Finite Group Databasebeta

← #97092

Subgroups — #97092

Order 512.

1070 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 1070 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C22×#400C211yesmaximal, characteristic
2#8698C214yesmaximal
3#8299C212yesmaximal
4C23×C4⋊C4C411yescharacteristic
5C23×C4⋊C4C2211yescharacteristic
6C2×#400—28no—
7C2×#400—24no—
8C22×#95C412yes—
9C22×#95C411yescharacteristic
10C22×#95C2212yes—
11#1779C2214yes—
12C2×#324—24no—
13#1280—28no—
14C24×C4C2×C411yescharacteristic
15C24×C4C2×C411yescharacteristic
16C24×C4C2×C412yes—
17C24×C4C2×C412yes—
18C24×C4C2311yescharacteristic
19C22×C4⋊C4—24no—
20C22×C4⋊C4—22no—
21C22×C4⋊C4—24no—
22C22×C4⋊C4—44no—
23C22×C4⋊C4—44no—
24C22×C4⋊C4D414yes—
25C2×C22⋊C8—28no—
26C2×C22⋊C8—24no—
27#400—232no—
28C2×#95—24no—
29C2×#95—24no—
30C2×#95—24no—
31C2×#95—24no—
32C2×#95—22no—
33C2×#95—24no—
34C2×#95—24no—
35C2×#95D418yes—
36#324—48no—
37C25C22×C411yescharacteristic
38C23×C4—22no—
39C23×C4—22no—
40C23×C4—24no—
41C23×C4—24no—
42C23×C4—22no—
43C23×C4—22no—
44C23×C4—22no—
45C23×C4—22no—
46C23×C4—24no—
47C23×C4—28no—
48C23×C4—42no—
49C23×C4—42no—
50C23×C4—44no—
51C23×C4—44no—
52C23×C4—44no—
53C23×C4—44no—
54C23×C4—44no—
55C23×C4—44no—
56C23×C4—44no—
57C23×C4C22⋊C412yes—
58C23×C4C22⋊C414yes—
59C23×C4C22⋊C414yes—
60C23×C4C22⋊C412yes—
61C23×C4C2×D414yes—
62C23×C4C2×D412yes—
63C22×C8—44no—
64C2×C4⋊C4—28no—
65C2×C4⋊C4—28no—
66C2×C4⋊C4—28no—
67C2×C4⋊C4—44no—
68C2×C4⋊C4—416no—
69C2×C4⋊C4—416no—
70C2×C4⋊C4—44no—
71C2×C4⋊C4—44no—
72C22⋊C8—48no—
73C22⋊C8—416no—
74#95—216no—
75#95—28no—
76#95—216no—
77C24—22no—
78C24—24no—
79C24—22no—
80C24—24no—
81C24C2×C22⋊C411yescharacteristic
82C24C2×C22⋊C412yes—
83C24#13114yes—
84C22×C4—28no—
85C22×C4—28no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4—24no—
89C22×C4—24no—
90C22×C4—22no—
91C22×C4—22no—
92C22×C4—24no—
93C22×C4—28no—
94C22×C4—24no—
95C22×C4—24no—
96C22×C4—28no—
97C22×C4—28no—
98C22×C4—44no—
99C22×C4—44no—
100C22×C4—44no—
101C22×C4—416no—
102C22×C4—44no—
103C22×C4—416no—
104C22×C4—44no—
105C22×C4—44no—
106C22×C4—44no—
107C22×C4—44no—
108C22×C4—44no—
109C22×C4—44no—
110C22×C4—44no—
111C22×C4—44no—
112C22×C4—44no—
113C22×C4—44no—
114C22×C4—44no—
115C22×C4—44no—
116C22×C4—44no—
117C22×C4—44no—
118C22×C4—44no—
119C22×C4—44no—
120C22×C4—44no—
121C22×C4—44no—
122C22×C4—44no—
123C22×C4—44no—
124C22×C4—88no—
125C22×C4—816no—
126C22×C4—816no—
127C22×C4#9914yes—
128C22×C4#10114yes—
129C22×C4#12014yes—
130C2×C8—84no—
131C2×C8—88no—
132C4⋊C4—416no—
133C4⋊C4—416no—
134C23—28no—
135C23—28no—
136C23—216no—
137C23—28no—
138C23—216no—
139C23—22no—
140C23—22no—
141C23—22no—
142C23—22no—
143C23—22no—
144C23—22no—
145C23#37911yescharacteristic
146C23#40812yes—
147C23#40814yes—
148C23C2×#9912yes—
149C23#41014yes—
150C23C2×#10112yes—
151C23#41314yes—
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—416no—
159C2×C4—416no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—44no—
164C2×C4—44no—
165C2×C4—44no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4—44no—
170C2×C4—44no—
171C2×C4—84no—
172C2×C4—88no—
173C2×C4—88no—
174C2×C4—88no—
175C2×C4—88no—
176C2×C4—88no—
177C2×C4—88no—
178C2×C4—88no—
179C8—164no—
180C22—232no—
181C22—22no—
182C22—24no—
183C22—22no—
184C22—24no—
185C22—24no—
186C22—24no—
187C22—24no—
188C22—24no—
189C22—24no—
190C22—24no—
191C22#147214yes—
192C22#147318yes—
193C22#178011yescharacteristic
194C22#178111yescharacteristic
195C22#178212yes—
196C22#178411yescharacteristic
197C22#178512yes—
198C4—44no—
199C4—44no—
200C4—44no—
201C4—84no—
202C4—84no—
203C2—24no—
204C2—28no—
205C2#830811yescharacteristic
206C2#830912yes—
207C2#854311yescharacteristic
208C2#855211yescharacteristic
209C2#855412yes—
subgroupG/H
center, socleC23#379
commutator, prime radicalC25C22×C4
Frattini, cosocleC24×C4C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
C22×#4002
#86982
#82992