Subgroups — Dic₂₆₉₁ #24924476

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	Dic₈₉₇	—	3	1	no	maximal
3	C₉×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₂₃	D₃	1	1	yes	characteristic
5	Dic₂₉₉	—	9	1	no	Hall
6	C₃×C₁₃×C₂₃	Dic₃	1	1	yes	characteristic
7	Dic₂₀₇	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₂₃	D₉	1	1	yes	characteristic
9	Dic₁₁₇	—	23	1	no	maximal, Hall
10	C₂×C₉×C₂₃	D₁₃	1	1	yes	characteristic
11	C₁₃×C₂₃	Dic₉	1	1	yes	characteristic, complemented, Hall
12	Dic₆₉	—	39	1	no	—
13	C₂×C₉×C₁₃	D₂₃	1	1	yes	characteristic
14	C₉×C₂₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
15	Dic₃₉	—	69	1	no	—
16	C₂×C₃×C₂₃	D₃₉	1	1	yes	characteristic
17	C₉×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
18	Dic₂₃	—	117	1	no	Hall
19	C₂×C₃×C₁₃	D₆₉	1	1	yes	characteristic
20	C₃×C₂₃	Dic₃₉	1	1	yes	characteristic
21	Dic₁₃	—	207	1	no	Hall
22	C₂×C₂₃	D₁₁₇	1	1	yes	characteristic
23	C₃×C₁₃	Dic₆₉	1	1	yes	characteristic
24	Dic₉	—	299	1	no	Hall
25	C₂×C₁₃	D₂₀₇	1	1	yes	characteristic
26	C₂₃	Dic₁₁₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	D₂₉₉	1	1	yes	characteristic
28	C₁₃	Dic₂₀₇	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	897	1	no	—
30	C₉	Dic₂₉₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₈₉₇	1	1	yes	characteristic
32	C₄	—	2691	1	no	Sylow
33	C₃	Dic₈₉₇	1	1	yes	characteristic
34	C₂	D₂₆₉₁	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.