Finite Group Databasebeta

← #25009042

Subgroups — #25009042

Order 11008.

390 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 67 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#19145940C211yesmaximal, characteristic, complemented
2#19136524C212yesmaximal
3#19132606C212yesmaximal, complemented
4#19132535C211yesmaximal, characteristic, complemented
5C43×#2054C211yesmaximal, characteristic
6#14583456—21no—
7C2×#13063269—22no—
8#14583195—22no—
9#14583140—21no—
10#14583140C2212yes—
11#14583110—22no—
12#14582700—22no—
13C22⋊(C43⋊C16)C2212yes—
14C22×D8×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×#102×C43—21no—
17C43×#390—21no—
18C43×#340C2211yescharacteristic
19C2×Dic172—21no—
20C2×Dic172D412yes—
21#13063325—21no—
22#13063325—21no—
23#13063317—41no—
24#13063304—22no—
25#13063304—41no—
26C4×Dic86—22no—
27C4×Dic86—41no—
28#13063284—41no—
29#13063269—44no—
30C2×C43⋊C16—22no—
31#13063259—21no—
32#13063259D412yes—
33#13063250—22no—
34#13063250—22no—
35C22×D4×C43—21no—
36C2×D8×C43—22no—
37C2×D8×C43—42no—
38C22×C8×C43D411yescharacteristic
39C22×C8×C43C2311yescharacteristic
40C2×C4⋊C4×C43—21no—
41C2×C22⋊C4×C43—41no—
42C2×C22⋊C4×C43—41no—
43C2×C42×C43D411yescharacteristic
44C4⋊C8×C43—22no—
45#102×C43—42no—
46C24×C43—41no—
47C2×D4×C43—22no—
48C2×D4×C43—41no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43—41no—
52C2×D4×C43—41no—
53C22×C4×C43—41no—
54C22×C4×C43D811yescharacteristic
55C22×C4×C43D811yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C2×Dic86—22no—
58C2×Dic86—41no—
59D8×C43—24no—
60D8×C43—42no—
61C2×C8×C43—21no—
62C2×C8×C43—41no—
63C2×C8×C43—41no—
64C2×C8×C43C2×D412yes—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C22⋊C4×C43—82no—
68C22⋊C4×C43—82no—
69C42×C43—21no—
70C42×C43—21no—
71C22⋊Dic43—42no—
72C4⋊Dic43—22no—
73C4⋊Dic43—41no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76Dic43⋊C4—42no—
77Dic43⋊C4—42no—
78C4×Dic43—42no—
79Dic172—42no—
80Dic172—81no—
81C43⋊C16—42no—
82C23×C43—42no—
83C23×C43—81no—
84C23×C43—81no—
85C23×C43—81no—
86C23×C43—81no—
87C23×C43—81no—
88C23×C43—81no—
89C23×C43C2×D811yescharacteristic
90D4×C43—42no—
91D4×C43—42no—
92D4×C43—81no—
93D4×C43—81no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—41no—
100C2×C4×C43—81no—
101C2×C4×C43—81no—
102C2×C4×C43—81no—
103C2×C4×C43SD3212yescomplemented
104C2×C4×C43#12011yescharacteristic
105C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
106C2×Dic43—42no—
107C2×Dic43—42no—
108Dic86—42no—
109Dic86—42no—
110Dic86—82no—
111C8×C43—22no—
112C8×C43—41no—
113#12159—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43—82no—
117C22×C43—82no—
118C22×C43—82no—
119C22×C43—161no—
120C22×C43—161no—
121C22×C43—161no—
122C22×C43—161no—
123C22×C43#44711yescharacteristic
124C22×C43C2×SD3211yescharacteristic
125C22×C43#51011yescharacteristic
126C4×C43—21no—
127C4×C43—22no—
128C4×C43—41no—
129C4×C43—161no—
130C4×C43#45411yescharacteristic
131C4×C43B(4,𝔽2)11yescharacteristic
132Dic43—82no—
133Dic43—82no—
134#3249—431no—
135#2187—432no—
136#2054D4311yescharacteristic
137#1348—432no—
138#1322—431no—
139C2×C43—21no—
140C2×C43—21no—
141C2×C43—162no—
142C2×C43#159811yescharacteristic
143C2×C43#218511yescharacteristic
144C2×C43#219011yescharacteristic
145C22×D8C2×D4311yescharacteristic
146#533—861no—
147C2×SD32—862no—
148#477—862no—
149#467—432no—
150#467—861no—
151#462—862no—
152C2×C4⋊C8C2×D4311yescharacteristic
153C2×#102—21no—
154#390—21no—
155#357—862no—
156C22⋊C16—432no—
157#340C2×D4311yescharacteristic
158C43#1215911yescharacteristic, complemented, Sylow
159C22×D4—21no—
160C2×Q16—432no—
161C2×Q16—861no—
162C2×D8—22no—
163C2×D8—42no—
164C22×C8C22⋊D4311yescharacteristic
165C22×C8C22×D4311yescharacteristic
166C4⋊Q8—861no—
167C4⋊Q8—861no—
168#125—1721no—
169C22⋊Q8—862no—
170C22⋊Q8—1721no—
171C4×Q8—862no—
172C4×Q8—1721no—
173#117—1721no—
174C2×C4⋊C4—21no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—41no—
177C2×C42C22⋊D4311yescharacteristic
178SD32—1724no—
179C2×C16—862no—
180#107—432no—
181#107—861no—
182C4⋊C8—22no—
183#103—862no—
184#103—862no—
185#102—42no—
186C24—41no—
187C2×Q8—862no—
188C2×Q8—1721no—
189C2×D4—22no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—41no—
195C22×C4—41no—
196C22×C4#1062188211yescharacteristic
197C22×C4#1062188211yescharacteristic
198C22×C4C2×C22⋊D4311yescharacteristic
199Q16—3441no—
200Q16—1722no—
201D8—24no—
202D8—42no—
203C2×C8—21no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8D4×D4312yes—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—862no—
210C4⋊C4—1721no—
211C4⋊C4—1721no—
212C4⋊C4—1722no—
213C4⋊C4—1721no—
214C4⋊C4—1722no—
215C22⋊C4—82no—
216C22⋊C4—82no—
217C22⋊C4—1722no—
218C42—21no—
219C42—21no—
220C42—1722no—
221C16—1722no—
222C23—42no—
223C23—81no—
224C23—81no—
225C23—81no—
226C23—81no—
227C23—81no—
228C23—81no—
229C23C2×#1062188211yescharacteristic
230Q8—3442no—
231Q8—1722no—
232Q8—1722no—
233D4—42no—
234D4—42no—
235D4—81no—
236D4—81no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—1722no—
247C2×C4—1722no—
248C2×C4#1306326912yescomplemented
249C2×C4#1306329311yescharacteristic
250C2×C4#1306335011yescharacteristic
251C8—22no—
252C8—41no—
253C22—21no—
254C22—21no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—161no—
259C22—161no—
260C22—161no—
261C22—161no—
262C22#1458303211yescharacteristic
263C22C2×#1306326911yescharacteristic
264C22#1458333911yescharacteristic
265C4—21no—
266C4—22no—
267C4—41no—
268C4—161no—
269C4—3442no—
270C4—3442no—
271C4#1458307111yescharacteristic
272C4#1458308511yescharacteristic
273C2—21no—
274C2—21no—
275C2—162no—
276C2#1913352911yescharacteristic
277C2#1913651111yescharacteristic
278C2#1913654011yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2054C2
socleC22×C43#447
prime radicalC22×D8×C43C22
hypercenter#2054D43
hypocenterC43#12159
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2054

Complements

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

NH ≅ G/Ntype
1. #19145940C2semidirect
3. #19132606C2semidirect
4. #19132535C2semidirect
103. C2×C4×C43SD32semidirect
158. C43#12159semidirect
248. C2×C4#13063269semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191365242
#191326062
#191325352
C43×#20542
#1215943