Group #22611397 — subgroups

Subgroups — #22611397

Order 9344.

184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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	#17988636	C₂	1	1	yes	maximal, characteristic
2	#17988597	C₂	1	1	yes	maximal, characteristic
3	#17988595	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556509	C₂	1	1	yes	maximal, characteristic
5	#17988358	C₂	1	1	yes	maximal, characteristic
6	#17988343	C₂	1	1	yes	maximal, characteristic
7	#344×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
9	C₂×#11924012	C₂²	1	1	yes	characteristic
10	C₂×#11924012	C₂²	1	1	yes	characteristic
11	#14556550	C₂²	1	1	yes	characteristic
12	#14556527	—	2	2	no	—
13	#14556516	—	2	2	no	—
14	#14556514	—	2	2	no	—
15	#14556509	—	2	2	no	—
16	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	#117×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₄₆	—	2	1	no	—
20	C₂×Dic₁₄₆	—	2	1	no	—
21	C₂×Dic₁₄₆	—	2	1	no	—
22	C₂×Dic₁₄₆	—	2	1	no	—
23	C₂×Dic₁₄₆	—	2	1	no	—
24	C₂×Dic₁₄₆	D₄	1	2	yes	—
25	C₂²×Dic₇₃	—	2	1	no	—
26	#11924012	—	2	1	no	—
27	#11924012	—	2	1	no	—
28	#11924012	—	2	1	no	—
29	#11924012	—	2	1	no	—
30	C₂×#10596831	—	2	1	no	—
31	C₂×#10596831	—	2	1	no	—
32	C₄⋊Dic₇₃	—	2	1	no	—
33	C₂²⋊Dic₇₃	—	2	1	no	—
34	C₄×Dic₇₃	—	2	1	no	—
35	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
36	M₁₆×C₇₃	—	2	1	no	—
37	M₁₆×C₇₃	—	2	1	no	—
38	M₁₆×C₇₃	—	2	1	no	—
39	M₁₆×C₇₃	—	2	1	no	—
40	C₂×C₈×C₇₃	—	2	1	no	—
41	C₂×C₈×C₇₃	D₄	1	2	yes	—
42	C₄⋊C₄×C₇₃	—	2	1	no	—
43	C₂²⋊C₄×C₇₃	—	2	1	no	—
44	C₄²×C₇₃	—	2	1	no	—
45	C₂³×C₇₃	#41	1	1	yes	characteristic
46	C₂×C₄×C₇₃	—	4	1	no	—
47	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
50	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
51	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
52	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
53	C₂×Dic₇₃	—	2	2	no	—
54	C₂×Dic₇₃	—	4	1	no	—
55	C₂×Dic₇₃	—	4	1	no	—
56	C₂×Dic₇₃	—	4	1	no	—
57	Dic₁₄₆	—	2	2	no	—
58	Dic₁₄₆	—	2	2	no	—
59	Dic₁₄₆	—	4	1	no	—
60	Dic₁₄₆	—	4	1	no	—
61	C₈×C₇₃	—	2	2	no	—
62	C₈×C₇₃	—	4	1	no	—
63	#10596831	—	4	1	no	—
64	#10596831	—	4	1	no	—
65	C₂²×C₇₃	—	4	1	no	—
66	C₂²×C₇₃	#123	1	1	yes	characteristic
67	C₂²×C₇₃	#124	1	1	yes	characteristic
68	C₂²×C₇₃	#126	1	1	yes	characteristic
69	C₄×C₇₃	—	8	1	no	—
70	C₄×C₇₃	#121	1	1	yes	characteristic
71	C₄×C₇₃	#123	1	1	yes	characteristic
72	C₄×C₇₃	#123	1	1	yes	characteristic
73	C₄×C₇₃	#126	1	1	yes	characteristic
74	Dic₇₃	—	4	2	no	—
75	Dic₇₃	—	8	1	no	—
76	C₂×C₇₃	—	2	1	no	—
77	C₂×C₇₃	—	2	1	no	—
78	C₂×C₇₃	—	2	1	no	—
79	C₂×C₇₃	#397	1	1	yes	characteristic
80	#2082	—	73	1	no	maximal, Sylow
81	C₇₃	#2082	1	1	yes	characteristic, complemented, Sylow
82	#430	—	73	1	no	—
83	#419	—	73	1	no	—
84	#419	—	73	1	no	—
85	C₂×#101	—	73	1	no	—
86	#344	—	73	1	no	—
87	#344	D₇₃	1	1	yes	characteristic
88	H(3,ℤ/4)	—	73	1	no	—
89	C₂²×Q₈	—	73	1	no	—
90	C₂×M₁₆	—	73	1	no	—
91	C₂×M₁₆	—	73	1	no	—
92	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
93	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
94	#117	—	73	1	no	—
95	#117	C₂×D₇₃	1	1	yes	characteristic
96	#108	—	146	2	no	—
97	#103	—	146	2	no	—
98	#103	—	146	2	no	—
99	#101	—	146	2	no	—
100	C₂×Q₈	—	73	2	no	—
101	C₂×Q₈	—	146	1	no	—
102	C₂×Q₈	—	146	1	no	—
103	C₂×Q₈	—	146	1	no	—
104	C₂×Q₈	—	146	1	no	—
105	C₂×Q₈	—	146	1	no	—
106	C₂²×C₄	—	146	1	no	—
107	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
108	M₁₆	—	2	1	no	—
109	M₁₆	—	2	1	no	—
110	M₁₆	—	2	1	no	—
111	M₁₆	—	2	1	no	—
112	M₁₆	—	146	1	no	—
113	M₁₆	—	146	1	no	—
114	M₁₆	—	146	1	no	—
115	M₁₆	—	146	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	146	1	no	—
118	C₂×C₈	—	146	1	no	—
119	C₂×C₈	D₂₉₂	1	2	yes	—
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	146	1	no	—
122	C₂²⋊C₄	—	2	1	no	—
123	C₂²⋊C₄	—	146	1	no	—
124	C₄²	—	2	1	no	—
125	C₄²	—	146	1	no	—
126	C₂³	#11924028	1	1	yes	characteristic
127	Q₈	—	292	1	no	—
128	Q₈	—	292	1	no	—
129	Q₈	—	146	2	no	—
130	Q₈	—	146	2	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	292	1	no	—
133	C₂×C₄	—	292	1	no	—
134	C₂×C₄	—	292	1	no	—
135	C₂×C₄	—	146	2	no	—
136	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
137	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
138	C₂×C₄	#11924027	1	1	yes	characteristic
139	C₂×C₄	#11924027	1	1	yes	characteristic
140	C₂×C₄	#11924028	1	1	yes	characteristic
141	C₂×C₄	#11924029	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	4	1	no	—
144	C₈	—	292	1	no	—
145	C₈	—	292	1	no	—
146	C₂²	—	4	1	no	—
147	C₂²	#14556573	1	1	yes	characteristic
148	C₂²	#14556579	1	1	yes	characteristic
149	C₂²	#14556586	1	1	yes	characteristic
150	C₄	—	8	1	no	—
151	C₄	—	292	2	no	—
152	C₄	—	584	1	no	—
153	C₄	#14556566	1	1	yes	characteristic
154	C₄	#14556573	1	1	yes	characteristic
155	C₄	#14556575	1	1	yes	characteristic
156	C₄	#14556586	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	#17988514	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988636

C₂

yes

maximal, characteristic

#17988597

C₂

yes

maximal, characteristic

#17988595

C₂

yes

maximal, characteristic

C₂×#14556509

C₂

yes

maximal, characteristic

#17988358

C₂

yes

maximal, characteristic

#17988343

C₂

yes

maximal, characteristic

#344×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

characteristic

#14556550

C₂²

yes

—

—

—

—

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂²×Dic₇₃

—

—

—

—

—

—

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₃

yes

characteristic

H(3,ℤ/4)

—

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

C₂×M₁₆

C₂×D₇₃

yes

characteristic

#117

—

#117

C₂×D₇₃

yes

characteristic

#108

—

146

—

#103

—

146

—

#103

—

146

—

#101

—

146

—

100

C₂×Q₈

—

101

C₂×Q₈

—

146

—

102

C₂×Q₈

—

146

—

103

C₂×Q₈

—

146

—

104

C₂×Q₈

—

146

—

105

C₂×Q₈

—

146

—

106

C₂²×C₄

—

146

—

107

C₂²×C₄

C₂²×D₇₃

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

146

—

113

M₁₆

—

146

—

114

M₁₆

—

146

—

115

M₁₆

—

146

—

116

C₂×C₈

—

117

C₂×C₈

—

146

—

118

C₂×C₈

—

146

—

119

C₂×C₈

D₂₉₂

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

146

—

122

C₂²⋊C₄

—

123

C₂²⋊C₄

—

146

—

124

C₄²

—

125

C₄²

—

146

—

126

C₂³

#11924028

yes

characteristic

127

Q₈

—

292

—

128

Q₈

—

292

—

129

Q₈

—

146

—

130

Q₈

—

146

—

131

C₂×C₄

—

132

C₂×C₄

—

292

—

133

C₂×C₄

—

292

—

134

C₂×C₄

—

292

—

135

C₂×C₄

—

146

—

136

C₂×C₄

D₄×D₇₃

yes

characteristic

137

C₂×C₄

C₂×D₂₉₂

yes

characteristic

138

C₂×C₄

#11924027

yes

characteristic

139

C₂×C₄

#11924027

yes

characteristic

140

C₂×C₄

#11924028

yes

characteristic

141

C₂×C₄

#11924029

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

292

—

145

C₈

—

292

—

146

C₂²

—

147

C₂²

#14556573

yes

characteristic

148

C₂²

#14556579

yes

characteristic

149

C₂²

#14556586

yes

characteristic

150

C₄

—

151

C₄

—

292

—

152

C₄

—

584

—

153

C₄

#14556566

yes

characteristic

154

C₄

#14556573

yes

characteristic

155

C₄

#14556575

yes

characteristic

156

C₄

#14556586

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#17988514

yes

characteristic

	subgroup	G/H
center	C₂	#17988514
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#344×C₇₃	C₂
socle	C₂×C₇₃	#397
hypercenter	#344	D₇₃
hypocenter	C₇₃	#2082
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #344

subgroup

G/H

center

C₂

#17988514

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#344×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #344

N	H ≅ G/N	type
81. C₇₃	#2082	semidirect

H ≅ G/N

type

81. C₇₃

#2082

semidirect

Subgroups — #22611397

Conjugacy classes of subgroups

Complements