Subgroups — #31772691

Order 17312.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₄₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#14524194	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₅₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14524194	—	2	1	no	—
5	#16864520	—	2	1	no	—
6	Dic₁₀₈₂	—	2	1	no	—
7	Dic₁₀₈₂	C₄	1	1	yes	characteristic, complemented
8	C₄×D₅₄₁	—	2	1	no	—
9	C₄×D₅₄₁	C₂²	1	1	yes	characteristic
10	Q₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
11	C₂×D₅₄₁	D₄	1	1	yes	characteristic
12	#14524194	—	4	1	no	—
13	C₄×C₅₄₁	—	2	1	no	—
14	C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
15	Dic₅₄₁	—	2	1	no	—
16	Dic₅₄₁	D₄	1	1	yes	characteristic
17	C₂×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
18	D₅₄₁	SD₁₆	1	1	yes	characteristic
19	D₅₄₁	Q₁₆	1	1	yes	characteristic
20	C₅₄₁	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	541	1	no	maximal, Sylow
22	C₂×Q₈	—	541	1	no	—
23	C₂×C₈	—	541	1	no	—
24	C₄⋊C₄	—	541	1	no	—
25	Q₈	—	541	1	no	—
26	Q₈	—	1082	1	no	—
27	Q₈	#14524194	1	1	yes	characteristic, complemented
28	C₂×C₄	—	541	1	no	—
29	C₂×C₄	—	1082	1	no	—
30	C₂×C₄	—	1082	1	no	—
31	C₈	—	1082	1	no	—
32	C₂²	—	541	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	541	1	no	—
35	C₄	—	1082	1	no	—
36	C₄	—	2164	1	no	—
37	C₄	C₂×#14524194	1	1	yes	characteristic
38	C₂	—	541	1	no	—
39	C₂	—	541	1	no	—
40	C₂	C₂²⋊#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.