Group #20252176 — subgroups

Subgroups — C₂×#15689231 #20252176

Order 6016.

480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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	C₂²×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₉₄	C₂	1	2	yes	maximal
3	#15689231	C₂	1	8	yes	maximal, direct product factor
4	C₂×#13093956	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093949	C₂	1	2	yes	maximal
6	C₂×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₉₄	C₂²	1	2	yes	—
8	C₂×Dic₁₈₈	C₄	1	8	yes	complemented
9	C₂×Dic₁₈₈	C₂²	1	4	yes	—
10	C₄×Dic₉₄	—	2	4	no	—
11	C₄×Dic₉₄	C₂²	1	8	yes	—
12	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂×Dic₄₇⋊C₄	—	2	2	no	—
14	C₂×C₄×Dic₄₇	—	2	2	no	—
15	#13093956	C₂²	1	4	yes	—
16	#13093949	C₂²	1	8	yes	—
17	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	#97×C₄₇	C₂²	1	4	yes	—
21	C₂²×C₄×C₄₇	D₄	1	2	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂²×Dic₄₇	—	2	2	no	—
24	C₂²×Dic₄₇	—	2	2	no	—
25	C₂×Dic₉₄	—	2	2	no	—
26	C₂×Dic₉₄	—	2	4	no	—
27	C₂×Dic₉₄	C₂×C₄	1	8	yes	—
28	C₂×Dic₉₄	C₂³	1	4	yes	—
29	C₂×C₈×C₄₇	—	2	2	no	—
30	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
31	C₂×C₈×C₄₇	C₂³	1	2	yes	—
32	C₂×C₈×C₄₇	C₂³	1	2	yes	—
33	C₄²×C₄₇	D₄	1	2	yes	—
34	C₄²×C₄₇	C₂³	1	2	yes	—
35	C₄⋊Dic₄₇	—	2	2	no	—
36	C₄⋊Dic₄₇	C₂³	1	4	yes	—
37	Dic₄₇⋊C₄	—	2	8	no	—
38	C₄×Dic₄₇	—	2	8	no	—
39	Dic₁₈₈	C₂×C₄	1	16	yes	complemented
40	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₇	—	2	4	no	—
42	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	#41	1	2	yes	—
46	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₄₇	—	2	8	no	—
48	C₂×Dic₄₇	—	2	4	no	—
49	C₂×Dic₄₇	—	2	4	no	—
50	C₂×Dic₄₇	—	4	4	no	—
51	Dic₉₄	—	2	8	no	—
52	Dic₉₄	—	2	4	no	—
53	Dic₉₄	C₂²×C₄	1	8	yes	—
54	C₈×C₄₇	—	2	2	no	—
55	C₈×C₄₇	C₂²×C₄	1	4	yes	—
56	C₂²×C₄₇	C₄×D₄	1	2	yes	—
57	C₂²×C₄₇	#137	1	4	yes	—
58	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
59	C₄×C₄₇	—	2	4	no	—
60	C₄×C₄₇	C₄×D₄	1	2	yes	—
61	C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
63	Dic₄₇	—	2	8	no	—
64	Dic₄₇	—	4	4	no	—
65	C₂×#441	—	47	1	no	maximal, Sylow
66	C₂×C₄₇	#441	1	4	yes	complemented
67	C₂×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
68	C₂×C₄₇	C₂×#137	1	2	yes	—
69	C₂²×Q₁₆	—	47	1	no	—
70	C₂×C₄×Q₈	—	47	2	no	—
71	#441	—	47	8	no	—
72	C₂×#106	—	47	1	no	—
73	C₂×#103	—	47	2	no	—
74	C₂×#97	D₄₇	1	1	yes	characteristic
75	C₄₇	C₂×#441	1	1	yes	characteristic, complemented, Sylow
76	C₂²×Q₈	—	47	2	no	—
77	C₂×Q₁₆	—	47	8	no	—
78	C₂×Q₁₆	—	47	4	no	—
79	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
80	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
81	C₄×Q₈	—	47	8	no	—
82	C₄×Q₈	—	94	4	no	—
83	C₂×C₄⋊C₄	—	47	2	no	—
84	C₂×C₄⋊C₄	—	94	2	no	—
85	C₂×C₄²	—	94	2	no	—
86	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
87	#106	—	47	4	no	—
88	#103	—	47	8	no	—
89	#97	C₂×D₄₇	1	4	yes	—
90	C₂×Q₈	—	47	8	no	—
91	C₂×Q₈	—	47	4	no	—
92	C₂×Q₈	—	94	2	no	—
93	C₂×Q₈	—	94	4	no	—
94	C₂²×C₄	—	94	2	no	—
95	C₂²×C₄	—	94	2	no	—
96	C₂²×C₄	D₁₈₈	1	2	yes	—
97	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
98	Q₁₆	—	47	16	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	C₄×D₄₇	1	4	yes	—
101	C₂×C₈	C₂²×D₄₇	1	2	yes	—
102	C₂×C₈	C₂²×D₄₇	1	2	yes	—
103	C₄⋊C₄	—	47	4	no	—
104	C₄⋊C₄	—	94	8	no	—
105	C₄⋊C₄	—	94	2	no	—
106	C₄²	—	94	8	no	—
107	C₄²	D₁₈₈	1	2	yes	—
108	C₄²	C₂²×D₄₇	1	2	yes	—
109	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
110	Q₈	—	47	8	no	—
111	Q₈	—	94	8	no	—
112	Q₈	—	94	4	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	94	8	no	—
115	C₂×C₄	—	94	4	no	—
116	C₂×C₄	—	94	4	no	—
117	C₂×C₄	—	188	4	no	—
118	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
119	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
120	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
121	C₂×C₄	#10625350	1	2	yes	—
122	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	C₂×C₄×D₄₇	1	4	yes	—
125	C₂²	C₄×D₁₈₈	1	2	yes	—
126	C₂²	#13094057	1	4	yes	—
127	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
128	C₄	—	2	4	no	—
129	C₄	—	94	8	no	—
130	C₄	—	188	4	no	—
131	C₄	C₄×D₁₈₈	1	2	yes	—
132	C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
133	C₄	C₂×#10625350	1	1	yes	characteristic
134	C₂	#15689231	1	4	yes	direct product factor
135	C₂	C₂×C₄×D₁₈₈	1	1	yes	characteristic
136	C₂	C₂×#13094057	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₈₈

C₂

yes

maximal, characteristic

C₂×C₄×Dic₉₄

C₂

yes

maximal

#15689231

C₂

yes

maximal, direct product factor

C₂×#13093956

C₂

yes

maximal, characteristic

C₂×#13093949

C₂

yes

maximal

C₂×#97×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

—

C₂×Dic₁₈₈

C₄

yes

complemented

C₂×Dic₁₈₈

C₂²

yes

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

#13093956

C₂²

yes

—

#13093949

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×Dic₉₄

C₂³

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

Dic₁₈₈

C₂×C₄

yes

complemented

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

C₂²×C₄

yes

—

C₈×C₄₇

—

C₈×C₄₇

C₂²×C₄

yes

—

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

#137

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

—

C₄×C₄₇

C₂³×C₄

yes

characteristic

C₄×C₄₇

C₂×#41

yes

characteristic

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₄×D₄

yes

characteristic

C₂×C₄₇

C₂×#137

yes

—

C₂²×Q₁₆

—

C₂×C₄×Q₈

—

#441

—

C₂×#106

—

C₂×#103

—

C₂×#97

D₄₇

yes

characteristic

C₄₇

C₂×#441

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

—

C₂×D₄₇

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

Q₁₆

—

C₂×C₈

—

100

C₂×C₈

C₄×D₄₇

yes

—

101

C₂×C₈

C₂²×D₄₇

yes

—

102

C₂×C₈

C₂²×D₄₇

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

D₁₈₈

yes

—

108

C₄²

C₂²×D₄₇

yes

—

109

C₂³

C₂×D₁₈₈

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

188

—

118

C₂×C₄

C₂×C₄×D₄₇

yes

—

119

C₂×C₄

C₂×D₁₈₈

yes

—

120

C₂×C₄

C₂×D₁₈₈

yes

characteristic

121

C₂×C₄

#10625350

yes

—

122

C₂×C₄

C₂³×D₄₇

yes

characteristic

123

C₈

—

124

C₈

C₂×C₄×D₄₇

yes

—

125

C₂²

C₄×D₁₈₈

yes

—

126

C₂²

#13094057

yes

—

127

C₂²

C₂²×D₁₈₈

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

188

—

131

C₄

C₄×D₁₈₈

yes

—

132

C₄

C₂²×C₄×D₄₇

yes

characteristic

133

C₄

C₂×#10625350

yes

characteristic

134

C₂

#15689231

yes

direct product factor

135

C₂

C₂×C₄×D₁₈₈

yes

characteristic

136

C₂

C₂×#13094057

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₄×C₄₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×#97×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#97	D₄₇
hypocenter	C₄₇	C₂×#441
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₁₈₈

commutator

C₄×C₄₇

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂×#97×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂×#97

D₄₇

hypocenter

C₄₇

C₂×#441

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
3. #15689231	C₂	direct (N × H)
8. C₂×Dic₁₈₈	C₄	semidirect
39. Dic₁₈₈	C₂×C₄	semidirect
66. C₂×C₄₇	#441	semidirect
75. C₄₇	C₂×#441	semidirect
134. C₂	#15689231	direct (N × H)

H ≅ G/N

type

3. #15689231

C₂

direct (N × H)

8. C₂×Dic₁₈₈

C₄

semidirect

39. Dic₁₈₈

C₂×C₄

semidirect

66. C₂×C₄₇

#441

semidirect

75. C₄₇

C₂×#441

semidirect

134. C₂

#15689231

direct (N × H)

Subgroups — C₂×#15689231 #20252176

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689231 #20252176

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689231 #20252176