Subgroups — D₁₂₂₂₄ #37570733

Order 24448.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁₁₂	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₀₅₆	—	2	2	no	—
4	C₃₂×C₁₉₁	C₂²	1	1	yes	characteristic
5	D₁₅₂₈	—	4	2	no	—
6	C₁₆×C₁₉₁	D₄	1	1	yes	characteristic
7	D₇₆₄	—	8	2	no	—
8	C₈×C₁₉₁	D₈	1	1	yes	characteristic
9	C₂×D₁₉₁	—	16	2	no	—
10	C₄×C₁₉₁	D₁₆	1	1	yes	characteristic
11	C₂×C₁₉₁	D₃₂	1	1	yes	characteristic
12	D₁₉₁	—	32	2	no	—
13	C₁₉₁	D₆₄	1	1	yes	characteristic, complemented, Sylow
14	D₆₄	—	191	1	no	maximal, Sylow
15	D₃₂	—	191	2	no	—
16	C₆₄	D₁₉₁	1	1	yes	characteristic, complemented
17	D₁₆	—	382	2	no	—
18	C₃₂	C₂×D₁₉₁	1	1	yes	characteristic
19	D₈	—	764	2	no	—
20	C₁₆	D₇₆₄	1	1	yes	characteristic
21	D₄	—	1528	2	no	—
22	C₈	D₁₅₂₈	1	1	yes	characteristic
23	C₂²	—	3056	2	no	—
24	C₄	D₃₀₅₆	1	1	yes	characteristic
25	C₂	—	6112	2	no	—
26	C₂	D₆₁₁₂	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.