Group #10643 — subgroups

Subgroups — #10643

Order 256.

149 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 149 conjugacy classes of subgroups — too many to draw. Only its 51 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	#1805	C₂	1	1	yes	maximal, characteristic
2	#1801	C₂	1	1	yes	maximal, characteristic
3	#1570	C₂	1	1	yes	maximal, characteristic
4	#1479	C₂	1	1	yes	maximal, characteristic
5	#1301	C₂	1	1	yes	maximal, characteristic
6	#1286	C₂	1	1	yes	maximal, characteristic
7	#1286	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
9	#431	C₂²	1	1	yes	characteristic
10	#431	C₂²	1	1	yes	characteristic
11	#423	C₂²	1	1	yes	characteristic
12	#423	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×#103	—	2	1	no	—
15	C₂×#101	—	2	1	no	—
16	#382	C₂²	1	1	yes	characteristic
17	#343	—	2	1	no	—
18	#340	—	2	1	no	—
19	#334	—	2	2	no	—
20	Q₈⋊C₈	—	2	2	no	—
21	C₂²×Q₈	D₄	1	1	yes	characteristic
22	C₂×M₁₆	—	2	1	no	—
23	C₂×M₁₆	—	2	1	no	—
24	C₂²×C₈	—	2	1	no	—
25	C₄×Q₈	—	2	1	no	—
26	C₄×Q₈	—	2	1	no	—
27	C₄×Q₈	—	2	1	no	—
28	C₄×Q₈	—	2	1	no	—
29	C₂×C₄⋊C₄	—	2	1	no	—
30	C₂×C₄⋊C₄	—	2	1	no	—
31	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
32	C₂×C₄²	—	2	1	no	—
33	C₂×C₄²	C₂³	1	1	yes	characteristic
34	C₄⋊C₈	—	2	1	no	—
35	C₄⋊C₈	—	2	1	no	—
36	C₄⋊C₈	—	2	1	no	—
37	C₄⋊C₈	—	2	1	no	—
38	C₄⋊C₈	—	2	1	no	—
39	C₄⋊C₈	—	2	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	2	1	no	—
42	#103	—	4	2	no	—
43	#101	—	4	2	no	—
44	C₂²⋊C₈	—	2	1	no	—
45	C₂²⋊C₈	—	2	1	no	—
46	C₄×C₈	—	2	1	no	—
47	C₄×C₈	D₄	1	2	yes	—
48	#95	—	2	1	no	—
49	#95	—	2	1	no	—
50	C₂×Q₈	—	2	1	no	—
51	C₂×Q₈	—	2	1	no	—
52	C₂×Q₈	—	2	1	no	—
53	C₂×Q₈	—	2	1	no	—
54	C₂×Q₈	—	2	1	no	—
55	C₂×Q₈	SD₁₆	1	2	yes	—
56	C₂²×C₄	—	2	1	no	—
57	C₂²×C₄	—	2	1	no	—
58	C₂²×C₄	—	4	1	no	—
59	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄	#41	1	1	yes	characteristic
61	C₂²×C₄	#41	1	1	yes	characteristic
62	M₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	M₁₆	—	4	1	no	—
65	M₁₆	—	4	1	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	4	1	no	—
68	C₂×C₈	—	4	1	no	—
69	C₂×C₈	—	4	1	no	—
70	C₂×C₈	—	4	1	no	—
71	C₂×C₈	—	4	1	no	—
72	C₂×C₈	—	4	1	no	—
73	C₄⋊C₄	—	2	1	no	—
74	C₄⋊C₄	—	2	1	no	—
75	C₄⋊C₄	—	4	1	no	—
76	C₄⋊C₄	—	4	1	no	—
77	C₄⋊C₄	—	4	1	no	—
78	C₄⋊C₄	—	4	1	no	—
79	C₄²	—	4	1	no	—
80	C₄²	—	4	1	no	—
81	C₄²	C₂×D₄	1	1	yes	characteristic
82	C₄²	#41	1	1	yes	characteristic
83	C₄²	#41	1	1	yes	characteristic
84	C₄²	#41	1	1	yes	characteristic
85	C₂³	#123	1	1	yes	characteristic
86	Q₈	—	2	2	no	—
87	Q₈	—	2	2	no	—
88	Q₈	—	4	1	no	—
89	Q₈	—	4	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	—	4	1	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	8	1	no	—
97	C₂×C₄	—	8	1	no	—
98	C₂×C₄	—	8	1	no	—
99	C₂×C₄	—	8	1	no	—
100	C₂×C₄	#121	1	1	yes	characteristic
101	C₂×C₄	#123	1	1	yes	characteristic
102	C₂×C₄	#123	1	1	yes	characteristic
103	C₂×C₄	#124	1	1	yes	characteristic
104	C₂×C₄	#126	1	1	yes	characteristic
105	C₂×C₄	#126	1	1	yes	characteristic
106	C₂×C₄	C₂×SD₁₆	1	1	yes	characteristic
107	C₂×C₄	#135	1	1	yes	characteristic
108	C₂×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×C₄	#137	1	1	yes	characteristic
110	C₈	—	4	2	no	—
111	C₈	—	8	1	no	—
112	C₈	—	8	1	no	—
113	C₈	—	8	1	no	—
114	C₈	—	8	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	#397	1	1	yes	characteristic
118	C₂²	#482	1	1	yes	characteristic
119	C₂²	#483	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	2	1	no	—
122	C₄	—	2	1	no	—
123	C₄	—	2	1	no	—
124	C₄	—	4	2	no	—
125	C₄	—	8	1	no	—
126	C₄	—	16	1	no	—
127	C₄	#465	1	1	yes	characteristic
128	C₄	#468	1	1	yes	characteristic
129	C₄	#481	1	1	yes	characteristic
130	C₄	#485	1	1	yes	characteristic
131	C₂	—	2	1	no	—
132	C₂	—	2	1	no	—
133	C₂	#2077	1	1	yes	characteristic
134	C₂	#2080	1	1	yes	characteristic
135	C₂	#2082	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#1805

C₂

yes

maximal, characteristic

#1801

C₂

yes

maximal, characteristic

#1570

C₂

yes

maximal, characteristic

#1479

C₂

yes

maximal, characteristic

#1301

C₂

yes

maximal, characteristic

#1286

C₂

yes

maximal, characteristic

#1286

C₂

yes

maximal, characteristic

C₂×C₄×Q₈

C₂²

yes

characteristic

#431

C₂²

yes

characteristic

#431

C₂²

yes

characteristic

#423

C₂²

yes

characteristic

#423

C₂²

yes

characteristic

C₂×C₄⋊C₈

C₂²

yes

—

—

C₂²

yes

—

—

—

Q₈⋊C₈

—

C₂²×Q₈

D₄

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂³

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#101

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

D₄

yes

—

#95

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

SD₁₆

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄

yes

C₂²×C₄

yes

C₂²×C₄

yes

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×D₄

yes

C₄²

yes

C₄²

yes

C₄²

yes

C₂³

yes

Q₈

—

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

#121

yes

characteristic

101

C₂×C₄

#123

yes

characteristic

102

C₂×C₄

#123

yes

characteristic

103

C₂×C₄

#124

yes

characteristic

104

C₂×C₄

#126

yes

characteristic

105

C₂×C₄

#126

yes

characteristic

106

C₂×C₄

C₂×SD₁₆

yes

characteristic

107

C₂×C₄

#135

yes

characteristic

108

C₂×C₄

AGL(1,ℤ/8)

yes

characteristic

109

C₂×C₄

#137

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

#397

yes

characteristic

118

C₂²

#482

yes

characteristic

119

C₂²

#483

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

#465

yes

characteristic

128

C₄

#468

yes

characteristic

129

C₄

#481

yes

characteristic

130

C₄

#485

yes

characteristic

131

C₂

—

132

C₂

—

133

C₂

#2077

yes

characteristic

134

C₂

#2080

yes

characteristic

135

C₂

#2082

yes

characteristic

	subgroup	G/H
center, socle	C₂²	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³
prime radical	C₂³	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

subgroup

G/H

center, socle

C₂²

#397

commutator, Frattini, cosocle

C₂×C₄²

C₂³

prime radical

C₂³

#123

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ G

LECS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

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

subgroup	index
#1805	2
#1801	2
#1570	2
#1479	2
#1301	2
#1286	2

subgroup

index

Subgroups — #10643

Conjugacy classes of subgroups

Maximal subgroups