Subgroups — D₂₃₁₂ #72210343

Order 4624.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁₅₆	C₂	1	2	yes	maximal, complemented
2	C₈×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₈₉	—	2	2	no	—
4	C₄×C₂₈₉	C₂²	1	1	yes	characteristic
5	C₂×C₂₈₉	D₄	1	1	yes	characteristic
6	D₂₈₉	—	4	2	no	—
7	C₂₈₉	D₈	1	1	yes	characteristic, complemented, Sylow
8	D₁₃₆	—	17	1	no	maximal
9	D₆₈	—	17	2	no	—
10	C₈×C₁₇	D₁₇	1	1	yes	characteristic
11	C₂×D₁₇	—	34	2	no	—
12	C₄×C₁₇	C₂×D₁₇	1	1	yes	characteristic
13	C₂×C₁₇	D₆₈	1	1	yes	characteristic
14	D₁₇	—	68	2	no	—
15	C₁₇	D₁₃₆	1	1	yes	characteristic
16	D₈	—	289	1	no	Sylow
17	D₄	—	289	2	no	—
18	C₈	D₂₈₉	1	1	yes	characteristic, complemented
19	C₂²	—	578	2	no	—
20	C₄	C₂×D₂₈₉	1	1	yes	characteristic
21	C₂	—	1156	2	no	—
22	C₂	D₁₁₅₆	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.