Group #22625021 — subgroups

Subgroups — #22625021

Order 9344.

158 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 38 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	#17989574	C₂	1	1	yes	maximal, characteristic
2	#17989560	C₂	1	1	yes	maximal, characteristic
3	#17988568	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924037	—	2	1	no	—
5	C₂×#11924037	C₄	1	1	yes	characteristic
6	C₂²×#10596833	C₄	1	1	yes	characteristic
7	#14556652	—	2	1	no	—
8	#14556651	C₄	1	2	yes	—
9	#14556648	—	2	1	no	—
10	C₂²⋊#10596833	—	2	1	no	—
11	C₂×#11924027	C₂²	1	1	yes	characteristic
12	M₁₆×D₇₃	—	2	1	no	—
13	#14556509	—	2	1	no	—
14	#14556508	C₄	1	1	yes	characteristic
15	#100×C₇₃	C₄	1	1	yes	characteristic
16	#11924037	—	2	2	no	—
17	#11924037	—	4	1	no	—
18	#11924037	—	4	1	no	—
19	C₂×#10596833	—	2	1	no	—
20	C₂×#10596833	—	2	1	no	—
21	C₂×#10596833	—	4	1	no	—
22	C₂×#10596833	—	4	1	no	—
23	#11924027	—	4	1	no	—
24	#11924027	—	4	1	no	—
25	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
26	C₂×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊D₇₃	Q₈	1	1	yes	characteristic
28	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
30	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
31	#11924012	—	2	1	no	—
32	#11924011	—	4	1	no	—
33	C₈×D₇₃	—	4	1	no	—
34	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
35	M₁₆×C₇₃	—	2	1	no	—
36	C₂³×C₇₃	C₄²	1	1	yes	characteristic
37	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
39	D₄×C₇₃	—	4	1	no	—
40	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²⋊D₇₃	—	4	1	no	—
42	C₂²⋊D₇₃	—	4	1	no	—
43	C₂×Dic₇₃	—	2	1	no	—
44	C₂×Dic₇₃	—	2	1	no	—
45	C₂×Dic₇₃	—	2	1	no	—
46	C₂×Dic₇₃	—	2	1	no	—
47	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
50	C₄×D₇₃	—	2	1	no	—
51	C₄×D₇₃	—	2	1	no	—
52	Dic₁₄₆	—	4	1	no	—
53	#10596833	—	4	2	no	—
54	#10596833	—	4	1	no	—
55	#10596833	—	4	1	no	—
56	C₈×C₇₃	—	4	1	no	—
57	#10596831	—	4	1	no	—
58	C₂²×C₇₃	—	2	1	no	—
59	C₂²×C₇₃	—	2	1	no	—
60	C₂²×C₇₃	—	4	1	no	—
61	C₂²×C₇₃	—	4	1	no	—
62	C₂²×C₇₃	#95	1	1	yes	characteristic
63	C₂×D₇₃	—	2	1	no	—
64	C₂×D₇₃	—	4	1	no	—
65	C₄×C₇₃	—	2	1	no	—
66	Dic₇₃	—	2	1	no	—
67	Dic₇₃	—	2	1	no	—
68	Dic₇₃	#99	1	1	yes	characteristic
69	Dic₇₃	#99	1	1	yes	characteristic
70	C₂×C₇₃	—	2	1	no	—
71	C₂×C₇₃	—	4	1	no	—
72	C₂×C₇₃	—	4	1	no	—
73	C₂×C₇₃	#342	1	1	yes	characteristic
74	D₇₃	—	4	1	no	—
75	#1392	—	73	1	no	maximal, Sylow
76	C₇₃	#1392	1	1	yes	characteristic, complemented, Sylow
77	#413	—	73	1	no	—
78	#413	—	73	1	no	—
79	#408	—	73	1	no	—
80	C₂×#41	—	73	1	no	—
81	C₂×M₁₆	—	73	1	no	—
82	C₂×M₁₆	—	146	1	no	—
83	C₂×M₁₆	—	146	1	no	—
84	C₂²×C₈	—	73	1	no	—
85	#101	—	146	1	no	—
86	#101	—	146	1	no	—
87	#100	—	73	2	no	—
88	#100	—	73	1	no	—
89	#100	#64408	1	1	yes	characteristic
90	C₂²⋊C₈	—	146	1	no	—
91	C₂²⋊C₈	—	146	1	no	—
92	#41	—	292	1	no	—
93	#41	—	292	1	no	—
94	C₂×Q₈	—	73	1	no	—
95	C₂×D₄	—	73	1	no	—
96	C₂×D₄	—	73	1	no	—
97	C₂×D₄	C₂×#64408	1	1	yes	characteristic
98	C₂²×C₄	—	73	1	no	—
99	C₂²×C₄	—	73	1	no	—
100	C₂²×C₄	—	73	1	no	—
101	M₁₆	—	2	1	no	—
102	M₁₆	—	292	1	no	—
103	M₁₆	—	292	1	no	—
104	M₁₆	—	292	1	no	—
105	M₁₆	—	146	2	no	—
106	M₁₆	—	146	1	no	—
107	C₂×C₈	—	292	1	no	—
108	C₂×C₈	—	292	1	no	—
109	C₂×C₈	—	292	1	no	—
110	C₂×C₈	—	146	1	no	—
111	C₂×C₈	—	146	1	no	—
112	C₂³	—	73	1	no	—
113	C₂³	C₄×#64408	1	1	yes	characteristic
114	C₂³	C₄⋊#64408	1	1	yes	characteristic
115	Q₈	—	292	1	no	—
116	D₄	—	4	1	no	—
117	D₄	—	292	1	no	—
118	D₄	—	292	1	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	73	1	no	—
121	C₂×C₄	—	73	1	no	—
122	C₂×C₄	—	146	1	no	—
123	C₂×C₄	—	146	1	no	—
124	C₂×C₄	—	146	1	no	—
125	C₂×C₄	—	146	1	no	—
126	C₂×C₄	—	146	1	no	—
127	C₂×C₄	—	146	1	no	—
128	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
129	C₈	—	4	1	no	—
130	C₈	—	292	1	no	—
131	C₈	—	292	1	no	—
132	C₈	—	292	1	no	—
133	C₈	—	292	2	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	4	1	no	—
137	C₂²	—	4	1	no	—
138	C₂²	—	292	1	no	—
139	C₂²	—	146	1	no	—
140	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	73	1	no	—
143	C₄	—	73	1	no	—
144	C₄	—	146	1	no	—
145	C₄	—	146	1	no	—
146	C₂	—	2	1	no	—
147	C₂	—	4	1	no	—
148	C₂	—	4	1	no	—
149	C₂	—	292	1	no	—
150	C₂	#17989464	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989574

C₂

yes

maximal, characteristic

#17989560

C₂

yes

maximal, characteristic

#17988568

C₂

yes

maximal, characteristic

C₂×#11924037

—

C₂×#11924037

C₄

yes

characteristic

C₂²×#10596833

C₄

yes

characteristic

#14556652

—

#14556651

C₄

yes

—

#14556648

—

C₂²⋊#10596833

—

C₂×#11924027

C₂²

yes

characteristic

M₁₆×D₇₃

—

#14556509

—

#14556508

C₄

yes

characteristic

#100×C₇₃

C₄

yes

—

—

—

—

—

—

—

—

—

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×C₂²⋊D₇₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₇₃

Q₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

#11924012

—

#11924011

—

C₈×D₇₃

—

C₂×D₄×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

—

C₂³×C₇₃

C₄²

yes

characteristic

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

#10596833

—

#10596833

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#95

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#342

yes

characteristic

D₇₃

—

#1392

—

maximal, Sylow

C₇₃

#1392

yes

characteristic, complemented, Sylow

#413

—

#413

—

#408

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

#101

—

146

—

#101

—

146

—

—

—

yes

C₂²⋊C₈

—

146

—

C₂²⋊C₈

—

146

—

#41

—

292

—

#41

—

292

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

M₁₆

—

102

M₁₆

—

292

—

103

M₁₆

—

292

—

104

M₁₆

—

292

—

105

M₁₆

—

146

—

106

M₁₆

—

146

—

107

C₂×C₈

—

292

—

108

C₂×C₈

—

292

—

109

C₂×C₈

—

292

—

110

C₂×C₈

—

146

—

111

C₂×C₈

—

146

—

112

C₂³

—

113

C₂³

C₄×#64408

yes

characteristic

114

C₂³

C₄⋊#64408

yes

characteristic

115

Q₈

—

292

—

116

D₄

—

117

D₄

—

292

—

118

D₄

—

292

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

146

—

123

C₂×C₄

—

146

—

124

C₂×C₄

—

146

—

125

C₂×C₄

—

146

—

126

C₂×C₄

—

146

—

127

C₂×C₄

—

146

—

128

C₂×C₄

C₂²⋊#64408

yes

characteristic

129

C₈

—

130

C₈

—

292

—

131

C₈

—

292

—

132

C₈

—

292

—

133

C₈

—

292

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

292

—

139

C₂²

—

146

—

140

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

146

—

145

C₄

—

146

—

146

C₂

—

147

C₂

—

148

C₂

—

149

C₂

—

292

—

150

C₂

#17989464

yes

characteristic

	subgroup	G/H
center	C₂	#17989464
commutator	C₂³×C₇₃	C₄²
Frattini	C₂×D₄	C₂×#64408
Fitting	#100×C₇₃	C₄
socle	C₂×C₇₃	#342
hypercenter	#100	#64408
hypocenter	C₇₃	#1392
LCS	G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #100

subgroup

G/H

center

C₂

#17989464

commutator

C₂³×C₇₃

C₄²

Frattini

C₂×D₄

C₂×#64408

Fitting

#100×C₇₃

C₄

C₂×C₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #100

N	H ≅ G/N	type
76. C₇₃	#1392	semidirect

H ≅ G/N

type

76. C₇₃

#1392

semidirect

Subgroups — #22625021

Conjugacy classes of subgroups

Complements