Subgroups — C₂₃×Dic₃₇₁ #46802417

Order 34132.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃×Dic₅₃	—	7	1	no	maximal, Hall
4	C₂×C₂₃×C₅₃	D₇	1	1	yes	characteristic
5	Dic₃₇₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂₃×C₅₃	Dic₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₅₃	C₂×C₂₃	1	1	yes	characteristic
8	C₂₃×Dic₇	—	53	1	no	maximal, Hall
9	C₇×C₅₃	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₂₃	D₅₃	1	1	yes	characteristic
11	Dic₅₃	—	7	1	no	Hall
12	C₇×C₂₃	Dic₅₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₃	D₇×C₂₃	1	1	yes	characteristic
14	C₄×C₂₃	—	371	1	no	Hall
15	C₅₃	C₂₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	D₃₇₁	1	1	yes	characteristic
17	Dic₇	—	53	1	no	Hall
18	C₂₃	Dic₃₇₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	C₂₃×D₅₃	1	1	yes	characteristic
20	C₇	C₂₃×Dic₅₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	371	1	no	Sylow
22	C₂	C₂₃×D₃₇₁	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.