Subgroups — C 73 × #8792 #32918196

#382×C₇₃

C₂²

yes

—

#341×C₇₃

—

#340×C₇₃

—

#322×C₇₃

C₄

yes

C₈²×C₇₃

C₄

yes

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

C₄×C₈×C₇₃

C₂×C₄

yes

C₄×C₈×C₇₃

Q₈

yes

—

#95×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

C₂²×C₄×C₇₃

#41

yes

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂²×C₄

yes

C₄²×C₇₃

C₂×Q₈

yes

C₄²×C₇₃

#41

yes

—

C₂³×C₇₃

#124

yes

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₇₃

#117

yes

—

C₂×C₄×C₇₃

#124

yes

C₂×C₄×C₇₃

#125

yes

—

C₂×C₄×C₇₃

#135

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#382

yes

C₂²×C₇₃

#488

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#427

yes

—

C₄×C₇₃

#488

yes

—

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₇₃

—

C₂×C₇₃

#1833

yes

—

C₂×C₇₃

#1835

yes

#1837

C₂×C₇₃

yes

#1835

C₂×C₇₃

yes

#1450

C₂×C₇₃

yes

#1286

C₂×C₇₃

yes

—

C₇₃

characteristic, direct product factor, Sylow

yes

#431

C₂²×C₇₃

yes

—

#423

C₂²×C₇₃

yes

—

C₂×C₄×C₈

C₂²×C₇₃

yes

#382

C₂²×C₇₃

yes

—

#341

—

#340

—

#322

C₄×C₇₃

yes

C₈²

C₄×C₇₃

yes

C₂×M₁₆

—

C₂²×C₈

D₄×C₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₇₃

yes

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₂×C₄×C₇₃

yes

—

C₄×C₈

C₂×C₄×C₇₃

yes

C₄×C₈

C₂×C₄×C₇₃

yes

C₄×C₈

Q₈×C₇₃

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₇₃

yes

C₂²×C₄

#41×C₇₃

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊C₄×C₇₃

yes

—

C₂×C₈

C₄⋊C₄×C₇₃

yes

—

C₄⋊C₄

—

C₄²

C₂²×C₄×C₇₃

yes

C₄²

C₂×Q₈×C₇₃

yes

100

C₄²

#41×C₇₃

yes

—

101

C₂³

#124×C₇₃

yes

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×C₄⋊C₄×C₇₃

yes

106

C₂×C₄

#117×C₇₃

yes

—

107

C₂×C₄

#124×C₇₃

yes

108

C₂×C₄

#125×C₇₃

yes

—

109

C₂×C₄

#135×C₇₃

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

#382×C₇₃

yes

116

C₂²

#488×C₇₃

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

#427×C₇₃

yes

—

121

C₄

#488×C₇₃

yes

—

122

C₂

—

123

C₂

C₇₃×#1833

yes

—

124

C₂

C₇₃×#1835

yes

	subgroup	G/H
center, socle	C₂²×C₇₃	#382
commutator	C₄²	C₂²×C₄×C₇₃
Frattini, cosocle	C₂×C₄²	C₂³×C₇₃
prime radical	C₂³×C₇₃	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₃

#382

commutator

C₄²

C₂²×C₄×C₇₃

Frattini, cosocle

C₂×C₄²

C₂³×C₇₃

C₂³×C₇₃

G ▷ C₄² ▷ C₂² ▷ C₁

C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

N	H ≅ G/N	type
11. #322×C₇₃	C₄	semidirect
12. C₈²×C₇₃	C₄	semidirect
59. #8792	C₇₃	direct (N × H)
67. C₇₃	#8792	direct (N × H)
74. #322	C₄×C₇₃	semidirect
75. C₈²	C₄×C₇₃	semidirect

H ≅ G/N

type

11. #322×C₇₃

C₄

semidirect

12. C₈²×C₇₃

C₄

semidirect

59. #8792

C₇₃

direct (N × H)

67. C₇₃

direct (N × H)

74. #322

C₄×C₇₃

semidirect

75. C₈²

C₄×C₇₃

semidirect

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

subgroup	index
C₇₃×#1837	2
C₇₃×#1835	2
C₇₃×#1450	2
C₇₃×#1286	2
#8792	73

subgroup

index

C₇₃×#1837

C₇₃×#1835

C₇₃×#1450

C₇₃×#1286