Group #20244995 — subgroups

Subgroups — C₂×(C₂×D₄₇)⋊C₁₆ #20244995

Order 6016.

272 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 117 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	C₂²×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₄₇)⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄×D₄₇	C₄	1	1	yes	characteristic
6	C₂²×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₈×D₄₇	—	2	2	no	—
8	C₂×C₈×D₄₇	—	2	2	no	—
9	C₂×C₈×D₄₇	C₄	1	2	yes	—
10	C₂×C₈×D₄₇	C₂²	1	2	yes	—
11	C₂×C₄₇⋊C₁₆	—	2	2	no	—
12	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₇	—	2	2	no	—
15	C₂×C₁₆×C₄₇	C₂²	1	2	yes	complemented
16	C₂³×D₄₇	C₈	1	1	yes	characteristic
17	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₄₇	C₈	1	1	yes	characteristic
19	C₂×C₄×D₄₇	—	2	2	no	—
20	C₂×C₄×D₄₇	—	2	2	no	—
21	C₂×C₄×D₄₇	C₈	1	2	yes	—
22	C₂×C₄×D₄₇	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₄₇	D₄	1	2	yes	—
25	C₂×C₈×C₄₇	D₄	1	2	yes	—
26	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
27	C₂×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
29	C₈×D₄₇	—	2	4	no	—
30	C₈×D₄₇	—	2	2	no	—
31	C₈×D₄₇	—	2	2	no	—
32	C₁₆×C₄₇	—	2	2	no	—
33	C₄₇⋊C₁₆	—	2	2	no	—
34	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₄₇	—	2	2	no	—
36	C₂²×D₄₇	—	2	2	no	—
37	C₂²×D₄₇	C₁₆	1	4	yes	complemented
38	C₂²×D₄₇	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₄₇	M₁₆	1	2	yes	—
42	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₄₇	—	2	2	no	—
44	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
45	C₄×D₄₇	—	2	4	no	—
46	C₄×D₄₇	—	2	2	no	—
47	C₄×D₄₇	—	2	2	no	—
48	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
49	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇	C₂²⋊C₈	1	2	yes	—
53	C₂²×C₄₇	C₂×C₁₆	1	2	yes	—
54	C₂²×C₄₇	M₃₂	1	2	yes	—
55	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
56	C₂×D₄₇	—	2	8	no	—
57	C₂×D₄₇	—	2	2	no	—
58	C₂×D₄₇	—	2	2	no	—
59	C₂×D₄₇	C₂×C₁₆	1	4	yes	complemented
60	C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
61	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
63	Dic₄₇	—	2	2	no	—
64	C₂×C₂²⋊C₁₆	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	C₂²⋊C₁₆	1	4	yes	complemented
66	C₂×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
67	C₂×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
68	C₂×C₄₇	C₂×M₃₂	1	1	yes	characteristic
69	D₄₇	—	2	4	no	—
70	C₂³×C₈	—	47	1	no	—
71	C₂²×C₁₆	—	47	1	no	—
72	C₂²×C₁₆	D₄₇	1	1	yes	characteristic, complemented
73	C₂²⋊C₁₆	—	47	4	no	—
74	C₄₇	C₂×C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
75	C₂³×C₄	—	47	1	no	—
76	C₂²×C₈	—	47	1	no	—
77	C₂²×C₈	—	47	2	no	—
78	C₂²×C₈	—	47	2	no	—
79	C₂²×C₈	—	94	2	no	—
80	C₂²×C₈	—	94	2	no	—
81	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
82	C₂×C₁₆	—	2	2	no	—
83	C₂×C₁₆	—	47	2	no	—
84	C₂×C₁₆	—	94	2	no	—
85	C₂×C₁₆	C₂×D₄₇	1	2	yes	complemented
86	C₂⁴	—	47	1	no	—
87	C₂²×C₄	—	47	1	no	—
88	C₂²×C₄	—	47	2	no	—
89	C₂²×C₄	—	47	2	no	—
90	C₂²×C₄	—	94	2	no	—
91	C₂²×C₄	—	94	2	no	—
92	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
93	C₂×C₈	—	47	2	no	—
94	C₂×C₈	—	94	2	no	—
95	C₂×C₈	—	94	4	no	—
96	C₂×C₈	—	94	2	no	—
97	C₂×C₈	—	94	2	no	—
98	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
99	C₂×C₈	D₁₈₈	1	2	yes	—
100	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
101	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
102	C₁₆	—	2	2	no	—
103	C₁₆	—	94	2	no	—
104	C₂³	—	47	4	no	—
105	C₂³	—	47	2	no	—
106	C₂³	—	94	2	no	—
107	C₂³	—	94	2	no	—
108	C₂³	C₈×D₄₇	1	1	yes	characteristic
109	C₂×C₄	—	47	2	no	—
110	C₂×C₄	—	94	2	no	—
111	C₂×C₄	—	94	4	no	—
112	C₂×C₄	—	94	2	no	—
113	C₂×C₄	—	94	2	no	—
114	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
115	C₂×C₄	#10625324	1	2	yes	—
116	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
117	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
118	C₈	—	94	2	no	—
119	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
120	C₈	C₂×D₁₈₈	1	1	yes	characteristic
121	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
122	C₂²	—	47	4	no	—
123	C₂²	—	94	2	no	—
124	C₂²	—	94	2	no	—
125	C₂²	—	94	8	no	—
126	C₂²	(C₂×D₄₇)⋊C₈	1	2	yes	—
127	C₂²	C₁₆×D₄₇	1	2	yes	—
128	C₂²	#13093963	1	2	yes	—
129	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
130	C₄	—	94	2	no	—
131	C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
132	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
133	C₄	C₂×#10625324	1	1	yes	characteristic
134	C₂	—	94	4	no	—
135	C₂	(C₂×D₄₇)⋊C₁₆	1	4	yes	direct product factor
136	C₂	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
137	C₂	C₂×C₁₆×D₄₇	1	1	yes	characteristic
138	C₂	C₂×#13093963	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₈×D₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal, direct product factor

C₂²×C₁₆×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₄

yes

characteristic

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

C₄

yes

—

C₂×C₈×D₄₇

C₂²

yes

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

C₂²

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

complemented

C₂³×D₄₇

C₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₈

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₈×D₄₇

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×C₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₁₆

yes

complemented

C₂²×D₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²⋊C₈

yes

—

C₂²×C₄₇

C₂×C₁₆

yes

—

C₂²×C₄₇

M₃₂

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₂×C₁₆

yes

complemented

C₄×C₄₇

C₂²⋊C₈

yes

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

C₂×C₂²⋊C₁₆

—

maximal, Sylow

C₂×C₄₇

C₂²⋊C₁₆

yes

complemented

C₂×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₄₇

C₂²×C₁₆

yes

characteristic

C₂×C₄₇

C₂×M₃₂

yes

characteristic

D₄₇

—

C₂³×C₈

—

C₂²×C₁₆

—

C₂²×C₁₆

D₄₇

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₄₇

C₂×C₂²⋊C₁₆

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

complemented

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

D₁₈₈

yes

—

100

C₂×C₈

C₂²⋊D₄₇

yes

—

101

C₂×C₈

C₂²×D₄₇

yes

characteristic

102

C₁₆

—

103

C₁₆

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₈×D₄₇

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₈×D₄₇

yes

characteristic

115

C₂×C₄

#10625324

yes

—

116

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

117

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

118

C₈

—

119

C₈

(C₂×D₄₇)⋊C₄

yes

—

120

C₈

C₂×D₁₈₈

yes

characteristic

121

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

(C₂×D₄₇)⋊C₈

yes

—

127

C₂²

C₁₆×D₄₇

yes

—

128

C₂²

#13093963

yes

—

129

C₂²

C₂×C₈×D₄₇

yes

characteristic

130

C₄

—

131

C₄

(C₂×D₄₇)⋊C₈

yes

—

132

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

133

C₄

C₂×#10625324

yes

characteristic

134

C₂

—

135

C₂

(C₂×D₄₇)⋊C₁₆

yes

direct product factor

136

C₂

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

137

C₂

C₂×C₁₆×D₄₇

yes

characteristic

138

C₂

C₂×#13093963

yes

characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₈
hypercenter	C₂²×C₁₆	D₄₇
hypocenter	C₄₇	C₂×C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂²×C₈

C₂×D₄₇

commutator

C₂×C₄₇

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂²×C₁₆×C₄₇

C₂

socle

C₂³×C₄₇

C₂×C₈

hypercenter

C₂²×C₁₆

D₄₇

hypocenter

C₄₇

C₂×C₂²⋊C₁₆

LCS

G ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
2. C₂²×C₄₇⋊C₁₆	C₂	semidirect
3. (C₂×D₄₇)⋊C₁₆	C₂	direct (N × H)
4. C₂²×C₁₆×C₄₇	C₂	semidirect
12. C₂×C₄₇⋊C₁₆	C₂²	semidirect
15. C₂×C₁₆×C₄₇	C₂²	semidirect
37. C₂²×D₄₇	C₁₆	semidirect
59. C₂×D₄₇	C₂×C₁₆	semidirect
65. C₂×C₄₇	C₂²⋊C₁₆	semidirect
72. C₂²×C₁₆	D₄₇	semidirect
74. C₄₇	C₂×C₂²⋊C₁₆	semidirect
85. C₂×C₁₆	C₂×D₄₇	semidirect
135. C₂	(C₂×D₄₇)⋊C₁₆	direct (N × H)

H ≅ G/N

type

2. C₂²×C₄₇⋊C₁₆

C₂

semidirect

3. (C₂×D₄₇)⋊C₁₆

C₂

direct (N × H)

4. C₂²×C₁₆×C₄₇

C₂

semidirect

12. C₂×C₄₇⋊C₁₆

C₂²

semidirect

15. C₂×C₁₆×C₄₇

C₂²

semidirect

37. C₂²×D₄₇

C₁₆

semidirect

59. C₂×D₄₇

C₂×C₁₆

semidirect

65. C₂×C₄₇

C₂²⋊C₁₆

semidirect

72. C₂²×C₁₆

D₄₇

semidirect

74. C₄₇

C₂×C₂²⋊C₁₆

semidirect

85. C₂×C₁₆

C₂×D₄₇

semidirect

135. C₂

(C₂×D₄₇)⋊C₁₆

direct (N × H)

Subgroups — C₂×(C₂×D₄₇)⋊C₁₆ #20244995

Conjugacy classes of subgroups

Complements

Subgroups — C2×(C2×D47)⋊C16 #20244995

Conjugacy classes of subgroups

Complements

Subgroups — C₂×(C₂×D₄₇)⋊C₁₆ #20244995