Group #20244644 — subgroups

Subgroups — #20244644

Order 6016.

296 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 69 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×D₃₇₆	C₂	1	1	yes	maximal, characteristic
2	#15689127	C₂	1	2	yes	maximal, complemented
3	C₂×#13093940	C₂	1	2	yes	maximal, complemented
4	#15688888	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₈₈	C₂²	1	2	yes	—
7	C₂×D₃₇₆	—	2	4	no	—
8	C₂×D₃₇₆	—	2	2	no	—
9	C₂×#10625329	C₂²	1	2	yes	—
10	#13093944	—	2	4	no	—
11	#13093940	—	2	4	no	—
12	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	#117×C₄₇	C₂²	1	1	yes	characteristic
15	C₄⋊C₈×C₄₇	—	2	2	no	—
16	C₂³×D₄₇	—	2	2	no	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂×D₁₈₈	—	2	2	no	—
19	C₂×D₁₈₈	—	2	2	no	—
20	C₂×D₁₈₈	—	2	2	no	—
21	C₂×D₁₈₈	—	2	2	no	—
22	C₂×D₁₈₈	—	2	2	no	—
23	C₂×D₁₈₈	D₄	1	4	yes	—
24	M₁₆×C₄₇	—	2	2	no	—
25	C₂×C₈×C₄₇	—	2	2	no	—
26	C₂×C₈×C₄₇	—	2	1	no	—
27	C₂×C₈×C₄₇	D₄	1	2	yes	—
28	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
29	C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₄²×C₄₇	—	2	1	no	—
31	#10625329	—	2	2	no	—
32	#10625329	—	2	2	no	—
33	C₂×C₄₇⋊C₈	—	2	2	no	—
34	D₃₇₆	—	2	8	no	—
35	C₂³×C₄₇	#41	1	1	yes	characteristic
36	C₂²×D₄₇	—	2	4	no	—
37	C₂²×D₄₇	—	4	2	no	—
38	C₂²×D₄₇	—	4	2	no	—
39	C₂²×D₄₇	—	8	4	no	—
40	C₂×C₄×C₄₇	—	2	2	no	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₇	#41	1	2	yes	—
45	D₁₈₈	—	2	4	no	—
46	D₁₈₈	—	2	4	no	—
47	D₁₈₈	—	4	2	no	—
48	D₁₈₈	—	4	2	no	—
49	C₈×C₄₇	—	2	2	no	—
50	C₈×C₄₇	—	4	1	no	—
51	C₄₇⋊C₈	—	4	2	no	—
52	C₂²×C₄₇	—	2	2	no	—
53	C₂²×C₄₇	#121	1	1	yes	characteristic
54	C₂²×C₄₇	#123	1	2	yes	—
55	C₂×D₄₇	—	4	4	no	—
56	C₂×D₄₇	—	8	4	no	—
57	C₂×D₄₇	—	8	4	no	—
58	C₂×D₄₇	—	8	4	no	—
59	C₄×C₄₇	—	4	2	no	—
60	C₄×C₄₇	#120	1	1	yes	characteristic
61	C₄×C₄₇	#121	1	2	yes	—
62	C₄×C₄₇	#124	1	1	yes	characteristic
63	#2045	—	47	1	no	maximal, Sylow
64	C₂×C₄₇	—	2	2	no	—
65	C₂×C₄₇	#394	1	1	yes	characteristic
66	C₂×C₄₇	#472	1	2	yes	—
67	D₄₇	—	8	4	no	—
68	C₂²×D₈	—	47	1	no	—
69	#424	D₄₇	1	1	yes	characteristic, complemented
70	#418	—	47	2	no	—
71	C₂×#100	—	47	2	no	—
72	#341	—	47	1	no	—
73	C₄₇	#2045	1	1	yes	characteristic, complemented, Sylow
74	C₂²×D₄	—	47	2	no	—
75	C₂×D₈	—	94	4	no	—
76	C₂×D₈	—	94	2	no	—
77	C₂×M₁₆	—	47	2	no	—
78	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
79	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
80	#117	C₂×D₄₇	1	1	yes	characteristic
81	C₄⋊C₈	—	2	2	no	—
82	#102	—	94	4	no	—
83	#100	—	94	4	no	—
84	C₂⁴	—	94	2	no	—
85	C₂×D₄	—	47	4	no	—
86	C₂×D₄	—	94	2	no	—
87	C₂×D₄	—	94	2	no	—
88	C₂×D₄	—	94	2	no	—
89	C₂×D₄	—	94	2	no	—
90	C₂×D₄	—	94	2	no	—
91	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
92	D₈	—	94	8	no	—
93	M₁₆	—	2	2	no	—
94	M₁₆	—	94	2	no	—
95	M₁₆	—	94	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	94	2	no	—
99	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
100	C₄⋊C₄	D₁₈₈	1	2	yes	—
101	C₂²⋊C₄	—	2	1	no	—
102	C₄²	—	2	1	no	—
103	C₂³	—	94	4	no	—
104	C₂³	—	376	4	no	—
105	C₂³	—	188	2	no	—
106	C₂³	—	188	2	no	—
107	C₂³	#10625350	1	1	yes	characteristic
108	D₄	—	94	4	no	—
109	D₄	—	94	4	no	—
110	D₄	—	188	2	no	—
111	D₄	—	188	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
114	C₂×C₄	D₄×D₄₇	1	2	yes	—
115	C₂×C₄	#10625354	1	2	yes	—
116	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	4	1	no	—
119	C₈	—	188	2	no	—
120	C₂²	—	2	2	no	—
121	C₂²	—	376	4	no	—
122	C₂²	—	376	4	no	—
123	C₂²	—	376	4	no	—
124	C₂²	—	188	4	no	—
125	C₂²	#13093998	1	1	yes	characteristic
126	C₂²	#13094009	1	2	yes	—
127	C₄	—	4	2	no	—
128	C₄	#13093992	1	1	yes	characteristic
129	C₄	#13093999	1	2	yes	—
130	C₄	#13094013	1	1	yes	characteristic
131	C₂	—	2	2	no	—
132	C₂	—	376	4	no	—
133	C₂	#15689040	1	1	yes	characteristic
134	C₂	#15689393	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₃₇₆

C₂

yes

maximal, characteristic

#15689127

C₂

yes

maximal, complemented

C₂×#13093940

C₂

yes

maximal, complemented

#15688888

C₂

yes

maximal, characteristic, complemented

C₄₇×#424

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×#10625329

C₂²

yes

—

#13093944

—

#13093940

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

D₄

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

D₄

yes

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

D₃₇₆

—

C₂³×C₄₇

#41

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₂²×C₄₇

#123

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#120

yes

characteristic

C₄×C₄₇

#121

yes

—

C₄×C₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

#394

yes

characteristic

C₂×C₄₇

#472

yes

—

D₄₇

—

C₂²×D₈

—

#424

D₄₇

yes

characteristic, complemented

#418

—

C₂×#100

—

#341

—

C₄₇

#2045

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

#102

—

#100

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

—

100

C₄⋊C₄

D₁₈₈

yes

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₂³

—

104

C₂³

—

376

—

105

C₂³

—

188

—

106

C₂³

—

188

—

107

C₂³

#10625350

yes

characteristic

108

D₄

—

109

D₄

—

110

D₄

—

188

—

111

D₄

—

188

—

112

C₂×C₄

—

113

C₂×C₄

C₂×D₁₈₈

yes

characteristic

114

C₂×C₄

D₄×D₄₇

yes

—

115

C₂×C₄

#10625354

yes

—

116

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

188

—

120

C₂²

—

121

C₂²

—

376

—

122

C₂²

—

376

—

123

C₂²

—

376

—

124

C₂²

—

188

—

125

C₂²

#13093998

yes

characteristic

126

C₂²

#13094009

yes

—

127

C₄

—

128

C₄

#13093992

yes

characteristic

129

C₄

#13093999

yes

—

130

C₄

#13094013

yes

characteristic

131

C₂

—

132

C₂

—

376

—

133

C₂

#15689040

yes

characteristic

134

C₂

#15689393

yes

—

	subgroup	G/H
center	C₂²	#13093998
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#424	C₂
socle	C₂²×C₄₇	#121
hypercenter	#424	D₄₇
hypocenter	C₄₇	#2045
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#13093998

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#424

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
2. #15689127	C₂	semidirect
3. C₂×#13093940	C₂	semidirect
4. #15688888	C₂	semidirect
5. C₄₇×#424	C₂	semidirect
69. #424	D₄₇	semidirect
73. C₄₇	#2045	semidirect

H ≅ G/N

type

2. #15689127

C₂

semidirect

3. C₂×#13093940

C₂

semidirect

4. #15688888

C₂

semidirect

5. C₄₇×#424

C₂

semidirect

69. #424

D₄₇

semidirect

73. C₄₇

#2045

semidirect

Subgroups — #20244644

Conjugacy classes of subgroups

Complements