Subgroups — C₇×Dic₈₆₉ #37566640

Order 24332.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₈₆₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×Dic₇₉	—	11	1	no	maximal, Hall
5	C₂×C₁₁×C₇₉	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₇₉	D₁₁	1	1	yes	characteristic
7	C₁₁×C₇₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₇₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₇₉	—	11	1	no	Hall
10	C₇×Dic₁₁	—	79	1	no	maximal, Hall
11	C₂×C₇₉	C₇×D₁₁	1	1	yes	characteristic
12	C₂×C₇×C₁₁	D₇₉	1	1	yes	characteristic
13	C₇₉	C₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₁₁	Dic₇₉	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁	—	79	1	no	Hall
16	C₄×C₇	—	869	1	no	Hall
17	C₂×C₁₁	C₇×D₇₉	1	1	yes	characteristic
18	C₂×C₇	D₈₆₉	1	1	yes	characteristic
19	C₁₁	C₇×Dic₇₉	1	1	yes	characteristic, complemented, Sylow
20	C₇	Dic₈₆₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	869	1	no	Sylow
22	C₂	C₇×D₈₆₉	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.