Finite Group Databasebeta

← #25007447

Subgroups — #25007447

Order 11008.

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

normal subgroups only

This group has 280 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#19145335C211yesmaximal, characteristic
2#19136404C211yesmaximal, characteristic
3#19134742C211yesmaximal, characteristic
4#19132590C211yesmaximal, characteristic
5#19132589C211yesmaximal, characteristic
6#19132582C211yesmaximal, characteristic
7C43×#1340C211yesmaximal, characteristic
8#14583451—21no—
9#14583296C411yescharacteristic, complemented
10#14583277C411yescharacteristic, complemented
11#14583248—21no—
12#14583157C2211yescharacteristic
13#14583155—21no—
14#14583006C411yescharacteristic, complemented
15#14583005C411yescharacteristic, complemented
16#14583003—21no—
17M16×Dic43C2211yescharacteristic
18#14582719—21no—
19#14582681C2211yescharacteristic
20#14582676—21no—
21#14582669—21no—
22#14582658—21no—
23C43⋊#338C2211yescharacteristic
24C43×#470C2211yescharacteristic
25C43×#349C2211yescharacteristic
26C43×H(3,ℤ/4)C2211yescharacteristic
27C2×Dic172C2×C411yescharacteristic
28C2×#10621885—21no—
29C2×#10621877—21no—
30C2×#10621877D411yescharacteristic
31#13063324—21no—
32#13063323—21no—
33#13063315—41no—
34#13063304—21no—
35#13063302—41no—
36Q8×Dic43—21no—
37#13063290—21no—
38#13063290—41no—
39#13063281—41no—
40C2×C4×Dic43D411yescharacteristic
41#13063265—21no—
42#13063257C2×C411yescharacteristic
43#13063256—21no—
44#13063250—21no—
45#13063249—21no—
46#13063248—21no—
47#13063235C2×C411yescharacteristic
48#13063235D411yescharacteristic
49C8×Dic43C2×C411yescharacteristic
50C8×Dic43D411yescharacteristic
51C2×Q16×C43C2×C411yescharacteristic
52C2×M16×C43C2311yescharacteristic
53C22⋊Q8×C43—21no—
54#117×C43—21no—
55M32×C43—21no—
56#106×C43C2×C411yescharacteristic
57#103×C43—21no—
58C2×Q8×C43—21no—
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—21no—
61C2×Dic86—21no—
62C2×Dic86—41no—
63Q16×C43—41no—
64M16×C43—41no—
65C2×C8×C43C22×C411yescharacteristic
66C2×C8×C43C2×D411yescharacteristic
67C4⋊C4×C43—21no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C22⋊C4×C43—41no—
71C22⋊C4×C43—41no—
72C42×C43—41no—
73C22⋊Dic43—41no—
74#10621885—42no—
75C4⋊Dic43—21no—
76C4⋊Dic43—41no—
77Dic43⋊C4—41no—
78Dic43⋊C4—41no—
79Dic43⋊C4—41no—
80Dic43⋊C4—41no—
81Dic43⋊C4—41no—
82C4×Dic43—21no—
83C4×Dic43—41no—
84C4×Dic43—41no—
85C4×Dic43C22⋊C411yescharacteristic
86C4×Dic43C22⋊C411yescharacteristic
87#10621877—41no—
88#10621877—41no—
89#10621877—41no—
90C2×C43⋊C8—41no—
91C2×C43⋊C8C22⋊C411yescharacteristic
92C2×C43⋊C8C22⋊C411yescharacteristic
93Dic172—41no—
94C16×C43—41no—
95C43⋊C16—41no—
96C23×C43AGL(1,ℤ/8)11yescharacteristic
97Q8×C43—41no—
98Q8×C43—41no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—81no—
104C2×C4×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
106C2×Dic43—21no—
107C2×Dic43—21no—
108C2×Dic43—42no—
109C2×Dic43—41no—
110C2×Dic43—41no—
111Dic86—41no—
112Dic86—41no—
113Dic86—82no—
114C8×C43—21no—
115C8×C43—21no—
116C43⋊C8—21no—
117C43⋊C8—21no—
118C43⋊C8—81no—
119#11838—431nomaximal, Sylow
120C22×C43—21no—
121C22×C43—41no—
122C22×C43#41811yescharacteristic
123C4×C43—21no—
124C4×C43—81no—
125C4×C43—81no—
126C4×C43—161no—
127C4×C43#41011yescharacteristic
128C4×C43#42111yescharacteristic
129Dic43—22no—
130Dic43—41no—
131Dic43—81no—
132Dic43—81no—
133#3185—431no—
134#2165—431no—
135#1841—431no—
136#1342—431no—
137#1342—431no—
138#1340—431no—
139#1340D4311yescharacteristic
140C2×C43—21no—
141C2×C43—41no—
142C2×C43#151411yescharacteristic
143#533—861no—
144#498—431no—
145#494—431no—
146#487—861no—
147#470—431no—
148#470—861no—
149#470C2×D4311yescharacteristic
150#441—431no—
151#441—431no—
152#441—861no—
153C4×M16—431no—
154#364—861no—
155#349—431no—
156#349C2×D4311yescharacteristic
157#347—861no—
158#344—861no—
159#339—861no—
160#338—431no—
161H(3,ℤ/4)C2×D4311yescharacteristic
162C43#1183811yescharacteristic, complemented, Sylow
163C2×Q16—431no—
164C2×Q16—861no—
165C2×Q16C4×D4311yescharacteristic
166C2×M16—431no—
167C2×M16—861no—
168C2×M16C22×D4311yescharacteristic
169C4⋊Q8—861no—
170C4⋊Q8—861no—
171#125—1721no—
172C22⋊Q8—21no—
173C22⋊Q8—861no—
174C22⋊Q8—1721no—
175C4×Q8—861no—
176C4×Q8—861no—
177C4×Q8—1721no—
178#117—21no—
179#117—1721no—
180C2×C42—431no—
181M32—21no—
182M32—861no—
183#106—431no—
184#106—861no—
185#106C4×D4311yescharacteristic
186#103—21no—
187#103—861no—
188#103—861no—
189#103—861no—
190#97—431no—
191#97—431no—
192C4×C8—431no—
193C4×C8—431no—
194C2×Q8—21no—
195C2×Q8—861no—
196C2×Q8—1721no—
197C22×C4—861no—
198C22×C4D4×D4311yescharacteristic
199Q16—41no—
200Q16—1721no—
201Q16—1722no—
202M16—41no—
203M16—1721no—
204M16—1721no—
205M16—1721no—
206C2×C8—431no—
207C2×C8—431no—
208C2×C8—1721no—
209C2×C8C2×C4×D4311yescharacteristic
210C2×C8D4×D4311yescharacteristic
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—861no—
215C4⋊C4—1721no—
216C4⋊C4—1721no—
217C4⋊C4—1721no—
218C4⋊C4—1721no—
219C4⋊C4—1721no—
220C4⋊C4—1721no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—1721no—
224C42—41no—
225C42—431no—
226C42—431no—
227C42—861no—
228C42—1721no—
229C42—1721no—
230C16—41no—
231C16—1721no—
232C23#1306334911yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—3442no—
236Q8—1721no—
237Q8—1721no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—81no—
243C2×C4—861no—
244C2×C4—861no—
245C2×C4—1722no—
246C2×C4—1721no—
247C2×C4—1721no—
248C2×C4C22⋊C4×D4311yescharacteristic
249C2×C4#1306335211yescharacteristic
250C8—21no—
251C8—21no—
252C8—861no—
253C8—861no—
254C8—3441no—
255C22—21no—
256C22—41no—
257C22#1458290211yescharacteristic
258C4—21no—
259C4—81no—
260C4—81no—
261C4—161no—
262C4—862no—
263C4—3441no—
264C4—3441no—
265C4—1721no—
266C4#1458287111yescharacteristic
267C4#1458291411yescharacteristic
268C2—21no—
269C2—41no—
270C2#1913314011yescharacteristic
subgroupG/H
centerC2#19133140
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1340C2
socleC2×C43#1514
prime radicalC23×C43AGL(1,ℤ/8)
cosocleC2×M16×C43C23
hypercenter#1340D43
hypocenterC43#11838
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1340

Complements

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

NH ≅ G/Ntype
9. #14583296C4semidirect
10. #14583277C4semidirect
14. #14583006C4semidirect
15. #14583005C4semidirect
162. C43#11838semidirect

Maximal subgroups

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

subgroupindex
#191453352
#191364042
#191347422
#191325902
#191325892
#191325822
C43×#13402
#1183843