Finite Group Databasebeta

← #25009033

Subgroups — #25009033

Order 11008.

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

normal subgroups only

This group has 372 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#19135824C211yesmaximal, characteristic
2#19133597C212yesmaximal
3#19132601C212yesmaximal, complemented
4#19132539C211yesmaximal, characteristic, complemented
5C43×#2822C211yesmaximal, characteristic, complemented
6#14583480C2211yescharacteristic
7#14583212—22no—
8C2×#13063253—21no—
9#14582898—21no—
10#14582668C2211yescharacteristic
11#14582632—22no—
12#14582625C2212yes—
13C2×#125×C43—21no—
14C43×#400—22no—
15C43×#398—21no—
16C43×#398—22no—
17C43×#398C2212yes—
18C43×#382C2211yescharacteristic
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—
30#125×C43—42no—
31#125×C43—42no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C4⋊C4×C43D412yes—
39C2×C4⋊C4×C43C2311yescharacteristic
40C2×C42×C43D411yescharacteristic
41#95×C43—22no—
42#95×C43—21no—
43#95×C43—22no—
44#95×C43—22no—
45#95×C43D412yes—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D412yes—
52C2×C22⋊D43—41no—
53#10621898—41no—
54#10621898—41no—
55#10621898—41no—
56#10621898—41no—
57C2×D172—21no—
58C2×D172—22no—
59C2×C4×D43—41no—
60C2×Dic86—21no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—44no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—42no—
68C4⋊C4×C43—42no—
69C4⋊C4×C43—81no—
70C42×C43—21no—
71C42×C43D812yes—
72(C2×D43)⋊C4—42no—
73C4⋊Dic43—22no—
74#10621877—41no—
75#10621877—41no—
76C2×C43⋊C8—42no—
77C2×C43⋊C8—41no—
78C23×C43#12011yescharacteristic
79C22×D43—41no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43—41no—
95C2×C4×C43C2×D811yescharacteristic
96C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
97C22⋊D43—81no—
98C22⋊D43—81no—
99C2×Dic43—41no—
100D172—41no—
101D172—41no—
102D172—82no—
103C4×D43—81no—
104C4×D43—81no—
105Dic86—41no—
106Dic86—41no—
107C43⋊C8—81no—
108C43⋊C8—82no—
109#12157—431nomaximal, Sylow
110C22×C43—21no—
111C22×C43—21no—
112C22×C43#44711yescharacteristic
113C22×C43#45411yescharacteristic
114C22×C43B(4,𝔽2)11yescharacteristic
115C2×D43—81no—
116C2×D43—81no—
117C2×D43—81no—
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—42no—
121C4×C43—42no—
122C4×C43—82no—
123C4×C43—82no—
124C4×C43—81no—
125Dic43—81no—
126#2822D4311yescharacteristic, complemented
127#2040—431no—
128#1610—432no—
129#1346—432no—
130#1324—431no—
131C2×C43—21no—
132C2×C43—21no—
133C2×C43#159811yescharacteristic
134C2×C43#220111yescharacteristic
135C2×C43#220311yescharacteristic
136D43—161no—
137#537—431no—
138C2×#125—21no—
139#480—862no—
140C2×#104—861no—
141#417—861no—
142#400—22no—
143#398—21no—
144#398—22no—
145#398C2×D4312yes—
146#382C2×D4311yescharacteristic
147#343—431no—
148#327—862no—
149#324—432no—
150C43#1215711yescharacteristic, complemented, Sylow
151C2×#41—861no—
152C2×M16—861no—
153#125—42no—
154#125—42no—
155C22⋊Q8—1721no—
156#121—862no—
157#121—1721no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4C22⋊D4311yescharacteristic
164C2×C4⋊C4C22⋊D4312yes—
165C2×C4⋊C4C22×D4311yescharacteristic
166C2×C42C22⋊D4311yescharacteristic
167#107—1722no—
168#104—1722no—
169#103—1721no—
170#102—1721no—
171#102—1722no—
172C22⋊C8—862no—
173#95—22no—
174#95—21no—
175#95—22no—
176#95—22no—
177#95C22⋊D4312yes—
178#41—1721no—
179#41—1721no—
180#41—1721no—
181#41—1721no—
182C2×Q8—861no—
183C2×D4—862no—
184C2×D4—861no—
185C2×D4—1721no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—1721no—
191C22×C4C2×C22⋊D4311yescharacteristic
192C22×C4C2×C22⋊D4312yes—
193M16—1721no—
194M16—1721no—
195C2×C8—1722no—
196C2×C8—1721no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—81no—
206C4⋊C4—862no—
207C22⋊C4—1722no—
208C42—21no—
209C42#1062188212yes—
210C23—1721no—
211C23#1306329411yescharacteristic
212Q8—1721no—
213Q8—1721no—
214D4—3442no—
215D4—3441no—
216D4—3441no—
217D4—1721no—
218D4—1721no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—3441no—
235C2×C4—3441no—
236C2×C4—1721no—
237C2×C4C2×#1062188211yescharacteristic
238C2×C4#1306335111yescharacteristic
239C8—3441no—
240C8—3442no—
241C22—21no—
242C22—21no—
243C22—3441no—
244C22—3441no—
245C22—3441no—
246C22#1458303311yescharacteristic
247C22#1458307211yescharacteristic
248C22#1458308611yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—3441no—
257C2—21no—
258C2—21no—
259C2—6881no—
260C2#1913353011yescharacteristic
261C2#1913660811yescharacteristic
262C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2822C2
socleC22×C43B(4,𝔽2)
prime radical#14583480C22
hypercenter#2822D43
hypocenterC43#12157
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2822

Complements

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

NH ≅ G/Ntype
3. #19132601C2semidirect
4. #19132539C2semidirect
5. C43×#2822C2semidirect
126. #2822D43semidirect
150. C43#12157semidirect

Maximal subgroups

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

subgroupindex
#191358242
#191335972
#191326012
#191325392
C43×#28222
#1215743