Group #20244835 — subgroups

Subgroups — #20244835

Order 6016.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689125	C₂	1	2	yes	maximal
3	#15689089	C₂	1	1	yes	maximal, characteristic
4	#15688891	C₂	1	2	yes	maximal, complemented
5	C₄₇×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625350	C₂²	1	1	yes	characteristic
7	C₂×#10625329	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	#13093956	—	2	2	no	—
10	#13093949	—	2	2	no	—
11	#13093946	—	2	2	no	—
12	(C₂×D₄₇)⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂×C₂²⋊D₄₇	—	2	1	no	—
17	C₂²×Dic₄₇	—	2	2	no	—
18	#10625350	—	2	2	no	—
19	#10625350	—	2	2	no	—
20	C₂×D₁₈₈	D₄	1	1	yes	characteristic
21	C₂×C₄×D₄₇	—	2	1	no	—
22	C₂×Dic₉₄	D₄	1	1	yes	characteristic
23	M₁₆×C₄₇	—	2	2	no	—
24	M₁₆×C₄₇	—	2	2	no	—
25	C₂×C₈×C₄₇	—	2	2	no	—
26	C₂×C₈×C₄₇	—	2	2	no	—
27	C₂×C₈×C₄₇	D₄	1	2	yes	—
28	C₄⋊Dic₄₇	—	2	2	no	—
29	C₄⋊Dic₄₇	—	2	2	no	—
30	#10625329	—	2	2	no	—
31	C₂×C₄₇⋊C₈	—	2	1	no	—
32	C₂³×C₄₇	#41	1	1	yes	characteristic
33	C₂²×D₄₇	—	2	1	no	—
34	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	#41	1	2	yes	—
37	C₂×C₄×C₄₇	#41	1	2	yes	—
38	C₂²⋊D₄₇	—	4	2	no	—
39	C₂×Dic₄₇	—	2	1	no	—
40	C₂×Dic₄₇	—	4	2	no	—
41	C₂×Dic₄₇	—	8	2	no	—
42	D₁₈₈	—	2	2	no	—
43	C₄×D₄₇	—	4	1	no	—
44	C₄×D₄₇	—	4	1	no	—
45	Dic₉₄	—	2	2	no	—
46	C₈×C₄₇	—	2	2	no	—
47	C₈×C₄₇	—	4	2	no	—
48	C₄₇⋊C₈	—	4	1	no	—
49	C₂²×C₄₇	—	2	2	no	—
50	C₂²×C₄₇	#121	1	1	yes	characteristic
51	C₂²×C₄₇	#126	1	2	yes	—
52	C₂×D₄₇	—	4	1	no	—
53	C₂×D₄₇	—	4	2	no	—
54	C₄×C₄₇	#123	1	2	yes	—
55	C₄×C₄₇	#123	1	1	yes	characteristic
56	C₄×C₄₇	#124	1	1	yes	characteristic
57	Dic₄₇	—	4	1	no	—
58	Dic₄₇	—	8	2	no	—
59	#2079	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	—	2	2	no	—
61	C₂×C₄₇	#397	1	1	yes	characteristic
62	C₂×C₄₇	#471	1	2	yes	—
63	D₄₇	—	8	1	no	—
64	C₂×#106	—	47	1	no	—
65	#417	—	47	2	no	—
66	#408	—	47	1	no	—
67	#343	—	47	2	no	—
68	#341	D₄₇	1	1	yes	characteristic, complemented
69	C₄₇	#2079	1	1	yes	characteristic, complemented, Sylow
70	C₂×#41	—	47	1	no	—
71	C₂×M₁₆	—	47	1	no	—
72	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
73	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
74	C₂×C₄⋊C₄	—	47	2	no	—
75	#106	—	94	2	no	—
76	#103	—	94	2	no	—
77	#102	—	94	2	no	—
78	C₂²⋊C₈	—	94	2	no	—
79	#41	—	94	2	no	—
80	#41	—	94	2	no	—
81	C₂×Q₈	—	47	1	no	—
82	C₂×D₄	—	47	1	no	—
83	C₂×D₄	—	94	1	no	—
84	C₂²×C₄	—	94	1	no	—
85	C₂²×C₄	—	94	2	no	—
86	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
87	M₁₆	—	2	2	no	—
88	M₁₆	—	2	2	no	—
89	M₁₆	—	94	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	94	1	no	—
93	C₂×C₈	D₁₈₈	1	2	yes	—
94	C₄⋊C₄	—	94	2	no	—
95	C₄⋊C₄	—	94	2	no	—
96	C₂³	—	94	1	no	—
97	C₂³	#10625354	1	1	yes	characteristic
98	Q₈	—	94	2	no	—
99	D₄	—	94	2	no	—
100	D₄	—	188	2	no	—
101	C₂×C₄	—	94	1	no	—
102	C₂×C₄	—	376	2	no	—
103	C₂×C₄	—	188	2	no	—
104	C₂×C₄	—	188	1	no	—
105	C₂×C₄	—	188	1	no	—
106	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
107	C₂×C₄	#10625350	1	2	yes	—
108	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
109	C₂×C₄	#10625352	1	2	yes	—
110	C₈	—	2	2	no	—
111	C₈	—	4	2	no	—
112	C₈	—	188	1	no	—
113	C₂²	—	2	2	no	—
114	C₂²	—	188	1	no	—
115	C₂²	—	188	2	no	—
116	C₂²	#13093999	1	1	yes	characteristic
117	C₂²	#13094019	1	2	yes	—
118	C₄	—	376	2	no	—
119	C₄	—	188	1	no	—
120	C₄	#13094006	1	2	yes	—
121	C₄	#13094008	1	1	yes	characteristic
122	C₄	#13094012	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	376	1	no	—
125	C₂	#15689050	1	1	yes	characteristic
126	C₂	#15689387	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093956

C₂

yes

maximal, characteristic, complemented

#15689125

C₂

yes

maximal

#15689089

C₂

yes

maximal, characteristic

#15688891

C₂

yes

maximal, complemented

C₄₇×#341

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

#13093956

—

#13093949

—

#13093946

—

(C₂×D₄₇)⋊C₈

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

D₄

yes

characteristic

C₂×C₄×D₄₇

—

C₂×Dic₉₄

D₄

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#41

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₂²×C₄₇

#126

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

#123

yes

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

#2079

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#397

yes

characteristic

C₂×C₄₇

#471

yes

—

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2079

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

#106

—

#103

—

#102

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂³

—

C₂³

#10625354

yes

characteristic

Q₈

—

D₄

—

100

D₄

—

188

—

101

C₂×C₄

—

102

C₂×C₄

—

376

—

103

C₂×C₄

—

188

—

104

C₂×C₄

—

188

—

105

C₂×C₄

—

188

—

106

C₂×C₄

C₂×D₁₈₈

yes

characteristic

107

C₂×C₄

#10625350

yes

—

108

C₂×C₄

D₄×D₄₇

yes

characteristic

109

C₂×C₄

#10625352

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

188

—

113

C₂²

—

114

C₂²

—

188

—

115

C₂²

—

188

—

116

C₂²

#13093999

yes

characteristic

117

C₂²

#13094019

yes

—

118

C₄

—

376

—

119

C₄

—

188

—

120

C₄

#13094006

yes

—

121

C₄

#13094008

yes

characteristic

122

C₄

#13094012

yes

characteristic

123

C₂

—

124

C₂

—

376

—

125

C₂

#15689050

yes

characteristic

126

C₂

#15689387

yes

—

	subgroup	G/H
center	C₂²	#13093999
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#341	C₂
socle	C₂²×C₄₇	#121
hypercenter	#341	D₄₇
hypocenter	C₄₇	#2079
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#13093999

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#341

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
1. C₂×#13093956	C₂	semidirect
4. #15688891	C₂	semidirect
5. C₄₇×#341	C₂	semidirect
68. #341	D₄₇	semidirect
69. C₄₇	#2079	semidirect

H ≅ G/N

type

1. C₂×#13093956

C₂

semidirect

4. #15688891

C₂

semidirect

5. C₄₇×#341

C₂

semidirect

68. #341

D₄₇

semidirect

69. C₄₇

#2079

semidirect

Subgroups — #20244835

Conjugacy classes of subgroups

Complements