Subgroups — C₄×C₇×C₆₇⋊C₁₁ #35207485

Order 20636.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₆₇⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₆₇⋊C₁₁	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₆₇⋊C₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₇×C₆₇	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₆₇⋊C₁₁	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₆₇	C₂×C₁₁	1	1	yes	characteristic
7	C₆₇⋊C₁₁	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₆₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₄×C₇×C₁₁	—	67	1	no	maximal, Hall
10	C₄×C₆₇	C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₁₁	—	67	1	no	—
12	C₂×C₆₇	C₂×C₇×C₁₁	1	1	yes	characteristic
13	C₇×C₁₁	—	67	1	no	Hall
14	C₆₇	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₁₁	—	67	1	no	Hall
16	C₄×C₇	C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₁	—	67	1	no	—
18	C₂×C₇	C₂×C₆₇⋊C₁₁	1	1	yes	characteristic
19	C₁₁	—	67	1	no	Sylow
20	C₇	C₄×C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₇×C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₆₇⋊C₁₁	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.