Subgroups — C₂²×D₂₁₆₄ #31772666

Order 17312.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₅₄₁	C₂	1	2	yes	maximal, complemented
2	C₂×D₂₁₆₄	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅₄₁	—	2	8	no	—
5	C₂²×D₅₄₁	C₂²	1	12	yes	complemented
6	D₂₁₆₄	C₂²	1	16	yes	direct product factor
7	C₂³×C₅₄₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅₄₁	C₂²	1	6	yes	complemented
9	C₂²×C₅₄₁	D₄	1	4	yes	complemented
10	C₂²×C₅₄₁	C₂³	1	3	yes	—
11	C₂×D₅₄₁	—	2	24	no	—
12	C₂×D₅₄₁	C₂³	1	8	yes	complemented
13	C₄×C₅₄₁	C₂³	1	4	yes	complemented
14	C₂×C₅₄₁	C₂×D₄	1	6	yes	complemented
15	C₂×C₅₄₁	C₂⁴	1	1	yes	characteristic
16	D₅₄₁	—	2	8	no	—
17	C₅₄₁	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×D₄	—	541	1	no	maximal, Sylow
19	C₂⁴	—	541	2	no	—
20	C₂×D₄	—	541	12	no	—
21	C₂²×C₄	D₅₄₁	1	1	yes	characteristic, complemented
22	C₂³	—	541	12	no	—
23	C₂³	—	1082	8	no	—
24	C₂³	C₂×D₅₄₁	1	1	yes	characteristic
25	D₄	—	541	16	no	—
26	C₂×C₄	C₂×D₅₄₁	1	6	yes	complemented
27	C₂²	—	541	8	no	—
28	C₂²	—	1082	24	no	—
29	C₂²	D₂₁₆₄	1	4	yes	direct product factor
30	C₂²	C₂²×D₅₄₁	1	3	yes	—
31	C₄	C₂²×D₅₄₁	1	4	yes	complemented
32	C₂	—	1082	8	no	—
33	C₂	C₂×D₂₁₆₄	1	6	yes	direct product factor
34	C₂	C₂³×D₅₄₁	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.