Group #22618247 — subgroups

Subgroups — #22618247

Order 9344.

582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄²×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988479	C₂	1	3	yes	maximal, complemented
4	#17988472	C₂	1	3	yes	maximal, complemented
5	#17988465	C₂	1	3	yes	maximal
6	#17988461	C₂	1	3	yes	maximal, complemented
7	#383×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic
9	C₂²×C₄×D₇₃	C₂²	1	3	yes	—
10	#14556585	—	2	4	no	—
11	C₂×C₄⋊Dic₇₃	C₂²	1	3	yes	—
12	C₂×#11924007	C₂²	1	3	yes	—
13	C₂×#11924005	C₂²	1	3	yes	—
14	C₂×#11924005	C₂²	1	3	yes	—
15	C₂×#11924005	C₂²	1	3	yes	—
16	C₂×C₄×Dic₇₃	C₂²	1	3	yes	—
17	C₄²×D₇₃	—	2	4	no	—
18	#14556498	C₂²	1	3	yes	—
19	#14556498	C₂²	1	3	yes	—
20	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
21	#95×C₇₃	C₂²	1	3	yes	—
22	#95×C₇₃	C₂²	1	3	yes	—
23	C₂³×D₇₃	C₂³	1	1	yes	characteristic
24	C₂³×D₇₃	C₂³	1	1	yes	characteristic
25	C₂×D₂₉₂	—	2	6	no	—
26	C₂²×Dic₇₃	C₂³	1	3	yes	—
27	C₂²×Dic₇₃	C₂³	1	3	yes	—
28	C₂×C₄×D₇₃	—	2	6	no	—
29	C₂×C₄×D₇₃	—	2	6	no	—
30	C₂×C₄×D₇₃	—	2	6	no	—
31	C₄⋊Dic₇₃	—	2	6	no	—
32	#11924007	—	2	6	no	—
33	#11924005	—	2	6	no	—
34	#11924005	—	2	6	no	—
35	#11924005	—	2	6	no	—
36	C₄×Dic₇₃	—	2	6	no	—
37	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
39	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
40	C₄²×C₇₃	D₄	1	4	yes	complemented
41	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
42	C₂²×D₇₃	—	2	1	no	—
43	C₂²×D₇₃	—	2	3	no	—
44	C₂²×D₇₃	—	2	1	no	—
45	C₂²×D₇₃	—	2	3	no	—
46	C₂²×D₇₃	—	2	3	no	—
47	C₂²×D₇₃	#41	1	6	yes	—
48	C₂×C₄×C₇₃	—	2	3	no	—
49	C₂×C₄×C₇₃	—	2	3	no	—
50	C₂×C₄×C₇₃	—	2	3	no	—
51	C₂×C₄×C₇₃	—	2	3	no	—
52	C₂×C₄×C₇₃	—	2	3	no	—
53	C₂×C₄×C₇₃	—	2	3	no	—
54	C₂×C₄×C₇₃	C₂×D₄	1	6	yes	—
55	C₂×Dic₇₃	—	2	3	no	—
56	C₂×Dic₇₃	—	2	3	no	—
57	C₂×Dic₇₃	—	2	3	no	—
58	C₂×Dic₇₃	—	2	3	no	—
59	C₂×Dic₇₃	—	2	3	no	—
60	C₂×Dic₇₃	#41	1	6	yes	—
61	D₂₉₂	—	4	4	no	—
62	C₄×D₇₃	—	2	24	no	—
63	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
64	C₂²×C₇₃	C₂×#41	1	3	yes	—
65	C₂²×C₇₃	C₂×#41	1	3	yes	—
66	C₂×D₇₃	—	2	6	no	—
67	C₂×D₇₃	—	2	6	no	—
68	C₂×D₇₃	—	4	3	no	—
69	C₂×D₇₃	—	4	1	no	—
70	C₂×D₇₃	—	4	3	no	—
71	C₂×D₇₃	#126	1	4	yes	complemented
72	C₄×C₇₃	—	2	6	no	—
73	C₄×C₇₃	—	4	1	no	—
74	C₄×C₇₃	—	4	3	no	—
75	Dic₇₃	—	2	6	no	—
76	Dic₇₃	—	4	3	no	—
77	C₂×C₇₃	#525	1	3	yes	—
78	C₂×C₇₃	C₂×#126	1	1	yes	characteristic
79	C₂×C₇₃	#529	1	3	yes	—
80	D₇₃	—	2	4	no	—
81	D₇₃	—	8	1	no	—
82	#2852	—	73	1	no	maximal, Sylow
83	C₇₃	#2852	1	1	yes	characteristic, complemented, Sylow
84	C₂×#126	—	73	1	no	—
85	C₂²×C₄²	—	73	1	no	—
86	#388	—	73	3	no	—
87	#387	—	73	3	no	—
88	#386	—	73	3	no	—
89	#385	—	73	3	no	—
90	#383	D₇₃	1	1	yes	characteristic, complemented
91	C₂²×D₄	—	73	1	no	—
92	C₂³×C₄	—	73	3	no	—
93	#126	—	146	4	no	—
94	C₂×C₄⋊C₄	—	73	3	no	—
95	C₂×C₄⋊C₄	—	73	3	no	—
96	C₂×C₂²⋊C₄	—	73	3	no	—
97	C₂×C₂²⋊C₄	—	73	3	no	—
98	C₂×C₂²⋊C₄	—	73	3	no	—
99	C₂×C₄²	—	73	3	no	—
100	C₂×C₄²	—	146	4	no	—
101	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
102	#95	—	73	3	no	—
103	#95	—	73	3	no	—
104	#95	C₂×D₇₃	1	3	yes	—
105	#95	C₂×D₇₃	1	3	yes	—
106	C₂⁴	—	73	1	no	—
107	C₂⁴	—	73	1	no	—
108	C₂×D₄	—	146	6	no	—
109	C₂²×C₄	—	73	3	no	—
110	C₂²×C₄	—	73	3	no	—
111	C₂²×C₄	—	146	6	no	—
112	C₂²×C₄	—	146	6	no	—
113	C₂²×C₄	—	146	6	no	—
114	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
115	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
116	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
117	C₄⋊C₄	—	146	6	no	—
118	C₄⋊C₄	—	146	6	no	—
119	C₂²⋊C₄	—	146	6	no	—
120	C₂²⋊C₄	—	146	6	no	—
121	C₂²⋊C₄	—	146	6	no	—
122	C₄²	—	146	6	no	—
123	C₄²	D₂₉₂	1	4	yes	complemented
124	C₂³	—	73	6	no	—
125	C₂³	—	146	1	no	—
126	C₂³	—	146	3	no	—
127	C₂³	—	146	3	no	—
128	C₂³	—	146	1	no	—
129	C₂³	—	146	3	no	—
130	C₂³	C₂³×D₇₃	1	1	yes	characteristic
131	D₄	—	292	4	no	—
132	C₂×C₄	—	2	3	no	—
133	C₂×C₄	—	2	3	no	—
134	C₂×C₄	—	2	3	no	—
135	C₂×C₄	—	2	3	no	—
136	C₂×C₄	—	2	3	no	—
137	C₂×C₄	—	2	3	no	—
138	C₂×C₄	—	73	6	no	—
139	C₂×C₄	—	146	24	no	—
140	C₂×C₄	—	146	3	no	—
141	C₂×C₄	—	146	3	no	—
142	C₂×C₄	—	146	3	no	—
143	C₂×C₄	—	146	3	no	—
144	C₂×C₄	—	146	3	no	—
145	C₂×C₄	C₂×D₂₉₂	1	6	yes	—
146	C₂²	—	292	3	no	—
147	C₂²	—	292	3	no	—
148	C₂²	—	292	1	no	—
149	C₂²	—	73	4	no	—
150	C₂²	—	146	6	no	—
151	C₂²	—	146	6	no	—
152	C₂²	C₂²×D₂₉₂	1	1	yes	characteristic
153	C₂²	#41×D₇₃	1	3	yes	—
154	C₂²	#41×D₇₃	1	3	yes	—
155	C₄	—	2	6	no	—
156	C₄	—	4	3	no	—
157	C₄	—	4	1	no	—
158	C₄	—	292	3	no	—
159	C₄	—	146	6	no	—
160	C₂	—	584	1	no	—
161	C₂	—	146	4	no	—
162	C₂	#17989099	1	3	yes	—
163	C₂	#126×D₇₃	1	1	yes	characteristic
164	C₂	#17989120	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556585

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₇₃

C₂

yes

maximal, characteristic, complemented

#17988479

C₂

yes

maximal, complemented

#17988472

C₂

yes

maximal, complemented

#17988465

C₂

yes

maximal

#17988461

C₂

yes

maximal, complemented

#383×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₂₉₂

C₂²

yes

characteristic

C₂²×C₄×D₇₃

C₂²

yes

—

#14556585

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×#11924005

C₂²

yes

—

C₂×#11924005

C₂²

yes

—

C₂×#11924005

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₄²×D₇₃

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

C₂³×D₇₃

C₂³

yes

characteristic

C₂³×D₇₃

C₂³

yes

characteristic

C₂×D₂₉₂

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₄⋊Dic₇₃

—

—

—

—

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₄²×C₇₃

D₄

yes

complemented

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

#41

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

#41

yes

—

D₂₉₂

—

C₄×D₇₃

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂²×C₇₃

C₂×#41

yes

—

C₂²×C₇₃

C₂×#41

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#126

yes

complemented

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#525

yes

—

C₂×C₇₃

C₂×#126

yes

characteristic

C₂×C₇₃

#529

yes

—

D₇₃

—

D₇₃

—

#2852

—

maximal, Sylow

C₇₃

#2852

yes

characteristic, complemented, Sylow

C₂×#126

—

C₂²×C₄²

—

—

—

—

—

D₇₃

yes

characteristic, complemented

C₂²×D₄

—

C₂³×C₄

—

#126

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

100

C₂×C₄²

—

146

—

101

C₂×C₄²

C₂×D₇₃

yes

characteristic

102

#95

—

103

#95

—

104

#95

C₂×D₇₃

yes

—

105

#95

C₂×D₇₃

yes

—

106

C₂⁴

—

107

C₂⁴

—

108

C₂×D₄

—

146

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

146

—

112

C₂²×C₄

—

146

—

113

C₂²×C₄

—

146

—

114

C₂²×C₄

C₂²×D₇₃

yes

characteristic

115

C₂²×C₄

C₂²×D₇₃

yes

—

116

C₂²×C₄

C₂²×D₇₃

yes

—

117

C₄⋊C₄

—

146

—

118

C₄⋊C₄

—

146

—

119

C₂²⋊C₄

—

146

—

120

C₂²⋊C₄

—

146

—

121

C₂²⋊C₄

—

146

—

122

C₄²

—

146

—

123

C₄²

D₂₉₂

yes

complemented

124

C₂³

—

125

C₂³

—

146

—

126

C₂³

—

146

—

127

C₂³

—

146

—

128

C₂³

—

146

—

129

C₂³

—

146

—

130

C₂³

C₂³×D₇₃

yes

characteristic

131

D₄

—

292

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

146

—

140

C₂×C₄

—

146

—

141

C₂×C₄

—

146

—

142

C₂×C₄

—

146

—

143

C₂×C₄

—

146

—

144

C₂×C₄

—

146

—

145

C₂×C₄

C₂×D₂₉₂

yes

—

146

C₂²

—

292

—

147

C₂²

—

292

—

148

C₂²

—

292

—

149

C₂²

—

150

C₂²

—

146

—

151

C₂²

—

146

—

152

C₂²

C₂²×D₂₉₂

yes

characteristic

153

C₂²

#41×D₇₃

yes

—

154

C₂²

#41×D₇₃

yes

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

292

—

159

C₄

—

146

—

160

C₂

—

584

—

161

C₂

—

146

—

162

C₂

#17989099

yes

—

163

C₂

#126×D₇₃

yes

characteristic

164

C₂

#17989120

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#383×C₇₃	C₂
hypercenter	#383	D₇₃
hypocenter	C₇₃	#2852
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#383×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
1. C₂×#14556585	C₂	semidirect
2. C₂×C₄²×D₇₃	C₂	semidirect
3. #17988479	C₂	semidirect
4. #17988472	C₂	semidirect
6. #17988461	C₂	semidirect
7. #383×C₇₃	C₂	semidirect
40. C₄²×C₇₃	D₄	semidirect
71. C₂×D₇₃	#126	semidirect
83. C₇₃	#2852	semidirect
90. #383	D₇₃	semidirect
123. C₄²	D₂₉₂	semidirect

H ≅ G/N

type

1. C₂×#14556585

C₂

semidirect

2. C₂×C₄²×D₇₃

C₂

semidirect

3. #17988479

C₂

semidirect

4. #17988472

C₂

semidirect

6. #17988461

C₂

semidirect

7. #383×C₇₃

C₂

semidirect

40. C₄²×C₇₃

D₄

semidirect

71. C₂×D₇₃

#126

semidirect

83. C₇₃

#2852

semidirect

90. #383

D₇₃

semidirect

123. C₄²

D₂₉₂

semidirect

Subgroups — #22618247

Conjugacy classes of subgroups

Complements