Finite Group Databasebeta

← #125469

Subgroups — #125469

Order 512.

446 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 80 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#15152C211yesmaximal, characteristic
2#8701C211yesmaximal, characteristic
3#8153C211yesmaximal, characteristic
4#7132C214yesmaximal
5C2×#400C412yes—
6C2×#384C411yescharacteristic
7C2×C4×C4⋊C4C2211yescharacteristic
8#1817—21no—
9#1749—21no—
10C2×#324—21no—
11#1445C2212yes—
12#1442—21no—
13#1441—21no—
14C4⋊#95—21no—
15C4⋊#95—21no—
16C4⋊#95C411yescharacteristic
17#1280—21no—
18#1280C2212yes—
19#1280C2212yes—
20C22×C4⋊C4—21no—
21C22×C4⋊C4—21no—
22C22×C4⋊C4—21no—
23C22×C4⋊C4C2×C411yescharacteristic
24C22×C4⋊C4C2×C412yes—
25C22×C4⋊C4D411yescharacteristic
26C22×C42C2×C411yescharacteristic
27C22×C42D411yescharacteristic
28C22×C42D411yescharacteristic
29C2×C22⋊C8—22no—
30C2×C22⋊C8—22no—
31C2×#97—41no—
32#400—44no—
33#384—41no—
34#384—41no—
35C4×C4⋊C4—41no—
36C4×C4⋊C4—41no—
37C2×#95—22no—
38C2×#95—22no—
39C2×#95—21no—
40C2×#95—22no—
41C2×#95—22no—
42C2×#95C2×C412yes—
43C2×#95D411yescharacteristic
44C2×#95C2311yescharacteristic
45#336—41no—
46#336—41no—
47#336—41no—
48#324—24no—
49C23×C4—22no—
50C23×C4—22no—
51C23×C4C22⋊C411yescharacteristic
52C23×C4C22⋊C411yescharacteristic
53C23×C4C22⋊C411yescharacteristic
54C23×C4C22⋊C411yescharacteristic
55C23×C4C22×C411yescharacteristic
56C23×C4C2×D411yescharacteristic
57C23×C4C2×D411yescharacteristic
58C22×C8—42no—
59C22×C8—42no—
60C2×C4⋊C4—22no—
61C2×C4⋊C4—22no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—24no—
65C2×C4⋊C4—41no—
66C2×C4⋊C4—41no—
67C2×C4⋊C4—42no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4—42no—
70C2×C4⋊C4—42no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—42no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—42no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—82no—
78C2×C42—21no—
79C2×C42—21no—
80C2×C42—21no—
81C2×C42—21no—
82C2×C42—21no—
83C2×C42—22no—
84C2×C42—21no—
85C2×C42—41no—
86C2×C42—42no—
87C2×C42—42no—
88C22⋊C8—24no—
89C22⋊C8—42no—
90C22⋊C8—42no—
91C22⋊C8—42no—
92#97—82no—
93#95—41no—
94#95—41no—
95#95—42no—
96#95—44no—
97#95—44no—
98#95—42no—
99#95—82no—
100#95—82no—
101C24C2×C22⋊C411yescharacteristic
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—22no—
105C22×C4—22no—
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—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—41no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4—41no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—41no—
133C22×C4—42no—
134C22×C4—42no—
135C22×C4—42no—
136C22×C4—42no—
137C22×C4—42no—
138C22×C4—42no—
139C22×C4—42no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4#9911yescharacteristic
148C22×C4#9911yescharacteristic
149C22×C4#10012yes—
150C22×C4#10412yes—
151C22×C4#13112yes—
152C22×C4#13712yes—
153C22×C4#13712yes—
154C2×C8—44no—
155C2×C8—82no—
156C2×C8—82no—
157C2×C8—82no—
158C2×C8—82no—
159C2×C8—82no—
160C4⋊C4—44no—
161C4⋊C4—44no—
162C4⋊C4—84no—
163C4⋊C4—84no—
164C4⋊C4—82no—
165C4⋊C4—84no—
166C4⋊C4—82no—
167C42—42no—
168C42—42no—
169C42—42no—
170C42—42no—
171C42—42no—
172C42—81no—
173C23—21no—
174C23—21no—
175C23—21no—
176C23—21no—
177C23#40811yescharacteristic
178C23C2×#9911yescharacteristic
179C23C2×#10011yescharacteristic
180C23#41911yescharacteristic
181C23#41911yescharacteristic
182C23C2×#10411yescharacteristic
183C23#42111yescharacteristic
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—82no—
228C2×C4—82no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4#35212yes—
237C2×C4#35512yes—
238C8—84no—
239C8—162no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22#147111yescharacteristic
253C22#148511yescharacteristic
254C22#149711yescharacteristic
255C22#150811yescharacteristic
256C22#151111yescharacteristic
257C22#153011yescharacteristic
258C22#155811yescharacteristic
259C22C2×#35211yescharacteristic
260C22#212311yescharacteristic
261C22#212811yescharacteristic
262C22C2×#35511yescharacteristic
263C4—22no—
264C4—22no—
265C4—42no—
266C4—42no—
267C4—42no—
268C4—42no—
269C4—42no—
270C4—81no—
271C4—162no—
272C4—162no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—21no—
277C2#770711yescharacteristic
278C2#1156211yescharacteristic
279C2#1156711yescharacteristic
280C2#1178611yescharacteristic
281C2#1179411yescharacteristic
282C2#1181311yescharacteristic
283C2#1181411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC2×#95C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C2×#95 ▷ C24 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#151522
#87012
#81532
#71322