Group #20253901 — subgroups

Subgroups — #20253901

Order 6016.

356 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 141 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	#15689679	C₂	1	2	yes	maximal
2	#15689527	C₂	1	2	yes	maximal, complemented
3	#15689525	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689522	C₂	1	2	yes	maximal, complemented
5	#15689520	C₂	1	2	yes	maximal, complemented
6	#15689160	C₂	1	2	yes	maximal
7	#15689158	C₂	1	2	yes	maximal
8	C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
12	#13094023	C₂²	1	4	yes	—
13	#13094016	C₂²	1	2	yes	—
14	#13094002	—	2	4	no	—
15	#13093989	—	2	4	no	—
16	#13093982	C₂²	1	4	yes	—
17	C₄²×D₄₇	C₂²	1	1	yes	characteristic
18	#13093958	C₂²	1	2	yes	—
19	#13093957	C₂²	1	4	yes	—
20	#13093956	C₂²	1	2	yes	—
21	#13093955	C₂²	1	4	yes	—
22	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#125×C₄₇	C₂²	1	2	yes	—
26	#107×C₄₇	C₂²	1	2	yes	—
27	#106×C₄₇	C₂²	1	2	yes	—
28	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄₇	D₄	1	2	yes	—
30	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
31	C₂×Dic₉₄	—	2	4	no	—
32	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₄₇	—	2	4	no	—
35	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
36	C₄²×C₄₇	C₂³	1	1	yes	characteristic
37	(C₂×D₄₇)⋊C₄	—	2	4	no	—
38	C₄⋊Dic₄₇	C₂³	1	4	yes	—
39	Dic₄₇⋊C₄	—	2	4	no	—
40	Dic₄₇⋊C₄	—	2	4	no	—
41	C₄×Dic₄₇	—	2	4	no	—
42	C₄×Dic₄₇	D₄	1	2	yes	—
43	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
44	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₈×D₄₇	Q₈	1	4	yes	complemented
47	C₈×D₄₇	Q₈	1	4	yes	complemented
48	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	—	2	4	no	—
50	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
52	C₂×Dic₄₇	—	2	4	no	—
53	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
55	C₄×D₄₇	—	2	4	no	—
56	C₄×D₄₇	C₂×Q₈	1	2	yes	—
57	C₄×D₄₇	C₂×Q₈	1	2	yes	—
58	Dic₉₄	—	4	8	no	—
59	C₈×C₄₇	C₂×Q₈	1	2	yes	—
60	C₈×C₄₇	C₂×Q₈	1	2	yes	—
61	C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
62	C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
63	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
64	C₂×D₄₇	—	2	2	no	—
65	C₂×D₄₇	C₄⋊Q₈	1	2	yes	—
66	C₄×C₄₇	—	2	2	no	—
67	C₄×C₄₇	—	4	4	no	—
68	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
69	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
70	Dic₄₇	—	4	4	no	—
71	Dic₄₇	C₄⋊Q₈	1	2	yes	—
72	Dic₄₇	#135	1	4	yes	—
73	#3160	—	47	1	no	maximal, Sylow
74	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄₇	C₂×#135	1	2	yes	—
76	D₄₇	—	2	2	no	—
77	#533	—	47	2	no	—
78	#500	—	47	2	no	—
79	#499	—	47	2	no	—
80	#499	—	47	1	no	—
81	#499	D₄₇	1	1	yes	characteristic, complemented
82	#498	—	47	2	no	—
83	#427	—	47	2	no	—
84	#427	—	47	2	no	—
85	C₂×C₄×C₈	—	47	1	no	—
86	C₄₇	#3160	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₈	—	47	1	no	—
88	C₂²×C₈	—	47	1	no	—
89	C₄⋊Q₈	—	47	4	no	—
90	#125	—	47	2	no	—
91	#125	C₂×D₄₇	1	2	yes	—
92	C₂²⋊Q₈	—	94	4	no	—
93	C₄×Q₈	—	94	4	no	—
94	#117	—	47	4	no	—
95	C₂×C₄²	—	47	1	no	—
96	#107	—	47	2	no	—
97	#107	—	47	4	no	—
98	#107	C₂×D₄₇	1	2	yes	—
99	#106	—	47	2	no	—
100	#106	—	47	4	no	—
101	#106	C₂×D₄₇	1	2	yes	—
102	C₄×C₈	—	47	1	no	—
103	C₄×C₈	—	47	1	no	—
104	C₄×C₈	—	47	1	no	—
105	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
106	C₂×Q₈	—	94	4	no	—
107	C₂²×C₄	—	47	1	no	—
108	C₂²×C₄	—	47	2	no	—
109	C₂×C₈	—	47	1	no	—
110	C₂×C₈	—	47	1	no	—
111	C₂×C₈	—	47	4	no	—
112	C₂×C₈	—	47	4	no	—
113	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
114	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
115	C₄⋊C₄	—	2	4	no	—
116	C₄⋊C₄	—	47	4	no	—
117	C₄⋊C₄	—	94	4	no	—
118	C₄⋊C₄	—	94	4	no	—
119	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
120	C₂²⋊C₄	—	94	4	no	—
121	C₄²	—	47	2	no	—
122	C₄²	—	47	1	no	—
123	C₄²	—	94	4	no	—
124	C₄²	C₂²×D₄₇	1	1	yes	characteristic
125	C₂³	—	47	1	no	—
126	Q₈	—	188	8	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	47	1	no	—
129	C₂×C₄	—	47	2	no	—
130	C₂×C₄	—	47	2	no	—
131	C₂×C₄	—	47	2	no	—
132	C₂×C₄	—	94	4	no	—
133	C₂×C₄	—	94	4	no	—
134	C₂×C₄	D₄×D₄₇	1	2	yes	—
135	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
136	C₈	—	47	2	no	—
137	C₈	—	47	2	no	—
138	C₈	Q₈×D₄₇	1	2	yes	—
139	C₈	Q₈×D₄₇	1	2	yes	—
140	C₂²	—	47	2	no	—
141	C₂²	—	94	2	no	—
142	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
143	C₄	—	2	2	no	—
144	C₄	—	4	4	no	—
145	C₄	—	47	4	no	—
146	C₄	—	47	2	no	—
147	C₄	—	188	4	no	—
148	C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
149	C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
150	C₂	—	94	2	no	—
151	C₂	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
152	C₂	#135×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689679

C₂

yes

maximal

#15689527

C₂

yes

maximal, complemented

#15689525

C₂

yes

maximal, characteristic, complemented

#15689522

C₂

yes

maximal, complemented

#15689520

C₂

yes

maximal, complemented

#15689160

C₂

yes

maximal

#15689158

C₂

yes

maximal

C₄×C₈×D₄₇

C₂

yes

maximal, characteristic

C₄₇×#499

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

C₂²

yes

characteristic

C₂×C₈×D₄₇

C₂²

yes

characteristic

#13094023

C₂²

yes

—

#13094016

C₂²

yes

—

#13094002

—

#13093989

—

#13093982

C₂²

yes

—

C₄²×D₄₇

C₂²

yes

characteristic

#13093958

C₂²

yes

—

#13093957

C₂²

yes

—

#13093956

C₂²

yes

—

#13093955

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

#125×C₄₇

C₂²

yes

—

#107×C₄₇

C₂²

yes

—

#106×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

characteristic

C₈×D₄₇

Q₈

yes

complemented

C₈×D₄₇

Q₈

yes

complemented

C₂²×D₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

C₂×D₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

C₂×Q₈

yes

—

C₄×D₄₇

C₂×Q₈

yes

—

Dic₉₄

—

C₈×C₄₇

C₂×Q₈

yes

—

C₈×C₄₇

C₂×Q₈

yes

—

C₄₇⋊C₈

C₂×Q₈

yes

—

C₄₇⋊C₈

C₂×Q₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

C₄⋊Q₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²×Q₈

yes

characteristic

C₄×C₄₇

C₂²×Q₈

yes

characteristic

Dic₄₇

—

Dic₄₇

C₄⋊Q₈

yes

—

Dic₄₇

#135

yes

—

#3160

—

maximal, Sylow

C₂×C₄₇

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₇

C₂×#135

yes

—

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

#498

—

#427

—

#427

—

C₂×C₄×C₈

—

C₄₇

#3160

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₄₇

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#107

—

#107

—

#107

C₂×D₄₇

yes

—

#106

—

100

#106

—

101

#106

C₂×D₄₇

yes

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

C₂×D₄₇

yes

characteristic

106

C₂×Q₈

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₄₇

yes

characteristic

114

C₂×C₈

C₂²×D₄₇

yes

characteristic

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

C₂²×D₄₇

yes

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₄²

C₂²×D₄₇

yes

characteristic

125

C₂³

—

126

Q₈

—

188

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

D₄×D₄₇

yes

—

135

C₂×C₄

C₂³×D₄₇

yes

characteristic

136

C₈

—

137

C₈

—

138

C₈

Q₈×D₄₇

yes

—

139

C₈

Q₈×D₄₇

yes

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₂×D₄×D₄₇

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

188

—

148

C₄

C₂×Q₈×D₄₇

yes

characteristic

149

C₄

C₂×Q₈×D₄₇

yes

characteristic

150

C₂

—

151

C₂

C₄⋊Q₈×D₄₇

yes

characteristic

152

C₂

#135×D₄₇

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#499	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#499	D₄₇
hypocenter	C₄₇	#3160
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #499

subgroup

G/H

center

C₂²

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#499

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #499

N	H ≅ G/N	type
2. #15689527	C₂	semidirect
3. #15689525	C₂	semidirect
4. #15689522	C₂	semidirect
5. #15689520	C₂	semidirect
9. C₄₇×#499	C₂	semidirect
46. C₈×D₄₇	Q₈	semidirect
47. C₈×D₄₇	Q₈	semidirect
81. #499	D₄₇	semidirect
86. C₄₇	#3160	semidirect

H ≅ G/N

type

2. #15689527

C₂

semidirect

3. #15689525

C₂

semidirect

4. #15689522

C₂

semidirect

5. #15689520

C₂

semidirect

9. C₄₇×#499

C₂

semidirect

46. C₈×D₄₇

Q₈

semidirect

47. C₈×D₄₇

Q₈

semidirect

81. #499

D₄₇

semidirect

86. C₄₇

#3160

semidirect

Subgroups — #20253901

Conjugacy classes of subgroups

Complements