Finite Group Databasebeta

← #119493

Subgroups — #119493

Order 512.

822 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C2×#1463C212yesmaximal
2#14339C211yesmaximal, characteristic
3C2×#1305C214yesmaximal
4C23×C4⋊C4C2211yescharacteristic
5C2×#407C2214yes—
6C2×#381C412yes—
7C2×#380C2212yes—
8#1463—28no—
9C2×#324—22no—
10C2×#324—22no—
11#1441—22no—
12#1441—22no—
13C22⋊#95C412yes—
14#1305—28no—
15C24×C4C2×C411yescharacteristic
16C24×C4C2×C411yescharacteristic
17C24×C4C2311yescharacteristic
18C22×M16—24no—
19C22×C4⋊C4—24no—
20C22×C4⋊C4—24no—
21C22×C4⋊C4—24no—
22C22×C4⋊C4—22no—
23C22×C4⋊C4D412yes—
24C22×C4⋊C4D412yes—
25C22×C22⋊C4C2×C414yes—
26#407—24no—
27#407—24no—
28#407—24no—
29#407D418yes—
30C2×C22⋊C8—24no—
31C2×C22⋊C8—24no—
32#381—44no—
33#380—24no—
34#380—24no—
35C2×#95—22no—
36C2×#95—22no—
37C2×#95—22no—
38C2×#95—24no—
39#324—28no—
40#324—28no—
41C25C22×C411yescharacteristic
42C23×C4—22no—
43C23×C4—22no—
44C23×C4—22no—
45C23×C4—24no—
46C23×C4—22no—
47C23×C4—24no—
48C23×C4—24no—
49C23×C4—42no—
50C23×C4—82no—
51C23×C4—82no—
52C23×C4C22⋊C411yescharacteristic
53C23×C4C22⋊C411yescharacteristic
54C23×C4C22⋊C412yes—
55C23×C4C2×D412yes—
56C23×C4C2×D414yes—
57C23×C4#4114yes—
58C23×C4#4114yes—
59C2×M16—28no—
60C2×M16—44no—
61C2×M16—88no—
62C22×C8—44no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—24no—
66C2×C4⋊C4—24no—
67C2×C4⋊C4—24no—
68C2×C4⋊C4—24no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—44no—
72C2×C4⋊C4—44no—
73C2×C4⋊C4—44no—
74C2×C4⋊C4—44no—
75C2×C4⋊C4—44no—
76C2×C4⋊C4—84no—
77C2×C22⋊C4—28no—
78C2×C22⋊C4—44no—
79C2×C22⋊C4—44no—
80C22⋊C8—28no—
81C22⋊C8—28no—
82C22⋊C8—44no—
83C22⋊C8—44no—
84#95—44no—
85#95—44no—
86#95—42no—
87#95—42no—
88#95—84no—
89C24—21no—
90C24—21no—
91C24—22no—
92C24—42no—
93C24—42no—
94C24C2×C22⋊C411yescharacteristic
95C24#11712yes—
96C24C4×D414yes—
97C22×C4—28no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4—22no—
101C22×C4—22no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—22no—
107C22×C4—22no—
108C22×C4—22no—
109C22×C4—44no—
110C22×C4—48no—
111C22×C4—48no—
112C22×C4—48no—
113C22×C4—44no—
114C22×C4—44no—
115C22×C4—44no—
116C22×C4—44no—
117C22×C4—48no—
118C22×C4—48no—
119C22×C4—44no—
120C22×C4—44no—
121C22×C4—44no—
122C22×C4—84no—
123C22×C4—84no—
124C22×C4—84no—
125C22×C4—88no—
126C22×C4#10012yes—
127C22×C4#10112yes—
128C22×C4#12012yes—
129C22×C4#12114yes—
130C22×C4#12114yes—
131C22×C4#12314yes—
132C22×C4#12314yes—
133C22×C4#12312yes—
134C22×C4#12414yes—
135C22×C4#12614yes—
136M16—88no—
137M16—88no—
138C2×C8—48no—
139C2×C8—88no—
140C4⋊C4—44no—
141C4⋊C4—44no—
142C4⋊C4—44no—
143C4⋊C4—44no—
144C4⋊C4—88no—
145C22⋊C4—88no—
146C23—22no—
147C23—22no—
148C23—22no—
149C23—22no—
150C23—24no—
151C23—24no—
152C23—24no—
153C23—24no—
154C23—44no—
155C23—44no—
156C23—44no—
157C23—44no—
158C23—48no—
159C23#38111yescharacteristic
160C23#38612yes—
161C23#38814yes—
162C23C2×#10011yescharacteristic
163C23C2×#10111yescharacteristic
164C23#41312yes—
165C2×C4—28no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—24no—
170C2×C4—44no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—42no—
174C2×C4—44no—
175C2×C4—42no—
176C2×C4—44no—
177C2×C4—416no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—88no—
187C2×C4—82no—
188C2×C4—82no—
189C2×C4—84no—
190C2×C4—88no—
191C2×C4—88no—
192C2×C4—84no—
193C2×C4—84no—
194C2×C4#39414yes—
195C2×C4#39714yes—
196C8—88no—
197C22—22no—
198C22—22no—
199C22—24no—
200C22—22no—
201C22—22no—
202C22—24no—
203C22—24no—
204C22—24no—
205C22—48no—
206C22—48no—
207C22—44no—
208C22—44no—
209C22#144011yescharacteristic
210C22#182111yescharacteristic
211C22#182211yescharacteristic
212C22#182812yes—
213C22#183012yes—
214C22#190012yes—
215C22#190112yes—
216C4—24no—
217C4—24no—
218C4—42no—
219C4—42no—
220C4—82no—
221C4—164no—
222C2—22no—
223C2—22no—
224C2—44no—
225C2#875712yes—
226C2#875812yes—
227C2#1116811yescharacteristic
228C2#1116911yescharacteristic
229C2#1119811yescharacteristic
subgroupG/H
center, socleC23#381
commutator, prime radicalC25C22×C4
Frattini, cosocleC24×C4C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#14632
#143392
C2×#13052