Group #21448925 — subgroups

Subgroups — #21448925

Order 7808.

448 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839648	C₂	1	4	yes	maximal
2	#16839648	C₂	1	4	yes	maximal
3	C₄⋊C₄×Dic₆₁	C₂	1	4	yes	maximal
4	#16839608	C₂	1	2	yes	maximal
5	C₂×#125×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₆₁	C₂²	1	4	yes	—
7	C₂×C₄×Dic₆₁	C₂²	1	4	yes	—
8	C₂×C₄×Dic₆₁	C₂²	1	4	yes	—
9	#14519684	C₂²	1	2	yes	—
10	#14519684	C₂²	1	2	yes	—
11	#14519684	C₂²	1	4	yes	—
12	#14519684	C₂²	1	4	yes	—
13	#14519684	C₂²	1	4	yes	—
14	#125×C₆₁	C₄	1	8	yes	complemented
15	C₂×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
20	C₂²×C₄×C₆₁	C₂³	1	4	yes	—
21	C₂²×Dic₆₁	C₂³	1	4	yes	—
22	C₂²×Dic₆₁	C₂³	1	4	yes	—
23	C₄⋊C₄×C₆₁	C₂×C₄	1	16	yes	—
24	C₄⋊C₄×C₆₁	C₂×C₄	1	8	yes	—
25	C₄²×C₆₁	C₂×C₄	1	4	yes	—
26	C₄⋊Dic₆₁	—	2	8	no	—
27	C₄×Dic₆₁	—	2	8	no	—
28	C₄×Dic₆₁	—	2	8	no	—
29	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	2	4	no	—
31	C₂×C₄×C₆₁	—	2	4	no	—
32	C₂×C₄×C₆₁	—	2	4	no	—
33	C₂×C₄×C₆₁	—	2	2	no	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	4	yes	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₆₁	C₂²×C₄	1	8	yes	—
37	C₂×Dic₆₁	—	2	4	no	—
38	C₂×Dic₆₁	—	2	4	no	—
39	C₂×Dic₆₁	—	2	4	no	—
40	C₂×Dic₆₁	—	2	4	no	—
41	C₂×Dic₆₁	—	2	4	no	—
42	C₂×Dic₆₁	#41	1	8	yes	—
43	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
44	C₂²×C₆₁	C₂×#41	1	4	yes	—
45	C₂²×C₆₁	2₋¹⁺⁴	1	2	yes	—
46	C₄×C₆₁	—	2	4	no	—
47	C₄×C₆₁	—	2	8	no	—
48	C₄×C₆₁	—	2	2	no	—
49	Dic₆₁	—	2	8	no	—
50	Dic₆₁	—	4	4	no	—
51	#2371	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	C₄×#41	1	2	yes	—
53	C₂×C₆₁	#519	1	1	yes	characteristic
54	C₂×C₆₁	#552	1	4	yes	—
55	C₂×#125	D₆₁	1	1	yes	characteristic
56	#387	—	61	4	no	—
57	#387	—	61	4	no	—
58	C₄×C₄⋊C₄	—	61	4	no	—
59	#376	—	61	2	no	—
60	C₆₁	#2371	1	1	yes	characteristic, complemented, Sylow
61	#125	Dic₆₁	1	8	yes	complemented
62	C₂×C₄⋊C₄	—	61	4	no	—
63	C₂×C₄⋊C₄	C₂×D₆₁	1	4	yes	—
64	C₂×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
65	C₂×C₄²	—	61	4	no	—
66	C₂×C₄²	—	61	4	no	—
67	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
68	#95	—	61	2	no	—
69	#95	—	61	4	no	—
70	#95	—	61	2	no	—
71	#95	—	61	4	no	—
72	#95	—	61	4	no	—
73	C₂²×C₄	—	61	4	no	—
74	C₂²×C₄	—	61	4	no	—
75	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
76	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
77	C₂²×C₄	C₂²×D₆₁	1	4	yes	—
78	C₄⋊C₄	—	122	8	no	—
79	C₄⋊C₄	C₂×Dic₆₁	1	16	yes	—
80	C₄⋊C₄	C₂×Dic₆₁	1	8	yes	—
81	C₄²	—	122	8	no	—
82	C₄²	—	122	8	no	—
83	C₄²	C₂×Dic₆₁	1	4	yes	—
84	C₂³	C₂³×D₆₁	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	61	8	no	—
90	C₂×C₄	—	122	4	no	—
91	C₂×C₄	—	122	4	no	—
92	C₂×C₄	—	122	4	no	—
93	C₂×C₄	—	122	4	no	—
94	C₂×C₄	—	122	4	no	—
95	C₂×C₄	C₂²×Dic₆₁	1	4	yes	—
96	C₂×C₄	C₂²×Dic₆₁	1	2	yes	—
97	C₂×C₄	C₂²×Dic₆₁	1	8	yes	—
98	C₂²	C₂³×Dic₆₁	1	1	yes	characteristic
99	C₂²	#41×D₆₁	1	4	yes	—
100	C₂²	#14519825	1	2	yes	—
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	2	2	no	—
104	C₄	—	122	8	no	—
105	C₄	—	244	4	no	—
106	C₂	#41×Dic₆₁	1	2	yes	—
107	C₂	#16840240	1	1	yes	characteristic
108	C₂	#16840444	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839648

C₂

yes

maximal

#16839648

C₂

yes

maximal

C₄⋊C₄×Dic₆₁

C₂

yes

maximal

#16839608

C₂

yes

maximal

C₂×#125×C₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

#125×C₆₁

C₄

yes

complemented

C₂×C₄⋊C₄×C₆₁

C₂²

yes

—

C₂×C₄⋊C₄×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×Dic₆₁

C₂³

yes

—

C₂²×Dic₆₁

C₂³

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₂³×C₆₁

C₂⁴

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

#41

yes

—

C₂²×C₆₁

C₂³×C₄

yes

characteristic

C₂²×C₆₁

C₂×#41

yes

—

C₂²×C₆₁

2₋¹⁺⁴

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

#2371

—

maximal, Sylow

C₂×C₆₁

C₄×#41

yes

—

C₂×C₆₁

#519

yes

characteristic

C₂×C₆₁

#552

yes

—

C₂×#125

D₆₁

yes

characteristic

#387

—

#387

—

C₄×C₄⋊C₄

—

#376

—

C₆₁

#2371

yes

characteristic, complemented, Sylow

#125

Dic₆₁

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₆₁

yes

—

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

C₂×Dic₆₁

yes

—

C₄⋊C₄

C₂×Dic₆₁

yes

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

C₂×Dic₆₁

yes

—

C₂³

C₂³×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂²×Dic₆₁

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

—

C₂²

C₂³×Dic₆₁

yes

characteristic

C₂²

#41×D₆₁

yes

—

100

C₂²

#14519825

yes

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

122

—

105

C₄

—

244

—

106

C₂

#41×Dic₆₁

yes

—

107

C₂

#16840240

yes

characteristic

108

C₂

#16840444

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₆₁
commutator	C₂²×C₆₁	C₂³×C₄
Fitting	C₂×#125×C₆₁	C₂
socle	C₂³×C₆₁	C₂⁴
hypercenter	C₂×#125	D₆₁
hypocenter	C₆₁	#2371
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₆₁

commutator

C₂²×C₆₁

C₂³×C₄

Fitting

C₂×#125×C₆₁

C₂

socle

C₂³×C₆₁

C₂⁴

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
14. #125×C₆₁	C₄	semidirect
60. C₆₁	#2371	semidirect
61. #125	Dic₆₁	semidirect

H ≅ G/N

type

14. #125×C₆₁

C₄

semidirect

60. C₆₁

#2371

semidirect

61. #125

Dic₆₁

semidirect

Subgroups — #21448925

Conjugacy classes of subgroups

Complements