Group #45691625 — subgroups

Subgroups — C₂×#30660578 #45691625

Order 33516.

160 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 43 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×#22552712	C₂	1	1	yes	maximal, characteristic, complemented
2	#30660578	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₇⋊D₁₃₃	C₃	1	1	yes	maximal, characteristic
4	#22552712	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇⋊D₁₃₃	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₂×#14558787	—	7	1	no	maximal
8	C₂×#14558786	—	7	1	no	maximal
9	C₂×C₇⋊D₁₃₃	C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
11	C₂×#11924777	—	7	1	no	—
12	C₂×#11924776	—	7	1	no	—
13	#14558787	—	7	2	no	—
14	#14558786	—	7	2	no	—
15	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
16	C₇⋊D₁₃₃	C₂×C₉	1	2	yes	complemented
17	C₂×#11725078	—	19	1	no	maximal, Hall
18	C₂×C₃×D₁₃₃	—	7	1	no	—
19	C₂×C₃×D₁₃₃	—	7	1	no	—
20	C₂×C₃×D₁₃₃	—	21	2	no	—
21	#11924777	—	7	1	no	—
22	#11924776	—	7	1	no	—
23	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×#89205	—	19	1	no	—
25	#11725078	—	19	2	no	—
26	C₂×C₃×C₇×C₁₉	—	3	2	no	—
27	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
28	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
29	C₃×D₁₃₃	—	7	2	no	—
30	C₃×D₁₃₃	—	7	2	no	—
31	C₃×D₁₃₃	—	21	4	no	—
32	C₂×#4294⋊C₂	—	49	1	no	Hall
33	C₂×C₃×C₇⋊D₇	—	19	1	no	—
34	C₂×D₁₃₃	—	7	1	no	—
35	C₂×D₁₃₃	—	7	1	no	—
36	C₂×D₁₃₃	—	21	2	no	—
37	#89205	—	19	1	no	Hall
38	C₃×C₇×C₁₉	—	3	2	no	—
39	C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
40	C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
41	C₂×#4294	—	49	1	no	—
42	#4294⋊C₂	—	49	2	no	—
43	C₂×C₃×C₇²	D₁₉⋊C₃	1	1	yes	characteristic
44	C₃×C₇⋊D₇	—	19	2	no	—
45	C₂×C₇×C₁₉	—	3	2	no	—
46	C₂×C₇×C₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented
47	C₂×C₇×C₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented
48	D₁₃₃	—	7	2	no	—
49	D₁₃₃	—	7	2	no	—
50	D₁₃₃	—	21	4	no	—
51	C₂×D₇⋊C₉	—	133	1	no	—
52	C₂×D₇⋊C₉	—	133	1	no	—
53	C₂×C₃×D₁₉	—	49	1	no	—
54	C₂×C₇⋊D₇	—	19	1	no	Hall
55	#4294	—	49	1	no	Hall
56	C₃×C₇²	C₂×D₁₉⋊C₃	1	1	yes	characteristic
57	C₇×C₁₉	—	3	2	no	—
58	C₇×C₁₉	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented
59	C₇×C₁₉	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented
60	C₂×C₇⋊C₉	—	133	1	no	—
61	C₂×C₇⋊C₉	—	133	1	no	—
62	D₇⋊C₉	—	133	2	no	—
63	D₇⋊C₉	—	133	2	no	—
64	C₂×C₃×C₁₉	#64425	1	1	yes	characteristic
65	C₃×D₁₉	—	49	2	no	—
66	C₂×C₇²	#4294⋊C₂	1	1	yes	characteristic, complemented
67	C₇⋊D₇	—	19	2	no	—
68	C₂×C₃×D₇	—	133	1	no	—
69	C₂×C₃×D₇	—	133	1	no	—
70	C₂×C₃×D₇	—	399	2	no	—
71	C₂×D₁₉	—	49	1	no	Hall
72	C₇⋊C₉	—	133	1	no	—
73	C₇⋊C₉	—	133	1	no	—
74	C₃×C₁₉	C₂×#64425	1	1	yes	characteristic
75	C₇²	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃×C₇	—	3	2	no	—
77	C₂×C₃×C₇	#11716327	1	1	yes	characteristic
78	C₂×C₃×C₇	#11716328	1	1	yes	characteristic
79	C₃×D₇	—	133	2	no	—
80	C₃×D₇	—	133	2	no	—
81	C₃×D₇	—	399	4	no	—
82	C₂×C₁₉	#11725078	1	1	yes	characteristic, complemented
83	D₁₉	—	49	2	no	—
84	C₂²×C₉	—	931	1	no	Hall
85	C₂×D₇	—	133	1	no	—
86	C₂×D₇	—	133	1	no	—
87	C₂×D₇	—	399	2	no	—
88	C₃×C₇	—	3	2	no	—
89	C₃×C₇	C₂×#11716327	1	1	yes	characteristic
90	C₃×C₇	C₂×#11716328	1	1	yes	characteristic
91	C₁₉	C₂×#11725078	1	1	yes	characteristic, complemented, Sylow
92	C₂×C₉	—	931	2	no	—
93	C₂×C₉	—	931	1	no	—
94	C₂×C₇	—	3	2	no	—
95	C₂×C₇	#14558786	1	1	yes	characteristic, complemented
96	C₂×C₇	#14558787	1	1	yes	characteristic, complemented
97	D₇	—	133	2	no	—
98	D₇	—	133	2	no	—
99	D₇	—	399	4	no	—
100	C₂²×C₃	—	931	1	no	—
101	C₉	—	931	1	no	Sylow
102	C₇	—	3	2	no	—
103	C₇	C₂×#14558786	1	1	yes	characteristic, complemented
104	C₇	C₂×#14558787	1	1	yes	characteristic, complemented
105	C₂×C₃	—	931	2	no	—
106	C₂×C₃	#19150290	1	1	yes	characteristic
107	C₂²	—	931	1	no	Sylow
108	C₃	C₂×#19150290	1	1	yes	characteristic
109	C₂	—	931	2	no	—
110	C₂	#30660578	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22552712

C₂

yes

maximal, characteristic, complemented

#30660578

C₂

yes

maximal, direct product factor

C₂×C₃×C₇⋊D₁₃₃

C₃

yes

maximal, characteristic

#22552712

C₂²

yes

characteristic, complemented, Hall

C₃×C₇⋊D₁₃₃

C₂×C₃

yes

—

C₂×C₃×C₇²×C₁₉

C₂×C₃

yes

—

—

C₂×C₇⋊D₁₃₃

C₉

yes

characteristic, complemented, Hall

C₃×C₇²×C₁₉

C₂²×C₃

yes

—

—

—

—

C₂×C₇²×C₁₉

C₂×C₉

yes

characteristic, complemented

C₇⋊D₁₃₃

C₂×C₉

yes

complemented

C₂×#11725078

—

maximal, Hall

C₂×C₃×D₁₃₃

—

C₂×C₃×D₁₃₃

—

C₂×C₃×D₁₃₃

—

#11924777

—

#11924776

—

C₇²×C₁₉

C₂²×C₉

yes

characteristic, complemented, Hall

C₂×#89205

—

#11725078

—

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

yes

C₂×C₃×C₇×C₁₉

yes

C₃×D₁₃₃

—

C₃×D₁₃₃

—

C₃×D₁₃₃

—

C₂×#4294⋊C₂

—

Hall

C₂×C₃×C₇⋊D₇

—

C₂×D₁₃₃

—

C₂×D₁₃₃

—

C₂×D₁₃₃

—

#89205

—

Hall

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

yes

C₃×C₇×C₁₉

yes

—

—

C₂×C₃×C₇²

D₁₉⋊C₃

yes

characteristic

C₃×C₇⋊D₇

—

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

D₇⋊C₉

yes

characteristic, complemented

C₂×C₇×C₁₉

D₇⋊C₉

yes

characteristic, complemented

D₁₃₃

—

D₁₃₃

—

D₁₃₃

—

C₂×D₇⋊C₉

—

133

—

C₂×D₇⋊C₉

—

133

—

C₂×C₃×D₁₉

—

C₂×C₇⋊D₇

—

Hall

#4294

—

Hall

C₃×C₇²

C₂×D₁₉⋊C₃

yes

characteristic

C₇×C₁₉

—

C₇×C₁₉

C₂×D₇⋊C₉

yes

characteristic, complemented

C₇×C₁₉

C₂×D₇⋊C₉

yes

characteristic, complemented

C₂×C₇⋊C₉

—

133

—

C₂×C₇⋊C₉

—

133

—

D₇⋊C₉

—

133

—

D₇⋊C₉

—

133

—

C₂×C₃×C₁₉

#64425

yes

characteristic

C₃×D₁₉

—

C₂×C₇²

#4294⋊C₂

yes

characteristic, complemented

C₇⋊D₇

—

C₂×C₃×D₇

—

133

—

C₂×C₃×D₇

—

133

—

C₂×C₃×D₇

—

399

—

C₂×D₁₉

—

Hall

C₇⋊C₉

—

133

—

C₇⋊C₉

—

133

—

C₃×C₁₉

C₂×#64425

yes

characteristic

C₇²

C₂×#4294⋊C₂

yes

characteristic, complemented, Sylow

C₂×C₃×C₇

—

C₂×C₃×C₇

yes

C₂×C₃×C₇

yes

C₃×D₇

—

133

—

C₃×D₇

—

133

—

C₃×D₇

—

399

—

C₂×C₁₉

#11725078

yes

characteristic, complemented

D₁₉

—

C₂²×C₉

—

931

Hall

C₂×D₇

—

133

—

C₂×D₇

—

133

—

C₂×D₇

—

399

—

C₃×C₇

—

C₃×C₇

yes

C₃×C₇

yes

C₁₉

yes

characteristic, complemented, Sylow

C₂×C₉

—

931

—

C₂×C₉

—

931

—

C₂×C₇

—

C₂×C₇

#14558786

yes

characteristic, complemented

C₂×C₇

#14558787

yes

characteristic, complemented

D₇

—

133

—

D₇

—

133

—

D₇

—

399

—

100

C₂²×C₃

—

931

—

101

C₉

—

931

Sylow

102

C₇

—

103

C₇

C₂×#14558786

yes

characteristic, complemented

104

C₇

C₂×#14558787

yes

characteristic, complemented

105

C₂×C₃

—

931

—

106

C₂×C₃

#19150290

yes

characteristic

107

C₂²

—

931

Sylow

108

C₃

C₂×#19150290

yes

characteristic

109

C₂

—

931

—

110

C₂

#30660578

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#19150290
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×#19150290
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₇⋊D₁₃₃	C₃
cosocle	C₃×C₇²×C₁₉	C₂²×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

subgroup

G/H

center, hypercenter

C₂×C₃

#19150290

commutator, hypocenter

C₇²×C₁₉

C₂²×C₉

Frattini

C₃

C₂×#19150290

Fitting, socle

C₂×C₃×C₇²×C₁₉

C₂×C₃

prime radical

C₂×C₃×C₇⋊D₁₃₃

C₃

cosocle

C₃×C₇²×C₁₉

C₂²×C₃

LCS

G ▷ C₇²×C₁₉

UCS

C₁ ◁ C₂×C₃

N	H ≅ G/N	type
1. C₂×#22552712	C₂	semidirect
2. #30660578	C₂	direct (N × H)
4. #22552712	C₂²	semidirect
9. C₂×C₇⋊D₁₃₃	C₉	semidirect
15. C₂×C₇²×C₁₉	C₂×C₉	semidirect
16. C₇⋊D₁₃₃	C₂×C₉	semidirect
23. C₇²×C₁₉	C₂²×C₉	semidirect
46. C₂×C₇×C₁₉	D₇⋊C₉	semidirect
47. C₂×C₇×C₁₉	D₇⋊C₉	semidirect
58. C₇×C₁₉	C₂×D₇⋊C₉	semidirect
59. C₇×C₁₉	C₂×D₇⋊C₉	semidirect
66. C₂×C₇²	#4294⋊C₂	semidirect
75. C₇²	C₂×#4294⋊C₂	semidirect
82. C₂×C₁₉	#11725078	semidirect
91. C₁₉	C₂×#11725078	semidirect
95. C₂×C₇	#14558786	semidirect
96. C₂×C₇	#14558787	semidirect
103. C₇	C₂×#14558786	semidirect
104. C₇	C₂×#14558787	semidirect
110. C₂	#30660578	direct (N × H)

H ≅ G/N

type

1. C₂×#22552712

C₂

semidirect

2. #30660578

C₂

direct (N × H)

4. #22552712

C₂²

semidirect

9. C₂×C₇⋊D₁₃₃

C₉

semidirect

15. C₂×C₇²×C₁₉

C₂×C₉

semidirect

16. C₇⋊D₁₃₃

C₂×C₉

semidirect

23. C₇²×C₁₉

C₂²×C₉

semidirect

46. C₂×C₇×C₁₉

D₇⋊C₉

semidirect

47. C₂×C₇×C₁₉

D₇⋊C₉

semidirect

58. C₇×C₁₉

C₂×D₇⋊C₉

semidirect

59. C₇×C₁₉

C₂×D₇⋊C₉

semidirect

66. C₂×C₇²

#4294⋊C₂

semidirect

75. C₇²

C₂×#4294⋊C₂

semidirect

82. C₂×C₁₉

#11725078

semidirect

91. C₁₉

C₂×#11725078

semidirect

95. C₂×C₇

#14558786

semidirect

96. C₂×C₇

#14558787

semidirect

103. C₇

C₂×#14558786

semidirect

104. C₇

C₂×#14558787

semidirect

110. C₂

#30660578

direct (N × H)

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

subgroup	index
C₂×#22552712	2
#30660578	2
C₂×C₃×C₇⋊D₁₃₃	3
C₂×#14558787	7
C₂×#14558786	7
C₂×#11725078	19

subgroup

index

C₂×C₃×C₇⋊D₁₃₃

Subgroups — C₂×#30660578 #45691625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#30660578 #45691625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30660578 #45691625