Subgroups — D₂₅₂ #92610

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₃	C₂	1	2	yes	maximal, complemented
2	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈₄	—	3	1	no	maximal
4	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
5	D₆₃	—	2	2	no	—
6	C₂×D₂₁	—	3	2	no	—
7	C₃×C₄×C₇	D₃	1	1	yes	characteristic
8	D₃₆	—	7	1	no	maximal, Hall
9	C₇×C₉	D₄	1	1	yes	characteristic, complemented, Hall
10	D₂₈	—	9	1	no	Hall
11	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
12	D₂₁	—	6	2	no	—
13	C₂×D₉	—	7	2	no	—
14	C₄×C₉	D₇	1	1	yes	characteristic, complemented
15	C₂×D₇	—	9	2	no	—
16	C₄×C₇	D₉	1	1	yes	characteristic, complemented
17	D₁₂	—	21	1	no	—
18	C₃×C₇	D₁₂	1	1	yes	characteristic
19	C₂×C₉	C₂×D₇	1	1	yes	characteristic
20	D₉	—	14	2	no	—
21	C₂×C₇	C₂×D₉	1	1	yes	characteristic
22	D₇	—	18	2	no	—
23	C₂×D₃	—	21	2	no	—
24	C₃×C₄	D₂₁	1	1	yes	characteristic
25	C₉	D₂₈	1	1	yes	characteristic, complemented, Sylow
26	D₄	—	63	1	no	Sylow
27	C₇	D₃₆	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	C₂×D₂₁	1	1	yes	characteristic
29	D₃	—	42	2	no	—
30	C₂²	—	63	2	no	—
31	C₄	D₆₃	1	1	yes	characteristic, complemented
32	C₃	D₈₄	1	1	yes	characteristic
33	C₂	—	126	2	no	—
34	C₂	C₂×D₆₃	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.