Group #20244169 — subgroups

Subgroups — #20244169

Order 6016.

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

normal subgroups only

This group has 196 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	#15689165	C₂	1	2	yes	maximal
2	C₂×#13093956	C₂	1	1	yes	maximal, characteristic
3	#15689078	C₂	1	1	yes	maximal, characteristic
4	#15688891	C₂	1	2	yes	maximal
5	C₂×#108×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	1	yes	characteristic
7	#13093983	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	#13093958	—	2	2	no	—
10	#13093956	—	2	1	no	—
11	#13093956	—	2	1	no	—
12	#13093956	—	2	2	no	—
13	#13093934	—	2	1	no	—
14	C₈×Dic₄₇	—	2	1	no	—
15	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	#108×C₄₇	C₄	1	4	yes	complemented
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₇	—	2	2	no	—
20	M₁₆×C₄₇	—	2	2	no	—
21	M₁₆×C₄₇	C₂×C₄	1	4	yes	—
22	C₂×C₈×C₄₇	—	2	2	no	—
23	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
25	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
26	C₂×C₈×C₄₇	Q₈	1	2	yes	—
27	C₂²⋊Dic₄₇	—	2	1	no	—
28	C₄⋊Dic₄₇	—	2	2	no	—
29	C₄⋊Dic₄₇	—	2	2	no	—
30	C₄⋊Dic₄₇	D₄	1	2	yes	—
31	C₄×Dic₄₇	—	2	1	no	—
32	#10625329	—	2	1	no	—
33	#10625329	Q₈	1	2	yes	—
34	C₂×C₄₇⋊C₈	—	2	1	no	—
35	C₂³×C₄₇	#41	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
42	C₂×Dic₄₇	—	2	2	no	—
43	C₂×Dic₄₇	—	4	2	no	—
44	C₂×Dic₄₇	—	8	2	no	—
45	C₈×C₄₇	—	2	4	no	—
46	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
47	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
48	C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇	—	2	2	no	—
50	C₂²×C₄₇	C₄×Q₈	1	1	yes	characteristic
51	C₂²×C₄₇	#121	1	1	yes	characteristic
52	C₂²×C₄₇	#125	1	1	yes	characteristic
53	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
55	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
56	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
57	Dic₄₇	—	4	2	no	—
58	Dic₄₇	—	8	2	no	—
59	#1951	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	—	2	1	no	—
61	C₂×C₄₇	—	2	1	no	—
62	C₂×C₄₇	#389	1	1	yes	characteristic
63	C₂×C₄₇	#471	1	2	yes	—
64	C₂×#108	D₄₇	1	1	yes	characteristic
65	#428	—	47	2	no	—
66	C₂×#106	—	47	1	no	—
67	#405	—	47	1	no	—
68	#343	—	47	2	no	—
69	C₄₇	#1951	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	47	1	no	—
71	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
72	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
73	#117	—	47	1	no	—
74	C₂×C₄⋊C₄	—	47	2	no	—
75	#108	Dic₄₇	1	4	yes	complemented
76	#107	—	94	2	no	—
77	#106	—	94	2	no	—
78	#106	—	94	1	no	—
79	#106	—	94	1	no	—
80	#97	—	94	1	no	—
81	C₄×C₈	—	94	1	no	—
82	C₂²×C₄	—	94	2	no	—
83	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	47	2	no	—
86	M₁₆	—	94	1	no	—
87	M₁₆	C₂×Dic₄₇	1	4	yes	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	94	1	no	—
90	C₂×C₈	Dic₉₄	1	2	yes	—
91	C₂×C₈	D₁₈₈	1	1	yes	characteristic
92	C₂×C₈	D₁₈₈	1	1	yes	characteristic
93	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
94	C₄⋊C₄	—	47	2	no	—
95	C₄⋊C₄	—	94	2	no	—
96	C₄⋊C₄	—	94	2	no	—
97	C₂²⋊C₄	—	94	1	no	—
98	C₄²	—	94	1	no	—
99	C₂³	#10625354	1	1	yes	characteristic
100	C₂×C₄	—	94	2	no	—
101	C₂×C₄	—	376	2	no	—
102	C₂×C₄	—	188	2	no	—
103	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
104	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
105	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
106	C₂×C₄	#10625352	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
108	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
109	C₈	—	2	4	no	—
110	C₈	—	94	2	no	—
111	C₈	C₄⋊Dic₄₇	1	2	yes	—
112	C₈	C₄⋊Dic₄₇	1	2	yes	—
113	C₂²	—	2	2	no	—
114	C₂²	Q₈×Dic₄₇	1	1	yes	characteristic
115	C₂²	#13093999	1	1	yes	characteristic
116	C₂²	#13094015	1	1	yes	characteristic
117	C₄	—	376	2	no	—
118	C₄	—	188	2	no	—
119	C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
120	C₄	D₄×Dic₄₇	1	1	yes	characteristic
121	C₄	#13094004	1	1	yes	characteristic
122	C₄	#13094023	1	1	yes	characteristic
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	#15689022	1	1	yes	characteristic
126	C₂	#15689387	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689165

C₂

yes

maximal

C₂×#13093956

C₂

yes

maximal, characteristic

#15689078

C₂

yes

maximal, characteristic

#15688891

C₂

yes

maximal

C₂×#108×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

characteristic

#13093983

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

—

—

—

—

—

C₈×Dic₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#108×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

—

C₄×Dic₄₇

—

#10625329

—

#10625329

Q₈

yes

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×Q₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#1951

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#389

yes

characteristic

C₂×C₄₇

#471

yes

—

C₂×#108

D₄₇

yes

—

—

—

—

C₄₇

#1951

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#108

Dic₄₇

yes

—

—

—

—

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₄₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#10625354

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

376

—

102

C₂×C₄

—

188

—

103

C₂×C₄

C₂×Dic₉₄

yes

characteristic

104

C₂×C₄

C₂×D₁₈₈

yes

characteristic

105

C₂×C₄

D₄×D₄₇

yes

characteristic

106

C₂×C₄

#10625352

yes

characteristic

107

C₂×C₄

Q₈×D₄₇

yes

characteristic

108

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

C₄⋊Dic₄₇

yes

—

112

C₈

C₄⋊Dic₄₇

yes

—

113

C₂²

—

114

C₂²

Q₈×Dic₄₇

yes

characteristic

115

C₂²

#13093999

yes

characteristic

116

C₂²

#13094015

yes

characteristic

117

C₄

—

376

—

118

C₄

—

188

—

119

C₄

C₂×C₄⋊Dic₄₇

yes

characteristic

120

C₄

D₄×Dic₄₇

yes

characteristic

121

C₄

#13094004

yes

characteristic

122

C₄

#13094023

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

#15689022

yes

characteristic

126

C₂

#15689387

yes

—

	subgroup	G/H
center	C₂²	#13093999
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#108×C₄₇	C₂
socle	C₂²×C₄₇	#121
hypercenter	C₂×#108	D₄₇
hypocenter	C₄₇	#1951
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#13093999

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#108×C₄₇

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
17. #108×C₄₇	C₄	semidirect
69. C₄₇	#1951	semidirect
75. #108	Dic₄₇	semidirect

H ≅ G/N

type

17. #108×C₄₇

C₄

semidirect

69. C₄₇

#1951

semidirect

75. #108

Dic₄₇

semidirect

Subgroups — #20244169

Conjugacy classes of subgroups

Complements