Subgroups — C₁₀₉×Dic₇₇ #46777090

Order 33572.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁×C₁₀₉	—	7	1	no	maximal, Hall
4	Dic₇×C₁₀₉	—	11	1	no	maximal, Hall
5	C₂×C₁₁×C₁₀₉	D₇	1	1	yes	characteristic
6	C₂×C₇×C₁₀₉	D₁₁	1	1	yes	characteristic
7	C₁₁×C₁₀₉	Dic₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₀₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	C₄×C₁₀₉	—	77	1	no	Hall
10	Dic₇₇	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₀₉	D₇₇	1	1	yes	characteristic
12	C₂×C₇×C₁₁	C₂×C₁₀₉	1	1	yes	characteristic
13	C₁₀₉	Dic₇₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₇×C₁₁	C₄×C₁₀₉	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁	—	7	1	no	Hall
16	Dic₇	—	11	1	no	Hall
17	C₂×C₁₁	D₇×C₁₀₉	1	1	yes	characteristic
18	C₂×C₇	D₁₁×C₁₀₉	1	1	yes	characteristic
19	C₁₁	Dic₇×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
20	C₇	Dic₁₁×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	77	1	no	Sylow
22	C₂	C₁₀₉×D₇₇	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.