Group #33013246 — subgroups

Subgroups — #33013246

Order 18688.

1550 conjugacy classes of subgroups; only the 651 normal subgroups are shown.

normal subgroups only

This group has 1550 conjugacy classes of subgroups — too many to draw. Only its 651 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×#17988457	C₂	1	3	yes	maximal
2	C₂×#17988453	C₂	1	3	yes	maximal
3	#22608196	C₂	1	8	yes	maximal
4	C₂×#376×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊Dic₇₃	C₂²	1	3	yes	—
7	C₂²×C₄⋊Dic₇₃	C₂²	1	12	yes	—
8	#17988457	—	2	12	no	—
9	#17988453	—	2	12	no	—
10	C₂×#14556498	C₂²	1	12	yes	—
11	C₂²×C₄²×C₇₃	C₂²	1	3	yes	—
12	#376×C₇₃	C₄	1	8	yes	complemented
13	C₂×#95×C₇₃	C₂²	1	4	yes	—
14	C₂³×Dic₇₃	C₂³	1	2	yes	—
15	C₂³×Dic₇₃	C₂³	1	6	yes	—
16	C₂×C₄⋊Dic₇₃	—	2	6	no	—
17	C₂×C₄⋊Dic₇₃	—	2	6	no	—
18	C₂×C₄⋊Dic₇₃	—	2	24	no	—
19	C₂×C₄⋊Dic₇₃	—	2	12	no	—
20	C₂×C₄⋊Dic₇₃	—	4	24	no	—
21	#14556498	—	2	24	no	—
22	C₂³×C₄×C₇₃	C₂³	1	6	yes	—
23	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
24	C₂×C₄²×C₇₃	C₂×C₄	1	12	yes	—
25	C₂×C₄²×C₇₃	D₄	1	12	yes	—
26	C₂×C₄²×C₇₃	Q₈	1	12	yes	—
27	#95×C₇₃	C₂×C₄	1	16	yes	—
28	C₂²×Dic₇₃	—	2	6	no	—
29	C₂²×Dic₇₃	—	2	6	no	—
30	C₂²×Dic₇₃	—	2	12	no	—
31	C₂²×Dic₇₃	—	2	24	no	—
32	C₂²×Dic₇₃	—	2	8	no	—
33	C₄⋊Dic₇₃	—	4	48	no	—
34	C₄⋊Dic₇₃	—	4	4	no	—
35	C₄⋊Dic₇₃	—	4	12	no	—
36	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
37	C₂²×C₄×C₇₃	—	2	12	no	—
38	C₂²×C₄×C₇₃	—	2	12	no	—
39	C₂²×C₄×C₇₃	C₂²×C₄	1	12	yes	—
40	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
41	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
42	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
43	C₂²×C₄×C₇₃	C₂×Q₈	1	12	yes	—
44	C₂²×C₄×C₇₃	C₂×Q₈	1	6	yes	—
45	C₄²×C₇₃	C₄⋊C₄	1	48	yes	complemented
46	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
47	C₂³×C₇₃	C₂²×D₄	1	3	yes	—
48	C₂³×C₇₃	C₂²×Q₈	1	3	yes	—
49	C₂³×C₇₃	H(5,𝔽₂)	1	4	yes	—
50	C₂³×C₇₃	2₋¹⁺⁴	1	4	yes	—
51	C₂×C₄×C₇₃	—	2	24	no	—
52	C₂×C₄×C₇₃	—	2	12	no	—
53	C₂×C₄×C₇₃	—	2	12	no	—
54	C₂×C₄×C₇₃	—	2	24	no	—
55	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	24	yes	—
56	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	12	yes	—
57	C₂×C₄×C₇₃	#127	1	4	yes	—
58	C₂×C₄×C₇₃	C₄⋊Q₈	1	12	yes	—
59	C₂×Dic₇₃	—	4	6	no	—
60	C₂×Dic₇₃	—	4	2	no	—
61	C₂×Dic₇₃	—	4	24	no	—
62	C₂×Dic₇₃	—	4	12	no	—
63	C₂×Dic₇₃	—	4	12	no	—
64	C₂²×C₇₃	C₂²×C₄⋊C₄	1	3	yes	—
65	C₂²×C₇₃	#520	1	4	yes	—
66	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
67	C₂²×C₇₃	C₂×C₄⋊Q₈	1	3	yes	—
68	C₂²×C₇₃	#535	1	6	yes	—
69	C₂²×C₇₃	#536	1	6	yes	—
70	C₂²×C₇₃	#544	1	12	yes	—
71	C₄×C₇₃	—	2	24	no	—
72	C₄×C₇₃	#384	1	8	yes	—
73	Dic₇₃	—	8	6	no	—
74	Dic₇₃	—	8	2	no	—
75	#14354	—	73	1	no	maximal, Sylow
76	C₂×C₇₃	C₂×#384	1	1	yes	characteristic
77	C₂×C₇₃	#2317	1	6	yes	—
78	C₂×C₇₃	#2657	1	1	yes	characteristic
79	C₂×C₇₃	#2658	1	1	yes	characteristic
80	C₂×C₇₃	#2660	1	6	yes	—
81	C₂×#384	—	73	3	no	—
82	C₂×#382	—	73	3	no	—
83	C₂×#376	D₇₃	1	1	yes	characteristic
84	#1444	—	73	8	no	—
85	C₇₃	#14354	1	1	yes	characteristic, complemented, Sylow
86	C₂²×C₄⋊C₄	—	73	12	no	—
87	C₂²×C₄⋊C₄	—	73	1	no	—
88	C₂²×C₄⋊C₄	—	73	3	no	—
89	C₂²×C₄²	C₂×D₇₃	1	3	yes	—
90	#384	—	146	12	no	—
91	#382	—	146	12	no	—
92	#376	Dic₇₃	1	8	yes	complemented
93	C₂×#95	—	73	12	no	—
94	C₂×#95	C₂×D₇₃	1	4	yes	—
95	C₂³×C₄	—	73	6	no	—
96	C₂³×C₄	—	73	2	no	—
97	C₂³×C₄	C₂²×D₇₃	1	6	yes	—
98	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
99	C₂×C₄⋊C₄	—	292	24	no	—
100	C₂×C₄⋊C₄	—	146	6	no	—
101	C₂×C₄⋊C₄	—	146	6	no	—
102	C₂×C₄⋊C₄	—	146	24	no	—
103	C₂×C₄⋊C₄	—	146	12	no	—
104	C₂×C₄²	Dic₁₄₆	1	12	yes	—
105	C₂×C₄²	D₂₉₂	1	12	yes	—
106	C₂×C₄²	C₂×Dic₇₃	1	12	yes	—
107	#95	—	146	24	no	—
108	#95	C₂×Dic₇₃	1	16	yes	—
109	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
110	C₂²×C₄	—	2	12	no	—
111	C₂²×C₄	—	2	12	no	—
112	C₂²×C₄	—	146	6	no	—
113	C₂²×C₄	—	146	6	no	—
114	C₂²×C₄	—	146	12	no	—
115	C₂²×C₄	—	146	24	no	—
116	C₂²×C₄	—	146	8	no	—
117	C₂²×C₄	C₂²×Dic₇₃	1	12	yes	—
118	C₂²×C₄	C₂²×Dic₇₃	1	2	yes	—
119	C₂²×C₄	C₂×D₂₉₂	1	12	yes	—
120	C₂²×C₄	C₂×D₂₉₂	1	6	yes	—
121	C₂²×C₄	C₂×Dic₁₄₆	1	12	yes	—
122	C₂²×C₄	C₂×Dic₁₄₆	1	6	yes	—
123	C₄⋊C₄	—	292	48	no	—
124	C₄⋊C₄	—	292	4	no	—
125	C₄⋊C₄	—	292	12	no	—
126	C₄²	C₄⋊Dic₇₃	1	48	yes	complemented
127	C₂³	C₂³×Dic₇₃	1	1	yes	characteristic
128	C₂³	C₂²×D₂₉₂	1	3	yes	—
129	C₂³	C₂²×Dic₁₄₆	1	3	yes	—
130	C₂³	#14556637	1	4	yes	—
131	C₂³	#14556638	1	4	yes	—
132	C₂×C₄	—	2	12	no	—
133	C₂×C₄	—	2	12	no	—
134	C₂×C₄	—	2	24	no	—
135	C₂×C₄	—	2	24	no	—
136	C₂×C₄	—	292	6	no	—
137	C₂×C₄	—	292	2	no	—
138	C₂×C₄	—	292	24	no	—
139	C₂×C₄	—	292	12	no	—
140	C₂×C₄	—	292	12	no	—
141	C₂×C₄	C₂×C₄⋊Dic₇₃	1	24	yes	—
142	C₂×C₄	C₂×C₄⋊Dic₇₃	1	12	yes	—
143	C₂×C₄	#14556588	1	4	yes	—
144	C₂×C₄	#14556591	1	12	yes	—
145	C₂²	C₂²×C₄⋊Dic₇₃	1	3	yes	—
146	C₂²	#17989070	1	4	yes	—
147	C₂²	C₂×#14556588	1	1	yes	characteristic
148	C₂²	C₂×#14556591	1	3	yes	—
149	C₂²	#17989156	1	6	yes	—
150	C₂²	#17989163	1	6	yes	—
151	C₂²	#17989215	1	12	yes	—
152	C₄	—	2	24	no	—
153	C₄	—	584	6	no	—
154	C₄	—	584	2	no	—
155	C₄	#17988457	1	8	yes	—
156	C₂	C₂×#17988457	1	1	yes	characteristic
157	C₂	#22612554	1	6	yes	—
158	C₂	#22616037	1	1	yes	characteristic
159	C₂	#22616041	1	1	yes	characteristic
160	C₂	#22616050	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988457

C₂

yes

maximal

C₂×#17988453

C₂

yes

maximal

#22608196

C₂

yes

maximal

C₂×#376×C₇₃

C₂

yes

maximal, characteristic

C₂²×C₄⋊Dic₇₃

C₂²

yes

characteristic

C₂²×C₄⋊Dic₇₃

C₂²

yes

—

C₂²×C₄⋊Dic₇₃

C₂²

yes

—

#17988457

—

#17988453

—

C₂×#14556498

C₂²

yes

—

C₂²×C₄²×C₇₃

C₂²

yes

—

#376×C₇₃

C₄

yes

complemented

C₂×#95×C₇₃

C₂²

yes

—

C₂³×Dic₇₃

C₂³

yes

—

C₂³×Dic₇₃

C₂³

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

#14556498

—

C₂³×C₄×C₇₃

C₂³

yes

—

C₂³×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

Q₈

yes

—

#95×C₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂⁴×C₇₃

C₂⁴

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×Q₈

yes

—

C₂²×C₄×C₇₃

C₂×Q₈

yes

—

C₄²×C₇₃

C₄⋊C₄

yes

complemented

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂³×C₇₃

C₂²×D₄

yes

—

C₂³×C₇₃

C₂²×Q₈

yes

—

C₂³×C₇₃

H(5,𝔽₂)

yes

—

C₂³×C₇₃

2₋¹⁺⁴

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

#127

yes

—

C₂×C₄×C₇₃

C₄⋊Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂²×C₇₃

C₂²×C₄⋊C₄

yes

—

C₂²×C₇₃

#520

yes

—

C₂²×C₇₃

C₂×#127

yes

characteristic

C₂²×C₇₃

C₂×C₄⋊Q₈

yes

—

C₂²×C₇₃

#535

yes

—

C₂²×C₇₃

#536

yes

—

C₂²×C₇₃

#544

yes

—

C₄×C₇₃

—

C₄×C₇₃

#384

yes

—

Dic₇₃

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×#384

—

C₂×#382

—

C₂×#376

D₇₃

yes

characteristic

#1444

—

C₇₃

#14354

yes

characteristic, complemented, Sylow

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

—

C₂²×C₄²

C₂×D₇₃

yes

—

#384

—

146

—

#382

—

146

—

#376

Dic₇₃

yes

complemented

C₂×#95

—

C₂×#95

C₂×D₇₃

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂²×D₇₃

yes

—

C₂³×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

292

—

100

C₂×C₄⋊C₄

—

146

—

101

C₂×C₄⋊C₄

—

146

—

102

C₂×C₄⋊C₄

—

146

—

103

C₂×C₄⋊C₄

—

146

—

104

C₂×C₄²

Dic₁₄₆

yes

—

105

C₂×C₄²

D₂₉₂

yes

—

106

C₂×C₄²

C₂×Dic₇₃

yes

—

107

#95

—

146

—

108

#95

C₂×Dic₇₃

yes

—

109

C₂⁴

C₂³×D₇₃

yes

characteristic

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

146

—

113

C₂²×C₄

—

146

—

114

C₂²×C₄

—

146

—

115

C₂²×C₄

—

146

—

116

C₂²×C₄

—

146

—

117

C₂²×C₄

C₂²×Dic₇₃

yes

—

118

C₂²×C₄

C₂²×Dic₇₃

yes

—

119

C₂²×C₄

C₂×D₂₉₂

yes

—

120

C₂²×C₄

C₂×D₂₉₂

yes

—

121

C₂²×C₄

C₂×Dic₁₄₆

yes

—

122

C₂²×C₄

C₂×Dic₁₄₆

yes

—

123

C₄⋊C₄

—

292

—

124

C₄⋊C₄

—

292

—

125

C₄⋊C₄

—

292

—

126

C₄²

C₄⋊Dic₇₃

yes

complemented

127

C₂³

C₂³×Dic₇₃

yes

characteristic

128

C₂³

C₂²×D₂₉₂

yes

—

129

C₂³

C₂²×Dic₁₄₆

yes

—

130

C₂³

#14556637

yes

—

131

C₂³

#14556638

yes

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

292

—

137

C₂×C₄

—

292

—

138

C₂×C₄

—

292

—

139

C₂×C₄

—

292

—

140

C₂×C₄

—

292

—

141

C₂×C₄

C₂×C₄⋊Dic₇₃

yes

—

142

C₂×C₄

C₂×C₄⋊Dic₇₃

yes

—

143

C₂×C₄

#14556588

yes

—

144

C₂×C₄

#14556591

yes

—

145

C₂²

C₂²×C₄⋊Dic₇₃

yes

—

146

C₂²

#17989070

yes

—

147

C₂²

C₂×#14556588

yes

characteristic

148

C₂²

C₂×#14556591

yes

—

149

C₂²

#17989156

yes

—

150

C₂²

#17989163

yes

—

151

C₂²

#17989215

yes

—

152

C₄

—

153

C₄

—

584

—

154

C₄

—

584

—

155

C₄

#17988457

yes

—

156

C₂

C₂×#17988457

yes

characteristic

157

C₂

#22612554

yes

—

158

C₂

#22616037

yes

characteristic

159

C₂

#22616041

yes

characteristic

160

C₂

#22616050

yes

—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₇₃
commutator	C₂³×C₇₃	C₂³×C₄
Fitting	C₂×#376×C₇₃	C₂
socle, prime radical, cosocle	C₂⁴×C₇₃	C₂⁴
hypercenter	C₂×#376	D₇₃
hypocenter	C₇₃	#14354
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#376

subgroup

G/H

center, Frattini

C₂⁴

C₂³×D₇₃

commutator

C₂³×C₇₃

C₂³×C₄

Fitting

C₂×#376×C₇₃

C₂

socle, prime radical, cosocle

C₂⁴×C₇₃

C₂⁴

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂⁴ ◁ C₂×#376

N	H ≅ G/N	type
12. #376×C₇₃	C₄	semidirect
45. C₄²×C₇₃	C₄⋊C₄	semidirect
85. C₇₃	#14354	semidirect
92. #376	Dic₇₃	semidirect
126. C₄²	C₄⋊Dic₇₃	semidirect

H ≅ G/N

type

12. #376×C₇₃

C₄

semidirect

45. C₄²×C₇₃

C₄⋊C₄

semidirect

85. C₇₃

#14354

semidirect

92. #376

Dic₇₃

semidirect

126. C₄²

C₄⋊Dic₇₃

semidirect

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

subgroup	index
C₂×#17988457	2
C₂×#17988453	2
#22608196	2
C₂×#376×C₇₃	2
#14354	73

subgroup

index

C₂×#376×C₇₃

Subgroups — #33013246

Conjugacy classes of subgroups

Complements

Maximal subgroups