Finite Group Databasebeta

← #8552268

Subgroups — #8552268

Order 512.

6362 conjugacy classes of subgroups.

The subgroup lattice has 1710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59104C212yesmaximal, complemented
2#57971C212yesmaximal, complemented
3#55437C214yesmaximal, complemented
4#55347C214yesmaximal, complemented
5#55312C214yesmaximal, complemented
6#55040C214yesmaximal, complemented
7#54816C214yesmaximal, complemented
8#53000C212yesmaximal, complemented
9#52986C211yesmaximal, characteristic, complemented
10#52405C212yesmaximal, complemented
11#52203C211yesmaximal, characteristic, complemented
12#47853C214yesmaximal, complemented
13#46350C212yesmaximal, complemented
14#45487C211yesmaximal, characteristic, complemented
15#44957C212yesmaximal, complemented
16#44870C211yesmaximal, characteristic, complemented
17#42976C212yesmaximal, complemented
18#42895C212yesmaximal, complemented
19#42890C211yesmaximal, characteristic, complemented
20#41234C212yesmaximal, complemented
21#39336C212yesmaximal, complemented
22#39135C211yesmaximal, characteristic, complemented
23#38061C212yesmaximal, complemented
24#37786C212yesmaximal, complemented
25#37677C212yesmaximal, complemented
26#37614C212yesmaximal, complemented
27#37331C212yesmaximal, complemented
28#36082C211yesmaximal, characteristic, complemented
29#35527C212yesmaximal, complemented
30C22×H(5,𝔽2)C2211yescharacteristic, complemented
31C2×#560C2212yescomplemented
32C2×#559C2211yescharacteristic, complemented
33C2×#548C2212yescomplemented
34C2×#548C2211yescharacteristic, complemented
35C2×D42C2212yescomplemented
36C2×#535C2212yes—
37C2×#535C2212yescomplemented
38C2×#534C2214yescomplemented
39C22×#127C2212yescomplemented
40C2×#529C2212yescomplemented
41C22×#124C2211yescharacteristic, complemented
42#2856C2212yescomplemented
43#2854C2212yescomplemented
44#2854C2211yescharacteristic, complemented
45#2829C2214yescomplemented
46#2828C2214yescomplemented
47#2828C2214yescomplemented
48#2828C2214yescomplemented
49#2825C2214yescomplemented
50#2819C2212yescomplemented
51#2818C2214yescomplemented
52#2818C2214yescomplemented
53#2815C2212yescomplemented
54#2813C2214yescomplemented
55#2812C2214yescomplemented
56#2812C2212yescomplemented
57#2812C2212yescomplemented
58#2803C2214yescomplemented
59#2797C2214yescomplemented
60#2778C2214yescomplemented
61#2764C2211yescharacteristic, complemented
62#2763C2211yescharacteristic, complemented
63#2762C2212yescomplemented
64#2761C2212yescomplemented
65#2760C2211yescharacteristic, complemented
66#2752C2214yescomplemented
67#2749C2212yescomplemented
68#2749C2214yescomplemented
69#2743C2212yescomplemented
70#2737C2212yescomplemented
71#2733C2214yescomplemented
72#2730C2214yescomplemented
73#2715C2214yescomplemented
74#2714C2214yescomplemented
75#2714C2214yescomplemented
76#2714C2214yescomplemented
77#2710C2214yescomplemented
78#2709C2214yescomplemented
79#2708C2214yescomplemented
80#2706C2214yescomplemented
81#2706C2212yescomplemented
82#2705C2214yescomplemented
83#2703C2214yescomplemented
84#2703C2214yescomplemented
85#2703C2214yescomplemented
86#2697C2214yescomplemented
87#2697C2214yescomplemented
88#2697C2214yescomplemented
89#2696C2214yescomplemented
90#2693C2211yescharacteristic, complemented
91#2685C2214yescomplemented
92#2685C2214yescomplemented
93#2685C2214yescomplemented
94#2685C2214yescomplemented
95#2684C2214yescomplemented
96#2682C2214yescomplemented
97#2682C2214yescomplemented
98#2679C2214yescomplemented
99#2679C2212yescomplemented
100#2678C2214yescomplemented
101#2678C2214yescomplemented
102#2678C2214yescomplemented
103#2678C2214yescomplemented
104#2678C2214yescomplemented
105#2676C2214yescomplemented
106#2676C2214yescomplemented
107#2675C2212yescomplemented
108#2673C2214yescomplemented
109#2673C2214yescomplemented
110#2673C2214yescomplemented
111#2671C2214yescomplemented
112#2670C2212yescomplemented
113#2670C2214yescomplemented
114#2670C2214yescomplemented
115#2670C2212yescomplemented
116#2670C2212yescomplemented
117#2670C2214yescomplemented
118#2669C2212yescomplemented
119#2669C2214yescomplemented
120#2669C2214yescomplemented
121#2669C2214yescomplemented
122#2668C2214yescomplemented
123#2668C2214yescomplemented
124#2662C2214yescomplemented
125#2661C2214yescomplemented
126#2657C2212yescomplemented
127#2657C2211yescharacteristic, complemented
128#2648C2214yescomplemented
129#2648C2214yescomplemented
130#2644C2212yescomplemented
131#2641C2212yescomplemented
132#2641C2212yescomplemented
133#2631C2212yescomplemented
134#2631C2212yescomplemented
135#2620C2212yescomplemented
136#2619C2214yescomplemented
137#2619C2214yescomplemented
138#2617C2212yescomplemented
139#2616C2212yescomplemented
140#2616C2211yescharacteristic, complemented
141#2613C2214yescomplemented
142#2613C2214yescomplemented
143#2613C2214yescomplemented
144#2592C2211yescharacteristic, complemented
145#2578C2214yescomplemented
146#2560C2214yescomplemented
147#2559C2214yescomplemented
148#2555C2214yescomplemented
149#2555C2212yescomplemented
150#2554C2214yescomplemented
151#2553C2214yescomplemented
152#2548C2212yescomplemented
153#2548C2212yescomplemented
154#2548C2212yescomplemented
155#2548C2212yescomplemented
156#2544C2212yescomplemented
157#2541C2212yescomplemented
158#2541C2211yescharacteristic, complemented
159#2541C2212yescomplemented
160#2541C2212yescomplemented
161#2539C2214yescomplemented
162#2539C2212yescomplemented
163#2535C2212yescomplemented
164#2534C2212yescomplemented
165#2518C2214yescomplemented
166#2518C2214yescomplemented
167#2512C2212yescomplemented
168#2512C2212yescomplemented
169#2490C2212yescomplemented
170#2490C2212yescomplemented
171#2477C2214yescomplemented
172#2474C2214yescomplemented
173#2467C2214yescomplemented
174#2464C2214yescomplemented
175#2464C2214yescomplemented
176#2459C2214yescomplemented
177#2453C2212yescomplemented
178#2448C2212yescomplemented
179#2448C2212yescomplemented
180#2445C2212yescomplemented
181#2445C2212yescomplemented
182#2445C2214yescomplemented
183#2445C2212yescomplemented
184#2441C2212yescomplemented
185#2436C2212yescomplemented
186#2435C2211yescharacteristic, complemented
187#2435C2214yescomplemented
188#2435C2212yescomplemented
189#2435C2212yescomplemented
190#2435C2212yescomplemented
191#2433C2212yes—
192#2433C2214yescomplemented
193#2433C2214yescomplemented
194#2433C2212yescomplemented
195#2433C2212yescomplemented
196#2433C2212yescomplemented
197#2433C2212yescomplemented
198#2433C2214yescomplemented
199#2433C2211yescharacteristic, complemented
200#2433C2212yescomplemented
201#2431C2212yes—
202#2431C2214yescomplemented
203#2431C2214yescomplemented
204#2431C2212yescomplemented
205#2431C2212yescomplemented
206#2431C2212yescomplemented
207#2428C2212yescomplemented
208#2428C2212yescomplemented
209#2428C2212yescomplemented
210#2427C2212yescomplemented
211#2426C2212yescomplemented
212#2424C2214yescomplemented
213#2424C2214yescomplemented
214#2424C2214yescomplemented
215#2422C2212yescomplemented
216#2418C2214yescomplemented
217#2414C2212yescomplemented
218#2411C2214yescomplemented
219#2410C2214yescomplemented
220#2410C2214yescomplemented
221#2410C2214yescomplemented
222#2408C2212yes—
223#2408C2214yescomplemented
224#2408C2214yescomplemented
225#2408C2214yescomplemented
226#2408C2211yescharacteristic, complemented
227#2408C2212yescomplemented
228#2408C2211yescharacteristic, complemented
229#2403C2214yescomplemented
230#2403C2214yescomplemented
231#2403C2214yescomplemented
232#2403C2212yescomplemented
233#2403C2214yescomplemented
234#2403C2214yescomplemented
235#2401C2212yescomplemented
236#2398C2211yescharacteristic, complemented
237#2396C2212yescomplemented
238#2388C2211yescharacteristic
239#2388C2212yescomplemented
240#2367C2212yescomplemented
241#2363C2214yescomplemented
242#2363C2212yescomplemented
243#2362C2212yescomplemented
244#2341C2211yescharacteristic, complemented
245#2341C2212yescomplemented
246Q8×C22⋊C4C2211yescharacteristic, complemented
247D4×C22⋊C4C2212yescomplemented
248#2326C2212yescomplemented
249#2324C2212yescomplemented
250#2321C2212yescomplemented
251#2320C2211yescharacteristic, complemented
252#2309C2212yescomplemented
253C4×#123C2212yescomplemented
254C4×#123C2211yescharacteristic, complemented
255#2297C2212yescomplemented
256#2297C2212yescomplemented
257#2290C2212yescomplemented
258#2283C2212yescomplemented
259C2×H(5,𝔽2)—48no—
260C2×H(5,𝔽2)—44no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2312yes—
265C23×Q8C2311yescharacteristic
266C23×D4C2312yes—
267C23×D4C2312yes—
268C23×D4C2312yes—
269C23×D4C2314yes—
270C23×D4C2311yescharacteristic
271C23×D4C2311yescharacteristic
272C23×D4C2314yes—
273C23×D4C2314yes—
274C23×D4C2314yes—
275#560—48no—
276#559—44no—
277#548—48no—
278#548—44no—
279D42—48no—
280#535—48no—
281#535—48no—
282#534—416no—
283C2×#127—48no—
284C2×#127C2314yes—
285C2×#127C2312yes—
286C2×#127C2314yes—
287C2×#127C2312yes—
288C2×#127C2312yes—
289C2×#127C2312yes—
290C2×#127C2311yescharacteristic
291C2×#127C2312yes—
292C2×#127C2314yes—
293C2×#127C2312yes—
294C2×#127C2312yes—
295C2×#127C2312yes—
296#529—48no—
297C2×#126C2314yes—
298C2×#126C2314yes—
299C2×#126C2314yes—
300C2×#125C2312yes—
301C2×#124—44no—
302C2×#124C2312yes—
303C2×#124C2312yes—
304C2×#124C2312yes—
305C2×#124C2312yes—
306C2×#124C2311yescharacteristic
307C2×#124C2312yes—
308C2×#124C2312yes—
309C2×#124C2312yes—
310C2×#124C2314yes—
311C2×#124C2314yes—
312C2×#124C2314yes—
313C2×#124C2314yes—
314C2×#123C2312yes—
315C2×#123C2311yescharacteristic
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2312yes—
323C2×#123C2314yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2311yescharacteristic
327C2×C22⋊Q8C2312yes—
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2314yes—
331C2×#121C2311yescharacteristic
332C2×#121C2312yes—
333C2×#121C2314yes—
334C2×#121C2312yes—
335C2×#121C2312yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2312yes—
340C2×#121C2314yes—
341C2×#121C2314yes—
342C2×#121C2314yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2312yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#120C2312yes—
352C2×#120C2314yes—
353C2×#120C2314yes—
354C2×#120C2314yes—
355C2×#120C2314yes—
356C2×#120C2314yes—
357C2×#120C2314yes—
358C2×#120C2314yes—
359C2×#120C2314yes—
360C2×#120C2312yes—
361C2×#120C2314yes—
362C2×#120C2314yes—
363C2×#120C2314yes—
364C2×#120C2314yes—
365C2×#120C2314yes—
366C2×#120C2314yes—
367C2×#120C2314yes—
368C2×#120C2312yes—
369C2×#120C2312yes—
370C2×#120C2314yes—
371C2×#120C2314yes—
372C2×#120C2314yes—
373C2×#120C2314yes—
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2314yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2314yes—
390C22×C22⋊C4C2312yes—
391C22×C22⋊C4C2314yes—
392C22×C22⋊C4C2312yes—
393C22×C42C2312yes—
394C22×C42C2311yescharacteristic
395#401C2312yes—
396#400C2312yes—
397#400C2312yes—
398#400C2314yes—
399#400C2312yes—
400#400C2312yes—
401#400C2312yes—
402#399C2314yes—
403#399C2312yes—
404#399C2314yes—
405#399C2314yes—
406#398C2314yes—
407#398C2312yes—
408#398C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2311yescharacteristic
422#397C2314yes—
423#397C2311yescharacteristic
424#397C2312yes—
425#397C2312yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2314yes—
435#396C2314yes—
436#395C2311yescharacteristic
437#395C2312yes—
438#395C2312yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2312yes—
455#394C2314yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2312yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2312yes—
483#394C2311yescharacteristic
484#394C2312yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#393C2314yes—
489#393C2311yescharacteristic
490#393C2312yes—
491#393C2311yescharacteristic
492#393C2314yes—
493#393C2311yescharacteristic
494#393C2312yes—
495#392C2312yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
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#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#392C2312yes—
524#392C2314yes—
525#392C2314yes—
526#392C2312yes—
527#392C2311yescharacteristic
528#392C2312yes—
529#392C2312yes—
530#392C2314yes—
531#392C2314yes—
532#392C2314yes—
533#392C2314yes—
534#392C2314yes—
535#392C2314yes—
536#392C2314yes—
537#392C2314yes—
538#392C2314yes—
539#392C2312yes—
540#391C2314yes—
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#391C2312yes—
545#391C2312yes—
546#390C2314yes—
547#390C2314yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2314yes—
552#390C2312yes—
553#390C2314yes—
554#390C2314yes—
555#390C2314yes—
556#390C2314yes—
557#390C2312yes—
558#390C2314yes—
559#390C2312yes—
560#390C2312yes—
561#390C2312yes—
562#390C2312yes—
563#390C2312yes—
564#390C2312yes—
565#390C2314yes—
566#390C2314yes—
567#390C2314yes—
568#390C2314yes—
569#390C2312yes—
570#390C2314yes—
571#390C2314yes—
572#390C2314yes—
573#390C2314yes—
574#390C2312yes—
575#390C2312yes—
576#390C2314yes—
577#390C2314yes—
578#390C2312yes—
579#390C2314yes—
580#390C2314yes—
581#390C2312yes—
582#390C2312yes—
583#390C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2314yes—
589#389C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
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#388C2312yes—
610#388C2314yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2314yes—
615#388C2312yes—
616#388C2314yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2312yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2311yescharacteristic
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2312yes—
648#386C2312yes—
649#386C2312yes—
650#386C2312yes—
651#386C2314yes—
652#386C2314yes—
653#386C2312yes—
654#386C2314yes—
655#386C2314yes—
656#386C2312yes—
657#386C2312yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#385C2311yescharacteristic
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2312yes—
667#385C2314yes—
668#385C2312yes—
669#385C2312yes—
670#384C2312yes—
671#383C2312yes—
672#383C2312yes—
673#383C2312yes—
674#382C2312yes—
675#382C2312yes—
676#382C2312yes—
677#381C2312yes—
678#381C2312yes—
679#381C2312yes—
680#381C2311yescharacteristic
681#380C2314yes—
682#380C2312yes—
683#380C2311yescharacteristic
684#380C2312yes—
685#380C2312yes—
686#380C2311yescharacteristic
687#380C2312yes—
688#380C2312yes—
689#380C2314yes—
690#379C2314yes—
691#379C2314yes—
692#379C2312yes—
693#379C2314yes—
694#379C2314yes—
695#379C2314yes—
696#379C2314yes—
697#379C2314yes—
698#379C2314yes—
699#379C2314yes—
700#379C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2311yescharacteristic
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723#376C2311yescharacteristic
724#376C2312yes—
725C25C2412yes—
726C25C2414yes—
727C25C2414yes—
728C25C2412yes—
729H(5,𝔽2)—464no—
730C2×#41—28no—
731C2×#41—24no—
732C2×#41—28no—
733C2×#41—28no—
734C2×#41—42no—
735C2×#41—44no—
736C2×#41—44no—
737C2×#41—48no—
738C2×#41—44no—
739C22×Q8—24no—
740C22×Q8—44no—
741C22×Q8C2411yescharacteristic
742C22×Q8C2411yescharacteristic
743C22×Q8C2411yescharacteristic
744C22×Q8C2412yes—
745C22×Q8C2411yescharacteristic
746C22×D4—28no—
747C22×D4—28no—
748C22×D4—44no—
749C22×D4—44no—
750C22×D4—44no—
751C22×D4—48no—
752C22×D4—42no—
753C22×D4—48no—
754C22×D4—44no—
755C22×D4—42no—
756C22×D4—48no—
757C22×D4—44no—
758C22×D4—44no—
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×D4C2412yes—
772C22×D4C2411yescharacteristic
773C22×D4C2412yes—
774C22×D4C2412yes—
775C22×D4C2411yescharacteristic
776C22×D4C2414yes—
777C22×D4C2412yes—
778C22×D4C2414yes—
779C22×D4C2414yes—
780C22×D4C2412yes—
781C22×D4C2411yescharacteristic
782C22×D4C2414yes—
783C22×D4C2414yes—
784C22×D4C2414yes—
785C22×D4C2414yes—
786C22×D4C2414yes—
787C22×D4C2412yes—
788C22×D4C2414yes—
789C22×D4C2412yes—
790C22×D4C2414yes—
791C22×D4C2414yes—
792C22×D4C2414yes—
793C22×D4C2414yes—
794C22×D4C2414yes—
795C22×D4C2414yes—
796C22×D4C2414yes—
797C22×D4C2412yes—
798C22×D4C2412yes—
799C22×D4C2414yes—
800C22×D4C2414yes—
801C22×D4C2414yes—
802C22×D4C2414yes—
803C22×D4C2414yes—
804C22×D4C2414yes—
805C22×D4C2414yes—
806C22×D4C2412yes—
807C23×C4C2411yescharacteristic
808C23×C4C2411yescharacteristic
809C23×C4C2412yes—
810C23×C4C2414yes—
811C23×C4C2412yes—
812C23×C4C2412yes—
813C23×C4C2411yescharacteristic
814C23×C4C2414yes—
815C23×C4C2412yes—
816C23×C4C2412yes—
817C23×C4C2411yescharacteristic
818C23×C4C2414yes—
819C23×C4C2414yes—
820#127—48no—
821#127—44no—
822#127—44no—
823#127—44no—
824#127—44no—
825#127—48no—
826#127—44no—
827#127—44no—
828#127—44no—
829#127—42no—
830#127—48no—
831#127—44no—
832#126—48no—
833#126—48no—
834#126—84no—
835#125—44no—
836#124—28no—
837#124—28no—
838#124—44no—
839#124—44no—
840#124—44no—
841#124—44no—
842#124—44no—
843#124—42no—
844#124—48no—
845#124—48no—
846#124—48no—
847#124—84no—
848#123—28no—
849#123—24no—
850#123—48no—
851#123—48no—
852#123—48no—
853#123—48no—
854#123—48no—
855#123—48no—
856#123—82no—
857#123—84no—
858C22⋊Q8—28no—
859C22⋊Q8—48no—
860C22⋊Q8—42no—
861C22⋊Q8—44no—
862#121—28no—
863#121—28no—
864#121—216no—
865#121—48no—
866#121—48no—
867#121—48no—
868#121—48no—
869#121—48no—
870#121—48no—
871#121—48no—
872#121—44no—
873#121—44no—
874#121—44no—
875#121—42no—
876#121—44no—
877#121—44no—
878#121—48no—
879#121—48no—
880#121—84no—
881#121—84no—
882#121—84no—
883#121—84no—
884#121—84no—
885#120—28no—
886#120—48no—
887#120—48no—
888#120—48no—
889#120—48no—
890#120—48no—
891#120—48no—
892#120—48no—
893#120—48no—
894#120—48no—
895#120—48no—
896#120—44no—
897#120—84no—
898#120—84no—
899#120—82no—
900#120—84no—
901#120—84no—
902#120—84no—
903#120—84no—
904#120—84no—
905#120—82no—
906#120—84no—
907#120—84no—
908C4×Q8—24no—
909C4×Q8—42no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×D4—28no—
913C4×D4—44no—
914C4×D4—44no—
915C4×D4—44no—
916C4×D4—44no—
917C4×D4—44no—
918C4×D4—42no—
919C4×D4—48no—
920C4×D4—48no—
921#117—44no—
922#117—48no—
923#117—44no—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2411yescharacteristic
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2411yescharacteristic
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C22⋊C4—44no—
956C2×C22⋊C4—44no—
957C2×C22⋊C4—48no—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2411yescharacteristic
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2411yescharacteristic
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2412yes—
991C2×C22⋊C4C2412yes—
992C2×C22⋊C4C2412yes—
993C2×C22⋊C4C2411yescharacteristic
994C2×C22⋊C4C2412yes—
995C2×C22⋊C4C2412yes—
996C2×C22⋊C4C2414yes—
997C2×C22⋊C4C2412yes—
998C2×C22⋊C4C2414yes—
999C2×C22⋊C4C2412yes—
1000C2×C22⋊C4C2414yes—
1001C2×C22⋊C4C2414yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C42—28no—
1038C2×C42—42no—
1039C2×C42C2412yes—
1040C2×C42C2412yes—
1041C2×C42C2412yes—
1042C2×C42C2412yes—
1043C2×C42C2412yes—
1044C2×C42C2411yescharacteristic
1045C2×C42C2412yes—
1046C2×C42C2412yes—
1047C2×C42C2412yes—
1048C2×C42C2414yes—
1049C2×C42C2414yes—
1050C2×C42C2414yes—
1051C2×C42C2412yes—
1052C2×C42C2414yes—
1053C2×C42C2412yes—
1054#95C2411yescharacteristic
1055#95C2412yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2411yescharacteristic
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2414yes—
1064#95C2411yescharacteristic
1065#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2414yes—
1069#95C2411yescharacteristic
1070#95C2412yes—
1071#95C2414yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2412yes—
1076#95C2412yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099C24—28no—
1100C24—28no—
1101C24—24no—
1102C24—44no—
1103C24—44no—
1104C24—44no—
1105C24—42no—
1106C24—44no—
1107C24—44no—
1108C24—42no—
1109C24—44no—
1110C24—44no—
1111C24—44no—
1112C24—44no—
1113C24—44no—
1114C24—42no—
1115C24—44no—
1116C24—44no—
1117C24—44no—
1118C24—44no—
1119C24—44no—
1120C24—42no—
1121C24—44no—
1122C24—42no—
1123C24C2514yes—
1124C24C2511yescharacteristic
1125C24C2514yes—
1126C24C2512yes—
1127C24C2514yes—
1128C24C2512yes—
1129C24C2511yescharacteristic
1130#41—416no—
1131#41—432no—
1132#41—416no—
1133#41—432no—
1134C2×Q8—24no—
1135C2×Q8—24no—
1136C2×Q8—22no—
1137C2×Q8—24no—
1138C2×Q8—24no—
1139C2×Q8—41no—
1140C2×Q8—41no—
1141C2×Q8—44no—
1142C2×Q8—42no—
1143C2×Q8—88no—
1144C2×Q8H(5,𝔽2)14yes—
1145C2×D4—24no—
1146C2×D4—24no—
1147C2×D4—24no—
1148C2×D4—28no—
1149C2×D4—24no—
1150C2×D4—28no—
1151C2×D4—24no—
1152C2×D4—28no—
1153C2×D4—28no—
1154C2×D4—22no—
1155C2×D4—28no—
1156C2×D4—24no—
1157C2×D4—24no—
1158C2×D4—24no—
1159C2×D4—24no—
1160C2×D4—28no—
1161C2×D4—24no—
1162C2×D4—24no—
1163C2×D4—22no—
1164C2×D4—24no—
1165C2×D4—24no—
1166C2×D4—24no—
1167C2×D4—28no—
1168C2×D4—24no—
1169C2×D4—24no—
1170C2×D4—24no—
1171C2×D4—28no—
1172C2×D4—28no—
1173C2×D4—28no—
1174C2×D4—44no—
1175C2×D4—44no—
1176C2×D4—44no—
1177C2×D4—42no—
1178C2×D4—44no—
1179C2×D4—44no—
1180C2×D4—41no—
1181C2×D4—42no—
1182C2×D4—42no—
1183C2×D4—432no—
1184C2×D4—42no—
1185C2×D4—41no—
1186C2×D4—44no—
1187C2×D4—42no—
1188C2×D4—44no—
1189C2×D4—44no—
1190C2×D4—44no—
1191C2×D4—44no—
1192C2×D4—44no—
1193C2×D4—44no—
1194C2×D4—41no—
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—44no—
1205C2×D4—44no—
1206C2×D4—44no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—44no—
1210C2×D4—44no—
1211C2×D4—44no—
1212C2×D4—44no—
1213C2×D4—44no—
1214C2×D4—44no—
1215C2×D4—44no—
1216C2×D4—44no—
1217C2×D4—42no—
1218C2×D4—44no—
1219C2×D4—44no—
1220C2×D4—44no—
1221C2×D4—44no—
1222C2×D4—44no—
1223C2×D4—44no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4—44no—
1228C2×D4—44no—
1229C2×D4—44no—
1230C2×D4—44no—
1231C2×D4—44no—
1232C2×D4—44no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—44no—
1236C2×D4—44no—
1237C2×D4—44no—
1238C2×D4—42no—
1239C2×D4—44no—
1240C2×D4—44no—
1241C2×D4—44no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—44no—
1248C2×D4—42no—
1249C2×D4—44no—
1250C2×D4—42no—
1251C2×D4—464no—
1252C2×D4—432no—
1253C2×D4—416no—
1254C2×D4—816no—
1255C2×D4—88no—
1256C2×D4—832no—
1257C2×D4—832no—
1258C2×D4—832no—
1259C22×C4—24no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—28no—
1267C22×C4—24no—
1268C22×C4—22no—
1269C22×C4—28no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—24no—
1273C22×C4—28no—
1274C22×C4—44no—
1275C22×C4—44no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—42no—
1279C22×C4—41no—
1280C22×C4—41no—
1281C22×C4—44no—
1282C22×C4—44no—
1283C22×C4—44no—
1284C22×C4—44no—
1285C22×C4—42no—
1286C22×C4—44no—
1287C22×C4—44no—
1288C22×C4—41no—
1289C22×C4—44no—
1290C22×C4—44no—
1291C22×C4—44no—
1292C22×C4H(5,𝔽2)18yes—
1293C22×C4C2512yes—
1294C22×C4C2512yes—
1295C22×C4C2511yescharacteristic
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2511yescharacteristic
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2511yescharacteristic
1302C22×C4C2514yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2514yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2512yes—
1308C22×C4C2512yes—
1309C22×C4C2512yes—
1310C22×C4C2514yes—
1311C22×C4C2512yes—
1312C22×C4C2512yes—
1313C22×C4C2512yes—
1314C22×C4C2511yescharacteristic
1315C4⋊C4—24no—
1316C4⋊C4—28no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—28no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—42no—
1327C4⋊C4—42no—
1328C4⋊C4—44no—
1329C4⋊C4—41no—
1330C4⋊C4—42no—
1331C4⋊C4—41no—
1332C4⋊C4—44no—
1333C4⋊C4—44no—
1334C4⋊C4—42no—
1335C4⋊C4—44no—
1336C4⋊C4—44no—
1337C4⋊C4—44no—
1338C4⋊C4—42no—
1339C4⋊C4—42no—
1340C4⋊C4—42no—
1341C4⋊C4—44no—
1342C4⋊C4—44no—
1343C4⋊C4—44no—
1344C4⋊C4—42no—
1345C4⋊C4—42no—
1346C22⋊C4—24no—
1347C22⋊C4—28no—
1348C22⋊C4—24no—
1349C22⋊C4—24no—
1350C22⋊C4—28no—
1351C22⋊C4—28no—
1352C22⋊C4—28no—
1353C22⋊C4—28no—
1354C22⋊C4—24no—
1355C22⋊C4—28no—
1356C22⋊C4—28no—
1357C22⋊C4—28no—
1358C22⋊C4—24no—
1359C22⋊C4—28no—
1360C22⋊C4—44no—
1361C22⋊C4—44no—
1362C22⋊C4—44no—
1363C22⋊C4—44no—
1364C22⋊C4—42no—
1365C22⋊C4—42no—
1366C22⋊C4—44no—
1367C22⋊C4—44no—
1368C22⋊C4—41no—
1369C22⋊C4—44no—
1370C22⋊C4—44no—
1371C22⋊C4—44no—
1372C22⋊C4—41no—
1373C22⋊C4—42no—
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—44no—
1383C22⋊C4—44no—
1384C22⋊C4—44no—
1385C22⋊C4—42no—
1386C22⋊C4—42no—
1387C22⋊C4—44no—
1388C22⋊C4—44no—
1389C22⋊C4—44no—
1390C22⋊C4—42no—
1391C22⋊C4—42no—
1392C22⋊C4—42no—
1393C22⋊C4—42no—
1394C22⋊C4—42no—
1395C22⋊C4—42no—
1396C22⋊C4—42no—
1397C22⋊C4—42no—
1398C22⋊C4—44no—
1399C22⋊C4—41no—
1400C22⋊C4—44no—
1401C22⋊C4—44no—
1402C22⋊C4—44no—
1403C22⋊C4—44no—
1404C22⋊C4—42no—
1405C22⋊C4—44no—
1406C22⋊C4—44no—
1407C22⋊C4—44no—
1408C22⋊C4—44no—
1409C22⋊C4—44no—
1410C22⋊C4—44no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—42no—
1415C22⋊C4—42no—
1416C22⋊C4—42no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—42no—
1421C22⋊C4—44no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4H(5,𝔽2)14yescomplemented
1425C42—24no—
1426C42—24no—
1427C42—24no—
1428C42—24no—
1429C42—24no—
1430C42—24no—
1431C42—24no—
1432C42—24no—
1433C42—22no—
1434C42—42no—
1435C42—44no—
1436C42—44no—
1437C42—44no—
1438C42—44no—
1439C42—42no—
1440C23—22no—
1441C23—22no—
1442C23—22no—
1443C23—22no—
1444C23—21no—
1445C23—21no—
1446C23—22no—
1447C23—22no—
1448C23—22no—
1449C23—22no—
1450C23—24no—
1451C23—21no—
1452C23—24no—
1453C23—24no—
1454C23—24no—
1455C23—24no—
1456C23—24no—
1457C23—22no—
1458C23—21no—
1459C23—22no—
1460C23—24no—
1461C23—24no—
1462C23—24no—
1463C23—24no—
1464C23—24no—
1465C23—22no—
1466C23—24no—
1467C23—24no—
1468C23—24no—
1469C23—24no—
1470C23—22no—
1471C23—24no—
1472C23—24no—
1473C23—24no—
1474C23—22no—
1475C23—24no—
1476C23—21no—
1477C23—24no—
1478C23—24no—
1479C23—24no—
1480C23—24no—
1481C23—416no—
1482C23—416no—
1483C23—48no—
1484C23—88no—
1485C23—88no—
1486C23—88no—
1487C23—88no—
1488C23—88no—
1489C23—84no—
1490C23—84no—
1491C23—84no—
1492C23—164no—
1493C23—164no—
1494C23—164no—
1495C23—164no—
1496C23—164no—
1497C23—164no—
1498C23—164no—
1499C23—164no—
1500C23—164no—
1501C23—162no—
1502C23—164no—
1503C23—164no—
1504C23—162no—
1505C23C2×H(5,𝔽2)14yes—
1506C23C2×H(5,𝔽2)12yes—
1507C23C2611yescharacteristic
1508Q8—28no—
1509Q8—44no—
1510Q8—44no—
1511Q8—84no—
1512Q8—82no—
1513D4—48no—
1514D4—416no—
1515D4—416no—
1516D4—48no—
1517D4—44no—
1518D4—48no—
1519D4—48no—
1520D4—44no—
1521D4—48no—
1522D4—48no—
1523D4—48no—
1524D4—88no—
1525D4—88no—
1526D4—88no—
1527D4—88no—
1528D4—88no—
1529D4—84no—
1530D4—82no—
1531D4—88no—
1532D4—88no—
1533D4—84no—
1534D4—88no—
1535D4—88no—
1536D4—88no—
1537D4—88no—
1538D4—88no—
1539D4—88no—
1540D4—88no—
1541D4—84no—
1542D4—164no—
1543D4—164no—
1544D4—164no—
1545D4—164no—
1546D4—164no—
1547D4—164no—
1548D4—164no—
1549D4—162no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—24no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—216no—
1556C2×C4—21no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—22no—
1568C2×C4—24no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—24no—
1572C2×C4—24no—
1573C2×C4—24no—
1574C2×C4—24no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—24no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—24no—
1588C2×C4—24no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—24no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—416no—
1607C2×C4—48no—
1608C2×C4—48no—
1609C2×C4—48no—
1610C2×C4—44no—
1611C2×C4—44no—
1612C2×C4—88no—
1613C2×C4—84no—
1614C2×C4—82no—
1615C2×C4—82no—
1616C2×C4—88no—
1617C2×C4—164no—
1618C2×C4C2×H(5,𝔽2)14yes—
1619C2×C4C2×H(5,𝔽2)14yes—
1620C2×C4C2×H(5,𝔽2)14yes—
1621C2×C4C2×H(5,𝔽2)12yes—
1622C2×C4C2×H(5,𝔽2)14yes—
1623C22—24no—
1624C22—24no—
1625C22—24no—
1626C22—22no—
1627C22—24no—
1628C22—41no—
1629C22—42no—
1630C22—42no—
1631C22—42no—
1632C22—42no—
1633C22—42no—
1634C22—41no—
1635C22—44no—
1636C22—44no—
1637C22—44no—
1638C22—42no—
1639C22—41no—
1640C22—44no—
1641C22—44no—
1642C22—44no—
1643C22—44no—
1644C22—44no—
1645C22—44no—
1646C22—42no—
1647C22—44no—
1648C22—44no—
1649C22—44no—
1650C22—44no—
1651C22—44no—
1652C22—44no—
1653C22—44no—
1654C22—44no—
1655C22—42no—
1656C22—44no—
1657C22—41no—
1658C22—42no—
1659C22—44no—
1660C22—44no—
1661C22—44no—
1662C22—42no—
1663C22—41no—
1664C22—44no—
1665C22—44no—
1666C22—1616no—
1667C22—1616no—
1668C22—168no—
1669C22—168no—
1670C22C22×H(5,𝔽2)11yescharacteristic
1671C22C22×H(5,𝔽2)12yes—
1672C22C22×H(5,𝔽2)11yescharacteristic
1673C22H(7,𝔽2)12yes—
1674C22H(7,𝔽2)11yescharacteristic
1675C4—24no—
1676C4—24no—
1677C4—24no—
1678C4—42no—
1679C4—41no—
1680C4—42no—
1681C4—42no—
1682C4—42no—
1683C4—44no—
1684C4—42no—
1685C4—42no—
1686C4—42no—
1687C4—44no—
1688C4—44no—
1689C4—42no—
1690C4—42no—
1691C4—42no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—42no—
1696C4#353214yes—
1697C2—42no—
1698C2—44no—
1699C2—84no—
1700C2—84no—
1701C2—84no—
1702C2—82no—
1703C2—81no—
1704C2C2×#353211yescharacteristic
1705C2#6287612yes—
1706C2#6291212yes—
1707C2#6291611yescharacteristic
1708C2#6306611yescharacteristic
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. #59104C2semidirect
2. #57971C2semidirect
3. #55437C2semidirect
4. #55347C2semidirect
5. #55312C2semidirect
6. #55040C2semidirect
7. #54816C2semidirect
8. #53000C2semidirect
9. #52986C2semidirect
10. #52405C2semidirect
11. #52203C2semidirect
12. #47853C2semidirect
13. #46350C2semidirect
14. #45487C2semidirect
15. #44957C2semidirect
16. #44870C2semidirect
17. #42976C2semidirect
18. #42895C2semidirect
19. #42890C2semidirect
20. #41234C2semidirect
21. #39336C2semidirect
22. #39135C2semidirect
23. #38061C2semidirect
24. #37786C2semidirect
25. #37677C2semidirect
26. #37614C2semidirect
27. #37331C2semidirect
28. #36082C2semidirect
29. #35527C2semidirect
30. C22×H(5,𝔽2)C22semidirect
31. C2×#560C22semidirect
32. C2×#559C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
35. C2×D42C22semidirect
37. C2×#535C22semidirect
38. C2×#534C22semidirect
39. C22×#127C22semidirect
40. C2×#529C22semidirect
41. C22×#124C22semidirect
42. #2856C22semidirect
43. #2854C22semidirect
44. #2854C22semidirect
45. #2829C22semidirect
46. #2828C22semidirect
47. #2828C22semidirect
48. #2828C22semidirect
49. #2825C22semidirect
50. #2819C22semidirect
51. #2818C22semidirect
52. #2818C22semidirect
53. #2815C22semidirect
54. #2813C22semidirect
55. #2812C22semidirect
56. #2812C22semidirect
57. #2812C22semidirect
58. #2803C22semidirect
59. #2797C22semidirect
60. #2778C22semidirect
61. #2764C22semidirect
62. #2763C22semidirect
63. #2762C22semidirect
64. #2761C22semidirect
65. #2760C22semidirect
66. #2752C22semidirect
67. #2749C22semidirect
68. #2749C22semidirect
69. #2743C22semidirect
70. #2737C22semidirect
71. #2733C22semidirect
72. #2730C22semidirect
73. #2715C22semidirect
74. #2714C22semidirect
75. #2714C22semidirect
76. #2714C22semidirect
77. #2710C22semidirect
78. #2709C22semidirect
79. #2708C22semidirect
80. #2706C22semidirect
81. #2706C22semidirect
82. #2705C22semidirect
83. #2703C22semidirect
84. #2703C22semidirect
85. #2703C22semidirect
86. #2697C22semidirect
87. #2697C22semidirect
88. #2697C22semidirect
89. #2696C22semidirect
90. #2693C22semidirect
91. #2685C22semidirect
92. #2685C22semidirect
93. #2685C22semidirect
94. #2685C22semidirect
95. #2684C22semidirect
96. #2682C22semidirect
97. #2682C22semidirect
98. #2679C22semidirect
99. #2679C22semidirect
100. #2678C22semidirect
101. #2678C22semidirect
102. #2678C22semidirect
103. #2678C22semidirect
104. #2678C22semidirect
105. #2676C22semidirect
106. #2676C22semidirect
107. #2675C22semidirect
108. #2673C22semidirect
109. #2673C22semidirect
110. #2673C22semidirect
111. #2671C22semidirect
112. #2670C22semidirect
113. #2670C22semidirect
114. #2670C22semidirect
115. #2670C22semidirect
116. #2670C22semidirect
117. #2670C22semidirect
118. #2669C22semidirect
119. #2669C22semidirect
120. #2669C22semidirect
121. #2669C22semidirect
122. #2668C22semidirect
123. #2668C22semidirect
124. #2662C22semidirect
125. #2661C22semidirect
126. #2657C22semidirect
127. #2657C22semidirect
128. #2648C22semidirect
129. #2648C22semidirect
130. #2644C22semidirect
131. #2641C22semidirect
132. #2641C22semidirect
133. #2631C22semidirect
134. #2631C22semidirect
135. #2620C22semidirect
136. #2619C22semidirect
137. #2619C22semidirect
138. #2617C22semidirect
139. #2616C22semidirect
140. #2616C22semidirect
141. #2613C22semidirect
142. #2613C22semidirect
143. #2613C22semidirect
144. #2592C22semidirect
145. #2578C22semidirect
146. #2560C22semidirect
147. #2559C22semidirect
148. #2555C22semidirect
149. #2555C22semidirect
150. #2554C22semidirect
151. #2553C22semidirect
152. #2548C22semidirect
153. #2548C22semidirect
154. #2548C22semidirect
155. #2548C22semidirect
156. #2544C22semidirect
157. #2541C22semidirect
158. #2541C22semidirect
159. #2541C22semidirect
160. #2541C22semidirect
161. #2539C22semidirect
162. #2539C22semidirect
163. #2535C22semidirect
164. #2534C22semidirect
165. #2518C22semidirect
166. #2518C22semidirect
167. #2512C22semidirect
168. #2512C22semidirect
169. #2490C22semidirect
170. #2490C22semidirect
171. #2477C22semidirect
172. #2474C22semidirect
173. #2467C22semidirect
174. #2464C22semidirect
175. #2464C22semidirect
176. #2459C22semidirect
177. #2453C22semidirect
178. #2448C22semidirect
179. #2448C22semidirect
180. #2445C22semidirect
181. #2445C22semidirect
182. #2445C22semidirect
183. #2445C22semidirect
184. #2441C22semidirect
185. #2436C22semidirect
186. #2435C22semidirect
187. #2435C22semidirect
188. #2435C22semidirect
189. #2435C22semidirect
190. #2435C22semidirect
192. #2433C22semidirect
193. #2433C22semidirect
194. #2433C22semidirect
195. #2433C22semidirect
196. #2433C22semidirect
197. #2433C22semidirect
198. #2433C22semidirect
199. #2433C22semidirect
200. #2433C22semidirect
202. #2431C22semidirect
203. #2431C22semidirect
204. #2431C22semidirect
205. #2431C22semidirect
206. #2431C22semidirect
207. #2428C22semidirect
208. #2428C22semidirect
209. #2428C22semidirect
210. #2427C22semidirect
211. #2426C22semidirect
212. #2424C22semidirect
213. #2424C22semidirect
214. #2424C22semidirect
215. #2422C22semidirect
216. #2418C22semidirect
217. #2414C22semidirect
218. #2411C22semidirect
219. #2410C22semidirect
220. #2410C22semidirect
221. #2410C22semidirect
223. #2408C22semidirect
224. #2408C22semidirect
225. #2408C22semidirect
226. #2408C22semidirect
227. #2408C22semidirect
228. #2408C22semidirect
229. #2403C22semidirect
230. #2403C22semidirect
231. #2403C22semidirect
232. #2403C22semidirect
233. #2403C22semidirect
234. #2403C22semidirect
235. #2401C22semidirect
236. #2398C22semidirect
237. #2396C22semidirect
239. #2388C22semidirect
240. #2367C22semidirect
241. #2363C22semidirect
242. #2363C22semidirect
243. #2362C22semidirect
244. #2341C22semidirect
245. #2341C22semidirect
246. Q8×C22⋊C4C22semidirect
247. D4×C22⋊C4C22semidirect
248. #2326C22semidirect
249. #2324C22semidirect
250. #2321C22semidirect
251. #2320C22semidirect
252. #2309C22semidirect
253. C4×#123C22semidirect
254. C4×#123C22semidirect
255. #2297C22semidirect
256. #2297C22semidirect
257. #2290C22semidirect
258. #2283C22semidirect
1424. 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
#591042
#579712
#554372
#553472
#553122
#550402
#548162
#530002
#529862
#524052
#522032
#478532
#463502
#454872
#449572
#448702
#429762
#428952
#428902
#412342
#393362
#391352
#380612
#377862
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