Group #22620587 — subgroups

Subgroups — #22620587

Order 9344.

338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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	#17989198	C₂	1	2	yes	maximal
2	#17988989	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988955	C₂	1	2	yes	maximal, complemented
4	#17988842	C₂	1	2	yes	maximal
5	#17988825	C₂	1	2	yes	maximal
6	#17988694	C₂	1	2	yes	maximal, complemented
7	Q₁₆×Dic₇₃	C₂	1	2	yes	maximal, complemented
8	#17988541	C₂	1	1	yes	maximal, characteristic
9	#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11924011	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	#14556586	—	2	4	no	—
13	#14556583	C₂²	1	2	yes	—
14	#14556581	—	2	4	no	—
15	#14556567	C₂²	1	4	yes	—
16	Q₈×Dic₇₃	C₂²	1	4	yes	—
17	#14556548	C₂²	1	1	yes	characteristic
18	#14556525	C₂²	1	2	yes	—
19	#14556523	C₂²	1	2	yes	—
20	#14556515	C₂²	1	4	yes	—
21	#14556515	C₂²	1	4	yes	—
22	#14556502	C₂²	1	1	yes	characteristic
23	#14556501	C₂²	1	1	yes	characteristic
24	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
25	C₂×Q₁₆×C₇₃	C₂²	1	2	yes	—
26	C₂×Q₁₆×C₇₃	C₂²	1	2	yes	—
27	C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
28	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
30	#11924011	—	2	2	no	—
31	C₂×#10596831	C₂³	1	1	yes	characteristic
32	C₂×#10596831	C₂³	1	1	yes	characteristic
33	C₈×D₇₃	—	2	2	no	—
34	C₄⋊Dic₇₃	—	2	4	no	—
35	C₄⋊Dic₇₃	C₂³	1	4	yes	—
36	#11924007	—	2	4	no	—
37	#11924007	—	2	4	no	—
38	#11924007	D₄	1	2	yes	—
39	#11924005	—	2	4	no	—
40	#11924005	D₄	1	2	yes	—
41	C₄×Dic₇₃	—	2	4	no	—
42	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
43	C₂×Q₈×C₇₃	C₂³	1	4	yes	—
44	Q₁₆×C₇₃	—	2	4	no	—
45	Q₁₆×C₇₃	—	2	4	no	—
46	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₄⋊C₄×C₇₃	—	2	4	no	—
49	C₄²×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₇₃	C₂×D₄	1	1	yes	characteristic
51	Q₈×C₇₃	—	2	4	no	—
52	Q₈×C₇₃	—	2	4	no	—
53	C₂×C₄×C₇₃	—	2	4	no	—
54	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
56	C₂×Dic₇₃	—	2	4	no	—
57	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
58	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
59	C₄×D₇₃	—	2	1	no	—
60	C₄×D₇₃	—	2	1	no	—
61	C₈×C₇₃	#41	1	2	yes	—
62	C₈×C₇₃	#41	1	2	yes	—
63	#10596831	—	2	1	no	—
64	#10596831	—	2	1	no	—
65	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
66	C₂×D₇₃	—	2	1	no	—
67	C₂×D₇₃	—	2	2	no	—
68	C₄×C₇₃	—	2	2	no	—
69	C₄×C₇₃	—	4	4	no	—
70	C₄×C₇₃	C₂×#41	1	1	yes	characteristic
71	C₄×C₇₃	C₂×#41	1	1	yes	characteristic
72	Dic₇₃	—	2	1	no	—
73	Dic₇₃	—	2	2	no	—
74	Dic₇₃	—	4	4	no	—
75	C₂×C₇₃	#532	1	1	yes	characteristic
76	C₂×C₇₃	#578	1	2	yes	—
77	D₇₃	—	4	1	no	—
78	#3177	—	73	1	no	maximal, Sylow
79	C₇₃	#3177	1	1	yes	characteristic, complemented, Sylow
80	#541	—	73	2	no	—
81	#499	—	73	1	no	—
82	#494	D₇₃	1	1	yes	characteristic, complemented
83	#491	—	73	2	no	—
84	#470	—	73	2	no	—
85	#467	—	73	2	no	—
86	#441	—	73	2	no	—
87	C₄×Q₁₆	—	73	2	no	—
88	#405	—	73	1	no	—
89	C₂×Q₁₆	C₂×D₇₃	1	2	yes	—
90	C₂×Q₁₆	C₂×D₇₃	1	2	yes	—
91	C₂×M₁₆	—	73	1	no	—
92	C₂²×C₈	—	73	1	no	—
93	C₄⋊Q₈	C₂×D₇₃	1	2	yes	—
94	#126	—	146	4	no	—
95	#125	—	73	2	no	—
96	#125	—	146	4	no	—
97	C₂²⋊Q₈	—	73	4	no	—
98	C₄×Q₈	—	73	4	no	—
99	#117	—	73	1	no	—
100	#107	—	73	2	no	—
101	#106	—	73	2	no	—
102	#103	—	73	4	no	—
103	#103	—	73	4	no	—
104	#97	—	73	1	no	—
105	#97	—	73	1	no	—
106	C₄×C₈	—	73	1	no	—
107	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
108	C₂×Q₈	C₂²×D₇₃	1	4	yes	—
109	C₂²×C₄	—	73	1	no	—
110	Q₁₆	—	2	4	no	—
111	Q₁₆	—	2	4	no	—
112	M₁₆	—	146	2	no	—
113	C₂×C₈	—	73	1	no	—
114	C₂×C₈	—	73	1	no	—
115	C₂×C₈	—	146	2	no	—
116	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
117	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
118	C₄⋊C₄	—	2	4	no	—
119	C₄⋊C₄	—	73	2	no	—
120	C₄⋊C₄	—	73	4	no	—
121	C₄⋊C₄	—	146	4	no	—
122	C₄⋊C₄	—	146	4	no	—
123	C₄⋊C₄	—	146	4	no	—
124	C₂²⋊C₄	—	73	2	no	—
125	C₂²⋊C₄	—	146	4	no	—
126	C₄²	—	73	1	no	—
127	C₄²	—	146	4	no	—
128	C₄²	C₂²×D₇₃	1	1	yes	characteristic
129	C₂³	—	73	1	no	—
130	Q₈	—	2	4	no	—
131	Q₈	—	2	4	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	73	2	no	—
134	C₂×C₄	—	73	1	no	—
135	C₂×C₄	—	146	4	no	—
136	C₂×C₄	—	146	1	no	—
137	C₂×C₄	—	146	1	no	—
138	C₂×C₄	D₄×D₇₃	1	2	yes	—
139	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
140	C₈	—	146	1	no	—
141	C₈	—	146	1	no	—
142	C₈	#11924027	1	2	yes	—
143	C₈	#11924027	1	2	yes	—
144	C₂²	—	146	1	no	—
145	C₂²	—	146	2	no	—
146	C₂²	C₂×D₄×D₇₃	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	4	4	no	—
149	C₄	—	292	4	no	—
150	C₄	—	146	1	no	—
151	C₄	—	146	2	no	—
152	C₄	C₂×#11924027	1	1	yes	characteristic
153	C₄	C₂×#11924027	1	1	yes	characteristic
154	C₂	—	292	1	no	—
155	C₂	#17989135	1	1	yes	characteristic
156	C₂	#17989400	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989198

C₂

yes

maximal

#17988989

C₂

yes

maximal, characteristic, complemented

#17988955

C₂

yes

maximal, complemented

#17988842

C₂

yes

maximal

#17988825

C₂

yes

maximal

#17988694

C₂

yes

maximal, complemented

Q₁₆×Dic₇₃

C₂

yes

maximal, complemented

#17988541

C₂

yes

maximal, characteristic

#494×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924011

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556586

—

#14556583

C₂²

yes

—

#14556581

—

#14556567

C₂²

yes

—

Q₈×Dic₇₃

C₂²

yes

—

#14556548

C₂²

yes

characteristic

#14556525

C₂²

yes

—

#14556523

C₂²

yes

—

#14556515

C₂²

yes

—

#14556515

C₂²

yes

—

#14556502

C₂²

yes

characteristic

#14556501

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

C₂²

yes

—

C₂×Q₁₆×C₇₃

C₂²

yes

—

C₄⋊Q₈×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄×D₇₃

C₂³

yes

characteristic

#11924011

—

C₂×#10596831

C₂³

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂³

yes

—

#11924007

—

#11924007

—

#11924007

D₄

yes

—

#11924005

—

#11924005

D₄

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×Q₈×C₇₃

C₂³

yes

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

#41

yes

—

C₈×C₇₃

#41

yes

—

#10596831

—

#10596831

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×#41

yes

characteristic

C₄×C₇₃

C₂×#41

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#532

yes

characteristic

C₂×C₇₃

#578

yes

—

D₇₃

—

#3177

—

maximal, Sylow

C₇₃

#3177

yes

characteristic, complemented, Sylow

#541

—

#499

—

#494

D₇₃

yes

characteristic, complemented

—

—

—

—

C₄×Q₁₆

—

#405

—

C₂×Q₁₆

C₂×D₇₃

yes

—

C₂×Q₁₆

C₂×D₇₃

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

C₂×D₇₃

yes

—

#126

—

146

—

#125

—

#125

—

146

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

100

#107

—

101

#106

—

102

#103

—

103

#103

—

104

#97

—

105

#97

—

106

C₄×C₈

—

107

C₄×C₈

C₂×D₇₃

yes

characteristic

108

C₂×Q₈

C₂²×D₇₃

yes

—

109

C₂²×C₄

—

110

Q₁₆

—

111

Q₁₆

—

112

M₁₆

—

146

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

146

—

116

C₂×C₈

C₂²×D₇₃

yes

characteristic

117

C₂×C₈

C₂²×D₇₃

yes

characteristic

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

146

—

122

C₄⋊C₄

—

146

—

123

C₄⋊C₄

—

146

—

124

C₂²⋊C₄

—

125

C₂²⋊C₄

—

146

—

126

C₄²

—

127

C₄²

—

146

—

128

C₄²

C₂²×D₇₃

yes

characteristic

129

C₂³

—

130

Q₈

—

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

146

—

136

C₂×C₄

—

146

—

137

C₂×C₄

—

146

—

138

C₂×C₄

D₄×D₇₃

yes

—

139

C₂×C₄

C₂³×D₇₃

yes

characteristic

140

C₈

—

146

—

141

C₈

—

146

—

142

C₈

#11924027

yes

—

143

C₈

#11924027

yes

—

144

C₂²

—

146

—

145

C₂²

—

146

—

146

C₂²

C₂×D₄×D₇₃

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

292

—

150

C₄

—

146

—

151

C₄

—

146

—

152

C₄

C₂×#11924027

yes

characteristic

153

C₄

C₂×#11924027

yes

characteristic

154

C₂

—

292

—

155

C₂

#17989135

yes

characteristic

156

C₂

#17989400

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	#494×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×D₄
hypercenter	#494	D₇₃
hypocenter	C₇₃	#3177
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

#494×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
2. #17988989	C₂	semidirect
3. #17988955	C₂	semidirect
6. #17988694	C₂	semidirect
7. Q₁₆×Dic₇₃	C₂	semidirect
9. #494×C₇₃	C₂	semidirect
79. C₇₃	#3177	semidirect
82. #494	D₇₃	semidirect

H ≅ G/N

type

2. #17988989

C₂

semidirect

3. #17988955

C₂

semidirect

6. #17988694

C₂

semidirect

7. Q₁₆×Dic₇₃

C₂

semidirect

9. #494×C₇₃

C₂

semidirect

79. C₇₃

#3177

semidirect

82. #494

D₇₃

semidirect

Subgroups — #22620587

Conjugacy classes of subgroups

Complements