Subgroups — #35232587

Order 21152.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×#14581558	C₂	1	1	yes	maximal, characteristic
3	C₈×D₆₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14581558	C₄	1	2	yes	—
5	#19126978	C₄	1	2	yes	complemented
6	C₄×D₆₆₁	C₂²	1	1	yes	characteristic
7	#19126971	C₄	1	1	yes	characteristic, complemented
8	C₈×C₆₆₁	C₄	1	1	yes	characteristic, complemented
9	C₂×D₆₆₁	C₂×C₄	1	1	yes	characteristic
10	#14581558	—	2	2	no	—
11	C₄×C₆₆₁	C₂×C₄	1	1	yes	characteristic
12	Dic₆₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₆₆₁	C₄²	1	1	yes	characteristic
14	D₆₆₁	M₁₆	1	2	yes	—
15	C₆₆₁	#97	1	1	yes	characteristic, complemented, Sylow
16	#97	—	661	1	no	maximal, Sylow
17	C₂×C₈	—	661	1	no	—
18	C₂×C₈	—	661	1	no	—
19	C₄²	—	661	1	no	—
20	C₂×C₄	—	661	2	no	—
21	C₂×C₄	—	661	1	no	—
22	C₈	—	661	2	no	—
23	C₈	—	661	1	no	—
24	C₈	#14581558	1	1	yes	characteristic, complemented
25	C₂²	—	661	1	no	—
26	C₄	—	1322	2	no	—
27	C₄	—	661	1	no	—
28	C₄	C₂×#14581558	1	1	yes	characteristic
29	C₂	—	661	2	no	—
30	C₂	C₄×#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.