Group #22610032 — subgroups

Subgroups — #22610032

Order 9344.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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	#41×Dic₇₃	C₂	1	1	yes	maximal, characteristic
2	#17988571	C₂	1	1	yes	maximal, characteristic
3	#17988346	C₂	1	2	yes	maximal, complemented
4	#17988343	C₂	1	2	yes	maximal, complemented
5	#410×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	Q₈×Dic₇₃	—	2	1	no	—
8	D₄×Dic₇₃	—	2	1	no	—
9	D₄×Dic₇₃	—	2	2	no	—
10	#14556550	C₄	1	2	yes	complemented
11	#14556550	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₇₃	C₄	1	2	yes	complemented
13	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
14	#14556510	—	2	1	no	—
15	#14556508	—	2	1	no	—
16	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic
17	#117×C₇₃	C₂²	1	2	yes	—
18	#99×C₇₃	—	2	2	no	—
19	C₂²×Dic₇₃	—	2	2	no	—
20	C₂²×Dic₇₃	—	2	1	no	—
21	#11924012	—	2	2	no	—
22	#11924012	—	2	2	no	—
23	C₂×#10596831	—	2	2	no	—
24	C₄⋊Dic₇₃	—	2	2	no	—
25	C₄⋊Dic₇₃	—	2	1	no	—
26	C₂²⋊Dic₇₃	—	2	2	no	—
27	C₂²⋊Dic₇₃	—	2	1	no	—
28	C₄×Dic₇₃	—	2	2	no	—
29	C₄×Dic₇₃	—	2	1	no	—
30	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
32	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
33	#41×C₇₃	—	2	2	no	—
34	#41×C₇₃	—	2	2	no	—
35	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
36	C₂×D₄×C₇₃	D₄	1	1	yes	characteristic
37	C₂×D₄×C₇₃	D₄	1	2	yes	—
38	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
39	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
40	C₄⋊C₄×C₇₃	—	2	2	no	—
41	C₂²⋊C₄×C₇₃	—	2	2	no	—
42	C₄²×C₇₃	—	2	2	no	—
43	C₂³×C₇₃	C₂²⋊C₄	1	2	yes	—
44	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
45	Q₈×C₇₃	—	2	2	no	—
46	D₄×C₇₃	—	2	4	no	—
47	D₄×C₇₃	—	2	2	no	—
48	C₂×C₄×C₇₃	—	2	2	no	—
49	C₂×C₄×C₇₃	—	2	2	no	—
50	C₂×C₄×C₇₃	—	4	2	no	—
51	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
52	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₇₃	#41	1	2	yes	—
55	C₂×C₄×C₇₃	#41	1	2	yes	—
56	C₂×Dic₇₃	—	2	1	no	—
57	C₂×Dic₇₃	—	2	2	no	—
58	C₂×Dic₇₃	—	2	1	no	—
59	C₂×Dic₇₃	—	4	2	no	—
60	C₂×Dic₇₃	—	4	4	no	—
61	#10596831	—	4	2	no	—
62	C₂²×C₇₃	—	2	2	no	—
63	C₂²×C₇₃	—	4	1	no	—
64	C₂²×C₇₃	—	4	2	no	—
65	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₇₃	#123	1	2	yes	—
67	C₄×C₇₃	—	2	2	no	—
68	C₄×C₇₃	—	8	2	no	—
69	C₄×C₇₃	#117	1	1	yes	characteristic
70	C₄×C₇₃	#117	1	1	yes	characteristic
71	C₄×C₇₃	#123	1	2	yes	—
72	Dic₇₃	—	2	2	no	—
73	Dic₇₃	—	4	2	no	—
74	Dic₇₃	—	4	1	no	—
75	C₂×C₇₃	—	2	1	no	—
76	C₂×C₇₃	—	2	2	no	—
77	C₂×C₇₃	—	4	2	no	—
78	C₂×C₇₃	#381	1	1	yes	characteristic
79	#1827	—	73	1	no	maximal, Sylow
80	C₇₃	#1827	1	1	yes	characteristic, complemented, Sylow
81	C₄×#41	—	73	1	no	—
82	#413	—	73	1	no	—
83	#410	D₇₃	1	1	yes	characteristic
84	#339	—	73	2	no	—
85	H(3,ℤ/4)	—	73	2	no	—
86	C₂×#41	C₂×D₇₃	1	1	yes	characteristic
87	C₂×M₁₆	—	73	2	no	—
88	C₄×Q₈	—	146	1	no	—
89	C₄×D₄	—	146	1	no	—
90	C₄×D₄	—	146	2	no	—
91	#117	—	73	2	no	—
92	#117	—	73	1	no	—
93	#117	C₂×D₇₃	1	2	yes	—
94	C₂×C₄²	—	73	2	no	—
95	C₂×C₄²	—	73	1	no	—
96	#101	—	146	1	no	—
97	#100	—	146	1	no	—
98	#99	—	2	2	no	—
99	#41	—	2	2	no	—
100	#41	—	2	2	no	—
101	C₂×Q₈	D₂₉₂	1	1	yes	characteristic
102	C₂×D₄	D₂₉₂	1	1	yes	characteristic
103	C₂×D₄	C₂²⋊D₇₃	1	2	yes	—
104	C₂²×C₄	—	146	2	no	—
105	C₂²×C₄	—	146	1	no	—
106	C₂²×C₄	C₄×D₇₃	1	2	yes	—
107	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
108	M₁₆	—	146	2	no	—
109	M₁₆	—	146	2	no	—
110	C₂×C₈	—	146	2	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	146	2	no	—
113	C₄⋊C₄	—	146	1	no	—
114	C₂²⋊C₄	—	2	2	no	—
115	C₂²⋊C₄	—	146	2	no	—
116	C₂²⋊C₄	—	146	1	no	—
117	C₄²	—	2	2	no	—
118	C₄²	—	73	1	no	—
119	C₄²	—	73	2	no	—
120	C₄²	—	73	1	no	—
121	C₄²	—	146	2	no	—
122	C₄²	—	146	1	no	—
123	C₂³	#11924005	1	2	yes	—
124	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
125	Q₈	—	2	2	no	—
126	D₄	—	2	4	no	—
127	D₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	292	2	no	—
132	C₂×C₄	—	292	4	no	—
133	C₂×C₄	—	146	2	no	—
134	C₂×C₄	—	146	1	no	—
135	C₂×C₄	—	146	1	no	—
136	C₂×C₄	#11924005	1	2	yes	—
137	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
138	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
139	C₂×C₄	#11924027	1	2	yes	—
140	C₂×C₄	#11924027	1	2	yes	—
141	C₈	—	292	2	no	—
142	C₂²	—	2	2	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	4	2	no	—
145	C₂²	C₂×#11924005	1	1	yes	characteristic
146	C₂²	#14556572	1	2	yes	—
147	C₄	—	2	2	no	—
148	C₄	—	8	2	no	—
149	C₄	—	292	1	no	—
150	C₄	—	292	2	no	—
151	C₄	—	146	2	no	—
152	C₄	#14556547	1	1	yes	characteristic
153	C₄	#14556547	1	1	yes	characteristic
154	C₄	#14556575	1	2	yes	—
155	C₂	—	2	2	no	—
156	C₂	—	2	1	no	—
157	C₂	—	4	2	no	—
158	C₂	#17988448	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#41×Dic₇₃

C₂

yes

maximal, characteristic

#17988571

C₂

yes

maximal, characteristic

#17988346

C₂

yes

maximal, complemented

#17988343

C₂

yes

maximal, complemented

#410×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

Q₈×Dic₇₃

—

D₄×Dic₇₃

—

D₄×Dic₇₃

—

#14556550

C₄

yes

complemented

#14556550

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₄

yes

complemented

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556510

—

#14556508

—

C₂×#41×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₂²

yes

—

#99×C₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

#123

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₄×#41

—

#413

—

#410

D₇₃

yes

characteristic

#339

—

H(3,ℤ/4)

—

C₂×#41

C₂×D₇₃

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

—

146

—

C₄×D₄

—

146

—

C₄×D₄

—

146

—

#117

—

#117

—

#117

C₂×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

#101

—

146

—

#100

—

146

—

#99

—

#41

—

100

#41

—

101

C₂×Q₈

D₂₉₂

yes

characteristic

102

C₂×D₄

D₂₉₂

yes

characteristic

103

C₂×D₄

C₂²⋊D₇₃

yes

—

104

C₂²×C₄

—

146

—

105

C₂²×C₄

—

146

—

106

C₂²×C₄

C₄×D₇₃

yes

—

107

C₂²×C₄

C₂²×D₇₃

yes

characteristic

108

M₁₆

—

146

—

109

M₁₆

—

146

—

110

C₂×C₈

—

146

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

146

—

113

C₄⋊C₄

—

146

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

146

—

116

C₂²⋊C₄

—

146

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

146

—

122

C₄²

—

146

—

123

C₂³

#11924005

yes

—

124

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

125

Q₈

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

292

—

132

C₂×C₄

—

292

—

133

C₂×C₄

—

146

—

134

C₂×C₄

—

146

—

135

C₂×C₄

—

146

—

136

C₂×C₄

#11924005

yes

—

137

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

138

C₂×C₄

C₂×D₂₉₂

yes

characteristic

139

C₂×C₄

#11924027

yes

—

140

C₂×C₄

#11924027

yes

—

141

C₈

—

292

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

C₂×#11924005

yes

characteristic

146

C₂²

#14556572

yes

—

147

C₄

—

148

C₄

—

149

C₄

—

292

—

150

C₄

—

292

—

151

C₄

—

146

—

152

C₄

#14556547

yes

characteristic

153

C₄

#14556547

yes

characteristic

154

C₄

#14556575

yes

—

155

C₂

—

156

C₂

—

157

C₂

—

158

C₂

#17988448

yes

characteristic

	subgroup	G/H
center	C₄	#14556547
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#410×C₇₃	C₂
socle	C₂×C₇₃	#381
hypercenter	#410	D₇₃
hypocenter	C₇₃	#1827
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

subgroup

G/H

center

C₄

#14556547

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#410×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

N	H ≅ G/N	type
3. #17988346	C₂	semidirect
4. #17988343	C₂	semidirect
10. #14556550	C₄	semidirect
12. C₂×C₄×Dic₇₃	C₄	semidirect
80. C₇₃	#1827	semidirect

H ≅ G/N

type

3. #17988346

C₂

semidirect

4. #17988343

C₂

semidirect

10. #14556550

C₄

semidirect

12. C₂×C₄×Dic₇₃

C₄

semidirect

80. C₇₃

#1827

semidirect

Subgroups — #22610032

Conjugacy classes of subgroups

Complements