Subgroups — C₄×#16864520 #31772681

Order 17312.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864520	C₂	1	2	yes	maximal
2	C₄×Dic₅₄₁	C₂	1	1	yes	maximal, characteristic
3	#16864520	C₄	1	4	yes	direct product factor
4	C₂×Dic₅₄₁	C₄	1	1	yes	characteristic
5	C₂×Dic₅₄₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅₄₁	C₄	1	1	yes	characteristic
7	C₂²×C₅₄₁	C₂×C₄	1	1	yes	characteristic
8	C₄×C₅₄₁	C₈	1	2	yes	complemented
9	Dic₅₄₁	C₈	1	2	yes	complemented
10	Dic₅₄₁	C₂×C₄	1	2	yes	—
11	C₂×C₅₄₁	C₄²	1	1	yes	characteristic
12	C₂×C₅₄₁	C₂×C₈	1	1	yes	characteristic
13	C₂×C₅₄₁	C₂×C₈	1	1	yes	characteristic
14	C₅₄₁	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₈	—	541	1	no	maximal, Sylow
16	C₂×C₈	—	541	2	no	—
17	C₄²	—	541	1	no	—
18	C₂×C₄	—	541	1	no	—
19	C₂×C₄	—	541	1	no	—
20	C₂×C₄	#14524194	1	1	yes	characteristic
21	C₈	—	541	4	no	—
22	C₂²	C₂×#14524194	1	1	yes	characteristic
23	C₄	—	541	2	no	—
24	C₄	—	541	2	no	—
25	C₄	#16864520	1	2	yes	direct product factor
26	C₂	C₄×#14524194	1	1	yes	characteristic
27	C₂	C₂×#16864520	1	1	yes	characteristic
28	C₂	D₅₄₁⋊C₈	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.