Group #22611355 — subgroups

Subgroups — #22611355

Order 9344.

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

normal subgroups only

This group has 256 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	C₂×#14556503	C₂	1	1	yes	maximal, characteristic
2	#17988444	C₂	1	2	yes	maximal
3	#17988350	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988349	C₂	1	2	yes	maximal, complemented
5	C₂×#107×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	C₂×#11924005	—	2	2	no	—
10	#14556503	—	2	2	no	—
11	#14556498	—	2	2	no	—
12	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
14	#107×C₇₃	—	2	2	no	—
15	C₂³×D₇₃	D₄	1	1	yes	characteristic
16	C₂²×Dic₇₃	—	2	2	no	—
17	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	—	2	1	no	—
19	C₂×C₄×D₇₃	—	2	1	no	—
20	C₂×C₄×D₇₃	—	2	2	no	—
21	C₂×C₄×D₇₃	—	2	2	no	—
22	C₂×#10596831	—	2	1	no	—
23	C₂×#10596831	—	2	2	no	—
24	C₄⋊Dic₇₃	—	2	2	no	—
25	C₄⋊Dic₇₃	—	2	2	no	—
26	#11924005	—	4	4	no	—
27	C₂²×C₄×C₇₃	—	2	2	no	—
28	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₂×C₈×C₇₃	D₄	1	2	yes	—
31	C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₄⋊C₄×C₇₃	—	2	2	no	—
33	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×D₇₃	—	2	1	no	—
35	C₂²×D₇₃	—	2	2	no	—
36	C₂²×D₇₃	—	2	1	no	—
37	C₂²×D₇₃	—	2	2	no	—
38	C₂²×D₇₃	D₈	1	2	yes	—
39	C₂×C₄×C₇₃	—	4	2	no	—
40	C₂×C₄×C₇₃	—	4	2	no	—
41	C₂×C₄×C₇₃	—	4	2	no	—
42	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
44	C₂×C₄×C₇₃	#41	1	2	yes	—
45	C₂×C₄×C₇₃	#41	1	2	yes	—
46	C₂×Dic₇₃	—	2	1	no	—
47	C₂×Dic₇₃	—	2	2	no	—
48	C₂×Dic₇₃	—	4	2	no	—
49	C₂×Dic₇₃	—	4	2	no	—
50	C₂×Dic₇₃	—	4	2	no	—
51	C₄×D₇₃	—	4	1	no	—
52	C₄×D₇₃	—	4	1	no	—
53	C₄×D₇₃	—	4	2	no	—
54	C₈×C₇₃	—	2	2	no	—
55	#10596831	—	4	1	no	—
56	C₂²×C₇₃	#121	1	1	yes	characteristic
57	C₂²×C₇₃	#123	1	2	yes	—
58	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
59	C₂²×C₇₃	#135	1	1	yes	characteristic
60	C₂²×C₇₃	#137	1	2	yes	—
61	C₂×D₇₃	—	2	2	no	—
62	C₂×D₇₃	—	2	4	no	—
63	C₂×D₇₃	—	4	1	no	—
64	C₂×D₇₃	—	4	1	no	—
65	C₂×D₇₃	—	4	2	no	—
66	C₄×C₇₃	—	8	2	no	—
67	C₄×C₇₃	#123	1	1	yes	characteristic
68	C₄×C₇₃	#124	1	1	yes	characteristic
69	C₄×C₇₃	#126	1	2	yes	—
70	Dic₇₃	—	4	1	no	—
71	Dic₇₃	—	8	2	no	—
72	C₂×C₇₃	#397	1	1	yes	characteristic
73	C₂×C₇₃	#466	1	1	yes	characteristic
74	C₂×C₇₃	#470	1	1	yes	characteristic
75	C₂×C₇₃	#480	1	2	yes	—
76	C₂×C₇₃	#485	1	2	yes	—
77	D₇₃	—	4	2	no	—
78	#2075	—	73	1	no	maximal, Sylow
79	C₇₃	#2075	1	1	yes	characteristic, complemented, Sylow
80	C₂×#107	D₇₃	1	1	yes	characteristic, complemented
81	C₂×C₂²⋊C₈	—	73	1	no	—
82	#380	—	73	2	no	—
83	#340	—	73	1	no	—
84	#340	—	73	2	no	—
85	C₂³×C₄	—	73	1	no	—
86	C₂²×C₈	—	73	1	no	—
87	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
88	C₂×C₄⋊C₄	—	73	2	no	—
89	C₂×C₄⋊C₄	C₂×D₇₃	1	2	yes	—
90	C₂×C₂²⋊C₄	—	146	2	no	—
91	#107	—	2	2	no	—
92	C₂²⋊C₈	—	146	2	no	—
93	#95	—	146	2	no	—
94	C₂⁴	—	73	1	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	73	1	no	—
97	C₂²×C₄	—	146	2	no	—
98	C₂²×C₄	—	146	1	no	—
99	C₂²×C₄	—	146	1	no	—
100	C₂²×C₄	—	146	2	no	—
101	C₂²×C₄	—	146	2	no	—
102	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	146	1	no	—
105	C₂×C₈	—	146	2	no	—
106	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	146	2	no	—
110	C₄⋊C₄	—	146	2	no	—
111	C₂²⋊C₄	—	292	4	no	—
112	C₂³	—	73	2	no	—
113	C₂³	—	146	1	no	—
114	C₂³	—	146	2	no	—
115	C₂³	—	146	1	no	—
116	C₂³	—	146	2	no	—
117	C₂³	D₄×D₇₃	1	1	yes	characteristic
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	292	1	no	—
122	C₂×C₄	—	292	1	no	—
123	C₂×C₄	—	292	2	no	—
124	C₂×C₄	—	292	2	no	—
125	C₂×C₄	—	292	2	no	—
126	C₂×C₄	—	292	2	no	—
127	C₂×C₄	—	146	1	no	—
128	C₂×C₄	—	146	2	no	—
129	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
130	C₂×C₄	#11924027	1	1	yes	characteristic
131	C₂×C₄	#11924028	1	2	yes	—
132	C₂×C₄	#11924029	1	2	yes	—
133	C₈	—	2	2	no	—
134	C₈	—	292	1	no	—
135	C₂²	—	292	2	no	—
136	C₂²	—	292	1	no	—
137	C₂²	—	292	1	no	—
138	C₂²	—	146	4	no	—
139	C₂²	—	146	2	no	—
140	C₂²	#14556562	1	1	yes	characteristic
141	C₂²	#14556576	1	2	yes	—
142	C₂²	D₈×D₇₃	1	1	yes	characteristic
143	C₂²	#14556610	1	1	yes	characteristic
144	C₂²	#14556623	1	2	yes	—
145	C₄	—	8	2	no	—
146	C₄	—	292	1	no	—
147	C₄	—	584	2	no	—
148	C₄	#14556574	1	1	yes	characteristic
149	C₄	#14556580	1	1	yes	characteristic
150	C₄	#14556586	1	2	yes	—
151	C₂	—	292	2	no	—
152	C₂	#17988513	1	1	yes	characteristic
153	C₂	#17988820	1	1	yes	characteristic
154	C₂	#17988842	1	1	yes	characteristic
155	C₂	#17988902	1	2	yes	—
156	C₂	#17988930	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556503

C₂

yes

maximal, characteristic

#17988444

C₂

yes

maximal

#17988350

C₂

yes

maximal, characteristic, complemented

#17988349

C₂

yes

maximal, complemented

C₂×#107×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₃

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924005

—

#14556503

—

#14556498

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

#107×C₇₃

—

C₂³×D₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

D₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#121

yes

characteristic

C₂²×C₇₃

#123

yes

—

C₂²×C₇₃

C₂×D₈

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#485

yes

—

D₇₃

—

#2075

—

maximal, Sylow

C₇₃

#2075

yes

characteristic, complemented, Sylow

C₂×#107

D₇₃

yes

characteristic, complemented

C₂×C₂²⋊C₈

—

#380

—

#340

—

#340

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₂²⋊C₄

—

146

—

#107

—

C₂²⋊C₈

—

146

—

#95

—

146

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

100

C₂²×C₄

—

146

—

101

C₂²×C₄

—

146

—

102

C₂²×C₄

C₂²×D₇₃

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

146

—

105

C₂×C₈

—

146

—

106

C₂×C₈

C₂²⋊D₇₃

yes

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

146

—

110

C₄⋊C₄

—

146

—

111

C₂²⋊C₄

—

292

—

112

C₂³

—

113

C₂³

—

146

—

114

C₂³

—

146

—

115

C₂³

—

146

—

116

C₂³

—

146

—

117

C₂³

D₄×D₇₃

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

292

—

122

C₂×C₄

—

292

—

123

C₂×C₄

—

292

—

124

C₂×C₄

—

292

—

125

C₂×C₄

—

292

—

126

C₂×C₄

—

292

—

127

C₂×C₄

—

146

—

128

C₂×C₄

—

146

—

129

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

130

C₂×C₄

#11924027

yes

characteristic

131

C₂×C₄

#11924028

yes

—

132

C₂×C₄

#11924029

yes

—

133

C₈

—

134

C₈

—

292

—

135

C₂²

—

292

—

136

C₂²

—

292

—

137

C₂²

—

292

—

138

C₂²

—

146

—

139

C₂²

—

146

—

140

C₂²

#14556562

yes

characteristic

141

C₂²

#14556576

yes

—

142

C₂²

D₈×D₇₃

yes

characteristic

143

C₂²

#14556610

yes

characteristic

144

C₂²

#14556623

yes

—

145

C₄

—

146

C₄

—

292

—

147

C₄

—

584

—

148

C₄

#14556574

yes

characteristic

149

C₄

#14556580

yes

characteristic

150

C₄

#14556586

yes

—

151

C₂

—

292

—

152

C₂

#17988513

yes

characteristic

153

C₂

#17988820

yes

characteristic

154

C₂

#17988842

yes

characteristic

155

C₂

#17988902

yes

—

156

C₂

#17988930

yes

—

	subgroup	G/H
center	C₂³	D₄×D₇₃
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#107×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	C₂×#107	D₇₃
hypocenter	C₇₃	#2075
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₇₃

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#107×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
3. #17988350	C₂	semidirect
4. #17988349	C₂	semidirect
5. C₂×#107×C₇₃	C₂	semidirect
79. C₇₃	#2075	semidirect
80. C₂×#107	D₇₃	semidirect

H ≅ G/N

type

3. #17988350

C₂

semidirect

4. #17988349

C₂

semidirect

5. C₂×#107×C₇₃

C₂

semidirect

79. C₇₃

#2075

semidirect

80. C₂×#107

D₇₃

semidirect

Subgroups — #22611355

Conjugacy classes of subgroups

Complements