Group #20244998 — subgroups

Subgroups — #20244998

Order 6016.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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	C₂×#13093964	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	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	#13093964	—	2	2	no	—
12	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	M₃₂×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	4	no	—
37	C₂²×D₄₇	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	M₁₆	1	2	yes	—
41	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₄₇	—	2	2	no	—
43	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
44	C₄×D₄₇	—	2	4	no	—
45	C₄×D₄₇	—	2	2	no	—
46	C₄×D₄₇	—	2	2	no	—
47	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
48	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₄₇⋊C₈	—	2	2	no	—
51	C₂²×C₄₇	—	2	2	no	—
52	C₂²×C₄₇	C₂²⋊C₈	1	2	yes	—
53	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
54	C₂×D₄₇	—	2	8	no	—
55	C₂×D₄₇	—	2	2	no	—
56	C₂×D₄₇	—	2	2	no	—
57	C₂×D₄₇	M₃₂	1	4	yes	complemented
58	C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
59	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
61	Dic₄₇	—	2	2	no	—
62	#2112	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	—	2	2	no	—
64	C₂×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
65	C₂×C₄₇	C₂×M₃₂	1	2	yes	—
66	D₄₇	—	2	4	no	—
67	C₂³×C₈	—	47	1	no	—
68	C₂×M₃₂	—	47	1	no	—
69	C₂×M₃₂	D₄₇	1	1	yes	characteristic, complemented
70	C₂²⋊C₁₆	—	47	4	no	—
71	C₄₇	#2112	1	1	yes	characteristic, complemented, Sylow
72	C₂³×C₄	—	47	1	no	—
73	C₂²×C₈	—	47	1	no	—
74	C₂²×C₈	—	47	2	no	—
75	C₂²×C₈	—	47	2	no	—
76	C₂²×C₈	—	94	2	no	—
77	C₂²×C₈	—	94	2	no	—
78	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
79	M₃₂	—	2	2	no	—
80	M₃₂	—	94	2	no	—
81	C₂×C₁₆	—	47	2	no	—
82	C₂×C₁₆	C₂×D₄₇	1	2	yes	complemented
83	C₂⁴	—	47	1	no	—
84	C₂²×C₄	—	47	1	no	—
85	C₂²×C₄	—	47	2	no	—
86	C₂²×C₄	—	47	2	no	—
87	C₂²×C₄	—	94	2	no	—
88	C₂²×C₄	—	94	2	no	—
89	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
90	C₂×C₈	—	47	2	no	—
91	C₂×C₈	—	94	2	no	—
92	C₂×C₈	—	94	4	no	—
93	C₂×C₈	—	94	2	no	—
94	C₂×C₈	—	94	2	no	—
95	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
96	C₂×C₈	D₁₈₈	1	2	yes	—
97	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
98	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
99	C₁₆	—	2	2	no	—
100	C₁₆	—	94	2	no	—
101	C₂³	—	47	2	no	—
102	C₂³	—	94	4	no	—
103	C₂³	—	94	2	no	—
104	C₂³	C₈×D₄₇	1	1	yes	characteristic
105	C₂×C₄	—	47	2	no	—
106	C₂×C₄	—	94	2	no	—
107	C₂×C₄	—	94	4	no	—
108	C₂×C₄	—	94	2	no	—
109	C₂×C₄	—	94	2	no	—
110	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
111	C₂×C₄	#10625324	1	2	yes	—
112	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
113	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
114	C₈	—	94	2	no	—
115	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
116	C₈	C₂×D₁₈₈	1	1	yes	characteristic
117	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
118	C₂²	—	2	2	no	—
119	C₂²	—	47	4	no	—
120	C₂²	—	94	8	no	—
121	C₂²	—	94	2	no	—
122	C₂²	—	94	2	no	—
123	C₂²	(C₂×D₄₇)⋊C₈	1	2	yes	—
124	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
125	C₄	—	94	2	no	—
126	C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
127	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
128	C₄	C₂×#10625324	1	1	yes	characteristic
129	C₂	—	2	2	no	—
130	C₂	—	94	4	no	—
131	C₂	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
132	C₂	M₃₂×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₈×D₄₇

C₂

yes

maximal, characteristic

C₂×#13093964

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal, complemented

C₂×M₃₂×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

—

#13093964

—

C₂×C₄₇⋊C₁₆

C₂²

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×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

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×C₄₇

C₂²⋊C₈

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

M₃₂

yes

complemented

C₄×C₄₇

C₂²⋊C₈

yes

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

#2112

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₄₇

C₂×M₃₂

yes

—

D₄₇

—

C₂³×C₈

—

C₂×M₃₂

—

C₂×M₃₂

D₄₇

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₄₇

#2112

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

M₃₂

—

M₃₂

—

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

—

C₂×C₈

C₂²⋊D₄₇

yes

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₁₆

—

100

C₁₆

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

C₈×D₄₇

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₈×D₄₇

yes

characteristic

111

C₂×C₄

#10625324

yes

—

112

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

113

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

114

C₈

—

115

C₈

(C₂×D₄₇)⋊C₄

yes

—

116

C₈

C₂×D₁₈₈

yes

characteristic

117

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

(C₂×D₄₇)⋊C₈

yes

—

124

C₂²

C₂×C₈×D₄₇

yes

characteristic

125

C₄

—

126

C₄

(C₂×D₄₇)⋊C₈

yes

—

127

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

128

C₄

C₂×#10625324

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

132

C₂

M₃₂×D₄₇

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	#2112
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. C₂×#13093964	C₂	semidirect
3. (C₂×D₄₇)⋊C₁₆	C₂	semidirect
4. C₂×M₃₂×C₄₇	C₂	semidirect
12. C₂×C₄₇⋊C₁₆	C₂²	semidirect
15. C₂×C₁₆×C₄₇	C₂²	semidirect
57. C₂×D₄₇	M₃₂	semidirect
69. C₂×M₃₂	D₄₇	semidirect
71. C₄₇	#2112	semidirect
82. C₂×C₁₆	C₂×D₄₇	semidirect

H ≅ G/N

type

2. C₂×#13093964

C₂

semidirect

3. (C₂×D₄₇)⋊C₁₆

C₂

semidirect

4. C₂×M₃₂×C₄₇

C₂

semidirect

12. C₂×C₄₇⋊C₁₆

C₂²

semidirect

15. C₂×C₁₆×C₄₇

C₂²

semidirect

57. C₂×D₄₇

M₃₂

semidirect

69. C₂×M₃₂

D₄₇

semidirect

71. C₄₇

#2112

semidirect

82. C₂×C₁₆

C₂×D₄₇

semidirect

Subgroups — #20244998

Conjugacy classes of subgroups

Complements