Finite Group Databasebeta

← #25010425

Subgroups — #25010425

Order 11008.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#19146316C211yesmaximal, characteristic
2#19136824C211yesmaximal, characteristic, complemented
3#19133991C211yesmaximal, characteristic, complemented
4#19132645C211yesmaximal, characteristic, complemented
5#19132556C211yesmaximal, characteristic, complemented
6#19132549C211yesmaximal, characteristic, complemented
7C43×#2226C211yesmaximal, characteristic, complemented
8C2×#13063344—21no—
9#14583553—21no—
10#14583279C2211yescharacteristic
11#14583186—21no—
12#14583141—21no—
13#14583104—21no—
14#14583062—22no—
15C8×D172C2211yescharacteristic
16#14582702—22no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582648—21no—
20C43×#500C2211yescharacteristic
21C4×D8×C43C2211yescharacteristic
22C43×#367—21no—
23C43×C4⋊C16C2211yescharacteristic
24C43×#357—21no—
25C2×#10621900—22no—
26#13063344—42no—
27#13063344—42no—
28C2×Dic172—21no—
29C2×Dic172D412yes—
30C2×#10621883—22no—
31C2×C8×D43—21no—
32#13063325—21no—
33#13063309—42no—
34#13063305—22no—
35#13063299—41no—
36C4×D172D411yescharacteristic
37C2×C4⋊Dic43—41no—
38C2×C43⋊C16—21no—
39#13063256—41no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)D411yescharacteristic
42#13063248—22no—
43#13063245—41no—
44(C2×D43)⋊C8—21no—
45C2×D8×C43D411yescharacteristic
46C4⋊Q8×C43—21no—
47C4×D4×C43—21no—
48C2×C16×C43—21no—
49#107×C43—21no—
50#107×C43—21no—
51#107×C43D411yescharacteristic
52#102×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—41no—
55C2×D4×C43—21no—
56C22×C4×C43—41no—
57C2×C22⋊D43—42no—
58C22×Dic43—42no—
59#10621900—44no—
60#10621900—82no—
61C2×D172D811yescharacteristic
62C2×C4×D43—21no—
63C2×Dic86—22no—
64D8×C43—21no—
65D8×C43SD1612yes—
66C2×C8×C43C2×D411yescharacteristic
67C2×C8×C43C2×D411yescharacteristic
68C4⋊C4×C43—21no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C22⋊C4×C43—41no—
72C42×C43C2×D411yescharacteristic
73#10621883—44no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—42no—
76C4⋊Dic43—42no—
77C4⋊Dic43—41no—
78C4⋊Dic43—41no—
79C4⋊Dic43D811yescharacteristic
80C2×C43⋊C8—21no—
81C2×C43⋊C8—41no—
82Dic172—42no—
83Dic172—41no—
84Dic172—41no—
85C8×D43—41no—
86C8×D43—41no—
87C16×C43—41no—
88C43⋊C16—41no—
89C23×C43—41no—
90C22×D43—21no—
91Q8×C43—161no—
92D4×C43—22no—
93D4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—81no—
96C2×C4×C43—81no—
97C2×C4×C43—81no—
98C2×C4×C43#12011yescharacteristic
99C2×C4×C43C2×D811yescharacteristic
100C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
101C22⋊D43—84no—
102C2×Dic43—21no—
103C2×Dic43—42no—
104C2×Dic43—84no—
105D172—21no—
106D172—21no—
107C4×D43—41no—
108C4×D43—41no—
109Dic86—42no—
110Dic86—42no—
111C8×C43—21no—
112C8×C43C2×SD1611yescharacteristic
113C8×C43AGL(1,ℤ/8)11yescharacteristic
114C43⋊C8—41no—
115C43⋊C8—81no—
116#12375—431nomaximal, Sylow
117C22×C43—42no—
118C22×C43—81no—
119C22×C43—81no—
120C22×C43#44711yescharacteristic
121C2×D43—41no—
122C2×D43—41no—
123C2×D43—41no—
124C4×C43—21no—
125C4×C43—81no—
126C4×C43—161no—
127C4×C43#45011yescharacteristic
128C4×C43#45511yescharacteristic
129C4×C43#50811yescharacteristic
130C4×C43#51011yescharacteristic
131Dic43—41no—
132Dic43—82no—
133#3283—431no—
134#2241—431no—
135#2226D4311yescharacteristic, complemented
136#1675—431no—
137#1362—431no—
138#1331—431no—
139D4⋊C16—431no—
140C2×C43—82no—
141C2×C43#163911yescharacteristic
142C2×C43#218911yescharacteristic
143C2×C43#219311yescharacteristic
144D43—81no—
145C2×#135—861no—
146#547—861no—
147#500C2×D4311yescharacteristic
148#494—431no—
149#476—861no—
150#467—861no—
151#461—861no—
152#452—862no—
153C4×D8C2×D4311yescharacteristic
154C8×D4—431no—
155#367—21no—
156C4⋊C16C2×D4311yescharacteristic
157#358—862no—
158#357—21no—
159C4×C16—431no—
160#335—431no—
161#333—861no—
162C43#1237511yescharacteristic, complemented, Sylow
163C2×#41—862no—
164#135—1722no—
165#135—1722no—
166C2×Q16—432no—
167C2×Q16—861no—
168C2×SD16—862no—
169C2×D8C22⋊D4311yescharacteristic
170C22×C8—861no—
171C4⋊Q8—21no—
172C4⋊Q8—861no—
173#123—1722no—
174C22⋊Q8—862no—
175#121—1721no—
176C4×D4—21no—
177C4×D4—431no—
178C2×C4⋊C4—1721no—
179C2×C16—21no—
180C2×C16—861no—
181#107—21no—
182#107—21no—
183#107C22⋊D4311yescharacteristic
184#106—1721no—
185C4⋊C8—431no—
186C4⋊C8—861no—
187#103—862no—
188#102—21no—
189#102—1721no—
190C22⋊C8—861no—
191C4×C8C22×D4311yescharacteristic
192#41—3442no—
193#41—1724no—
194C2×Q8—41no—
195C2×Q8—862no—
196C2×D4—21no—
197C2×D4—431no—
198C2×D4—1722no—
199C22×C4—41no—
200C22×C4—861no—
201C22×C4—1722no—
202Q16—1722no—
203Q16—1721no—
204Q16—1721no—
205SD16—1724no—
206D8—21no—
207D8#1062188412yes—
208C2×C8—861no—
209C2×C8—1721no—
210C2×C8—1721no—
211C2×C8—1721no—
212C2×C8D4×D4311yescharacteristic
213C2×C8C2×C22⋊D4311yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—431no—
218C4⋊C4—1722no—
219C4⋊C4—1721no—
220C4⋊C4—1721no—
221C22⋊C4—41no—
222C22⋊C4—861no—
223C22⋊C4—1722no—
224C42D4×D4311yescharacteristic
225C16—41no—
226C16—1721no—
227C23—41no—
228C23—861no—
229Q8—161no—
230Q8—1722no—
231Q8—1722no—
232D4—22no—
233D4—41no—
234D4—861no—
235D4—861no—
236D4—3444no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—861no—
242C2×C4—3444no—
243C2×C4—1722no—
244C2×C4—1721no—
245C2×C4—1721no—
246C2×C4#1306329311yescharacteristic
247C2×C4D8×D4311yescharacteristic
248C2×C4#1306334911yescharacteristic
249C8—21no—
250C8—3441no—
251C8—1721no—
252C8C2×#1062188411yescharacteristic
253C8#1306335011yescharacteristic
254C22—42no—
255C22—81no—
256C22—81no—
257C22—1721no—
258C22—1721no—
259C22—1721no—
260C22#1458303111yescharacteristic
261C4—21no—
262C4—81no—
263C4—161no—
264C4—3442no—
265C4—1721no—
266C4#1458304911yescharacteristic
267C4#1458307511yescharacteristic
268C4#1458333011yescharacteristic
269C4#1458333811yescharacteristic
270C2—82no—
271C2—3441no—
272C2#1913377311yescharacteristic
273C2#1913653211yescharacteristic
274C2#1913655611yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2226C2
socleC22×C43#447
prime radical#19146316C2
hypercenter#2226D43
hypocenterC43#12375
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
2. #19136824C2semidirect
3. #19133991C2semidirect
4. #19132645C2semidirect
5. #19132556C2semidirect
6. #19132549C2semidirect
7. C43×#2226C2semidirect
135. #2226D43semidirect
162. C43#12375semidirect

Maximal subgroups

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

subgroupindex
#191463162
#191368242
#191339912
#191326452
#191325562
#191325492
C43×#22262
#1237543