
1321C4⋊C4—44no—
1322C4⋊C4—44no—
1323C4⋊C4—42no—
1324C4⋊C4—42no—
1325C4⋊C4—44no—
1326C4⋊C4—44no—
1327C4⋊C4—44no—
1328C4⋊C4—42no—
1329C22⋊C4—24no—
1330C22⋊C4—28no—
1331C22⋊C4—28no—
1332C22⋊C4—24no—
1333C22⋊C4—24no—
1334C22⋊C4—24no—
1335C22⋊C4—28no—
1336C22⋊C4—28no—
1337C22⋊C4—28no—
1338C22⋊C4—24no—
1339C22⋊C4—24no—
1340C22⋊C4—28no—
1341C22⋊C4—28no—
1342C22⋊C4—24no—
1343C22⋊C4—41no—
1344C22⋊C4—44no—
1345C22⋊C4—42no—
1346C22⋊C4—42no—
1347C22⋊C4—42no—
1348C22⋊C4—44no—
1349C22⋊C4—44no—
1350C22⋊C4—44no—
1351C22⋊C4—42no—
1352C22⋊C4—44no—
1353C22⋊C4—44no—
1354C22⋊C4—44no—
1355C22⋊C4—44no—
1356C22⋊C4—44no—
1357C22⋊C4—44no—
1358C22⋊C4—44no—
1359C22⋊C4—42no—
1360C22⋊C4—42no—
1361C22⋊C4—42no—
1362C22⋊C4—41no—
1363C22⋊C4—42no—
1364C22⋊C4—42no—
1365C22⋊C4—44no—
1366C22⋊C4—44no—
1367C22⋊C4—44no—
1368C22⋊C4—41no—
1369C22⋊C4—44no—
1370C22⋊C4—44no—
1371C22⋊C4—44no—
1372C22⋊C4—44no—
1373C22⋊C4—44no—
1374C22⋊C4—44no—
1375C22⋊C4—44no—
1376C22⋊C4—44no—
1377C22⋊C4—44no—
1378C22⋊C4—44no—
1379C22⋊C4—44no—
1380C22⋊C4—44no—
1381C22⋊C4—44no—
1382C22⋊C4—42no—
1383C22⋊C4—42no—
1384C22⋊C4—44no—
1385C22⋊C4—42no—
1386C22⋊C4—42no—
1387C22⋊C4—42no—
1388C22⋊C4—42no—
1389C22⋊C4—44no—
1390C22⋊C4—44no—
1391C22⋊C4—44no—
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—44no—
1401C22⋊C4—42no—
1402C22⋊C4H(5,𝔽2)14yescomplemented
1403C42—24no—
1404C42—24no—
1405C42—24no—
1406C42—24no—
1407C42—24no—
1408C42—24no—
1409C42—24no—
1410C42—22no—
1411C42—42no—
1412C42—44no—
1413C42—44no—
1414C42—42no—
1415C23—22no—
1416C23—22no—
1417C23—22no—
1418C23—21no—
1419C23—22no—
1420C23—24no—
1421C23—22no—
1422C23—22no—
1423C23—24no—
1424C23—22no—
1425C23—22no—
1426C23—22no—
1427C23—21no—
1428C23—22no—
1429C23—21no—
1430C23—24no—
1431C23—24no—
1432C23—24no—
1433C23—22no—
1434C23—24no—
1435C23—22no—
1436C23—24no—
1437C23—24no—
1438C23—22no—
1439C23—24no—
1440C23—21no—
1441C23—24no—
1442C23—24no—
1443C23—24no—
1444C23—22no—
1445C23—24no—
1446C23—24no—
1447C23—24no—
1448C23—24no—
1449C23—21no—
1450C23—24no—
1451C23—22no—
1452C23—24no—
1453C23—416no—
1454C23—48no—
1455C23—48no—
1456C23—88no—
1457C23—88no—
1458C23—84no—
1459C23—84no—
1460C23—88no—
1461C23—88no—
1462C23—88no—
1463C23—164no—
1464C23—164no—
1465C23—164no—
1466C23—162no—
1467C23—164no—
1468C23—164no—
1469C23—162no—
1470C23C2×H(5,𝔽2)14yes—
1471C23C2×H(5,𝔽2)12yes—
1472C23C2×H(5,𝔽2)14yes—
1473C23C2611yescharacteristic
1474Q8—44no—
1475Q8—44no—
1476Q8—48no—
1477Q8—44no—
1478Q8—84no—
1479Q8—88no—
1480D4—28no—
1481D4—48no—
1482D4—416no—
1483D4—44no—
1484D4—48no—
1485D4—416no—
1486D4—48no—
1487D4—416no—
1488D4—48no—
1489D4—48no—
1490D4—44no—
1491D4—48no—
1492D4—88no—
1493D4—88no—
1494D4—88no—
1495D4—82no—
1496D4—88no—
1497D4—84no—
1498D4—88no—
1499D4—88no—
1500D4—88no—
1501D4—88no—
1502D4—88no—
1503D4—88no—
1504D4—84no—
1505D4—88no—
1506D4—162no—
1507D4—164no—
1508D4—164no—
1509D4—164no—
1510D4—164no—
1511D4—162no—
1512C2×C4—22no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—216no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—21no—
1524C2×C4—22no—
1525C2×C4—21no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—24no—
1532C2×C4—24no—
1533C2×C4—24no—
1534C2×C4—24no—
1535C2×C4—24no—
1536C2×C4—24no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—24no—
1542C2×C4—24no—
1543C2×C4—24no—
1544C2×C4—21no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—24no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—24no—
1554C2×C4—24no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—24no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—48no—
1570C2×C4—416no—
1571C2×C4—48no—
1572C2×C4—44no—
1573C2×C4—44no—
1574C2×C4—88no—
1575C2×C4—88no—
1576C2×C4—88no—
1577C2×C4—84no—
1578C2×C4—82no—
1579C2×C4—84no—
1580C2×C4—82no—
1581C2×C4—88no—
1582C2×C4—84no—
1583C2×C4—88no—
1584C2×C4—164no—
1585C2×C4C2×H(5,𝔽2)14yes—
1586C2×C4C2×H(5,𝔽2)14yes—
1587C2×C4C2×H(5,𝔽2)12yes—
1588C2×C4C2×H(5,𝔽2)14yes—
1589C22—24no—
1590C22—24no—
1591C22—24no—
1592C22—24no—
1593C22—22no—
1594C22—24no—
1595C22—24no—
1596C22—24no—
1597C22—41no—
1598C22—42no—
1599C22—44no—
1600C22—42no—
1601C22—42no—
1602C22—44no—
1603C22—42no—
1604C22—42no—
1605C22—41no—
1606C22—44no—
1607C22—41no—
1608C22—42no—
1609C22—44no—
1610C22—44no—
1611C22—44no—
1612C22—44no—
1613C22—44no—
1614C22—44no—
1615C22—42no—
1616C22—44no—
1617C22—44no—
1618C22—44no—
1619C22—44no—
1620C22—44no—
1621C22—42no—
1622C22—44no—
1623C22—41no—
1624C22—44no—
1625C22—42no—
1626C22—44no—
1627C22—41no—
1628C22—44no—
1629C22—42no—
1630C22—168no—
1631C22—1616no—
1632C22—168no—
1633C22C22×H(5,𝔽2)11yescharacteristic
1634C22C22×H(5,𝔽2)12yes—
1635C22C22×H(5,𝔽2)11yescharacteristic
1636C22H(7,𝔽2)12yes—
1637C222−1+611yescharacteristic
1638C4—24no—
1639C4—24no—
1640C4—42no—
1641C4—41no—
1642C4—42no—
1643C4—42no—
1644C4—42no—
1645C4—42no—
1646C4—42no—
1647C4—42no—
1648C4—42no—
1649C4—44no—
1650C4—44no—
1651C4—44no—
1652C4—42no—
1653C4—42no—
1654C4—41no—
1655C4—41no—
1656C4—42no—
1657C4—41no—
1658C4—44no—
1659C4#353214yes—
1660C2—44no—
1661C2—42no—
1662C2—44no—
1663C2—84no—
1664C2—82no—
1665C2—81no—
1666C2—84no—
1667C2C2×#353211yescharacteristic
1668C2#6287812yes—
1669C2#6291212yes—
1670C2#6291411yescharacteristic
1671C2#6304111yescharacteristic
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. #59095C2semidirect
2. #57964C2semidirect
3. #57272C2semidirect
4. #57209C2semidirect
5. #57149C2semidirect
6. #56660C2semidirect
7. #55430C2semidirect
8. #53000C2semidirect
9. #52990C2semidirect
10. #52398C2semidirect
11. #52203C2semidirect
12. #47934C2semidirect
13. #47063C2semidirect
14. #45487C2semidirect
15. #45244C2semidirect
16. #44876C2semidirect
17. #42560C2semidirect
18. #42519C2semidirect
19. #42483C2semidirect
20. #40586C2semidirect
21. #39864C2semidirect
22. #38918C2semidirect
23. #38054C2semidirect
24. #37780C2semidirect
25. #37677C2semidirect
26. #37618C2semidirect
27. #37346C2semidirect
28. #35680C2semidirect
29. #35513C2semidirect
31. C2×#560C22semidirect
32. C2×#550C22semidirect
33. C2×#548C22semidirect
35. C2×#546C22semidirect
37. C2×#537C22semidirect
39. C2×#532C22semidirect
40. C2×#532C22semidirect
41. C22×#124C22semidirect
42. #2856C22semidirect
43. #2855C22semidirect
44. #2855C22semidirect
45. #2840C22semidirect
46. #2832C22semidirect
47. #2828C22semidirect
48. #2825C22semidirect
49. #2824C22semidirect
50. #2824C22semidirect
51. #2824C22semidirect
52. #2815C22semidirect
53. #2815C22semidirect
54. #2815C22semidirect
55. #2815C22semidirect
56. #2813C22semidirect
57. #2812C22semidirect
58. #2797C22semidirect
59. #2797C22semidirect
60. #2786C22semidirect
61. #2786C22semidirect
62. #2784C22semidirect
63. #2784C22semidirect
64. #2779C22semidirect
65. #2764C22semidirect
66. #2763C22semidirect
67. #2762C22semidirect
68. #2761C22semidirect
69. #2761C22semidirect
70. #2760C22semidirect
71. #2757C22semidirect
72. #2751C22semidirect
73. #2750C22semidirect
74. #2749C22semidirect
75. #2743C22semidirect
76. #2737C22semidirect
77. #2737C22semidirect
78. #2736C22semidirect
79. #2723C22semidirect
80. #2717C22semidirect
81. #2714C22semidirect
82. #2712C22semidirect
83. #2708C22semidirect
84. #2706C22semidirect
85. #2703C22semidirect
86. #2703C22semidirect
87. #2700C22semidirect
88. #2699C22semidirect
89. #2699C22semidirect
90. #2696C22semidirect
91. #2696C22semidirect
92. #2695C22semidirect
93. #2693C22semidirect
94. #2688C22semidirect
95. #2688C22semidirect
96. #2688C22semidirect
97. #2688C22semidirect
98. #2686C22semidirect
99. #2686C22semidirect
100. #2686C22semidirect
101. #2686C22semidirect
102. #2684C22semidirect
103. #2683C22semidirect
104. #2678C22semidirect
105. #2678C22semidirect
106. #2678C22semidirect
107. #2678C22semidirect
108. #2676C22semidirect
109. #2676C22semidirect
110. #2676C22semidirect
111. #2676C22semidirect
112. #2676C22semidirect
113. #2676C22semidirect
114. #2675C22semidirect
115. #2675C22semidirect
116. #2671C22semidirect
117. #2670C22semidirect
118. #2670C22semidirect
119. #2670C22semidirect
120. #2669C22semidirect
121. #2669C22semidirect
122. #2668C22semidirect
123. #2668C22semidirect
124. #2657C22semidirect
125. #2657C22semidirect
126. #2648C22semidirect
127. #2644C22semidirect
128. #2643C22semidirect
129. #2640C22semidirect
130. #2640C22semidirect
131. #2638C22semidirect
132. #2631C22semidirect
133. #2631C22semidirect
134. #2630C22semidirect
135. #2630C22semidirect
136. #2622C22semidirect
137. #2620C22semidirect
138. #2617C22semidirect
140. #2615C22semidirect
141. #2615C22semidirect
142. #2615C22semidirect
144. #2600C22semidirect
145. #2592C22semidirect
146. #2592C22semidirect
147. #2564C22semidirect
148. #2561C22semidirect
149. #2555C22semidirect
150. #2548C22semidirect
151. #2547C22semidirect
152. #2547C22semidirect
153. #2544C22semidirect
154. #2544C22semidirect
155. #2543C22semidirect
156. #2541C22semidirect
157. #2541C22semidirect
158. #2541C22semidirect
159. #2535C22semidirect
160. #2535C22semidirect
161. #2512C22semidirect
162. #2511C22semidirect
163. #2492C22semidirect
164. #2491C22semidirect
165. #2483C22semidirect
166. #2483C22semidirect
167. #2480C22semidirect
168. #2467C22semidirect
169. #2463C22semidirect
170. #2456C22semidirect
171. #2456C22semidirect
172. #2452C22semidirect
173. #2450C22semidirect
174. #2450C22semidirect
175. #2448C22semidirect
176. #2447C22semidirect
177. #2446C22semidirect
178. #2445C22semidirect
179. #2445C22semidirect
180. #2440C22semidirect
181. #2437C22semidirect
182. #2436C22semidirect
184. #2435C22semidirect
185. #2434C22semidirect
188. #2433C22semidirect
189. #2433C22semidirect
191. #2432C22semidirect
194. #2431C22semidirect
195. #2431C22semidirect
196. #2431C22semidirect
198. #2430C22semidirect
199. #2430C22semidirect
200. #2428C22semidirect
201. #2428C22semidirect
202. #2428C22semidirect
203. #2427C22semidirect
204. #2427C22semidirect
205. #2426C22semidirect
206. #2424C22semidirect
207. #2424C22semidirect
208. #2424C22semidirect
209. #2424C22semidirect
210. #2424C22semidirect
211. #2422C22semidirect
212. #2416C22semidirect
213. #2412C22semidirect
215. #2410C22semidirect
216. #2410C22semidirect
217. #2410C22semidirect
218. #2410C22semidirect
219. #2410C22semidirect
220. #2410C22semidirect
221. #2410C22semidirect
222. #2409C22semidirect
224. #2408C22semidirect
225. #2408C22semidirect
227. #2407C22semidirect
228. #2407C22semidirect
229. #2407C22semidirect
231. #2404C22semidirect
232. #2404C22semidirect
233. #2404C22semidirect
235. #2401C22semidirect
236. #2398C22semidirect
237. #2396C22semidirect
240. #2366C22semidirect
241. #2361C22semidirect
242. #2360C22semidirect
244. #2339C22semidirect
246. D4×C22⋊C4C22semidirect
247. #2326C22semidirect
248. #2325C22semidirect
249. #2324C22semidirect
250. #2319C22semidirect
251. #2315C22semidirect
252. #2311C22semidirect
253. C4×#123C22semidirect
254. C4×#123C22semidirect
255. #2297C22semidirect
257. #2290C22semidirect
258. #2283C22semidirect
1402. C22⋊C4H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
#590952
#579642
#572722
#572092
#571492
#566602
#554302
#530002
#529902
#523982
#522032
#479342
#470632
#454872
#452442
#448762
#425602
#425192
#424832
#405862
#398642
#389182
#380542
#377802
#376772
#376182
#373462
#356802
#355132