Subgroups — #35232621

Order 21152.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24902382	C₂	1	3	yes	maximal, complemented
2	D₆₆₁⋊C₈	C₂	1	3	yes	maximal, complemented
3	#24902373	C₂	1	1	yes	maximal, characteristic
4	#19126978	C₂²	1	1	yes	characteristic
5	#19126978	C₂²	1	3	yes	—
6	D₂₆₄₄	C₄	1	3	yes	—
7	C₄×D₆₆₁	C₂²	1	3	yes	—
8	Q₈×C₆₆₁	C₄	1	1	yes	characteristic
9	C₂×D₆₆₁	C₂×C₄	1	3	yes	—
10	C₄×C₆₆₁	C₂×C₄	1	3	yes	—
11	Dic₆₆₁	C₂³	1	1	yes	characteristic
12	C₂×C₆₆₁	C₂²×C₄	1	1	yes	characteristic
13	D₆₆₁	—	2	3	no	—
14	C₆₆₁	#131	1	1	yes	characteristic, complemented, Sylow
15	#131	—	661	1	no	maximal, Sylow
16	#41	—	661	1	no	—
17	M₁₆	—	661	3	no	—
18	C₂×C₈	—	661	3	no	—
19	Q₈	#14581558	1	1	yes	characteristic
20	D₄	—	661	3	no	—
21	C₂×C₄	—	661	3	no	—
22	C₈	—	661	1	no	—
23	C₈	—	661	3	no	—
24	C₂²	—	661	3	no	—
25	C₄	—	661	1	no	—
26	C₄	C₂×#14581558	1	3	yes	—
27	C₂	—	1322	3	no	—
28	C₂	C₂²×#14581558	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.