Finite Group Databasebeta

← #7715880

Subgroups — #7715880

Order 512.

8208 conjugacy classes of subgroups.

The subgroup lattice has 1765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3534C212yesmaximal, complemented
2#49587C214yesmaximal, complemented
3#49582C214yesmaximal, complemented
4#47874C214yesmaximal, complemented
5#47871C214yesmaximal, complemented
6#44022C214yesmaximal, complemented
7#43976C214yesmaximal, complemented
8#43932C214yesmaximal, complemented
9#43886C214yesmaximal, complemented
10#39742C212yesmaximal, complemented
11#39738C212yesmaximal, complemented
12#37678C212yesmaximal, complemented
13#37673C212yesmaximal, complemented
14#37673C212yesmaximal, complemented
15#37672C212yesmaximal, complemented
16#36741C212yesmaximal, complemented
17#36739C212yesmaximal, complemented
18#36123C212yesmaximal, complemented
19D4×#121C212yesmaximal, complemented
20#35252C212yesmaximal, complemented
21#35166C211yesmaximal, characteristic, complemented
22#35051C211yesmaximal, characteristic, complemented
23#35004C211yesmaximal, characteristic, complemented
24#35003C211yesmaximal, characteristic, complemented
25#35001C211yesmaximal, characteristic, complemented
26C2×#2656C211yesmaximal, characteristic, complemented
27C2×#2359C211yesmaximal, characteristic, complemented
28#3534—232no—
29C2×#562C2214yescomplemented
30C2×#560C2214yescomplemented
31C2×#553C2214yescomplemented
32C2×#551C2214yescomplemented
33C2×#546C2214yescomplemented
34C2×#546C2214yescomplemented
35C2×#546C2214yescomplemented
36C2×D42C2214yes—
37C2×D42C2212yescomplemented
38C2×#540C2214yescomplemented
39C2×#539C2212yescomplemented
40C2×#539C2214yescomplemented
41C2×#538C2214yescomplemented
42C2×#538C2212yescomplemented
43C2×#537C2212yescomplemented
44C2×#537C2212yescomplemented
45C2×#535C2212yescomplemented
46C2×#534C2214yescomplemented
47C2×#534C2212yescomplemented
48C2×#534C2212yescomplemented
49C2×#532C2212yescomplemented
50C2×#525C2212yescomplemented
51C22×#123C2211yescharacteristic
52C22×#121C2212yescomplemented
53C22×#121C2212yescomplemented
54C22×#121C2212yescomplemented
55C22×#121C2212yescomplemented
56C22×C4×D4C2211yescharacteristic
57C22×#117C2211yescharacteristic, complemented
58#2856C2212yescomplemented
59#2856C2212yescomplemented
60#2856C2212yescomplemented
61#2856C2212yescomplemented
62#2854C2212yescomplemented
63#2850C2212yescomplemented
64#2850C2212yescomplemented
65#2847C2212yescomplemented
66#2847C2212yescomplemented
67#2847C2212yescomplemented
68#2727C2214yescomplemented
69#2723C2214yescomplemented
70#2721C2214yescomplemented
71#2720C2214yescomplemented
72#2718C2214yescomplemented
73#2714C2214yescomplemented
74#2714C2214yescomplemented
75#2711C2214yescomplemented
76#2710C2214yescomplemented
77#2706C2214yescomplemented
78#2705C2214yescomplemented
79#2705C2214yescomplemented
80#2703C2214yescomplemented
81#2696C2214yescomplemented
82#2694C2214yescomplemented
83#2692C2214yescomplemented
84#2685C2214yescomplemented
85#2682C2214yescomplemented
86#2678C2214yescomplemented
87#2676C2214yescomplemented
88#2676C2214yescomplemented
89#2676C2214yescomplemented
90#2675C2214yescomplemented
91#2675C2214yescomplemented
92#2674C2214yescomplemented
93#2673C2214yescomplemented
94#2673C2214yescomplemented
95#2673C2214yescomplemented
96#2672C2214yescomplemented
97#2672C2214yescomplemented
98#2672C2214yescomplemented
99#2671C2214yescomplemented
100#2671C2214yescomplemented
101#2671C2214yescomplemented
102#2670C2214yescomplemented
103#2670C2214yescomplemented
104#2669C2214yescomplemented
105#2669C2214yescomplemented
106#2669C2214yescomplemented
107#2668C2214yescomplemented
108#2659C2211yescharacteristic, complemented
109#2656C2211yescharacteristic
110#2656C2214yescomplemented
111#2656C2212yescomplemented
112#2656C2212yescomplemented
113#2656C2211yescharacteristic, complemented
114#2656C2212yescomplemented
115#2656C2214yescomplemented
116#2656C2212yescomplemented
117#2656C2212yescomplemented
118#2656C2211yescharacteristic, complemented
119#2639C2212yescomplemented
120#2620C2212yescomplemented
121#2620C2212yescomplemented
122#2619C2212yescomplemented
123#2619C2212yescomplemented
124#2618C2212yescomplemented
125#2617C2212yescomplemented
126#2564C2214yescomplemented
127#2556C2214yescomplemented
128#2555C2214yescomplemented
129#2555C2214yescomplemented
130#2554C2214yescomplemented
131#2553C2214yescomplemented
132#2543C2214yescomplemented
133#2543C2214yescomplemented
134#2543C2214yescomplemented
135#2542C2214yescomplemented
136#2541C2214yescomplemented
137#2541C2212yescomplemented
138#2540C2214yescomplemented
139#2540C2214yescomplemented
140#2539C2214yescomplemented
141#2539C2214yescomplemented
142#2537C2212yescomplemented
143#2521C2214yescomplemented
144#2519C2214yescomplemented
145#2501C2214yescomplemented
146#2498C2214yescomplemented
147#2491C2212yescomplemented
148#2479C2214yescomplemented
149#2472C2214yescomplemented
150#2471C2214yescomplemented
151#2467C2214yescomplemented
152#2464C2214yescomplemented
153#2464C2214yescomplemented
154#2461C2214yescomplemented
155#2456C2214yescomplemented
156#2456C2214yescomplemented
157#2455C2214yescomplemented
158#2454C2214yescomplemented
159#2449C2214yescomplemented
160#2449C2214yescomplemented
161#2443C2214yescomplemented
162#2441C2214yescomplemented
163#2440C2212yescomplemented
164#2437C2214yescomplemented
165#2437C2214yescomplemented
166#2433C2212yescomplemented
167#2433C2214yescomplemented
168#2430C2214yescomplemented
169#2430C2214yescomplemented
170#2430C2214yescomplemented
171#2428C2212yescomplemented
172#2428C2212yescomplemented
173#2428C2214yescomplemented
174#2428C2214yescomplemented
175#2424C2214yes—
176#2424C2214yescomplemented
177#2424C2214yescomplemented
178#2424C2214yescomplemented
179#2424C2214yescomplemented
180#2422C2212yescomplemented
181#2418C2214yescomplemented
182#2418C2214yescomplemented
183#2416C2212yes—
184#2416C2214yescomplemented
185#2416C2214yescomplemented
186#2416C2214yescomplemented
187#2416C2214yescomplemented
188#2416C2212yescomplemented
189#2414C2214yescomplemented
190#2414C2214yescomplemented
191#2414C2214yescomplemented
192#2411C2214yescomplemented
193#2411C2214yescomplemented
194#2410C2214yescomplemented
195#2410C2214yescomplemented
196#2410C2214yescomplemented
197#2410C2214yescomplemented
198#2410C2214yescomplemented
199#2410C2214yescomplemented
200#2410C2214yescomplemented
201#2408C2212yes—
202#2408C2212yescomplemented
203#2403C2214yescomplemented
204C2×#399C2214yescomplemented
205C2×#392C2214yescomplemented
206#2361C2212yescomplemented
207#2359C2214yescomplemented
208#2359C2214yescomplemented
209#2359C2214yescomplemented
210#2359C2214yescomplemented
211#2358C2214yescomplemented
212D4×C4⋊C4C2212yescomplemented
213D4×C22⋊C4C2212yescomplemented
214D4×C22⋊C4C2214yescomplemented
215#2325C2212yescomplemented
216#2325C2212yescomplemented
217#2325C2212yescomplemented
218#2325C2212yescomplemented
219#2317C2212yescomplemented
220#2311C2212yescomplemented
221#2309C2212yescomplemented
222C4×#121C2212yescomplemented
223C4×#121C2212yescomplemented
224C2×#389C2211yescharacteristic, complemented
225C2×#388C2211yescharacteristic, complemented
226C2×#388C2211yescharacteristic, complemented
227C2×#387C2211yescharacteristic, complemented
228C2×#387C2211yescharacteristic, complemented
229C2×#386C2211yescharacteristic
230C2×#385C2211yescharacteristic, complemented
231C2×#385C2211yescharacteristic, complemented
232C2×C4×C4⋊C4C2211yescharacteristic, complemented
233C2×C4×C22⋊C4C2211yescharacteristic, complemented
234C2×C4×C22⋊C4C2211yescharacteristic, complemented
235C22×#95C2211yescharacteristic, complemented
236C22×#41C2312yes—
237C22×#41C2314yes—
238C23×D4C2312yes—
239C23×D4C2314yes—
240C23×D4C2314yes—
241C23×D4C2314yes—
242C23×D4C2312yes—
243C23×D4C2312yes—
244C23×D4C2312yes—
245C23×D4C2311yescharacteristic
246C24×C4C2311yescharacteristic
247C24×C4C2311yescharacteristic
248C24×C4C2311yescharacteristic
249C24×C4C2311yescharacteristic
250#562—232no—
251#560—232no—
252#553—232no—
253#551—232no—
254#546—232no—
255#546—232no—
256#546—232no—
257D42—232no—
258D42—48no—
259#540—232no—
260#539—232no—
261#539—216no—
262#538—232no—
263#538—216no—
264#537—216no—
265#537—48no—
266#535—48no—
267#534—232no—
268#534—216no—
269#534—48no—
270#532—48no—
271C2×C4⋊Q8C2312yes—
272C2×#127C2314yes—
273C2×#127C2312yes—
274C2×#127C2312yes—
275C2×#127C2312yes—
276C2×#127C2312yes—
277C2×#127C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290#525—216no—
291C2×#123D4116yescomplemented
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×#121—216no—
316C2×#121—48no—
317C2×#121—48no—
318C2×#121—48no—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
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×#121C2314yes—
342C2×#121C2314yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#121C2314yes—
352C2×#121C2314yes—
353C2×#121C2312yes—
354C2×#121C2314yes—
355C2×#121C2314yes—
356C2×#121C2312yes—
357C2×#121C2314yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2314yes—
364C2×#121C2314yes—
365C2×#121C2314yes—
366C2×#121C2314yes—
367C2×#121C2314yes—
368C2×#121C2314yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2314yes—
373C2×#120C2314yes—
374C2×#120C2314yes—
375C2×#120C2314yes—
376C2×#120C2314yes—
377C2×#120C2314yes—
378C2×#120C2314yes—
379C2×#120C2314yes—
380C2×#120C2314yes—
381C2×#120C2314yes—
382C2×#120C2314yes—
383C2×#120C2314yes—
384C2×#120C2314yes—
385C2×#120C2314yes—
386C2×#120C2314yes—
387C2×C4×D4—44no—
388C2×C4×D4C2314yes—
389C2×C4×D4C2314yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2314yes—
392C2×C4×D4C2314yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2314yes—
395C2×C4×D4C2314yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2314yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×#117—44no—
406C2×#117C2312yes—
407C2×#117C2312yes—
408C2×#117C2314yes—
409C2×#117C2312yes—
410C2×#117C2312yes—
411C2×#117C2312yes—
412C22×C4⋊C4C2312yes—
413C22×C4⋊C4C2311yescharacteristic
414C22×C4⋊C4C2312yes—
415C22×C4⋊C4C2312yes—
416C22×C4⋊C4C2312yes—
417C22×C4⋊C4C2311yescharacteristic
418C22×C4⋊C4C2311yescharacteristic
419C22×C4⋊C4C2311yescharacteristic
420C22×C4⋊C4C2311yescharacteristic
421C22×C4⋊C4C2311yescharacteristic
422C22×C4⋊C4C2311yescharacteristic
423C22×C22⋊C4C2314yes—
424C22×C22⋊C4C2311yescharacteristic
425C22×C22⋊C4C2314yes—
426C22×C22⋊C4C2311yescharacteristic
427C22×C22⋊C4C2314yes—
428C22×C22⋊C4C2314yes—
429C22×C22⋊C4C2314yes—
430C22×C22⋊C4C2314yes—
431C22×C22⋊C4C2311yescharacteristic
432C22×C22⋊C4C2311yescharacteristic
433C22×C22⋊C4C2311yescharacteristic
434C22×C22⋊C4C2311yescharacteristic
435C22×C22⋊C4C2311yescharacteristic
436C22×C22⋊C4C2311yescharacteristic
437C22×C42C2311yescharacteristic
438C22×C42C2311yescharacteristic
439C22×C42C2311yescharacteristic
440C22×C42C2311yescharacteristic
441C22×C42C2311yescharacteristic
442#400C2314yes—
443#399C2314yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#399C2314yes—
448#399C2314yes—
449#399C2314yes—
450#399C2314yes—
451#399C2314yes—
452#399C2314yes—
453#399C2314yes—
454#399C2314yes—
455#399C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
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#392C2314yes—
524#392C2314yes—
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#391C2312yes—
531#391C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2314yes—
537#390C2314yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2314yes—
542#390C2312yes—
543#390C2314yes—
544#390C2312yes—
545#390C2314yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2314yes—
550#390C2314yes—
551#390C2314yes—
552#390C2314yes—
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2314yes—
557#390C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
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#386C2314yes—
625#386C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#384C2312yes—
643#384C2312yes—
644#384C2312yes—
645#384C2312yes—
646#382C2312yes—
647#382C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#379C2314yes—
661#379C2314yes—
662#379C2314yes—
663#379C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C2×#95C2314yes—
677C2×#95C2311yescharacteristic
678C2×#95C2311yescharacteristic
679C2×#95C2311yescharacteristic
680C2×#95C2311yescharacteristic
681C2×#95C2314yes—
682C2×#95C2311yescharacteristic
683C2×#95C2311yescharacteristic
684C2×#95C2311yescharacteristic
685C2×#95C2311yescharacteristic
686C2×#95C2311yescharacteristic
687C2×#95C2311yescharacteristic
688C25C2411yescharacteristic
689C25C2414yes—
690C25C2411yescharacteristic
691C25C2414yes—
692C2×#41—28no—
693C2×#41—216no—
694C2×#41—48no—
695C2×#41—44no—
696C2×#41—48no—
697C2×#41—44no—
698C22×Q8C2414yes—
699C22×Q8C2412yes—
700C22×D4—216no—
701C22×D4—216no—
702C22×D4—216no—
703C22×D4—28no—
704C22×D4—44no—
705C22×D4—44no—
706C22×D4—44no—
707C22×D4—44no—
708C22×D4—44no—
709C22×D4—44no—
710C22×D4—44no—
711C22×D4—44no—
712C22×D4—42no—
713C22×D4—42no—
714C22×D4—48no—
715C22×D4—48no—
716C22×D4—48no—
717C22×D4—48no—
718C22×D4—48no—
719C22×D4—48no—
720C22×D4—82no—
721C22×D4—82no—
722C22×D4—82no—
723C22×D4C2×D418yes—
724C22×D4C2414yes—
725C22×D4C2414yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2414yes—
731C22×D4C2414yes—
732C22×D4C2414yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2414yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2412yes—
750C22×D4C2414yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C22×D4C2412yes—
756C23×C4—24no—
757C23×C4—24no—
758C23×C4—24no—
759C23×C4—42no—
760C23×C4—42no—
761C23×C4—42no—
762C23×C4—42no—
763C23×C4—42no—
764C23×C4—81no—
765C23×C4—81no—
766C23×C4—81no—
767C23×C4C2×D418yescomplemented
768C23×C4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2412yes—
771C23×C4C2411yescharacteristic
772C23×C4C2412yes—
773C23×C4C2411yescharacteristic
774C23×C4C2412yes—
775C23×C4C2414yes—
776C23×C4C2411yescharacteristic
777C23×C4C2411yescharacteristic
778C23×C4C2412yes—
779C23×C4C2411yescharacteristic
780C23×C4C2414yes—
781C23×C4C2414yes—
782C23×C4C2414yes—
783C23×C4C2414yes—
784C23×C4C2414yes—
785C23×C4C2411yescharacteristic
786C23×C4C2414yes—
787C23×C4C2412yes—
788C23×C4C2412yes—
789C23×C4C2411yescharacteristic
790C23×C4C2411yescharacteristic
791C23×C4C2411yescharacteristic
792C23×C4C2411yescharacteristic
793C23×C4C2412yes—
794C23×C4C2411yescharacteristic
795C23×C4C2411yescharacteristic
796C4⋊Q8—44no—
797#127—216no—
798#127—44no—
799#127—44no—
800#127—44no—
801#127—44no—
802#127—82no—
803#126—216no—
804#126—216no—
805#126—216no—
806#126—216no—
807#125—216no—
808#125—216no—
809#124—216no—
810#124—216no—
811#124—216no—
812#124—48no—
813#124—44no—
814#124—44no—
815#123—216no—
816#123—216no—
817#123—216no—
818#123—216no—
819#123—216no—
820#123—216no—
821#123—216no—
822#123—216no—
823#123—216no—
824#123—216no—
825#123—48no—
826#123—48no—
827#123C2×D4132yescomplemented
828#123C2×D4132yescomplemented
829C22⋊Q8—28no—
830C22⋊Q8—28no—
831C22⋊Q8—216no—
832C22⋊Q8—216no—
833C22⋊Q8—216no—
834C22⋊Q8—216no—
835C22⋊Q8—216no—
836C22⋊Q8—48no—
837C22⋊Q8—48no—
838#121—216no—
839#121—216no—
840#121—216no—
841#121—28no—
842#121—28no—
843#121—28no—
844#121—28no—
845#121—216no—
846#121—216no—
847#121—28no—
848#121—28no—
849#121—216no—
850#121—216no—
851#121—28no—
852#121—28no—
853#121—28no—
854#121—28no—
855#121—28no—
856#121—28no—
857#121—216no—
858#121—216no—
859#121—216no—
860#121—216no—
861#121—216no—
862#121—216no—
863#121—216no—
864#121—216no—
865#121—48no—
866#121—48no—
867#121—48no—
868#121—44no—
869#121—48no—
870#121—48no—
871#121—48no—
872#121—48no—
873#121—48no—
874#121—44no—
875#121—44no—
876#121—44no—
877#121—44no—
878#121—44no—
879#121—44no—
880#121—48no—
881#121—48no—
882#121—48no—
883#121—44no—
884#121—48no—
885#121—48no—
886#121—48no—
887#121—44no—
888#121—82no—
889#121—82no—
890#121—84no—
891#121—82no—
892#120—216no—
893#120—216no—
894#120—216no—
895#120—216no—
896#120—216no—
897#120—216no—
898#120—216no—
899#120—216no—
900#120—216no—
901#120—48no—
902#120—48no—
903#120—48no—
904#120—48no—
905#120—84no—
906C4×D4—216no—
907C4×D4—216no—
908C4×D4—216no—
909C4×D4—216no—
910C4×D4—216no—
911C4×D4—216no—
912C4×D4—216no—
913C4×D4—216no—
914C4×D4—28no—
915C4×D4—44no—
916C4×D4—48no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—44no—
920C4×D4—44no—
921C4×D4—44no—
922C4×D4—82no—
923#117—28no—
924#117—216no—
925#117—28no—
926#117—44no—
927#117—44no—
928#117—44no—
929C2×C4⋊C4—28no—
930C2×C4⋊C4—24no—
931C2×C4⋊C4—42no—
932C2×C4⋊C4—42no—
933C2×C4⋊C4—42no—
934C2×C4⋊C4—44no—
935C2×C4⋊C4—44no—
936C2×C4⋊C4—44no—
937C2×C4⋊C4—81no—
938C2×C4⋊C4C2×D418yescomplemented
939C2×C4⋊C4C2×D418yescomplemented
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C22⋊C4—216no—
980C2×C22⋊C4—24no—
981C2×C22⋊C4—216no—
982C2×C22⋊C4—216no—
983C2×C22⋊C4—24no—
984C2×C22⋊C4—42no—
985C2×C22⋊C4—48no—
986C2×C22⋊C4—48no—
987C2×C22⋊C4—48no—
988C2×C22⋊C4—42no—
989C2×C22⋊C4—81no—
990C2×C22⋊C4C2×D418yescomplemented
991C2×C22⋊C4C2×D418yescomplemented
992C2×C22⋊C4C2×D418yescomplemented
993C2×C22⋊C4C2414yes—
994C2×C22⋊C4C2414yes—
995C2×C22⋊C4C2411yescharacteristic
996C2×C22⋊C4C2411yescharacteristic
997C2×C22⋊C4C2411yescharacteristic
998C2×C22⋊C4C2412yes—
999C2×C22⋊C4C2414yes—
1000C2×C22⋊C4C2414yes—
1001C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C42—24no—
1057C2×C42—42no—
1058C2×C42—42no—
1059C2×C42—42no—
1060C2×C42—81no—
1061C2×C42C2414yes—
1062C2×C42C2412yes—
1063C2×C42C2412yes—
1064C2×C42C2414yes—
1065C2×C42C2414yes—
1066C2×C42C2412yes—
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2414yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100C24—22no—
1101C24—22no—
1102C24—22no—
1103C24—22no—
1104C24—22no—
1105C24—22no—
1106C24—28no—
1107C24—28no—
1108C24—28no—
1109C24—28no—
1110C24—41no—
1111C24—41no—
1112C24—41no—
1113C24—41no—
1114C24—41no—
1115C24—41no—
1116C24—44no—
1117C24—44no—
1118C24—44no—
1119C24—44no—
1120C24—44no—
1121C24—44no—
1122C24—44no—
1123C24—44no—
1124C24—44no—
1125C24—44no—
1126C24C22×D414yes—
1127C24C22×D414yes—
1128C24C2514yes—
1129C24C2514yes—
1130C24C2514yes—
1131C24C2512yes—
1132C24C2511yescharacteristic
1133C24C2511yescharacteristic
1134C24C2511yescharacteristic
1135#41—816no—
1136#41—832no—
1137C2×Q8—24no—
1138C2×Q8—28no—
1139C2×Q8—44no—
1140C2×Q8—42no—
1141C2×Q8—44no—
1142C2×Q8—42no—
1143C2×D4—24no—
1144C2×D4—24no—
1145C2×D4—28no—
1146C2×D4—28no—
1147C2×D4—28no—
1148C2×D4—28no—
1149C2×D4—28no—
1150C2×D4—28no—
1151C2×D4—28no—
1152C2×D4—28no—
1153C2×D4—28no—
1154C2×D4—28no—
1155C2×D4—28no—
1156C2×D4—28no—
1157C2×D4—28no—
1158C2×D4—28no—
1159C2×D4—28no—
1160C2×D4—28no—
1161C2×D4—28no—
1162C2×D4—28no—
1163C2×D4—28no—
1164C2×D4—28no—
1165C2×D4—24no—
1166C2×D4—28no—
1167C2×D4—24no—
1168C2×D4—28no—
1169C2×D4—24no—
1170C2×D4—28no—
1171C2×D4—24no—
1172C2×D4—24no—
1173C2×D4—24no—
1174C2×D4—28no—
1175C2×D4—28no—
1176C2×D4—24no—
1177C2×D4—24no—
1178C2×D4—24no—
1179C2×D4—42no—
1180C2×D4—42no—
1181C2×D4—42no—
1182C2×D4—42no—
1183C2×D4—42no—
1184C2×D4—42no—
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—44no—
1198C2×D4—44no—
1199C2×D4—44no—
1200C2×D4—44no—
1201C2×D4—44no—
1202C2×D4—44no—
1203C2×D4—44no—
1204C2×D4—42no—
1205C2×D4—42no—
1206C2×D4—42no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—42no—
1210C2×D4—42no—
1211C2×D4—42no—
1212C2×D4—44no—
1213C2×D4—42no—
1214C2×D4—42no—
1215C2×D4—44no—
1216C2×D4—42no—
1217C2×D4—42no—
1218C2×D4—44no—
1219C2×D4—42no—
1220C2×D4—44no—
1221C2×D4—42no—
1222C2×D4—42no—
1223C2×D4—44no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4—44no—
1228C2×D4—44no—
1229C2×D4—44no—
1230C2×D4—42no—
1231C2×D4—44no—
1232C2×D4—44no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—44no—
1236C2×D4—44no—
1237C2×D4—416no—
1238C2×D4—816no—
1239C2×D4—816no—
1240C2×D4—816no—
1241C2×D4—816no—
1242C2×D4—832no—
1243C2×D4—832no—
1244C2×D4—832no—
1245C2×D4C22×D418yes—
1246C2×D4C22×D418yes—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—24no—
1250C22×C4—24no—
1251C22×C4—22no—
1252C22×C4—24no—
1253C22×C4—22no—
1254C22×C4—24no—
1255C22×C4—28no—
1256C22×C4—28no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—28no—
1268C22×C4—28no—
1269C22×C4—28no—
1270C22×C4—28no—
1271C22×C4—28no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—41no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—41no—
1281C22×C4—41no—
1282C22×C4—42no—
1283C22×C4—416no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—42no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—42no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—44no—
1299C22×C4—44no—
1300C22×C4—44no—
1301C22×C4—41no—
1302C22×C4—41no—
1303C22×C4—41no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—42no—
1314C22×C4—42no—
1315C22×C4—42no—
1316C22×C4—44no—
1317C22×C4—42no—
1318C22×C4—41no—
1319C22×C4—44no—
1320C22×C4—41no—
1321C22×C4—44no—
1322C22×C4—44no—
1323C22×C4—88no—
1324C22×C4—88no—
1325C22×C4—88no—
1326C22×C4C22×D418yes—
1327C22×C4C22×D414yes—
1328C22×C4C22×D414yes—
1329C22×C4C22×D414yes—
1330C22×C4C22×D414yes—
1331C22×C4C22×D414yes—
1332C22×C4C22×D418yes—
1333C22×C4H(5,𝔽2)14yes—
1334C22×C4H(5,𝔽2)14yes—
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2514yes—
1339C22×C4C2514yes—
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C22×C4C2512yes—
1343C22×C4C2514yes—
1344C22×C4C2514yes—
1345C22×C4C2514yes—
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2511yescharacteristic
1354C22×C4C2511yescharacteristic
1355C4⋊C4—24no—
1356C4⋊C4—28no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—28no—
1360C4⋊C4—24no—
1361C4⋊C4—28no—
1362C4⋊C4—28no—
1363C4⋊C4—28no—
1364C4⋊C4—28no—
1365C4⋊C4—28no—
1366C4⋊C4—28no—
1367C4⋊C4—28no—
1368C4⋊C4—28no—
1369C4⋊C4—24no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—42no—
1386C4⋊C4—44no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—42no—
1392C4⋊C4C22×D4116yes—
1393C4⋊C4C22×D4116yes—
1394C22⋊C4—28no—
1395C22⋊C4—28no—
1396C22⋊C4—28no—
1397C22⋊C4—28no—
1398C22⋊C4—28no—
1399C22⋊C4—22no—
1400C22⋊C4—24no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—28no—
1404C22⋊C4—28no—
1405C22⋊C4—28no—
1406C22⋊C4—28no—
1407C22⋊C4—28no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—28no—
1411C22⋊C4—28no—
1412C22⋊C4—28no—
1413C22⋊C4—28no—
1414C22⋊C4—28no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—28no—
1418C22⋊C4—28no—
1419C22⋊C4—24no—
1420C22⋊C4—28no—
1421C22⋊C4—28no—
1422C22⋊C4—28no—
1423C22⋊C4—28no—
1424C22⋊C4—28no—
1425C22⋊C4—28no—
1426C22⋊C4—28no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4C22×D418yes—
1453C22⋊C4C22×D4116yes—
1454C22⋊C4C22×D4116yes—
1455C22⋊C4C22×D418yes—
1456C22⋊C4H(5,𝔽2)14yes—
1457C42—28no—
1458C42—28no—
1459C42—28no—
1460C42—24no—
1461C42—24no—
1462C42—24no—
1463C42—24no—
1464C42—24no—
1465C42—42no—
1466C42—42no—
1467C42—42no—
1468C42—42no—
1469C42—42no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—22no—
1480C23—22no—
1481C23—22no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—22no—
1486C23—22no—
1487C23—21no—
1488C23—21no—
1489C23—22no—
1490C23—28no—
1491C23—28no—
1492C23—28no—
1493C23—24no—
1494C23—24no—
1495C23—24no—
1496C23—24no—
1497C23—24no—
1498C23—24no—
1499C23—24no—
1500C23—24no—
1501C23—24no—
1502C23—24no—
1503C23—24no—
1504C23—24no—
1505C23—24no—
1506C23—24no—
1507C23—24no—
1508C23—24no—
1509C23—24no—
1510C23—24no—
1511C23—24no—
1512C23—24no—
1513C23—24no—
1514C23—44no—
1515C23—44no—
1516C23—44no—
1517C23—44no—
1518C23—44no—
1519C23—44no—
1520C23—44no—
1521C23—416no—
1522C23—82no—
1523C23—82no—
1524C23—82no—
1525C23—82no—
1526C23—88no—
1527C23—88no—
1528C23—88no—
1529C23—88no—
1530C23—88no—
1531C23—88no—
1532C23—88no—
1533C23—88no—
1534C23—88no—
1535C23—88no—
1536C23—88no—
1537C23—164no—
1538C23—164no—
1539C23C23×D414yes—
1540C23C23×D412yes—
1541C23C23×D412yes—
1542C23C23×D412yes—
1543C23C2×H(5,𝔽2)12yes—
1544C23C2×H(5,𝔽2)12yes—
1545C23C2×H(5,𝔽2)12yes—
1546C23#58512yes—
1547C23C2611yescharacteristic
1548Q8—84no—
1549Q8—88no—
1550D4—216no—
1551D4—48no—
1552D4—48no—
1553D4—48no—
1554D4—416no—
1555D4—416no—
1556D4—416no—
1557D4—416no—
1558D4—88no—
1559D4—84no—
1560D4—88no—
1561D4—88no—
1562D4—84no—
1563D4—84no—
1564D4—88no—
1565D4—84no—
1566D4—84no—
1567D4—88no—
1568D4—84no—
1569D4—84no—
1570D4—88no—
1571D4—88no—
1572D4—88no—
1573D4—88no—
1574D4—88no—
1575D4—88no—
1576D4—88no—
1577D4—88no—
1578D4—88no—
1579D4—88no—
1580D4—164no—
1581D4—164no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—216no—
1601C2×C4—28no—
1602C2×C4—24no—
1603C2×C4—24no—
1604C2×C4—24no—
1605C2×C4—24no—
1606C2×C4—24no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—24no—
1614C2×C4—22no—
1615C2×C4—24no—
1616C2×C4—24no—
1617C2×C4—24no—
1618C2×C4—24no—
1619C2×C4—24no—
1620C2×C4—24no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—21no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—44no—
1636C2×C4—48no—
1637C2×C4—44no—
1638C2×C4—44no—
1639C2×C4—44no—
1640C2×C4—44no—
1641C2×C4—44no—
1642C2×C4—48no—
1643C2×C4—44no—
1644C2×C4—44no—
1645C2×C4—48no—
1646C2×C4—48no—
1647C2×C4—88no—
1648C2×C4—84no—
1649C2×C4—84no—
1650C2×C4—84no—
1651C2×C4—88no—
1652C2×C4—88no—
1653C2×C4—88no—
1654C2×C4—88no—
1655C2×C4—82no—
1656C2×C4—82no—
1657C2×C4—82no—
1658C2×C4—82no—
1659C2×C4—88no—
1660C2×C4—88no—
1661C2×C4C23×D414yes—
1662C2×C4C23×D414yes—
1663C2×C4C23×D414yes—
1664C2×C4C23×D414yes—
1665C2×C4C23×D414yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4C2×H(5,𝔽2)14yes—
1668C2×C4C2×H(5,𝔽2)12yes—
1669C2×C4C2×H(5,𝔽2)14yes—
1670C22—22no—
1671C22—22no—
1672C22—22no—
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—22no—
1679C22—22no—
1680C22—22no—
1681C22—22no—
1682C22—22no—
1683C22—24no—
1684C22—24no—
1685C22—22no—
1686C22—22no—
1687C22—24no—
1688C22—416no—
1689C22—42no—
1690C22—41no—
1691C22—41no—
1692C22—42no—
1693C22—41no—
1694C22—42no—
1695C22—41no—
1696C22—42no—
1697C22—44no—
1698C22—44no—
1699C22—44no—
1700C22—44no—
1701C22—44no—
1702C22—44no—
1703C22—44no—
1704C22—44no—
1705C22—44no—
1706C22—44no—
1707C22—44no—
1708C22—44no—
1709C22—44no—
1710C22—44no—
1711C22—44no—
1712C22—44no—
1713C22—44no—
1714C22—44no—
1715C22—44no—
1716C22—44no—
1717C22—44no—
1718C22—88no—
1719C22—1616no—
1720C22—1616no—
1721C22#349614yes—
1722C22#349814yes—
1723C22C24×D411yescharacteristic
1724C22C22×H(5,𝔽2)11yescharacteristic
1725C22C22×H(5,𝔽2)11yescharacteristic
1726C22C22×H(5,𝔽2)11yescharacteristic
1727C22C2×#58511yescharacteristic
1728C22H(7,𝔽2)11yescharacteristic
1729C222−1+611yescharacteristic
1730C4—24no—
1731C4—24no—
1732C4—24no—
1733C4—24no—
1734C4—24no—
1735C4—24no—
1736C4—22no—
1737C4—24no—
1738C4—22no—
1739C4—44no—
1740C4—44no—
1741C4—44no—
1742C4—44no—
1743C4—44no—
1744C4—41no—
1745C4—42no—
1746C4—42no—
1747C4—42no—
1748C4—41no—
1749C4—42no—
1750C2—24no—
1751C2—24no—
1752C2—42no—
1753C2—44no—
1754C2—84no—
1755C2—84no—
1756C2—84no—
1757C2C2×#349611yescharacteristic
1758C2C2×#349811yescharacteristic
1759C2#6285311yescharacteristic
1760C2#6289211yescharacteristic
1761C2#6290011yescharacteristic
1762C2#6291411yescharacteristic
1763C2#6292711yescharacteristic
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. C2×#3534C2semidirect
2. #49587C2semidirect
3. #49582C2semidirect
4. #47874C2semidirect
5. #47871C2semidirect
6. #44022C2semidirect
7. #43976C2semidirect
8. #43932C2semidirect
9. #43886C2semidirect
10. #39742C2semidirect
11. #39738C2semidirect
12. #37678C2semidirect
13. #37673C2semidirect
14. #37673C2semidirect
15. #37672C2semidirect
16. #36741C2semidirect
17. #36739C2semidirect
18. #36123C2semidirect
19. D4×#121C2semidirect
20. #35252C2semidirect
21. #35166C2semidirect
22. #35051C2semidirect
23. #35004C2semidirect
24. #35003C2semidirect
25. #35001C2semidirect
26. C2×#2656C2semidirect
27. C2×#2359C2semidirect
29. C2×#562C22semidirect
30. C2×#560C22semidirect
31. C2×#553C22semidirect
32. C2×#551C22semidirect
33. C2×#546C22semidirect
34. C2×#546C22semidirect
35. C2×#546C22semidirect
37. C2×D42C22semidirect
38. C2×#540C22semidirect
39. C2×#539C22semidirect
40. C2×#539C22semidirect
41. C2×#538C22semidirect
42. C2×#538C22semidirect
43. C2×#537C22semidirect
44. C2×#537C22semidirect
45. C2×#535C22semidirect
46. C2×#534C22semidirect
47. C2×#534C22semidirect
48. C2×#534C22semidirect
49. C2×#532C22semidirect
50. C2×#525C22semidirect
52. C22×#121C22semidirect
53. C22×#121C22semidirect
54. C22×#121C22semidirect
55. C22×#121C22semidirect
57. C22×#117C22semidirect
58. #2856C22semidirect
59. #2856C22semidirect
60. #2856C22semidirect
61. #2856C22semidirect
62. #2854C22semidirect
63. #2850C22semidirect
64. #2850C22semidirect
65. #2847C22semidirect
66. #2847C22semidirect
67. #2847C22semidirect
68. #2727C22semidirect
69. #2723C22semidirect
70. #2721C22semidirect
71. #2720C22semidirect
72. #2718C22semidirect
73. #2714C22semidirect
74. #2714C22semidirect
75. #2711C22semidirect
76. #2710C22semidirect
77. #2706C22semidirect
78. #2705C22semidirect
79. #2705C22semidirect
80. #2703C22semidirect
81. #2696C22semidirect
82. #2694C22semidirect
83. #2692C22semidirect
84. #2685C22semidirect
85. #2682C22semidirect
86. #2678C22semidirect
87. #2676C22semidirect
88. #2676C22semidirect
89. #2676C22semidirect
90. #2675C22semidirect
91. #2675C22semidirect
92. #2674C22semidirect
93. #2673C22semidirect
94. #2673C22semidirect
95. #2673C22semidirect
96. #2672C22semidirect
97. #2672C22semidirect
98. #2672C22semidirect
99. #2671C22semidirect
100. #2671C22semidirect
101. #2671C22semidirect
102. #2670C22semidirect
103. #2670C22semidirect
104. #2669C22semidirect
105. #2669C22semidirect
106. #2669C22semidirect
107. #2668C22semidirect
108. #2659C22semidirect
110. #2656C22semidirect
111. #2656C22semidirect
112. #2656C22semidirect
113. #2656C22semidirect
114. #2656C22semidirect
115. #2656C22semidirect
116. #2656C22semidirect
117. #2656C22semidirect
118. #2656C22semidirect
119. #2639C22semidirect
120. #2620C22semidirect
121. #2620C22semidirect
122. #2619C22semidirect
123. #2619C22semidirect
124. #2618C22semidirect
125. #2617C22semidirect
126. #2564C22semidirect
127. #2556C22semidirect
128. #2555C22semidirect
129. #2555C22semidirect
130. #2554C22semidirect
131. #2553C22semidirect
132. #2543C22semidirect
133. #2543C22semidirect
134. #2543C22semidirect
135. #2542C22semidirect
136. #2541C22semidirect
137. #2541C22semidirect
138. #2540C22semidirect
139. #2540C22semidirect
140. #2539C22semidirect
141. #2539C22semidirect
142. #2537C22semidirect
143. #2521C22semidirect
144. #2519C22semidirect
145. #2501C22semidirect
146. #2498C22semidirect
147. #2491C22semidirect
148. #2479C22semidirect
149. #2472C22semidirect
150. #2471C22semidirect
151. #2467C22semidirect
152. #2464C22semidirect
153. #2464C22semidirect
154. #2461C22semidirect
155. #2456C22semidirect
156. #2456C22semidirect
157. #2455C22semidirect
158. #2454C22semidirect
159. #2449C22semidirect
160. #2449C22semidirect
161. #2443C22semidirect
162. #2441C22semidirect
163. #2440C22semidirect
164. #2437C22semidirect
165. #2437C22semidirect
166. #2433C22semidirect
167. #2433C22semidirect
168. #2430C22semidirect
169. #2430C22semidirect
170. #2430C22semidirect
171. #2428C22semidirect
172. #2428C22semidirect
173. #2428C22semidirect
174. #2428C22semidirect
176. #2424C22semidirect
177. #2424C22semidirect
178. #2424C22semidirect
179. #2424C22semidirect
180. #2422C22semidirect
181. #2418C22semidirect
182. #2418C22semidirect
184. #2416C22semidirect
185. #2416C22semidirect
186. #2416C22semidirect
187. #2416C22semidirect
188. #2416C22semidirect
189. #2414C22semidirect
190. #2414C22semidirect
191. #2414C22semidirect
192. #2411C22semidirect
193. #2411C22semidirect
194. #2410C22semidirect
195. #2410C22semidirect
196. #2410C22semidirect
197. #2410C22semidirect
198. #2410C22semidirect
199. #2410C22semidirect
200. #2410C22semidirect
202. #2408C22semidirect
203. #2403C22semidirect
204. C2×#399C22semidirect
205. C2×#392C22semidirect
206. #2361C22semidirect
207. #2359C22semidirect
208. #2359C22semidirect
209. #2359C22semidirect
210. #2359C22semidirect
211. #2358C22semidirect
212. D4×C4⋊C4C22semidirect
213. D4×C22⋊C4C22semidirect
214. D4×C22⋊C4C22semidirect
215. #2325C22semidirect
216. #2325C22semidirect
217. #2325C22semidirect
218. #2325C22semidirect
219. #2317C22semidirect
220. #2311C22semidirect
221. #2309C22semidirect
222. C4×#121C22semidirect
223. C4×#121C22semidirect
224. C2×#389C22semidirect
225. C2×#388C22semidirect
226. C2×#388C22semidirect
227. C2×#387C22semidirect
228. C2×#387C22semidirect
230. C2×#385C22semidirect
231. C2×#385C22semidirect
232. C2×C4×C4⋊C4C22semidirect
233. C2×C4×C22⋊C4C22semidirect
234. C2×C4×C22⋊C4C22semidirect
235. C22×#95C22semidirect
291. C2×#123D4semidirect
767. C23×C4C2×D4semidirect
827. #123C2×D4semidirect
828. #123C2×D4semidirect
938. C2×C4⋊C4C2×D4semidirect
939. C2×C4⋊C4C2×D4semidirect
990. C2×C22⋊C4C2×D4semidirect
991. C2×C22⋊C4C2×D4semidirect
992. C2×C22⋊C4C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35342
#495872
#495822
#478742
#478712
#440222
#439762
#439322
#438862
#397422
#397382
#376782
#376732
#376722
#367412
#367392
#361232
D4×#1212
#352522
#351662
#350512
#350042
#350032
#350012
C2×#26562
C2×#23592