Group #20243184 — subgroups

Subgroups — C₄×#13093943 #20243184

Order 6016.

296 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13093943	C₂	1	2	yes	maximal
2	C₄×#10625329	C₂	1	2	yes	maximal
3	#15688892	C₂	1	2	yes	maximal
4	C₂×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10625329	C₂²	1	4	yes	—
6	#13093943	C₄	1	8	yes	direct product factor
7	#13093935	—	2	2	no	—
8	C₄×C₄₇⋊C₈	—	2	2	no	—
9	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₄×Q₈×C₄₇	—	2	2	no	—
11	C₄×Q₈×C₄₇	—	2	2	no	—
12	C₂×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₇	C₄	1	2	yes	—
15	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₄₇	—	2	2	no	—
17	C₂×Q₈×C₄₇	—	2	2	no	—
18	C₂×Q₈×C₄₇	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	4	no	—
25	C₄⋊C₄×C₄₇	—	2	2	no	—
26	C₄²×C₄₇	—	2	2	no	—
27	C₄²×C₄₇	—	2	2	no	—
28	C₄²×C₄₇	D₄	1	2	yes	—
29	C₄²×C₄₇	D₄	1	2	yes	—
30	#10625329	—	2	4	no	—
31	#10625329	C₂×C₄	1	8	yes	—
32	C₂×C₄₇⋊C₈	—	2	4	no	—
33	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	Q₈×C₄₇	—	2	8	no	—
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	2	2	no	—
39	C₂×C₄×C₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	—	4	2	no	—
41	C₂×C₄×C₄₇	C₄²	1	4	yes	—
42	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
44	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₄₇	#41	1	2	yes	—
48	C₄₇⋊C₈	—	2	8	no	—
49	C₂²×C₄₇	—	2	1	no	—
50	C₂²×C₄₇	—	2	1	no	—
51	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
52	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄₇	#117	1	1	yes	characteristic
54	C₄×C₄₇	—	2	4	no	—
55	C₄×C₄₇	—	2	1	no	—
56	C₄×C₄₇	—	2	2	no	—
57	C₄×C₄₇	—	4	2	no	—
58	C₄×C₄₇	#101	1	2	yes	complemented
59	C₄×C₄₇	C₄×D₄	1	4	yes	—
60	C₄×#101	—	47	1	no	maximal, Sylow
61	C₂×C₄₇	—	2	1	no	—
62	C₂×C₄₇	—	2	1	no	—
63	C₂×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₄₇	C₂×#101	1	1	yes	characteristic
65	C₂×C₄₇	#413	1	1	yes	characteristic
66	C₂×C₄×Q₈	D₄₇	1	1	yes	characteristic
67	C₂×#101	—	47	2	no	—
68	C₄×M₁₆	—	47	2	no	—
69	#343	—	47	2	no	—
70	C₄₇	C₄×#101	1	1	yes	characteristic, complemented, Sylow
71	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
72	C₂×M₁₆	—	47	4	no	—
73	C₄×Q₈	—	2	2	no	—
74	C₄×Q₈	—	2	2	no	—
75	C₂×C₄⋊C₄	Dic₄₇	1	2	yes	—
76	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
77	C₂×C₄²	Dic₄₇	1	2	yes	—
78	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
79	#101	—	47	8	no	—
80	#97	—	94	2	no	—
81	C₄×C₈	—	94	2	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	C₄×D₄₇	1	4	yes	—
85	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
86	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
87	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
88	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
89	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
90	M₁₆	—	47	8	no	—
91	M₁₆	—	94	4	no	—
92	C₂×C₈	—	94	4	no	—
93	C₄⋊C₄	—	2	4	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄²	—	2	2	no	—
96	C₄²	—	2	2	no	—
97	C₄²	C₂²⋊D₄₇	1	2	yes	—
98	C₄²	C₂²⋊D₄₇	1	2	yes	—
99	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
100	Q₈	—	2	8	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	C₄×Dic₄₇	1	4	yes	—
108	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
109	C₂×C₄	C₂²⋊Dic₄₇	1	2	yes	—
110	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
111	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
112	C₂×C₄	#10625350	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
114	C₈	—	94	8	no	—
115	C₂²	—	2	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	C₂×C₄×Dic₄₇	1	1	yes	characteristic
118	C₂²	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
119	C₂²	#13093983	1	1	yes	characteristic
120	C₄	—	2	4	no	—
121	C₄	—	2	1	no	—
122	C₄	—	2	2	no	—
123	C₄	—	4	2	no	—
124	C₄	#13093943	1	2	yes	direct product factor
125	C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
126	C₂	—	2	1	no	—
127	C₂	—	2	1	no	—
128	C₂	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
129	C₂	C₂×#13093943	1	1	yes	characteristic
130	C₂	#15689107	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093943

C₂

yes

maximal

C₄×#10625329

C₂

yes

maximal

#15688892

C₂

yes

maximal

C₂×C₄×Q₈×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

#13093943

C₄

yes

direct product factor

#13093935

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₄

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₄

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

D₄

yes

—

#10625329

—

#10625329

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#101

yes

complemented

C₄×C₄₇

C₄×D₄

yes

—

C₄×#101

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

C₄×C₂²⋊C₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄×Q₈

D₄₇

yes

characteristic

C₂×#101

—

C₄×M₁₆

—

#343

—

C₄₇

C₄×#101

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

Dic₄₇

yes

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

C₂×C₄²

Dic₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#101

—

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄×D₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²⋊D₄₇

yes

—

C₄²

C₂²⋊D₄₇

yes

—

C₂³

C₂²×Dic₄₇

yes

characteristic

100

Q₈

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₄×Dic₄₇

yes

—

108

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

109

C₂×C₄

C₂²⋊Dic₄₇

yes

—

110

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

111

C₂×C₄

C₂×C₄×D₄₇

yes

—

112

C₂×C₄

#10625350

yes

—

113

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×C₄×Dic₄₇

yes

characteristic

118

C₂²

C₂×C₂²⋊Dic₄₇

yes

characteristic

119

C₂²

#13093983

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#13093943

yes

direct product factor

125

C₄

C₄×C₂²⋊D₄₇

yes

—

126

C₂

—

127

C₂

—

128

C₂

C₄×C₂²⋊Dic₄₇

yes

characteristic

129

C₂

C₂×#13093943

yes

characteristic

130

C₂

#15689107

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₄₇
commutator	C₂²×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×Q₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	C₂×C₄×Q₈	D₄₇
hypocenter	C₄₇	C₄×#101
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₄₇

commutator

C₂²×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×C₄×Q₈×C₄₇

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

hypercenter

C₂×C₄×Q₈

D₄₇

hypocenter

C₄₇

C₄×#101

LCS

G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
6. #13093943	C₄	direct (N × H)
58. C₄×C₄₇	#101	semidirect
70. C₄₇	C₄×#101	semidirect
124. C₄	#13093943	direct (N × H)

H ≅ G/N

type

6. #13093943

C₄

direct (N × H)

58. C₄×C₄₇

#101

semidirect

70. C₄₇

C₄×#101

semidirect

124. C₄

#13093943

direct (N × H)

Subgroups — C₄×#13093943 #20243184

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13093943 #20243184

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13093943 #20243184