Subgroups — #44442991

Order 29504.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₆₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#28414189	C₂	1	1	yes	maximal, characteristic, complemented
3	#28414141	C₂	1	1	yes	maximal, characteristic
4	#20301511	—	2	1	no	—
5	#20301504	—	2	1	no	—
6	#20301502	—	2	1	no	—
7	#20301488	—	2	1	no	—
8	D₃₆₈₈	C₄	1	1	yes	characteristic
9	C₈×D₄₆₁	C₂²	1	1	yes	characteristic
10	Q₁₆×C₄₆₁	C₄	1	1	yes	characteristic
11	#16814786	—	4	1	no	—
12	D₁₈₄₄	—	2	1	no	—
13	D₁₈₄₄	—	4	1	no	—
14	C₄×D₄₆₁	—	4	1	no	—
15	C₄×D₄₆₁	D₄	1	1	yes	characteristic
16	#16814779	D₄	1	1	yes	characteristic
17	Q₈×C₄₆₁	—	2	1	no	—
18	C₈×C₄₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×D₄₆₁	—	4	1	no	—
20	C₂×D₄₆₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₄₆₁	—	4	1	no	—
22	C₄×C₄₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₄₆₁	D₈	1	1	yes	characteristic
24	C₂×C₄₆₁	#102	1	1	yes	characteristic
25	D₄₆₁	—	2	1	no	—
26	D₄₆₁	—	8	1	no	—
27	C₄₆₁	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	461	1	no	maximal, Sylow
29	#135	—	461	1	no	—
30	C₂×C₁₆	—	461	1	no	—
31	#108	—	461	1	no	—
32	#41	—	922	1	no	—
33	Q₁₆	#14270406	1	1	yes	characteristic
34	SD₁₆	—	922	1	no	—
35	D₈	—	461	1	no	—
36	M₁₆	—	922	1	no	—
37	C₂×C₈	—	461	1	no	—
38	C₁₆	—	922	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	1844	1	no	—
41	D₄	—	922	1	no	—
42	C₂×C₄	—	1844	1	no	—
43	C₂×C₄	—	461	1	no	—
44	C₈	—	1844	1	no	—
45	C₈	—	461	1	no	—
46	C₈	C₂×#14270406	1	1	yes	characteristic
47	C₂²	—	1844	1	no	—
48	C₂²	—	461	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	461	1	no	—
51	C₄	C₂²⋊#14270406	1	1	yes	characteristic
52	C₂	—	3688	1	no	—
53	C₂	—	922	1	no	—
54	C₂	#28414180	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28414180
commutator	C₈×C₄₆₁	C₂×C₄
Frattini	C₈	C₂×#14270406
Fitting	Q₁₆×C₄₆₁	C₄
socle	C₂×C₄₆₁	#102
prime radical	#28414141	C₂
cosocle	C₈×D₄₆₁	C₂²
hypercenter	Q₁₆	#14270406
hypocenter	C₄₆₁	#359
LCS	G ▷ C₈×C₄₆₁ ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₄₆₁⋊C₁₆	C₂	semidirect
2. #28414189	C₂	semidirect
27. C₄₆₁	#359	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄₆₁⋊C₁₆	2
#28414189	2
#28414141	2
#359	461