Subgroups — D₇₈₀₈ #29567926

Order 15616.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉₀₄	C₂	1	2	yes	maximal, complemented
2	C₆₁×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₉₅₂	—	2	2	no	—
4	C₆₁×C₆₄	C₂²	1	1	yes	characteristic
5	D₉₇₆	—	4	2	no	—
6	C₃₂×C₆₁	D₄	1	1	yes	characteristic
7	D₄₈₈	—	8	2	no	—
8	C₁₆×C₆₁	D₈	1	1	yes	characteristic
9	D₂₄₄	—	16	2	no	—
10	C₈×C₆₁	D₁₆	1	1	yes	characteristic
11	D₁₂₈	—	61	1	no	maximal, Sylow
12	C₂×D₆₁	—	32	2	no	—
13	C₄×C₆₁	D₃₂	1	1	yes	characteristic
14	D₆₄	—	61	2	no	—
15	C₁₂₈	D₆₁	1	1	yes	characteristic, complemented
16	C₂×C₆₁	D₆₄	1	1	yes	characteristic
17	D₆₁	—	64	2	no	—
18	D₃₂	—	122	2	no	—
19	C₆₄	C₂×D₆₁	1	1	yes	characteristic
20	C₆₁	D₁₂₈	1	1	yes	characteristic, complemented, Sylow
21	D₁₆	—	244	2	no	—
22	C₃₂	D₂₄₄	1	1	yes	characteristic
23	D₈	—	488	2	no	—
24	C₁₆	D₄₈₈	1	1	yes	characteristic
25	D₄	—	976	2	no	—
26	C₈	D₉₇₆	1	1	yes	characteristic
27	C₂²	—	1952	2	no	—
28	C₄	D₁₉₅₂	1	1	yes	characteristic
29	C₂	—	3904	2	no	—
30	C₂	D₃₉₀₄	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.