Group #21445669 — subgroups

Subgroups — C₄×#14519706 #21445669

Order 7808.

316 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₂×#14519706	C₂	1	2	yes	maximal
2	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic
3	C₄²×Dic₆₁	C₂	1	1	yes	maximal, characteristic
4	#16839516	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#92418	C₂²	1	2	yes	—
7	C₂×C₄×Dic₆₁	C₄	1	2	yes	—
8	C₂×C₄×Dic₆₁	C₄	1	2	yes	—
9	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
11	#14519706	C₄	1	8	yes	direct product factor
12	C₄×#92418	—	2	2	no	—
13	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₆₁	—	2	2	no	—
16	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
18	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
20	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	—	2	2	no	—
22	C₂×C₈×C₆₁	—	2	2	no	—
23	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
24	C₄²×C₆₁	D₄	1	2	yes	—
25	C₄²×C₆₁	Q₈	1	2	yes	—
26	C₄×Dic₆₁	—	2	4	no	—
27	C₄×Dic₆₁	—	2	2	no	—
28	C₄×Dic₆₁	C₈	1	8	yes	complemented
29	C₄×Dic₆₁	C₂×C₄	1	4	yes	—
30	C₂×#92418	—	2	2	no	—
31	C₂×#92418	—	2	2	no	—
32	C₂×#92418	C₂×C₄	1	4	yes	—
33	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
35	C₂×C₄×C₆₁	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₆₁	M₁₆	1	4	yes	—
37	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₆₁	#41	1	2	yes	—
41	C₂×Dic₆₁	—	2	2	no	—
42	C₂×Dic₆₁	—	2	2	no	—
43	C₂×Dic₆₁	—	2	2	no	—
44	C₂×Dic₆₁	C₄²	1	2	yes	—
45	C₂×Dic₆₁	C₄²	1	2	yes	—
46	C₂×Dic₆₁	C₂×C₈	1	4	yes	—
47	C₂×Dic₆₁	C₂×C₈	1	4	yes	—
48	C₈×C₆₁	—	2	4	no	—
49	#92418	—	2	4	no	—
50	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
51	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₆₁	#117	1	1	yes	characteristic
53	C₂²×C₆₁	C₂²×C₈	1	2	yes	—
54	C₂²×C₆₁	C₂×M₁₆	1	2	yes	—
55	C₄×C₆₁	C₄⋊C₈	1	8	yes	complemented
56	C₄×C₆₁	C₄×D₄	1	2	yes	—
57	C₄×C₆₁	C₄×Q₈	1	2	yes	—
58	Dic₆₁	—	2	2	no	—
59	Dic₆₁	—	2	4	no	—
60	Dic₆₁	C₄×C₈	1	4	yes	complemented
61	C₄×C₄⋊C₈	—	61	1	no	maximal, Sylow
62	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
64	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
65	C₂×C₆₁	C₂×C₄⋊C₈	1	2	yes	—
66	C₂×C₆₁	#431	1	2	yes	—
67	C₂×C₄⋊C₈	—	61	2	no	—
68	C₂×C₄×C₈	—	61	1	no	—
69	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
70	C₄³	—	61	1	no	—
71	#336	—	61	2	no	—
72	C₆₁	C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₈	—	61	2	no	—
74	C₂²×C₈	C₂×D₆₁	1	2	yes	—
75	C₂×C₄²	—	61	2	no	—
76	C₂×C₄²	—	61	1	no	—
77	C₂×C₄²	—	61	2	no	—
78	C₂×C₄²	—	61	1	no	—
79	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
80	C₄⋊C₈	—	61	8	no	—
81	C₄×C₈	—	2	2	no	—
82	C₄×C₈	—	122	2	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	1	no	—
85	C₂²×C₄	—	61	2	no	—
86	C₂²×C₄	C₄×D₆₁	1	2	yes	—
87	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	61	4	no	—
91	C₂×C₈	—	122	2	no	—
92	C₂×C₈	—	122	2	no	—
93	C₂×C₈	C₄×D₆₁	1	4	yes	—
94	C₄²	—	61	8	no	—
95	C₄²	—	61	4	no	—
96	C₄²	—	122	4	no	—
97	C₄²	—	122	2	no	—
98	C₄²	Dic₁₂₂	1	2	yes	—
99	C₄²	C₂²⋊D₆₁	1	2	yes	—
100	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
101	C₂×C₄	—	61	2	no	—
102	C₂×C₄	—	61	4	no	—
103	C₂×C₄	—	61	2	no	—
104	C₂×C₄	—	61	4	no	—
105	C₂×C₄	—	122	2	no	—
106	C₂×C₄	—	122	2	no	—
107	C₂×C₄	—	122	2	no	—
108	C₂×C₄	C₈×D₆₁	1	4	yes	—
109	C₂×C₄	#11758189	1	4	yes	—
110	C₂×C₄	#11758196	1	4	yes	—
111	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
113	C₂×C₄	#11758222	1	2	yes	—
114	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
115	C₈	—	2	4	no	—
116	C₈	—	122	4	no	—
117	C₂²	C₄²×D₆₁	1	1	yes	characteristic
118	C₂²	C₂×#11758196	1	1	yes	characteristic
119	C₂²	#14519734	1	1	yes	characteristic
120	C₂²	C₂×C₈×D₆₁	1	2	yes	—
121	C₂²	C₂×#11758189	1	2	yes	—
122	C₄	—	61	4	no	—
123	C₄	—	122	2	no	—
124	C₄	—	122	4	no	—
125	C₄	#14519706	1	8	yes	direct product factor
126	C₄	C₄×C₂²⋊D₆₁	1	2	yes	—
127	C₄	C₄×Dic₁₂₂	1	2	yes	—
128	C₂	C₄×#11758196	1	1	yes	characteristic
129	C₂	C₄×C₈×D₆₁	1	1	yes	characteristic
130	C₂	C₄×#11758189	1	1	yes	characteristic
131	C₂	C₂×#14519706	1	2	yes	—
132	C₂	#16839813	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519706

C₂

yes

maximal

C₂×C₄×#92418

C₂

yes

maximal, characteristic

C₄²×Dic₆₁

C₂

yes

maximal, characteristic

#16839516

C₂

yes

maximal

C₂×C₄×C₈×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄×Dic₆₁

C₄

yes

—

C₂×C₄×Dic₆₁

C₄

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

C₄

yes

direct product factor

C₄×#92418

—

C₂²×C₈×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

D₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₈

yes

complemented

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄²

yes

—

C₂×Dic₆₁

C₄²

yes

—

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#117

yes

characteristic

C₂²×C₆₁

C₂²×C₈

yes

—

C₂²×C₆₁

C₂×M₁₆

yes

—

C₄×C₆₁

C₄⋊C₈

yes

complemented

C₄×C₆₁

C₄×D₄

yes

—

C₄×C₆₁

C₄×Q₈

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

C₄×C₈

yes

complemented

C₄×C₄⋊C₈

—

maximal, Sylow

C₂×C₆₁

C₄×C₄⋊C₄

yes

characteristic

C₂×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×C₆₁

C₄×M₁₆

yes

characteristic

C₂×C₆₁

C₂×C₄⋊C₈

yes

—

C₂×C₆₁

#431

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₆₁

yes

characteristic

C₄³

—

#336

—

C₆₁

C₄×C₄⋊C₈

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₂²⋊D₆₁

yes

—

100

C₂³

C₂×C₄×D₆₁

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

122

—

106

C₂×C₄

—

122

—

107

C₂×C₄

—

122

—

108

C₂×C₄

C₈×D₆₁

yes

—

109

C₂×C₄

#11758189

yes

—

110

C₂×C₄

#11758196

yes

—

111

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

112

C₂×C₄

C₂×C₄×D₆₁

yes

—

113

C₂×C₄

#11758222

yes

—

114

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

115

C₈

—

116

C₈

—

122

—

117

C₂²

C₄²×D₆₁

yes

characteristic

118

C₂²

C₂×#11758196

yes

characteristic

119

C₂²

#14519734

yes

characteristic

120

C₂²

C₂×C₈×D₆₁

yes

—

121

C₂²

C₂×#11758189

yes

—

122

C₄

—

123

C₄

—

122

—

124

C₄

—

122

—

125

C₄

#14519706

yes

direct product factor

126

C₄

C₄×C₂²⋊D₆₁

yes

—

127

C₄

C₄×Dic₁₂₂

yes

—

128

C₂

C₄×#11758196

yes

characteristic

129

C₂

C₄×C₈×D₆₁

yes

characteristic

130

C₂

C₄×#11758189

yes

characteristic

131

C₂

C₂×#14519706

yes

—

132

C₂

#16839813

yes

—

	subgroup	G/H
center	C₂×C₄²	C₂×D₆₁
commutator	C₂×C₆₁	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×C₄×C₈×C₆₁	C₂
socle	C₂³×C₆₁	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	C₄×C₄⋊C₈
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄²

C₂×D₆₁

commutator

C₂×C₆₁

C₂×C₄×C₈

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×C₄×C₈×C₆₁

C₂

socle

C₂³×C₆₁

C₂²×C₄

hypercenter

C₂×C₄×C₈

D₆₁

hypocenter

C₆₁

C₄×C₄⋊C₈

LCS

G ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
11. #14519706	C₄	direct (N × H)
28. C₄×Dic₆₁	C₈	semidirect
55. C₄×C₆₁	C₄⋊C₈	semidirect
60. Dic₆₁	C₄×C₈	semidirect
72. C₆₁	C₄×C₄⋊C₈	semidirect
125. C₄	#14519706	direct (N × H)

H ≅ G/N

type

11. #14519706

C₄

direct (N × H)

28. C₄×Dic₆₁

C₈

semidirect

55. C₄×C₆₁

C₄⋊C₈

semidirect

60. Dic₆₁

C₄×C₈

semidirect

72. C₆₁

C₄×C₄⋊C₈

semidirect

125. C₄

#14519706

direct (N × H)

Subgroups — C₄×#14519706 #21445669

Conjugacy classes of subgroups

Complements

Subgroups — C4×#14519706 #21445669

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14519706 #21445669