Subgroups — C 2 × D 7 × #11924781 #45692160

maximal, direct product factor

C₂

yes

C₂×C₇×D₇×C₁₉⋊C₃

C₃

yes

maximal, characteristic

C₇×#11924781

C₂²

yes

C₂×C₇²×C₁₉⋊C₃

C₂×C₃

yes

C₇×D₇×C₁₉⋊C₃

C₂×C₃

yes

—

—

maximal

—

maximal

C₂×C₇×D₇×C₁₉

C₉

yes

C₇²×C₁₉⋊C₃

C₂²×C₃

yes

—

D₇

yes

C₂×C₇×#4296

—

D₇×#4296

—

C₂×C₇²×C₁₉

C₂×C₉

yes

C₇×D₇×C₁₉

C₂×C₉

yes

complemented

C₂×D₇×C₇⋊C₉

—

maximal, Hall

C₂²×C₇×C₁₉⋊C₃

—

C₂×D₇×C₁₉⋊C₃

ΓL(1,𝔽₈)

yes

#11924781

C₂×D₇

yes

C₇×#4296

—

C₇²×C₁₉

C₂²×C₉

yes

C₂×C₇×C₇⋊C₉

—

D₇×C₇⋊C₉

—

C₂×C₇×C₁₉⋊C₃

—

C₂×C₇×C₁₉⋊C₃

—

C₂×C₇×C₁₉⋊C₃

C₂×ΓL(1,𝔽₈)

yes

C₂×C₇×C₁₉⋊C₃

C₃×D₇

yes

D₇×C₁₉⋊C₃

C₂×ΓL(1,𝔽₈)

yes

—

C₂²×#4296

—

C₂×C₃×C₇×D₇

—

C₂²×C₇×C₁₉

—

C₂×D₇×C₁₉

C₇⋊C₉

yes

C₇×C₇⋊C₉

—

C₇×C₁₉⋊C₃

—

C₇×C₁₉⋊C₃

C₂²×ΓL(1,𝔽₈)

yes

C₇×C₁₉⋊C₃

C₂×C₃×D₇

yes

—

—

C₂×C₃×C₇²

—

C₃×C₇×D₇

—

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

C₂×C₇⋊C₉

yes

C₂×C₇×C₁₉

C₉×D₇

yes

D₇×C₁₉

C₂×C₇⋊C₉

yes

complemented

C₂×C₉×D₇

—

133

—

C₂²×C₇⋊C₉

—

133

—

C₂²×C₁₉⋊C₃

—

C₂×C₇×D₇

#4296

yes

#4296

—

C₃×C₇²

—

C₇×C₁₉

—

C₇×C₁₉

C₂²×C₇⋊C₉

yes

C₇×C₁₉

C₂×C₉×D₇

yes

C₂×C₇×C₉

—

133

—

C₉×D₇

—

133

—

C₂×C₇⋊C₉

—

C₂×C₇⋊C₉

—

133

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

D₇×ΓL(1,𝔽₈)

yes

C₂×C₇²

yes

C₇×D₇

yes

complemented

C₂²×C₃×C₇

—

133

—

C₂×C₃×D₇

—

C₂²×C₁₉

—

C₇×C₉

—

133

—

C₇⋊C₉

—

C₁₉⋊C₃

C₂×D₇×ΓL(1,𝔽₈)

yes

C₇²

C₂²×#4296

yes

characteristic, complemented, Sylow

C₂×C₃×C₇

—

C₂×C₃×C₇

—

C₂×C₃×C₇

—

114

—

C₂×C₃×C₇

—

133

—

C₃×D₇

—

C₂×C₁₉

—

C₂×C₁₉

D₇×C₇⋊C₉

yes

C₂²×C₉

—

931

C₂²×C₇

—

C₂×D₇

#11924781

yes

C₃×C₇

—

C₃×C₇

—

C₃×C₇

—

114

—

C₁₉

C₂×D₇×C₇⋊C₉

yes

characteristic, complemented, Sylow

C₂×C₉

—

133

—

C₂×C₉

—

931

—

C₂×C₇

—

C₂×C₇

—

C₂×C₇

D₇×#4296

yes

C₂×C₇

yes

D₇

yes

direct product factor

C₂²×C₃

—

133

—

C₉

—

133

Sylow

C₇

—

C₇

yes

C₇

yes

C₂×C₃

—

C₂×C₃

—

133

—

C₂²

—

Sylow

100

C₃

—

101

C₂

—

102

C₂

yes

	subgroup	G/H
center, hypercenter	C₂	D₇×#11924781
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₉	C₂×C₉
prime radical	C₂×C₇×D₇×C₁₉⋊C₃	C₃
cosocle	C₇²×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂

subgroup

G/H

center, hypercenter

C₂

commutator, hypocenter

C₇²×C₁₉

C₂²×C₉

Frattini

C₁

Fitting, socle

C₂×C₇²×C₁₉

C₂×C₉

prime radical

C₂×C₇×D₇×C₁₉⋊C₃

C₃

cosocle

C₇²×C₁₉⋊C₃

C₂²×C₃

LCS

G ▷ C₇²×C₁₉

UCS

C₁ ◁ C₂

N	H ≅ G/N	type
1. C₂×C₇×#11924781	C₂	semidirect
2. D₇×#11924781	C₂	direct (N × H)
4. C₇×#11924781	C₂²	semidirect
9. C₂×C₇×D₇×C₁₉	C₉	semidirect
12. C₂×#11924781	D₇	direct (N × H)
15. C₂×C₇²×C₁₉	C₂×C₉	semidirect
16. C₇×D₇×C₁₉	C₂×C₉	semidirect
20. #11924781	C₂×D₇	direct (N × H)
22. C₇²×C₁₉	C₂²×C₉	semidirect
33. C₂×D₇×C₁₉	C₇⋊C₉	semidirect
44. C₂×C₇×C₁₉	C₂×C₇⋊C₉	semidirect
45. C₂×C₇×C₁₉	C₉×D₇	semidirect
46. D₇×C₁₉	C₂×C₇⋊C₉	semidirect
50. C₂×C₇×D₇	#4296	semidirect
54. C₇×C₁₉	C₂²×C₇⋊C₉	semidirect
55. C₇×C₁₉	C₂×C₉×D₇	semidirect
62. C₂×C₇²	C₂×#4296	semidirect
63. C₇×D₇	C₂×#4296	semidirect
70. C₇²	C₂²×#4296	semidirect
77. C₂×C₁₉	D₇×C₇⋊C₉	semidirect
80. C₂×D₇	#11924781	direct (N × H)
84. C₁₉	C₂×D₇×C₇⋊C₉	semidirect
89. C₂×C₇	D₇×#4296	semidirect
90. C₂×C₇	C₂×#11924781	semidirect
91. D₇	C₂×#11924781	direct (N × H)
95. C₇	C₂×D₇×#4296	semidirect
96. C₇	C₂²×#11924781	semidirect
102. C₂	D₇×#11924781	direct (N × H)

H ≅ G/N

type

1. C₂×C₇×#11924781

C₂

semidirect

2. D₇×#11924781

C₂

direct (N × H)

4. C₇×#11924781

C₂²

semidirect

9. C₂×C₇×D₇×C₁₉

C₉

semidirect

12. C₂×#11924781

D₇

direct (N × H)

15. C₂×C₇²×C₁₉

C₂×C₉

semidirect

16. C₇×D₇×C₁₉

C₂×C₉

semidirect

20. #11924781

C₂×D₇

direct (N × H)

22. C₇²×C₁₉

C₂²×C₉

semidirect

33. C₂×D₇×C₁₉

C₇⋊C₉

semidirect

44. C₂×C₇×C₁₉

C₂×C₇⋊C₉

semidirect

45. C₂×C₇×C₁₉

C₉×D₇

semidirect

46. D₇×C₁₉

C₂×C₇⋊C₉

semidirect

50. C₂×C₇×D₇

#4296

semidirect

54. C₇×C₁₉

C₂²×C₇⋊C₉

semidirect

55. C₇×C₁₉

C₂×C₉×D₇

semidirect

62. C₂×C₇²

semidirect

63. C₇×D₇

semidirect

70. C₇²

C₂²×#4296

semidirect

77. C₂×C₁₉

D₇×C₇⋊C₉

semidirect

80. C₂×D₇

#11924781

direct (N × H)

84. C₁₉

C₂×D₇×C₇⋊C₉

semidirect

89. C₂×C₇

D₇×#4296

semidirect

90. C₂×C₇

semidirect

91. D₇

direct (N × H)

95. C₇

semidirect

96. C₇

semidirect

102. C₂

direct (N × H)

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

subgroup	index
C₂×C₇×#11924781	2
D₇×#11924781	2
C₂×C₇×D₇×C₁₉⋊C₃	3
C₂²×#11924781	7
C₂×D₇×#4296	7
C₂×D₇×C₇⋊C₉	19

subgroup

index

C₂×C₇×#11924781

C₂×C₇×D₇×C₁₉⋊C₃