Group #32938635 — subgroups

Subgroups — C₇₃×#29231 #32938635

Order 18688.

404 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 218 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	C₇₃×#2102	C₂	1	4	yes	maximal
2	C₇₃×#1953	C₂	1	4	yes	maximal
3	C₇₃×#1849	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1833	C₂	1	4	yes	maximal
5	C₇₃×#1773	C₂	1	2	yes	maximal
6	#430×C₇₃	C₂²	1	4	yes	—
7	C₂×#108×C₇₃	C₂²	1	2	yes	—
8	C₂×#108×C₇₃	C₂²	1	4	yes	—
9	#427×C₇₃	C₂²	1	2	yes	—
10	#423×C₇₃	C₂²	1	2	yes	—
11	#405×C₇₃	C₂²	1	4	yes	—
12	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
13	#344×C₇₃	C₂²	1	8	yes	—
14	#339×C₇₃	C₂²	1	4	yes	—
15	H(3,ℤ/4)×C₇₃	C₂²	1	4	yes	—
16	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
17	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
18	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
19	#117×C₇₃	C₂³	1	4	yes	—
20	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
21	#108×C₇₃	—	2	4	no	—
22	#108×C₇₃	—	2	4	no	—
23	#108×C₇₃	—	2	4	no	—
24	#108×C₇₃	—	4	4	no	—
25	#107×C₇₃	—	2	2	no	—
26	#106×C₇₃	—	2	2	no	—
27	C₄⋊C₈×C₇₃	—	4	2	no	—
28	#97×C₇₃	—	2	4	no	—
29	#97×C₇₃	Q₈	1	4	yes	—
30	C₄×C₈×C₇₃	—	2	4	no	—
31	C₂²×C₄×C₇₃	—	2	1	no	—
32	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
33	M₁₆×C₇₃	—	2	4	no	—
34	M₁₆×C₇₃	—	2	8	no	—
35	M₁₆×C₇₃	—	2	4	no	—
36	C₂×C₈×C₇₃	—	2	4	no	—
37	C₂×C₈×C₇₃	—	2	4	no	—
38	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	—
39	C₂×C₈×C₇₃	#41	1	4	yes	—
40	C₂×C₈×C₇₃	#41	1	2	yes	—
41	C₂×C₈×C₇₃	#41	1	2	yes	—
42	C₄⋊C₄×C₇₃	—	2	4	no	—
43	C₂²⋊C₄×C₇₃	—	2	4	no	—
44	C₄²×C₇₃	—	2	1	no	—
45	C₄²×C₇₃	—	2	4	no	—
46	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
47	C₂³×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
48	C₂×C₄×C₇₃	—	2	2	no	—
49	C₂×C₄×C₇₃	—	4	4	no	—
50	C₂×C₄×C₇₃	—	8	1	no	—
51	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
53	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
54	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
55	C₈×C₇₃	—	4	4	no	—
56	C₈×C₇₃	—	4	4	no	—
57	C₈×C₇₃	#125	1	4	yes	—
58	C₈×C₇₃	#125	1	4	yes	—
59	C₂²×C₇₃	—	4	1	no	—
60	C₂²×C₇₃	#544	1	1	yes	characteristic
61	C₂²×C₇₃	#556	1	2	yes	—
62	C₄×C₇₃	—	4	2	no	—
63	C₄×C₇₃	—	8	4	no	—
64	C₄×C₇₃	C₂×#125	1	2	yes	—
65	C₄×C₇₃	#555	1	1	yes	characteristic
66	C₄×C₇₃	#559	1	1	yes	characteristic
67	#29231	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	—	2	2	no	—
70	C₂×C₇₃	#2571	1	1	yes	characteristic
71	#2102	C₂×C₇₃	1	4	yes	—
72	#1953	C₂×C₇₃	1	4	yes	—
73	#1849	C₂×C₇₃	1	1	yes	characteristic
74	#1833	C₂×C₇₃	1	4	yes	—
75	#1773	C₂×C₇₃	1	2	yes	—
76	C₇₃	#29231	1	1	yes	characteristic, direct product factor, Sylow
77	#430	C₂²×C₇₃	1	4	yes	—
78	C₂×#108	C₂²×C₇₃	1	4	yes	—
79	C₂×#108	C₂²×C₇₃	1	2	yes	—
80	#427	C₂²×C₇₃	1	2	yes	—
81	#423	C₂²×C₇₃	1	2	yes	—
82	#405	C₂²×C₇₃	1	4	yes	—
83	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
84	#344	C₂²×C₇₃	1	8	yes	—
85	#339	C₂²×C₇₃	1	4	yes	—
86	H(3,ℤ/4)	C₂²×C₇₃	1	4	yes	—
87	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
88	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
89	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
90	#117	C₂³×C₇₃	1	4	yes	—
91	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
92	#108	—	2	4	no	—
93	#108	—	2	4	no	—
94	#108	—	2	4	no	—
95	#108	—	4	4	no	—
96	#107	—	2	2	no	—
97	#106	—	2	2	no	—
98	C₄⋊C₈	—	4	2	no	—
99	#97	—	2	4	no	—
100	#97	Q₈×C₇₃	1	4	yes	—
101	C₄×C₈	—	2	4	no	—
102	C₂²×C₄	—	2	1	no	—
103	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
104	M₁₆	—	2	4	no	—
105	M₁₆	—	2	8	no	—
106	M₁₆	—	2	4	no	—
107	C₂×C₈	—	2	4	no	—
108	C₂×C₈	—	2	4	no	—
109	C₂×C₈	C₂×Q₈×C₇₃	1	4	yes	—
110	C₂×C₈	#41×C₇₃	1	4	yes	—
111	C₂×C₈	#41×C₇₃	1	2	yes	—
112	C₂×C₈	#41×C₇₃	1	2	yes	—
113	C₄⋊C₄	—	2	4	no	—
114	C₂²⋊C₄	—	2	4	no	—
115	C₄²	—	2	1	no	—
116	C₄²	—	2	4	no	—
117	C₄²	C₂×Q₈×C₇₃	1	2	yes	—
118	C₂³	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	4	4	no	—
121	C₂×C₄	—	8	1	no	—
122	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
123	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
124	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
125	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
126	C₈	—	4	4	no	—
127	C₈	—	4	4	no	—
128	C₈	#125×C₇₃	1	4	yes	—
129	C₈	#125×C₇₃	1	4	yes	—
130	C₂²	—	4	1	no	—
131	C₂²	#544×C₇₃	1	1	yes	characteristic
132	C₂²	#556×C₇₃	1	2	yes	—
133	C₄	—	4	2	no	—
134	C₄	—	8	4	no	—
135	C₄	C₂×#125×C₇₃	1	2	yes	—
136	C₄	#555×C₇₃	1	1	yes	characteristic
137	C₄	#559×C₇₃	1	1	yes	characteristic
138	C₂	—	2	1	no	—
139	C₂	—	2	2	no	—
140	C₂	C₇₃×#2571	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#2102

C₂

yes

maximal

C₇₃×#1953

C₂

yes

maximal

C₇₃×#1849

C₂

yes

maximal, characteristic

C₇₃×#1833

C₂

yes

maximal

C₇₃×#1773

C₂

yes

maximal

#430×C₇₃

C₂²

yes

—

C₂×#108×C₇₃

C₂²

yes

—

C₂×#108×C₇₃

C₂²

yes

—

#427×C₇₃

C₂²

yes

—

#423×C₇₃

C₂²

yes

—

#405×C₇₃

C₂²

yes

—

C₂×#97×C₇₃

C₂²

yes

characteristic

#344×C₇₃

C₂²

yes

—

#339×C₇₃

C₂²

yes

—

H(3,ℤ/4)×C₇₃

C₂²

yes

—

C₂×M₁₆×C₇₃

C₂³

yes

—

C₂×M₁₆×C₇₃

C₂³

yes

—

C₂²×C₈×C₇₃

C₂³

yes

—

#117×C₇₃

C₂³

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#108×C₇₃

—

#108×C₇₃

—

#108×C₇₃

—

#108×C₇₃

—

#107×C₇₃

—

#106×C₇₃

—

C₄⋊C₈×C₇₃

—

#97×C₇₃

—

#97×C₇₃

Q₈

yes

—

C₄×C₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂⁴

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×Q₈

yes

—

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

#41

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×Q₈

yes

—

C₂³×C₇₃

2₋¹⁺⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×Q₈

yes

characteristic

C₂×C₄×C₇₃

C₂×#41

yes

—

C₂×C₄×C₇₃

C₂×#41

yes

—

C₂×C₄×C₇₃

H(5,𝔽₂)

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

#125

yes

—

C₈×C₇₃

#125

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

#544

yes

characteristic

C₂²×C₇₃

#556

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×#125

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#2571

yes

characteristic

#2102

C₂×C₇₃

yes

—

#1953

C₂×C₇₃

yes

—

#1849

C₂×C₇₃

yes

characteristic

#1833

C₂×C₇₃

yes

—

#1773

C₂×C₇₃

yes

—

C₇₃

#29231

yes

characteristic, direct product factor, Sylow

#430

C₂²×C₇₃

yes

—

C₂×#108

C₂²×C₇₃

yes

—

C₂×#108

C₂²×C₇₃

yes

—

#427

C₂²×C₇₃

yes

—

#423

C₂²×C₇₃

yes

—

#405

C₂²×C₇₃

yes

—

C₂×#97

C₂²×C₇₃

yes

characteristic

#344

C₂²×C₇₃

yes

—

#339

C₂²×C₇₃

yes

—

H(3,ℤ/4)

C₂²×C₇₃

yes

—

C₂×M₁₆

C₂³×C₇₃

yes

—

C₂×M₁₆

C₂³×C₇₃

yes

—

C₂²×C₈

C₂³×C₇₃

yes

—

#117

C₂³×C₇₃

yes

—

C₂×C₄²

C₂³×C₇₃

yes

—

—

—

—

—

—

C₄⋊C₈

—

#97

—

100

#97

Q₈×C₇₃

yes

—

101

C₄×C₈

—

102

C₂²×C₄

—

103

C₂²×C₄

C₂⁴×C₇₃

yes

characteristic

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂×Q₈×C₇₃

yes

—

110

C₂×C₈

#41×C₇₃

yes

—

111

C₂×C₈

#41×C₇₃

yes

—

112

C₂×C₈

#41×C₇₃

yes

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

—

116

C₄²

—

117

C₄²

C₂×Q₈×C₇₃

yes

—

118

C₂³

2₋¹⁺⁴×C₇₃

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₂²×Q₈×C₇₃

yes

characteristic

123

C₂×C₄

C₂×#41×C₇₃

yes

—

124

C₂×C₄

C₂×#41×C₇₃

yes

—

125

C₂×C₄

H(5,𝔽₂)×C₇₃

yes

characteristic

126

C₈

—

127

C₈

—

128

C₈

#125×C₇₃

yes

—

129

C₈

#125×C₇₃

yes

—

130

C₂²

—

131

C₂²

#544×C₇₃

yes

characteristic

132

C₂²

#556×C₇₃

yes

—

133

C₄

—

134

C₄

—

135

C₄

C₂×#125×C₇₃

yes

—

136

C₄

#555×C₇₃

yes

characteristic

137

C₄

#559×C₇₃

yes

characteristic

138

C₂

—

139

C₂

—

140

C₂

C₇₃×#2571

yes

characteristic

	subgroup	G/H
center	C₄×C₇₃	#555
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂×C₇₃	#2571
prime radical	C₂³×C₇₃	2₋¹⁺⁴
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ G

subgroup

G/H

center

C₄×C₇₃

#555

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₇₃

socle

C₂×C₇₃

#2571

prime radical

C₂³×C₇₃

2₋¹⁺⁴

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ G

N	H ≅ G/N	type
67. #29231	C₇₃	direct (N × H)
76. C₇₃	#29231	direct (N × H)

H ≅ G/N

type

67. #29231

C₇₃

direct (N × H)

76. C₇₃

#29231

direct (N × H)

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

subgroup	index
C₇₃×#2102	2
C₇₃×#1953	2
C₇₃×#1849	2
C₇₃×#1833	2
C₇₃×#1773	2
#29231	73

subgroup

index

C₇₃×#2102

C₇₃×#1953

C₇₃×#1849

C₇₃×#1833

C₇₃×#1773

#29231

Subgroups — C₇₃×#29231 #32938635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#29231 #32938635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#29231 #32938635