Group #20249355 — subgroups

Subgroups — #20249355

Order 6016.

352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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	C₄₇⋊#401	C₂	1	1	yes	maximal, characteristic
2	#15689065	C₂	1	3	yes	maximal
3	#15689063	C₂	1	3	yes	maximal
4	#15689027	C₂	1	3	yes	maximal
5	#15689020	C₂	1	3	yes	maximal
6	#15688968	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#401	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
10	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
11	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
13	C₄₇⋊#95	C₂²	1	3	yes	—
14	C₄₇⋊#95	C₂²	1	3	yes	—
15	C₄₇⋊#95	C₂²	1	3	yes	—
16	C₄₇⋊#95	C₂²	1	3	yes	—
17	C₄₇⋊#95	C₂²	1	3	yes	—
18	#95×C₄₇	C₂²	1	1	yes	characteristic
19	#95×C₄₇	C₂²	1	3	yes	—
20	#95×C₄₇	C₂²	1	3	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
24	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₇	C₂³	1	3	yes	—
26	C₂²×Dic₄₇	C₂³	1	3	yes	—
27	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₉₄	—	2	6	no	—
29	C₄⋊Dic₄₇	—	4	3	no	—
30	Dic₄₇⋊C₄	—	2	6	no	—
31	Dic₄₇⋊C₄	—	4	3	no	—
32	C₄×Dic₄₇	—	2	6	no	—
33	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
34	C₂×C₄×C₄₇	—	2	3	no	—
35	C₂×C₄×C₄₇	—	2	3	no	—
36	C₂×C₄×C₄₇	—	2	3	no	—
37	C₂×C₄×C₄₇	—	2	3	no	—
38	C₂×C₄×C₄₇	—	2	6	no	—
39	C₂×C₄×C₄₇	—	2	3	no	—
40	C₂×Dic₄₇	—	2	3	no	—
41	C₂×Dic₄₇	—	2	3	no	—
42	C₂×Dic₄₇	—	2	3	no	—
43	C₂×Dic₄₇	—	2	3	no	—
44	C₂×Dic₄₇	—	2	3	no	—
45	C₂×Dic₄₇	—	2	3	no	—
46	C₂×Dic₄₇	—	2	3	no	—
47	C₂×Dic₄₇	#41	1	6	yes	—
48	Dic₉₄	—	4	4	no	—
49	C₂²×C₄₇	C₂×#41	1	3	yes	—
50	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
51	C₂²×C₄₇	2₋¹⁺⁴	1	3	yes	—
52	C₄×C₄₇	—	4	1	no	—
53	C₄×C₄₇	—	4	3	no	—
54	C₄×C₄₇	—	4	3	no	—
55	Dic₄₇	—	4	1	no	—
56	Dic₄₇	—	4	3	no	—
57	Dic₄₇	—	4	3	no	—
58	Dic₄₇	#126	1	4	yes	—
59	#2645	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	C₂×#126	1	1	yes	characteristic
61	C₂×C₄₇	#541	1	3	yes	—
62	C₂×C₄₇	#542	1	3	yes	—
63	#401	—	47	1	no	—
64	#401	D₄₇	1	1	yes	characteristic
65	#400	—	47	3	no	—
66	#400	—	47	3	no	—
67	#391	—	47	3	no	—
68	#389	—	47	3	no	—
69	#376	—	47	1	no	—
70	C₄₇	#2645	1	1	yes	characteristic, complemented, Sylow
71	C₂²×Q₈	—	47	1	no	—
72	C₂×C₄⋊C₄	—	47	3	no	—
73	C₂×C₄⋊C₄	—	47	3	no	—
74	C₂×C₄⋊C₄	—	47	3	no	—
75	C₂×C₄²	—	47	3	no	—
76	#95	—	47	3	no	—
77	#95	—	47	3	no	—
78	#95	—	47	3	no	—
79	#95	—	47	3	no	—
80	#95	—	47	3	no	—
81	#95	C₂×D₄₇	1	1	yes	characteristic
82	#95	C₂×D₄₇	1	3	yes	—
83	#95	C₂×D₄₇	1	3	yes	—
84	C₂×Q₈	—	94	6	no	—
85	C₂²×C₄	—	47	1	no	—
86	C₂²×C₄	—	47	1	no	—
87	C₂²×C₄	—	47	3	no	—
88	C₂²×C₄	—	47	3	no	—
89	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
90	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
91	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
92	C₄⋊C₄	—	94	6	no	—
93	C₄⋊C₄	—	188	3	no	—
94	C₄⋊C₄	—	188	3	no	—
95	C₄²	—	94	6	no	—
96	C₂³	C₂³×D₄₇	1	1	yes	characteristic
97	Q₈	—	188	4	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	2	6	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	47	6	no	—
105	C₂×C₄	—	94	3	no	—
106	C₂×C₄	—	94	3	no	—
107	C₂×C₄	—	94	3	no	—
108	C₂×C₄	—	94	3	no	—
109	C₂×C₄	—	94	3	no	—
110	C₂×C₄	—	94	3	no	—
111	C₂×C₄	—	94	3	no	—
112	C₂²	#41×D₄₇	1	3	yes	—
113	C₂²	#13094070	1	1	yes	characteristic
114	C₂²	#13094071	1	3	yes	—
115	C₄	—	4	3	no	—
116	C₄	—	4	3	no	—
117	C₄	—	4	1	no	—
118	C₄	—	47	4	no	—
119	C₄	—	188	3	no	—
120	C₄	—	188	3	no	—
121	C₄	—	188	1	no	—
122	C₂	#126×D₄₇	1	1	yes	characteristic
123	C₂	#15689730	1	3	yes	—
124	C₂	#15689739	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇⋊#401

C₂

yes

maximal, characteristic

#15689065

C₂

yes

maximal

#15689063

C₂

yes

maximal

#15689027

C₂

yes

maximal

#15689020

C₂

yes

maximal

#15688968

C₂

yes

maximal, characteristic

C₄₇×#401

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

#95×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

Dic₉₄

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

#126

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#542

yes

—

#401

—

#401

D₄₇

yes

—

—

—

—

—

C₄₇

#2645

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

—

—

—

C₂×D₄₇

yes

characteristic

#95

C₂×D₄₇

yes

—

#95

C₂×D₄₇

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

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

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂²

#41×D₄₇

yes

—

113

C₂²

#13094070

yes

characteristic

114

C₂²

#13094071

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

188

—

120

C₄

—

188

—

121

C₄

—

188

—

122

C₂

#126×D₄₇

yes

characteristic

123

C₂

#15689730

yes

—

124

C₂

#15689739

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#401	C₂
hypercenter	#401	D₄₇
hypocenter	C₄₇	#2645
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #401

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#401

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #401

N	H ≅ G/N	type
70. C₄₇	#2645	semidirect

H ≅ G/N

type

70. C₄₇

#2645

semidirect

Subgroups — #20249355

Conjugacy classes of subgroups

Complements