Subgroups — #46830010

Order 34624.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₆₅₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#31772534	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃₂₈	—	2	1	no	—
5	D₈×C₅₄₁	—	2	1	no	—
6	C₁₆×C₅₄₁	C₂²	1	1	yes	characteristic
7	D₂₁₆₄	—	4	1	no	—
8	D₄×C₅₄₁	—	4	1	no	—
9	C₈×C₅₄₁	D₄	1	1	yes	characteristic
10	C₂²×C₅₄₁	—	8	1	no	—
11	C₂×D₅₄₁	—	8	1	no	—
12	C₄×C₅₄₁	D₈	1	1	yes	characteristic
13	C₂×C₅₄₁	—	16	1	no	—
14	C₂×C₅₄₁	D₁₆	1	1	yes	characteristic
15	D₅₄₁	—	16	1	no	—
16	C₅₄₁	D₃₂	1	1	yes	characteristic, complemented, Sylow
17	D₃₂	—	541	1	no	maximal, Sylow
18	D₁₆	—	541	1	no	—
19	D₁₆	D₅₄₁	1	1	yes	characteristic, complemented
20	C₃₂	—	541	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	1082	1	no	—
23	C₁₆	C₂×D₅₄₁	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	2164	1	no	—
26	C₈	C₂²⋊D₅₄₁	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	4328	1	no	—
29	C₄	#22575821	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	8656	1	no	—
32	C₂	#31772569	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.