Subgroups — C₇×Dic₁₁₈₉ #45685607

Order 33292.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₂₉×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₉×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₉×C₄₁	C₂×C₇	1	1	yes	characteristic
5	C₂₉×C₄₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×Dic₄₁	—	29	1	no	maximal, Hall
7	C₇×Dic₂₉	—	41	1	no	maximal, Hall
8	C₂×C₇×C₄₁	D₂₉	1	1	yes	characteristic
9	C₂×C₇×C₂₉	D₄₁	1	1	yes	characteristic
10	C₇×C₄₁	Dic₂₉	1	1	yes	characteristic, complemented, Hall
11	C₇×C₂₉	Dic₄₁	1	1	yes	characteristic, complemented, Hall
12	Dic₄₁	—	29	1	no	Hall
13	Dic₂₉	—	41	1	no	Hall
14	C₂×C₄₁	C₇×D₂₉	1	1	yes	characteristic
15	C₂×C₂₉	C₇×D₄₁	1	1	yes	characteristic
16	C₄₁	C₇×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₇×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₇	—	1189	1	no	Hall
19	C₂×C₇	D₁₁₈₉	1	1	yes	characteristic
20	C₇	Dic₁₁₈₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1189	1	no	Sylow
22	C₂	C₇×D₁₁₈₉	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.