Group #93607 — subgroups

Subgroups — #93607

Order 512.

161 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 161 conjugacy classes of subgroups — too many to draw. Only its 70 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	#12901	C₂	1	1	yes	maximal, characteristic
2	#12881	C₂	1	1	yes	maximal, characteristic
3	#8780	C₂	1	1	yes	maximal, characteristic
4	C₂×#364	—	2	1	no	—
5	C₂×#364	—	2	1	no	—
6	C₂×#364	C₄	1	2	yes	—
7	#2150	—	2	1	no	—
8	#1726	C₂²	1	1	yes	characteristic
9	#1564	—	2	1	no	—
10	#1377	C₄	1	2	yes	—
11	#1375	—	2	1	no	—
12	#1281	—	2	1	no	—
13	#1274	C₄	1	2	yes	—
14	C₂×M₃₂	—	2	2	no	—
15	C₂×M₃₂	—	2	2	no	—
16	#431	—	2	2	no	—
17	C₂×#97	C₂×C₄	1	1	yes	characteristic
18	C₂×#97	D₄	1	1	yes	characteristic
19	C₂×#97	Q₈	1	1	yes	characteristic
20	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₈	D₄	1	1	yes	characteristic
22	C₂×C₄×C₈	D₄	1	1	yes	characteristic
23	#376	C₂×C₄	1	1	yes	characteristic
24	#364	—	4	2	no	—
25	#364	—	4	1	no	—
26	#364	—	4	1	no	—
27	#364	—	4	1	no	—
28	#364	—	4	1	no	—
29	C₄⋊C₁₆	—	4	1	no	—
30	C₄⋊C₁₆	—	4	1	no	—
31	#335	—	4	1	no	—
32	#334	—	4	1	no	—
33	C₂²×C₈	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₈	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄²	C₄²	1	1	yes	characteristic
38	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
40	M₃₂	—	4	2	no	—
41	M₃₂	—	4	2	no	—
42	M₃₂	—	4	2	no	—
43	M₃₂	—	4	2	no	—
44	C₂×C₁₆	—	4	2	no	—
45	C₂×C₁₆	—	4	2	no	—
46	C₄⋊C₈	—	4	2	no	—
47	C₂²⋊C₈	—	4	2	no	—
48	#97	—	2	2	no	—
49	#97	—	4	1	no	—
50	#97	—	4	1	no	—
51	C₄×C₈	—	2	1	no	—
52	C₄×C₈	—	2	1	no	—
53	C₄×C₈	—	4	2	no	—
54	C₄×C₈	D₈	1	1	yes	characteristic
55	C₄×C₈	D₈	1	1	yes	characteristic
56	C₄×C₈	SD₁₆	1	1	yes	characteristic
57	C₄×C₈	SD₁₆	1	1	yes	characteristic
58	C₄×C₈	SD₁₆	1	1	yes	characteristic
59	C₄×C₈	SD₁₆	1	1	yes	characteristic
60	C₄×C₈	Q₁₆	1	1	yes	characteristic
61	C₄×C₈	Q₁₆	1	1	yes	characteristic
62	#95	—	4	1	no	—
63	C₂²×C₄	—	2	1	no	—
64	C₂²×C₄	—	2	1	no	—
65	C₂²×C₄	—	2	1	no	—
66	C₂²×C₄	#95	1	1	yes	characteristic
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	2	1	no	—
70	C₂×C₈	—	2	1	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	8	2	no	—
74	C₂×C₈	#100	1	1	yes	characteristic
75	C₂×C₈	#101	1	1	yes	characteristic
76	C₂×C₈	#102	1	1	yes	characteristic
77	C₂×C₈	#102	1	1	yes	characteristic
78	C₂×C₈	#102	1	1	yes	characteristic
79	C₂×C₈	#103	1	1	yes	characteristic
80	C₂×C₈	#103	1	1	yes	characteristic
81	C₂×C₈	#103	1	1	yes	characteristic
82	C₂×C₈	#106	1	1	yes	characteristic
83	C₂×C₈	#107	1	1	yes	characteristic
84	C₂×C₈	#108	1	2	yes	—
85	C₄²	—	2	1	no	—
86	C₄²	—	2	1	no	—
87	C₄²	—	2	1	no	—
88	C₄²	—	2	1	no	—
89	C₄²	#102	1	1	yes	characteristic
90	C₄²	#103	1	1	yes	characteristic
91	C₄²	#106	1	1	yes	characteristic
92	C₄²	#107	1	1	yes	characteristic
93	C₁₆	—	8	2	no	—
94	C₁₆	—	8	2	no	—
95	C₂³	#344	1	1	yes	characteristic
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	8	1	no	—
102	C₂×C₄	—	8	1	no	—
103	C₂×C₄	—	8	1	no	—
104	C₂×C₄	H(3,ℤ/4)	1	1	yes	characteristic
105	C₂×C₄	#340	1	1	yes	characteristic
106	C₂×C₄	#340	1	1	yes	characteristic
107	C₂×C₄	#341	1	1	yes	characteristic
108	C₂×C₄	#343	1	1	yes	characteristic
109	C₂×C₄	#344	1	1	yes	characteristic
110	C₈	—	2	1	no	—
111	C₈	—	2	1	no	—
112	C₈	—	2	2	no	—
113	C₈	—	2	1	no	—
114	C₈	—	2	1	no	—
115	C₈	—	16	2	no	—
116	C₈	#331	1	1	yes	characteristic
117	C₈	#332	1	1	yes	characteristic
118	C₈	#332	1	1	yes	characteristic
119	C₈	#333	1	1	yes	characteristic
120	C₂²	—	4	1	no	—
121	C₂²	#1286	1	1	yes	characteristic
122	C₂²	#1301	1	1	yes	characteristic
123	C₂²	#1307	1	1	yes	characteristic
124	C₄	—	4	1	no	—
125	C₄	—	4	1	no	—
126	C₄	—	4	1	no	—
127	C₄	—	4	1	no	—
128	C₄	—	8	1	no	—
129	C₄	#1286	1	1	yes	characteristic
130	C₄	#1290	1	1	yes	characteristic
131	C₄	#1296	1	1	yes	characteristic
132	C₄	#1301	1	1	yes	characteristic
133	C₂	—	2	1	no	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	#7040	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#12901

C₂

yes

maximal, characteristic

#12881

C₂

yes

maximal, characteristic

#8780

C₂

yes

maximal, characteristic

C₂×#364

—

C₂×#364

—

C₂×#364

C₄

yes

—

#2150

—

#1726

C₂²

yes

characteristic

#1564

—

#1377

C₄

yes

—

#1375

—

#1281

—

#1274

C₄

yes

—

C₂×M₃₂

—

C₂×M₃₂

—

#431

—

C₂×#97

C₂×C₄

yes

characteristic

C₂×#97

D₄

yes

characteristic

C₂×#97

Q₈

yes

characteristic

C₂×C₄×C₈

C₂×C₄

yes

characteristic

C₂×C₄×C₈

D₄

yes

characteristic

C₂×C₄×C₈

D₄

yes

characteristic

#376

C₂×C₄

yes

—

—

—

—

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#335

—

#334

—

C₂²×C₈

C₂²⋊C₄

yes

characteristic

C₂²×C₈

C₂²⋊C₄

yes

characteristic

C₂²×C₈

C₄⋊C₄

yes

characteristic

C₂²×C₈

C₄⋊C₄

yes

characteristic

C₂×C₄²

C₄²

yes

characteristic

C₂×C₄²

C₂²⋊C₄

yes

characteristic

C₂×C₄²

C₄⋊C₄

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

D₈

yes

characteristic

C₄×C₈

D₈

yes

characteristic

C₄×C₈

SD₁₆

yes

characteristic

C₄×C₈

SD₁₆

yes

characteristic

C₄×C₈

SD₁₆

yes

characteristic

C₄×C₈

SD₁₆

yes

characteristic

C₄×C₈

Q₁₆

yes

characteristic

C₄×C₈

Q₁₆

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#95

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

yes

C₄²

yes

C₄²

yes

C₄²

yes

C₁₆

—

C₁₆

—

C₂³

#344

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

H(3,ℤ/4)

yes

characteristic

105

C₂×C₄

#340

yes

characteristic

106

C₂×C₄

#340

yes

characteristic

107

C₂×C₄

#341

yes

characteristic

108

C₂×C₄

#343

yes

characteristic

109

C₂×C₄

#344

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

#331

yes

characteristic

117

C₈

#332

yes

characteristic

118

C₈

#332

yes

characteristic

119

C₈

#333

yes

characteristic

120

C₂²

—

121

C₂²

#1286

yes

characteristic

122

C₂²

#1301

yes

characteristic

123

C₂²

#1307

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

#1286

yes

characteristic

130

C₄

#1290

yes

characteristic

131

C₄

#1296

yes

characteristic

132

C₄

#1301

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

—

136

C₂

#7040

yes

characteristic

	subgroup	G/H
center	C₄	#1286
commutator	C₂×C₄²	C₄²
Frattini, cosocle	#1726	C₂²
socle	C₂	#7040
prime radical	C₂³	#344
LCS	G ▷ C₂×C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1726 ◁ G
LECS	G ▷ #1726 ▷ C₂²×C₄ ▷ C₂ ▷ C₁

subgroup

G/H

center

C₄

#1286

commutator

C₂×C₄²

C₄²

C₂²

C₂

C₂³

G ▷ C₂×C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1726 ◁ G

LECS

G ▷ #1726 ▷ C₂²×C₄ ▷ C₂ ▷ C₁

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

subgroup	index
#12901	2
#12881	2
#8780	2

subgroup

index

#12901

#12881

#8780

Subgroups — #93607

Conjugacy classes of subgroups

Maximal subgroups