Finite Group Databasebeta

← #101044

Subgroups — #101044

Order 512.

526 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 104 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#21916C211yesmaximal, characteristic
2#15196C211yesmaximal, characteristic
3#8724C212yesmaximal
4#8558C211yesmaximal, characteristic
5#7039C212yesmaximal
6C2×#389—21no—
7C2×#384C2211yescharacteristic
8C2×C4×C4⋊C4C2211yescharacteristic
9#1917—24no—
10#1817—21no—
11#1797C2212yes—
12#1797C2212yes—
13#1749—21no—
14C2×#324—21no—
15#1444—21no—
16#1444C412yes—
17#1441—21no—
18#1441C412yes—
19C4⋊#95—21no—
20C4⋊#95C2211yescharacteristic
21#1296—24no—
22#1280—21no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C412yes—
29C22×C4⋊C4D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42C2311yescharacteristic
33C2×C4⋊C8—22no—
34C2×C4⋊C8D414yes—
35C2×C22⋊C8—22no—
36C2×C22⋊C8—22no—
37C2×#97—22no—
38#389—44no—
39#384—22no—
40#384—22no—
41C4×C4⋊C4—22no—
42C4×C4⋊C4—22no—
43C2×#95—22no—
44C2×#95—21no—
45C2×#95—22no—
46C2×#95—22no—
47C2×#95C2×C411yescharacteristic
48C2×#95C2×C412yes—
49C2×#95D411yescharacteristic
50#336—24no—
51#336—22no—
52#336—22no—
53#336—22no—
54#324—42no—
55C23×C4—22no—
56C23×C4—22no—
57C23×C4C22⋊C411yescharacteristic
58C23×C4C22⋊C411yescharacteristic
59C23×C4C22⋊C411yescharacteristic
60C23×C4C22⋊C411yescharacteristic
61C23×C4C22×C411yescharacteristic
62C23×C4C2×D411yescharacteristic
63C23×C4C2×D411yescharacteristic
64C22×C8—24no—
65C22×C8—42no—
66C2×C4⋊C4—24no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—21no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—21no—
73C2×C4⋊C4—24no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—42no—
76C2×C4⋊C4—42no—
77C2×C4⋊C4—44no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—42no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—42no—
82C2×C4⋊C4—42no—
83C2×C4⋊C4—82no—
84C2×C4⋊C4—82no—
85C2×C4⋊C4—82no—
86C2×C4⋊C4—82no—
87C2×C42—21no—
88C2×C42—21no—
89C2×C42—21no—
90C2×C42—22no—
91C2×C42—22no—
92C2×C42—21no—
93C2×C42—42no—
94C2×C42—42no—
95C2×C42C2×D412yes—
96C2×C42#4112yes—
97C4⋊C8—44no—
98C4⋊C8—44no—
99C22⋊C8—42no—
100C22⋊C8—42no—
101C22⋊C8—42no—
102C22⋊C8—42no—
103#97—82no—
104#95—22no—
105#95—22no—
106#95—42no—
107#95—44no—
108#95—41no—
109#95—41no—
110#95—82no—
111#95—82no—
112C24C2×C22⋊C411yescharacteristic
113C22×C4—22no—
114C22×C4—22no—
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—24no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4—41no—
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—42no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4#10112yes—
157C22×C4C4×D412yes—
158C22×C4#12011yescharacteristic
159C22×C4#12112yes—
160C22×C4#12311yescharacteristic
161C22×C4#13512yes—
162C22×C4AGL(1,ℤ/8)12yes—
163C22×C4AGL(1,ℤ/8)11yescharacteristic
164C22×C4#13712yes—
165C22×C4#13711yescharacteristic
166C2×C8—44no—
167C2×C8—44no—
168C2×C8—44no—
169C2×C8—82no—
170C2×C8—82no—
171C2×C8—82no—
172C4⋊C4—44no—
173C4⋊C4—48no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—84no—
177C4⋊C4—84no—
178C4⋊C4—88no—
179C4⋊C4—82no—
180C4⋊C4—82no—
181C42—24no—
182C42—42no—
183C42—42no—
184C42—42no—
185C42—42no—
186C42—81no—
187C23—21no—
188C23—21no—
189C23—21no—
190C23—21no—
191C23#38611yescharacteristic
192C23C2×#10111yescharacteristic
193C23#41311yescharacteristic
194C23#41611yescharacteristic
195C23#41711yescharacteristic
196C23#41811yescharacteristic
197C23#41911yescharacteristic
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4#44912yes—
249C2×C4#45612yes—
250C2×C4#45812yes—
251C2×C4#46812yes—
252C2×C4#47012yes—
253C2×C4#48212yes—
254C8—84no—
255C8—162no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22#155211yescharacteristic
269C22#155411yescharacteristic
270C22#155611yescharacteristic
271C22#155711yescharacteristic
272C22#187511yescharacteristic
273C22#188611yescharacteristic
274C22#189011yescharacteristic
275C22#189411yescharacteristic
276C22#190111yescharacteristic
277C22#191011yescharacteristic
278C22#191411yescharacteristic
279C4—22no—
280C4—22no—
281C4—22no—
282C4—42no—
283C4—42no—
284C4—84no—
285C4—81no—
286C4—81no—
287C4—81no—
288C4—162no—
289C4#160914yes—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2#902611yescharacteristic
295C2#914011yescharacteristic
296C2#919811yescharacteristic
297C2#940011yescharacteristic
298C2#945411yescharacteristic
299C2#947311yescharacteristic
300C2#951011yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#219162
#151962
#87242
#85582
#70392