Subgroups — #16840147

Order 3904.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758201	C₂	1	2	yes	maximal, complemented
2	C₂×D₄₈₈	C₂	1	1	yes	maximal, characteristic
3	#14519766	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₆₁	C₂²	1	2	yes	—
7	C₂×D₂₄₄	C₂²	1	2	yes	—
8	Q₁₆×C₆₁	—	2	2	no	—
9	C₂×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	#11758201	—	2	4	no	—
11	#11758198	—	2	4	no	—
12	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₂×#92418	C₂²	1	1	yes	characteristic
14	D₄₈₈	—	2	2	no	—
15	C₂²×D₆₁	—	2	2	no	—
16	Q₈×C₆₁	—	2	2	no	—
17	Q₈×C₆₁	—	2	2	no	—
18	C₂×C₄×C₆₁	—	2	2	no	—
19	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
20	C₂×Dic₆₁	D₄	1	2	yes	—
21	D₂₄₄	—	2	2	no	—
22	D₂₄₄	—	2	2	no	—
23	C₈×C₆₁	D₄	1	2	yes	—
24	#92418	D₄	1	2	yes	—
25	C₂²×C₆₁	C₂×D₄	1	1	yes	characteristic
26	C₂×D₆₁	—	4	2	no	—
27	C₂×D₆₁	—	4	4	no	—
28	C₄×C₆₁	—	4	2	no	—
29	C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	Dic₆₁	—	2	2	no	—
32	C₂×C₆₁	#127	1	1	yes	characteristic
33	C₂×C₆₁	#135	1	2	yes	—
34	D₆₁	—	8	2	no	—
35	#495	—	61	1	no	maximal, Sylow
36	C₆₁	#495	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	D₆₁	1	1	yes	characteristic, complemented
38	C₂×SD₁₆	—	61	2	no	—
39	C₂×D₈	—	61	1	no	—
40	#124	—	61	2	no	—
41	C₄×C₈	—	61	1	no	—
42	C₂×Q₈	C₂×D₆₁	1	2	yes	—
43	C₂×D₄	—	61	2	no	—
44	Q₁₆	—	2	2	no	—
45	SD₁₆	—	122	4	no	—
46	D₈	—	122	2	no	—
47	C₂×C₈	—	61	1	no	—
48	C₂×C₈	C₂×D₆₁	1	1	yes	characteristic
49	C₂²⋊C₄	—	122	4	no	—
50	C₄²	—	61	1	no	—
51	C₂³	—	122	2	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	D₄	—	122	2	no	—
55	D₄	—	122	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	61	2	no	—
58	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
59	C₈	—	61	2	no	—
60	C₈	C₂²⋊D₆₁	1	2	yes	—
61	C₂²	—	244	2	no	—
62	C₂²	—	244	4	no	—
63	C₂²	D₄×D₆₁	1	1	yes	characteristic
64	C₄	—	4	2	no	—
65	C₄	—	122	2	no	—
66	C₄	D₄×D₆₁	1	1	yes	characteristic
67	C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
68	C₂	—	488	2	no	—
69	C₂	#14519773	1	1	yes	characteristic
70	C₂	#14519800	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₆₁
commutator, cosocle	C₂×C₄×C₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₆₁
Fitting	C₂×Q₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₄
prime radical	C₂×D₄₈₈	C₂
hypercenter	C₂×Q₁₆	D₆₁
hypocenter	C₆₁	#495
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11758201	C₂	semidirect
3. #14519766	C₂	semidirect
4. C₈×Dic₆₁	C₂	semidirect
5. C₂×Q₁₆×C₆₁	C₂	semidirect
36. C₆₁	#495	semidirect
37. C₂×Q₁₆	D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758201	2
C₂×D₄₈₈	2
#14519766	2
C₈×Dic₆₁	2
C₂×Q₁₆×C₆₁	2
#495	61