Group #20249058 — subgroups

Subgroups — #20249058

Order 6016.

428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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	#15689046	C₂	1	4	yes	maximal
2	#15689020	C₂	1	4	yes	maximal, complemented
3	#15689006	C₂	1	4	yes	maximal, complemented
4	C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
5	C₄₇×#381	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
7	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
9	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
10	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
11	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
12	C₄₇⋊#95	C₂²	1	4	yes	—
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
16	#95×C₄₇	C₂²	1	4	yes	—
17	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	—	4	2	no	—
19	C₂²×C₄×C₄₇	Q₈	1	4	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
22	C₂²×Dic₄₇	C₂³	1	4	yes	—
23	C₂²×Dic₄₇	C₂³	1	4	yes	—
24	C₂²⋊C₄×C₄₇	—	4	2	no	—
25	C₂²⋊Dic₄₇	—	2	8	no	—
26	C₄⋊Dic₄₇	—	2	8	no	—
27	Dic₄₇⋊C₄	—	2	8	no	—
28	Dic₄₇⋊C₄	—	4	4	no	—
29	C₄×Dic₄₇	—	4	2	no	—
30	C₄×Dic₄₇	—	4	2	no	—
31	C₂³×C₄₇	—	2	4	no	—
32	C₂³×C₄₇	—	2	2	no	—
33	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
34	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	—	2	4	no	—
38	C₂×C₄×C₄₇	—	2	4	no	—
39	C₂×C₄×C₄₇	—	2	4	no	—
40	C₂×C₄×C₄₇	—	4	4	no	—
41	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
42	C₂×Dic₄₇	—	2	4	no	—
43	C₂×Dic₄₇	—	2	4	no	—
44	C₂×Dic₄₇	—	2	4	no	—
45	C₂×Dic₄₇	—	2	4	no	—
46	C₂×Dic₄₇	—	2	4	no	—
47	C₂×Dic₄₇	#41	1	8	yes	—
48	C₂²×C₄₇	—	2	4	no	—
49	C₂²×C₄₇	—	2	2	no	—
50	C₂²×C₄₇	—	4	4	no	—
51	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
52	C₂²×C₄₇	C₂×#41	1	4	yes	—
53	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
54	C₄×C₄₇	—	2	4	no	—
55	C₄×C₄₇	—	4	4	no	—
56	Dic₄₇	—	2	8	no	—
57	Dic₄₇	—	4	4	no	—
58	#2608	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	—	4	2	no	—
60	C₂×C₄₇	#533	1	2	yes	—
61	C₂×C₄₇	#543	1	1	yes	characteristic
62	C₂×C₄₇	#553	1	4	yes	—
63	#396	—	47	4	no	—
64	#389	—	47	4	no	—
65	#387	—	47	4	no	—
66	#381	D₄₇	1	1	yes	characteristic
67	C₄×C₂²⋊C₄	—	47	2	no	—
68	C₄₇	#2608	1	1	yes	characteristic, complemented, Sylow
69	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
70	C₂×C₄⋊C₄	—	47	4	no	—
71	C₂×C₄⋊C₄	—	47	4	no	—
72	C₂×C₄⋊C₄	—	47	4	no	—
73	C₂×C₂²⋊C₄	—	47	4	no	—
74	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
75	C₂×C₄²	—	47	2	no	—
76	C₂×C₄²	—	47	2	no	—
77	#95	—	47	4	no	—
78	#95	—	47	4	no	—
79	#95	C₂×D₄₇	1	4	yes	—
80	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
81	C₂²×C₄	—	4	2	no	—
82	C₂²×C₄	—	47	4	no	—
83	C₂²×C₄	—	47	4	no	—
84	C₂²×C₄	Dic₉₄	1	4	yes	—
85	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
86	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
87	C₄⋊C₄	—	94	8	no	—
88	C₄⋊C₄	—	94	8	no	—
89	C₄⋊C₄	—	188	4	no	—
90	C₂²⋊C₄	—	4	2	no	—
91	C₂²⋊C₄	—	94	8	no	—
92	C₄²	—	188	2	no	—
93	C₄²	—	188	2	no	—
94	C₂³	—	2	4	no	—
95	C₂³	—	2	2	no	—
96	C₂³	C₂×Dic₉₄	1	2	yes	—
97	C₂³	C₂³×D₄₇	1	1	yes	characteristic
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	4	no	—
103	C₂×C₄	—	4	4	no	—
104	C₂×C₄	—	47	8	no	—
105	C₂×C₄	—	94	4	no	—
106	C₂×C₄	—	94	4	no	—
107	C₂×C₄	—	94	4	no	—
108	C₂×C₄	—	94	4	no	—
109	C₂×C₄	—	94	4	no	—
110	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
111	C₂²	—	2	2	no	—
112	C₂²	—	2	4	no	—
113	C₂²	—	4	4	no	—
114	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
115	C₂²	#41×D₄₇	1	4	yes	—
116	C₂²	#13094069	1	2	yes	—
117	C₄	—	2	4	no	—
118	C₄	—	4	4	no	—
119	C₄	—	94	8	no	—
120	C₄	—	188	4	no	—
121	C₂	—	4	2	no	—
122	C₂	#15689676	1	2	yes	—
123	C₂	#15689749	1	1	yes	characteristic
124	C₂	#15689818	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689046

C₂

yes

maximal

#15689020

C₂

yes

maximal, complemented

#15689006

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₄₇

C₂

yes

maximal

C₄₇×#381

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2608

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#533

yes

—

C₂×C₄₇

#543

yes

characteristic

C₂×C₄₇

#553

yes

—

—

—

—

D₄₇

yes

characteristic

C₄×C₂²⋊C₄

—

C₄₇

#2608

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

#95

—

#95

—

#95

C₂×D₄₇

yes

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₉₄

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

188

—

C₄²

—

188

—

C₂³

—

C₂³

—

C₂³

C₂×Dic₉₄

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

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

C₂×Dic₉₄

yes

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂²×Dic₉₄

yes

characteristic

115

C₂²

#41×D₄₇

yes

—

116

C₂²

#13094069

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

188

—

121

C₂

—

122

C₂

#15689676

yes

—

123

C₂

#15689749

yes

characteristic

124

C₂

#15689818

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#381	C₂
hypercenter	#381	D₄₇
hypocenter	C₄₇	#2608
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#381

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
2. #15689020	C₂	semidirect
3. #15689006	C₂	semidirect
68. C₄₇	#2608	semidirect

H ≅ G/N

type

2. #15689020

C₂

semidirect

3. #15689006

C₂

semidirect

68. C₄₇

#2608

semidirect

Subgroups — #20249058

Conjugacy classes of subgroups

Complements