Subgroups — C₂×D₁₁₃⋊C₄₉ #36370577

Order 22148.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁₃⋊C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₁₃⋊C₄₉	C₂	1	2	yes	maximal, direct product factor
3	C₁₁₃⋊C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₁₁₃	C₇	1	1	yes	maximal, characteristic
5	C₂×C₇×C₁₁₃	C₂×C₇	1	1	yes	characteristic
6	C₇×D₁₁₃	C₂×C₇	1	2	yes	—
7	C₇×C₁₁₃	C₂²×C₇	1	1	yes	characteristic
8	C₂×D₁₁₃	C₄₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁₃	C₂×C₄₉	1	1	yes	characteristic, complemented
10	D₁₁₃	C₂×C₄₉	1	2	yes	complemented
11	C₂²×C₄₉	—	113	1	no	maximal, Hall
12	C₁₁₃	C₂²×C₄₉	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₄₉	—	113	2	no	—
14	C₂×C₄₉	—	113	1	no	—
15	C₄₉	—	113	1	no	Sylow
16	C₂²×C₇	—	791	1	no	—
17	C₂×C₇	—	791	2	no	—
18	C₂×C₇	D₁₁₃⋊C₇	1	1	yes	characteristic
19	C₇	C₂×D₁₁₃⋊C₇	1	1	yes	characteristic
20	C₂²	—	791	1	no	Sylow
21	C₂	—	791	2	no	—
22	C₂	D₁₁₃⋊C₄₉	1	1	yes	characteristic, direct product factor

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.