Subgroups — Dic₃₁₂ #11928113

Order 1248.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₅₆	C₂	1	2	yes	maximal
2	C₃×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₁₀₄	—	3	1	no	maximal, Hall
4	Dic₇₈	—	2	2	no	—
5	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	Dic₅₂	—	3	2	no	—
7	C₁₃×C₁₆	D₃	1	1	yes	characteristic
8	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
9	Dic₃₉	—	4	2	no	—
10	Dic₂₆	—	6	2	no	—
11	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
12	Dic₂₄	—	13	1	no	maximal, Hall
13	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
14	C₄×C₁₃	D₁₂	1	1	yes	characteristic
15	Dic₁₃	—	12	2	no	—
16	Dic₁₂	—	13	2	no	—
17	C₃×C₁₆	D₁₃	1	1	yes	characteristic
18	C₃×C₁₃	Q₃₂	1	1	yes	characteristic, complemented, Hall
19	Q₃₂	—	39	1	no	Sylow
20	C₂×C₁₃	D₂₄	1	1	yes	characteristic
21	Dic₆	—	26	2	no	—
22	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
23	Q₁₆	—	39	2	no	—
24	C₁₆	D₃₉	1	1	yes	characteristic
25	C₁₃	Dic₂₄	1	1	yes	characteristic, complemented, Sylow
26	C₃×C₄	D₅₂	1	1	yes	characteristic
27	Dic₃	—	52	2	no	—
28	Q₈	—	78	2	no	—
29	C₈	C₂×D₃₉	1	1	yes	characteristic
30	C₂×C₃	D₁₀₄	1	1	yes	characteristic
31	C₄	—	156	2	no	—
32	C₄	D₁₅₆	1	1	yes	characteristic
33	C₃	Dic₁₀₄	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₃₁₂	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.