Group #20254133 — subgroups

Subgroups — #20254133

Order 6016.

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

normal subgroups only

This group has 358 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	#15689680	C₂	1	2	yes	maximal
2	#15689521	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689503	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689474	C₂	1	2	yes	maximal, complemented
5	#15689381	C₂	1	4	yes	maximal
6	#15689231	C₂	1	4	yes	maximal, complemented
7	C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₈₈	C₂²	1	4	yes	—
9	#13094024	C₂²	1	2	yes	—
10	#13094024	C₂²	1	2	yes	—
11	#13094016	—	2	2	no	—
12	#13094003	—	2	2	no	—
13	#13094003	C₂²	1	4	yes	—
14	C₄×Dic₉₄	—	2	2	no	—
15	C₄×Dic₉₄	C₂²	1	4	yes	—
16	#13093983	—	2	2	no	—
17	#13093956	C₂²	1	4	yes	—
18	#13093949	C₂²	1	8	yes	—
19	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
20	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	#97×C₄₇	C₂²	1	2	yes	—
22	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₄₇	D₄	1	2	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₉₄	—	2	2	no	—
27	C₂×Dic₉₄	C₂³	1	4	yes	—
28	M₁₆×C₄₇	—	2	4	no	—
29	C₂×C₈×C₄₇	C₂³	1	2	yes	—
30	C₂×C₈×C₄₇	C₂³	1	2	yes	—
31	C₄²×C₄₇	D₄	1	2	yes	—
32	C₄²×C₄₇	C₂³	1	1	yes	characteristic
33	C₄²×C₄₇	C₂³	1	1	yes	characteristic
34	C₂²⋊Dic₄₇	—	2	4	no	—
35	C₄⋊Dic₄₇	—	2	2	no	—
36	C₄⋊Dic₄₇	—	2	2	no	—
37	C₄⋊Dic₄₇	—	2	2	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	Dic₁₈₈	—	2	8	no	—
43	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₇	—	2	4	no	—
45	C₂×C₄×C₄₇	—	2	2	no	—
46	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₄₇	—	2	4	no	—
51	C₂×Dic₄₇	—	2	4	no	—
52	Dic₉₄	—	2	8	no	—
53	Dic₉₄	—	4	4	no	—
54	C₈×C₄₇	—	2	2	no	—
55	C₈×C₄₇	#41	1	4	yes	—
56	C₂²×C₄₇	—	2	1	no	—
57	C₂²×C₄₇	—	2	2	no	—
58	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
59	C₄×C₄₇	—	2	1	no	—
60	C₄×C₄₇	—	2	2	no	—
61	C₄×C₄₇	#137	1	4	yes	—
62	C₄×C₄₇	C₂×#41	1	2	yes	—
63	Dic₄₇	—	4	4	no	—
64	Dic₄₇	—	4	4	no	—
65	#3185	—	47	1	no	maximal, Sylow
66	C₂×C₄₇	—	4	1	no	—
67	C₂×C₄₇	#532	1	1	yes	characteristic
68	C₂×C₄₇	C₂×#137	1	2	yes	—
69	#533	—	47	2	no	—
70	#498	—	47	1	no	—
71	#494	—	47	1	no	—
72	#487	—	47	2	no	—
73	#470	—	47	4	no	—
74	#441	—	47	4	no	—
75	C₄×M₁₆	D₄₇	1	1	yes	characteristic
76	C₄₇	#3185	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₁₆	—	47	4	no	—
78	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
79	C₄⋊Q₈	—	47	2	no	—
80	C₄⋊Q₈	—	47	2	no	—
81	#125	—	94	2	no	—
82	C₂²⋊Q₈	—	47	4	no	—
83	C₂²⋊Q₈	—	94	2	no	—
84	C₄×Q₈	—	47	4	no	—
85	C₄×Q₈	—	94	2	no	—
86	#117	—	94	2	no	—
87	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
88	#106	—	47	4	no	—
89	#103	—	47	8	no	—
90	#97	C₂×D₄₇	1	2	yes	—
91	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
92	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
93	C₂×Q₈	—	47	4	no	—
94	C₂×Q₈	—	94	2	no	—
95	C₂²×C₄	D₁₈₈	1	2	yes	—
96	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
97	Q₁₆	—	94	8	no	—
98	M₁₆	—	2	4	no	—
99	C₂×C₈	C₂²×D₄₇	1	2	yes	—
100	C₂×C₈	C₂²×D₄₇	1	2	yes	—
101	C₄⋊C₄	—	47	4	no	—
102	C₄⋊C₄	—	94	4	no	—
103	C₄⋊C₄	—	94	4	no	—
104	C₄⋊C₄	—	94	2	no	—
105	C₄⋊C₄	—	94	2	no	—
106	C₄⋊C₄	—	94	2	no	—
107	C₂²⋊C₄	—	94	4	no	—
108	C₄²	—	94	4	no	—
109	C₄²	D₁₈₈	1	2	yes	—
110	C₄²	C₂²×D₄₇	1	1	yes	characteristic
111	C₄²	C₂²×D₄₇	1	1	yes	characteristic
112	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
113	Q₈	—	94	8	no	—
114	Q₈	—	188	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	94	4	no	—
118	C₂×C₄	—	94	4	no	—
119	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
120	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
121	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
122	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	#10625350	1	4	yes	—
125	C₂²	—	2	2	no	—
126	C₂²	—	2	1	no	—
127	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
128	C₄	—	2	2	no	—
129	C₄	—	2	1	no	—
130	C₄	—	188	4	no	—
131	C₄	—	188	4	no	—
132	C₄	#13094057	1	4	yes	—
133	C₄	C₂×#10625350	1	2	yes	—
134	C₂	—	4	1	no	—
135	C₂	#15689673	1	1	yes	characteristic
136	C₂	C₂×#13094057	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689680

C₂

yes

maximal

#15689521

C₂

yes

maximal, characteristic, complemented

#15689503

C₂

yes

maximal, characteristic, complemented

#15689474

C₂

yes

maximal, complemented

#15689381

C₂

yes

maximal

#15689231

C₂

yes

maximal, complemented

C₄×M₁₆×C₄₇

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

—

#13094024

C₂²

yes

—

#13094024

C₂²

yes

—

#13094016

—

#13094003

—

#13094003

C₂²

yes

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂²

yes

—

#13093983

—

#13093956

C₂²

yes

—

#13093949

C₂²

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂³

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

Dic₁₈₈

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#137

yes

—

C₄×C₄₇

C₂×#41

yes

—

Dic₄₇

—

Dic₄₇

—

#3185

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#532

yes

characteristic

C₂×C₄₇

C₂×#137

yes

—

—

—

—

—

—

—

C₄×M₁₆

D₄₇

yes

characteristic

C₄₇

#3185

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₄₇

yes

—

—

C₂×D₄₇

yes

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

Q₁₆

—

M₁₆

—

C₂×C₈

C₂²×D₄₇

yes

—

100

C₂×C₈

C₂²×D₄₇

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

D₁₈₈

yes

—

110

C₄²

C₂²×D₄₇

yes

characteristic

111

C₄²

C₂²×D₄₇

yes

characteristic

112

C₂³

C₂×D₁₈₈

yes

characteristic

113

Q₈

—

114

Q₈

—

188

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×D₁₈₈

yes

—

120

C₂×C₄

C₂×D₁₈₈

yes

characteristic

121

C₂×C₄

C₂×D₁₈₈

yes

—

122

C₂×C₄

C₂³×D₄₇

yes

characteristic

123

C₈

—

124

C₈

#10625350

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂²×D₁₈₈

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

188

—

131

C₄

—

188

—

132

C₄

#13094057

yes

—

133

C₄

C₂×#10625350

yes

—

134

C₂

—

135

C₂

#15689673

yes

characteristic

136

C₂

C₂×#13094057

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	C₄×M₁₆	D₄₇
hypocenter	C₄₇	#3185
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂²×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄×M₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂²×D₄

hypercenter

C₄×M₁₆

D₄₇

hypocenter

C₄₇

#3185

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
2. #15689521	C₂	semidirect
3. #15689503	C₂	semidirect
4. #15689474	C₂	semidirect
6. #15689231	C₂	semidirect
76. C₄₇	#3185	semidirect

H ≅ G/N

type

2. #15689521

C₂

semidirect

3. #15689503

C₂

semidirect

4. #15689474

C₂

semidirect

6. #15689231

C₂

semidirect

76. C₄₇

#3185

semidirect

Subgroups — #20254133

Conjugacy classes of subgroups

Complements