Subgroups — C₄⋊C₈×C₃₁₇ #23778646

Order 10144.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₃₁₇	C₂	1	2	yes	maximal
2	C₄²×C₃₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₃₁₇	C₄	1	1	yes	characteristic
4	C₂×C₄×C₃₁₇	C₄	1	1	yes	characteristic
5	C₂×C₄×C₃₁₇	C₂²	1	1	yes	characteristic
6	C₈×C₃₁₇	—	2	2	no	—
7	C₂²×C₃₁₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₃₁₇	—	2	1	no	—
9	C₄×C₃₁₇	C₈	1	2	yes	complemented
10	C₄×C₃₁₇	D₄	1	1	yes	characteristic
11	C₄×C₃₁₇	Q₈	1	1	yes	characteristic
12	C₂×C₃₁₇	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₃₁₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₃₁₇	M₁₆	1	1	yes	characteristic
15	C₃₁₇	C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
16	C₄⋊C₈	C₃₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₈	C₂×C₃₁₇	1	2	yes	—
18	C₄²	C₂×C₃₁₇	1	1	yes	characteristic
19	C₂×C₄	C₄×C₃₁₇	1	1	yes	characteristic
20	C₂×C₄	C₄×C₃₁₇	1	1	yes	characteristic
21	C₂×C₄	C₂²×C₃₁₇	1	1	yes	characteristic
22	C₈	—	2	2	no	—
23	C₂²	C₂×C₄×C₃₁₇	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	C₈×C₃₁₇	1	2	yes	complemented
26	C₄	D₄×C₃₁₇	1	1	yes	characteristic
27	C₄	Q₈×C₃₁₇	1	1	yes	characteristic
28	C₂	C₄⋊C₄×C₃₁₇	1	1	yes	characteristic
29	C₂	C₂×C₈×C₃₁₇	1	1	yes	characteristic
30	C₂	M₁₆×C₃₁₇	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.