Group #20243276 — subgroups

Subgroups — #20243276

Order 6016.

280 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13093955	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal
4	#15688886	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#340	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄×Dic₄₇	—	2	2	no	—
9	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	#13093955	C₄	1	8	yes	complemented
11	C₈×Dic₄₇	C₄	1	4	yes	complemented
12	C₄₇⋊#95	—	2	2	no	—
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₇	—	2	2	no	—
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	2	2	no	—
18	C₂²×Dic₄₇	D₄	1	1	yes	characteristic
19	C₂²×Dic₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	—	2	2	no	—
21	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
22	C₄⋊C₄×C₄₇	—	2	2	no	—
23	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
26	C₄×Dic₄₇	—	4	4	no	—
27	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
28	C₄×Dic₄₇	Q₈	1	2	yes	—
29	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
31	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	—	2	4	no	—
33	C₂×C₄×C₄₇	—	4	2	no	—
34	C₂×C₄×C₄₇	—	4	2	no	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₄₇	#41	1	2	yes	—
39	C₂×Dic₄₇	—	2	1	no	—
40	C₂×Dic₄₇	—	2	1	no	—
41	C₂×Dic₄₇	—	2	4	no	—
42	C₂×Dic₄₇	—	4	2	no	—
43	C₂×Dic₄₇	—	4	2	no	—
44	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
45	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
46	C₂×Dic₄₇	SD₁₆	1	4	yes	—
47	C₈×C₄₇	—	2	2	no	—
48	C₄₇⋊C₈	C₄²	1	4	yes	complemented
49	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄₇	C₄×D₄	1	2	yes	—
51	C₂²×C₄₇	C₂×SD₁₆	1	2	yes	—
52	C₂²×C₄₇	#135	1	1	yes	characteristic
53	C₂²×C₄₇	#135	1	1	yes	characteristic
54	C₄×C₄₇	—	4	4	no	—
55	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
56	C₄×C₄₇	#117	1	1	yes	characteristic
57	C₄×C₄₇	C₄×Q₈	1	2	yes	—
58	Dic₄₇	—	2	2	no	—
59	Dic₄₇	—	4	4	no	—
60	Dic₄₇	#106	1	4	yes	complemented
61	C₄×#106	—	47	1	no	maximal, Sylow
62	C₂×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄₇	C₂×#106	1	1	yes	characteristic
64	C₂×C₄₇	#427	1	1	yes	characteristic
65	C₂×C₄₇	C₄×SD₁₆	1	2	yes	—
66	C₂×C₄₇	C₄×SD₁₆	1	2	yes	—
67	C₂×#106	—	47	2	no	—
68	C₂×C₄×C₈	—	47	1	no	—
69	C₄×C₄⋊C₄	—	47	2	no	—
70	#340	—	47	1	no	—
71	#340	D₄₇	1	1	yes	characteristic
72	C₄₇	C₄×#106	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₈	—	47	1	no	—
74	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	47	2	no	—
76	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
77	C₂×C₄²	—	47	1	no	—
78	C₂×C₄²	—	94	2	no	—
79	#106	—	47	8	no	—
80	C₄×C₈	—	47	4	no	—
81	#95	—	94	2	no	—
82	C₂²×C₄	—	2	2	no	—
83	C₂²×C₄	—	47	1	no	—
84	C₂²×C₄	—	47	1	no	—
85	C₂²×C₄	—	94	2	no	—
86	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	47	2	no	—
89	C₂×C₈	—	47	4	no	—
90	C₂×C₈	C₄×D₄₇	1	2	yes	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	47	4	no	—
93	C₄⋊C₄	—	94	2	no	—
94	C₄⋊C₄	C₄×D₄₇	1	4	yes	—
95	C₄²	—	47	2	no	—
96	C₄²	—	47	2	no	—
97	C₄²	—	188	4	no	—
98	C₂³	D₄×D₄₇	1	1	yes	characteristic
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	47	2	no	—
103	C₂×C₄	—	47	4	no	—
104	C₂×C₄	—	47	2	no	—
105	C₂×C₄	—	94	1	no	—
106	C₂×C₄	—	94	1	no	—
107	C₂×C₄	—	94	4	no	—
108	C₂×C₄	—	188	2	no	—
109	C₂×C₄	—	188	2	no	—
110	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
111	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
112	C₂×C₄	#10625352	1	2	yes	—
113	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	47	4	no	—
116	C₂²	C₄⋊C₄×D₄₇	1	1	yes	characteristic
117	C₂²	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
118	C₂²	SD₁₆×D₄₇	1	2	yes	—
119	C₂²	#13094043	1	1	yes	characteristic
120	C₂²	#13094047	1	1	yes	characteristic
121	C₄	—	4	4	no	—
122	C₄	—	47	4	no	—
123	C₄	—	94	2	no	—
124	C₄	—	188	4	no	—
125	C₄	C₄²×D₄₇	1	1	yes	characteristic
126	C₄	#13093980	1	1	yes	characteristic
127	C₄	#13093989	1	2	yes	—
128	C₂	#15688974	1	1	yes	characteristic
129	C₂	#106×D₄₇	1	1	yes	characteristic
130	C₂	#15689160	1	1	yes	characteristic
131	C₂	#15689208	1	2	yes	—
132	C₂	#15689214	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093955

C₂

yes

maximal

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

C₄⋊C₄×Dic₄₇

C₂

yes

maximal

#15688886

C₂

yes

maximal, characteristic

C₄₇×#340

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093955

C₄

yes

complemented

C₈×Dic₄₇

C₄

yes

complemented

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

characteristic

C₂²×Dic₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

Q₈

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₂×Dic₄₇

SD₁₆

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

C₄²

yes

complemented

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

C₂×SD₁₆

yes

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₄×Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

yes

—

C₂×C₄₇

C₄×C₄⋊C₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₄×SD₁₆

yes

—

C₂×C₄₇

C₄×SD₁₆

yes

—

C₂×#106

—

C₂×C₄×C₈

—

C₄×C₄⋊C₄

—

#340

—

#340

D₄₇

yes

characteristic

C₄₇

C₄×#106

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

#106

—

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₄₇

yes

—

C₄²

—

C₄²

—

C₄²

—

188

—

C₂³

D₄×D₄₇

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

188

—

109

C₂×C₄

—

188

—

110

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

111

C₂×C₄

C₂×C₄×D₄₇

yes

—

112

C₂×C₄

#10625352

yes

—

113

C₂×C₄

Q₈×D₄₇

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

C₄⋊C₄×D₄₇

yes

characteristic

117

C₂²

(C₂²⋊D₄₇)⋊C₄

yes

—

118

C₂²

SD₁₆×D₄₇

yes

—

119

C₂²

#13094043

yes

characteristic

120

C₂²

#13094047

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

188

—

125

C₄

C₄²×D₄₇

yes

characteristic

126

C₄

#13093980

yes

characteristic

127

C₄

#13093989

yes

—

128

C₂

#15688974

yes

characteristic

129

C₂

#106×D₄₇

yes

characteristic

130

C₂

#15689160

yes

characteristic

131

C₂

#15689208

yes

—

132

C₂

#15689214

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₇
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#340	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#340	D₄₇
hypocenter	C₄₇	C₄×#106
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₄₇

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#340

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
10. #13093955	C₄	semidirect
11. C₈×Dic₄₇	C₄	semidirect
48. C₄₇⋊C₈	C₄²	semidirect
60. Dic₄₇	#106	semidirect
72. C₄₇	C₄×#106	semidirect

H ≅ G/N

type

10. #13093955

C₄

semidirect

11. C₈×Dic₄₇

C₄

semidirect

48. C₄₇⋊C₈

C₄²

semidirect

60. Dic₄₇

#106

semidirect

72. C₄₇

C₄×#106

semidirect

Subgroups — #20243276

Conjugacy classes of subgroups

Complements