Finite Group Databasebeta

← #25009168

Subgroups — #25009168

Order 11008.

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

normal subgroups only

This group has 472 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#19133563C212yesmaximal
3#19132625C212yesmaximal, complemented
4#19132541C211yesmaximal, characteristic, complemented
5C43×#2551C211yesmaximal, characteristic, complemented
6#14583480C2211yescharacteristic
7#14583038—22no—
8C2×#13063253—21no—
9#14582898—21no—
10#14582668C2211yescharacteristic
11#14582632—22no—
12#14582625C2212yes—
13C2×C4⋊Q8×C43—22no—
14C43×#395—21no—
15C43×#395C2212yes—
16C43×#389—22no—
17C43×#384C2211yescharacteristic
18C4×C4⋊C4×C43—21no—
19C2×#10621898—21no—
20C2×#10621884—42no—
21C2×#10621877—21no—
22#13063305—41no—
23#13063300—41no—
24#13063299—22no—
25#13063253—42no—
26#13063249—42no—
27#13063248—41no—
28#13063245—41no—
29C22⋊(C43⋊C8)—22no—
30C22×Q8×C43—21no—
31C22×Q8×C43D412yes—
32C4⋊Q8×C43—48no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C4⋊C4×C43C2311yescharacteristic
40C2×C42×C43—22no—
41C2×C42×C43D411yescharacteristic
42#95×C43—21no—
43#95×C43—22no—
44#95×C43D412yes—
45C2×Q8×C43—44no—
46C2×Q8×C43—44no—
47C2×Q8×C43—42no—
48C2×Q8×C43—81no—
49C22×C4×C43—21no—
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—21no—
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—24no—
65C4⋊C4×C43—24no—
66C4⋊C4×C43—41no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—44no—
69C4⋊C4×C43—44no—
70C4⋊C4×C43—44no—
71C42×C43—21no—
72C42×C43—44no—
73C42×C43SD1612yescomplemented
74#10621884—84no—
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—44no—
84Q8×C43—82no—
85Q8×C43—84no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—24no—
92C2×C4×C43—24no—
93C2×C4×C43—22no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—41no—
101C2×C4×C43C2×SD1611yescharacteristic
102C2×C4×C43#13711yescharacteristic
103C22⋊D43—81no—
104C22⋊D43—81no—
105C2×Dic43—41no—
106D172—41no—
107D172—41no—
108D172—82no—
109C4×D43—81no—
110C4×D43—81no—
111Dic86—41no—
112Dic86—41no—
113C43⋊C8—81no—
114C43⋊C8—82no—
115#12180—431nomaximal, Sylow
116C22×C43—21no—
117C22×C43—21no—
118C22×C43#44811yescharacteristic
119C22×C43#45411yescharacteristic
120C22×C43B(4,𝔽2)11yescharacteristic
121C2×D43—81no—
122C2×D43—81no—
123C2×D43—81no—
124C4×C43—24no—
125C4×C43—21no—
126C4×C43—21no—
127C4×C43—44no—
128C4×C43—42no—
129C4×C43—44no—
130C4×C43—81no—
131Dic43—81no—
132#2551D4311yescharacteristic, complemented
133#2039—431no—
134#1604—432no—
135#1354—432no—
136#1325—431no—
137C2×C43—21no—
138C2×C43—21no—
139C2×C43#159911yescharacteristic
140C2×C43#219611yescharacteristic
141C2×C43#220511yescharacteristic
142D43—161no—
143#537—431no—
144C2×C4⋊Q8—22no—
145#448—862no—
146C2×#104—861no—
147#417—861no—
148#395—21no—
149#395C2×D4312yes—
150#389—22no—
151#384C2×D4311yescharacteristic
152C4×C4⋊C4—21no—
153#343—431no—
154#327—862no—
155#324—432no—
156C43#1218011yescharacteristic, complemented, Sylow
157C2×#41—861no—
158C22×Q8—21no—
159C22×Q8C22⋊D4312yes—
160C2×SD16—1722no—
161C2×M16—861no—
162C4⋊Q8—48no—
163C22⋊Q8—1721no—
164#121—862no—
165#121—1721no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C22⋊D4311yescharacteristic
172C2×C4⋊C4C22×D4311yescharacteristic
173C2×C42—22no—
174C2×C42C22⋊D4311yescharacteristic
175#104—1722no—
176#103—1721no—
177#103—1722no—
178#102—1721no—
179C22⋊C8—862no—
180#95—21no—
181#95—22no—
182#95C22⋊D4312yes—
183#41—1721no—
184#41—1721no—
185#41—1721no—
186#41—1721no—
187C2×Q8—44no—
188C2×Q8—44no—
189C2×Q8—42no—
190C2×Q8—81no—
191C2×Q8—861no—
192C2×D4—862no—
193C2×D4—861no—
194C2×D4—1721no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—1721no—
200C22×C4C2×C22⋊D4311yescharacteristic
201C22×C4C2×C22⋊D4312yes—
202SD16—3444no—
203M16—1721no—
204M16—1721no—
205C2×C8—1722no—
206C2×C8—1721no—
207C4⋊C4—24no—
208C4⋊C4—24no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—44no—
212C4⋊C4—44no—
213C4⋊C4—44no—
214C4⋊C4—862no—
215C22⋊C4—1722no—
216C42—21no—
217C42—44no—
218C42#1062188412yescomplemented
219C23—1721no—
220C23#1306329411yescharacteristic
221Q8—44no—
222Q8—82no—
223Q8—84no—
224Q8—1721no—
225Q8—1721no—
226D4—3442no—
227D4—3441no—
228D4—3441no—
229D4—1721no—
230D4—1721no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—24no—
237C2×C4—24no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—3441no—
247C2×C4—3441no—
248C2×C4—1721no—
249C2×C4C2×#1062188411yescharacteristic
250C2×C4#1306335611yescharacteristic
251C8—3441no—
252C8—3442no—
253C22—21no—
254C22—21no—
255C22—3441no—
256C22—3441no—
257C22—3441no—
258C22#1458303811yescharacteristic
259C22#1458307211yescharacteristic
260C22#1458308611yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—44no—
265C4—42no—
266C4—44no—
267C4—81no—
268C4—3441no—
269C2—21no—
270C2—21no—
271C2—6881no—
272C2#1913353511yescharacteristic
273C2#1913657911yescharacteristic
274C2#1913662511yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2551C2
socleC22×C43B(4,𝔽2)
prime radical#14583480C22
hypercenter#2551D43
hypocenterC43#12180
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
3. #19132625C2semidirect
4. #19132541C2semidirect
5. C43×#2551C2semidirect
73. C42×C43SD16semidirect
132. #2551D43semidirect
156. C43#12180semidirect
218. C42#10621884semidirect

Maximal subgroups

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

subgroupindex
#191358192
#191335632
#191326252
#191325412
C43×#25512
#1218043