Group #46857218 — subgroups

Subgroups — C₁₃₇×#7832 #46857218

Order 35072.

322 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 94 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	#2810×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2100×C₁₃₇	C₂	1	3	yes	maximal
3	#1271×C₁₃₇	C₂	1	3	yes	maximal
4	#400×C₁₃₇	—	2	3	no	—
5	#389×C₁₃₇	C₂²	1	3	yes	—
6	#387×C₁₃₇	—	2	3	no	—
7	#384×C₁₃₇	C₂²	1	1	yes	characteristic
8	#340×C₁₃₇	—	2	3	no	—
9	#340×C₁₃₇	—	2	3	no	—
10	#336×C₁₃₇	C₂²	1	3	yes	—
11	C₂²×C₈×C₁₃₇	—	2	3	no	—
12	C₂×C₄⋊C₄×C₁₃₇	—	2	3	no	—
13	C₂×C₄⋊C₄×C₁₃₇	—	2	3	no	—
14	C₂×C₄⋊C₄×C₁₃₇	D₄	1	3	yes	—
15	C₂×C₄⋊C₄×C₁₃₇	D₄	1	3	yes	—
16	C₂×C₄²×C₁₃₇	—	2	1	no	—
17	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
18	#95×C₁₃₇	—	2	3	no	—
19	#95×C₁₃₇	—	2	3	no	—
20	#95×C₁₃₇	—	2	1	no	—
21	#95×C₁₃₇	—	2	3	no	—
22	C₂²×C₄×C₁₃₇	—	2	3	no	—
23	C₂²×C₄×C₁₃₇	—	2	3	no	—
24	C₂²×C₄×C₁₃₇	—	4	1	no	—
25	C₂²×C₄×C₁₃₇	C₂×D₄	1	3	yes	—
26	C₂×C₈×C₁₃₇	—	4	3	no	—
27	C₂×C₈×C₁₃₇	—	4	3	no	—
28	C₂×C₈×C₁₃₇	—	4	3	no	—
29	C₄⋊C₄×C₁₃₇	—	2	3	no	—
30	C₄⋊C₄×C₁₃₇	—	2	3	no	—
31	C₄⋊C₄×C₁₃₇	—	4	3	no	—
32	C₄⋊C₄×C₁₃₇	—	4	6	no	—
33	C₄⋊C₄×C₁₃₇	—	4	3	no	—
34	C₄⋊C₄×C₁₃₇	—	4	3	no	—
35	C₄²×C₁₃₇	—	4	1	no	—
36	C₄²×C₁₃₇	—	8	1	no	—
37	C₂³×C₁₃₇	#120	1	1	yes	characteristic
38	C₂×C₄×C₁₃₇	—	2	3	no	—
39	C₂×C₄×C₁₃₇	—	2	3	no	—
40	C₂×C₄×C₁₃₇	—	4	3	no	—
41	C₂×C₄×C₁₃₇	—	4	3	no	—
42	C₂×C₄×C₁₃₇	—	4	3	no	—
43	C₂×C₄×C₁₃₇	—	4	3	no	—
44	C₂×C₄×C₁₃₇	—	4	3	no	—
45	C₂×C₄×C₁₃₇	—	4	3	no	—
46	C₂×C₄×C₁₃₇	—	8	3	no	—
47	C₂×C₄×C₁₃₇	#135	1	3	yes	—
48	C₂×C₄×C₁₃₇	#137	1	3	yes	—
49	C₈×C₁₃₇	—	8	3	no	—
50	C₂²×C₁₃₇	#452	1	3	yes	—
51	C₂²×C₁₃₇	#454	1	3	yes	—
52	C₂²×C₁₃₇	#458	1	1	yes	characteristic
53	C₄×C₁₃₇	—	2	3	no	—
54	C₄×C₁₃₇	—	2	3	no	—
55	C₄×C₁₃₇	—	8	3	no	—
56	C₄×C₁₃₇	—	8	3	no	—
57	C₄×C₁₃₇	—	16	1	no	—
58	C₂×C₁₃₇	#1615	1	3	yes	—
59	C₂×C₁₃₇	#1638	1	3	yes	—
60	C₂×C₁₃₇	#1658	1	1	yes	characteristic
61	#7832	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₁₃₇	#7832	1	1	yes	characteristic, direct product factor, Sylow
63	#2810	C₂×C₁₃₇	1	1	yes	characteristic
64	#2100	C₂×C₁₃₇	1	3	yes	—
65	#1271	C₂×C₁₃₇	1	3	yes	—
66	#400	—	2	3	no	—
67	#389	C₂²×C₁₃₇	1	3	yes	—
68	#387	—	2	3	no	—
69	#384	C₂²×C₁₃₇	1	1	yes	characteristic
70	#340	—	2	3	no	—
71	#340	—	2	3	no	—
72	#336	C₂²×C₁₃₇	1	3	yes	—
73	C₂²×C₈	—	2	3	no	—
74	C₂×C₄⋊C₄	—	2	3	no	—
75	C₂×C₄⋊C₄	—	2	3	no	—
76	C₂×C₄⋊C₄	D₄×C₁₃₇	1	3	yes	—
77	C₂×C₄⋊C₄	D₄×C₁₃₇	1	3	yes	—
78	C₂×C₄²	—	2	1	no	—
79	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
80	#95	—	2	3	no	—
81	#95	—	2	3	no	—
82	#95	—	2	1	no	—
83	#95	—	2	3	no	—
84	C₂²×C₄	—	2	3	no	—
85	C₂²×C₄	—	2	3	no	—
86	C₂²×C₄	—	4	1	no	—
87	C₂²×C₄	C₂×D₄×C₁₃₇	1	3	yes	—
88	C₂×C₈	—	4	3	no	—
89	C₂×C₈	—	4	3	no	—
90	C₂×C₈	—	4	3	no	—
91	C₄⋊C₄	—	2	3	no	—
92	C₄⋊C₄	—	2	3	no	—
93	C₄⋊C₄	—	4	3	no	—
94	C₄⋊C₄	—	4	6	no	—
95	C₄⋊C₄	—	4	3	no	—
96	C₄⋊C₄	—	4	3	no	—
97	C₄²	—	4	1	no	—
98	C₄²	—	8	1	no	—
99	C₂³	#120×C₁₃₇	1	1	yes	characteristic
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	4	3	no	—
103	C₂×C₄	—	4	3	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	—	4	3	no	—
106	C₂×C₄	—	4	3	no	—
107	C₂×C₄	—	4	3	no	—
108	C₂×C₄	—	8	3	no	—
109	C₂×C₄	#135×C₁₃₇	1	3	yes	—
110	C₂×C₄	#137×C₁₃₇	1	3	yes	—
111	C₈	—	8	3	no	—
112	C₂²	#452×C₁₃₇	1	3	yes	—
113	C₂²	#454×C₁₃₇	1	3	yes	—
114	C₂²	#458×C₁₃₇	1	1	yes	characteristic
115	C₄	—	2	3	no	—
116	C₄	—	2	3	no	—
117	C₄	—	8	3	no	—
118	C₄	—	8	3	no	—
119	C₄	—	16	1	no	—
120	C₂	#1615×C₁₃₇	1	3	yes	—
121	C₂	#1638×C₁₃₇	1	3	yes	—
122	C₂	#1658×C₁₃₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#2810×C₁₃₇

C₂

yes

maximal, characteristic

#2100×C₁₃₇

C₂

yes

maximal

#1271×C₁₃₇

C₂

yes

maximal

#400×C₁₃₇

—

#389×C₁₃₇

C₂²

yes

—

#387×C₁₃₇

—

#384×C₁₃₇

C₂²

yes

characteristic

#340×C₁₃₇

—

#340×C₁₃₇

—

#336×C₁₃₇

C₂²

yes

—

C₂²×C₈×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

D₄

yes

—

C₂×C₄⋊C₄×C₁₃₇

D₄

yes

—

C₂×C₄²×C₁₃₇

—

C₂×C₄²×C₁₃₇

C₂³

yes

characteristic

#95×C₁₃₇

—

#95×C₁₃₇

—

#95×C₁₃₇

—

#95×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

C₂×D₄

yes

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄²×C₁₃₇

—

C₄²×C₁₃₇

—

C₂³×C₁₃₇

#120

yes

characteristic

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

#135

yes

—

C₂×C₄×C₁₃₇

#137

yes

—

C₈×C₁₃₇

—

C₂²×C₁₃₇

#452

yes

—

C₂²×C₁₃₇

#454

yes

—

C₂²×C₁₃₇

#458

yes

characteristic

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₂×C₁₃₇

#1615

yes

—

C₂×C₁₃₇

#1638

yes

—

C₂×C₁₃₇

#1658

yes

characteristic

#7832

C₁₃₇

yes

maximal, characteristic, direct product factor, Sylow

C₁₃₇

#7832

yes

characteristic, direct product factor, Sylow

#2810

C₂×C₁₃₇

yes

characteristic

#2100

C₂×C₁₃₇

yes

—

#1271

C₂×C₁₃₇

yes

—

#400

—

#389

C₂²×C₁₃₇

yes

—

#387

—

#384

C₂²×C₁₃₇

yes

—

—

C₂²×C₁₃₇

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₃₇

yes

—

C₂×C₄⋊C₄

D₄×C₁₃₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂³×C₁₃₇

yes

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂³

#120×C₁₃₇

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

#135×C₁₃₇

yes

—

110

C₂×C₄

#137×C₁₃₇

yes

—

111

C₈

—

112

C₂²

#452×C₁₃₇

yes

—

113

C₂²

#454×C₁₃₇

yes

—

114

C₂²

#458×C₁₃₇

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

#1615×C₁₃₇

yes

—

121

C₂

#1638×C₁₃₇

yes

—

122

C₂

#1658×C₁₃₇

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃₇

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃₇

LCS

G ▷ C₂×C₄² ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

N	H ≅ G/N	type
61. #7832	C₁₃₇	direct (N × H)
62. C₁₃₇	#7832	direct (N × H)

H ≅ G/N

type

61. #7832

C₁₃₇

direct (N × H)

62. C₁₃₇

#7832

direct (N × H)

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

subgroup	index
#2810×C₁₃₇	2
#2100×C₁₃₇	2
#1271×C₁₃₇	2
#7832	137

subgroup

index

#2810×C₁₃₇

#2100×C₁₃₇

#1271×C₁₃₇

#7832

137

Subgroups — C₁₃₇×#7832 #46857218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C137×#7832 #46857218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#7832 #46857218