Subgroups — D₁₃₅₀₄ #41011611

Order 27008.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₅₂	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₃₇₆	—	2	2	no	—
4	C₃₂×C₂₁₁	C₂²	1	1	yes	characteristic
5	D₁₆₈₈	—	4	2	no	—
6	C₁₆×C₂₁₁	D₄	1	1	yes	characteristic
7	D₈₄₄	—	8	2	no	—
8	C₈×C₂₁₁	D₈	1	1	yes	characteristic
9	C₂×D₂₁₁	—	16	2	no	—
10	C₄×C₂₁₁	D₁₆	1	1	yes	characteristic
11	C₂×C₂₁₁	D₃₂	1	1	yes	characteristic
12	D₂₁₁	—	32	2	no	—
13	C₂₁₁	D₆₄	1	1	yes	characteristic, complemented, Sylow
14	D₆₄	—	211	1	no	maximal, Sylow
15	D₃₂	—	211	2	no	—
16	C₆₄	D₂₁₁	1	1	yes	characteristic, complemented
17	D₁₆	—	422	2	no	—
18	C₃₂	C₂×D₂₁₁	1	1	yes	characteristic
19	D₈	—	844	2	no	—
20	C₁₆	D₈₄₄	1	1	yes	characteristic
21	D₄	—	1688	2	no	—
22	C₈	D₁₆₈₈	1	1	yes	characteristic
23	C₂²	—	3376	2	no	—
24	C₄	D₃₃₇₆	1	1	yes	characteristic
25	C₂	—	6752	2	no	—
26	C₂	D₆₇₅₂	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.