Group #20242680 — subgroups

Subgroups — #20242680

Order 6016.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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	#15689871	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689510	C₂	1	2	yes	maximal, complemented
3	#15688865	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688862	C₂	1	2	yes	maximal, complemented
5	C₄₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625335	—	2	2	no	—
7	C₂×#10625334	—	2	2	no	—
8	#13094012	C₂²	1	2	yes	—
9	#13094009	—	2	2	no	—
10	#13094002	—	2	2	no	—
11	#13093999	—	2	2	no	—
12	#13093935	C₂²	1	2	yes	—
13	#127×C₄₇	C₂²	1	1	yes	characteristic
14	#125×C₄₇	C₂²	1	1	yes	characteristic
15	#102×C₄₇	—	2	2	no	—
16	#97×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₄₇	—	2	2	no	—
18	C₂×D₄×C₄₇	—	2	1	no	—
19	C₂×D₁₈₈	—	2	2	no	—
20	C₂×D₁₈₈	D₄	1	2	yes	—
21	C₂×C₄×D₄₇	—	2	2	no	—
22	C₂×Dic₉₄	D₄	1	2	yes	—
23	C₂×C₈×C₄₇	—	2	1	no	—
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
26	C₄²×C₄₇	C₂³	1	1	yes	characteristic
27	#10625335	—	4	4	no	—
28	#10625334	—	4	4	no	—
29	(C₂×D₄₇)⋊C₄	—	2	2	no	—
30	(C₂×D₄₇)⋊C₄	—	2	2	no	—
31	(C₂×D₄₇)⋊C₄	—	2	2	no	—
32	Dic₄₇⋊C₄	—	2	2	no	—
33	C₂×C₄₇⋊C₈	—	2	2	no	—
34	C₂³×C₄₇	—	4	1	no	—
35	C₂²×D₄₇	—	2	2	no	—
36	D₄×C₄₇	—	4	2	no	—
37	D₄×C₄₇	—	4	2	no	—
38	D₄×C₄₇	—	4	2	no	—
39	C₂×C₄×C₄₇	—	2	2	no	—
40	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₇	—	2	2	no	—
43	D₁₈₈	—	4	2	no	—
44	D₁₈₈	—	8	2	no	—
45	C₄×D₄₇	—	8	2	no	—
46	Dic₉₄	—	4	2	no	—
47	C₈×C₄₇	—	4	1	no	—
48	C₄₇⋊C₈	—	2	4	no	—
49	C₂²×C₄₇	—	8	2	no	—
50	C₂²×C₄₇	—	8	1	no	—
51	C₂²×C₄₇	#120	1	1	yes	characteristic
52	C₂×D₄₇	—	4	2	no	—
53	C₂×D₄₇	—	4	2	no	—
54	C₂×D₄₇	—	4	2	no	—
55	C₄×C₄₇	—	2	2	no	—
56	C₄×C₄₇	—	2	1	no	—
57	C₄×C₄₇	—	4	2	no	—
58	Dic₄₇	—	4	2	no	—
59	#1656	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	—	16	1	no	—
61	C₂×C₄₇	#453	1	2	yes	—
62	C₂×C₄₇	#454	1	1	yes	characteristic
63	D₄₇	—	8	2	no	—
64	#562	—	47	1	no	—
65	#496	—	47	2	no	—
66	#490	D₄₇	1	1	yes	characteristic, complemented
67	#330	—	47	1	no	—
68	#329	—	47	2	no	—
69	C₄₇	#1656	1	1	yes	characteristic, complemented, Sylow
70	C₂×SD₁₆	—	94	2	no	—
71	C₂×D₈	—	94	2	no	—
72	#127	C₂×D₄₇	1	1	yes	characteristic
73	#125	C₂×D₄₇	1	1	yes	characteristic
74	#124	—	47	2	no	—
75	#123	—	94	2	no	—
76	C₂²⋊Q₈	—	94	2	no	—
77	#121	—	94	2	no	—
78	#102	—	2	2	no	—
79	#97	—	47	2	no	—
80	#97	C₂×D₄₇	1	1	yes	characteristic
81	C₂×Q₈	—	47	2	no	—
82	C₂×D₄	—	2	2	no	—
83	C₂×D₄	—	2	1	no	—
84	C₂×D₄	—	47	2	no	—
85	C₂×D₄	—	94	2	no	—
86	C₂²×C₄	—	94	2	no	—
87	SD₁₆	—	188	4	no	—
88	D₈	—	188	4	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	94	2	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	94	2	no	—
93	C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
94	C₂²⋊C₄	—	94	2	no	—
95	C₂²⋊C₄	—	94	2	no	—
96	C₂²⋊C₄	—	94	2	no	—
97	C₄²	C₂²×D₄₇	1	1	yes	characteristic
98	C₂³	—	4	1	no	—
99	C₂³	—	94	2	no	—
100	Q₈	—	188	2	no	—
101	D₄	—	4	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	376	2	no	—
105	D₄	—	188	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	94	2	no	—
108	C₂×C₄	—	376	2	no	—
109	C₂×C₄	D₄×D₄₇	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
111	C₈	—	4	1	no	—
112	C₈	—	94	4	no	—
113	C₂²	—	8	2	no	—
114	C₂²	—	8	1	no	—
115	C₂²	—	188	2	no	—
116	C₂²	—	188	2	no	—
117	C₂²	—	188	2	no	—
118	C₂²	#13093992	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	—	2	1	no	—
121	C₄	—	4	2	no	—
122	C₄	—	188	2	no	—
123	C₂	—	16	1	no	—
124	C₂	—	376	2	no	—
125	C₂	#15689289	1	2	yes	—
126	C₂	#15689295	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689871

C₂

yes

maximal, characteristic, complemented

#15689510

C₂

yes

maximal, complemented

#15688865

C₂

yes

maximal, characteristic, complemented

#15688862

C₂

yes

maximal, complemented

C₄₇×#490

C₂

yes

maximal, characteristic, complemented

C₂×#10625335

—

C₂×#10625334

—

#13094012

C₂²

yes

—

—

—

—

C₂²

yes

—

#127×C₄₇

C₂²

yes

characteristic

#125×C₄₇

C₂²

yes

characteristic

#102×C₄₇

—

#97×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

D₄

yes

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

D₄

yes

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625335

—

#10625334

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂²×D₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#120

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

#1656

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#453

yes

—

C₂×C₄₇

#454

yes

characteristic

D₄₇

—

#562

—

#496

—

#490

D₄₇

yes

characteristic, complemented

#330

—

#329

—

C₄₇

#1656

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

#127

C₂×D₄₇

yes

characteristic

#125

C₂×D₄₇

yes

characteristic

#124

—

#123

—

C₂²⋊Q₈

—

—

—

—

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

SD₁₆

—

188

—

D₈

—

188

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₄₇

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

C₂³

—

100

Q₈

—

188

—

101

D₄

—

102

D₄

—

103

D₄

—

104

D₄

—

376

—

105

D₄

—

188

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

376

—

109

C₂×C₄

D₄×D₄₇

yes

—

110

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

111

C₈

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

188

—

116

C₂²

—

188

—

117

C₂²

—

188

—

118

C₂²

#13093992

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

188

—

123

C₂

—

124

C₂

—

376

—

125

C₂

#15689289

yes

—

126

C₂

#15689295

yes

characteristic

	subgroup	G/H
center	C₂²	#13093992
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#490	C₂
socle	C₂²×C₄₇	#120
hypercenter	#490	D₄₇
hypocenter	C₄₇	#1656
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #490

subgroup

G/H

center

C₂²

#13093992

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#490

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #490

N	H ≅ G/N	type
1. #15689871	C₂	semidirect
2. #15689510	C₂	semidirect
3. #15688865	C₂	semidirect
4. #15688862	C₂	semidirect
5. C₄₇×#490	C₂	semidirect
66. #490	D₄₇	semidirect
69. C₄₇	#1656	semidirect

H ≅ G/N

type

1. #15689871

C₂

semidirect

2. #15689510

C₂

semidirect

3. #15688865

C₂

semidirect

4. #15688862

C₂

semidirect

5. C₄₇×#490

C₂

semidirect

66. #490

D₄₇

semidirect

69. C₄₇

#1656

semidirect

Subgroups — #20242680

Conjugacy classes of subgroups

Complements