Group #20243515 — subgroups

Subgroups — #20243515

Order 6016.

248 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 133 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×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#15688993	C₂	1	1	yes	maximal, characteristic
3	#15688885	C₂	1	4	yes	maximal
4	C₄₇×#384	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₄×C₄₇⋊C₈	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
11	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
12	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
13	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	—	2	2	no	—
15	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₇	—	2	2	no	—
19	C₄⋊C₄×C₄₇	—	2	4	no	—
20	C₄⋊C₄×C₄₇	—	4	2	no	—
21	C₄⋊C₄×C₄₇	—	4	2	no	—
22	C₄²×C₄₇	C₂×C₄	1	2	yes	—
23	C₄²×C₄₇	Q₈	1	2	yes	—
24	C₄⋊Dic₄₇	—	2	4	no	—
25	C₄⋊Dic₄₇	—	4	2	no	—
26	C₄⋊Dic₄₇	—	4	2	no	—
27	C₂×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄₇⋊C₈	—	2	2	no	—
29	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
30	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	—	4	2	no	—
32	C₂×C₄×C₄₇	—	4	2	no	—
33	C₂×C₄×C₄₇	—	4	2	no	—
34	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₄₇	D₈	1	2	yes	—
37	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
38	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
39	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
40	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₄₇	#41	1	2	yes	—
43	C₂×C₄×C₄₇	#41	1	2	yes	—
44	C₂×Dic₄₇	—	4	2	no	—
45	C₂×Dic₄₇	—	4	2	no	—
46	C₂×Dic₄₇	—	4	2	no	—
47	C₄₇⋊C₈	—	2	4	no	—
48	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄₇	#124	1	1	yes	characteristic
50	C₂²×C₄₇	#124	1	1	yes	characteristic
51	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
52	C₂²×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
53	C₂²×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
54	C₂²×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
55	C₄×C₄₇	—	8	2	no	—
56	C₄×C₄₇	#106	1	4	yes	—
57	C₄×C₄₇	#107	1	4	yes	—
58	C₄×C₄₇	#117	1	2	yes	—
59	C₄×C₄₇	#125	1	2	yes	—
60	Dic₄₇	—	8	2	no	—
61	#1834	—	47	1	no	maximal, Sylow
62	C₂×C₄₇	#382	1	1	yes	characteristic
63	C₂×C₄₇	C₂×#106	1	1	yes	characteristic
64	C₂×C₄₇	C₂×#107	1	1	yes	characteristic
65	C₂×C₄₇	#486	1	1	yes	characteristic
66	C₂×C₄₇	#486	1	1	yes	characteristic
67	C₂×C₄₇	#487	1	1	yes	characteristic
68	C₂×C₄₇	#487	1	1	yes	characteristic
69	C₂×C₄×C₈	—	47	1	no	—
70	#384	—	47	1	no	—
71	#384	D₄₇	1	1	yes	characteristic
72	#340	—	47	4	no	—
73	C₄₇	#1834	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₈	—	47	2	no	—
75	C₂×C₄⋊C₄	—	2	1	no	—
76	C₂×C₄⋊C₄	—	2	1	no	—
77	C₂×C₄⋊C₄	—	47	2	no	—
78	C₂×C₄⋊C₄	—	94	1	no	—
79	C₂×C₄⋊C₄	—	94	1	no	—
80	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
81	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
82	C₄×C₈	—	47	4	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	94	2	no	—
85	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
86	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
87	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
88	C₂×C₈	—	47	4	no	—
89	C₂×C₈	—	94	2	no	—
90	C₂×C₈	—	94	2	no	—
91	C₄⋊C₄	—	2	4	no	—
92	C₄⋊C₄	—	4	2	no	—
93	C₄⋊C₄	—	4	2	no	—
94	C₄⋊C₄	—	94	4	no	—
95	C₄⋊C₄	—	188	2	no	—
96	C₄⋊C₄	—	188	2	no	—
97	C₄²	Dic₉₄	1	2	yes	—
98	C₄²	C₄×D₄₇	1	2	yes	—
99	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	—	188	2	no	—
104	C₂×C₄	—	188	2	no	—
105	C₂×C₄	—	188	2	no	—
106	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
107	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
108	C₂×C₄	#10625334	1	2	yes	—
109	C₂×C₄	#10625335	1	2	yes	—
110	C₂×C₄	#10625336	1	2	yes	—
111	C₂×C₄	#10625337	1	2	yes	—
112	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
113	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
114	C₂×C₄	#10625352	1	2	yes	—
115	C₂×C₄	#10625354	1	2	yes	—
116	C₈	—	94	4	no	—
117	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
118	C₂²	#13094011	1	1	yes	characteristic
119	C₂²	#13094013	1	1	yes	characteristic
120	C₂²	C₂×#10625334	1	1	yes	characteristic
121	C₂²	C₂×#10625336	1	1	yes	characteristic
122	C₂²	C₂×#10625335	1	1	yes	characteristic
123	C₂²	C₂×#10625337	1	1	yes	characteristic
124	C₄	—	8	2	no	—
125	C₄	—	376	2	no	—
126	C₄	#13093955	1	4	yes	—
127	C₄	#13093957	1	4	yes	—
128	C₄	#13093982	1	2	yes	—
129	C₄	#13094015	1	2	yes	—
130	C₂	#15688988	1	1	yes	characteristic
131	C₂	C₂×#13093955	1	1	yes	characteristic
132	C₂	C₂×#13093957	1	1	yes	characteristic
133	C₂	#15689469	1	1	yes	characteristic
134	C₂	#15689471	1	1	yes	characteristic
135	C₂	#15689473	1	1	yes	characteristic
136	C₂	#15689475	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₄₇⋊C₈

C₂

yes

maximal, characteristic

#15688993

C₂

yes

maximal, characteristic

#15688885

C₂

yes

maximal

C₄₇×#384

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₄×C₄₇⋊C₈

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂²×C₄₇

C₂×SD₁₆

yes

characteristic

C₂²×C₄₇

C₂×SD₁₆

yes

characteristic

C₂²×C₄₇

C₂×Q₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#106

yes

—

C₄×C₄₇

#107

yes

—

C₄×C₄₇

#117

yes

—

C₄×C₄₇

#125

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄×C₈

—

#384

—

#384

D₄₇

yes

characteristic

#340

—

C₄₇

#1834

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

Dic₉₄

yes

—

C₄²

C₄×D₄₇

yes

—

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

188

—

104

C₂×C₄

—

188

—

105

C₂×C₄

—

188

—

106

C₂×C₄

Dic₄₇⋊C₄

yes

—

107

C₂×C₄

Dic₄₇⋊C₄

yes

—

108

C₂×C₄

#10625334

yes

—

109

C₂×C₄

#10625335

yes

—

110

C₂×C₄

#10625336

yes

—

111

C₂×C₄

#10625337

yes

—

112

C₂×C₄

C₂×Dic₉₄

yes

characteristic

113

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

114

C₂×C₄

#10625352

yes

—

115

C₂×C₄

#10625354

yes

—

116

C₈

—

117

C₂²

C₂×Dic₄₇⋊C₄

yes

characteristic

118

C₂²

#13094011

yes

characteristic

119

C₂²

#13094013

yes

characteristic

120

C₂²

C₂×#10625334

yes

characteristic

121

C₂²

C₂×#10625336

yes

characteristic

122

C₂²

C₂×#10625335

yes

characteristic

123

C₂²

C₂×#10625337

yes

characteristic

124

C₄

—

125

C₄

—

376

—

126

C₄

#13093955

yes

—

127

C₄

#13093957

yes

—

128

C₄

#13093982

yes

—

129

C₄

#13094015

yes

—

130

C₂

#15688988

yes

characteristic

131

C₂

C₂×#13093955

yes

characteristic

132

C₂

C₂×#13093957

yes

characteristic

133

C₂

#15689469

yes

characteristic

134

C₂

#15689471

yes

characteristic

135

C₂

#15689473

yes

characteristic

136

C₂

#15689475

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#384	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#384	D₄₇
hypocenter	C₄₇	#1834
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#384

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
9. C₄×C₄₇⋊C₈	C₄	semidirect
73. C₄₇	#1834	semidirect

H ≅ G/N

type

9. C₄×C₄₇⋊C₈

C₄

semidirect

73. C₄₇

#1834

semidirect

Subgroups — #20243515

Conjugacy classes of subgroups

Complements