Subgroups — #37566897

Order 24352.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₀₄₄	C₂	1	6	yes	maximal, complemented
2	C₄²×C₇₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₇₆₁	C₂²	1	4	yes	—
4	D₃₀₄₄	—	2	12	no	—
5	C₂×C₄×C₇₆₁	C₂²	1	3	yes	—
6	C₂²×C₇₆₁	C₂³	1	1	yes	characteristic
7	C₂×D₇₆₁	—	2	12	no	—
8	C₄×C₇₆₁	D₄	1	6	yes	complemented
9	C₂×C₇₆₁	C₂×D₄	1	3	yes	—
10	D₇₆₁	—	4	4	no	—
11	C₇₆₁	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	761	1	no	maximal, Sylow
13	C₂×D₄	—	761	6	no	—
14	C₄²	D₇₆₁	1	1	yes	characteristic, complemented
15	C₂³	—	761	4	no	—
16	D₄	—	1522	12	no	—
17	C₂×C₄	C₂×D₇₆₁	1	3	yes	—
18	C₂²	—	1522	12	no	—
19	C₂²	C₂²×D₇₆₁	1	1	yes	characteristic
20	C₄	D₃₀₄₄	1	6	yes	complemented
21	C₂	—	3044	4	no	—
22	C₂	C₂×D₃₀₄₄	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.