Subgroups — Dic₈₁₈₈ #72272575

Order 32752.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₀₉₄	C₂	1	2	yes	maximal
2	C₈×C₂₃×C₈₉	C₂	1	1	yes	maximal, characteristic
3	Dic₂₀₄₇	—	2	2	no	—
4	C₄×C₂₃×C₈₉	C₂²	1	1	yes	characteristic
5	C₂×C₂₃×C₈₉	D₄	1	1	yes	characteristic
6	C₂₃×C₈₉	Q₁₆	1	1	yes	characteristic, complemented, Hall
7	Dic₃₅₆	—	23	1	no	maximal, Hall
8	Dic₁₇₈	—	23	2	no	—
9	C₈×C₈₉	D₂₃	1	1	yes	characteristic
10	Dic₉₂	—	89	1	no	maximal, Hall
11	C₄×C₈₉	C₂×D₂₃	1	1	yes	characteristic
12	Dic₈₉	—	46	2	no	—
13	Dic₄₆	—	89	2	no	—
14	C₈×C₂₃	D₈₉	1	1	yes	characteristic
15	C₂×C₈₉	D₉₂	1	1	yes	characteristic
16	C₄×C₂₃	C₂×D₈₉	1	1	yes	characteristic
17	Dic₂₃	—	178	2	no	—
18	C₈₉	Dic₉₂	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₂₃	D₃₅₆	1	1	yes	characteristic
20	C₂₃	Dic₃₅₆	1	1	yes	characteristic, complemented, Sylow
21	Q₁₆	—	2047	1	no	Sylow
22	Q₈	—	2047	2	no	—
23	C₈	D₂₀₄₇	1	1	yes	characteristic
24	C₄	—	4094	2	no	—
25	C₄	C₂×D₂₀₄₇	1	1	yes	characteristic
26	C₂	D₈₁₈₈	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.