Group #22612486 — subgroups

Subgroups — #22612486

Order 9344.

484 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 209 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×#14556583	C₂	1	1	yes	maximal, characteristic
2	#17988483	C₂	1	2	yes	maximal
3	#17988469	C₂	1	4	yes	maximal
4	C₄⋊C₄×Dic₇₃	C₂	1	2	yes	maximal
5	#17988438	C₂	1	4	yes	maximal
6	C₄²×Dic₇₃	C₂	1	1	yes	maximal, characteristic
7	#382×C₇₃	C₂	1	1	yes	maximal, characteristic
8	#14556583	C₄	1	8	yes	complemented
9	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
10	C₂×#11924007	C₂²	1	4	yes	—
11	C₂×#11924007	C₂²	1	4	yes	—
12	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
13	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
14	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₇₃	C₂²	1	4	yes	—
16	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
17	#14556498	C₂²	1	4	yes	—
18	#14556498	C₂²	1	4	yes	—
19	C₂×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
20	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
21	#95×C₇₃	C₂²	1	4	yes	—
22	C₂²×Dic₇₃	C₂³	1	4	yes	—
23	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₇₃	C₂³	1	2	yes	—
25	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₇₃	C₂×C₄	1	8	yes	—
27	#11924007	—	2	8	no	—
28	#11924007	C₂×C₄	1	16	yes	—
29	C₄×Dic₇₃	—	2	2	no	—
30	C₄×Dic₇₃	—	2	4	no	—
31	C₄×Dic₇₃	—	2	4	no	—
32	C₄×Dic₇₃	—	2	8	no	—
33	C₄×Dic₇₃	Q₈	1	4	yes	—
34	C₂²×C₄×C₇₃	C₂³	1	4	yes	—
35	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
36	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
37	C₄⋊C₄×C₇₃	—	2	4	no	—
38	C₄²×C₇₃	C₂×C₄	1	4	yes	—
39	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	—	2	2	no	—
42	C₂×C₄×C₇₃	—	2	4	no	—
43	C₂×C₄×C₇₃	—	2	4	no	—
44	C₂×C₄×C₇₃	—	2	4	no	—
45	C₂×C₄×C₇₃	C₂²×C₄	1	4	yes	—
46	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₇₃	#41	1	2	yes	—
49	C₂×Dic₇₃	—	2	4	no	—
50	C₂×Dic₇₃	—	2	2	no	—
51	C₂×Dic₇₃	—	2	2	no	—
52	C₂×Dic₇₃	—	2	2	no	—
53	C₂×Dic₇₃	—	2	4	no	—
54	C₂×Dic₇₃	C₂²×C₄	1	8	yes	—
55	C₂×Dic₇₃	C₂×Q₈	1	2	yes	—
56	C₂×Dic₇₃	C₂×Q₈	1	2	yes	—
57	C₂×Dic₇₃	#41	1	4	yes	—
58	C₂×Dic₇₃	#41	1	4	yes	—
59	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₇₃	C₂²×Q₈	1	1	yes	characteristic
61	C₂²×C₇₃	C₂×#41	1	2	yes	—
62	C₂²×C₇₃	C₂×#41	1	2	yes	—
63	C₂²×C₇₃	C₂×#41	1	1	yes	characteristic
64	C₄×C₇₃	—	2	4	no	—
65	C₄×C₇₃	—	4	4	no	—
66	C₄×C₇₃	C₄×Q₈	1	4	yes	—
67	Dic₇₃	—	2	8	no	—
68	Dic₇₃	—	2	4	no	—
69	Dic₇₃	—	2	2	no	—
70	Dic₇₃	#125	1	4	yes	complemented
71	C₂×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
72	C₂×C₇₃	C₄×#41	1	2	yes	—
73	C₂×C₇₃	C₂×#125	1	1	yes	characteristic
74	C₂×C₇₃	#529	1	2	yes	—
75	C₂×C₇₃	#533	1	1	yes	characteristic
76	C₄×#125	—	73	1	no	maximal, Sylow
77	C₇₃	C₄×#125	1	1	yes	characteristic, complemented, Sylow
78	C₂×#125	—	73	1	no	—
79	#389	—	73	2	no	—
80	#387	—	73	4	no	—
81	#382	D₇₃	1	1	yes	characteristic
82	C₄×C₄⋊C₄	—	73	2	no	—
83	C₄×C₄⋊C₄	—	73	4	no	—
84	C₄³	—	73	1	no	—
85	#125	—	73	8	no	—
86	C₂×C₄⋊C₄	—	73	4	no	—
87	C₂×C₄⋊C₄	—	73	2	no	—
88	C₂×C₄⋊C₄	—	73	4	no	—
89	C₂×C₄⋊C₄	C₂×D₇₃	1	2	yes	—
90	C₂×C₄²	—	73	1	no	—
91	C₂×C₄²	—	73	2	no	—
92	C₂×C₄²	—	73	2	no	—
93	C₂×C₄²	—	73	1	no	—
94	C₂×C₄²	—	73	4	no	—
95	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
96	#95	—	73	4	no	—
97	#95	—	73	4	no	—
98	#95	C₂×D₇₃	1	4	yes	—
99	C₂²×C₄	—	73	1	no	—
100	C₂²×C₄	—	73	1	no	—
101	C₂²×C₄	—	73	2	no	—
102	C₂²×C₄	—	73	4	no	—
103	C₂²×C₄	C₂²×D₇₃	1	4	yes	—
104	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
105	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
106	C₄⋊C₄	—	2	4	no	—
107	C₄⋊C₄	—	73	16	no	—
108	C₄⋊C₄	—	73	8	no	—
109	C₄⋊C₄	—	146	8	no	—
110	C₄²	—	73	4	no	—
111	C₄²	—	146	4	no	—
112	C₄²	—	146	4	no	—
113	C₄²	—	146	8	no	—
114	C₄²	—	146	2	no	—
115	C₄²	C₄×D₇₃	1	4	yes	—
116	C₂³	C₂³×D₇₃	1	1	yes	characteristic
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	73	2	no	—
123	C₂×C₄	—	73	4	no	—
124	C₂×C₄	—	73	8	no	—
125	C₂×C₄	—	73	2	no	—
126	C₂×C₄	—	73	4	no	—
127	C₂×C₄	—	146	2	no	—
128	C₂×C₄	—	146	4	no	—
129	C₂×C₄	—	146	2	no	—
130	C₂×C₄	—	146	4	no	—
131	C₂×C₄	—	146	2	no	—
132	C₂×C₄	C₂×C₄×D₇₃	1	4	yes	—
133	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
134	C₂×C₄	Q₈×D₇₃	1	2	yes	—
135	C₂×C₄	#11924027	1	2	yes	—
136	C₂²	C₂²×C₄×D₇₃	1	1	yes	characteristic
137	C₂²	C₂×Q₈×D₇₃	1	1	yes	characteristic
138	C₂²	#41×D₇₃	1	2	yes	—
139	C₂²	#41×D₇₃	1	2	yes	—
140	C₂²	C₂×#11924027	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	4	4	no	—
143	C₄	—	73	4	no	—
144	C₄	—	146	2	no	—
145	C₄	—	146	8	no	—
146	C₄	—	146	4	no	—
147	C₄	#14556556	1	4	yes	—
148	C₂	C₂×#14556556	1	1	yes	characteristic
149	C₂	#17989055	1	2	yes	—
150	C₂	#125×D₇₃	1	1	yes	characteristic
151	C₂	#17989116	1	2	yes	—
152	C₂	#17989143	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556583

C₂

yes

maximal, characteristic

#17988483

C₂

yes

maximal

#17988469

C₂

yes

maximal

C₄⋊C₄×Dic₇₃

C₂

yes

maximal

#17988438

C₂

yes

maximal

C₄²×Dic₇₃

C₂

yes

maximal, characteristic

#382×C₇₃

C₂

yes

maximal, characteristic

#14556583

C₄

yes

complemented

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₂²

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

characteristic

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

C₂×C₄

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

#41

yes

—

C₂×Dic₇₃

#41

yes

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₂²×C₇₃

C₂²×Q₈

yes

characteristic

C₂²×C₇₃

C₂×#41

yes

—

C₂²×C₇₃

C₂×#41

yes

—

C₂²×C₇₃

C₂×#41

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×Q₈

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#125

yes

complemented

C₂×C₇₃

C₂×C₄×Q₈

yes

characteristic

C₂×C₇₃

C₄×#41

yes

—

C₂×C₇₃

C₂×#125

yes

characteristic

C₂×C₇₃

#529

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

C₄³

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

—

—

C₂×D₇₃

yes

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₂²×D₇₃

yes

—

104

C₂²×C₄

C₂²×D₇₃

yes

—

105

C₂²×C₄

C₂²×D₇₃

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

146

—

110

C₄²

—

111

C₄²

—

146

—

112

C₄²

—

146

—

113

C₄²

—

146

—

114

C₄²

—

146

—

115

C₄²

C₄×D₇₃

yes

—

116

C₂³

C₂³×D₇₃

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

146

—

128

C₂×C₄

—

146

—

129

C₂×C₄

—

146

—

130

C₂×C₄

—

146

—

131

C₂×C₄

—

146

—

132

C₂×C₄

C₂×C₄×D₇₃

yes

—

133

C₂×C₄

C₂×C₄×D₇₃

yes

—

134

C₂×C₄

Q₈×D₇₃

yes

—

135

C₂×C₄

#11924027

yes

—

136

C₂²

C₂²×C₄×D₇₃

yes

characteristic

137

C₂²

C₂×Q₈×D₇₃

yes

characteristic

138

C₂²

#41×D₇₃

yes

—

139

C₂²

#41×D₇₃

yes

—

140

C₂²

C₂×#11924027

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

146

—

145

C₄

—

146

—

146

C₄

—

146

—

147

C₄

#14556556

yes

—

148

C₂

C₂×#14556556

yes

characteristic

149

C₂

#17989055

yes

—

150

C₂

#125×D₇₃

yes

characteristic

151

C₂

#17989116

yes

—

152

C₂

#17989143

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂³×C₄
Fitting	#382×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁴
hypercenter	#382	D₇₃
hypocenter	C₇₃	C₄×#125
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator

C₂²×C₇₃

C₂³×C₄

Fitting

#382×C₇₃

C₂

socle

C₂³×C₇₃

C₂⁴

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
8. #14556583	C₄	semidirect
70. Dic₇₃	#125	semidirect
77. C₇₃	C₄×#125	semidirect

H ≅ G/N

type

8. #14556583

C₄

semidirect

70. Dic₇₃

#125

semidirect

77. C₇₃

C₄×#125

semidirect

Subgroups — #22612486

Conjugacy classes of subgroups

Complements