Subgroups — Dic₁₂₇₈₈ #72288198

Order 51152.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₃₉₄	C₂	1	2	yes	maximal
2	C₈×C₂₃×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	Dic₃₁₉₇	—	2	2	no	—
4	C₄×C₂₃×C₁₃₉	C₂²	1	1	yes	characteristic
5	C₂×C₂₃×C₁₃₉	D₄	1	1	yes	characteristic
6	C₂₃×C₁₃₉	Q₁₆	1	1	yes	characteristic, complemented, Hall
7	Dic₅₅₆	—	23	1	no	maximal, Hall
8	Dic₂₇₈	—	23	2	no	—
9	C₈×C₁₃₉	D₂₃	1	1	yes	characteristic
10	C₄×C₁₃₉	C₂×D₂₃	1	1	yes	characteristic
11	Dic₁₃₉	—	46	2	no	—
12	Dic₉₂	—	139	1	no	maximal, Hall
13	C₂×C₁₃₉	D₉₂	1	1	yes	characteristic
14	Dic₄₆	—	139	2	no	—
15	C₈×C₂₃	D₁₃₉	1	1	yes	characteristic
16	C₁₃₉	Dic₉₂	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₂₃	C₂×D₁₃₉	1	1	yes	characteristic
18	Dic₂₃	—	278	2	no	—
19	C₂×C₂₃	D₅₅₆	1	1	yes	characteristic
20	C₂₃	Dic₅₅₆	1	1	yes	characteristic, complemented, Sylow
21	Q₁₆	—	3197	1	no	Sylow
22	Q₈	—	3197	2	no	—
23	C₈	D₃₁₉₇	1	1	yes	characteristic
24	C₄	—	6394	2	no	—
25	C₄	C₂×D₃₁₉₇	1	1	yes	characteristic
26	C₂	D₁₂₇₈₈	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.