Subgroups — #15693018

Order 3296.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₁₂	C₂	1	6	yes	maximal, complemented
2	C₄²×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₀₃	C₂²	1	4	yes	—
4	C₂×C₄×C₁₀₃	C₂²	1	3	yes	—
5	D₄₁₂	—	2	12	no	—
6	C₂²×C₁₀₃	C₂³	1	1	yes	characteristic
7	C₂×D₁₀₃	—	2	12	no	—
8	C₄×C₁₀₃	D₄	1	6	yes	complemented
9	C₂×C₁₀₃	C₂×D₄	1	3	yes	—
10	D₁₀₃	—	4	4	no	—
11	C₁₀₃	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	103	1	no	maximal, Sylow
13	C₂×D₄	—	103	6	no	—
14	C₄²	D₁₀₃	1	1	yes	characteristic, complemented
15	C₂³	—	103	4	no	—
16	D₄	—	206	12	no	—
17	C₂×C₄	C₂×D₁₀₃	1	3	yes	—
18	C₂²	—	206	12	no	—
19	C₂²	C₂²×D₁₀₃	1	1	yes	characteristic
20	C₄	D₄₁₂	1	6	yes	complemented
21	C₂	—	412	4	no	—
22	C₂	C₂×D₄₁₂	1	3	yes	—

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.