Subgroups — #31772687

Order 17312.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#14524194	C₂	1	2	yes	maximal, complemented
2	C₂×D₂₁₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×#14524194	—	2	2	no	—
4	C₂²×D₅₄₁	C₄	1	1	yes	characteristic, complemented
5	C₂²×D₅₄₁	C₂²	1	1	yes	characteristic
6	D₂₁₆₄	—	2	2	no	—
7	C₂×C₄×C₅₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₅₄₁	C₂×C₄	1	1	yes	characteristic
9	C₂×D₅₄₁	—	2	1	no	—
10	C₂×D₅₄₁	—	4	1	no	—
11	C₂×D₅₄₁	—	4	1	no	—
12	C₂×D₅₄₁	D₄	1	2	yes	—
13	#14524194	—	4	2	no	—
14	C₄×C₅₄₁	—	2	1	no	—
15	C₂×C₅₄₁	—	2	1	no	—
16	C₂×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
17	D₅₄₁	—	2	2	no	—
18	D₅₄₁	—	4	1	no	—
19	C₅₄₁	#99	1	1	yes	characteristic, complemented, Sylow
20	#99	—	541	1	no	maximal, Sylow
21	C₂×D₄	—	541	1	no	—
22	C₂²⋊C₄	—	541	2	no	—
23	C₂³	—	541	1	no	—
24	C₂³	—	541	1	no	—
25	D₄	—	1082	2	no	—
26	C₂×C₄	—	1082	2	no	—
27	C₂×C₄	#14524194	1	1	yes	characteristic, complemented
28	C₂²	—	541	2	no	—
29	C₂²	—	1082	1	no	—
30	C₂²	—	2164	1	no	—
31	C₂²	—	2164	1	no	—
32	C₂²	C₂×#14524194	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	2164	2	no	—
35	C₂	—	2	1	no	—
36	C₂	—	1082	2	no	—
37	C₂	—	2164	1	no	—
38	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.