Group #20244211 — subgroups

Subgroups — #20244211

Order 6016.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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×#13094021	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093944	C₂	1	4	yes	maximal, complemented
3	C₂×#13093935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₈₈	—	2	2	no	—
6	C₂²×D₁₈₈	C₂²	1	2	yes	—
7	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
8	#13094021	—	2	2	no	—
9	#13094021	C₄	1	4	yes	complemented
10	#13093944	—	2	8	no	—
11	#13093935	—	2	2	no	—
12	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
13	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	#95×C₄₇	—	2	2	no	—
15	C₂³×D₄₇	—	2	2	no	—
16	C₂²×C₄×C₄₇	—	2	2	no	—
17	C₂²×C₄×C₄₇	D₄	1	2	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×D₁₈₈	—	2	4	no	—
20	C₂×D₁₈₈	—	2	4	no	—
21	C₂×D₁₈₈	—	2	8	no	—
22	C₂×D₁₈₈	—	2	2	no	—
23	C₂×D₁₈₈	—	4	8	no	—
24	C₂×D₁₈₈	C₂×C₄	1	4	yes	—
25	C₄⋊C₄×C₄₇	—	2	4	no	—
26	C₄²×C₄₇	C₂×C₄	1	2	yes	—
27	C₄²×C₄₇	D₄	1	2	yes	—
28	C₂×C₄₇⋊C₈	—	2	2	no	—
29	C₂×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄₇⋊C₈	D₄	1	4	yes	complemented
31	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₂²×D₄₇	—	2	4	no	—
33	C₂²×D₄₇	—	4	2	no	—
34	C₂²×D₄₇	—	4	2	no	—
35	C₂²×D₄₇	—	4	8	no	—
36	C₂×C₄×C₄₇	—	2	4	no	—
37	C₂×C₄×C₄₇	—	4	2	no	—
38	C₂×C₄×C₄₇	—	4	4	no	—
39	C₂×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
40	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₇	#41	1	2	yes	—
44	D₁₈₈	—	2	8	no	—
45	D₁₈₈	—	4	16	no	—
46	D₁₈₈	—	4	4	no	—
47	C₄₇⋊C₈	—	2	4	no	—
48	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄₇	#124	1	1	yes	characteristic
50	C₂²×C₄₇	#127	1	1	yes	characteristic
51	C₂²×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
52	C₂×D₄₇	—	4	4	no	—
53	C₂×D₄₇	—	4	8	no	—
54	C₂×D₄₇	—	8	4	no	—
55	C₂×D₄₇	—	8	4	no	—
56	C₄×C₄₇	—	2	4	no	—
57	C₄×C₄₇	—	8	2	no	—
58	C₄×C₄₇	C₄×D₄	1	2	yes	—
59	C₄×C₄₇	#121	1	2	yes	—
60	#1961	—	47	1	no	maximal, Sylow
61	C₂×C₄₇	#390	1	1	yes	characteristic
62	C₂×C₄₇	#418	1	2	yes	—
63	C₂×C₄₇	#490	1	2	yes	—
64	C₂×C₄₇	#496	1	2	yes	—
65	D₄₇	—	8	4	no	—
66	C₂×#127	—	47	1	no	—
67	C₂×#102	—	47	4	no	—
68	C₂×#97	—	47	1	no	—
69	#382	D₄₇	1	1	yes	characteristic, complemented
70	C₄₇	#1961	1	1	yes	characteristic, complemented, Sylow
71	C₂²×D₄	—	47	2	no	—
72	C₂²×D₄	—	94	2	no	—
73	C₂²×C₈	—	47	2	no	—
74	#127	—	47	4	no	—
75	#127	—	94	2	no	—
76	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
77	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
78	#102	—	94	8	no	—
79	#97	—	94	2	no	—
80	#95	—	2	2	no	—
81	C₂⁴	—	94	2	no	—
82	C₂×D₄	—	47	4	no	—
83	C₂×D₄	—	94	8	no	—
84	C₂×D₄	—	94	2	no	—
85	C₂×D₄	—	94	4	no	—
86	C₂×D₄	—	94	4	no	—
87	C₂×D₄	—	188	8	no	—
88	C₂²×C₄	—	2	2	no	—
89	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
91	C₂×C₈	—	47	4	no	—
92	C₂×C₈	—	94	2	no	—
93	C₂×C₈	—	94	2	no	—
94	C₄⋊C₄	—	2	4	no	—
95	C₄²	C₄×D₄₇	1	2	yes	—
96	C₄²	D₁₈₈	1	2	yes	—
97	C₂³	—	94	4	no	—
98	C₂³	—	188	2	no	—
99	C₂³	—	188	2	no	—
100	C₂³	—	188	8	no	—
101	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
102	D₄	—	94	8	no	—
103	D₄	—	188	16	no	—
104	D₄	—	188	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	4	4	no	—
108	C₂×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
109	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
110	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
111	C₂×C₄	D₄×D₄₇	1	2	yes	—
112	C₂×C₄	#10625354	1	2	yes	—
113	C₈	—	94	4	no	—
114	C₂²	—	376	4	no	—
115	C₂²	—	376	4	no	—
116	C₂²	—	188	4	no	—
117	C₂²	—	188	8	no	—
118	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
119	C₂²	#13094013	1	1	yes	characteristic
120	C₂²	#13094020	1	1	yes	characteristic
121	C₂²	#13094049	1	4	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	8	2	no	—
124	C₄	#13093986	1	2	yes	—
125	C₄	#13093999	1	2	yes	—
126	C₂	—	376	4	no	—
127	C₂	#15689024	1	1	yes	characteristic
128	C₂	#15689127	1	2	yes	—
129	C₂	#15689489	1	2	yes	—
130	C₂	#15689513	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094021

C₂

yes

maximal, characteristic

C₂×#13093944

C₂

yes

maximal, complemented

C₂×#13093935

C₂

yes

maximal, characteristic, complemented

C₄₇×#382

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

—

C₂²×D₁₈₈

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

—

#13094021

—

#13094021

C₄

yes

complemented

#13093944

—

#13093935

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂×C₄

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

complemented

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

—

C₄×C₄₇

#121

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#490

yes

—

C₂×C₄₇

#496

yes

—

D₄₇

—

C₂×#127

—

C₂×#102

—

C₂×#97

—

#382

D₄₇

yes

characteristic, complemented

C₄₇

#1961

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

C₄×D₄₇

yes

—

C₄²

D₁₈₈

yes

—

C₂³

—

C₂³

—

188

—

C₂³

—

188

—

100

C₂³

—

188

—

101

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

102

D₄

—

103

D₄

—

188

—

104

D₄

—

188

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

109

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

110

C₂×C₄

C₂×D₁₈₈

yes

characteristic

111

C₂×C₄

D₄×D₄₇

yes

—

112

C₂×C₄

#10625354

yes

—

113

C₈

—

114

C₂²

—

376

—

115

C₂²

—

376

—

116

C₂²

—

188

—

117

C₂²

—

188

—

118

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

119

C₂²

#13094013

yes

characteristic

120

C₂²

#13094020

yes

characteristic

121

C₂²

#13094049

yes

—

122

C₄

—

123

C₄

—

124

C₄

#13093986

yes

—

125

C₄

#13093999

yes

—

126

C₂

—

376

—

127

C₂

#15689024

yes

characteristic

128

C₂

#15689127

yes

—

129

C₂

#15689489

yes

—

130

C₂

#15689513

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#382	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#382	D₄₇
hypocenter	C₄₇	#1961
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#382

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
2. C₂×#13093944	C₂	semidirect
3. C₂×#13093935	C₂	semidirect
4. C₄₇×#382	C₂	semidirect
9. #13094021	C₄	semidirect
30. C₂×C₄₇⋊C₈	D₄	semidirect
69. #382	D₄₇	semidirect
70. C₄₇	#1961	semidirect

H ≅ G/N

type

2. C₂×#13093944

C₂

semidirect

3. C₂×#13093935

C₂

semidirect

4. C₄₇×#382

C₂

semidirect

9. #13094021

C₄

semidirect

30. C₂×C₄₇⋊C₈

D₄

semidirect

69. #382

D₄₇

semidirect

70. C₄₇

#1961

semidirect

Subgroups — #20244211

Conjugacy classes of subgroups

Complements