Subgroups — #35232602

Order 21152.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14581558	C₂	1	2	yes	maximal
2	C₈×D₆₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#14581558	—	2	2	no	—
4	C₄×D₆₆₁	C₂²	1	1	yes	characteristic
5	#19126971	C₄	1	1	yes	characteristic, complemented
6	C₈×C₆₆₁	C₄	1	1	yes	characteristic, complemented
7	C₂×D₆₆₁	D₄	1	1	yes	characteristic
8	#14581558	—	4	2	no	—
9	C₄×C₆₆₁	C₂×C₄	1	1	yes	characteristic
10	Dic₆₆₁	Q₈	1	1	yes	characteristic
11	C₂×C₆₆₁	C₄⋊C₄	1	1	yes	characteristic
12	D₆₆₁	D₈	1	1	yes	characteristic
13	D₆₆₁	Q₁₆	1	1	yes	characteristic
14	C₆₆₁	#107	1	1	yes	characteristic, complemented, Sylow
15	#107	—	661	1	no	maximal, Sylow
16	C₂×C₈	—	661	1	no	—
17	C₄⋊C₄	—	661	2	no	—
18	C₂×C₄	—	1322	2	no	—
19	C₂×C₄	—	661	1	no	—
20	C₈	—	661	1	no	—
21	C₈	#14581558	1	1	yes	characteristic, complemented
22	C₂²	—	661	1	no	—
23	C₄	—	2644	2	no	—
24	C₄	—	661	1	no	—
25	C₄	C₂×#14581558	1	1	yes	characteristic
26	C₂	—	661	1	no	—
27	C₂	—	661	1	no	—
28	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.