Finite Group Databasebeta

← #129390

Subgroups — #129390

Order 512.

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

normal subgroups only

This group has 672 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×#446C211yesmaximal, characteristic
2#12846C212yesmaximal
3#11440C212yesmaximal
4#11440C212yesmaximal
5C22×C4×Q8C411yescharacteristic
6C2×#446—24no—
7C2×#446—24no—
8C2×#446—24no—
9C22×C4⋊C8C411yescharacteristic
10C22×C4⋊C8C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×#97C411yescharacteristic
13C22×#97C2211yescharacteristic
14C22×C4×C8C411yescharacteristic
15#2112C2214yes—
16#1377—24no—
17#1322—24no—
18#1322—24no—
19C23×Q8C811yescharacteristic
20C23×C8C2×C411yescharacteristic
21C23×C8C2×C411yescharacteristic
22C23×C8C2×C411yescharacteristic
23C23×C8C2311yescharacteristic
24C2×C4×Q8—22no—
25C2×C4×Q8—22no—
26C2×C4×Q8—22no—
27C2×C4×Q8—22no—
28C2×C4×Q8—22no—
29C2×C4×Q8—22no—
30C22×C4⋊C4C811yescharacteristic
31C22×C4⋊C4C811yescharacteristic
32C22×C4⋊C4C811yescharacteristic
33C22×C42C2×C411yescharacteristic
34C22×C42C2×C411yescharacteristic
35C22×C42C2×C411yescharacteristic
36C2×M32—24no—
37#446—232no—
38C2×C4⋊C8—22no—
39C2×C4⋊C8—22no—
40C2×C4⋊C8—22no—
41C2×C4⋊C8—22no—
42C2×C4⋊C8—22no—
43C2×C4⋊C8—22no—
44C2×C4⋊C8—22no—
45C2×C4⋊C8D414yes—
46C2×C4⋊C8D414yes—
47C2×#97—22no—
48C2×#97—22no—
49C2×#97—22no—
50C2×#97—22no—
51C2×#97—22no—
52C2×#97D414yes—
53C2×C4×C8—22no—
54C2×C4×C8—22no—
55C2×C4×C8—22no—
56C22⋊C16—24no—
57C22⋊C16—24no—
58C22×Q8—22no—
59C22×Q8—22no—
60C22×Q8—22no—
61C22×Q8—44no—
62C23×C4C2×C811yescharacteristic
63C23×C4C2×C811yescharacteristic
64C23×C4C2×C811yescharacteristic
65C23×C4C2×C811yescharacteristic
66C23×C4C2×C811yescharacteristic
67C23×C4C2×C811yescharacteristic
68C23×C4C22×C411yescharacteristic
69C22×C8—21no—
70C22×C8—21no—
71C22×C8—24no—
72C22×C8—21no—
73C22×C8—21no—
74C22×C8—21no—
75C22×C8—21no—
76C22×C8—42no—
77C22×C8—42no—
78C22×C8—42no—
79C22×C8C22⋊C412yes—
80C22×C8C22⋊C412yes—
81C22×C8C22⋊C412yes—
82C22×C8C2×D412yes—
83C22×C8C2×D412yes—
84C22×C8C2×D412yes—
85C4×Q8—28no—
86C4×Q8—28no—
87C4×Q8—28no—
88C4×Q8—28no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4—22no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—22no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—21no—
101C2×C42—21no—
102C2×C42—21no—
103C2×C42—21no—
104C2×C42—21no—
105C2×C42—21no—
106C2×C42—21no—
107C2×C42—21no—
108C2×C42—21no—
109C2×C42—21no—
110C2×C42C22⋊C412yes—
111C2×C42C22⋊C412yes—
112C2×C42C22⋊C412yes—
113C2×C42M1612yes—
114C2×C42M1612yes—
115C2×C42M1612yes—
116M32—48no—
117C2×C16—44no—
118C4⋊C8—28no—
119C4⋊C8—28no—
120C4⋊C8—28no—
121#97—28no—
122#97—28no—
123C4×C8—28no—
124C24C22×C811yescharacteristic
125C2×Q8—28no—
126C2×Q8—48no—
127C2×Q8—48no—
128C2×Q8—44no—
129C2×Q8—44no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4C22⋊C812yes—
151C22×C4C22⋊C812yes—
152C22×C4C22⋊C812yes—
153C22×C4C22⋊C812yes—
154C22×C4C22⋊C812yes—
155C22×C4C22⋊C812yes—
156C22×C4C2×C22⋊C411yescharacteristic
157C22×C4C2×C22⋊C411yescharacteristic
158C22×C4C2×C22⋊C411yescharacteristic
159C22×C4C2×M1611yescharacteristic
160C22×C4C2×M1611yescharacteristic
161C22×C4C2×M1611yescharacteristic
162C2×C8—24no—
163C2×C8—24no—
164C2×C8—22no—
165C2×C8—24no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8#10114yes—
178C2×C8#12014yes—
179C4⋊C4—28no—
180C4⋊C4—28no—
181C4⋊C4—28no—
182C42—22no—
183C42—22no—
184C42—22no—
185C42—22no—
186C42—22no—
187C42—22no—
188C42—22no—
189C42—22no—
190C42—22no—
191C42—22no—
192C42—22no—
193C42—22no—
194C16—84no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23C2×C22⋊C811yescharacteristic
199C23C2×C22⋊C811yescharacteristic
200C23C2×C22⋊C811yescharacteristic
201Q8—416no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—24no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4#34914yes—
234C2×C4#37911yescharacteristic
235C2×C4#40711yescharacteristic
236C2×C4#40711yescharacteristic
237C2×C4#40711yescharacteristic
238C2×C4#41012yes—
239C2×C4C2×#10112yes—
240C8—24no—
241C8—24no—
242C8—42no—
243C8—42no—
244C22—28no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22#146112yes—
252C22#177911yescharacteristic
253C22C2×#34912yes—
254C22#211512yes—
255C4—21no—
256C4—21no—
257C4—24no—
258C4—42no—
259C4—42no—
260C4—42no—
261C4—42no—
262C4—42no—
263C4#146712yes—
264C4#178211yescharacteristic
265C4#178411yescharacteristic
266C2—22no—
267C2—22no—
268C2—22no—
269C2#830311yescharacteristic
270C2#1268111yescharacteristic
271C2#1268211yescharacteristic
subgroupG/H
centerC2×C4#379
commutator, prime radicalC24C22×C8
Frattini, cosocleC23×C8C23
socleC22#1779
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ G
LECSG ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C22×#4462
#128462
#114402