Finite Group Databasebeta

← #120889

Subgroups — #120889

Order 512.

371 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 114 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#17823C211yesmaximal, characteristic
2#8110C211yesmaximal, characteristic
3#8106C211yesmaximal, characteristic
4#7958C211yesmaximal, characteristic
5#7956C211yesmaximal, characteristic
6#7945C211yesmaximal, characteristic
7#7936C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12C2×#431C2211yescharacteristic
13#2283C2211yescharacteristic
14#2283C2211yescharacteristic
15#1574—22no—
16#1572—22no—
17#1569—22no—
18#1305—22no—
19#1305—22no—
20#1286—22no—
21#1286—22no—
22#1284C414yes—
23#1283—22no—
24C22×C42C2311yescharacteristic
25#432—21no—
26#432—21no—
27#432—21no—
28#432—21no—
29#432—21no—
30#432—21no—
31#432—21no—
32#432Q812yes—
33#431—21no—
34#431—21no—
35#431—21no—
36#431—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44#431D412yes—
45#423—21no—
46#423—21no—
47#423D412yes—
48#423D412yes—
49C2×C4⋊C8—21no—
50#407—21no—
51#407—21no—
52#407C2×C412yes—
53#407D412yes—
54C2×C22⋊C8—21no—
55C4×M16—21no—
56C4×M16—21no—
57C4×M16—21no—
58C4×M16—21no—
59C2×C4×C8Q812yes—
60#383—21no—
61#383—21no—
62#382—21no—
63#382—21no—
64#381—21no—
65#381C2×C412yes—
66#380—21no—
67#380—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4C2×C412yes—
72#376—21no—
73#376—21no—
74#335—24no—
75#334—24no—
76C23×C4C22×C411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C23×C4#4111yescharacteristic
79C2×M16—22no—
80C2×M16—22no—
81C2×M16—22no—
82C2×M16—22no—
83C22×C8—22no—
84C2×C4⋊C4—41no—
85C2×C4⋊C4—41no—
86C2×C22⋊C4—22no—
87C2×C22⋊C4—22no—
88C2×C42—22no—
89C2×C42—41no—
90C2×C42C2×D411yescharacteristic
91C2×C42C2×D411yescharacteristic
92C2×C42C2×D411yescharacteristic
93C2×C42C2×Q811yescharacteristic
94C2×C42C2×Q811yescharacteristic
95C2×C42#4111yescharacteristic
96C2×C42#4111yescharacteristic
97C2×C42#4111yescharacteristic
98C2×C42#4111yescharacteristic
99C2×C42#4111yescharacteristic
100C2×C42#4111yescharacteristic
101C2×C42#4111yescharacteristic
102C4⋊C8—22no—
103C4⋊C8—22no—
104C4⋊C8—22no—
105C4⋊C8—22no—
106C4⋊C8—22no—
107C4⋊C8—22no—
108C4⋊C8—41no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C22⋊C8—22no—
113C22⋊C8—22no—
114C22⋊C8—22no—
115C22⋊C8—41no—
116C22⋊C8—41no—
117C22⋊C8—41no—
118C22⋊C8—41no—
119C22⋊C8—41no—
120C22⋊C8—41no—
121C22⋊C8C4⋊C414yes—
122#97—22no—
123#97—41no—
124#97—41no—
125#97—41no—
126C4×C8—22no—
127C4×C8—22no—
128C4×C8—22no—
129C4×C8—41no—
130C4×C8—41no—
131C4×C8—41no—
132#95—22no—
133#95—22no—
134#95—22no—
135#95—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140C24C4×D411yescharacteristic
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—81no—
145C22×C4—81no—
146C22×C4C2×C4⋊C411yescharacteristic
147C22×C4#11711yescharacteristic
148C22×C4#11711yescharacteristic
149C22×C4C4×D411yescharacteristic
150C22×C4C4×D411yescharacteristic
151C22×C4C4×Q811yescharacteristic
152C22×C4#12111yescharacteristic
153C22×C4#12111yescharacteristic
154C22×C4#12111yescharacteristic
155C22×C4C22⋊Q811yescharacteristic
156C22×C4#12311yescharacteristic
157C22×C4#12311yescharacteristic
158C22×C4#12411yescharacteristic
159C22×C4#12411yescharacteristic
160C22×C4#12511yescharacteristic
161C22×C4#12611yescharacteristic
162C22×C4#12611yescharacteristic
163C22×C4C4⋊Q811yescharacteristic
164M16—44no—
165M16—82no—
166M16—82no—
167M16—82no—
168C2×C8—24no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—82no—
174C4⋊C4—82no—
175C4⋊C4—82no—
176C22⋊C4—82no—
177C22⋊C4—82no—
178C42—82no—
179C42—82no—
180C42#12011yescharacteristic
181C42C22⋊Q811yescharacteristic
182C42C22⋊Q811yescharacteristic
183C42C22⋊Q811yescharacteristic
184C42C22⋊Q811yescharacteristic
185C42#12311yescharacteristic
186C42#12311yescharacteristic
187C42#12311yescharacteristic
188C42#12411yescharacteristic
189C42#12411yescharacteristic
190C42#12511yescharacteristic
191C42#12511yescharacteristic
192C42#12511yescharacteristic
193C42#12511yescharacteristic
194C42#12611yescharacteristic
195C42#12611yescharacteristic
196C23—41no—
197C23—41no—
198C23—41no—
199C23#38811yescharacteristic
200C23#38811yescharacteristic
201C23#38911yescharacteristic
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—82no—
221C2×C4—82no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—82no—
226C2×C4#38211yescharacteristic
227C2×C4#38511yescharacteristic
228C2×C4#38711yescharacteristic
229C2×C4#38711yescharacteristic
230C2×C4#39311yescharacteristic
231C2×C4#39411yescharacteristic
232C2×C4#39711yescharacteristic
233C2×C4#39811yescharacteristic
234C2×C4#39811yescharacteristic
235C2×C4#40011yescharacteristic
236C2×C4#40011yescharacteristic
237C2×C4#40011yescharacteristic
238C8—44no—
239C8—82no—
240C8—82no—
241C8—82no—
242C8—82no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—82no—
253C22#144211yescharacteristic
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—162no—
266C4—162no—
267C4#205312yes—
268C2—41no—
269C2—41no—
270C2—41no—
271C2#1127811yescharacteristic
272C2#1128011yescharacteristic
273C2#1128511yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#178232
#81102
#81062
#79582
#79562
#79452
#79362