Finite Group Databasebeta

← #97089

Subgroups — #97089

Order 512.

1222 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 130 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×#398C211yesmaximal, characteristic
2#8698C214yesmaximal
3#8299C212yesmaximal
4C23×C4⋊C4C412yes—
5C23×C4⋊C4C411yescharacteristic
6C23×C4⋊C4C2211yescharacteristic
7C2×#398—28no—
8C2×#398—24no—
9C22×#95C411yescharacteristic
10C22×#95C2212yes—
11#1779C2214yes—
12C2×#324—24no—
13#1280—28no—
14C24×C4C2×C411yescharacteristic
15C24×C4C2×C412yes—
16C24×C4C2×C411yescharacteristic
17C24×C4C2×C412yes—
18C24×C4C2311yescharacteristic
19C22×C4⋊C4—24no—
20C22×C4⋊C4—24no—
21C22×C4⋊C4—24no—
22C22×C4⋊C4—22no—
23C22×C4⋊C4—24no—
24C22×C4⋊C4—24no—
25C22×C4⋊C4—44no—
26C22×C4⋊C4—44no—
27C22×C4⋊C4—48no—
28C22×C4⋊C4D414yes—
29C2×C22⋊C8—28no—
30C2×C22⋊C8—24no—
31#398—232no—
32C2×#95—24no—
33C2×#95—22no—
34C2×#95—24no—
35C2×#95—24no—
36C2×#95D418yes—
37#324—48no—
38C25C22×C411yescharacteristic
39C23×C4—22no—
40C23×C4—22no—
41C23×C4—22no—
42C23×C4—22no—
43C23×C4—24no—
44C23×C4—24no—
45C23×C4—28no—
46C23×C4—22no—
47C23×C4—22no—
48C23×C4—24no—
49C23×C4—28no—
50C23×C4—42no—
51C23×C4—42no—
52C23×C4—44no—
53C23×C4—44no—
54C23×C4—44no—
55C23×C4—44no—
56C23×C4—44no—
57C23×C4—44no—
58C23×C4C22⋊C412yes—
59C23×C4C22⋊C414yes—
60C23×C4C22⋊C412yes—
61C23×C4C22⋊C414yes—
62C23×C4C2×D414yes—
63C23×C4C2×D412yes—
64C22×C8—44no—
65C2×C4⋊C4—216no—
66C2×C4⋊C4—28no—
67C2×C4⋊C4—28no—
68C2×C4⋊C4—28no—
69C2×C4⋊C4—44no—
70C2×C4⋊C4—416no—
71C2×C4⋊C4—416no—
72C2×C4⋊C4—416no—
73C2×C4⋊C4—416no—
74C2×C4⋊C4—44no—
75C2×C4⋊C4—48no—
76C2×C4⋊C4—44no—
77C2×C4⋊C4—48no—
78C22⋊C8—48no—
79C22⋊C8—416no—
80#95—28no—
81#95—216no—
82C24—22no—
83C24—24no—
84C24—22no—
85C24—24no—
86C24C2×C22⋊C411yescharacteristic
87C24C2×C22⋊C412yes—
88C24#13114yes—
89C22×C4—28no—
90C22×C4—28no—
91C22×C4—28no—
92C22×C4—28no—
93C22×C4—24no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—24no—
97C22×C4—24no—
98C22×C4—22no—
99C22×C4—22no—
100C22×C4—24no—
101C22×C4—24no—
102C22×C4—28no—
103C22×C4—24no—
104C22×C4—28no—
105C22×C4—44no—
106C22×C4—44no—
107C22×C4—44no—
108C22×C4—416no—
109C22×C4—44no—
110C22×C4—44no—
111C22×C4—416no—
112C22×C4—432no—
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—44no—
125C22×C4—44no—
126C22×C4—44no—
127C22×C4—44no—
128C22×C4—44no—
129C22×C4—44no—
130C22×C4—88no—
131C22×C4—816no—
132C22×C4#9914yes—
133C22×C4#10014yes—
134C22×C4#10118yes—
135C22×C4#12014yes—
136C2×C8—84no—
137C2×C8—88no—
138C4⋊C4—416no—
139C4⋊C4—416no—
140C4⋊C4—432no—
141C23—28no—
142C23—216no—
143C23—28no—
144C23—216no—
145C23—28no—
146C23—22no—
147C23—22no—
148C23—22no—
149C23—22no—
150C23—22no—
151C23—22no—
152C23#37911yescharacteristic
153C23#40814yes—
154C23#40812yes—
155C23C2×#9912yes—
156C23#41014yes—
157C23C2×#10012yes—
158C23C2×#10114yes—
159C2×C4—28no—
160C2×C4—24no—
161C2×C4—24no—
162C2×C4—28no—
163C2×C4—24no—
164C2×C4—28no—
165C2×C4—44no—
166C2×C4—416no—
167C2×C4—416no—
168C2×C4—416no—
169C2×C4—48no—
170C2×C4—416no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—44no—
178C2×C4—48no—
179C2×C4—44no—
180C2×C4—44no—
181C2×C4—44no—
182C2×C4—84no—
183C2×C4—88no—
184C2×C4—88no—
185C2×C4—88no—
186C2×C4—88no—
187C8—164no—
188C22—232no—
189C22—22no—
190C22—24no—
191C22—22no—
192C22—24no—
193C22—24no—
194C22—24no—
195C22—24no—
196C22—24no—
197C22—24no—
198C22—24no—
199C22#147018yes—
200C22#147114yes—
201C22#178011yescharacteristic
202C22#178111yescharacteristic
203C22#178212yes—
204C22#178311yescharacteristic
205C22#178412yes—
206C4—44no—
207C4—44no—
208C4—48no—
209C4—44no—
210C4—84no—
211C2—28no—
212C2—24no—
213C2#830612yes—
214C2#830711yescharacteristic
215C2#854311yescharacteristic
216C2#855111yescharacteristic
217C2#855512yes—
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×#3982
#86982
#82992