Group #21461475 — subgroups

Subgroups — #21461475

Order 7808.

328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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	#16840721	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519831	C₂	1	2	yes	maximal
3	C₂×C₈×#6923	C₂	1	2	yes	maximal
4	#16840698	C₂	1	1	yes	maximal, characteristic
5	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×D₆₁⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×#6923	C₂²	1	2	yes	—
8	#14519832	C₄	1	4	yes	complemented
9	#14519831	C₄	1	8	yes	complemented
10	C₈×#6923	C₄	1	8	yes	complemented
11	(C₂×#6923)⋊C₄	C₄	1	4	yes	—
12	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
14	C₄²×D₆₁	C₂²	1	1	yes	characteristic
15	C₄×#92418	C₄	1	1	yes	characteristic, complemented
16	C₈×Dic₆₁	C₄	1	1	yes	characteristic, complemented
17	C₈×Dic₆₁	C₄	1	1	yes	characteristic, complemented
18	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
19	C₂²×#6923	C₂×C₄	1	4	yes	—
20	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
22	C₂×#92420	C₂×C₄	1	4	yes	—
23	C₄×#6923	C₂×C₄	1	4	yes	—
24	C₄×#6923	C₂×C₄	1	4	yes	—
25	D₆₁⋊C₈	C₂×C₄	1	4	yes	—
26	D₆₁⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
32	C₂×#92418	C₂×C₄	1	1	yes	characteristic
33	C₂×#92418	C₂×C₄	1	1	yes	characteristic
34	C₈×D₆₁	C₂×C₄	1	4	yes	—
35	C₈×D₆₁	C₂×C₄	1	4	yes	—
36	C₂²×D₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×#6923	—	2	8	no	—
38	C₂×#6923	C₄²	1	8	yes	—
39	C₂×C₄×C₆₁	C₄²	1	2	yes	—
40	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₆₁	C₄²	1	2	yes	—
42	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
43	C₄×D₆₁	—	2	4	no	—
44	C₄×D₆₁	C₂²×C₄	1	2	yes	—
45	C₄×D₆₁	C₂²×C₄	1	2	yes	—
46	#92420	C₄²	1	8	yes	—
47	C₈×C₆₁	C₄²	1	2	yes	—
48	C₈×C₆₁	C₄²	1	2	yes	—
49	#92418	C₄²	1	2	yes	—
50	#92418	C₄²	1	2	yes	—
51	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
52	C₂×D₆₁	C₂×C₄²	1	2	yes	—
53	C₂×D₆₁	#131	1	4	yes	—
54	#6923	—	2	8	no	—
55	C₄×C₆₁	—	2	2	no	—
56	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
57	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
58	Dic₆₁	—	2	2	no	—
59	Dic₆₁	C₂×C₄²	1	2	yes	—
60	#1726	—	61	1	no	maximal, Sylow
61	C₂×C₆₁	C₄³	1	1	yes	characteristic
62	C₂×C₆₁	#405	1	2	yes	—
63	D₆₁	#405	1	4	yes	—
64	C₂×#97	—	61	2	no	—
65	C₂×#97	—	61	1	no	—
66	C₂×C₄×C₈	—	61	2	no	—
67	C₂×C₄×C₈	—	61	1	no	—
68	#376	—	61	1	no	—
69	C₆₁	#1726	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₈	—	61	2	no	—
71	C₂²×C₈	—	61	1	no	—
72	C₂²×C₈	—	61	1	no	—
73	C₂×C₄²	—	61	2	no	—
74	C₂×C₄²	—	61	1	no	—
75	#97	—	61	8	no	—
76	#97	—	61	4	no	—
77	C₄×C₈	—	61	8	no	—
78	C₄×C₈	—	61	1	no	—
79	C₄×C₈	—	61	1	no	—
80	C₄×C₈	—	61	1	no	—
81	C₄×C₈	#6923	1	1	yes	characteristic, complemented
82	#95	—	61	4	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	4	no	—
85	C₂²×C₄	—	61	2	no	—
86	C₂×C₈	—	61	4	no	—
87	C₂×C₈	—	61	4	no	—
88	C₂×C₈	—	61	4	no	—
89	C₂×C₈	—	61	1	no	—
90	C₂×C₈	—	61	1	no	—
91	C₂×C₈	—	61	4	no	—
92	C₂×C₈	—	61	4	no	—
93	C₂×C₈	C₂×#6923	1	1	yes	characteristic
94	C₂×C₈	C₂×#6923	1	1	yes	characteristic
95	C₄²	—	61	4	no	—
96	C₄²	—	61	4	no	—
97	C₄²	—	61	2	no	—
98	C₄²	—	61	1	no	—
99	C₄²	C₂×#6923	1	1	yes	characteristic
100	C₂³	—	61	1	no	—
101	C₂×C₄	—	61	1	no	—
102	C₂×C₄	—	61	2	no	—
103	C₂×C₄	—	61	2	no	—
104	C₂×C₄	—	61	8	no	—
105	C₂×C₄	—	61	2	no	—
106	C₂×C₄	—	122	4	no	—
107	C₂×C₄	—	122	8	no	—
108	C₂×C₄	C₄×#6923	1	2	yes	—
109	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
110	C₈	—	61	8	no	—
111	C₈	—	61	2	no	—
112	C₈	—	61	2	no	—
113	C₈	C₄×#6923	1	2	yes	—
114	C₈	C₄×#6923	1	2	yes	—
115	C₂²	—	61	4	no	—
116	C₂²	—	61	2	no	—
117	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	61	2	no	—
120	C₄	—	122	8	no	—
121	C₄	—	122	2	no	—
122	C₄	C₂×C₄×#6923	1	1	yes	characteristic
123	C₄	C₂×C₄×#6923	1	1	yes	characteristic
124	C₂	—	61	4	no	—
125	C₂	C₄²×#6923	1	1	yes	characteristic
126	C₂	#16840725	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840721

C₂

yes

maximal, characteristic

C₂×#14519831

C₂

yes

maximal

C₂×C₈×#6923

C₂

yes

maximal

#16840698

C₂

yes

maximal, characteristic

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

C₂²

yes

—

C₂×C₄×#6923

C₂²

yes

—

#14519832

C₄

yes

complemented

#14519831

C₄

yes

complemented

C₈×#6923

C₄

yes

complemented

(C₂×#6923)⋊C₄

C₄

yes

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic, complemented

C₈×Dic₆₁

C₄

yes

characteristic, complemented

C₈×Dic₆₁

C₄

yes

characteristic, complemented

C₄×C₈×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂×#92420

C₂×C₄

yes

—

C₄×#6923

C₂×C₄

yes

—

C₄×#6923

C₂×C₄

yes

—

D₆₁⋊C₈

C₂×C₄

yes

—

D₆₁⋊C₈

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₂²×D₆₁

C₂²×C₄

yes

characteristic

C₂×#6923

—

C₂×#6923

C₄²

yes

—

C₂×C₄×C₆₁

C₄²

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₂²×C₄

yes

—

C₄×D₆₁

C₂²×C₄

yes

—

#92420

C₄²

yes

—

C₈×C₆₁

C₄²

yes

—

C₈×C₆₁

C₄²

yes

—

#92418

C₄²

yes

—

#92418

C₄²

yes

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

C₂×C₄²

yes

—

C₂×D₆₁

#131

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₂×C₄²

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂×C₄²

yes

—

#1726

—

maximal, Sylow

C₂×C₆₁

C₄³

yes

characteristic

C₂×C₆₁

#405

yes

—

D₆₁

#405

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₆₁

#1726

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic, complemented

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

100

C₂³

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

122

—

107

C₂×C₄

—

122

—

108

C₂×C₄

C₄×#6923

yes

—

109

C₂×C₄

C₂²×#6923

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

C₄×#6923

yes

—

114

C₈

C₄×#6923

yes

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×C₄×#6923

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

122

—

121

C₄

—

122

—

122

C₄

C₂×C₄×#6923

yes

characteristic

123

C₄

C₂×C₄×#6923

yes

characteristic

124

C₂

—

125

C₂

C₄²×#6923

yes

characteristic

126

C₂

#16840725

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#6923
commutator	C₂×C₆₁	C₄³
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄²
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1726
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#6923

commutator

C₂×C₆₁

C₄³

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄²

C₄×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
8. #14519832	C₄	semidirect
9. #14519831	C₄	semidirect
10. C₈×#6923	C₄	semidirect
15. C₄×#92418	C₄	semidirect
16. C₈×Dic₆₁	C₄	semidirect
17. C₈×Dic₆₁	C₄	semidirect
18. C₄×C₈×C₆₁	C₄	semidirect
69. C₆₁	#1726	semidirect
81. C₄×C₈	#6923	semidirect

H ≅ G/N

type

8. #14519832

C₄

semidirect

9. #14519831

C₄

semidirect

10. C₈×#6923

C₄

semidirect

15. C₄×#92418

C₄

semidirect

16. C₈×Dic₆₁

C₄

semidirect

17. C₈×Dic₆₁

C₄

semidirect

18. C₄×C₈×C₆₁

C₄

semidirect

69. C₆₁

#1726

semidirect

81. C₄×C₈

#6923

semidirect

Subgroups — #21461475

Conjugacy classes of subgroups

Complements