Group #22608662 — subgroups

Subgroups — #22608662

Order 9344.

202 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 73 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	#17989144	C₂	1	1	yes	maximal, characteristic
2	#17988611	C₂	1	1	yes	maximal, characteristic
3	#17988335	C₂	1	2	yes	maximal, complemented
4	#17988332	C₂	1	2	yes	maximal, complemented
5	#432×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	—	2	1	no	—
7	#14556591	C₂²	1	1	yes	characteristic
8	#14556591	C₂²	1	1	yes	characteristic
9	#14556583	—	2	1	no	—
10	#14556570	—	2	1	no	—
11	#14556570	C₄	1	2	yes	—
12	C₄×Dic₁₄₆	—	2	1	no	—
13	C₄×Dic₁₄₆	C₄	1	2	yes	—
14	#14556550	—	2	1	no	—
15	C₄⋊#10596831	—	2	1	no	—
16	C₄⋊#10596831	C₂²	1	2	yes	—
17	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
19	C₂²⋊C₈×C₇₃	—	2	1	no	—
20	#97×C₇₃	—	2	1	no	—
21	C₂×Dic₁₄₆	—	2	1	no	—
22	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
23	#11924012	—	4	2	no	—
24	C₂×#10596831	—	2	2	no	—
25	C₄⋊Dic₇₃	—	2	1	no	—
26	C₄⋊Dic₇₃	—	2	1	no	—
27	C₄⋊Dic₇₃	—	2	1	no	—
28	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
29	#11924007	—	2	2	no	—
30	#11924007	—	2	2	no	—
31	C₂²⋊Dic₇₃	—	2	2	no	—
32	C₄×Dic₇₃	—	2	2	no	—
33	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
36	C₂×C₈×C₇₃	—	2	2	no	—
37	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₄²×C₇₃	D₄	1	1	yes	characteristic
39	C₄²×C₇₃	D₄	1	1	yes	characteristic
40	C₄²×C₇₃	C₂³	1	1	yes	characteristic
41	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₇₃	—	2	1	no	—
43	C₂×C₄×C₇₃	—	2	2	no	—
44	C₂×C₄×C₇₃	—	2	1	no	—
45	C₂×C₄×C₇₃	—	4	1	no	—
46	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₇₃	—	2	2	no	—
53	C₂×Dic₇₃	—	2	2	no	—
54	Dic₁₄₆	—	4	1	no	—
55	Dic₁₄₆	—	4	1	no	—
56	Dic₁₄₆	—	4	2	no	—
57	C₈×C₇₃	—	4	2	no	—
58	#10596831	—	4	2	no	—
59	C₂²×C₇₃	—	2	1	no	—
60	C₂²×C₇₃	—	2	1	no	—
61	C₂²×C₇₃	—	2	1	no	—
62	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₄×C₇₃	—	2	1	no	—
64	C₄×C₇₃	—	2	1	no	—
65	C₄×C₇₃	—	2	1	no	—
66	C₄×C₇₃	—	2	1	no	—
67	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
68	C₄×C₇₃	#137	1	2	yes	—
69	C₄×C₇₃	#137	1	1	yes	characteristic
70	Dic₇₃	—	4	2	no	—
71	Dic₇₃	—	4	2	no	—
72	C₂×C₇₃	—	4	1	no	—
73	C₂×C₇₃	#413	1	1	yes	characteristic
74	C₂×C₇₃	#417	1	1	yes	characteristic
75	C₂×C₇₃	#419	1	1	yes	characteristic
76	#1559	—	73	1	no	maximal, Sylow
77	C₇₃	#1559	1	1	yes	characteristic, complemented, Sylow
78	#533	—	73	1	no	—
79	#432	D₇₃	1	1	yes	characteristic
80	#423	—	73	1	no	—
81	#333	—	73	2	no	—
82	#332	—	73	2	no	—
83	C₂×M₁₆	—	146	1	no	—
84	C₄⋊Q₈	—	73	1	no	—
85	C₄⋊Q₈	—	73	1	no	—
86	#125	—	146	1	no	—
87	C₂²⋊Q₈	—	73	2	no	—
88	C₂²⋊Q₈	—	146	1	no	—
89	C₄×Q₈	—	73	2	no	—
90	C₄×Q₈	—	146	1	no	—
91	#117	—	146	1	no	—
92	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
93	C₄⋊C₈	—	73	2	no	—
94	C₄⋊C₈	—	146	1	no	—
95	C₄⋊C₈	C₂×D₇₃	1	2	yes	—
96	C₂²⋊C₈	—	2	1	no	—
97	#97	—	2	1	no	—
98	C₂×Q₈	—	73	2	no	—
99	C₂×Q₈	—	146	1	no	—
100	C₂²×C₄	C₄×D₇₃	1	1	yes	characteristic
101	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
102	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
103	M₁₆	—	292	2	no	—
104	C₂×C₈	—	2	2	no	—
105	C₂×C₈	—	146	2	no	—
106	C₄⋊C₄	—	73	2	no	—
107	C₄⋊C₄	—	146	2	no	—
108	C₄⋊C₄	—	146	2	no	—
109	C₄⋊C₄	—	146	1	no	—
110	C₄⋊C₄	—	146	1	no	—
111	C₄⋊C₄	—	146	1	no	—
112	C₂²⋊C₄	—	146	2	no	—
113	C₄²	—	146	2	no	—
114	C₄²	C₄×D₇₃	1	1	yes	characteristic
115	C₄²	D₂₉₂	1	1	yes	characteristic
116	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
117	C₄²	C₂²×D₇₃	1	1	yes	characteristic
118	C₂³	#11924005	1	1	yes	characteristic
119	Q₈	—	292	2	no	—
120	Q₈	—	292	1	no	—
121	Q₈	—	292	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	146	2	no	—
127	C₂×C₄	—	146	2	no	—
128	C₂×C₄	#11924005	1	1	yes	characteristic
129	C₂×C₄	#11924005	1	1	yes	characteristic
130	C₂×C₄	#11924005	1	1	yes	characteristic
131	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
132	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
133	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
134	C₈	—	4	2	no	—
135	C₈	—	292	2	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	C₂×#11924005	1	1	yes	characteristic
140	C₄	—	2	1	no	—
141	C₄	—	2	1	no	—
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	292	2	no	—
145	C₄	—	292	2	no	—
146	C₄	#14556619	1	1	yes	characteristic
147	C₄	#14556621	1	2	yes	—
148	C₄	#14556624	1	1	yes	characteristic
149	C₂	—	4	1	no	—
150	C₂	#17988569	1	1	yes	characteristic
151	C₂	#17988589	1	1	yes	characteristic
152	C₂	#17988595	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989144

C₂

yes

maximal, characteristic

#17988611

C₂

yes

maximal, characteristic

#17988335

C₂

yes

maximal, complemented

#17988332

C₂

yes

maximal, complemented

#432×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

—

#14556591

C₂²

yes

characteristic

#14556591

C₂²

yes

—

—

C₄

yes

—

C₄×Dic₁₄₆

—

C₄×Dic₁₄₆

C₄

yes

—

#14556550

—

C₄⋊#10596831

—

C₄⋊#10596831

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

—

C₂²⋊C₈×C₇₃

—

#97×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₄×C₇₃

#137

yes

—

C₄×C₇₃

#137

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#533

—

#432

D₇₃

yes

—

—

—

C₂×M₁₆

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

146

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

146

—

C₄×Q₈

—

C₄×Q₈

—

146

—

#117

—

146

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

—

C₂²⋊C₈

—

#97

—

C₂×Q₈

—

C₂×Q₈

—

146

—

100

C₂²×C₄

C₄×D₇₃

yes

characteristic

101

C₂²×C₄

D₂₉₂

yes

characteristic

102

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

103

M₁₆

—

292

—

104

C₂×C₈

—

105

C₂×C₈

—

146

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

146

—

108

C₄⋊C₄

—

146

—

109

C₄⋊C₄

—

146

—

110

C₄⋊C₄

—

146

—

111

C₄⋊C₄

—

146

—

112

C₂²⋊C₄

—

146

—

113

C₄²

—

146

—

114

C₄²

C₄×D₇₃

yes

characteristic

115

C₄²

D₂₉₂

yes

characteristic

116

C₄²

C₂²⋊D₇₃

yes

characteristic

117

C₄²

C₂²×D₇₃

yes

characteristic

118

C₂³

#11924005

yes

characteristic

119

Q₈

—

292

—

120

Q₈

—

292

—

121

Q₈

—

292

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

146

—

127

C₂×C₄

—

146

—

128

C₂×C₄

#11924005

yes

characteristic

129

C₂×C₄

#11924005

yes

characteristic

130

C₂×C₄

#11924005

yes

characteristic

131

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

132

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

133

C₂×C₄

C₂×D₂₉₂

yes

characteristic

134

C₈

—

135

C₈

—

292

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

C₂×#11924005

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

292

—

145

C₄

—

292

—

146

C₄

#14556619

yes

characteristic

147

C₄

#14556621

yes

—

148

C₄

#14556624

yes

characteristic

149

C₂

—

150

C₂

#17988569

yes

characteristic

151

C₂

#17988589

yes

characteristic

152

C₂

#17988595

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11924005
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#432×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#432	D₇₃
hypocenter	C₇₃	#1559
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂²

C₂×#11924005

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#432×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
3. #17988335	C₂	semidirect
4. #17988332	C₂	semidirect
77. C₇₃	#1559	semidirect

H ≅ G/N

type

3. #17988335

C₂

semidirect

4. #17988332

C₂

semidirect

77. C₇₃

#1559

semidirect

Subgroups — #22608662

Conjugacy classes of subgroups

Complements