Group #32916883 — subgroups

Subgroups — C₇₃×#7479 #32916883

Order 18688.

162 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 98 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×M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#368×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#368×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
5	C₂×#108×C₇₃	—	2	1	no	—
6	C₂×#108×C₇₃	—	2	1	no	—
7	M₆₄×C₇₃	—	2	1	no	—
8	M₆₄×C₇₃	C₄	1	2	yes	—
9	C₂×C₃₂×C₇₃	—	2	1	no	—
10	#368×C₇₃	—	2	1	no	—
11	#368×C₇₃	—	2	1	no	—
12	#368×C₇₃	C₄	1	2	yes	—
13	#368×C₇₃	C₄	1	2	yes	—
14	C₂×M₁₆×C₇₃	—	4	1	no	—
15	C₂×M₁₆×C₇₃	—	4	1	no	—
16	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
17	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
22	C₂×C₁₆×C₇₃	Q₈	1	1	yes	characteristic
23	#108×C₇₃	—	2	2	no	—
24	#108×C₇₃	—	2	2	no	—
25	#108×C₇₃	—	4	1	no	—
26	#108×C₇₃	—	4	1	no	—
27	C₃₂×C₇₃	—	2	2	no	—
28	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
29	M₁₆×C₇₃	—	4	2	no	—
30	M₁₆×C₇₃	—	4	2	no	—
31	M₁₆×C₇₃	—	8	1	no	—
32	M₁₆×C₇₃	—	8	1	no	—
33	C₂×C₈×C₇₃	—	8	1	no	—
34	C₂×C₈×C₇₃	—	8	1	no	—
35	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
39	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
40	C₂×C₈×C₇₃	Q₁₆	1	1	yes	characteristic
41	C₁₆×C₇₃	C₄²	1	1	yes	characteristic
42	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
44	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂³×C₇₃	Q₃₂	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
47	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
48	C₂×C₄×C₇₃	#107	1	1	yes	characteristic
49	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
50	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
51	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
52	C₈×C₇₃	—	8	2	no	—
53	C₈×C₇₃	—	8	2	no	—
54	C₈×C₇₃	#95	1	1	yes	characteristic
55	C₈×C₇₃	#103	1	1	yes	characteristic
56	C₈×C₇₃	#103	1	1	yes	characteristic
57	C₈×C₇₃	#106	1	1	yes	characteristic
58	C₂²×C₇₃	—	4	1	no	—
59	C₂²×C₇₃	#358	1	1	yes	characteristic
60	C₂²×C₇₃	#358	1	1	yes	characteristic
61	C₂²×C₇₃	#366	1	1	yes	characteristic
62	C₄×C₇₃	#340	1	1	yes	characteristic
63	C₄×C₇₃	#357	1	1	yes	characteristic
64	C₄×C₇₃	#357	1	1	yes	characteristic
65	C₄×C₇₃	#367	1	1	yes	characteristic
66	#7479	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂×C₇₃	—	2	1	no	—
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	—	2	1	no	—
70	C₂×C₇₃	#1380	1	1	yes	characteristic
71	C₂×M₆₄	C₂×C₇₃	1	1	yes	characteristic
72	C₂×#368	C₂×C₇₃	1	1	yes	characteristic
73	C₂×#368	C₂×C₇₃	1	1	yes	characteristic
74	C₇₃	#7479	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²×C₁₆	C₂²×C₇₃	1	1	yes	characteristic
76	C₂×#108	—	2	1	no	—
77	C₂×#108	—	2	1	no	—
78	M₆₄	—	2	1	no	—
79	M₆₄	C₄×C₇₃	1	2	yes	—
80	C₂×C₃₂	—	2	1	no	—
81	#368	—	2	1	no	—
82	#368	—	2	1	no	—
83	#368	C₄×C₇₃	1	2	yes	—
84	#368	C₄×C₇₃	1	2	yes	—
85	C₂×M₁₆	—	4	1	no	—
86	C₂×M₁₆	—	4	1	no	—
87	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
88	C₂×C₁₆	C₂×C₄×C₇₃	1	1	yes	characteristic
89	C₂×C₁₆	C₂×C₄×C₇₃	1	1	yes	characteristic
90	C₂×C₁₆	C₂×C₄×C₇₃	1	1	yes	characteristic
91	C₂×C₁₆	D₄×C₇₃	1	1	yes	characteristic
92	C₂×C₁₆	D₄×C₇₃	1	1	yes	characteristic
93	C₂×C₁₆	Q₈×C₇₃	1	1	yes	characteristic
94	#108	—	2	2	no	—
95	#108	—	2	2	no	—
96	#108	—	4	1	no	—
97	#108	—	4	1	no	—
98	C₃₂	—	2	2	no	—
99	C₂²×C₄	D₈×C₇₃	1	1	yes	characteristic
100	M₁₆	—	4	2	no	—
101	M₁₆	—	4	2	no	—
102	M₁₆	—	8	1	no	—
103	M₁₆	—	8	1	no	—
104	C₂×C₈	—	8	1	no	—
105	C₂×C₈	—	8	1	no	—
106	C₂×C₈	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
107	C₂×C₈	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
108	C₂×C₈	C₄⋊C₄×C₇₃	1	1	yes	characteristic
109	C₂×C₈	SD₁₆×C₇₃	1	1	yes	characteristic
110	C₂×C₈	SD₁₆×C₇₃	1	1	yes	characteristic
111	C₂×C₈	Q₁₆×C₇₃	1	1	yes	characteristic
112	C₁₆	C₄²×C₇₃	1	1	yes	characteristic
113	C₁₆	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
114	C₁₆	C₄⋊C₄×C₇₃	1	1	yes	characteristic
115	C₁₆	C₄⋊C₄×C₇₃	1	1	yes	characteristic
116	C₂³	Q₃₂×C₇₃	1	1	yes	characteristic
117	C₂×C₄	#102×C₇₃	1	1	yes	characteristic
118	C₂×C₄	#102×C₇₃	1	1	yes	characteristic
119	C₂×C₄	#107×C₇₃	1	1	yes	characteristic
120	C₂×C₄	D₁₆×C₇₃	1	1	yes	characteristic
121	C₂×C₄	SD₃₂×C₇₃	1	1	yes	characteristic
122	C₂×C₄	SD₃₂×C₇₃	1	1	yes	characteristic
123	C₈	—	8	2	no	—
124	C₈	—	8	2	no	—
125	C₈	#95×C₇₃	1	1	yes	characteristic
126	C₈	#103×C₇₃	1	1	yes	characteristic
127	C₈	#103×C₇₃	1	1	yes	characteristic
128	C₈	#106×C₇₃	1	1	yes	characteristic
129	C₂²	—	4	1	no	—
130	C₂²	#358×C₇₃	1	1	yes	characteristic
131	C₂²	#358×C₇₃	1	1	yes	characteristic
132	C₂²	#366×C₇₃	1	1	yes	characteristic
133	C₄	#340×C₇₃	1	1	yes	characteristic
134	C₄	#357×C₇₃	1	1	yes	characteristic
135	C₄	#357×C₇₃	1	1	yes	characteristic
136	C₄	#367×C₇₃	1	1	yes	characteristic
137	C₂	—	2	1	no	—
138	C₂	—	2	1	no	—
139	C₂	—	2	1	no	—
140	C₂	C₇₃×#1380	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×M₆₄×C₇₃

C₂

yes

maximal, characteristic

C₂×#368×C₇₃

C₂

yes

maximal, characteristic

C₂×#368×C₇₃

C₂

yes

maximal, characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#108×C₇₃

—

C₂×#108×C₇₃

—

M₆₄×C₇₃

—

M₆₄×C₇₃

C₄

yes

—

C₂×C₃₂×C₇₃

—

#368×C₇₃

—

#368×C₇₃

—

#368×C₇₃

C₄

yes

—

#368×C₇₃

C₄

yes

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

Q₈

yes

characteristic

#108×C₇₃

—

#108×C₇₃

—

#108×C₇₃

—

#108×C₇₃

—

C₃₂×C₇₃

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

characteristic

C₂×C₈×C₇₃

Q₁₆

yes

characteristic

C₁₆×C₇₃

C₄²

yes

characteristic

C₁₆×C₇₃

C₂²⋊C₄

yes

characteristic

C₁₆×C₇₃

C₄⋊C₄

yes

characteristic

C₁₆×C₇₃

C₄⋊C₄

yes

characteristic

C₂³×C₇₃

Q₃₂

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

D₁₆

yes

characteristic

C₂×C₄×C₇₃

SD₃₂

yes

characteristic

C₂×C₄×C₇₃

SD₃₂

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#1380

yes

characteristic

C₂×M₆₄

C₂×C₇₃

yes

characteristic

C₂×#368

C₂×C₇₃

yes

characteristic

C₂×#368

C₂×C₇₃

yes

characteristic

C₇₃

#7479

yes

characteristic, direct product factor, Sylow

C₂²×C₁₆

C₂²×C₇₃

yes

characteristic

C₂×#108

—

C₂×#108

—

M₆₄

—

M₆₄

C₄×C₇₃

yes

—

C₂×C₃₂

—

#368

—

#368

—

#368

C₄×C₇₃

yes

—

#368

C₄×C₇₃

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

D₄×C₇₃

yes

characteristic

C₂×C₁₆

C₂×C₄×C₇₃

yes

characteristic

C₂×C₁₆

C₂×C₄×C₇₃

yes

characteristic

C₂×C₁₆

C₂×C₄×C₇₃

yes

characteristic

C₂×C₁₆

D₄×C₇₃

yes

characteristic

C₂×C₁₆

D₄×C₇₃

yes

characteristic

C₂×C₁₆

Q₈×C₇₃

yes

—

—

—

—

C₃₂

—

C₂²×C₄

D₈×C₇₃

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂²⋊C₄×C₇₃

yes

characteristic

107

C₂×C₈

C₂²⋊C₄×C₇₃

yes

characteristic

108

C₂×C₈

C₄⋊C₄×C₇₃

yes

characteristic

109

C₂×C₈

SD₁₆×C₇₃

yes

characteristic

110

C₂×C₈

SD₁₆×C₇₃

yes

characteristic

111

C₂×C₈

Q₁₆×C₇₃

yes

characteristic

112

C₁₆

C₄²×C₇₃

yes

characteristic

113

C₁₆

C₂²⋊C₄×C₇₃

yes

characteristic

114

C₁₆

C₄⋊C₄×C₇₃

yes

characteristic

115

C₁₆

C₄⋊C₄×C₇₃

yes

characteristic

116

C₂³

Q₃₂×C₇₃

yes

characteristic

117

C₂×C₄

#102×C₇₃

yes

characteristic

118

C₂×C₄

#102×C₇₃

yes

characteristic

119

C₂×C₄

#107×C₇₃

yes

characteristic

120

C₂×C₄

D₁₆×C₇₃

yes

characteristic

121

C₂×C₄

SD₃₂×C₇₃

yes

characteristic

122

C₂×C₄

SD₃₂×C₇₃

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

#95×C₇₃

yes

characteristic

126

C₈

#103×C₇₃

yes

characteristic

127

C₈

#103×C₇₃

yes

characteristic

128

C₈

#106×C₇₃

yes

characteristic

129

C₂²

—

130

C₂²

#358×C₇₃

yes

characteristic

131

C₂²

#358×C₇₃

yes

characteristic

132

C₂²

#366×C₇₃

yes

characteristic

133

C₄

#340×C₇₃

yes

characteristic

134

C₄

#357×C₇₃

yes

characteristic

135

C₄

#357×C₇₃

yes

characteristic

136

C₄

#367×C₇₃

yes

characteristic

137

C₂

—

138

C₂

—

139

C₂

—

140

C₂

C₇₃×#1380

yes

characteristic

	subgroup	G/H
center	C₄×C₇₃	#357
commutator	C₁₆	C₄²×C₇₃
Frattini, cosocle	C₂²×C₁₆	C₂²×C₇₃
socle	C₂×C₇₃	#1380
prime radical	C₂³×C₇₃	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂²×C₈×C₇₃ ◁ C₂²×C₁₆×C₇₃ ◁ G

subgroup

G/H

center

C₄×C₇₃

#357

commutator

C₁₆

C₄²×C₇₃

Frattini, cosocle

C₂²×C₁₆

C₂²×C₇₃

socle

C₂×C₇₃

#1380

prime radical

C₂³×C₇₃

Q₃₂

LCS

G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂²×C₈×C₇₃ ◁ C₂²×C₁₆×C₇₃ ◁ G

N	H ≅ G/N	type
66. #7479	C₇₃	direct (N × H)
74. C₇₃	#7479	direct (N × H)

H ≅ G/N

type

66. #7479

C₇₃

direct (N × H)

74. C₇₃

#7479

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×M₆₄×C₇₃	2
C₂×#368×C₇₃	2
#7479	73

subgroup

index

C₂×M₆₄×C₇₃

C₂×#368×C₇₃

#7479

Subgroups — C₇₃×#7479 #32916883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#7479 #32916883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#7479 #32916883