Group #22626032 — subgroups

Subgroups — #22626032

Order 9344.

248 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14556658	C₂	1	2	yes	maximal
2	C₂×C₄⋊#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556646	C₂	1	1	yes	maximal, characteristic
4	#17989453	C₂	1	2	yes	maximal
5	#17988438	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596833	C₂²	1	2	yes	—
7	C₂²×#10596833	C₂²	1	1	yes	characteristic
8	C₂²×#10596833	C₂²	1	1	yes	characteristic
9	#14556658	—	2	4	no	—
10	C₄⋊#10596833	—	2	2	no	—
11	#14556646	—	2	2	no	—
12	C₂×#11924007	C₄	1	2	yes	—
13	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
14	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
15	#14556498	C₄	1	1	yes	characteristic
16	#95×C₇₃	C₄	1	1	yes	characteristic
17	C₂×#10596833	—	2	1	no	—
18	C₂×#10596833	—	2	1	no	—
19	C₂×#10596833	—	2	1	no	—
20	C₂×#10596833	—	2	1	no	—
21	C₂×#10596833	—	2	2	no	—
22	C₂×#10596833	—	2	2	no	—
23	C₂×#10596833	—	2	2	no	—
24	C₂×#10596833	D₄	1	2	yes	—
25	C₂×#10596833	Q₈	1	2	yes	—
26	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
28	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
29	#11924007	—	2	4	no	—
30	C₄×Dic₇₃	—	2	2	no	—
31	C₄×Dic₇₃	—	2	2	no	—
32	C₄×Dic₇₃	D₄	1	2	yes	—
33	C₄×Dic₇₃	Q₈	1	2	yes	—
34	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
35	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	—	2	2	no	—
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
42	C₂×Dic₇₃	—	2	2	no	—
43	C₂×Dic₇₃	—	2	2	no	—
44	C₂×Dic₇₃	—	2	2	no	—
45	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
46	C₂×Dic₇₃	M₁₆	1	4	yes	—
47	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
50	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×Dic₇₃	#41	1	1	yes	characteristic
52	C₂×Dic₇₃	#41	1	1	yes	characteristic
53	#10596833	—	2	2	no	—
54	#10596833	—	2	2	no	—
55	#10596833	—	4	2	no	—
56	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
58	C₂²×C₇₃	C₄×Q₈	1	1	yes	characteristic
59	C₂²×C₇₃	C₂×M₁₆	1	2	yes	—
60	C₂²×C₇₃	#131	1	2	yes	—
61	C₄×C₇₃	—	2	2	no	—
62	C₄×C₇₃	—	4	2	no	—
63	Dic₇₃	—	2	2	no	—
64	Dic₇₃	—	2	4	no	—
65	Dic₇₃	#121	1	1	yes	characteristic
66	Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
67	Dic₇₃	#125	1	1	yes	characteristic
68	Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₇₃	#389	1	1	yes	characteristic
70	C₂×C₇₃	#423	1	1	yes	characteristic
71	C₂×C₇₃	#424	1	1	yes	characteristic
72	C₂×C₇₃	#435	1	2	yes	—
73	C₂×C₇₃	#446	1	2	yes	—
74	#1940	—	73	1	no	maximal, Sylow
75	C₇₃	#1940	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₄⋊C₈	—	73	1	no	—
77	C₂×C₄⋊C₈	—	73	2	no	—
78	C₂×#97	—	73	1	no	—
79	C₄×C₄⋊C₄	—	73	1	no	—
80	#336	—	73	2	no	—
81	C₂²×C₈	—	73	1	no	—
82	C₂²×C₈	—	73	1	no	—
83	C₂²×C₈	—	73	2	no	—
84	C₂×C₄⋊C₄	—	73	2	no	—
85	C₂×C₄²	—	73	1	no	—
86	C₂×C₄²	—	73	2	no	—
87	C₄⋊C₈	—	146	2	no	—
88	C₄⋊C₈	—	146	4	no	—
89	#97	—	146	2	no	—
90	#95	—	73	1	no	—
91	#95	#64408	1	1	yes	characteristic
92	C₂²×C₄	—	73	1	no	—
93	C₂²×C₄	—	73	2	no	—
94	C₂²×C₄	—	73	1	no	—
95	C₂²×C₄	C₂×#64408	1	2	yes	—
96	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
97	C₂×C₈	—	73	2	no	—
98	C₂×C₈	—	73	2	no	—
99	C₂×C₈	—	146	2	no	—
100	C₂×C₈	—	146	2	no	—
101	C₂×C₈	—	146	2	no	—
102	C₂×C₈	—	146	1	no	—
103	C₂×C₈	—	146	1	no	—
104	C₂×C₈	—	146	1	no	—
105	C₂×C₈	—	146	1	no	—
106	C₄⋊C₄	—	146	4	no	—
107	C₄²	—	73	2	no	—
108	C₄²	—	73	2	no	—
109	C₄²	—	146	2	no	—
110	C₄²	—	146	2	no	—
111	C₂³	C₂²×#64408	1	1	yes	characteristic
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	73	1	no	—
117	C₂×C₄	—	73	1	no	—
118	C₂×C₄	—	73	1	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	73	1	no	—
121	C₂×C₄	—	73	1	no	—
122	C₂×C₄	—	73	4	no	—
123	C₂×C₄	—	73	2	no	—
124	C₂×C₄	—	146	2	no	—
125	C₂×C₄	—	146	2	no	—
126	C₂×C₄	—	146	2	no	—
127	C₂×C₄	C₄⋊#64408	1	2	yes	—
128	C₈	—	292	2	no	—
129	C₈	—	146	2	no	—
130	C₈	—	146	2	no	—
131	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
132	C₂²	D₄×#64408	1	1	yes	characteristic
133	C₂²	Q₈×#64408	1	1	yes	characteristic
134	C₂²	D₇₃⋊M₁₆	1	2	yes	—
135	C₂²	#14556678	1	2	yes	—
136	C₄	—	2	2	no	—
137	C₄	—	4	2	no	—
138	C₄	—	73	1	no	—
139	C₄	—	73	1	no	—
140	C₄	—	73	1	no	—
141	C₄	—	73	1	no	—
142	C₄	—	146	2	no	—
143	C₄	—	146	4	no	—
144	C₂	#17989538	1	1	yes	characteristic
145	C₂	#17989592	1	1	yes	characteristic
146	C₂	#17989593	1	1	yes	characteristic
147	C₂	#17989619	1	2	yes	—
148	C₂	#17989639	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556658

C₂

yes

maximal

C₂×C₄⋊#10596833

C₂

yes

maximal, characteristic

C₂×#14556646

C₂

yes

maximal, characteristic

#17989453

C₂

yes

maximal

#17988438

C₂

yes

maximal, characteristic

C₂²×#10596833

C₂²

yes

—

C₂²×#10596833

C₂²

yes

characteristic

C₂²×#10596833

C₂²

yes

—

—

—

C₄

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556498

C₄

yes

characteristic

#95×C₇₃

C₄

yes

—

—

—

—

—

—

—

D₄

yes

—

C₂×#10596833

Q₈

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂³

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

M₁₆

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

C₂×Dic₇₃

yes

C₂×Dic₇₃

yes

—

—

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₂²×C₇₃

C₄×Q₈

yes

characteristic

C₂²×C₇₃

C₂×M₁₆

yes

—

C₂²×C₇₃

#131

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#121

yes

characteristic

Dic₇₃

C₂²⋊Q₈

yes

characteristic

Dic₇₃

#125

yes

characteristic

Dic₇₃

C₄⋊Q₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#446

yes

—

#1940

—

maximal, Sylow

C₇₃

#1940

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₄×C₄⋊C₄

—

#336

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

#97

—

146

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

100

C₂×C₈

—

146

—

101

C₂×C₈

—

146

—

102

C₂×C₈

—

146

—

103

C₂×C₈

—

146

—

104

C₂×C₈

—

146

—

105

C₂×C₈

—

146

—

106

C₄⋊C₄

—

146

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

146

—

110

C₄²

—

146

—

111

C₂³

C₂²×#64408

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

146

—

125

C₂×C₄

—

146

—

126

C₂×C₄

—

146

—

127

C₂×C₄

C₄⋊#64408

yes

—

128

C₈

—

292

—

129

C₈

—

146

—

130

C₈

—

146

—

131

C₂²

C₂×C₄⋊#64408

yes

characteristic

132

C₂²

D₄×#64408

yes

characteristic

133

C₂²

Q₈×#64408

yes

characteristic

134

C₂²

D₇₃⋊M₁₆

yes

—

135

C₂²

#14556678

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

146

—

143

C₄

—

146

—

144

C₂

#17989538

yes

characteristic

145

C₂

#17989592

yes

characteristic

146

C₂

#17989593

yes

characteristic

147

C₂

#17989619

yes

—

148

C₂

#17989639

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#64408
commutator, socle	C₂³×C₇₃	C₂²×C₄
Fitting	#95×C₇₃	C₄
hypercenter	#95	#64408
hypocenter	C₇₃	#1940
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#64408

commutator, socle

C₂³×C₇₃

C₂²×C₄

Fitting

#95×C₇₃

C₄

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
75. C₇₃	#1940	semidirect

H ≅ G/N

type

75. C₇₃

#1940

semidirect

Subgroups — #22626032

Conjugacy classes of subgroups

Complements