Finite Group Databasebeta

← #141992

Subgroups — #141992

Order 512.

506 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 100 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#13911C211yesmaximal, characteristic
2#8560C211yesmaximal, characteristic
3#8153C211yesmaximal, characteristic
4#7189C214yesmaximal
5C2×#384C411yescharacteristic
6C2×#382C412yes—
7C2×C4×C4⋊C4C411yescharacteristic
8C2×C4×C4⋊C4C2211yescharacteristic
9#1797—21no—
10#1749—21no—
11C2×#324C2212yes—
12C2×#324C2212yes—
13#1442—21no—
14#1442—21no—
15C4⋊#95—21no—
16C4⋊#95—21no—
17C4⋊#95C2212yes—
18#1280—21no—
19#1280—21no—
20C22×C4⋊C4—21no—
21C22×C4⋊C4—21no—
22C22×C4⋊C4—21no—
23C22×C4⋊C4C2×C411yescharacteristic
24C22×C4⋊C4C2×C412yes—
25C22×C4⋊C4C2311yescharacteristic
26C22×C42C2×C411yescharacteristic
27C22×C42C2×C412yes—
28C22×C42D411yescharacteristic
29C22×C42D411yescharacteristic
30C2×C4⋊C8—41no—
31C2×C22⋊C8—22no—
32C2×C22⋊C8—22no—
33C2×#97—41no—
34#384—41no—
35#384—41no—
36#382—44no—
37C4×C4⋊C4—24no—
38C4×C4⋊C4—41no—
39C4×C4⋊C4—41no—
40C2×#95—21no—
41C2×#95—22no—
42C2×#95—22no—
43C2×#95—22no—
44C2×#95—22no—
45C2×#95D411yescharacteristic
46C2×#95D411yescharacteristic
47#336—41no—
48#336—41no—
49#324—22no—
50#324—24no—
51#324Q814yes—
52C23×C4—22no—
53C23×C4—22no—
54C23×C4C22⋊C411yescharacteristic
55C23×C4C22⋊C411yescharacteristic
56C23×C4C22⋊C411yescharacteristic
57C23×C4C22⋊C411yescharacteristic
58C23×C4C22×C411yescharacteristic
59C23×C4C2×D411yescharacteristic
60C23×C4C2×D411yescharacteristic
61C22×C8—42no—
62C22×C8—42no—
63C2×C4⋊C4—24no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—24no—
67C2×C4⋊C4—41no—
68C2×C4⋊C4—41no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—42no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—42no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—42no—
75C2×C4⋊C4—42no—
76C2×C4⋊C4—42no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—82no—
80C2×C4⋊C4C2×Q812yes—
81C2×C4⋊C4#4112yes—
82C2×C42—21no—
83C2×C42—21no—
84C2×C42—22no—
85C2×C42—22no—
86C2×C42—21no—
87C2×C42—21no—
88C2×C42—22no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42—42no—
92C2×C42—42no—
93C2×C42—42no—
94C2×C42—42no—
95C2×C42M1614yes—
96C4⋊C8—82no—
97C22⋊C8—24no—
98C22⋊C8—42no—
99C22⋊C8—42no—
100C22⋊C8—42no—
101#97—82no—
102#95—24no—
103#95—41no—
104#95—41no—
105#95—44no—
106#95—44no—
107#95—82no—
108#95—82no—
109C24C2×C22⋊C411yescharacteristic
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—24no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—41no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4#9911yescharacteristic
154C22×C4#9911yescharacteristic
155C22×C4#10012yes—
156C22×C4#10112yes—
157C22×C4C4×Q812yes—
158C22×C4C22⋊Q812yes—
159C22×C4#12411yescharacteristic
160C22×C4C4⋊Q811yescharacteristic
161C22×C4C2×M1612yes—
162C22×C4#13112yes—
163C2×C8—44no—
164C2×C8—82no—
165C2×C8—82no—
166C2×C8—82no—
167C2×C8—82no—
168C2×C8—82no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—44no—
172C4⋊C4—48no—
173C4⋊C4—84no—
174C4⋊C4—82no—
175C4⋊C4—84no—
176C4⋊C4—82no—
177C42—24no—
178C42—24no—
179C42—44no—
180C42—44no—
181C42—42no—
182C42—42no—
183C42—81no—
184C42—81no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—21no—
189C23#39111yescharacteristic
190C23#40711yescharacteristic
191C23#40811yescharacteristic
192C23C2×#9911yescharacteristic
193C23#41011yescharacteristic
194C23C2×#10011yescharacteristic
195C23C2×#10111yescharacteristic
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—44no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4#35412yes—
250C2×C4#35512yes—
251C2×C4#44614yes—
252C8—84no—
253C8—162no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22#146311yescharacteristic
267C22#146611yescharacteristic
268C22#147011yescharacteristic
269C22#147111yescharacteristic
270C22#198511yescharacteristic
271C22#199611yescharacteristic
272C22#199711yescharacteristic
273C22C2×#35411yescharacteristic
274C22#212811yescharacteristic
275C22C2×#35511yescharacteristic
276C22#213511yescharacteristic
277C4—24no—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—42no—
282C4—41no—
283C4—41no—
284C4—42no—
285C4—84no—
286C4—81no—
287C4—162no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2#988311yescharacteristic
293C2#1151111yescharacteristic
294C2#1151611yescharacteristic
295C2#1156411yescharacteristic
296C2#1156711yescharacteristic
297C2#1329911yescharacteristic
298C2#1330111yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#139112
#85602
#81532
#71892