Group #48001842 — subgroups

Subgroups — C₁₃₉×#7246 #48001842

Order 35584.

184 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 90 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	#2150×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1568×C₁₃₉	C₂	1	2	yes	maximal
3	C₂×M₃₂×C₁₃₉	C₄	1	2	yes	—
4	#432×C₁₃₉	—	2	2	no	—
5	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
6	C₄⋊C₁₆×C₁₃₉	—	2	2	no	—
7	#335×C₁₃₉	—	2	2	no	—
8	#334×C₁₃₉	C₄	1	4	yes	—
9	C₂²×C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₃₉	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
12	M₃₂×C₁₃₉	—	4	2	no	—
13	C₂×C₁₆×C₁₃₉	—	2	2	no	—
14	C₄⋊C₈×C₁₃₉	—	2	4	no	—
15	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
16	#97×C₁₃₉	—	4	2	no	—
17	C₄×C₈×C₁₃₉	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₃₉	D₄	1	2	yes	—
19	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₃₉	SD₁₆	1	2	yes	—
21	C₂×C₈×C₁₃₉	—	2	1	no	—
22	C₂×C₈×C₁₃₉	—	2	1	no	—
23	C₂×C₈×C₁₃₉	—	4	1	no	—
24	C₂×C₈×C₁₃₉	—	4	4	no	—
25	C₂×C₈×C₁₃₉	C₄²	1	1	yes	characteristic
26	C₂×C₈×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₃₉	C₄⋊C₄	1	2	yes	—
28	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
29	C₄²×C₁₃₉	D₈	1	1	yes	characteristic
30	C₄²×C₁₃₉	Q₁₆	1	1	yes	characteristic
31	C₁₆×C₁₃₉	—	4	2	no	—
32	C₂³×C₁₃₉	#106	1	1	yes	characteristic
33	C₂×C₄×C₁₃₉	—	2	1	no	—
34	C₂×C₄×C₁₃₉	—	2	1	no	—
35	C₂×C₄×C₁₃₉	—	4	2	no	—
36	C₂×C₄×C₁₃₉	#95	1	1	yes	characteristic
37	C₂×C₄×C₁₃₉	#102	1	2	yes	—
38	C₂×C₄×C₁₃₉	#103	1	2	yes	—
39	C₂×C₄×C₁₃₉	#107	1	1	yes	characteristic
40	C₈×C₁₃₉	—	2	2	no	—
41	C₈×C₁₃₉	—	2	1	no	—
42	C₈×C₁₃₉	—	8	4	no	—
43	C₈×C₁₃₉	#100	1	1	yes	characteristic
44	C₈×C₁₃₉	#101	1	1	yes	characteristic
45	C₂²×C₁₃₉	—	2	1	no	—
46	C₂²×C₁₃₉	—	2	2	no	—
47	C₂²×C₁₃₉	#340	1	1	yes	characteristic
48	C₄×C₁₃₉	—	2	1	no	—
49	C₄×C₁₃₉	—	2	2	no	—
50	C₄×C₁₃₉	—	2	2	no	—
51	C₄×C₁₃₉	#338	1	1	yes	characteristic
52	C₄×C₁₃₉	#343	1	1	yes	characteristic
53	C₂×C₁₃₉	—	4	1	no	—
54	C₂×C₁₃₉	#1292	1	1	yes	characteristic
55	C₂×C₁₃₉	#1389	1	2	yes	—
56	#7246	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₁₃₉	#7246	1	1	yes	characteristic, direct product factor, Sylow
58	#2150	C₂×C₁₃₉	1	1	yes	characteristic
59	#1568	C₂×C₁₃₉	1	2	yes	—
60	C₂×M₃₂	C₄×C₁₃₉	1	2	yes	—
61	#432	—	2	2	no	—
62	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
63	C₄⋊C₁₆	—	2	2	no	—
64	#335	—	2	2	no	—
65	#334	C₄×C₁₃₉	1	4	yes	—
66	C₂²×C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
67	C₂²×C₈	Q₈×C₁₃₉	1	1	yes	characteristic
68	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
69	M₃₂	—	4	2	no	—
70	C₂×C₁₆	—	2	2	no	—
71	C₄⋊C₈	—	2	4	no	—
72	C₂²⋊C₈	—	4	2	no	—
73	#97	—	4	2	no	—
74	C₄×C₈	C₂×C₄×C₁₃₉	1	2	yes	—
75	C₄×C₈	D₄×C₁₃₉	1	2	yes	—
76	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
77	C₂²×C₄	SD₁₆×C₁₃₉	1	2	yes	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	4	1	no	—
81	C₂×C₈	—	4	4	no	—
82	C₂×C₈	C₄²×C₁₃₉	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
84	C₂×C₈	C₄⋊C₄×C₁₃₉	1	2	yes	—
85	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
86	C₄²	D₈×C₁₃₉	1	1	yes	characteristic
87	C₄²	Q₁₆×C₁₃₉	1	1	yes	characteristic
88	C₁₆	—	4	2	no	—
89	C₂³	#106×C₁₃₉	1	1	yes	characteristic
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	4	2	no	—
93	C₂×C₄	#95×C₁₃₉	1	1	yes	characteristic
94	C₂×C₄	#102×C₁₃₉	1	2	yes	—
95	C₂×C₄	#103×C₁₃₉	1	2	yes	—
96	C₂×C₄	#107×C₁₃₉	1	1	yes	characteristic
97	C₈	—	2	2	no	—
98	C₈	—	2	1	no	—
99	C₈	—	8	4	no	—
100	C₈	#100×C₁₃₉	1	1	yes	characteristic
101	C₈	#101×C₁₃₉	1	1	yes	characteristic
102	C₂²	—	2	1	no	—
103	C₂²	—	2	2	no	—
104	C₂²	#340×C₁₃₉	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	2	2	no	—
107	C₄	—	2	2	no	—
108	C₄	#338×C₁₃₉	1	1	yes	characteristic
109	C₄	#343×C₁₃₉	1	1	yes	characteristic
110	C₂	—	4	1	no	—
111	C₂	#1292×C₁₃₉	1	1	yes	characteristic
112	C₂	#1389×C₁₃₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#2150×C₁₃₉

C₂

yes

maximal, characteristic

#1568×C₁₃₉

C₂

yes

maximal

C₂×M₃₂×C₁₃₉

C₄

yes

—

#432×C₁₃₉

—

C₂×C₄×C₈×C₁₃₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₁₃₉

—

#335×C₁₃₉

—

#334×C₁₃₉

C₄

yes

—

C₂²×C₈×C₁₃₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃₉

Q₈

yes

characteristic

C₂×C₄²×C₁₃₉

D₄

yes

characteristic

M₃₂×C₁₃₉

—

C₂×C₁₆×C₁₃₉

—

C₄⋊C₈×C₁₃₉

—

C₂²⋊C₈×C₁₃₉

—

#97×C₁₃₉

—

C₄×C₈×C₁₃₉

C₂×C₄

yes

—

C₄×C₈×C₁₃₉

D₄

yes

—

C₂²×C₄×C₁₃₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₃₉

SD₁₆

yes

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

C₄²

yes

characteristic

C₂×C₈×C₁₃₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃₉

C₄⋊C₄

yes

—

C₄²×C₁₃₉

C₂²⋊C₄

yes

—

C₄²×C₁₃₉

D₈

yes

characteristic

C₄²×C₁₃₉

Q₁₆

yes

characteristic

C₁₆×C₁₃₉

—

C₂³×C₁₃₉

#106

yes

characteristic

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

#95

yes

characteristic

C₂×C₄×C₁₃₉

#102

yes

—

C₂×C₄×C₁₃₉

#103

yes

—

C₂×C₄×C₁₃₉

#107

yes

characteristic

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₈×C₁₃₉

yes

C₈×C₁₃₉

yes

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

#340

yes

characteristic

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

yes

C₄×C₁₃₉

yes

C₂×C₁₃₉

—

C₂×C₁₃₉

#1292

yes

characteristic

C₂×C₁₃₉

#1389

yes

—

#7246

C₁₃₉

yes

maximal, characteristic, direct product factor, Sylow

C₁₃₉

#7246

yes

characteristic, direct product factor, Sylow

#2150

C₂×C₁₃₉

yes

characteristic

#1568

C₂×C₁₃₉

yes

—

C₂×M₃₂

C₄×C₁₃₉

yes

—

#432

—

C₂×C₄×C₈

C₂²×C₁₃₉

yes

characteristic

C₄⋊C₁₆

—

#335

—

#334

C₄×C₁₃₉

yes

—

C₂²×C₈

C₂×C₄×C₁₃₉

yes

characteristic

C₂²×C₈

Q₈×C₁₃₉

yes

characteristic

C₂×C₄²

D₄×C₁₃₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

C₂×C₄×C₁₃₉

yes

—

C₄×C₈

D₄×C₁₃₉

yes

—

C₂²×C₄

C₄⋊C₄×C₁₃₉

yes

characteristic

C₂²×C₄

SD₁₆×C₁₃₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₁₃₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₃₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₃₉

yes

—

C₄²

C₂²⋊C₄×C₁₃₉

yes

—

C₄²

D₈×C₁₃₉

yes

characteristic

C₄²

Q₁₆×C₁₃₉

yes

characteristic

C₁₆

—

C₂³

#106×C₁₃₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#95×C₁₃₉

yes

characteristic

C₂×C₄

#102×C₁₃₉

yes

—

C₂×C₄

#103×C₁₃₉

yes

—

C₂×C₄

#107×C₁₃₉

yes

characteristic

C₈

—

C₈

—

C₈

—

100

C₈

#100×C₁₃₉

yes

characteristic

101

C₈

#101×C₁₃₉

yes

characteristic

102

C₂²

—

103

C₂²

—

104

C₂²

#340×C₁₃₉

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#338×C₁₃₉

yes

characteristic

109

C₄

#343×C₁₃₉

yes

characteristic

110

C₂

—

111

C₂

#1292×C₁₃₉

yes

characteristic

112

C₂

#1389×C₁₃₉

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃₉	#340
commutator	C₂×C₈	C₄²×C₁₃₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₃₉
prime radical	C₂³×C₁₃₉	#106
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ C₂×C₄×C₈×C₁₃₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃₉

#340

commutator

C₂×C₈

C₄²×C₁₃₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₁₃₉

prime radical

C₂³×C₁₃₉

#106

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ C₂×C₄×C₈×C₁₃₉ ◁ G

N	H ≅ G/N	type
56. #7246	C₁₃₉	direct (N × H)
57. C₁₃₉	#7246	direct (N × H)

H ≅ G/N

type

56. #7246

C₁₃₉

direct (N × H)

57. C₁₃₉

#7246

direct (N × H)

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

subgroup	index
#2150×C₁₃₉	2
#1568×C₁₃₉	2
#7246	139

subgroup

index

#2150×C₁₃₉

#1568×C₁₃₉

#7246

139

Subgroups — C₁₃₉×#7246 #48001842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C139×#7246 #48001842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#7246 #48001842