Group #39934570 — subgroups

Subgroups — C₁₀₃×#29295 #39934570

Order 26368.

630 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 270 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	C₁₀₃×#2330	C₂	1	2	yes	maximal
2	C₁₀₃×#2088	C₂	1	4	yes	maximal
3	C₁₀₃×#1989	C₂	1	4	yes	maximal
4	C₁₀₃×#1948	C₂	1	4	yes	maximal
5	C₁₀₃×#1843	C₂	1	1	yes	maximal, characteristic
6	C₂×#125×C₁₀₃	C₂²	1	2	yes	—
7	C₂×#106×C₁₀₃	C₂²	1	4	yes	—
8	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	4	yes	—
9	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
10	#389×C₁₀₃	—	2	4	no	—
11	#389×C₁₀₃	C₂²	1	4	yes	—
12	#387×C₁₀₃	—	2	4	no	—
13	#384×C₁₀₃	C₂²	1	2	yes	—
14	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	4	yes	—
15	#376×C₁₀₃	C₂²	1	1	yes	characteristic
16	#340×C₁₀₃	C₂²	1	8	yes	—
17	#340×C₁₀₃	C₂²	1	4	yes	—
18	C₂²×C₈×C₁₀₃	C₂³	1	4	yes	—
19	#125×C₁₀₃	—	2	4	no	—
20	#125×C₁₀₃	Q₈	1	8	yes	—
21	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
22	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
23	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
24	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	4	yes	—
25	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	4	yes	—
26	C₂×C₄²×C₁₀₃	—	2	4	no	—
27	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
28	C₂×C₄²×C₁₀₃	C₂³	1	2	yes	—
29	#106×C₁₀₃	—	4	4	no	—
30	C₄⋊C₈×C₁₀₃	—	2	8	no	—
31	C₄⋊C₈×C₁₀₃	—	4	2	no	—
32	#95×C₁₀₃	—	2	4	no	—
33	#95×C₁₀₃	—	2	4	no	—
34	#95×C₁₀₃	D₄	1	4	yes	—
35	C₂²×C₄×C₁₀₃	—	2	4	no	—
36	C₂²×C₄×C₁₀₃	—	2	4	no	—
37	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
38	C₂²×C₄×C₁₀₃	C₂×D₄	1	4	yes	—
39	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
40	C₂×C₈×C₁₀₃	—	2	8	no	—
41	C₂×C₈×C₁₀₃	—	2	4	no	—
42	C₄⋊C₄×C₁₀₃	—	2	16	no	—
43	C₄⋊C₄×C₁₀₃	—	2	4	no	—
44	C₄⋊C₄×C₁₀₃	—	2	4	no	—
45	C₄⋊C₄×C₁₀₃	—	2	4	no	—
46	C₄⋊C₄×C₁₀₃	—	8	4	no	—
47	C₄⋊C₄×C₁₀₃	—	8	4	no	—
48	C₄⋊C₄×C₁₀₃	C₂×Q₈	1	8	yes	—
49	C₄²×C₁₀₃	—	2	1	no	—
50	C₄²×C₁₀₃	—	2	1	no	—
51	C₄²×C₁₀₃	—	8	4	no	—
52	C₄²×C₁₀₃	C₂×Q₈	1	4	yes	—
53	C₄²×C₁₀₃	#41	1	4	yes	—
54	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₀₃	—	2	4	no	—
56	C₂×C₄×C₁₀₃	—	2	4	no	—
57	C₂×C₄×C₁₀₃	—	2	8	no	—
58	C₂×C₄×C₁₀₃	—	2	2	no	—
59	C₂×C₄×C₁₀₃	—	2	4	no	—
60	C₂×C₄×C₁₀₃	—	4	4	no	—
61	C₂×C₄×C₁₀₃	—	4	4	no	—
62	C₂×C₄×C₁₀₃	—	4	4	no	—
63	C₂×C₄×C₁₀₃	—	4	4	no	—
64	C₂×C₄×C₁₀₃	—	4	4	no	—
65	C₂×C₄×C₁₀₃	C₂²⋊Q₈	1	8	yes	—
66	C₂×C₄×C₁₀₃	C₂²×Q₈	1	2	yes	—
67	C₂×C₄×C₁₀₃	C₂×#41	1	2	yes	—
68	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
69	C₂×C₄×C₁₀₃	2₋¹⁺⁴	1	1	yes	characteristic
70	C₈×C₁₀₃	—	4	4	no	—
71	C₂²×C₁₀₃	C₂×C₂²⋊Q₈	1	2	yes	—
72	C₂²×C₁₀₃	#537	1	1	yes	characteristic
73	C₂²×C₁₀₃	#577	1	4	yes	—
74	C₄×C₁₀₃	—	2	8	no	—
75	C₄×C₁₀₃	—	4	8	no	—
76	C₄×C₁₀₃	—	4	2	no	—
77	C₄×C₁₀₃	—	8	4	no	—
78	C₄×C₁₀₃	#557	1	2	yes	—
79	C₄×C₁₀₃	Q₈²	1	1	yes	characteristic
80	C₄×C₁₀₃	#559	1	1	yes	characteristic
81	#29295	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂×C₁₀₃	#2582	1	1	yes	characteristic
83	C₂×C₁₀₃	#3084	1	4	yes	—
84	C₂×C₁₀₃	#3260	1	2	yes	—
85	#2330	C₂×C₁₀₃	1	2	yes	—
86	#2088	C₂×C₁₀₃	1	4	yes	—
87	#1989	C₂×C₁₀₃	1	4	yes	—
88	#1948	C₂×C₁₀₃	1	4	yes	—
89	#1843	C₂×C₁₀₃	1	1	yes	characteristic
90	C₁₀₃	#29295	1	1	yes	characteristic, direct product factor, Sylow
91	C₂×#125	C₂²×C₁₀₃	1	2	yes	—
92	C₂×#106	C₂²×C₁₀₃	1	4	yes	—
93	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	4	yes	—
94	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
95	#389	—	2	4	no	—
96	#389	C₂²×C₁₀₃	1	4	yes	—
97	#387	—	2	4	no	—
98	#384	C₂²×C₁₀₃	1	2	yes	—
99	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	4	yes	—
100	#376	C₂²×C₁₀₃	1	1	yes	characteristic
101	#340	C₂²×C₁₀₃	1	8	yes	—
102	#340	C₂²×C₁₀₃	1	4	yes	—
103	C₂²×C₈	C₂³×C₁₀₃	1	4	yes	—
104	#125	—	2	4	no	—
105	#125	Q₈×C₁₀₃	1	8	yes	—
106	C₂×C₄⋊C₄	—	2	4	no	—
107	C₂×C₄⋊C₄	—	2	4	no	—
108	C₂×C₄⋊C₄	—	2	4	no	—
109	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	4	yes	—
110	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	4	yes	—
111	C₂×C₄²	—	2	4	no	—
112	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
113	C₂×C₄²	C₂³×C₁₀₃	1	2	yes	—
114	#106	—	4	4	no	—
115	C₄⋊C₈	—	2	8	no	—
116	C₄⋊C₈	—	4	2	no	—
117	#95	—	2	4	no	—
118	#95	—	2	4	no	—
119	#95	D₄×C₁₀₃	1	4	yes	—
120	C₂²×C₄	—	2	4	no	—
121	C₂²×C₄	—	2	4	no	—
122	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
123	C₂²×C₄	C₂×D₄×C₁₀₃	1	4	yes	—
124	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
125	C₂×C₈	—	2	8	no	—
126	C₂×C₈	—	2	4	no	—
127	C₄⋊C₄	—	2	16	no	—
128	C₄⋊C₄	—	2	4	no	—
129	C₄⋊C₄	—	2	4	no	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	8	4	no	—
132	C₄⋊C₄	—	8	4	no	—
133	C₄⋊C₄	C₂×Q₈×C₁₀₃	1	8	yes	—
134	C₄²	—	2	1	no	—
135	C₄²	—	2	1	no	—
136	C₄²	—	8	4	no	—
137	C₄²	C₂×Q₈×C₁₀₃	1	4	yes	—
138	C₄²	#41×C₁₀₃	1	4	yes	—
139	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	2	8	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	4	4	no	—
146	C₂×C₄	—	4	4	no	—
147	C₂×C₄	—	4	4	no	—
148	C₂×C₄	—	4	4	no	—
149	C₂×C₄	—	4	4	no	—
150	C₂×C₄	C₂²⋊Q₈×C₁₀₃	1	8	yes	—
151	C₂×C₄	C₂²×Q₈×C₁₀₃	1	2	yes	—
152	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
153	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
154	C₂×C₄	2₋¹⁺⁴×C₁₀₃	1	1	yes	characteristic
155	C₈	—	4	4	no	—
156	C₂²	C₂×C₂²⋊Q₈×C₁₀₃	1	2	yes	—
157	C₂²	#537×C₁₀₃	1	1	yes	characteristic
158	C₂²	#577×C₁₀₃	1	4	yes	—
159	C₄	—	2	8	no	—
160	C₄	—	4	2	no	—
161	C₄	—	4	8	no	—
162	C₄	—	8	4	no	—
163	C₄	#557×C₁₀₃	1	2	yes	—
164	C₄	Q₈²×C₁₀₃	1	1	yes	characteristic
165	C₄	#559×C₁₀₃	1	1	yes	characteristic
166	C₂	C₁₀₃×#2582	1	1	yes	characteristic
167	C₂	C₁₀₃×#3084	1	4	yes	—
168	C₂	C₁₀₃×#3260	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₀₃×#2330

C₂

yes

maximal

C₁₀₃×#2088

C₂

yes

maximal

C₁₀₃×#1989

C₂

yes

maximal

C₁₀₃×#1948

C₂

yes

maximal

C₁₀₃×#1843

C₂

yes

maximal, characteristic

C₂×#125×C₁₀₃

C₂²

yes

—

C₂×#106×C₁₀₃

C₂²

yes

—

C₂×C₄⋊C₈×C₁₀₃

C₂²

yes

—

C₂×C₄⋊C₈×C₁₀₃

C₂²

yes

—

#389×C₁₀₃

—

#389×C₁₀₃

C₂²

yes

—

#387×C₁₀₃

—

#384×C₁₀₃

C₂²

yes

—

C₄×C₄⋊C₄×C₁₀₃

C₂²

yes

—

#376×C₁₀₃

C₂²

yes

characteristic

#340×C₁₀₃

C₂²

yes

—

#340×C₁₀₃

C₂²

yes

—

C₂²×C₈×C₁₀₃

C₂³

yes

—

#125×C₁₀₃

—

#125×C₁₀₃

Q₈

yes

—

C₂×C₄⋊C₄×C₁₀₃

—

C₂×C₄⋊C₄×C₁₀₃

—

C₂×C₄⋊C₄×C₁₀₃

—

C₂×C₄⋊C₄×C₁₀₃

C₂³

yes

—

C₂×C₄⋊C₄×C₁₀₃

C₂³

yes

—

C₂×C₄²×C₁₀₃

—

C₂×C₄²×C₁₀₃

C₂³

yes

characteristic

C₂×C₄²×C₁₀₃

C₂³

yes

—

#106×C₁₀₃

—

C₄⋊C₈×C₁₀₃

—

C₄⋊C₈×C₁₀₃

—

#95×C₁₀₃

—

#95×C₁₀₃

—

#95×C₁₀₃

D₄

yes

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

C₂×D₄

yes

—

C₂²×C₄×C₁₀₃

C₂×D₄

yes

—

C₂²×C₄×C₁₀₃

C₂⁴

yes

characteristic

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

C₂×Q₈

yes

—

C₄²×C₁₀₃

—

C₄²×C₁₀₃

—

C₄²×C₁₀₃

—

C₄²×C₁₀₃

C₂×Q₈

yes

—

C₄²×C₁₀₃

#41

yes

—

C₂³×C₁₀₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₀₃

C₂²×Q₈

yes

—

C₂×C₄×C₁₀₃

C₂×#41

yes

—

C₂×C₄×C₁₀₃

H(5,𝔽₂)

yes

characteristic

C₂×C₄×C₁₀₃

2₋¹⁺⁴

yes

characteristic

C₈×C₁₀₃

—

C₂²×C₁₀₃

C₂×C₂²⋊Q₈

yes

—

C₂²×C₁₀₃

#537

yes

characteristic

C₂²×C₁₀₃

#577

yes

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

#557

yes

—

C₄×C₁₀₃

Q₈²

yes

C₄×C₁₀₃

yes

C₁₀₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₁₀₃

#2582

yes

characteristic

C₂×C₁₀₃

#3084

yes

—

C₂×C₁₀₃

#3260

yes

—

#2330

C₂×C₁₀₃

yes

—

#2088

C₂×C₁₀₃

yes

—

#1989

C₂×C₁₀₃

yes

—

#1948

C₂×C₁₀₃

yes

—

#1843

C₂×C₁₀₃

yes

characteristic

C₁₀₃

#29295

yes

characteristic, direct product factor, Sylow

C₂×#125

C₂²×C₁₀₃

yes

—

C₂×#106

C₂²×C₁₀₃

yes

—

C₂×C₄⋊C₈

C₂²×C₁₀₃

yes

—

C₂×C₄⋊C₈

C₂²×C₁₀₃

yes

—

#389

—

#389

C₂²×C₁₀₃

yes

—

#387

—

#384

C₂²×C₁₀₃

yes

—

C₄×C₄⋊C₄

C₂²×C₁₀₃

yes

—

100

#376

C₂²×C₁₀₃

yes

characteristic

101

#340

C₂²×C₁₀₃

yes

—

102

#340

C₂²×C₁₀₃

yes

—

103

C₂²×C₈

C₂³×C₁₀₃

yes

—

104

#125

—

105

#125

Q₈×C₁₀₃

yes

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

C₂³×C₁₀₃

yes

—

110

C₂×C₄⋊C₄

C₂³×C₁₀₃

yes

—

111

C₂×C₄²

—

112

C₂×C₄²

C₂³×C₁₀₃

yes

characteristic

113

C₂×C₄²

C₂³×C₁₀₃

yes

—

114

#106

—

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

#95

—

118

#95

—

119

#95

D₄×C₁₀₃

yes

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

C₂×D₄×C₁₀₃

yes

—

123

C₂²×C₄

C₂×D₄×C₁₀₃

yes

—

124

C₂²×C₄

C₂⁴×C₁₀₃

yes

characteristic

125

C₂×C₈

—

126

C₂×C₈

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

C₂×Q₈×C₁₀₃

yes

—

134

C₄²

—

135

C₄²

—

136

C₄²

—

137

C₄²

C₂×Q₈×C₁₀₃

yes

—

138

C₄²

#41×C₁₀₃

yes

—

139

C₂³

C₂²×D₄×C₁₀₃

yes

characteristic

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₂²⋊Q₈×C₁₀₃

yes

—

151

C₂×C₄

C₂²×Q₈×C₁₀₃

yes

—

152

C₂×C₄

C₂×#41×C₁₀₃

yes

—

153

C₂×C₄

H(5,𝔽₂)×C₁₀₃

yes

characteristic

154

C₂×C₄

2₋¹⁺⁴×C₁₀₃

yes

characteristic

155

C₈

—

156

C₂²

C₂×C₂²⋊Q₈×C₁₀₃

yes

—

157

C₂²

#537×C₁₀₃

yes

characteristic

158

C₂²

#577×C₁₀₃

yes

—

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

#557×C₁₀₃

yes

—

164

C₄

Q₈²×C₁₀₃

yes

characteristic

165

C₄

#559×C₁₀₃

yes

characteristic

166

C₂

C₁₀₃×#2582

yes

characteristic

167

C₂

C₁₀₃×#3084

yes

—

168

C₂

C₁₀₃×#3260

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ #376×C₁₀₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₀₃

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₀₃

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₀₃ ◁ #376×C₁₀₃ ◁ G

N	H ≅ G/N	type
81. #29295	C₁₀₃	direct (N × H)
90. C₁₀₃	#29295	direct (N × H)

H ≅ G/N

type

81. #29295

C₁₀₃

direct (N × H)

90. C₁₀₃

#29295

direct (N × H)

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

subgroup	index
C₁₀₃×#2330	2
C₁₀₃×#2088	2
C₁₀₃×#1989	2
C₁₀₃×#1948	2
C₁₀₃×#1843	2
#29295	103

subgroup

index

C₁₀₃×#2330

C₁₀₃×#2088

C₁₀₃×#1989

C₁₀₃×#1948

C₁₀₃×#1843

#29295

103

Subgroups — C₁₀₃×#29295 #39934570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C103×#29295 #39934570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#29295 #39934570