Finite Group Databasebeta

← #25010122

Subgroups — #25010122

Order 11008.

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

normal subgroups only

This group has 322 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#19147600C211yesmaximal, characteristic, complemented
2#19136851C211yesmaximal, characteristic
3#19136635C211yesmaximal, characteristic
4#19133956C211yesmaximal, characteristic
5#19132643C211yesmaximal, characteristic, complemented
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1332C211yesmaximal, characteristic, complemented
8#14583627—21no—
9C2×#13063270—22no—
10C2×#13063268—21no—
11#14583279C2211yescharacteristic
12#14583277—21no—
13#14583276C2211yescharacteristic
14#14583109—21no—
15#14583108—22no—
16#14583100—21no—
17C8×Dic86C2211yescharacteristic
18#14582993—21no—
19C4⋊(C43⋊C16)C2211yescharacteristic
20#14582699—21no—
21#14582642—21no—
22C4×Q16×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—21no—
26C2×Dic172D412yes—
27C2×#10621885—22no—
28C2×#10621873—41no—
29C2×D344—21no—
30C2×D344—21no—
31#13063325—21no—
32#13063323—22no—
33#13063322—21no—
34#13063317—41no—
35#13063315—42no—
36C4×Dic86—41no—
37C4×Dic86D411yescharacteristic
38#13063290—22no—
39#13063270—44no—
40#13063268—42no—
41C2×C43⋊C16—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43Dic43⋊C8—21no—
44#13063248—22no—
45#13063247—41no—
46C8×Dic43—21no—
47C2×Q16×C43D411yescharacteristic
48C4×Q8×C43—21no—
49C2×C16×C43—21no—
50#107×C43D411yescharacteristic
51C4⋊C8×C43—21no—
52#103×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—21no—
55C2×D172—41no—
56C2×D172—41no—
57C2×D172—41no—
58C2×Dic86—22no—
59C2×Dic86D811yescharacteristic
60Q16×C43—21no—
61Q16×C43—21no—
62C2×C8×C43—41no—
63C2×C8×C43C2×D411yescharacteristic
64C2×C8×C43C2×D411yescharacteristic
65C4⋊C4×C43—21no—
66C4⋊C4×C43—41no—
67C42×C43—41no—
68C42×C43C2×D411yescharacteristic
69#10621885—82no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72C4⋊Dic43D811yescharacteristic
73Dic43⋊C4—21no—
74Dic43⋊C4—42no—
75Dic43⋊C4—42no—
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—
89C22×D43—81no—
90Q8×C43—41no—
91Q8×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43#12011yescharacteristic
95C2×C4×C43C2×D811yescharacteristic
96C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—42no—
100D172—81no—
101D172—81no—
102D172—81no—
103D172—81no—
104D172—161no—
105Dic86—21no—
106Dic86—42no—
107Dic86—42no—
108Dic86SD3212yescomplemented
109C8×C43—21no—
110C8×C43—81no—
111C8×C43#13511yescharacteristic
112C8×C43AGL(1,ℤ/8)11yescharacteristic
113C43⋊C8—41no—
114#12330—431nomaximal, Sylow
115C22×C43#44711yescharacteristic
116C2×D43—161no—
117C2×D43—161no—
118C2×D43—161no—
119C4×C43—21no—
120C4×C43—81no—
121C4×C43—81no—
122C4×C43#44911yescharacteristic
123C4×C43#45311yescharacteristic
124C4×C43C2×SD3211yescharacteristic
125C4×C43#51011yescharacteristic
126Dic43—22no—
127Dic43—41no—
128Dic43—82no—
129#3395—431no—
130#2248—431no—
131#2207—431no—
132#1668—431no—
133#1362—431no—
134Q8⋊C16—431no—
135#1332D4311yescharacteristic, complemented
136C2×C43#162111yescharacteristic
137C2×C43#218511yescharacteristic
138C2×C43#219311yescharacteristic
139D43—321no—
140#557—861no—
141C2×SD32—862no—
142C2×SD32—861no—
143#494—431no—
144#494—861no—
145#493—431no—
146#462—862no—
147#462—861no—
148#460—861no—
149C8×Q8—431no—
150C4×Q16—861no—
151C4×Q16C2×D4311yescharacteristic
152C4⋊C16—431no—
153#357—861no—
154C4×C16C2×D4311yescharacteristic
155#335C2×D4311yescharacteristic
156#331—861no—
157C43#1233011yescharacteristic, complemented, Sylow
158C2×Q16—432no—
159C2×Q16—862no—
160C2×Q16—861no—
161C2×Q16D17211yescharacteristic
162C2×SD16—1721no—
163C2×D8—861no—
164C2×D8—861no—
165C4⋊Q8—862no—
166C4⋊Q8—861no—
167#127—861no—
168#125—1721no—
169#125—1722no—
170C4×Q8—21no—
171C4×Q8—431no—
172C4×Q8—862no—
173C4×Q8—1721no—
174SD32—1724no—
175SD32—1722no—
176C2×C16—21no—
177C2×C16—861no—
178#107D17211yescharacteristic
179C4⋊C8—21no—
180C4⋊C8—431no—
181C4⋊C8—861no—
182#103—21no—
183#103—862no—
184#102—1721no—
185C4×C8—861no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—21no—
188C2×Q8—431no—
189C2×Q8—862no—
190C2×D4—1721no—
191C2×D4—1721no—
192C2×D4—1721no—
193Q16—21no—
194Q16—21no—
195Q16—3442no—
196Q16—1722no—
197Q16—1721no—
198Q16—1721no—
199SD16—3442no—
200D8—1722no—
201D8—1721no—
202D8—1721no—
203C2×C8—41no—
204C2×C8—861no—
205C2×C8C2×D17211yescharacteristic
206C2×C8D4×D4311yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—1722no—
212C4⋊C4—1722no—
213C4⋊C4—1722no—
214C4⋊C4—1721no—
215C4⋊C4—1721no—
216C42—41no—
217C42—861no—
218C42—1722no—
219C42D4×D4311yescharacteristic
220C16—22no—
221C16—1721no—
222C23—3441no—
223Q8—41no—
224Q8—41no—
225Q8—432no—
226Q8—861no—
227Q8—1722no—
228Q8—1722no—
229D4—3441no—
230D4—3441no—
231D4—3441no—
232D4—3441no—
233D4—6881no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—861no—
237C2×C4—861no—
238C2×C4—1722no—
239C2×C4#1306329511yescharacteristic
240C2×C4D8×D4311yescharacteristic
241C2×C4#1306335211yescharacteristic
242C8—21no—
243C8—81no—
244C8—1721no—
245C8#1306334711yescharacteristic
246C8#1306335311yescharacteristic
247C22—6881no—
248C22—6881no—
249C22—6881no—
250C22#1458303411yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—862no—
255C4—3442no—
256C4—1721no—
257C4#1458304611yescharacteristic
258C4#1458306811yescharacteristic
259C4SD32×D4311yescharacteristic
260C4#1458334111yescharacteristic
261C2—13761no—
262C2#1913366311yescharacteristic
263C2#1913651311yescharacteristic
264C2#1913656011yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1332C2
socleC22×C43#447
prime radical#14583276C22
hypercenter#1332D43
hypocenterC43#12330
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
1. #19147600C2semidirect
5. #19132643C2semidirect
6. #19132575C2semidirect
7. C43×#1332C2semidirect
108. Dic86SD32semidirect
135. #1332D43semidirect
157. C43#12330semidirect

Maximal subgroups

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

subgroupindex
#191476002
#191368512
#191366352
#191339562
#191326432
#191325752
C43×#13322
#1233043