Finite Group Databasebeta

← #7708556

Subgroups — #7708556

Order 512.

8312 conjugacy classes of subgroups.

The subgroup lattice has 1938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3534C212yesmaximal, complemented
2#59800C214yesmaximal, complemented
3#59273C212yesmaximal, complemented
4#59095C212yesmaximal, complemented
5#45791C214yesmaximal, complemented
6#45487C212yesmaximal, complemented
7#45486C212yesmaximal, complemented
8#39738C212yesmaximal, complemented
9#39457C214yesmaximal, complemented
10#39430C214yesmaximal, complemented
11#39402C212yesmaximal, complemented
12#39401C212yesmaximal, complemented
13#39354C212yesmaximal, complemented
14#39348C212yesmaximal, complemented
15#39336C212yesmaximal, complemented
16#37673C212yesmaximal, complemented
17#37672C212yesmaximal, complemented
18#37446C212yesmaximal, complemented
19#36741C212yesmaximal, complemented
20#36739C212yesmaximal, complemented
21#36624C211yesmaximal, characteristic, complemented
22C2×#2856C211yesmaximal, characteristic, complemented
23#36596C212yesmaximal, complemented
24#36123C212yesmaximal, complemented
25#36123C212yesmaximal, complemented
26D4×#121C212yesmaximal, complemented
27#35166C211yesmaximal, characteristic, complemented
28#35006C211yesmaximal, characteristic, complemented
29#35005C211yesmaximal, characteristic, complemented
30#35001C211yesmaximal, characteristic, complemented
31C2×C4×#123C211yesmaximal, characteristic, complemented
32#3534—232no—
33C2×#562C2214yescomplemented
34C2×#560C2214yescomplemented
35C2×#553C2214yescomplemented
36C2×#551C2214yescomplemented
37C2×#546C2214yescomplemented
38C2×#546C2214yescomplemented
39C2×#546C2214yescomplemented
40C2×D42C2214yes—
41C2×D42C2212yescomplemented
42C2×#540C2214yescomplemented
43C2×#539C2214yescomplemented
44C2×#539C2212yescomplemented
45C2×#538C2214yescomplemented
46C2×#538C2212yescomplemented
47C2×#537C2212yescomplemented
48C2×#537C2212yescomplemented
49C2×#534C2214yescomplemented
50C2×#534C2212yescomplemented
51C2×#534C2212yescomplemented
52C2×#532C2211yescharacteristic, complemented
53C2×#532C2212yescomplemented
54C22×#127C2211yescharacteristic, complemented
55C2×#525C2212yescomplemented
56C22×#123C2211yescharacteristic
57C22×#121C2212yescomplemented
58C22×#121C2212yescomplemented
59C22×#121C2212yescomplemented
60C22×#121C2212yescomplemented
61C22×C4×D4C2211yescharacteristic
62C23×C42C2211yescharacteristic, complemented
63#2857C2211yescharacteristic, complemented
64#2857C2211yescharacteristic, complemented
65#2856C2211yescharacteristic
66#2856C2212yescomplemented
67#2856C2212yescomplemented
68#2856C2212yescomplemented
69#2856C2211yescharacteristic, complemented
70#2856C2212yescomplemented
71#2856C2212yescomplemented
72#2856C2212yescomplemented
73#2856C2211yescharacteristic, complemented
74#2856C2211yescharacteristic, complemented
75#2856C2211yescharacteristic, complemented
76#2856C2211yescharacteristic, complemented
77#2856C2212yescomplemented
78#2856C2212yescomplemented
79#2854C2212yescomplemented
80#2854C2212yescomplemented
81#2854C2212yescomplemented
82#2850C2212yescomplemented
83#2850C2212yescomplemented
84#2847C2212yescomplemented
85#2847C2212yescomplemented
86#2847C2212yescomplemented
87#2816C2214yescomplemented
88#2815C2214yescomplemented
89#2723C2214yescomplemented
90#2721C2214yescomplemented
91#2720C2214yescomplemented
92#2718C2214yescomplemented
93#2714C2214yescomplemented
94#2714C2214yescomplemented
95#2711C2214yescomplemented
96#2710C2214yescomplemented
97#2706C2214yescomplemented
98#2703C2214yescomplemented
99#2696C2214yescomplemented
100#2694C2214yescomplemented
101#2692C2214yescomplemented
102#2685C2214yescomplemented
103#2681C2214yescomplemented
104#2680C2214yescomplemented
105#2678C2214yescomplemented
106#2678C2214yescomplemented
107#2676C2214yescomplemented
108#2676C2214yescomplemented
109#2675C2214yescomplemented
110#2673C2214yescomplemented
111#2673C2214yescomplemented
112#2673C2214yescomplemented
113#2672C2214yescomplemented
114#2671C2214yescomplemented
115#2671C2214yescomplemented
116#2670C2214yescomplemented
117#2669C2214yescomplemented
118#2669C2214yescomplemented
119#2669C2214yescomplemented
120#2668C2214yescomplemented
121#2656C2212yescomplemented
122#2656C2212yescomplemented
123#2656C2212yescomplemented
124#2656C2212yescomplemented
125#2639C2212yescomplemented
126#2639C2212yescomplemented
127#2635C2214yescomplemented
128#2635C2214yescomplemented
129#2623C2214yescomplemented
130#2618C2212yescomplemented
131#2617C2212yescomplemented
132#2613C2214yescomplemented
133#2560C2214yescomplemented
134#2559C2214yescomplemented
135#2558C2214yescomplemented
136#2557C2214yescomplemented
137#2555C2214yescomplemented
138#2555C2214yescomplemented
139#2554C2214yescomplemented
140#2554C2214yescomplemented
141#2552C2212yescomplemented
142#2543C2214yescomplemented
143#2543C2214yescomplemented
144#2543C2214yescomplemented
145#2543C2214yescomplemented
146#2542C2212yescomplemented
147#2542C2212yescomplemented
148#2541C2212yescomplemented
149#2541C2212yescomplemented
150#2541C2212yescomplemented
151#2541C2212yescomplemented
152#2540C2214yescomplemented
153#2540C2214yescomplemented
154#2539C2214yescomplemented
155#2539C2214yescomplemented
156#2537C2212yescomplemented
157#2512C2212yescomplemented
158#2512C2212yescomplemented
159#2512C2212yescomplemented
160#2506C2212yescomplemented
161#2501C2212yescomplemented
162#2501C2212yescomplemented
163#2496C2212yescomplemented
164#2491C2212yescomplemented
165#2491C2212yescomplemented
166#2491C2212yescomplemented
167#2490C2214yescomplemented
168#2482C2214yescomplemented
169#2479C2214yescomplemented
170#2472C2214yescomplemented
171#2472C2214yescomplemented
172#2472C2214yescomplemented
173#2471C2214yescomplemented
174#2467C2214yescomplemented
175#2464C2214yescomplemented
176#2464C2214yescomplemented
177#2464C2214yescomplemented
178#2461C2214yescomplemented
179#2456C2214yescomplemented
180#2452C2212yescomplemented
181#2449C2214yescomplemented
182#2445C2212yescomplemented
183#2445C2212yescomplemented
184#2445C2212yescomplemented
185#2443C2214yescomplemented
186#2440C2212yescomplemented
187#2440C2212yescomplemented
188#2437C2214yescomplemented
189#2433C2212yescomplemented
190#2433C2212yescomplemented
191#2433C2212yescomplemented
192#2433C2212yescomplemented
193#2430C2214yescomplemented
194#2430C2214yescomplemented
195#2428C2212yescomplemented
196#2428C2212yescomplemented
197#2428C2212yescomplemented
198#2428C2212yescomplemented
199#2428C2214yescomplemented
200#2428C2212yescomplemented
201#2424C2214yes—
202#2424C2214yescomplemented
203#2424C2214yescomplemented
204#2424C2214yescomplemented
205#2422C2212yescomplemented
206#2422C2212yescomplemented
207#2422C2212yescomplemented
208#2418C2214yescomplemented
209#2416C2212yes—
210#2416C2214yescomplemented
211#2416C2214yescomplemented
212#2416C2212yescomplemented
213#2410C2214yescomplemented
214#2410C2214yescomplemented
215#2410C2214yescomplemented
216#2410C2214yescomplemented
217#2410C2214yescomplemented
218#2410C2214yescomplemented
219#2408C2212yes—
220#2408C2212yescomplemented
221#2404C2214yescomplemented
222#2403C2214yescomplemented
223#2366C2212yescomplemented
224#2363C2214yescomplemented
225#2361C2212yescomplemented
226#2361C2212yescomplemented
227#2358C2214yescomplemented
228#2358C2214yescomplemented
229#2354C2212yescomplemented
230D4×C4⋊C4C2212yescomplemented
231D4×C22⋊C4C2214yescomplemented
232D4×C22⋊C4C2212yescomplemented
233D4×C22⋊C4C2212yescomplemented
234#2325C2212yescomplemented
235#2325C2212yescomplemented
236C4×#123C2212yescomplemented
237C4×#123C2212yescomplemented
238C4×#123C2212yescomplemented
239C4×#123C2212yescomplemented
240C4×#123C2212yescomplemented
241C4×#123C2212yescomplemented
242C4×#123C2212yescomplemented
243C4×#123C2212yescomplemented
244C4×#121C2212yescomplemented
245C4×#121C2212yescomplemented
246C4×#121C2212yescomplemented
247C4×#121C2212yescomplemented
248C4×#121C2212yescomplemented
249C4×#121C2212yescomplemented
250#2297C2212yescomplemented
251C2×#390C2212yescomplemented
252C2×#390C2212yescomplemented
253C2×#390C2212yescomplemented
254C2×#388C2211yescharacteristic, complemented
255C2×#388C2211yescharacteristic, complemented
256C2×#387C2211yescharacteristic, complemented
257C2×#387C2211yescharacteristic, complemented
258C2×#386C2211yescharacteristic
259C2×#385C2211yescharacteristic, complemented
260#2285C2211yescharacteristic, complemented
261C2×#384C2211yescharacteristic, complemented
262C2×#381C2211yescharacteristic, complemented
263C2×C4×C4⋊C4C2211yescharacteristic, complemented
264C2×C4×C4⋊C4C2211yescharacteristic, complemented
265C2×C4×C22⋊C4C2211yescharacteristic, complemented
266C2×C4×C22⋊C4C2211yescharacteristic, complemented
267C2×C4×C22⋊C4C2211yescharacteristic, complemented
268C22×#41C2312yes—
269C22×#41C2314yes—
270C23×D4C2314yes—
271C23×D4C2312yes—
272C23×D4C2312yes—
273C23×D4C2314yes—
274C23×D4C2314yes—
275C23×D4C2312yes—
276C23×D4C2312yes—
277C23×D4C2311yescharacteristic
278C24×C4C2311yescharacteristic
279C24×C4C2311yescharacteristic
280C24×C4C2311yescharacteristic
281C24×C4C2311yescharacteristic
282#562—232no—
283#560—232no—
284#553—232no—
285#551—232no—
286#546—232no—
287#546—232no—
288#546—232no—
289D42—232no—
290D42—48no—
291#540—232no—
292#539—232no—
293#539—216no—
294#538—232no—
295#538—216no—
296#537—216no—
297#537—48no—
298#534—232no—
299#534—216no—
300#534—48no—
301#532—48no—
302#532—44no—
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×#127—44no—
306C2×#127C2314yes—
307C2×#127C2311yescharacteristic
308C2×#127C2312yes—
309C2×#127C2312yes—
310C2×#127C2311yescharacteristic
311C2×#127C2312yes—
312C2×#127C2311yescharacteristic
313C2×#127C2312yes—
314C2×#127C2312yes—
315C2×#127C2312yes—
316C2×#126C2314yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#125C2314yes—
321C2×#125C2314yes—
322C2×#124C2314yes—
323C2×#124C2314yes—
324C2×#124C2314yes—
325C2×#124C2312yes—
326C2×#124C2314yes—
327#525—216no—
328C2×#123D4116yescomplemented
329C2×#123C2314yes—
330C2×#123C2314yes—
331C2×#123C2314yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2312yes—
342C2×#123C2312yes—
343C2×#123C2312yes—
344C2×#123C2312yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2314yes—
354C2×#121—216no—
355C2×#121—48no—
356C2×#121—48no—
357C2×#121—48no—
358C2×#121C2314yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2314yes—
373C2×#121C2314yes—
374C2×#121C2314yes—
375C2×#121C2314yes—
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2314yes—
379C2×#121C2314yes—
380C2×#121C2314yes—
381C2×#121C2314yes—
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C2×#121C2314yes—
386C2×#121C2312yes—
387C2×#121C2312yes—
388C2×#121C2312yes—
389C2×#121C2312yes—
390C2×#121C2312yes—
391C2×#121C2312yes—
392C2×#121C2314yes—
393C2×#121C2314yes—
394C2×#121C2312yes—
395C2×#121C2314yes—
396C2×#121C2312yes—
397C2×#121C2312yes—
398C2×#121C2314yes—
399C2×#121C2314yes—
400C2×#121C2314yes—
401C2×#121C2314yes—
402C2×#121C2314yes—
403C2×#121C2314yes—
404C2×#121C2312yes—
405C2×#121C2312yes—
406C2×#121C2314yes—
407C2×#121C2314yes—
408C2×#121C2314yes—
409C2×#121C2314yes—
410C2×#120C2314yes—
411C2×#120C2314yes—
412C2×#120C2314yes—
413C2×#120C2314yes—
414C2×#120C2314yes—
415C2×#120C2314yes—
416C2×#120C2314yes—
417C2×#120C2314yes—
418C2×#120C2314yes—
419C2×#120C2314yes—
420C2×#120C2314yes—
421C2×#120C2314yes—
422C2×#120C2314yes—
423C2×#120C2314yes—
424C2×C4×D4—44no—
425C2×C4×D4C2314yes—
426C2×C4×D4C2314yes—
427C2×C4×D4C2314yes—
428C2×C4×D4C2312yes—
429C2×C4×D4C2314yes—
430C2×C4×D4C2314yes—
431C2×C4×D4C2314yes—
432C2×C4×D4C2314yes—
433C2×C4×D4C2314yes—
434C2×C4×D4C2312yes—
435C2×C4×D4C2312yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2312yes—
438C2×C4×D4C2312yes—
439C2×C4×D4C2314yes—
440C2×C4×D4C2312yes—
441C2×C4×D4C2312yes—
442C2×C4×D4C2312yes—
443C2×C4×D4C2312yes—
444C2×#117C2314yes—
445C2×#117C2312yes—
446C22×C4⋊C4C2311yescharacteristic
447C22×C4⋊C4C2312yes—
448C22×C4⋊C4C2312yes—
449C22×C4⋊C4C2312yes—
450C22×C4⋊C4C2311yescharacteristic
451C22×C4⋊C4C2312yes—
452C22×C4⋊C4C2311yescharacteristic
453C22×C4⋊C4C2311yescharacteristic
454C22×C4⋊C4C2311yescharacteristic
455C22×C22⋊C4C2314yes—
456C22×C22⋊C4C2314yes—
457C22×C22⋊C4C2311yescharacteristic
458C22×C22⋊C4C2314yes—
459C22×C22⋊C4C2314yes—
460C22×C22⋊C4C2314yes—
461C22×C22⋊C4C2311yescharacteristic
462C22×C22⋊C4C2311yescharacteristic
463C22×C22⋊C4C2314yes—
464C22×C22⋊C4C2311yescharacteristic
465C22×C22⋊C4C2311yescharacteristic
466C22×C22⋊C4C2311yescharacteristic
467C22×C22⋊C4C2311yescharacteristic
468C22×C22⋊C4C2311yescharacteristic
469C22×C42—44no—
470C22×C42C2311yescharacteristic
471C22×C42C2311yescharacteristic
472C22×C42C2311yescharacteristic
473C22×C42C2311yescharacteristic
474C22×C42C2311yescharacteristic
475C22×C42C2311yescharacteristic
476C22×C42C2311yescharacteristic
477C22×C42C2311yescharacteristic
478C22×C42C2311yescharacteristic
479C22×C42C2311yescharacteristic
480C22×C42C2311yescharacteristic
481C22×C42C2311yescharacteristic
482C22×C42C2311yescharacteristic
483C22×C42C2311yescharacteristic
484C22×C42C2311yescharacteristic
485#400C2314yes—
486#400C2314yes—
487#399C2314yes—
488#399C2314yes—
489#399C2314yes—
490#399C2314yes—
491#399C2314yes—
492#399C2314yes—
493#399C2314yes—
494#399C2314yes—
495#398C2314yes—
496#398C2314yes—
497#398C2314yes—
498#398C2314yes—
499#398C2314yes—
500#397C2314yes—
501#397C2314yes—
502#397C2314yes—
503#397C2314yes—
504#397C2314yes—
505#397C2314yes—
506#397C2314yes—
507#396C2314yes—
508#396C2314yes—
509#396C2314yes—
510#396C2314yes—
511#396C2314yes—
512#396C2314yes—
513#395C2314yes—
514#395C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2314yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#393C2314yes—
539#393C2314yes—
540#393C2314yes—
541#393C2314yes—
542#392C2314yes—
543#392C2314yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2314yes—
549#392C2314yes—
550#392C2314yes—
551#392C2314yes—
552#392C2314yes—
553#392C2314yes—
554#392C2314yes—
555#392C2314yes—
556#392C2314yes—
557#392C2314yes—
558#392C2314yes—
559#392C2314yes—
560#392C2314yes—
561#392C2314yes—
562#392C2314yes—
563#392C2314yes—
564#392C2314yes—
565#391C2312yes—
566#391C2312yes—
567#390C2312yes—
568#390C2312yes—
569#390C2312yes—
570#390C2312yes—
571#390C2314yes—
572#390C2312yes—
573#390C2314yes—
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#390C2312yes—
578#390C2312yes—
579#390C2312yes—
580#390C2312yes—
581#390C2312yes—
582#390C2312yes—
583#390C2314yes—
584#390C2314yes—
585#390C2312yes—
586#390C2314yes—
587#390C2314yes—
588#390C2314yes—
589#390C2312yes—
590#390C2312yes—
591#390C2312yes—
592#390C2314yes—
593#390C2312yes—
594#390C2312yes—
595#390C2312yes—
596#390C2312yes—
597#390C2314yes—
598#390C2312yes—
599#390C2314yes—
600#390C2314yes—
601#390C2312yes—
602#390C2314yes—
603#390C2312yes—
604#390C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2314yes—
612#389C2314yes—
613#389C2312yes—
614#389C2312yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2312yes—
633#388C2312yes—
634#388C2312yes—
635#388C2312yes—
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#388C2312yes—
640#388C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2312yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2312yes—
682#386C2312yes—
683#386C2312yes—
684#386C2312yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2312yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#384C2311yescharacteristic
700#384C2312yes—
701#384C2312yes—
702#384C2312yes—
703#384C2311yescharacteristic
704#384C2311yescharacteristic
705#384C2311yescharacteristic
706#384C2312yes—
707#384C2312yes—
708#382C2312yes—
709#381C2312yes—
710#381C2312yes—
711#381C2312yes—
712#381C2312yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2314yes—
722#380C2314yes—
723#379C2314yes—
724#379C2314yes—
725#379C2314yes—
726#379C2314yes—
727C4×C4⋊C4C2312yes—
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C22⋊C4C2314yes—
740C4×C22⋊C4C2312yes—
741C4×C22⋊C4C2312yes—
742C4×C22⋊C4C2312yes—
743C4×C22⋊C4C2312yes—
744C4×C22⋊C4C2314yes—
745C4×C22⋊C4C2314yes—
746C4×C22⋊C4C2312yes—
747C4×C22⋊C4C2312yes—
748C4×C22⋊C4C2312yes—
749C4×C22⋊C4C2312yes—
750C4×C22⋊C4C2312yes—
751C4×C22⋊C4C2312yes—
752C4×C22⋊C4C2314yes—
753C4×C22⋊C4C2312yes—
754C4×C22⋊C4C2312yes—
755C2×#95C2311yescharacteristic
756C2×#95C2311yescharacteristic
757C2×#95C2311yescharacteristic
758C2×#95C2311yescharacteristic
759C2×#95C2311yescharacteristic
760C2×#95C2311yescharacteristic
761C2×#95C2311yescharacteristic
762C2×#95C2311yescharacteristic
763C2×#95C2311yescharacteristic
764C2×#95C2311yescharacteristic
765C25C2411yescharacteristic
766C25C2414yes—
767C25C2411yescharacteristic
768C25C2414yes—
769C2×#41—28no—
770C2×#41—216no—
771C2×#41—44no—
772C2×#41—48no—
773C2×#41—48no—
774C2×#41—44no—
775C22×Q8C2414yes—
776C22×Q8C2412yes—
777C22×D4—216no—
778C22×D4—216no—
779C22×D4—216no—
780C22×D4—28no—
781C22×D4—28no—
782C22×D4—44no—
783C22×D4—44no—
784C22×D4—44no—
785C22×D4—44no—
786C22×D4—44no—
787C22×D4—44no—
788C22×D4—44no—
789C22×D4—44no—
790C22×D4—44no—
791C22×D4—44no—
792C22×D4—42no—
793C22×D4—42no—
794C22×D4—48no—
795C22×D4—48no—
796C22×D4—48no—
797C22×D4—48no—
798C22×D4—48no—
799C22×D4—48no—
800C22×D4C2×D418yes—
801C22×D4C2412yes—
802C22×D4C2412yes—
803C22×D4C2414yes—
804C22×D4C2414yes—
805C22×D4C2414yes—
806C22×D4C2414yes—
807C22×D4C2412yes—
808C22×D4C2412yes—
809C22×D4C2414yes—
810C22×D4C2414yes—
811C22×D4C2414yes—
812C22×D4C2412yes—
813C22×D4C2414yes—
814C22×D4C2414yes—
815C22×D4C2414yes—
816C22×D4C2414yes—
817C22×D4C2412yes—
818C22×D4C2412yes—
819C22×D4C2412yes—
820C22×D4C2414yes—
821C22×D4C2414yes—
822C22×D4C2414yes—
823C22×D4C2414yes—
824C22×D4C2414yes—
825C22×D4C2412yes—
826C22×D4C2414yes—
827C22×D4C2412yes—
828C22×D4C2414yes—
829C22×D4C2414yes—
830C22×D4C2414yes—
831C22×D4C2414yes—
832C22×D4C2412yes—
833C23×C4—24no—
834C23×C4—24no—
835C23×C4—24no—
836C23×C4—24no—
837C23×C4—42no—
838C23×C4—42no—
839C23×C4—42no—
840C23×C4—42no—
841C23×C4—42no—
842C23×C4—42no—
843C23×C4—42no—
844C23×C4C2×D418yescomplemented
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2414yes—
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2414yes—
865C23×C4C2411yescharacteristic
866C23×C4C2414yes—
867C23×C4C2414yes—
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2414yes—
871C23×C4C2411yescharacteristic
872C23×C4C2411yescharacteristic
873C23×C4C2411yescharacteristic
874C23×C4C2411yescharacteristic
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2411yescharacteristic
878C23×C4C2411yescharacteristic
879C4⋊Q8—42no—
880C4⋊Q8—44no—
881#127—216no—
882#127—42no—
883#127—44no—
884#127—42no—
885#127—44no—
886#127—44no—
887#127—44no—
888#127—42no—
889#127—44no—
890#127—44no—
891#126—216no—
892#126—216no—
893#126—216no—
894#126—216no—
895#125—216no—
896#125—216no—
897#124—216no—
898#124—216no—
899#124—216no—
900#124—44no—
901#124—48no—
902#123—216no—
903#123—216no—
904#123—216no—
905#123—216no—
906#123—216no—
907#123—216no—
908#123—216no—
909#123—216no—
910#123—216no—
911#123—216no—
912#123—48no—
913#123—48no—
914#123C2×D4116yescomplemented
915#123C2×D4116yescomplemented
916#123C2×D4116yescomplemented
917#123C2×D4116yescomplemented
918C22⋊Q8—28no—
919C22⋊Q8—28no—
920C22⋊Q8—216no—
921C22⋊Q8—216no—
922C22⋊Q8—216no—
923C22⋊Q8—216no—
924C22⋊Q8—216no—
925C22⋊Q8—48no—
926C22⋊Q8—48no—
927#121—216no—
928#121—216no—
929#121—216no—
930#121—28no—
931#121—28no—
932#121—28no—
933#121—28no—
934#121—216no—
935#121—216no—
936#121—28no—
937#121—28no—
938#121—216no—
939#121—216no—
940#121—28no—
941#121—28no—
942#121—28no—
943#121—28no—
944#121—28no—
945#121—28no—
946#121—28no—
947#121—216no—
948#121—216no—
949#121—216no—
950#121—216no—
951#121—216no—
952#121—216no—
953#121—216no—
954#121—216no—
955#121—48no—
956#121—48no—
957#121—48no—
958#121—44no—
959#121—48no—
960#121—48no—
961#121—48no—
962#121—48no—
963#121—44no—
964#121—44no—
965#121—44no—
966#121—44no—
967#121—44no—
968#121—44no—
969#121—44no—
970#121—44no—
971#121—44no—
972#121—48no—
973#121—48no—
974#121—48no—
975#121—44no—
976#121—48no—
977#121—48no—
978#121—48no—
979#120—216no—
980#120—216no—
981#120—216no—
982#120—216no—
983#120—216no—
984#120—216no—
985#120—216no—
986#120—216no—
987#120—48no—
988#120—48no—
989#120—48no—
990#120—48no—
991#120—48no—
992#120—48no—
993C4×D4—216no—
994C4×D4—216no—
995C4×D4—216no—
996C4×D4—216no—
997C4×D4—216no—
998C4×D4—28no—
999C4×D4—216no—
1000C4×D4—216no—
1001C4×D4—216no—
1002C4×D4—44no—
1003C4×D4—48no—
1004C4×D4—44no—
1005C4×D4—44no—
1006C4×D4—44no—
1007C4×D4—44no—
1008C4×D4—44no—
1009C4×D4—44no—
1010C4×D4—44no—
1011C4×D4—44no—
1012#117—28no—
1013#117—216no—
1014C2×C4⋊C4—28no—
1015C2×C4⋊C4—24no—
1016C2×C4⋊C4—42no—
1017C2×C4⋊C4—42no—
1018C2×C4⋊C4—44no—
1019C2×C4⋊C4—44no—
1020C2×C4⋊C4—44no—
1021C2×C4⋊C4C2×D418yescomplemented
1022C2×C4⋊C4C2×D418yescomplemented
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C22⋊C4—216no—
1063C2×C22⋊C4—24no—
1064C2×C22⋊C4—216no—
1065C2×C22⋊C4—216no—
1066C2×C22⋊C4—42no—
1067C2×C22⋊C4—42no—
1068C2×C22⋊C4—48no—
1069C2×C22⋊C4—48no—
1070C2×C22⋊C4—48no—
1071C2×C22⋊C4—42no—
1072C2×C22⋊C4—42no—
1073C2×C22⋊C4C2×D418yescomplemented
1074C2×C22⋊C4C2×D418yescomplemented
1075C2×C22⋊C4C2×D418yescomplemented
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2412yes—
1136C2×C22⋊C4C2412yes—
1137C2×C22⋊C4C2412yes—
1138C2×C22⋊C4C2412yes—
1139C2×C22⋊C4C2412yes—
1140C2×C22⋊C4C2412yes—
1141C2×C42—24no—
1142C2×C42—24no—
1143C2×C42—24no—
1144C2×C42—42no—
1145C2×C42—42no—
1146C2×C42—42no—
1147C2×C42—42no—
1148C2×C42—42no—
1149C2×C42—42no—
1150C2×C42—42no—
1151C2×C42—42no—
1152C2×C42—42no—
1153C2×C42—42no—
1154C2×C42—42no—
1155C2×C42—42no—
1156C2×C42C2414yes—
1157C2×C42C2414yes—
1158C2×C42C2414yes—
1159C2×C42C2412yes—
1160C2×C42C2412yes—
1161C2×C42C2412yes—
1162C2×C42C2411yescharacteristic
1163C2×C42C2411yescharacteristic
1164C2×C42C2412yes—
1165C2×C42C2411yescharacteristic
1166C2×C42C2411yescharacteristic
1167C2×C42C2411yescharacteristic
1168C2×C42C2411yescharacteristic
1169C2×C42C2411yescharacteristic
1170C2×C42C2411yescharacteristic
1171C2×C42C2412yes—
1172C2×C42C2412yes—
1173C2×C42C2411yescharacteristic
1174C2×C42C2411yescharacteristic
1175C2×C42C2411yescharacteristic
1176C2×C42C2411yescharacteristic
1177C2×C42C2411yescharacteristic
1178C2×C42C2411yescharacteristic
1179C2×C42C2411yescharacteristic
1180C2×C42C2411yescharacteristic
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215C24—22no—
1216C24—22no—
1217C24—22no—
1218C24—22no—
1219C24—22no—
1220C24—22no—
1221C24—28no—
1222C24—28no—
1223C24—28no—
1224C24—28no—
1225C24—41no—
1226C24—41no—
1227C24—41no—
1228C24—41no—
1229C24—41no—
1230C24—41no—
1231C24—44no—
1232C24—44no—
1233C24—44no—
1234C24—44no—
1235C24—44no—
1236C24—44no—
1237C24—44no—
1238C24—44no—
1239C24—44no—
1240C24—44no—
1241C24C22×D414yes—
1242C24C22×D414yes—
1243C24C2514yes—
1244C24C2514yes—
1245C24C2514yes—
1246C24C2512yes—
1247C24C2511yescharacteristic
1248C24C2511yescharacteristic
1249C24C2511yescharacteristic
1250#41—816no—
1251#41—832no—
1252C2×Q8—24no—
1253C2×Q8—28no—
1254C2×Q8—44no—
1255C2×Q8—42no—
1256C2×Q8—44no—
1257C2×Q8—42no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—28no—
1261C2×D4—28no—
1262C2×D4—28no—
1263C2×D4—28no—
1264C2×D4—28no—
1265C2×D4—28no—
1266C2×D4—28no—
1267C2×D4—28no—
1268C2×D4—28no—
1269C2×D4—28no—
1270C2×D4—28no—
1271C2×D4—28no—
1272C2×D4—28no—
1273C2×D4—28no—
1274C2×D4—28no—
1275C2×D4—28no—
1276C2×D4—28no—
1277C2×D4—28no—
1278C2×D4—28no—
1279C2×D4—28no—
1280C2×D4—24no—
1281C2×D4—28no—
1282C2×D4—24no—
1283C2×D4—28no—
1284C2×D4—24no—
1285C2×D4—28no—
1286C2×D4—24no—
1287C2×D4—24no—
1288C2×D4—24no—
1289C2×D4—24no—
1290C2×D4—24no—
1291C2×D4—24no—
1292C2×D4—24no—
1293C2×D4—24no—
1294C2×D4—28no—
1295C2×D4—24no—
1296C2×D4—24no—
1297C2×D4—24no—
1298C2×D4—24no—
1299C2×D4—28no—
1300C2×D4—42no—
1301C2×D4—42no—
1302C2×D4—42no—
1303C2×D4—44no—
1304C2×D4—44no—
1305C2×D4—44no—
1306C2×D4—44no—
1307C2×D4—44no—
1308C2×D4—44no—
1309C2×D4—44no—
1310C2×D4—44no—
1311C2×D4—44no—
1312C2×D4—44no—
1313C2×D4—44no—
1314C2×D4—44no—
1315C2×D4—44no—
1316C2×D4—44no—
1317C2×D4—44no—
1318C2×D4—44no—
1319C2×D4—44no—
1320C2×D4—44no—
1321C2×D4—44no—
1322C2×D4—44no—
1323C2×D4—42no—
1324C2×D4—44no—
1325C2×D4—44no—
1326C2×D4—44no—
1327C2×D4—42no—
1328C2×D4—44no—
1329C2×D4—42no—
1330C2×D4—42no—
1331C2×D4—44no—
1332C2×D4—44no—
1333C2×D4—42no—
1334C2×D4—42no—
1335C2×D4—44no—
1336C2×D4—44no—
1337C2×D4—42no—
1338C2×D4—42no—
1339C2×D4—44no—
1340C2×D4—42no—
1341C2×D4—42no—
1342C2×D4—44no—
1343C2×D4—44no—
1344C2×D4—44no—
1345C2×D4—42no—
1346C2×D4—44no—
1347C2×D4—44no—
1348C2×D4—44no—
1349C2×D4—44no—
1350C2×D4—44no—
1351C2×D4—44no—
1352C2×D4—416no—
1353C2×D4—816no—
1354C2×D4—816no—
1355C2×D4—816no—
1356C2×D4—816no—
1357C2×D4—832no—
1358C2×D4—832no—
1359C2×D4—832no—
1360C2×D4C22×D418yes—
1361C2×D4C22×D418yes—
1362C22×C4—22no—
1363C22×C4—22no—
1364C22×C4—22no—
1365C22×C4—22no—
1366C22×C4—22no—
1367C22×C4—22no—
1368C22×C4—22no—
1369C22×C4—22no—
1370C22×C4—22no—
1371C22×C4—22no—
1372C22×C4—22no—
1373C22×C4—22no—
1374C22×C4—22no—
1375C22×C4—22no—
1376C22×C4—22no—
1377C22×C4—22no—
1378C22×C4—22no—
1379C22×C4—28no—
1380C22×C4—28no—
1381C22×C4—22no—
1382C22×C4—22no—
1383C22×C4—22no—
1384C22×C4—22no—
1385C22×C4—22no—
1386C22×C4—22no—
1387C22×C4—22no—
1388C22×C4—22no—
1389C22×C4—22no—
1390C22×C4—24no—
1391C22×C4—24no—
1392C22×C4—22no—
1393C22×C4—22no—
1394C22×C4—22no—
1395C22×C4—22no—
1396C22×C4—22no—
1397C22×C4—22no—
1398C22×C4—22no—
1399C22×C4—24no—
1400C22×C4—28no—
1401C22×C4—28no—
1402C22×C4—28no—
1403C22×C4—28no—
1404C22×C4—28no—
1405C22×C4—24no—
1406C22×C4—41no—
1407C22×C4—41no—
1408C22×C4—41no—
1409C22×C4—41no—
1410C22×C4—41no—
1411C22×C4—41no—
1412C22×C4—41no—
1413C22×C4—41no—
1414C22×C4—41no—
1415C22×C4—41no—
1416C22×C4—41no—
1417C22×C4—416no—
1418C22×C4—41no—
1419C22×C4—41no—
1420C22×C4—41no—
1421C22×C4—41no—
1422C22×C4—41no—
1423C22×C4—41no—
1424C22×C4—41no—
1425C22×C4—41no—
1426C22×C4—41no—
1427C22×C4—41no—
1428C22×C4—41no—
1429C22×C4—416no—
1430C22×C4—41no—
1431C22×C4—41no—
1432C22×C4—41no—
1433C22×C4—44no—
1434C22×C4—44no—
1435C22×C4—44no—
1436C22×C4—41no—
1437C22×C4—41no—
1438C22×C4—41no—
1439C22×C4—41no—
1440C22×C4—42no—
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—42no—
1451C22×C4—41no—
1452C22×C4—44no—
1453C22×C4—44no—
1454C22×C4—416no—
1455C22×C4—88no—
1456C22×C4C22×D414yes—
1457C22×C4C22×D414yes—
1458C22×C4C22×D414yes—
1459C22×C4C22×D414yes—
1460C22×C4C22×D414yes—
1461C22×C4C22×D414yes—
1462C22×C4C22×D414yes—
1463C22×C4C22×D414yes—
1464C22×C4C22×D414yes—
1465C22×C4H(5,𝔽2)14yes—
1466C22×C4H(5,𝔽2)14yes—
1467C22×C4H(5,𝔽2)14yes—
1468C22×C4C2512yes—
1469C22×C4C2512yes—
1470C22×C4C2512yes—
1471C22×C4C2511yescharacteristic
1472C22×C4C2511yescharacteristic
1473C22×C4C2514yes—
1474C22×C4C2512yes—
1475C22×C4C2514yes—
1476C22×C4C2514yes—
1477C22×C4C2514yes—
1478C22×C4C2514yes—
1479C22×C4C2511yescharacteristic
1480C22×C4C2512yes—
1481C22×C4C2511yescharacteristic
1482C22×C4C2511yescharacteristic
1483C22×C4C2511yescharacteristic
1484C22×C4C2512yes—
1485C22×C4C2512yes—
1486C22×C4C2511yescharacteristic
1487C22×C4C2511yescharacteristic
1488C22×C4C2511yescharacteristic
1489C22×C4C2511yescharacteristic
1490C22×C4C2511yescharacteristic
1491C22×C4C2511yescharacteristic
1492C4⋊C4—24no—
1493C4⋊C4—28no—
1494C4⋊C4—24no—
1495C4⋊C4—24no—
1496C4⋊C4—28no—
1497C4⋊C4—24no—
1498C4⋊C4—28no—
1499C4⋊C4—28no—
1500C4⋊C4—28no—
1501C4⋊C4—28no—
1502C4⋊C4—28no—
1503C4⋊C4—28no—
1504C4⋊C4—28no—
1505C4⋊C4—24no—
1506C4⋊C4—24no—
1507C4⋊C4—24no—
1508C4⋊C4—24no—
1509C4⋊C4—24no—
1510C4⋊C4—24no—
1511C4⋊C4—24no—
1512C4⋊C4—24no—
1513C4⋊C4—24no—
1514C4⋊C4—24no—
1515C4⋊C4—24no—
1516C4⋊C4—24no—
1517C4⋊C4—42no—
1518C4⋊C4—42no—
1519C4⋊C4—44no—
1520C4⋊C4—44no—
1521C4⋊C4—44no—
1522C4⋊C4—42no—
1523C4⋊C4—44no—
1524C4⋊C4—42no—
1525C4⋊C4—44no—
1526C4⋊C4—44no—
1527C4⋊C4C22×D418yes—
1528C4⋊C4C22×D418yes—
1529C4⋊C4C22×D418yes—
1530C4⋊C4C22×D418yes—
1531C22⋊C4—28no—
1532C22⋊C4—28no—
1533C22⋊C4—28no—
1534C22⋊C4—28no—
1535C22⋊C4—28no—
1536C22⋊C4—24no—
1537C22⋊C4—24no—
1538C22⋊C4—28no—
1539C22⋊C4—28no—
1540C22⋊C4—28no—
1541C22⋊C4—28no—
1542C22⋊C4—28no—
1543C22⋊C4—28no—
1544C22⋊C4—28no—
1545C22⋊C4—28no—
1546C22⋊C4—28no—
1547C22⋊C4—28no—
1548C22⋊C4—28no—
1549C22⋊C4—28no—
1550C22⋊C4—28no—
1551C22⋊C4—28no—
1552C22⋊C4—24no—
1553C22⋊C4—24no—
1554C22⋊C4—28no—
1555C22⋊C4—24no—
1556C22⋊C4—28no—
1557C22⋊C4—28no—
1558C22⋊C4—28no—
1559C22⋊C4—28no—
1560C22⋊C4—28no—
1561C22⋊C4—28no—
1562C22⋊C4—24no—
1563C22⋊C4—28no—
1564C22⋊C4—42no—
1565C22⋊C4—42no—
1566C22⋊C4—42no—
1567C22⋊C4—42no—
1568C22⋊C4—44no—
1569C22⋊C4—44no—
1570C22⋊C4—44no—
1571C22⋊C4—44no—
1572C22⋊C4—44no—
1573C22⋊C4—44no—
1574C22⋊C4—44no—
1575C22⋊C4—44no—
1576C22⋊C4—44no—
1577C22⋊C4—44no—
1578C22⋊C4—44no—
1579C22⋊C4—44no—
1580C22⋊C4—44no—
1581C22⋊C4—44no—
1582C22⋊C4—44no—
1583C22⋊C4—44no—
1584C22⋊C4—44no—
1585C22⋊C4—44no—
1586C22⋊C4—44no—
1587C22⋊C4—44no—
1588C22⋊C4—44no—
1589C22⋊C4—44no—
1590C22⋊C4C22×D418yes—
1591C22⋊C4C22×D418yes—
1592C22⋊C4C22×D418yes—
1593C22⋊C4C22×D418yes—
1594C22⋊C4C22×D418yes—
1595C22⋊C4C22×D418yes—
1596C42—28no—
1597C42—28no—
1598C42—28no—
1599C42—22no—
1600C42—22no—
1601C42—22no—
1602C42—22no—
1603C42—22no—
1604C42—22no—
1605C42—22no—
1606C42—22no—
1607C42—24no—
1608C42—24no—
1609C42—24no—
1610C42—24no—
1611C42—41no—
1612C42—41no—
1613C42—41no—
1614C42—41no—
1615C42—41no—
1616C42—41no—
1617C42—41no—
1618C42—41no—
1619C42—42no—
1620C42—42no—
1621C23—21no—
1622C23—21no—
1623C23—21no—
1624C23—21no—
1625C23—21no—
1626C23—21no—
1627C23—21no—
1628C23—21no—
1629C23—22no—
1630C23—22no—
1631C23—21no—
1632C23—22no—
1633C23—21no—
1634C23—21no—
1635C23—22no—
1636C23—21no—
1637C23—21no—
1638C23—21no—
1639C23—22no—
1640C23—22no—
1641C23—28no—
1642C23—28no—
1643C23—28no—
1644C23—24no—
1645C23—24no—
1646C23—24no—
1647C23—24no—
1648C23—24no—
1649C23—24no—
1650C23—24no—
1651C23—24no—
1652C23—24no—
1653C23—24no—
1654C23—24no—
1655C23—24no—
1656C23—24no—
1657C23—24no—
1658C23—24no—
1659C23—24no—
1660C23—24no—
1661C23—24no—
1662C23—24no—
1663C23—24no—
1664C23—24no—
1665C23—44no—
1666C23—44no—
1667C23—44no—
1668C23—44no—
1669C23—44no—
1670C23—44no—
1671C23—44no—
1672C23—416no—
1673C23—82no—
1674C23—82no—
1675C23—82no—
1676C23—82no—
1677C23—88no—
1678C23—88no—
1679C23—88no—
1680C23—88no—
1681C23—88no—
1682C23—88no—
1683C23—88no—
1684C23—88no—
1685C23—88no—
1686C23—88no—
1687C23—88no—
1688C23—164no—
1689C23—164no—
1690C23C23×D414yes—
1691C23C23×D412yes—
1692C23C23×D412yes—
1693C23C23×D412yes—
1694C23C2×H(5,𝔽2)12yes—
1695C23C2×H(5,𝔽2)12yes—
1696C23C2×H(5,𝔽2)12yes—
1697C23#58512yes—
1698C23C2611yescharacteristic
1699Q8—84no—
1700Q8—88no—
1701D4—216no—
1702D4—48no—
1703D4—416no—
1704D4—416no—
1705D4—416no—
1706D4—416no—
1707D4—48no—
1708D4—48no—
1709D4—48no—
1710D4—88no—
1711D4—84no—
1712D4—88no—
1713D4—84no—
1714D4—88no—
1715D4—84no—
1716D4—88no—
1717D4—84no—
1718D4—84no—
1719D4—88no—
1720D4—84no—
1721D4—88no—
1722D4—88no—
1723D4—88no—
1724D4—88no—
1725D4—88no—
1726D4—88no—
1727D4—88no—
1728D4—88no—
1729D4—88no—
1730D4—88no—
1731D4—164no—
1732D4—164no—
1733C2×C4—28no—
1734C2×C4—21no—
1735C2×C4—21no—
1736C2×C4—21no—
1737C2×C4—21no—
1738C2×C4—21no—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—22no—
1742C2×C4—22no—
1743C2×C4—21no—
1744C2×C4—22no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—22no—
1748C2×C4—21no—
1749C2×C4—22no—
1750C2×C4—21no—
1751C2×C4—21no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—21no—
1756C2×C4—21no—
1757C2×C4—22no—
1758C2×C4—28no—
1759C2×C4—28no—
1760C2×C4—28no—
1761C2×C4—28no—
1762C2×C4—28no—
1763C2×C4—24no—
1764C2×C4—24no—
1765C2×C4—24no—
1766C2×C4—24no—
1767C2×C4—24no—
1768C2×C4—21no—
1769C2×C4—22no—
1770C2×C4—22no—
1771C2×C4—21no—
1772C2×C4—22no—
1773C2×C4—22no—
1774C2×C4—24no—
1775C2×C4—24no—
1776C2×C4—24no—
1777C2×C4—24no—
1778C2×C4—24no—
1779C2×C4—24no—
1780C2×C4—24no—
1781C2×C4—21no—
1782C2×C4—21no—
1783C2×C4—22no—
1784C2×C4—22no—
1785C2×C4—22no—
1786C2×C4—22no—
1787C2×C4—22no—
1788C2×C4—22no—
1789C2×C4—24no—
1790C2×C4—21no—
1791C2×C4—24no—
1792C2×C4—22no—
1793C2×C4—21no—
1794C2×C4—22no—
1795C2×C4—24no—
1796C2×C4—44no—
1797C2×C4—44no—
1798C2×C4—44no—
1799C2×C4—44no—
1800C2×C4—44no—
1801C2×C4—44no—
1802C2×C4—44no—
1803C2×C4—44no—
1804C2×C4—44no—
1805C2×C4—44no—
1806C2×C4—44no—
1807C2×C4—44no—
1808C2×C4—44no—
1809C2×C4—44no—
1810C2×C4—44no—
1811C2×C4—48no—
1812C2×C4—88no—
1813C2×C4—84no—
1814C2×C4—88no—
1815C2×C4—88no—
1816C2×C4—88no—
1817C2×C4—88no—
1818C2×C4—82no—
1819C2×C4—82no—
1820C2×C4—82no—
1821C2×C4—82no—
1822C2×C4—88no—
1823C2×C4—88no—
1824C2×C4C23×D412yes—
1825C2×C4C23×D414yes—
1826C2×C4C23×D414yes—
1827C2×C4C23×D412yes—
1828C2×C4C23×D414yes—
1829C2×C4C23×D412yes—
1830C2×C4C23×D412yes—
1831C2×C4C2×H(5,𝔽2)12yes—
1832C2×C4C2×H(5,𝔽2)12yes—
1833C2×C4C2×H(5,𝔽2)12yes—
1834C2×C4C2×H(5,𝔽2)12yes—
1835C2×C4C2×H(5,𝔽2)12yes—
1836C2×C4C2×H(5,𝔽2)12yes—
1837C2×C4#58512yes—
1838C2×C4#58512yes—
1839C22—22no—
1840C22—22no—
1841C22—22no—
1842C22—22no—
1843C22—22no—
1844C22—22no—
1845C22—22no—
1846C22—22no—
1847C22—22no—
1848C22—22no—
1849C22—22no—
1850C22—22no—
1851C22—22no—
1852C22—24no—
1853C22—24no—
1854C22—22no—
1855C22—22no—
1856C22—24no—
1857C22—416no—
1858C22—41no—
1859C22—42no—
1860C22—41no—
1861C22—42no—
1862C22—41no—
1863C22—42no—
1864C22—41no—
1865C22—42no—
1866C22—44no—
1867C22—44no—
1868C22—44no—
1869C22—44no—
1870C22—44no—
1871C22—44no—
1872C22—44no—
1873C22—44no—
1874C22—44no—
1875C22—44no—
1876C22—44no—
1877C22—44no—
1878C22—44no—
1879C22—44no—
1880C22—44no—
1881C22—44no—
1882C22—44no—
1883C22—44no—
1884C22—44no—
1885C22—44no—
1886C22—44no—
1887C22—88no—
1888C22—1616no—
1889C22—1616no—
1890C22#349614yes—
1891C22#349814yes—
1892C22C24×D411yescharacteristic
1893C22C22×H(5,𝔽2)11yescharacteristic
1894C22C22×H(5,𝔽2)11yescharacteristic
1895C22C22×H(5,𝔽2)11yescharacteristic
1896C22C2×#58511yescharacteristic
1897C22C2×#58511yescharacteristic
1898C22C2×#58511yescharacteristic
1899C4—22no—
1900C4—22no—
1901C4—22no—
1902C4—22no—
1903C4—22no—
1904C4—22no—
1905C4—24no—
1906C4—24no—
1907C4—24no—
1908C4—22no—
1909C4—22no—
1910C4—22no—
1911C4—41no—
1912C4—42no—
1913C4—42no—
1914C4—44no—
1915C4—44no—
1916C4—44no—
1917C4—44no—
1918C4—44no—
1919C4—41no—
1920C4—42no—
1921C4—42no—
1922C4#353414yescomplemented
1923C2—24no—
1924C2—24no—
1925C2—42no—
1926C2—44no—
1927C2—84no—
1928C2—84no—
1929C2—84no—
1930C2C2×#353411yescharacteristic
1931C2#6274811yescharacteristic
1932C2C2×#349611yescharacteristic
1933C2C2×#349811yescharacteristic
1934C2#6281211yescharacteristic
1935C2#6281811yescharacteristic
1936C2#6283011yescharacteristic
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. #59800C2semidirect
3. #59273C2semidirect
4. #59095C2semidirect
5. #45791C2semidirect
6. #45487C2semidirect
7. #45486C2semidirect
8. #39738C2semidirect
9. #39457C2semidirect
10. #39430C2semidirect
11. #39402C2semidirect
12. #39401C2semidirect
13. #39354C2semidirect
14. #39348C2semidirect
15. #39336C2semidirect
16. #37673C2semidirect
17. #37672C2semidirect
18. #37446C2semidirect
19. #36741C2semidirect
20. #36739C2semidirect
21. #36624C2semidirect
22. C2×#2856C2semidirect
23. #36596C2semidirect
24. #36123C2semidirect
25. #36123C2semidirect
26. D4×#121C2semidirect
27. #35166C2semidirect
28. #35006C2semidirect
29. #35005C2semidirect
30. #35001C2semidirect
31. C2×C4×#123C2semidirect
33. C2×#562C22semidirect
34. C2×#560C22semidirect
35. C2×#553C22semidirect
36. C2×#551C22semidirect
37. C2×#546C22semidirect
38. C2×#546C22semidirect
39. C2×#546C22semidirect
41. C2×D42C22semidirect
42. C2×#540C22semidirect
43. C2×#539C22semidirect
44. C2×#539C22semidirect
45. C2×#538C22semidirect
46. C2×#538C22semidirect
47. C2×#537C22semidirect
48. C2×#537C22semidirect
49. C2×#534C22semidirect
50. C2×#534C22semidirect
51. C2×#534C22semidirect
52. C2×#532C22semidirect
53. C2×#532C22semidirect
54. C22×#127C22semidirect
55. C2×#525C22semidirect
57. C22×#121C22semidirect
58. C22×#121C22semidirect
59. C22×#121C22semidirect
60. C22×#121C22semidirect
62. C23×C42C22semidirect
63. #2857C22semidirect
64. #2857C22semidirect
66. #2856C22semidirect
67. #2856C22semidirect
68. #2856C22semidirect
69. #2856C22semidirect
70. #2856C22semidirect
71. #2856C22semidirect
72. #2856C22semidirect
73. #2856C22semidirect
74. #2856C22semidirect
75. #2856C22semidirect
76. #2856C22semidirect
77. #2856C22semidirect
78. #2856C22semidirect
79. #2854C22semidirect
80. #2854C22semidirect
81. #2854C22semidirect
82. #2850C22semidirect
83. #2850C22semidirect
84. #2847C22semidirect
85. #2847C22semidirect
86. #2847C22semidirect
87. #2816C22semidirect
88. #2815C22semidirect
89. #2723C22semidirect
90. #2721C22semidirect
91. #2720C22semidirect
92. #2718C22semidirect
93. #2714C22semidirect
94. #2714C22semidirect
95. #2711C22semidirect
96. #2710C22semidirect
97. #2706C22semidirect
98. #2703C22semidirect
99. #2696C22semidirect
100. #2694C22semidirect
101. #2692C22semidirect
102. #2685C22semidirect
103. #2681C22semidirect
104. #2680C22semidirect
105. #2678C22semidirect
106. #2678C22semidirect
107. #2676C22semidirect
108. #2676C22semidirect
109. #2675C22semidirect
110. #2673C22semidirect
111. #2673C22semidirect
112. #2673C22semidirect
113. #2672C22semidirect
114. #2671C22semidirect
115. #2671C22semidirect
116. #2670C22semidirect
117. #2669C22semidirect
118. #2669C22semidirect
119. #2669C22semidirect
120. #2668C22semidirect
121. #2656C22semidirect
122. #2656C22semidirect
123. #2656C22semidirect
124. #2656C22semidirect
125. #2639C22semidirect
126. #2639C22semidirect
127. #2635C22semidirect
128. #2635C22semidirect
129. #2623C22semidirect
130. #2618C22semidirect
131. #2617C22semidirect
132. #2613C22semidirect
133. #2560C22semidirect
134. #2559C22semidirect
135. #2558C22semidirect
136. #2557C22semidirect
137. #2555C22semidirect
138. #2555C22semidirect
139. #2554C22semidirect
140. #2554C22semidirect
141. #2552C22semidirect
142. #2543C22semidirect
143. #2543C22semidirect
144. #2543C22semidirect
145. #2543C22semidirect
146. #2542C22semidirect
147. #2542C22semidirect
148. #2541C22semidirect
149. #2541C22semidirect
150. #2541C22semidirect
151. #2541C22semidirect
152. #2540C22semidirect
153. #2540C22semidirect
154. #2539C22semidirect
155. #2539C22semidirect
156. #2537C22semidirect
157. #2512C22semidirect
158. #2512C22semidirect
159. #2512C22semidirect
160. #2506C22semidirect
161. #2501C22semidirect
162. #2501C22semidirect
163. #2496C22semidirect
164. #2491C22semidirect
165. #2491C22semidirect
166. #2491C22semidirect
167. #2490C22semidirect
168. #2482C22semidirect
169. #2479C22semidirect
170. #2472C22semidirect
171. #2472C22semidirect
172. #2472C22semidirect
173. #2471C22semidirect
174. #2467C22semidirect
175. #2464C22semidirect
176. #2464C22semidirect
177. #2464C22semidirect
178. #2461C22semidirect
179. #2456C22semidirect
180. #2452C22semidirect
181. #2449C22semidirect
182. #2445C22semidirect
183. #2445C22semidirect
184. #2445C22semidirect
185. #2443C22semidirect
186. #2440C22semidirect
187. #2440C22semidirect
188. #2437C22semidirect
189. #2433C22semidirect
190. #2433C22semidirect
191. #2433C22semidirect
192. #2433C22semidirect
193. #2430C22semidirect
194. #2430C22semidirect
195. #2428C22semidirect
196. #2428C22semidirect
197. #2428C22semidirect
198. #2428C22semidirect
199. #2428C22semidirect
200. #2428C22semidirect
202. #2424C22semidirect
203. #2424C22semidirect
204. #2424C22semidirect
205. #2422C22semidirect
206. #2422C22semidirect
207. #2422C22semidirect
208. #2418C22semidirect
210. #2416C22semidirect
211. #2416C22semidirect
212. #2416C22semidirect
213. #2410C22semidirect
214. #2410C22semidirect
215. #2410C22semidirect
216. #2410C22semidirect
217. #2410C22semidirect
218. #2410C22semidirect
220. #2408C22semidirect
221. #2404C22semidirect
222. #2403C22semidirect
223. #2366C22semidirect
224. #2363C22semidirect
225. #2361C22semidirect
226. #2361C22semidirect
227. #2358C22semidirect
228. #2358C22semidirect
229. #2354C22semidirect
230. D4×C4⋊C4C22semidirect
231. D4×C22⋊C4C22semidirect
232. D4×C22⋊C4C22semidirect
233. D4×C22⋊C4C22semidirect
234. #2325C22semidirect
235. #2325C22semidirect
236. C4×#123C22semidirect
237. C4×#123C22semidirect
238. C4×#123C22semidirect
239. C4×#123C22semidirect
240. C4×#123C22semidirect
241. C4×#123C22semidirect
242. C4×#123C22semidirect
243. C4×#123C22semidirect
244. C4×#121C22semidirect
245. C4×#121C22semidirect
246. C4×#121C22semidirect
247. C4×#121C22semidirect
248. C4×#121C22semidirect
249. C4×#121C22semidirect
250. #2297C22semidirect
251. C2×#390C22semidirect
252. C2×#390C22semidirect
253. C2×#390C22semidirect
254. C2×#388C22semidirect
255. C2×#388C22semidirect
256. C2×#387C22semidirect
257. C2×#387C22semidirect
259. C2×#385C22semidirect
260. #2285C22semidirect
261. C2×#384C22semidirect
262. C2×#381C22semidirect
263. C2×C4×C4⋊C4C22semidirect
264. C2×C4×C4⋊C4C22semidirect
265. C2×C4×C22⋊C4C22semidirect
266. C2×C4×C22⋊C4C22semidirect
267. C2×C4×C22⋊C4C22semidirect
328. C2×#123D4semidirect
844. C23×C4C2×D4semidirect
914. #123C2×D4semidirect
915. #123C2×D4semidirect
916. #123C2×D4semidirect
917. #123C2×D4semidirect
1021. C2×C4⋊C4C2×D4semidirect
1022. C2×C4⋊C4C2×D4semidirect
1073. C2×C22⋊C4C2×D4semidirect
1074. C2×C22⋊C4C2×D4semidirect
1075. C2×C22⋊C4C2×D4semidirect
1922. C4#3534semidirect

Maximal subgroups

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

subgroupindex
C2×#35342
#598002
#592732
#590952
#457912
#454872
#454862
#397382
#394572
#394302
#394022
#394012
#393542
#393482
#393362
#376732
#376722
#374462
#367412
#367392
#366242
C2×#28562
#365962
#361232
D4×#1212
#351662
#350062
#350052
#350012
C2×C4×#1232