Group #20254134 — subgroups

Subgroups — #20254134

Order 6016.

358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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	#15689678	C₂	1	2	yes	maximal
2	#15689503	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689475	C₂	1	2	yes	maximal, complemented
4	#15689382	C₂	1	4	yes	maximal
5	#15689229	C₂	1	4	yes	maximal, complemented
6	C₄×#10625324	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₈₈	C₂²	1	4	yes	—
9	C₂×#10625324	C₂²	1	2	yes	—
10	#13094024	C₂²	1	2	yes	—
11	#13094015	—	2	2	no	—
12	#13094004	C₂²	1	4	yes	—
13	#13094000	—	2	2	no	—
14	Q₈×Dic₄₇	—	2	2	no	—
15	#13093989	C₂²	1	4	yes	—
16	#13093982	—	2	2	no	—
17	C₄²×D₄₇	C₂²	1	1	yes	characteristic
18	#13093947	C₂²	1	8	yes	—
19	#13093934	C₂²	1	2	yes	—
20	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
22	#106×C₄₇	C₂²	1	4	yes	—
23	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₄₇	—	2	2	no	—
25	C₂×C₄×D₄₇	D₄	1	2	yes	—
26	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₉₄	C₂³	1	4	yes	—
28	C₂×C₈×C₄₇	C₂³	1	2	yes	—
29	C₄⋊C₄×C₄₇	—	2	2	no	—
30	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
31	C₄²×C₄₇	C₂³	1	1	yes	characteristic
32	(C₂×D₄₇)⋊C₄	—	2	4	no	—
33	C₄⋊Dic₄₇	—	2	2	no	—
34	C₄⋊Dic₄₇	—	2	2	no	—
35	C₄⋊Dic₄₇	—	2	4	no	—
36	Dic₄₇⋊C₄	—	2	4	no	—
37	C₄×Dic₄₇	—	2	4	no	—
38	C₄×Dic₄₇	D₄	1	2	yes	—
39	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
40	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
41	Dic₁₈₈	—	2	8	no	—
42	#10625324	—	2	4	no	—
43	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₄₇	—	4	4	no	—
45	C₂×C₄×C₄₇	—	2	4	no	—
46	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₄₇	—	2	4	no	—
49	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
50	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
51	C₄×D₄₇	—	2	4	no	—
52	C₄×D₄₇	—	2	2	no	—
53	Dic₉₄	—	2	8	no	—
54	C₈×C₄₇	#41	1	4	yes	—
55	C₄₇⋊C₈	—	2	2	no	—
56	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
57	C₂×D₄₇	—	2	1	no	—
58	C₂×D₄₇	—	2	2	no	—
59	C₄×C₄₇	—	4	4	no	—
60	C₄×C₄₇	#137	1	4	yes	—
61	C₄×C₄₇	C₂×#41	1	2	yes	—
62	Dic₄₇	—	2	1	no	—
63	Dic₄₇	—	2	2	no	—
64	Dic₄₇	—	4	4	no	—
65	#3185	—	47	1	no	maximal, Sylow
66	C₂×C₄₇	#532	1	1	yes	characteristic
67	C₂×C₄₇	C₂×#137	1	2	yes	—
68	D₄₇	—	4	1	no	—
69	#533	—	47	2	no	—
70	#498	D₄₇	1	1	yes	characteristic, complemented
71	#494	—	47	1	no	—
72	#487	—	47	2	no	—
73	#470	—	47	4	no	—
74	#441	—	47	4	no	—
75	C₄×M₁₆	—	47	1	no	—
76	C₄₇	#3185	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₁₆	—	47	4	no	—
78	C₂×M₁₆	—	47	2	no	—
79	C₄⋊Q₈	—	47	2	no	—
80	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
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	—	47	1	no	—
88	#106	C₂×D₄₇	1	4	yes	—
89	#103	—	47	8	no	—
90	#97	—	47	2	no	—
91	C₄×C₈	—	47	1	no	—
92	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	—	47	4	no	—
95	C₂²×C₄	—	47	2	no	—
96	C₂²×C₄	—	47	1	no	—
97	Q₁₆	—	94	8	no	—
98	M₁₆	—	94	4	no	—
99	C₂×C₈	—	47	2	no	—
100	C₂×C₈	C₂²×D₄₇	1	2	yes	—
101	C₄⋊C₄	—	2	2	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	C₂²×D₄₇	1	4	yes	—
107	C₂²⋊C₄	—	94	4	no	—
108	C₄²	—	47	2	no	—
109	C₄²	—	47	1	no	—
110	C₄²	—	94	4	no	—
111	C₄²	C₂²×D₄₇	1	1	yes	characteristic
112	C₂³	—	47	1	no	—
113	Q₈	—	4	4	no	—
114	Q₈	—	94	8	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	47	2	no	—
117	C₂×C₄	—	47	1	no	—
118	C₂×C₄	—	94	4	no	—
119	C₂×C₄	—	94	2	no	—
120	C₂×C₄	—	94	4	no	—
121	C₂×C₄	D₄×D₄₇	1	2	yes	—
122	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
123	C₈	—	94	2	no	—
124	C₈	#10625354	1	4	yes	—
125	C₂²	—	94	2	no	—
126	C₂²	—	94	1	no	—
127	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
128	C₄	—	4	4	no	—
129	C₄	—	94	2	no	—
130	C₄	—	94	1	no	—
131	C₄	—	188	4	no	—
132	C₄	#13094053	1	4	yes	—
133	C₄	C₂×#10625354	1	2	yes	—
134	C₂	—	188	1	no	—
135	C₂	#15689674	1	1	yes	characteristic
136	C₂	C₂×#13094053	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689678

C₂

yes

maximal

#15689503

C₂

yes

maximal, characteristic, complemented

#15689475

C₂

yes

maximal, complemented

#15689382

C₂

yes

maximal

#15689229

C₂

yes

maximal, complemented

C₄×#10625324

C₂

yes

maximal, characteristic

C₄₇×#498

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

C₂²

yes

—

C₂×#10625324

C₂²

yes

—

#13094024

C₂²

yes

—

#13094015

—

#13094004

C₂²

yes

—

#13094000

—

Q₈×Dic₄₇

—

#13093989

C₂²

yes

—

#13093982

—

C₄²×D₄₇

C₂²

yes

characteristic

#13093947

C₂²

yes

—

#13093934

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

—

#106×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

C₂³

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

—

Dic₁₈₈

—

#10625324

—

C₂²×D₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

#41

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#137

yes

—

C₄×C₄₇

C₂×#41

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

#533

—

#498

D₄₇

yes

characteristic, complemented

—

—

—

—

C₄×M₁₆

—

C₄₇

#3185

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#106

C₂×D₄₇

yes

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

Q₁₆

—

M₁₆

—

C₂×C₈

—

100

C₂×C₈

C₂²×D₄₇

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

C₂²×D₄₇

yes

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

C₂²×D₄₇

yes

characteristic

112

C₂³

—

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

D₄×D₄₇

yes

—

122

C₂×C₄

C₂³×D₄₇

yes

characteristic

123

C₈

—

124

C₈

#10625354

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂×D₄×D₄₇

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

188

—

132

C₄

#13094053

yes

—

133

C₄

C₂×#10625354

yes

—

134

C₂

—

188

—

135

C₂

#15689674

yes

characteristic

136

C₂

C₂×#13094053

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#498	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#498	D₄₇
hypocenter	C₄₇	#3185
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#498

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #15689503	C₂	semidirect
3. #15689475	C₂	semidirect
5. #15689229	C₂	semidirect
7. C₄₇×#498	C₂	semidirect
70. #498	D₄₇	semidirect
76. C₄₇	#3185	semidirect

H ≅ G/N

type

2. #15689503

C₂

semidirect

3. #15689475

C₂

semidirect

5. #15689229

C₂

semidirect

7. C₄₇×#498

C₂

semidirect

70. #498

D₄₇

semidirect

76. C₄₇

#3185

semidirect

Subgroups — #20254134

Conjugacy classes of subgroups

Complements