Subgroups — #35232600

Order 21152.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19126978	C₂	1	2	yes	maximal
2	C₄×Dic₆₆₁	C₂	1	1	yes	maximal, characteristic
3	#19126978	—	2	2	no	—
4	C₂×Dic₆₆₁	C₄	1	1	yes	characteristic
5	C₂×Dic₆₆₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₆₆₁	C₄	1	1	yes	characteristic
7	C₂²×C₆₆₁	C₂×C₄	1	1	yes	characteristic
8	C₄×C₆₆₁	—	2	1	no	—
9	Dic₆₆₁	C₈	1	2	yes	complemented
10	Dic₆₆₁	D₄	1	1	yes	characteristic
11	Dic₆₆₁	Q₈	1	1	yes	characteristic
12	C₂×C₆₆₁	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₆₆₁	C₂×C₈	1	1	yes	characteristic
14	C₂×C₆₆₁	M₁₆	1	1	yes	characteristic
15	C₆₆₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	661	1	no	maximal, Sylow
17	C₂×C₈	—	661	2	no	—
18	C₄²	—	661	1	no	—
19	C₂×C₄	—	661	1	no	—
20	C₂×C₄	—	661	1	no	—
21	C₂×C₄	#14581558	1	1	yes	characteristic
22	C₈	—	1322	2	no	—
23	C₂²	C₂×#14581558	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	661	1	no	—
26	C₄	—	661	1	no	—
27	C₄	—	661	2	no	—
28	C₂	C₄⋊#14581558	1	1	yes	characteristic
29	C₂	D₆₆₁⋊C₈	1	1	yes	characteristic
30	C₂	#24902381	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. Dic₆₆₁	C₈	semidirect
15. C₆₆₁	C₄⋊C₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.