Finite Group Databasebeta

← #25009962

Subgroups — #25009962

Order 11008.

262 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 53 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#19146046C211yesmaximal, characteristic
2#19136815C211yesmaximal, characteristic
3#19136812C211yesmaximal, characteristic
4#19136176C211yesmaximal, characteristic
5#19132588C211yesmaximal, characteristic
6#19132547C211yesmaximal, characteristic
7C43×#1342C211yesmaximal, characteristic
8#14583509—21no—
9#14583209—21no—
10#14583204—21no—
11#14583157C2211yescharacteristic
12#14583138—21no—
13#14583108—21no—
14#14583107—21no—
15#14582948C2211yescharacteristic
16#14582927C2211yescharacteristic
17#14582722—21no—
18#14582721—21no—
19#14582716—21no—
20#14582715—21no—
21#14582681C2211yescharacteristic
22#14582671—21no—
23#14582663—21no—
24C43×#470C2211yescharacteristic
25C43×#349C2211yescharacteristic
26C43×#338C2211yescharacteristic
27C2×Dic172D411yescharacteristic
28C2×#10621885—21no—
29C2×#10621877—21no—
30C22×C43⋊C8D411yescharacteristic
31#13063323—21no—
32#13063318—41no—
33#13063318—41no—
34#13063316—21no—
35#13063316—41no—
36#13063315—41no—
37#13063304—21no—
38Q8×Dic43—21no—
39#13063290—21no—
40#13063284D411yescharacteristic
41#13063265—21no—
42#13063261—21no—
43#13063261—21no—
44#13063258—21no—
45#13063257D411yescharacteristic
46Dic43⋊C8—21no—
47Dic43⋊C8—21no—
48#13063250—21no—
49#13063249—21no—
50#13063248—21no—
51C2×Q16×C43D411yescharacteristic
52C2×M16×C43—21no—
53C2×M16×C43C2311yescharacteristic
54C22⋊Q8×C43—21no—
55M32×C43—21no—
56#106×C43D411yescharacteristic
57#103×C43—21no—
58C2×Q8×C43—21no—
59C22×C4×C43C2×D411yescharacteristic
60C2×Dic86—21no—
61Q16×C43—41no—
62M16×C43—41no—
63M16×C43—41no—
64M16×C43—41no—
65C2×C8×C43—41no—
66C2×C8×C43C2×D411yescharacteristic
67C2×C8×C43C2×D411yescharacteristic
68C4⋊C4×C43—21no—
69C4⋊C4×C43—41no—
70C22⋊C4×C43—41no—
71C22⋊Dic43—41no—
72C22⋊Dic43SD1611yescharacteristic
73C22⋊Dic43SD1611yescharacteristic
74#10621885—81no—
75C4⋊Dic43—21no—
76C4⋊Dic43—21no—
77C4⋊Dic43—41no—
78C4⋊Dic43—41no—
79Dic43⋊C4—41no—
80Dic43⋊C4—41no—
81Dic43⋊C4—41no—
82Dic43⋊C4—41no—
83Dic43⋊C4—41no—
84C4×Dic43—21no—
85C4×Dic43—41no—
86C4×Dic43—41no—
87#10621877—41no—
88#10621877—41no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—41no—
91C2×C43⋊C8—41no—
92Dic172—41no—
93C16×C43—41no—
94C43⋊C16—41no—
95C23×C43C2×SD1611yescharacteristic
96Q8×C43—41no—
97Q8×C43—41no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43#12011yescharacteristic
103C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
104C2×Dic43—21no—
105C2×Dic43—21no—
106C2×Dic43—41no—
107C2×Dic43—41no—
108Dic86—41no—
109Dic86—41no—
110C8×C43—21no—
111C8×C43—21no—
112C8×C43—81no—
113C43⋊C8—41no—
114C43⋊C8—81no—
115#12305—431nomaximal, Sylow
116C22×C43—21no—
117C22×C43—41no—
118C22×C43#45011yescharacteristic
119C4×C43—21no—
120C4×C43—81no—
121C4×C43—81no—
122C4×C43#45411yescharacteristic
123C4×C43#45811yescharacteristic
124Dic43—41no—
125Dic43—41no—
126Dic43—81no—
127Dic43—81no—
128#3261—431no—
129#2239—431no—
130#2239—431no—
131#2103—431no—
132#1342—431no—
133#1342D4311yescharacteristic
134#1328—431no—
135C2×C43—21no—
136C2×C43—41no—
137C2×C43#161611yescharacteristic
138#541—861no—
139#479—861no—
140#479—861no—
141#470—431no—
142#470C2×D4311yescharacteristic
143#467—861no—
144#462—861no—
145#462—861no—
146#430—431no—
147#424—431no—
148#365—861no—
149#365—861no—
150#362—861no—
151#362—861no—
152#349—431no—
153#349C2×D4311yescharacteristic
154#344—861no—
155#341—861no—
156#338C2×D4311yescharacteristic
157C43#1230511yescharacteristic, complemented, Sylow
158C2×Q16—431no—
159C2×Q16—861no—
160C2×Q16D17211yescharacteristic
161C2×M16—21no—
162C2×M16—861no—
163C2×M16C22×D4311yescharacteristic
164C22×C8—431no—
165C4⋊Q8—861no—
166#126—1721no—
167#126—1721no—
168#125—861no—
169#125—1721no—
170#125—1721no—
171C22⋊Q8—21no—
172C22⋊Q8—861no—
173C4×Q8—861no—
174C4×Q8—861no—
175#117—431no—
176M32—21no—
177M32—861no—
178#108—861no—
179#108—861no—
180#107—861no—
181#106—431no—
182#106D17211yescharacteristic
183C4⋊C8—861no—
184C4⋊C8—861no—
185#103—21no—
186#103—861no—
187#103—861no—
188#103—861no—
189C2×Q8—21no—
190C2×Q8—861no—
191C22×C4D4×D4311yescharacteristic
192Q16—41no—
193Q16—3441no—
194Q16—1721no—
195M16—41no—
196M16—41no—
197M16—41no—
198M16—1721no—
199M16—1721no—
200C2×C8—41no—
201C2×C8—861no—
202C2×C8—1721no—
203C2×C8—1721no—
204C2×C8C2×D17211yescharacteristic
205C2×C8D4×D4311yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—861no—
209C4⋊C4—861no—
210C4⋊C4—1721no—
211C4⋊C4—1721no—
212C4⋊C4—1721no—
213C4⋊C4—1721no—
214C4⋊C4—1721no—
215C4⋊C4—1721no—
216C4⋊C4—1721no—
217C22⋊C4—41no—
218C22⋊C4—431no—
219C22⋊C4—431no—
220C22⋊C4—1721no—
221C42—861no—
222C42—1721no—
223C42—1721no—
224C16—41no—
225C16—1721no—
226C23SD16×D4311yescharacteristic
227Q8—41no—
228Q8—41no—
229Q8—1721no—
230Q8—1721no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—861no—
236C2×C4—861no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4#1306329511yescharacteristic
240C2×C4#1306334911yescharacteristic
241C8—21no—
242C8—21no—
243C8—81no—
244C8—3441no—
245C8—1721no—
246C22—21no—
247C22—41no—
248C22#1458305111yescharacteristic
249C4—21no—
250C4—81no—
251C4—81no—
252C4—3441no—
253C4—3441no—
254C4—1721no—
255C4—1721no—
256C4#1458307311yescharacteristic
257C4#1458309011yescharacteristic
258C2—21no—
259C2—41no—
260C2#1913363311yescharacteristic
subgroupG/H
centerC2#19133633
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#1342C2
socleC2×C43#1616
prime radicalC23×C43C2×SD16
hypercenter#1342D43
hypocenterC43#12305
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1342

Complements

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

NH ≅ G/Ntype
157. C43#12305semidirect

Maximal subgroups

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

subgroupindex
#191460462
#191368152
#191368122
#191361762
#191325882
#191325472
C43×#13422
#1230543