Group #14545968 — subgroups

Subgroups — #14545968

Order 2176.

220 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 67 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	#11763928	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763928	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763910	C₂	1	4	yes	maximal, complemented
4	C₂×#10587680	C₂	1	1	yes	maximal, characteristic
5	C₂×#63256	C₄	1	1	yes	characteristic
6	#10587680	—	2	1	no	—
7	#10587680	—	2	1	no	—
8	#10587680	C₄	1	2	yes	—
9	#10587680	C₂²	1	2	yes	—
10	C₂×#63243	—	2	1	no	—
11	C₂×#63243	C₄	1	1	yes	characteristic
12	C₂×#63242	—	2	1	no	—
13	C₂×#63242	C₂²	1	1	yes	characteristic
14	#10587670	—	2	1	no	—
15	#10587670	—	2	1	no	—
16	#10587666	—	2	1	no	—
17	#10587666	C₂²	1	2	yes	complemented
18	#10587665	—	2	1	no	—
19	#10587665	C₂²	1	2	yes	complemented
20	C₂×Q₈×C₁₇	C₈	1	1	yes	characteristic
21	#63256	—	2	1	no	—
22	#63256	—	2	1	no	—
23	#63256	C₈	1	2	yes	—
24	#63256	C₂×C₄	1	2	yes	—
25	C₂×D₆₈	—	2	1	no	—
26	C₂×D₆₈	C₈	1	1	yes	characteristic
27	C₂×C₄×D₁₇	—	2	1	no	—
28	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
29	C₂×#3624	—	2	1	no	—
30	C₂×#3624	D₄	1	1	yes	characteristic
31	C₂×#3624	D₄	1	1	yes	characteristic
32	#63243	—	2	1	no	—
33	#63243	—	2	2	no	—
34	#63243	—	2	2	no	—
35	#63243	C₂×C₄	1	2	yes	—
36	#63242	—	2	2	no	—
37	#63242	—	2	2	no	—
38	#63242	C₂×C₄	1	1	yes	characteristic
39	#63242	D₄	1	1	yes	characteristic
40	#63242	D₄	1	1	yes	characteristic
41	#63242	C₂³	1	1	yes	characteristic
42	#63241	—	2	2	no	—
43	#63241	—	2	2	no	—
44	C₂²×D₁₇	—	2	1	no	—
45	C₂²×D₁₇	M₁₆	1	1	yes	characteristic
46	Q₈×C₁₇	—	2	1	no	—
47	Q₈×C₁₇	C₂×C₈	1	2	yes	—
48	C₂×C₄×C₁₇	—	2	1	no	—
49	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
50	C₂×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
51	D₆₈	—	2	2	no	—
52	D₆₈	—	2	2	no	—
53	D₆₈	—	2	1	no	—
54	D₆₈	C₂×C₈	1	2	yes	—
55	C₄×D₁₇	—	2	2	no	—
56	C₄×D₁₇	—	2	2	no	—
57	C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
58	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
59	C₄×D₁₇	M₁₆	1	1	yes	characteristic
60	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
61	#3624	—	2	2	no	—
62	#3624	C₂²⋊C₄	1	1	yes	characteristic
63	#3624	C₂²⋊C₄	1	1	yes	characteristic
64	#3624	C₂×D₄	1	1	yes	characteristic
65	#3624	C₂×D₄	1	1	yes	characteristic
66	#2117	—	17	1	no	maximal, Sylow
67	C₂²×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
68	C₂×D₁₇	—	2	2	no	—
69	C₂×D₁₇	—	4	1	no	—
70	C₂×D₁₇	—	4	2	no	—
71	C₂×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
72	C₂×D₁₇	C₂×M₁₆	1	1	yes	characteristic
73	C₄×C₁₇	—	2	2	no	—
74	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
75	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
76	Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
77	Dic₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×#131	—	17	1	no	—
79	C₂×M₃₂	—	17	1	no	—
80	C₂×M₃₂	—	17	1	no	—
81	#350	—	17	4	no	—
82	C₂×C₁₇	—	2	1	no	—
83	C₂×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
84	D₁₇	—	2	1	no	—
85	D₁₇	—	2	1	no	—
86	D₁₇	—	4	2	no	—
87	C₂×#41	—	17	1	no	—
88	#131	—	17	2	no	—
89	#131	—	17	2	no	—
90	#131	—	34	1	no	—
91	#131	—	34	1	no	—
92	C₂×M₁₆	—	17	1	no	—
93	C₂×M₁₆	—	34	1	no	—
94	C₂²×C₈	—	17	1	no	—
95	C₂²×C₈	—	34	1	no	—
96	M₃₂	—	17	2	no	—
97	M₃₂	—	34	1	no	—
98	M₃₂	—	34	1	no	—
99	M₃₂	—	34	1	no	—
100	C₂×C₁₆	—	17	2	no	—
101	C₂×C₁₆	—	34	1	no	—
102	C₁₇	#2117	1	1	yes	characteristic, complemented, Sylow
103	#41	—	17	2	no	—
104	#41	—	17	2	no	—
105	#41	—	34	1	no	—
106	#41	—	34	1	no	—
107	C₂×Q₈	#3633	1	1	yes	characteristic
108	C₂×D₄	—	17	1	no	—
109	C₂×D₄	—	34	1	no	—
110	C₂²×C₄	—	17	1	no	—
111	C₂²×C₄	—	34	1	no	—
112	M₁₆	—	17	2	no	—
113	M₁₆	—	34	2	no	—
114	M₁₆	—	34	2	no	—
115	M₁₆	—	34	1	no	—
116	C₂×C₈	—	17	1	no	—
117	C₂×C₈	—	17	1	no	—
118	C₂×C₈	—	17	1	no	—
119	C₂×C₈	—	17	1	no	—
120	C₂×C₈	—	17	1	no	—
121	C₂×C₈	—	17	1	no	—
122	C₂×C₈	—	34	2	no	—
123	C₂×C₈	—	34	2	no	—
124	C₂×C₈	—	34	1	no	—
125	C₁₆	—	34	2	no	—
126	C₁₆	—	34	2	no	—
127	C₂³	—	17	1	no	—
128	C₂³	—	34	1	no	—
129	Q₈	—	2	1	no	—
130	Q₈	C₂×#3633	1	2	yes	—
131	D₄	—	17	2	no	—
132	D₄	—	34	2	no	—
133	D₄	—	34	2	no	—
134	D₄	—	34	1	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	17	1	no	—
137	C₂×C₄	—	17	1	no	—
138	C₂×C₄	—	17	1	no	—
139	C₂×C₄	—	17	1	no	—
140	C₂×C₄	—	17	1	no	—
141	C₂×C₄	—	34	2	no	—
142	C₂×C₄	—	34	2	no	—
143	C₂×C₄	C₂×#3633	1	1	yes	characteristic
144	C₈	—	17	1	no	—
145	C₈	—	17	1	no	—
146	C₈	—	17	1	no	—
147	C₈	—	17	1	no	—
148	C₈	—	34	2	no	—
149	C₂²	—	17	1	no	—
150	C₂²	—	17	1	no	—
151	C₂²	—	34	2	no	—
152	C₂²	—	68	1	no	—
153	C₂²	—	68	2	no	—
154	C₂²	C₂²⋊#3633	1	1	yes	characteristic
155	C₄	—	2	2	no	—
156	C₄	—	17	1	no	—
157	C₄	—	17	1	no	—
158	C₄	C₂²⋊#3633	1	1	yes	characteristic
159	C₄	C₂²×#3633	1	1	yes	characteristic
160	C₂	—	2	1	no	—
161	C₂	—	34	1	no	—
162	C₂	—	34	1	no	—
163	C₂	—	68	2	no	—
164	C₂	C₂×C₂²⋊#3633	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763928

C₂

yes

maximal, characteristic, complemented

#11763928

C₂

yes

maximal, characteristic, complemented

#11763910

C₂

yes

maximal, complemented

C₂×#10587680

C₂

yes

maximal, characteristic

C₂×#63256

C₄

yes

—

—

C₄

yes

—

#10587680

C₂²

yes

—

C₂×#63243

—

C₂×#63243

C₄

yes

characteristic

C₂×#63242

—

C₂×#63242

C₂²

yes

—

—

—

C₂²

yes

complemented

#10587665

—

#10587665

C₂²

yes

complemented

C₂×Q₈×C₁₇

C₈

yes

—

—

C₈

yes

—

#63256

C₂×C₄

yes

—

C₂×D₆₈

—

C₂×D₆₈

C₈

yes

characteristic

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×#3624

—

C₂×#3624

D₄

yes

characteristic

C₂×#3624

D₄

yes

—

—

—

C₂×C₄

yes

—

#63242

—

#63242

—

#63242

C₂×C₄

yes

characteristic

#63242

D₄

yes

characteristic

#63242

D₄

yes

characteristic

#63242

C₂³

yes

characteristic

#63241

—

#63241

—

C₂²×D₁₇

—

C₂²×D₁₇

M₁₆

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂²⋊C₄

yes

characteristic

D₆₈

—

D₆₈

—

D₆₈

—

D₆₈

C₂×C₈

yes

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

C₂²⋊C₄

yes

characteristic

C₄×D₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

M₁₆

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

characteristic

#3624

—

#3624

C₂²⋊C₄

yes

characteristic

#3624

C₂²⋊C₄

yes

characteristic

#3624

C₂×D₄

yes

characteristic

#3624

C₂×D₄

yes

characteristic

#2117

—

maximal, Sylow

C₂²×C₁₇

C₂²⋊C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

C₂²⋊C₈

yes

characteristic

C₂×D₁₇

C₂×M₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

C₂²⋊C₈

yes

characteristic

C₄×C₁₇

C₂²×C₈

yes

characteristic

Dic₁₇

C₂²⋊C₈

yes

characteristic

Dic₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×#131

—

C₂×M₃₂

—

C₂×M₃₂

—

#350

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₂²⋊C₈

yes

characteristic

D₁₇

—

D₁₇

—

D₁₇

—

C₂×#41

—

—

—

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₁₇

#2117

yes

characteristic, complemented, Sylow

103

#41

—

104

#41

—

105

#41

—

106

#41

—

107

C₂×Q₈

#3633

yes

characteristic

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₁₆

—

126

C₁₆

—

127

C₂³

—

128

C₂³

—

129

Q₈

—

130

Q₈

C₂×#3633

yes

—

131

D₄

—

132

D₄

—

133

D₄

—

134

D₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

C₂×#3633

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

—

148

C₈

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

C₂²⋊#3633

yes

characteristic

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

C₂²⋊#3633

yes

characteristic

159

C₄

C₂²×#3633

yes

characteristic

160

C₂

—

161

C₂

—

162

C₂

—

163

C₂

—

164

C₂

C₂×C₂²⋊#3633

yes

characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#3633
commutator	C₄×C₁₇	C₂²×C₈
Frattini	C₄	C₂²×#3633
Fitting	C₂×Q₈×C₁₇	C₈
socle	C₂×C₁₇	C₂×C₂²⋊C₈
prime radical	C₂×#63256	C₄
cosocle	#63242	C₂³
hypercenter	C₂×Q₈	#3633
hypocenter	C₁₇	#2117
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

subgroup

G/H

center

C₂

C₂×C₂²⋊#3633

commutator

C₄×C₁₇

C₂²×C₈

Frattini

C₄

C₂²×#3633

Fitting

C₂×Q₈×C₁₇

C₈

socle

C₂×C₁₇

C₂×C₂²⋊C₈

C₄

C₂³

C₂×Q₈

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

N	H ≅ G/N	type
1. #11763928	C₂	semidirect
2. #11763928	C₂	semidirect
3. #11763910	C₂	semidirect
17. #10587666	C₂²	semidirect
19. #10587665	C₂²	semidirect
102. C₁₇	#2117	semidirect

H ≅ G/N

type

1. #11763928

C₂

semidirect

2. #11763928

C₂

semidirect

3. #11763910

C₂

semidirect

17. #10587666

C₂²

semidirect

19. #10587665

C₂²

semidirect

102. C₁₇

#2117

semidirect

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

subgroup	index
#11763928	2
#11763910	2
C₂×#10587680	2
#2117	17

subgroup

index

Subgroups — #14545968

Conjugacy classes of subgroups

Complements

Maximal subgroups