Finite Group Databasebeta

← #93158

Subgroups — #93158

Order 512.

479 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 479 conjugacy classes of subgroups — too many to draw. Only its 48 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#11381C211yesmaximal, characteristic
2#8550C211yesmaximal, characteristic
3#8308C211yesmaximal, characteristic
4C22×C22⋊Q8C2211yescharacteristic
5#1784C412yescomplemented
6#1779—21no—
7C2×#342—21no—
8C2×#342C412yes—
9#1463—21no—
10#1462—21no—
11C2×#324—21no—
12C2×#324C412yescomplemented
13C22⋊#95—21no—
14C23×Q8C2×C411yescharacteristic
15C24×C4D411yescharacteristic
16C2×C22⋊Q8—42no—
17C2×C22⋊Q8—42no—
18C2×C22⋊Q8—42no—
19C22×C4⋊C4C2×C411yescharacteristic
20C22×C4⋊C4D411yescharacteristic
21C22×C4⋊C4Q811yescharacteristic
22C22×C22⋊C4—22no—
23C22×C22⋊C4C2×C411yescharacteristic
24C22×C22⋊C4D411yescharacteristic
25C2×#101—42no—
26#407—22no—
27C2×C22⋊C8—22no—
28C2×C22⋊C8—42no—
29C2×#95—42no—
30#342—42no—
31#342—42no—
32#324—42no—
33#324—42no—
34#324—42no—
35#323—42no—
36C25C22⋊C411yescharacteristic
37C22×Q8—22no—
38C22×Q8—41no—
39C22×Q8—41no—
40C22×Q8—82no—
41C23×C4—22no—
42C23×C4—22no—
43C23×C4—41no—
44C23×C4—42no—
45C23×C4—82no—
46C23×C4C4211yescharacteristic
47C23×C4C22⋊C411yescharacteristic
48C23×C4C22⋊C411yescharacteristic
49C23×C4C4⋊C411yescharacteristic
50C23×C4C4⋊C411yescharacteristic
51C23×C4C4⋊C411yescharacteristic
52C2×M16—42no—
53C22×C8—42no—
54C22⋊Q8—416no—
55C2×C4⋊C4—22no—
56C2×C4⋊C4—22no—
57C2×C4⋊C4—22no—
58C2×C4⋊C4—41no—
59C2×C4⋊C4—41no—
60C2×C4⋊C4—41no—
61C2×C4⋊C4—41no—
62C2×C4⋊C4—41no—
63C2×C4⋊C4—41no—
64C2×C22⋊C4—22no—
65C2×C22⋊C4—22no—
66C2×C22⋊C4—22no—
67C2×C22⋊C4—24no—
68C2×C22⋊C4—41no—
69C2×C22⋊C4—41no—
70C2×C22⋊C4—41no—
71C2×C22⋊C4—42no—
72C2×C22⋊C4—42no—
73C2×C22⋊C4—42no—
74C2×C22⋊C4—42no—
75C2×C22⋊C4—42no—
76#101—84no—
77C22⋊C8—42no—
78C22⋊C8—42no—
79C22⋊C8—42no—
80C22⋊C8—42no—
81C22⋊C8—84no—
82#95—84no—
83C24—21no—
84C24—21no—
85C24—22no—
86C24—22no—
87C24—42no—
88C24—81no—
89C24#9511yescharacteristic
90C24#9912yes—
91C2×Q8—44no—
92C2×Q8—44no—
93C2×Q8—82no—
94C2×Q8—82no—
95C2×Q8—82no—
96C2×Q8—82no—
97C2×Q8—82no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—42no—
115C22×C4—44no—
116C22×C4—44no—
117C22×C4—44no—
118C22×C4—42no—
119C22×C4—42no—
120C22×C4—44no—
121C22×C4—82no—
122C22×C4—81no—
123C22×C4—82no—
124C22×C4—82no—
125C22×C4—81no—
126C22×C4—81no—
127C22×C4—82no—
128C22×C4—82no—
129C22×C4—82no—
130C22×C4—84no—
131C22×C4—84no—
132C22×C4#9912yes—
133C22×C4#9912yes—
134M16—84no—
135C2×C8—82no—
136C2×C8—82no—
137C2×C8—84no—
138C4⋊C4—44no—
139C4⋊C4—44no—
140C4⋊C4—44no—
141C22⋊C4—44no—
142C22⋊C4—44no—
143C22⋊C4—44no—
144C22⋊C4—44no—
145C22⋊C4—82no—
146C22⋊C4—82no—
147C23—22no—
148C23—21no—
149C23—21no—
150C23—22no—
151C23—21no—
152C23—21no—
153C23—22no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—41no—
158C23—42no—
159C23—42no—
160C23—42no—
161C23—42no—
162C23—81no—
163C23—81no—
164C23—84no—
165C23—84no—
166C23#34211yescharacteristic
167C23#34211yescharacteristic
168C23#34211yescharacteristic
169C23#35512yes—
170C23#35612yes—
171Q8—88no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—81no—
194C2×C4—88no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—84no—
201C2×C4—88no—
202C2×C4—164no—
203C2×C4—162no—
204C2×C4—162no—
205C8—162no—
206C8—162no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—21no—
213C22—22no—
214C22—21no—
215C22—21no—
216C22—44no—
217C22—42no—
218C22—42no—
219C22—44no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—82no—
225C22—81no—
226C22—82no—
227C22—81no—
228C22#130411yescharacteristic
229C22#139412yes—
230C22#139512yes—
231C4—42no—
232C4—42no—
233C4—42no—
234C4—81no—
235C4—81no—
236C4—81no—
237C4—164no—
238C2—22no—
239C2—22no—
240C2—42no—
241C2—41no—
242C2—42no—
243C2#730811yescharacteristic
244C2#730911yescharacteristic
245C2#731011yescharacteristic
subgroupG/H
center, socleC22#1304
commutatorC23×C4C42
Frattini, cosocleC22×C22⋊Q8C22
prime radicalC25C22⋊C4
LCSG ▷ C23×C4 ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊Q8 ◁ G
LECSG ▷ C22×C22⋊Q8 ▷ C24 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. #1784C4semidirect
12. C2×#324C4semidirect

Maximal subgroups

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

subgroupindex
#113812
#85502
#83082