Subgroups — #28414205

Order 14752.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301511	C₂	1	1	yes	maximal, characteristic, complemented
2	#20301510	C₂	1	2	yes	maximal, complemented
3	D₄₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16814786	C₂	1	2	yes	maximal, complemented
5	#20301500	C₂	1	1	yes	maximal, characteristic
6	#16814786	C₂²	1	1	yes	characteristic
7	#16814786	C₂²	1	2	yes	—
8	#16814786	C₂²	1	1	yes	characteristic
9	Dic₉₂₂	C₄	1	1	yes	characteristic
10	C₂²⋊D₄₆₁	C₄	1	2	yes	—
11	C₂×Dic₄₆₁	C₂²	1	2	yes	—
12	C₄×D₄₆₁	C₂²	1	1	yes	characteristic
13	D₄×C₄₆₁	C₄	1	1	yes	characteristic
14	C₂²×C₄₆₁	C₂×C₄	1	2	yes	—
15	C₂×D₄₆₁	C₂×C₄	1	1	yes	characteristic
16	C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
17	Dic₄₆₁	C₂×C₄	1	2	yes	—
18	Dic₄₆₁	C₂³	1	1	yes	characteristic
19	C₂×C₄₆₁	—	2	2	no	—
20	C₂×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
21	D₄₆₁	—	2	1	no	—
22	C₄₆₁	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	461	1	no	maximal, Sylow
24	#41	—	461	1	no	—
25	M₁₆	—	461	2	no	—
26	M₁₆	—	461	1	no	—
27	C₂×C₈	—	461	2	no	—
28	C₂×C₈	—	461	1	no	—
29	Q₈	—	461	1	no	—
30	D₄	—	461	2	no	—
31	D₄	#14270406	1	1	yes	characteristic
32	C₂×C₄	—	461	2	no	—
33	C₂×C₄	—	461	1	no	—
34	C₈	—	461	1	no	—
35	C₈	—	461	2	no	—
36	C₈	—	461	1	no	—
37	C₂²	—	461	1	no	—
38	C₂²	C₂×#14270406	1	2	yes	—
39	C₄	—	461	1	no	—
40	C₄	—	461	2	no	—
41	C₄	C₂×#14270406	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	922	1	no	—
44	C₂	C₂²×#14270406	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.