Finite Group Databasebeta

← #93044

Subgroups — #93044

Order 512.

225 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11459C211yesmaximal, characteristic
2#8599C211yesmaximal, characteristic
3#8007C211yesmaximal, characteristic
4#2920—21no—
5C2×#431C2211yescharacteristic
6#2162—21no—
7#1797—21no—
8C2×#335C411yescharacteristic
9C2×#335C411yescharacteristic
10#1322C412yes—
11#1314—21no—
12#1293—21no—
13#1293C412yes—
14#1277—21no—
15C22×C42D411yescharacteristic
16#432—22no—
17#432—41no—
18#431—22no—
19#431—41no—
20#431—41no—
21#431—41no—
22#423—41no—
23C2×C4⋊C8—21no—
24C2×C4⋊C8—21no—
25C2×C4⋊C8C2×C411yescharacteristic
26C2×C4⋊C8Q811yescharacteristic
27#407—22no—
28C2×C22⋊C8—41no—
29C2×C22⋊C8C2×C411yescharacteristic
30C2×C22⋊C8D411yescharacteristic
31C4×M16—41no—
32C2×C4×C8C2×C411yescharacteristic
33C2×C4×C8D411yescharacteristic
34C4⋊C16—41no—
35C22⋊C16—22no—
36C4×C16—41no—
37#336—41no—
38#335—41no—
39#335—41no—
40C23×C4C22⋊C411yescharacteristic
41C23×C4SD1611yescharacteristic
42C23×C4Q1611yescharacteristic
43C2×M16—42no—
44C22×C8—41no—
45C22×C8—41no—
46C22×C8C4211yescharacteristic
47C22×C8C22⋊C411yescharacteristic
48C22×C8C4⋊C411yescharacteristic
49C22×C8C4⋊C411yescharacteristic
50C2×C42—21no—
51C2×C42—21no—
52C2×C42—21no—
53C2×C42—21no—
54C2×C42C22⋊C411yescharacteristic
55C2×C42C4⋊C411yescharacteristic
56C2×C42D811yescharacteristic
57C2×C42SD1611yescharacteristic
58C2×C16—42no—
59C4⋊C8—41no—
60C4⋊C8—41no—
61C4⋊C8—42no—
62C4⋊C8—42no—
63C4⋊C8—41no—
64C4⋊C8—41no—
65C4⋊C8—41no—
66C4⋊C8—41no—
67C22⋊C8—24no—
68C22⋊C8—41no—
69C22⋊C8—41no—
70C22⋊C8—42no—
71C22⋊C8—82no—
72#97—42no—
73C4×C8—21no—
74C4×C8—21no—
75C4×C8—21no—
76C4×C8—21no—
77C4×C8—42no—
78C24#10311yescharacteristic
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—41no—
90C22×C4—41no—
91C22×C4—81no—
92C22×C4#9511yescharacteristic
93C22×C4#10211yescharacteristic
94C22×C4#10211yescharacteristic
95C22×C4#10311yescharacteristic
96C22×C4#10611yescharacteristic
97C22×C4#10711yescharacteristic
98M16—82no—
99M16—82no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—41no—
105C2×C8—41no—
106C2×C8—41no—
107C2×C8—41no—
108C2×C8—44no—
109C2×C8—81no—
110C2×C8—81no—
111C2×C8—81no—
112C2×C8—81no—
113C2×C8—81no—
114C2×C8—81no—
115C42—21no—
116C42—21no—
117C42—21no—
118C42—21no—
119C42—21no—
120C42—21no—
121C42#9911yescharacteristic
122C42#9911yescharacteristic
123C42#10411yescharacteristic
124C42#10411yescharacteristic
125C16—82no—
126C23—21no—
127C23—21no—
128C23—21no—
129C23—41no—
130C23—41no—
131C23#34011yescharacteristic
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—42no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4#32711yescharacteristic
152C2×C4#32711yescharacteristic
153C2×C4#32811yescharacteristic
154C2×C4#32811yescharacteristic
155C2×C4#33911yescharacteristic
156C2×C4#34211yescharacteristic
157C2×C4#35911yescharacteristic
158C2×C4#35911yescharacteristic
159C2×C4#36111yescharacteristic
160C2×C4#36211yescharacteristic
161C8—41no—
162C8—41no—
163C8—41no—
164C8—41no—
165C8—84no—
166C8—161no—
167C8—161no—
168C22—21no—
169C22—21no—
170C22—42no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—81no—
175C22#129411yescharacteristic
176C22#138211yescharacteristic
177C22#138711yescharacteristic
178C4—21no—
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4#134911yescharacteristic
185C4#134911yescharacteristic
186C4#135011yescharacteristic
187C4#135011yescharacteristic
188C4#139111yescharacteristic
189C4#139511yescharacteristic
190C2—21no—
191C2—21no—
192C2—81no—
193C2#725211yescharacteristic
194C2#725711yescharacteristic
195C2#725911yescharacteristic
subgroupG/H
centerC2×C4#327
commutatorC22×C8C42
Frattini, cosocleC2×#431C22
socleC22#1294
prime radicalC24#103
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#431 ◁ G
LECSG ▷ C2×#431 ▷ C22×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#114592
#85992
#80072