Subgroups — #31772696

Order 17312.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14524194	C₂	1	2	yes	maximal
2	C₈×D₅₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#14524194	—	2	2	no	—
4	C₄×D₅₄₁	C₂²	1	1	yes	characteristic
5	#16864513	C₄	1	1	yes	characteristic, complemented
6	C₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
7	C₂×D₅₄₁	D₄	1	1	yes	characteristic
8	#14524194	—	4	2	no	—
9	C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
10	Dic₅₄₁	Q₈	1	1	yes	characteristic
11	C₂×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
12	D₅₄₁	SD₁₆	1	2	yes	—
13	C₅₄₁	#106	1	1	yes	characteristic, complemented, Sylow
14	#106	—	541	1	no	maximal, Sylow
15	C₂×C₈	—	541	1	no	—
16	C₄⋊C₄	—	541	2	no	—
17	C₂×C₄	—	541	1	no	—
18	C₂×C₄	—	1082	2	no	—
19	C₈	—	541	1	no	—
20	C₈	#14524194	1	1	yes	characteristic, complemented
21	C₂²	—	541	1	no	—
22	C₄	—	541	1	no	—
23	C₄	—	2164	2	no	—
24	C₄	C₂×#14524194	1	1	yes	characteristic
25	C₂	—	541	2	no	—
26	C₂	C₄⋊#14524194	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.