Group #22612049 — subgroups

Subgroups — #22612049

Order 9344.

148 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 47 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×#14556532	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989004	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988857	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988416	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988400	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988399	C₂	1	1	yes	maximal, characteristic, complemented
7	#472×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#14556616	—	2	1	no	—
9	C₂×D₅₈₄	C₂²	1	1	yes	characteristic
10	#14556532	—	2	1	no	—
11	#14556532	—	2	1	no	—
12	#14556531	—	2	1	no	—
13	#14556531	C₂²	1	1	yes	characteristic
14	C₂×#11924003	—	2	1	no	—
15	C₂×#11924003	C₂²	1	1	yes	characteristic
16	#14556527	C₂²	1	1	yes	characteristic
17	#14556507	—	2	1	no	—
18	AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
19	C₂×D₈×C₇₃	C₂²	1	1	yes	characteristic
20	#131×C₇₃	C₂²	1	1	yes	characteristic
21	#108×C₇₃	C₂²	1	1	yes	characteristic
22	#100×C₇₃	—	2	1	no	—
23	C₂×D₂₉₂	—	2	1	no	—
24	#11924015	—	4	1	no	—
25	D₅₈₄	—	2	1	no	—
26	D₅₈₄	—	2	1	no	—
27	#11924013	—	4	1	no	—
28	#11924012	—	2	1	no	—
29	#11924003	—	2	1	no	—
30	#11924003	D₄	1	1	yes	characteristic
31	#11924003	D₄	1	1	yes	characteristic
32	#41×C₇₃	D₄	1	1	yes	characteristic
33	C₂×D₄×C₇₃	—	2	1	no	—
34	SD₁₆×C₇₃	—	4	1	no	—
35	D₈×C₇₃	—	2	1	no	—
36	D₈×C₇₃	—	2	1	no	—
37	D₈×C₇₃	—	4	1	no	—
38	M₁₆×C₇₃	—	2	1	no	—
39	M₁₆×C₇₃	—	2	1	no	—
40	M₁₆×C₇₃	D₄	1	1	yes	characteristic
41	C₂×C₈×C₇₃	—	2	1	no	—
42	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	C₂³×C₇₃	—	4	1	no	—
44	C₂²×D₇₃	—	4	1	no	—
45	Q₈×C₇₃	D₈	1	1	yes	characteristic
46	D₄×C₇₃	—	2	1	no	—
47	D₄×C₇₃	—	4	1	no	—
48	D₄×C₇₃	—	4	1	no	—
49	D₄×C₇₃	D₈	1	1	yes	characteristic
50	C₂×C₄×C₇₃	—	2	1	no	—
51	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
52	D₂₉₂	—	4	1	no	—
53	D₂₉₂	—	4	1	no	—
54	C₈×C₇₃	—	2	1	no	—
55	C₈×C₇₃	—	4	1	no	—
56	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
57	C₈×C₇₃	#41	1	1	yes	characteristic
58	#10596831	—	4	1	no	—
59	C₂²×C₇₃	—	2	1	no	—
60	C₂²×C₇₃	—	8	1	no	—
61	C₂²×C₇₃	—	16	1	no	—
62	C₂²×C₇₃	#135	1	1	yes	characteristic
63	C₂×D₇₃	—	8	1	no	—
64	C₂×D₇₃	—	16	1	no	—
65	C₄×C₇₃	—	2	1	no	—
66	C₄×C₇₃	#121	1	1	yes	characteristic
67	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	—	4	1	no	—
70	C₂×C₇₃	—	16	1	no	—
71	C₂×C₇₃	#466	1	1	yes	characteristic
72	D₇₃	—	16	1	no	—
73	#2221	—	73	1	no	maximal, Sylow
74	C₇₃	#2221	1	1	yes	characteristic, complemented, Sylow
75	C₂×D₁₆	—	73	1	no	—
76	#504	—	73	1	no	—
77	#472	—	73	1	no	—
78	#472	D₇₃	1	1	yes	characteristic, complemented
79	#368	—	73	1	no	—
80	#361	—	73	1	no	—
81	#361	—	73	1	no	—
82	AGL(1,ℤ/8)	—	2	1	no	—
83	AGL(1,ℤ/8)	—	146	1	no	—
84	C₂×D₈	—	73	1	no	—
85	C₂×D₈	C₂×D₇₃	1	1	yes	characteristic
86	#131	C₂×D₇₃	1	1	yes	characteristic
87	D₁₆	—	146	1	no	—
88	D₁₆	—	146	1	no	—
89	M₃₂	—	73	1	no	—
90	M₃₂	—	146	1	no	—
91	C₂×C₁₆	—	73	1	no	—
92	C₂×C₁₆	—	146	1	no	—
93	#108	—	73	1	no	—
94	#108	C₂×D₇₃	1	1	yes	characteristic
95	#100	—	2	1	no	—
96	#100	—	146	1	no	—
97	#41	C₂²⋊D₇₃	1	1	yes	characteristic
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	146	1	no	—
100	SD₁₆	—	4	1	no	—
101	SD₁₆	—	292	1	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	4	1	no	—
105	D₈	—	292	1	no	—
106	D₈	—	146	1	no	—
107	D₈	—	146	1	no	—
108	M₁₆	—	2	1	no	—
109	M₁₆	—	2	1	no	—
110	M₁₆	—	146	1	no	—
111	M₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
114	C₁₆	—	73	1	no	—
115	C₁₆	—	73	1	no	—
116	C₁₆	—	146	1	no	—
117	C₂³	—	4	1	no	—
118	C₂³	—	292	1	no	—
119	Q₈	#11924013	1	1	yes	characteristic
120	D₄	—	2	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	4	1	no	—
123	D₄	—	292	1	no	—
124	D₄	—	292	1	no	—
125	D₄	#11924013	1	1	yes	characteristic
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
128	C₈	—	2	1	no	—
129	C₈	—	4	1	no	—
130	C₈	—	292	1	no	—
131	C₈	D₄×D₇₃	1	1	yes	characteristic
132	C₈	#11924027	1	1	yes	characteristic
133	C₂²	—	2	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	16	1	no	—
136	C₂²	—	584	1	no	—
137	C₂²	—	1168	1	no	—
138	C₂²	#14556611	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	#14556563	1	1	yes	characteristic
141	C₄	C₂×#11924013	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	4	1	no	—
144	C₂	—	16	1	no	—
145	C₂	—	1168	1	no	—
146	C₂	#17988821	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556532

C₂

yes

maximal, characteristic, complemented

#17989004

C₂

yes

maximal, characteristic, complemented

#17988857

C₂

yes

maximal, characteristic, complemented

#17988416

C₂

yes

maximal, characteristic, complemented

#17988400

C₂

yes

maximal, characteristic, complemented

#17988399

C₂

yes

maximal, characteristic, complemented

#472×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556616

—

C₂×D₅₈₄

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×#11924003

—

C₂×#11924003

C₂²

yes

characteristic

#14556527

C₂²

yes

characteristic

#14556507

—

AGL(1,ℤ/8)×C₇₃

—

C₂×D₈×C₇₃

C₂²

yes

characteristic

#131×C₇₃

C₂²

yes

characteristic

#108×C₇₃

C₂²

yes

characteristic

#100×C₇₃

—

C₂×D₂₉₂

—

#11924015

—

D₅₈₄

—

D₅₈₄

—

—

—

—

D₄

yes

characteristic

#11924003

D₄

yes

characteristic

#41×C₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

—

SD₁₆×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂²×D₇₃

—

Q₈×C₇₃

D₈

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#135

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#121

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#466

yes

characteristic

D₇₃

—

#2221

—

maximal, Sylow

C₇₃

#2221

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

#504

—

#472

—

#472

D₇₃

yes

characteristic, complemented

—

—

—

—

—

146

—

C₂×D₈

—

C₂×D₈

C₂×D₇₃

yes

characteristic

#131

C₂×D₇₃

yes

characteristic

D₁₆

—

146

—

D₁₆

—

146

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#108

—

#108

C₂×D₇₃

yes

characteristic

#100

—

#100

—

146

—

#41

C₂²⋊D₇₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

146

—

100

SD₁₆

—

101

SD₁₆

—

292

—

102

D₈

—

103

D₈

—

104

D₈

—

105

D₈

—

292

—

106

D₈

—

146

—

107

D₈

—

146

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

146

—

111

M₁₆

C₂²⋊D₇₃

yes

characteristic

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₇₃

yes

characteristic

114

C₁₆

—

115

C₁₆

—

116

C₁₆

—

146

—

117

C₂³

—

118

C₂³

—

292

—

119

Q₈

#11924013

yes

characteristic

120

D₄

—

121

D₄

—

122

D₄

—

123

D₄

—

292

—

124

D₄

—

292

—

125

D₄

#11924013

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

292

—

131

C₈

D₄×D₇₃

yes

characteristic

132

C₈

#11924027

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

584

—

137

C₂²

—

1168

—

138

C₂²

#14556611

yes

characteristic

139

C₄

—

140

C₄

#14556563

yes

characteristic

141

C₄

C₂×#11924013

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

—

145

C₂

—

1168

—

146

C₂

#17988821

yes

characteristic

	subgroup	G/H
center	C₂	#17988821
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#472×C₇₃	C₂
socle	C₂×C₇₃	#466
hypercenter	#472	D₇₃
hypocenter	C₇₃	#2221
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

subgroup

G/H

center

C₂

#17988821

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#472×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

N	H ≅ G/N	type
1. C₂×#14556532	C₂	semidirect
2. #17989004	C₂	semidirect
3. #17988857	C₂	semidirect
4. #17988416	C₂	semidirect
5. #17988400	C₂	semidirect
6. #17988399	C₂	semidirect
7. #472×C₇₃	C₂	semidirect
74. C₇₃	#2221	semidirect
78. #472	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556532

C₂

semidirect

2. #17989004

C₂

semidirect

3. #17988857

C₂

semidirect

4. #17988416

C₂

semidirect

5. #17988400

C₂

semidirect

6. #17988399

C₂

semidirect

7. #472×C₇₃

C₂

semidirect

74. C₇₃

#2221

semidirect

78. #472

D₇₃

semidirect

Subgroups — #22612049

Conjugacy classes of subgroups

Complements