Group #20245003 — subgroups

Subgroups — #20245003

Order 6016.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094030	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, complemented
4	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625350	C₄	1	1	yes	characteristic
6	#13094030	—	2	2	no	—
7	#13094030	—	2	2	no	—
8	C₂×#10625329	C₄	1	1	yes	characteristic
9	C₂×#10625324	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	—
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	M₃₂×C₄₇	—	2	2	no	—
15	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₄₇	C₈	1	2	yes	—
18	#10625350	—	2	2	no	—
19	#10625350	—	2	2	no	—
20	C₂×D₁₈₈	C₈	1	1	yes	characteristic
21	C₂×C₄×D₄₇	C₂×C₄	1	2	yes	—
22	C₂×Dic₉₄	C₈	1	1	yes	characteristic
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	#10625329	—	2	2	no	—
28	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
29	#10625324	—	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	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₄₇	M₁₆	1	2	yes	—
39	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₄₇	—	2	4	no	—
41	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
42	D₁₈₈	—	2	2	no	—
43	C₄×D₄₇	—	2	2	no	—
44	C₄×D₄₇	—	2	2	no	—
45	Dic₉₄	—	2	2	no	—
46	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
47	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₄₇⋊C₈	—	2	2	no	—
50	C₂²×C₄₇	—	2	2	no	—
51	C₂²×C₄₇	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
53	C₂×D₄₇	—	2	2	no	—
54	C₂×D₄₇	—	2	4	no	—
55	C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
56	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
58	Dic₄₇	—	2	2	no	—
59	#2113	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	—	2	2	no	—
61	C₂×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
62	C₂×C₄₇	#504	1	2	yes	—
63	D₄₇	—	4	2	no	—
64	C₂×#131	—	47	1	no	—
65	C₂×M₃₂	D₄₇	1	1	yes	characteristic, complemented
66	C₂²×C₁₆	—	47	1	no	—
67	C₂²⋊C₁₆	—	47	4	no	—
68	C₄₇	#2113	1	1	yes	characteristic, complemented, Sylow
69	C₂×#41	—	47	1	no	—
70	#131	—	94	2	no	—
71	#131	—	94	2	no	—
72	C₂×M₁₆	—	47	1	no	—
73	C₂×M₁₆	—	47	2	no	—
74	C₂²×C₈	—	47	2	no	—
75	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
76	M₃₂	—	2	2	no	—
77	C₂×C₁₆	—	47	2	no	—
78	C₂×C₁₆	—	94	2	no	—
79	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
80	#41	—	94	2	no	—
81	#41	—	94	2	no	—
82	C₂×Q₈	—	47	1	no	—
83	C₂×D₄	—	47	2	no	—
84	C₂×D₄	—	47	1	no	—
85	C₂²×C₄	—	47	2	no	—
86	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
87	M₁₆	—	94	2	no	—
88	M₁₆	—	94	4	no	—
89	C₂×C₈	—	47	2	no	—
90	C₂×C₈	—	94	2	no	—
91	C₂×C₈	—	94	2	no	—
92	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
93	C₂×C₈	D₁₈₈	1	2	yes	—
94	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
95	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
96	C₁₆	—	2	2	no	—
97	C₁₆	—	94	2	no	—
98	C₂³	—	47	2	no	—
99	C₂³	C₈×D₄₇	1	1	yes	characteristic
100	Q₈	—	94	2	no	—
101	D₄	—	94	4	no	—
102	D₄	—	94	2	no	—
103	C₂×C₄	—	47	2	no	—
104	C₂×C₄	—	94	2	no	—
105	C₂×C₄	—	94	2	no	—
106	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
107	C₂×C₄	#10625324	1	2	yes	—
108	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
109	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
110	C₈	—	94	2	no	—
111	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
112	C₈	C₂×D₁₈₈	1	1	yes	characteristic
113	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	94	4	no	—
116	C₂²	—	94	2	no	—
117	C₂²	(C₂×D₄₇)⋊C₈	1	2	yes	—
118	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
119	C₄	—	94	2	no	—
120	C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
121	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
122	C₄	C₂×#10625324	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	188	2	no	—
125	C₂	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
126	C₂	#15689541	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094030

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

C₄

yes

—

—

C₄

yes

characteristic

C₂×#10625324

C₄

yes

—

C₂×C₈×D₄₇

C₂²

yes

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₇

C₈

yes

—

#10625350

—

#10625350

—

C₂×D₁₈₈

C₈

yes

characteristic

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×Dic₉₄

C₈

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

#10625324

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×C₈

yes

characteristic

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

C₂²⋊D₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

C₂²⋊C₈

yes

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

#2113

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₄₇

#504

yes

—

D₄₇

—

C₂×#131

—

C₂×M₃₂

D₄₇

yes

characteristic, complemented

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₄₇

#2113

yes

characteristic, complemented, Sylow

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

D₁₈₈

yes

—

C₂×C₈

C₂²⋊D₄₇

yes

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂³

C₈×D₄₇

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₈×D₄₇

yes

characteristic

107

C₂×C₄

#10625324

yes

—

108

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

109

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

110

C₈

—

111

C₈

(C₂×D₄₇)⋊C₄

yes

—

112

C₈

C₂×D₁₈₈

yes

characteristic

113

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

(C₂×D₄₇)⋊C₈

yes

—

118

C₂²

C₂×C₈×D₄₇

yes

characteristic

119

C₄

—

120

C₄

(C₂×D₄₇)⋊C₈

yes

—

121

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

122

C₄

C₂×#10625324

yes

characteristic

123

C₂

—

124

C₂

—

188

—

125

C₂

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

126

C₂

#15689541

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₈
Fitting	C₂×M₃₂×C₄₇	C₂
hypercenter	C₂×M₃₂	D₄₇
hypocenter	C₄₇	#2113
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂²×C₈

Fitting

C₂×M₃₂×C₄₇

C₂

hypercenter

C₂×M₃₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
2. C₂²×C₄₇⋊C₁₆	C₂	semidirect
3. (C₂×D₄₇)⋊C₁₆	C₂	semidirect
4. C₂×M₃₂×C₄₇	C₂	semidirect
65. C₂×M₃₂	D₄₇	semidirect
68. C₄₇	#2113	semidirect

H ≅ G/N

type

2. C₂²×C₄₇⋊C₁₆

C₂

semidirect

3. (C₂×D₄₇)⋊C₁₆

C₂

semidirect

4. C₂×M₃₂×C₄₇

C₂

semidirect

65. C₂×M₃₂

D₄₇

semidirect

68. C₄₇

#2113

semidirect

Subgroups — #20245003

Conjugacy classes of subgroups

Complements