Subgroups — D₁₁₇₂₄ #72223948

Order 23448.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₉₃₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₉₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₉₀₈	—	3	1	no	maximal, Hall
4	C₂×C₃×C₉₇₇	C₂²	1	1	yes	characteristic
5	D₂₉₃₁	—	2	2	no	—
6	C₂×D₉₇₇	—	3	2	no	—
7	C₄×C₉₇₇	D₃	1	1	yes	characteristic, complemented
8	C₃×C₉₇₇	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₉₇₇	C₂×D₃	1	1	yes	characteristic
10	D₉₇₇	—	6	2	no	—
11	C₉₇₇	D₁₂	1	1	yes	characteristic, complemented, Sylow
12	D₁₂	—	977	1	no	maximal, Hall
13	C₂×D₃	—	977	2	no	—
14	C₃×C₄	D₉₇₇	1	1	yes	characteristic, complemented
15	D₄	—	2931	1	no	Sylow
16	C₂×C₃	C₂×D₉₇₇	1	1	yes	characteristic
17	D₃	—	1954	2	no	—
18	C₂²	—	2931	2	no	—
19	C₄	D₂₉₃₁	1	1	yes	characteristic, complemented
20	C₃	D₃₉₀₈	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	5862	2	no	—
22	C₂	C₂×D₂₉₃₁	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.