Subgroups — #16840123

Order 3904.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519776	C₂	1	1	yes	maximal, characteristic, complemented
2	#14519766	C₂	1	1	yes	maximal, characteristic
3	#14519701	C₂	1	1	yes	maximal, characteristic, complemented
4	#14519699	C₂	1	1	yes	maximal, characteristic
5	#14519697	C₂	1	1	yes	maximal, characteristic
6	#14519687	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×D₂₄₄	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₂₂	—	2	1	no	—
11	C₂×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
13	#11758198	—	2	1	no	—
14	#11758198	—	2	1	no	—
15	C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
16	#11758196	—	2	1	no	—
17	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
18	C₂×#92418	C₂²	1	1	yes	characteristic
19	C₂²×D₆₁	—	2	1	no	—
20	Q₈×C₆₁	—	2	1	no	—
21	Q₈×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₆₁	—	2	1	no	—
26	C₂×Dic₆₁	D₄	1	1	yes	characteristic
27	C₂×Dic₆₁	D₄	1	1	yes	characteristic
28	D₂₄₄	—	2	1	no	—
29	D₂₄₄	—	2	1	no	—
30	Dic₁₂₂	—	4	2	no	—
31	C₈×C₆₁	—	2	1	no	—
32	#92418	—	2	1	no	—
33	C₂²×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×D₆₁	—	4	1	no	—
35	C₂×D₆₁	—	4	1	no	—
36	C₂×D₆₁	—	4	1	no	—
37	C₄×C₆₁	—	4	1	no	—
38	C₄×C₆₁	—	4	1	no	—
39	C₄×C₆₁	#41	1	1	yes	characteristic
40	C₄×C₆₁	#41	1	1	yes	characteristic
41	Dic₆₁	—	2	1	no	—
42	Dic₆₁	—	2	1	no	—
43	Dic₆₁	—	4	1	no	—
44	C₂×C₆₁	#124	1	1	yes	characteristic
45	C₂×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₆₁	#137	1	1	yes	characteristic
47	D₆₁	—	8	1	no	—
48	#489	—	61	1	no	maximal, Sylow
49	C₆₁	#489	1	1	yes	characteristic, complemented, Sylow
50	C₄⋊Q₈	—	61	1	no	—
51	#124	—	61	1	no	—
52	#103	—	61	1	no	—
53	#103	D₆₁	1	1	yes	characteristic, complemented
54	#102	—	61	1	no	—
55	#102	—	61	1	no	—
56	#97	—	61	1	no	—
57	C₂×Q₈	—	122	1	no	—
58	C₂×Q₈	C₂×D₆₁	1	1	yes	characteristic
59	C₂×D₄	—	61	1	no	—
60	C₂×C₈	—	61	1	no	—
61	C₂×C₈	C₂×D₆₁	1	1	yes	characteristic
62	C₄⋊C₄	—	61	1	no	—
63	C₄⋊C₄	—	122	1	no	—
64	C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	122	1	no	—
66	C₂²⋊C₄	—	122	1	no	—
67	C₄²	—	61	1	no	—
68	C₂³	—	122	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	244	2	no	—
72	D₄	—	122	1	no	—
73	D₄	—	122	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	61	1	no	—
77	C₂×C₄	—	61	1	no	—
78	C₂×C₄	—	122	1	no	—
79	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	122	1	no	—
82	C₂²	—	244	1	no	—
83	C₂²	—	244	1	no	—
84	C₂²	—	244	1	no	—
85	C₂²	D₄×D₆₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	122	1	no	—
89	C₄	—	122	1	no	—
90	C₄	—	244	1	no	—
91	C₄	#11758222	1	1	yes	characteristic
92	C₄	#11758224	1	1	yes	characteristic
93	C₂	—	488	1	no	—
94	C₂	#14519763	1	1	yes	characteristic
95	C₂	#14519804	1	1	yes	characteristic
96	C₂	#14519809	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₆₁
commutator, cosocle	C₂×C₄×C₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₆₁
Fitting	#103×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₄
prime radical	C₂×D₂₄₄	C₂²
hypercenter	#103	D₆₁
hypocenter	C₆₁	#489
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
1. #14519776	C₂	semidirect
3. #14519701	C₂	semidirect
6. #14519687	C₂	semidirect
7. #103×C₆₁	C₂	semidirect
49. C₆₁	#489	semidirect
53. #103	D₆₁	semidirect

Maximal subgroups

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

subgroup	index
#14519776	2
#14519766	2
#14519701	2
#14519699	2
#14519697	2
#14519687	2
#103×C₆₁	2
#489	61