Subgroups — Dic₆₁₁₁ #37567749

Order 24444.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉×C₉₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₀₃₇	—	3	1	no	maximal
3	C₇×C₉×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₉₇	D₃	1	1	yes	characteristic
5	Dic₈₇₃	—	7	1	no	maximal, Hall
6	Dic₆₇₉	—	9	1	no	Hall
7	C₃×C₇×C₉₇	Dic₃	1	1	yes	characteristic
8	C₂×C₉×C₉₇	D₇	1	1	yes	characteristic
9	C₂×C₇×C₉₇	D₉	1	1	yes	characteristic
10	Dic₂₉₁	—	21	1	no	—
11	C₉×C₉₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉₇	Dic₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₉₇	D₂₁	1	1	yes	characteristic
14	Dic₉₇	—	63	1	no	Hall
15	C₃×C₉₇	Dic₂₁	1	1	yes	characteristic
16	Dic₆₃	—	97	1	no	maximal, Hall
17	C₂×C₉₇	D₆₃	1	1	yes	characteristic
18	C₂×C₇×C₉	D₉₇	1	1	yes	characteristic
19	C₉₇	Dic₆₃	1	1	yes	characteristic, complemented, Sylow
20	Dic₂₁	—	291	1	no	—
21	C₇×C₉	Dic₉₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₂₉₁	1	1	yes	characteristic
23	Dic₉	—	679	1	no	Hall
24	Dic₇	—	873	1	no	Hall
25	C₃×C₇	Dic₂₉₁	1	1	yes	characteristic
26	C₂×C₉	D₆₇₉	1	1	yes	characteristic
27	C₂×C₇	D₈₇₃	1	1	yes	characteristic
28	Dic₃	—	2037	1	no	—
29	C₉	Dic₆₇₉	1	1	yes	characteristic, complemented, Sylow
30	C₇	Dic₈₇₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₂₀₃₇	1	1	yes	characteristic
32	C₄	—	6111	1	no	Sylow
33	C₃	Dic₂₀₃₇	1	1	yes	characteristic
34	C₂	D₆₁₁₁	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.