Finite Group Databasebeta

← #25009009

Subgroups — #25009009

Order 11008.

424 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135819C211yesmaximal, characteristic
2#19133597C212yesmaximal
3#19132601C212yesmaximal, complemented
4#19132541C211yesmaximal, characteristic, complemented
5C43×#2582C211yesmaximal, characteristic, complemented
6#14583480C2211yescharacteristic
7#14583212—22no—
8C2×#13063253—21no—
9#14582898—21no—
10#14582668C2211yescharacteristic
11#14582632—22no—
12#14582625C2212yes—
13C2×C4×Q8×C43—21no—
14C43×#398—21no—
15C43×#398C2212yes—
16C43×#391—22no—
17C43×#389—22no—
18C43×#384C2211yescharacteristic
19C2×#10621898—21no—
20C2×#10621877—21no—
21#13063305—41no—
22#13063300—41no—
23#13063299—22no—
24#13063258—42no—
25#13063253—42no—
26#13063248—41no—
27#13063245—41no—
28#13063245—42no—
29C22⋊(C43⋊C8)—22no—
30C22×Q8×C43—21no—
31C4×Q8×C43—42no—
32C4×Q8×C43—42no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C4⋊C4×C43D412yes—
39C2×C4⋊C4×C43C2311yescharacteristic
40C2×C42×C43—22no—
41C2×C42×C43D411yescharacteristic
42#95×C43—22no—
43#95×C43—21no—
44#95×C43—22no—
45#95×C43D412yes—
46C2×Q8×C43—24no—
47C2×Q8×C43—42no—
48C2×Q8×C43—42no—
49C22×C4×C43—21no—
50C22×C4×C43—22no—
51C22×C4×C43—21no—
52C22×C4×C43—22no—
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43C2×D412yes—
55C2×C22⋊D43—41no—
56#10621898—41no—
57#10621898—41no—
58#10621898—41no—
59#10621898—41no—
60C2×D172—21no—
61C2×D172—22no—
62C2×C4×D43—41no—
63C2×Dic86—21no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—44no—
68C4⋊C4×C43—42no—
69C4⋊C4×C43—42no—
70C4⋊C4×C43—42no—
71C4⋊C4×C43—81no—
72C42×C43—21no—
73C42×C43—44no—
74C42×C43D812yes—
75(C2×D43)⋊C4—42no—
76C4⋊Dic43—22no—
77#10621877—41no—
78#10621877—41no—
79C2×C43⋊C8—42no—
80C2×C43⋊C8—41no—
81C23×C43#12011yescharacteristic
82C22×D43—41no—
83Q8×C43—48no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—24no—
90C2×C4×C43—22no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—41no—
99C2×C4×C43C2×D811yescharacteristic
100C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
101C22⋊D43—81no—
102C22⋊D43—81no—
103C2×Dic43—41no—
104D172—41no—
105D172—41no—
106D172—82no—
107C4×D43—81no—
108C4×D43—81no—
109Dic86—41no—
110Dic86—41no—
111C43⋊C8—81no—
112C43⋊C8—82no—
113#12153—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43#44711yescharacteristic
117C22×C43#45411yescharacteristic
118C22×C43B(4,𝔽2)11yescharacteristic
119C2×D43—81no—
120C2×D43—81no—
121C2×D43—81no—
122C4×C43—24no—
123C4×C43—21no—
124C4×C43—21no—
125C4×C43—44no—
126C4×C43—42no—
127C4×C43—82no—
128C4×C43—81no—
129Dic43—81no—
130#2582D4311yescharacteristic, complemented
131#2039—431no—
132#1610—432no—
133#1346—432no—
134#1325—431no—
135C2×C43—21no—
136C2×C43—21no—
137C2×C43#159811yescharacteristic
138C2×C43#219811yescharacteristic
139C2×C43#220511yescharacteristic
140D43—161no—
141#537—431no—
142C2×C4×Q8—21no—
143#480—862no—
144C2×#104—861no—
145#417—861no—
146#398—21no—
147#398C2×D4312yes—
148#391—22no—
149#389—22no—
150#384C2×D4311yescharacteristic
151#343—431no—
152#327—862no—
153#324—432no—
154C43#1215311yescharacteristic, complemented, Sylow
155C2×#41—861no—
156C22×Q8—21no—
157C2×M16—861no—
158C22⋊Q8—1721no—
159#121—862no—
160#121—1721no—
161C4×Q8—42no—
162C4×Q8—42no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C22⋊D4311yescharacteristic
168C2×C4⋊C4C22⋊D4312yes—
169C2×C4⋊C4C22×D4311yescharacteristic
170C2×C42—22no—
171C2×C42C22⋊D4311yescharacteristic
172#107—1722no—
173#104—1722no—
174#103—1721no—
175#102—1721no—
176#102—1722no—
177C22⋊C8—862no—
178#95—22no—
179#95—21no—
180#95—22no—
181#95C22⋊D4312yes—
182#41—1721no—
183#41—1721no—
184#41—1721no—
185#41—1721no—
186C2×Q8—24no—
187C2×Q8—42no—
188C2×Q8—42no—
189C2×Q8—861no—
190C2×D4—862no—
191C2×D4—861no—
192C2×D4—1721no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—1721no—
198C22×C4C2×C22⋊D4311yescharacteristic
199C22×C4C2×C22⋊D4312yes—
200M16—1721no—
201M16—1721no—
202C2×C8—1722no—
203C2×C8—1721no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—44no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—81no—
212C4⋊C4—862no—
213C22⋊C4—1722no—
214C42—21no—
215C42—44no—
216C42#1062188212yes—
217C23—1721no—
218C23#1306329411yescharacteristic
219Q8—48no—
220Q8—1721no—
221Q8—1721no—
222D4—3442no—
223D4—3441no—
224D4—3441no—
225D4—1721no—
226D4—1721no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—3441no—
243C2×C4—3441no—
244C2×C4—1721no—
245C2×C4C2×#1062188211yescharacteristic
246C2×C4#1306335111yescharacteristic
247C8—3441no—
248C8—3442no—
249C22—21no—
250C22—21no—
251C22—3441no—
252C22—3441no—
253C22—3441no—
254C22#1458303311yescharacteristic
255C22#1458307211yescharacteristic
256C22#1458308611yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—42no—
262C4—81no—
263C4—82no—
264C4—3441no—
265C2—21no—
266C2—21no—
267C2—6881no—
268C2#1913353011yescharacteristic
269C2#1913659111yescharacteristic
270C2#1913662511yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2582C2
socleC22×C43B(4,𝔽2)
prime radical#14583480C22
hypercenter#2582D43
hypocenterC43#12153
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2582

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #19132601C2semidirect
4. #19132541C2semidirect
5. C43×#2582C2semidirect
130. #2582D43semidirect
154. C43#12153semidirect

Maximal subgroups

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

subgroupindex
#191358192
#191335972
#191326012
#191325412
C43×#25822
#1215343