Subgroups — D₁₁₂₂₄ #72215873

Order 22448.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₆₁₂	C₂	1	2	yes	maximal, complemented
2	C₈×C₂₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₄₀₃	—	2	2	no	—
4	C₄×C₂₃×C₆₁	C₂²	1	1	yes	characteristic
5	C₂×C₂₃×C₆₁	D₄	1	1	yes	characteristic
6	D₁₄₀₃	—	4	2	no	—
7	C₂₃×C₆₁	D₈	1	1	yes	characteristic, complemented, Hall
8	D₄₈₈	—	23	1	no	maximal, Hall
9	D₂₄₄	—	23	2	no	—
10	C₈×C₆₁	D₂₃	1	1	yes	characteristic, complemented
11	D₁₈₄	—	61	1	no	maximal, Hall
12	C₂×D₆₁	—	46	2	no	—
13	C₄×C₆₁	C₂×D₂₃	1	1	yes	characteristic
14	D₉₂	—	61	2	no	—
15	C₈×C₂₃	D₆₁	1	1	yes	characteristic, complemented
16	C₂×C₆₁	D₉₂	1	1	yes	characteristic
17	D₆₁	—	92	2	no	—
18	C₂×D₂₃	—	122	2	no	—
19	C₄×C₂₃	C₂×D₆₁	1	1	yes	characteristic
20	C₆₁	D₁₈₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₂₃	D₂₄₄	1	1	yes	characteristic
22	D₂₃	—	244	2	no	—
23	C₂₃	D₄₈₈	1	1	yes	characteristic, complemented, Sylow
24	D₈	—	1403	1	no	Sylow
25	D₄	—	1403	2	no	—
26	C₈	D₁₄₀₃	1	1	yes	characteristic, complemented
27	C₂²	—	2806	2	no	—
28	C₄	C₂×D₁₄₀₃	1	1	yes	characteristic
29	C₂	—	5612	2	no	—
30	C₂	D₅₆₁₂	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.