Group #21461626 — subgroups

Subgroups — #21461626

Order 7808.

224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14519847	C₂	1	1	yes	maximal, characteristic
2	#16840727	C₂	1	2	yes	maximal
3	C₂×#14519831	C₂	1	1	yes	maximal, characteristic
4	#16840632	C₂	1	2	yes	maximal
5	#16839799	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₂²	1	2	yes	—
7	C₂×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×#6923	C₂²	1	1	yes	characteristic
9	#14519847	C₄	1	4	yes	complemented
10	#14519832	—	2	2	no	—
11	#14519831	C₄	1	4	yes	complemented
12	C₄×#92420	—	2	2	no	—
13	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
14	#14519735	C₂²	1	2	yes	—
15	#14519711	C₄	1	1	yes	characteristic, complemented
16	#14519708	C₄	1	2	yes	complemented
17	#107×C₆₁	C₄	1	1	yes	characteristic, complemented
18	C₂²×#6923	—	2	1	no	—
19	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
20	C₂×#92420	—	2	2	no	—
21	C₂×#92420	D₄	1	2	yes	—
22	C₄×#6923	—	2	1	no	—
23	C₄×#6923	C₂×C₄	1	2	yes	—
24	#11758213	—	2	2	no	—
25	#11758213	C₂×C₄	1	4	yes	—
26	D₆₁⋊C₈	C₂×C₄	1	2	yes	—
27	D₆₁⋊C₈	Q₈	1	2	yes	—
28	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
30	#11758198	—	2	2	no	—
31	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
32	C₄×Dic₆₁	—	2	2	no	—
33	C₂×#92418	C₂×C₄	1	1	yes	characteristic
34	C₈×D₆₁	C₂×C₄	1	2	yes	—
35	C₈×D₆₁	C₂×C₄	1	2	yes	—
36	C₂²×D₆₁	#41	1	1	yes	characteristic
37	C₂×#6923	—	2	2	no	—
38	C₂×#6923	—	4	1	no	—
39	C₂×#6923	—	4	1	no	—
40	C₂×C₄×C₆₁	—	2	2	no	—
41	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₆₁	—	2	2	no	—
43	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
44	C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
45	C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
46	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
47	C₄×D₆₁	#41	1	1	yes	characteristic
48	#92420	—	2	4	no	—
49	#92420	C₄⋊C₄	1	4	yes	—
50	C₈×C₆₁	C₄²	1	2	yes	—
51	#92418	C₄²	1	2	yes	—
52	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
53	C₂×D₆₁	—	2	1	no	—
54	C₂×D₆₁	—	2	1	no	—
55	C₂×D₆₁	#117	1	1	yes	characteristic
56	C₂×D₆₁	C₄×Q₈	1	1	yes	characteristic
57	#6923	—	4	2	no	—
58	C₄×C₆₁	—	4	2	no	—
59	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
60	C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
61	Dic₆₁	—	4	2	no	—
62	Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
63	Dic₆₁	C₄×D₄	1	1	yes	characteristic
64	#1773	—	61	1	no	maximal, Sylow
65	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₆₁	#444	1	1	yes	characteristic
67	C₂×C₆₁	#444	1	1	yes	characteristic
68	D₆₁	—	2	1	no	—
69	D₆₁	—	2	1	no	—
70	C₂×#108	—	61	1	no	—
71	#427	—	61	1	no	—
72	#405	—	61	2	no	—
73	C₂×#97	—	61	1	no	—
74	#339	—	61	2	no	—
75	C₆₁	#1773	1	1	yes	characteristic, complemented, Sylow
76	C₂×M₁₆	—	61	2	no	—
77	C₂²×C₈	—	61	1	no	—
78	C₂²×C₈	—	61	1	no	—
79	#117	—	61	2	no	—
80	C₂×C₄²	—	61	1	no	—
81	#108	—	61	4	no	—
82	#107	—	61	1	no	—
83	#107	#6923	1	1	yes	characteristic, complemented
84	#106	—	61	2	no	—
85	#97	—	61	4	no	—
86	#97	—	122	2	no	—
87	C₄×C₈	—	122	2	no	—
88	C₂²×C₄	—	61	1	no	—
89	C₂²×C₄	—	122	1	no	—
90	M₁₆	—	61	4	no	—
91	M₁₆	—	122	2	no	—
92	C₂×C₈	—	61	2	no	—
93	C₂×C₈	—	61	2	no	—
94	C₂×C₈	—	61	2	no	—
95	C₂×C₈	—	61	1	no	—
96	C₂×C₈	—	61	2	no	—
97	C₂×C₈	—	61	2	no	—
98	C₂×C₈	—	122	2	no	—
99	C₂×C₈	C₂×#6923	1	1	yes	characteristic
100	C₄⋊C₄	—	61	2	no	—
101	C₄⋊C₄	C₂×#6923	1	2	yes	—
102	C₂²⋊C₄	—	122	2	no	—
103	C₄²	—	61	2	no	—
104	C₄²	—	122	2	no	—
105	C₄²	—	122	1	no	—
106	C₂³	—	61	1	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	61	1	no	—
109	C₂×C₄	—	61	1	no	—
110	C₂×C₄	—	61	1	no	—
111	C₂×C₄	—	61	1	no	—
112	C₂×C₄	—	61	1	no	—
113	C₂×C₄	—	122	2	no	—
114	C₂×C₄	—	122	2	no	—
115	C₂×C₄	—	244	1	no	—
116	C₂×C₄	—	244	1	no	—
117	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
118	C₈	—	61	4	no	—
119	C₈	—	61	2	no	—
120	C₈	—	122	4	no	—
121	C₈	C₄×#6923	1	2	yes	—
122	C₂²	—	61	1	no	—
123	C₂²	—	61	1	no	—
124	C₂²	—	122	1	no	—
125	C₂²	—	122	1	no	—
126	C₂²	D₄×#6923	1	1	yes	characteristic
127	C₄	—	4	2	no	—
128	C₄	—	61	1	no	—
129	C₄	—	61	1	no	—
130	C₄	—	244	2	no	—
131	C₄	—	244	2	no	—
132	C₄	C₂×C₄×#6923	1	1	yes	characteristic
133	C₄	Q₈×#6923	1	1	yes	characteristic
134	C₂	—	122	1	no	—
135	C₂	—	122	1	no	—
136	C₂	C₄⋊C₄×#6923	1	1	yes	characteristic
137	C₂	#16840808	1	1	yes	characteristic
138	C₂	#16840809	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519847

C₂

yes

maximal, characteristic

#16840727

C₂

yes

maximal

C₂×#14519831

C₂

yes

maximal, characteristic

#16840632

C₂

yes

maximal

#16839799

C₂

yes

maximal, characteristic

C₂×#11758213

C₂²

yes

—

C₂×D₆₁⋊C₈

C₂²

yes

characteristic

C₂×C₄×#6923

C₂²

yes

characteristic

#14519847

C₄

yes

complemented

#14519832

—

#14519831

C₄

yes

complemented

C₄×#92420

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519735

C₂²

yes

—

#14519711

C₄

yes

characteristic, complemented

#14519708

C₄

yes

complemented

#107×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂×#92420

—

C₂×#92420

D₄

yes

—

C₄×#6923

—

C₄×#6923

C₂×C₄

yes

—

#11758213

—

#11758213

C₂×C₄

yes

—

D₆₁⋊C₈

C₂×C₄

yes

—

D₆₁⋊C₈

Q₈

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

#11758198

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

—

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₂²×D₆₁

yes

—

—

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

C₄×D₆₁

yes

—

C₄⋊C₄

yes

—

C₈×C₆₁

C₄²

yes

—

#92418

C₄²

yes

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#117

yes

characteristic

C₂×D₆₁

C₄×Q₈

yes

characteristic

#6923

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₄×Q₈

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂×C₄⋊C₄

yes

characteristic

Dic₆₁

C₄×D₄

yes

characteristic

#1773

—

maximal, Sylow

C₂×C₆₁

C₄×C₄⋊C₄

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

D₆₁

—

C₂×#108

—

#427

—

#405

—

C₂×#97

—

#339

—

C₆₁

#1773

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#106

—

#97

—

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

122

—

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

C₂×#6923

yes

—

102

C₂²⋊C₄

—

122

—

103

C₄²

—

104

C₄²

—

122

—

105

C₄²

—

122

—

106

C₂³

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

122

—

114

C₂×C₄

—

122

—

115

C₂×C₄

—

244

—

116

C₂×C₄

—

244

—

117

C₂×C₄

C₂²×#6923

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

122

—

121

C₈

C₄×#6923

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

122

—

125

C₂²

—

122

—

126

C₂²

D₄×#6923

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

244

—

131

C₄

—

244

—

132

C₄

C₂×C₄×#6923

yes

characteristic

133

C₄

Q₈×#6923

yes

characteristic

134

C₂

—

122

—

135

C₂

—

122

—

136

C₂

C₄⋊C₄×#6923

yes

characteristic

137

C₂

#16840808

yes

characteristic

138

C₂

#16840809

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#6923
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×#6923
Fitting	#107×C₆₁	C₄
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#107	#6923
hypocenter	C₆₁	#1773
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×#6923

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂×C₄

C₂²×#6923

Fitting

#107×C₆₁

C₄

socle

C₂²×C₆₁

C₄×D₄

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

N	H ≅ G/N	type
9. #14519847	C₄	semidirect
11. #14519831	C₄	semidirect
15. #14519711	C₄	semidirect
16. #14519708	C₄	semidirect
17. #107×C₆₁	C₄	semidirect
75. C₆₁	#1773	semidirect
83. #107	#6923	semidirect

H ≅ G/N

type

9. #14519847

C₄

semidirect

11. #14519831

C₄

semidirect

15. #14519711

C₄

semidirect

16. #14519708

C₄

semidirect

17. #107×C₆₁

C₄

semidirect

75. C₆₁

#1773

semidirect

83. #107

#6923

semidirect

Subgroups — #21461626

Conjugacy classes of subgroups

Complements