Finite Group Databasebeta

← #25010129

Subgroups — #25010129

Order 11008.

328 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147581C211yesmaximal, characteristic, complemented
2#19136851C211yesmaximal, characteristic, complemented
3#19136630C211yesmaximal, characteristic
4#19133956C211yesmaximal, characteristic, complemented
5#19132643C211yesmaximal, characteristic, complemented
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1331C211yesmaximal, characteristic, complemented
8#14583619—21no—
9C2×#13063270—22no—
10C2×#13063266—21no—
11#14583282—21no—
12#14583279C2211yescharacteristic
13#14583276C2211yescharacteristic
14#14583120—22no—
15#14583104—21no—
16#14583100—21no—
17C8×Dic86C2211yescharacteristic
18#14582993—21no—
19C4⋊(C43⋊C16)C2211yescharacteristic
20#14582699—21no—
21#14582642—21no—
22C4×D8×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—21no—
26C2×Dic172D412yes—
27C2×#10621873—41no—
28C2×#10621883—22no—
29C2×D344—21no—
30C2×D344—21no—
31#13063325—21no—
32#13063322—21no—
33#13063318—42no—
34#13063312—22no—
35#13063304—41no—
36C4×Dic86D411yescharacteristic
37#13063290—22no—
38#13063284—41no—
39#13063270—44no—
40#13063266—42no—
41C2×C43⋊C16—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43Dic43⋊C8—21no—
44#13063248—22no—
45#13063247—41no—
46C8×Dic43—21no—
47C2×D8×C43D411yescharacteristic
48C4×D4×C43—21no—
49C2×C16×C43—21no—
50#107×C43D411yescharacteristic
51C4⋊C8×C43—21no—
52#102×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×D4×C43—21no—
55C22×C4×C43—41no—
56C2×D172—41no—
57C2×D172—41no—
58C2×D172—41no—
59C2×Dic86—22no—
60C2×Dic86D811yescharacteristic
61D8×C43—21no—
62D8×C43—21no—
63C2×C8×C43—41no—
64C2×C8×C43C2×D411yescharacteristic
65C2×C8×C43C2×D411yescharacteristic
66C4⋊C4×C43—21no—
67C22⋊C4×C43—41no—
68C42×C43C2×D411yescharacteristic
69C22⋊Dic43—42no—
70C22⋊Dic43—42no—
71#10621883—82no—
72C4⋊Dic43—41no—
73C4⋊Dic43—41no—
74C4⋊Dic43D811yescharacteristic
75Dic43⋊C4—21no—
76Dic43⋊C4—42no—
77C4×Dic43—21no—
78C4×Dic43—42no—
79C2×C43⋊C8—21no—
80Dic172—42no—
81Dic172—41no—
82Dic172—41no—
83D344—42no—
84D344—41no—
85D344—41no—
86#10621873—82no—
87C16×C43—22no—
88C43⋊C16—41no—
89C23×C43—41no—
90C22×D43—81no—
91D4×C43—41no—
92D4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—81no—
95C2×C4×C43—81no—
96C2×C4×C43#12011yescharacteristic
97C2×C4×C43C2×D811yescharacteristic
98C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—42no—
102D172—81no—
103D172—81no—
104D172—81no—
105D172—81no—
106D172—161no—
107Dic86—21no—
108Dic86—21no—
109Dic86—42no—
110Dic86—42no—
111C8×C43—21no—
112C8×C43—81no—
113C8×C43#13511yescharacteristic
114C8×C43AGL(1,ℤ/8)11yescharacteristic
115C43⋊C8—41no—
116#12331—431nomaximal, Sylow
117C22×C43—81no—
118C22×C43—81no—
119C22×C43—81no—
120C22×C43#44711yescharacteristic
121C2×D43—161no—
122C2×D43—161no—
123C2×D43—161no—
124C4×C43—21no—
125C4×C43—81no—
126C4×C43#44911yescharacteristic
127C4×C43#45311yescharacteristic
128C4×C43#50811yescharacteristic
129C4×C43#50911yescharacteristic
130Dic43—41no—
131Dic43—41no—
132Dic43—82no—
133#3393—431no—
134#2248—431no—
135#2206—431no—
136#1668—431no—
137#1362—431no—
138Q8⋊C16—431no—
139#1331D4311yescharacteristic, complemented
140C2×C43—161no—
141C2×C43#162111yescharacteristic
142C2×C43#218611yescharacteristic
143C2×C43#219311yescharacteristic
144D43—321no—
145#556—861no—
146C2×SD32—862no—
147C2×D16—861no—
148#495—861no—
149#494—431no—
150#493—431no—
151#464—862no—
152#461—861no—
153#460—861no—
154C8×Q8—431no—
155C4×Q16—861no—
156C4×D8C2×D4311yescharacteristic
157C4⋊C16—431no—
158#357—861no—
159C4×C16C2×D4311yescharacteristic
160#335C2×D4311yescharacteristic
161#331—861no—
162C43#1233111yescharacteristic, complemented, Sylow
163C2×Q16—432no—
164C2×Q16—861no—
165C2×SD16—862no—
166C2×SD16—1721no—
167C2×D8—861no—
168C2×D8—861no—
169C2×D8D17211yescharacteristic
170C4⋊Q8—861no—
171#127—861no—
172#126—1722no—
173#124—862no—
174C22⋊Q8—1721no—
175C4×Q8—431no—
176C4×Q8—862no—
177C4×D4—21no—
178#117—1721no—
179SD32—1724no—
180D16—1722no—
181C2×C16—21no—
182C2×C16—861no—
183#107D17211yescharacteristic
184C4⋊C8—21no—
185C4⋊C8—431no—
186C4⋊C8—861no—
187#103—862no—
188#102—21no—
189#102—1721no—
190C4×C8—861no—
191C4×C8C22×D4311yescharacteristic
192C2×Q8—431no—
193C2×Q8—862no—
194C2×D4—21no—
195C2×D4—1721no—
196C2×D4—1721no—
197C2×D4—1721no—
198C22×C4—41no—
199Q16—1722no—
200Q16—1721no—
201Q16—1721no—
202SD16—3442no—
203SD16—3442no—
204D8—21no—
205D8—21no—
206D8—1722no—
207D8—1721no—
208D8—1721no—
209C2×C8—41no—
210C2×C8—861no—
211C2×C8C2×D17211yescharacteristic
212C2×C8D4×D4311yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—431no—
215C4⋊C4—861no—
216C4⋊C4—1722no—
217C4⋊C4—1721no—
218C4⋊C4—1721no—
219C22⋊C4—41no—
220C22⋊C4—1722no—
221C22⋊C4—1722no—
222C42—861no—
223C42—1722no—
224C42D4×D4311yescharacteristic
225C16—22no—
226C16—1721no—
227C23—41no—
228C23—3441no—
229Q8—861no—
230Q8—861no—
231Q8—1722no—
232Q8—1722no—
233D4—41no—
234D4—41no—
235D4—3441no—
236D4—3441no—
237D4—3441no—
238D4—3441no—
239D4—6881no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—861no—
244C2×C4—861no—
245C2×C4—1722no—
246C2×C4#1306329511yescharacteristic
247C2×C4D8×D4311yescharacteristic
248C2×C4#1306335211yescharacteristic
249C8—21no—
250C8—81no—
251C8—1721no—
252C8#1306334711yescharacteristic
253C8#1306335311yescharacteristic
254C22—81no—
255C22—81no—
256C22—81no—
257C22—6881no—
258C22—6881no—
259C22—6881no—
260C22#1458303411yescharacteristic
261C4—21no—
262C4—81no—
263C4—3442no—
264C4—1721no—
265C4—1721no—
266C4#1458304611yescharacteristic
267C4#1458306811yescharacteristic
268C4#1458333011yescharacteristic
269C4#1458333311yescharacteristic
270C2—161no—
271C2—13761no—
272C2#1913366311yescharacteristic
273C2#1913651911yescharacteristic
274C2#1913656011yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1331C2
socleC22×C43#447
prime radical#19136630C2
hypercenter#1331D43
hypocenterC43#12331
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
1. #19147581C2semidirect
2. #19136851C2semidirect
4. #19133956C2semidirect
5. #19132643C2semidirect
6. #19132575C2semidirect
7. C43×#1331C2semidirect
139. #1331D43semidirect
162. C43#12331semidirect

Maximal subgroups

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

subgroupindex
#191475812
#191368512
#191366302
#191339562
#191326432
#191325752
C43×#13312
#1233143