Subgroups — C₄⋊(C₈₆₃⋊C₈) #42120366

Order 27616.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈₆₃⋊C₈	C₂	1	2	yes	maximal
2	C₄²×C₈₆₃	C₂	1	1	yes	maximal, characteristic
3	C₈₆₃⋊C₈	—	2	2	no	—
4	C₂×C₄×C₈₆₃	C₄	1	1	yes	characteristic
5	C₂×C₄×C₈₆₃	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈₆₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈₆₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₈₆₃	—	2	1	no	—
9	C₄×C₈₆₃	C₈	1	2	yes	complemented
10	C₄×C₈₆₃	D₄	1	1	yes	characteristic
11	C₄×C₈₆₃	Q₈	1	1	yes	characteristic
12	C₂×C₈₆₃	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₈₆₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₈₆₃	M₁₆	1	1	yes	characteristic
15	C₈₆₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	863	1	no	maximal, Sylow
17	C₂×C₈	—	863	2	no	—
18	C₄²	D₈₆₃	1	1	yes	characteristic
19	C₂×C₄	Dic₈₆₃	1	1	yes	characteristic
20	C₂×C₄	Dic₈₆₃	1	1	yes	characteristic
21	C₂×C₄	C₂×D₈₆₃	1	1	yes	characteristic
22	C₈	—	1726	2	no	—
23	C₂²	C₂×Dic₈₆₃	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	C₈₆₃⋊C₈	1	2	yes	complemented
26	C₄	D₃₄₅₂	1	1	yes	characteristic
27	C₄	Dic₁₇₂₆	1	1	yes	characteristic
28	C₂	C₄⋊Dic₈₆₃	1	1	yes	characteristic
29	C₂	C₂×C₈₆₃⋊C₈	1	1	yes	characteristic
30	C₂	#28352410	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

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