Group #49094687 — subgroups

Subgroups — #49094687

Order 35968.

150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 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	#31823859	C₂	1	1	yes	maximal, characteristic
2	#31823673	C₂	1	1	yes	maximal, characteristic
3	Q₈×#14555886	C₂	1	1	yes	maximal, characteristic
4	#31823213	C₂	1	1	yes	maximal, characteristic
5	#31823212	C₂	1	1	yes	maximal, characteristic
6	#31823210	C₂	1	1	yes	maximal, characteristic
7	#477×C₂₈₁	C₂	1	1	yes	maximal, characteristic
8	C₂×#17985128	—	2	1	no	—
9	#22582879	C₂²	1	1	yes	characteristic
10	#22582810	—	2	1	no	—
11	#22582810	—	2	1	no	—
12	C₄⋊#14555886	—	2	1	no	—
13	C₄⋊#14555886	C₂²	1	1	yes	characteristic
14	C₄⋊#14555886	C₂²	1	1	yes	characteristic
15	#22582802	—	2	1	no	—
16	C₄×#14555886	—	2	1	no	—
17	C₄×#14555886	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₂₈₁	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₂₈₁	C₂²	1	1	yes	characteristic
20	#107×C₂₈₁	—	2	1	no	—
21	C₄⋊C₈×C₂₈₁	C₂²	1	1	yes	characteristic
22	#103×C₂₈₁	—	2	1	no	—
23	C₂×Dic₅₆₂	—	2	1	no	—
24	#17985128	—	4	2	no	—
25	C₂×#14555886	—	2	1	no	—
26	C₂×#14555886	—	2	1	no	—
27	C₂×#14555886	D₄	1	1	yes	characteristic
28	C₂×#14555886	D₄	1	1	yes	characteristic
29	C₄⋊Dic₂₈₁	—	2	1	no	—
30	C₄⋊Dic₂₈₁	—	2	1	no	—
31	C₂×Q₈×C₂₈₁	—	2	1	no	—
32	C₂×Q₈×C₂₈₁	D₄	1	1	yes	characteristic
33	C₂×C₈×C₂₈₁	—	2	1	no	—
34	C₄⋊C₄×C₂₈₁	—	2	1	no	—
35	C₄⋊C₄×C₂₈₁	—	2	1	no	—
36	C₄⋊C₄×C₂₈₁	—	2	1	no	—
37	C₄⋊C₄×C₂₈₁	D₄	1	1	yes	characteristic
38	C₄²×C₂₈₁	—	2	1	no	—
39	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
40	Dic₅₆₂	—	4	1	no	—
41	Dic₅₆₂	—	4	1	no	—
42	C₂×Dic₂₈₁	—	4	1	no	—
43	#14555886	—	2	1	no	—
44	#14555886	—	4	1	no	—
45	#14555886	—	4	1	no	—
46	#14555886	Q₁₆	1	2	yes	complemented
47	Q₈×C₂₈₁	—	2	1	no	—
48	Q₈×C₂₈₁	—	8	1	no	—
49	Q₈×C₂₈₁	SD₁₆	1	2	yes	—
50	C₂×C₄×C₂₈₁	—	2	1	no	—
51	C₂×C₄×C₂₈₁	—	2	1	no	—
52	C₂×C₄×C₂₈₁	—	4	1	no	—
53	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₂₈₁	#41	1	1	yes	characteristic
56	C₈×C₂₈₁	—	4	1	no	—
57	C₂²×C₂₈₁	#121	1	1	yes	characteristic
58	C₄×C₂₈₁	—	2	2	no	—
59	C₄×C₂₈₁	—	2	1	no	—
60	C₄×C₂₈₁	—	4	1	no	—
61	C₄×C₂₈₁	—	8	1	no	—
62	C₄×C₂₈₁	C₂×SD₁₆	1	1	yes	characteristic
63	C₄×C₂₈₁	C₂×Q₁₆	1	1	yes	characteristic
64	C₄×C₂₈₁	#135	1	1	yes	characteristic
65	C₄×C₂₈₁	#137	1	1	yes	characteristic
66	Dic₂₈₁	—	8	1	no	—
67	C₂×C₂₈₁	#462	1	1	yes	characteristic
68	C₂×C₂₈₁	#465	1	1	yes	characteristic
69	C₂×C₂₈₁	#471	1	1	yes	characteristic
70	C₂₈₁	#1672	1	1	yes	characteristic, complemented, Sylow
71	#1672	—	281	1	no	maximal, Sylow
72	#498	—	281	1	no	—
73	#477	D₂₈₁	1	1	yes	characteristic
74	#462	—	281	1	no	—
75	C₈×Q₈	—	281	1	no	—
76	#334	—	281	1	no	—
77	#333	—	281	1	no	—
78	#332	—	281	1	no	—
79	C₂×Q₁₆	—	562	1	no	—
80	C₄⋊Q₈	—	281	1	no	—
81	C₄⋊Q₈	C₂×D₂₈₁	1	1	yes	characteristic
82	C₄×Q₈	C₂×D₂₈₁	1	1	yes	characteristic
83	#107	—	2	1	no	—
84	#106	—	562	1	no	—
85	#106	—	562	1	no	—
86	C₄⋊C₈	—	281	1	no	—
87	C₄⋊C₈	—	281	1	no	—
88	C₄⋊C₈	—	562	1	no	—
89	C₄⋊C₈	C₂×D₂₈₁	1	1	yes	characteristic
90	#103	—	2	1	no	—
91	#103	—	562	1	no	—
92	C₄×C₈	—	281	1	no	—
93	C₄×C₈	—	562	1	no	—
94	C₂×Q₈	—	2	1	no	—
95	C₂×Q₈	—	562	1	no	—
96	C₂×Q₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
97	Q₁₆	—	1124	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	281	1	no	—
100	C₂×C₈	—	281	1	no	—
101	C₂×C₈	—	562	1	no	—
102	C₂×C₈	—	562	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	562	1	no	—
107	C₄⋊C₄	—	562	1	no	—
108	C₄⋊C₄	C₂²⋊D₂₈₁	1	1	yes	characteristic
109	C₄²	—	2	1	no	—
110	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
111	Q₈	—	2	1	no	—
112	Q₈	—	8	1	no	—
113	Q₈	—	1124	1	no	—
114	Q₈	—	1124	1	no	—
115	Q₈	#17985125	1	2	yes	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	1124	1	no	—
120	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
121	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
122	C₂×C₄	#17985137	1	1	yes	characteristic
123	C₈	—	4	1	no	—
124	C₈	—	281	2	no	—
125	C₈	—	562	1	no	—
126	C₈	—	1124	1	no	—
127	C₈	—	1124	1	no	—
128	C₂²	#22582851	1	1	yes	characteristic
129	C₄	—	2	2	no	—
130	C₄	—	2	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	8	1	no	—
133	C₄	—	2248	1	no	—
134	C₄	C₂×#17985125	1	1	yes	characteristic
135	C₄	Q₁₆×D₂₈₁	1	1	yes	characteristic
136	C₄	#22582899	1	1	yes	characteristic
137	C₄	#22582911	1	1	yes	characteristic
138	C₂	#31823671	1	1	yes	characteristic
139	C₂	#31823694	1	1	yes	characteristic
140	C₂	#31823724	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31823859

C₂

yes

maximal, characteristic

#31823673

C₂

yes

maximal, characteristic

Q₈×#14555886

C₂

yes

maximal, characteristic

#31823213

C₂

yes

maximal, characteristic

#31823212

C₂

yes

maximal, characteristic

#31823210

C₂

yes

maximal, characteristic

#477×C₂₈₁

C₂

yes

maximal, characteristic

C₂×#17985128

—

#22582879

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₄⋊#14555886

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊Q₈×C₂₈₁

C₂²

yes

characteristic

C₄×Q₈×C₂₈₁

C₂²

yes

characteristic

#107×C₂₈₁

—

C₄⋊C₈×C₂₈₁

C₂²

yes

characteristic

#103×C₂₈₁

—

C₂×Dic₅₆₂

—

—

—

—

D₄

yes

characteristic

C₂×#14555886

D₄

yes

characteristic

C₄⋊Dic₂₈₁

—

C₄⋊Dic₂₈₁

—

C₂×Q₈×C₂₈₁

—

C₂×Q₈×C₂₈₁

D₄

yes

characteristic

C₂×C₈×C₂₈₁

—

C₄⋊C₄×C₂₈₁

—

C₄⋊C₄×C₂₈₁

—

C₄⋊C₄×C₂₈₁

—

C₄⋊C₄×C₂₈₁

D₄

yes

characteristic

C₄²×C₂₈₁

—

C₄²×C₂₈₁

C₂³

yes

characteristic

Dic₅₆₂

—

Dic₅₆₂

—

C₂×Dic₂₈₁

—

—

—

—

Q₁₆

yes

complemented

Q₈×C₂₈₁

—

Q₈×C₂₈₁

—

Q₈×C₂₈₁

SD₁₆

yes

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

#41

yes

characteristic

C₈×C₂₈₁

—

C₂²×C₂₈₁

#121

yes

characteristic

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

C₂×SD₁₆

yes

characteristic

C₄×C₂₈₁

C₂×Q₁₆

yes

C₄×C₂₈₁

yes

C₄×C₂₈₁

yes

Dic₂₈₁

—

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂₈₁

yes

characteristic, complemented, Sylow

#1672

—

281

maximal, Sylow

#498

—

281

—

#477

D₂₈₁

yes

characteristic

#462

—

281

—

C₈×Q₈

—

281

—

#334

—

281

—

#333

—

281

—

#332

—

281

—

C₂×Q₁₆

—

562

—

C₄⋊Q₈

—

281

—

C₄⋊Q₈

C₂×D₂₈₁

yes

characteristic

C₄×Q₈

C₂×D₂₈₁

yes

characteristic

#107

—

#106

—

562

—

#106

—

562

—

C₄⋊C₈

—

281

—

C₄⋊C₈

—

281

—

C₄⋊C₈

—

562

—

C₄⋊C₈

C₂×D₂₈₁

yes

characteristic

#103

—

#103

—

562

—

C₄×C₈

—

281

—

C₄×C₈

—

562

—

C₂×Q₈

—

C₂×Q₈

—

562

—

C₂×Q₈

C₂²⋊D₂₈₁

yes

characteristic

Q₁₆

—

1124

—

C₂×C₈

—

C₂×C₈

—

281

—

100

C₂×C₈

—

281

—

101

C₂×C₈

—

562

—

102

C₂×C₈

—

562

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

562

—

107

C₄⋊C₄

—

562

—

108

C₄⋊C₄

C₂²⋊D₂₈₁

yes

characteristic

109

C₄²

—

110

C₄²

C₂²×D₂₈₁

yes

characteristic

111

Q₈

—

112

Q₈

—

113

Q₈

—

1124

—

114

Q₈

—

1124

—

115

Q₈

#17985125

yes

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

1124

—

120

C₂×C₄

D₄×D₂₈₁

yes

characteristic

121

C₂×C₄

C₂×C₂²⋊D₂₈₁

yes

characteristic

122

C₂×C₄

#17985137

yes

characteristic

123

C₈

—

124

C₈

—

281

—

125

C₈

—

562

—

126

C₈

—

1124

—

127

C₈

—

1124

—

128

C₂²

#22582851

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

2248

—

134

C₄

C₂×#17985125

yes

characteristic

135

C₄

Q₁₆×D₂₈₁

yes

characteristic

136

C₄

#22582899

yes

characteristic

137

C₄

#22582911

yes

characteristic

138

C₂

#31823671

yes

characteristic

139

C₂

#31823694

yes

characteristic

140

C₂

#31823724

yes

characteristic

	subgroup	G/H
center	C₂²	#22582851
commutator, cosocle	C₄²×C₂₈₁	C₂³
Frattini	C₄²	C₂²×D₂₈₁
Fitting	#477×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	#121
hypercenter	#477	D₂₈₁
hypocenter	C₂₈₁	#1672
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #477

subgroup

G/H

center

C₂²

#22582851

commutator, cosocle

C₄²×C₂₈₁

C₂³

Frattini

C₄²

C₂²×D₂₈₁

Fitting

#477×C₂₈₁

C₂

C₂²×C₂₈₁

D₂₈₁

C₂₈₁

G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #477

N	H ≅ G/N	type
46. #14555886	Q₁₆	semidirect
70. C₂₈₁	#1672	semidirect

H ≅ G/N

type

46. #14555886

Q₁₆

semidirect

70. C₂₈₁

#1672

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#31823859	2
#31823673	2
Q₈×#14555886	2
#31823213	2
#31823212	2
#31823210	2
#477×C₂₈₁	2
#1672	281

subgroup

index

#477×C₂₈₁

281

Subgroups — #49094687

Conjugacy classes of subgroups

Complements

Maximal subgroups