Subgroups — D₃₁₀₄ #20260571

Order 6208.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₅₂	C₂	1	2	yes	maximal, complemented
2	C₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇₇₆	—	2	2	no	—
4	C₁₆×C₉₇	C₂²	1	1	yes	characteristic
5	D₃₈₈	—	4	2	no	—
6	C₈×C₉₇	D₄	1	1	yes	characteristic
7	C₂×D₉₇	—	8	2	no	—
8	C₄×C₉₇	D₈	1	1	yes	characteristic
9	C₂×C₉₇	D₁₆	1	1	yes	characteristic
10	D₉₇	—	16	2	no	—
11	C₉₇	D₃₂	1	1	yes	characteristic, complemented, Sylow
12	D₃₂	—	97	1	no	maximal, Sylow
13	D₁₆	—	97	2	no	—
14	C₃₂	D₉₇	1	1	yes	characteristic, complemented
15	D₈	—	194	2	no	—
16	C₁₆	C₂×D₉₇	1	1	yes	characteristic
17	D₄	—	388	2	no	—
18	C₈	D₃₈₈	1	1	yes	characteristic
19	C₂²	—	776	2	no	—
20	C₄	D₇₇₆	1	1	yes	characteristic
21	C₂	—	1552	2	no	—
22	C₂	D₁₅₅₂	1	1	yes	characteristic

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