Finite Group Databasebeta

← #25009981

Subgroups — #25009981

Order 11008.

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

normal subgroups only

This group has 280 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#19145990C211yesmaximal, characteristic
2#19136814C211yesmaximal, characteristic, complemented
3#19136169C211yesmaximal, characteristic, complemented
4#19132584C211yesmaximal, characteristic, complemented
5#19132580C211yesmaximal, characteristic
6#19132545C211yesmaximal, characteristic, complemented
7C43×#2238C211yesmaximal, characteristic
8#14583430—21no—
9#14583209—21no—
10#14583201—21no—
11#14583157C2211yescharacteristic
12#14583143—21no—
13#14583120—21no—
14#14583112—21no—
15#14582922C2211yescharacteristic
16#14582723—21no—
17#14582714—21no—
18#14582681C2211yescharacteristic
19#14582670—21no—
20#14582660—21no—
21#14582656C2211yescharacteristic
22C43×#469C2211yescharacteristic
23C43×#430C2211yescharacteristic
24C43×#365—21no—
25C43×#361—21no—
26C43×#349C2211yescharacteristic
27C2×Dic172D411yescharacteristic
28C2×#10621883—21no—
29C2×#10621877D411yescharacteristic
30#13063318—41no—
31#13063316—21no—
32#13063312—21no—
33#13063306—41no—
34#13063304—21no—
35#13063290—21no—
36D4×Dic43—21no—
37D4×Dic43—41no—
38#13063284—21no—
39#13063281—41no—
40C2×C4×Dic43D411yescharacteristic
41#13063265—21no—
42#13063258—21no—
43#13063257D411yescharacteristic
44Dic43⋊C8—21no—
45Dic43⋊C8—21no—
46#13063250—21no—
47#13063248—21no—
48#13063246—21no—
49C2×D8×C43D411yescharacteristic
50C2×M16×C43—21no—
51C2×M16×C43C2311yescharacteristic
52#121×C43—21no—
53M32×C43—21no—
54#108×C43—21no—
55#108×C43—21no—
56#106×C43D411yescharacteristic
57#102×C43—21no—
58C2×D4×C43—21no—
59C2×D4×C43—41no—
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—21no—
62C22×Dic43—41no—
63C2×Dic86—21no—
64D8×C43—41no—
65M16×C43—41no—
66M16×C43—41no—
67M16×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43C2×D411yescharacteristic
70C2×C8×C43C2×D411yescharacteristic
71C4⋊C4×C43—21no—
72C22⋊C4×C43—41no—
73C22⋊Dic43—41no—
74C22⋊Dic43—41no—
75C22⋊Dic43—41no—
76C22⋊Dic43—41no—
77C22⋊Dic43—41no—
78#10621883—81no—
79C4⋊Dic43—21no—
80C4⋊Dic43—41no—
81C4⋊Dic43—41no—
82Dic43⋊C4—41no—
83Dic43⋊C4—41no—
84Dic43⋊C4—41no—
85C4×Dic43—21no—
86C4×Dic43—41no—
87C4×Dic43—41no—
88C4×Dic43SD1611yescharacteristic
89C4×Dic43SD1611yescharacteristic
90#10621877—41no—
91C2×C43⋊C8—21no—
92Dic172—41no—
93C16×C43—41no—
94C43⋊C16—41no—
95C23×C43—41no—
96C23×C43AGL(1,ℤ/8)11yescharacteristic
97D4×C43—41no—
98D4×C43—41no—
99D4×C43—82no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—41no—
103C2×C4×C43#12011yescharacteristic
104C2×C4×C43C2×SD1611yescharacteristic
105C2×Dic43—21no—
106C2×Dic43—21no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—81no—
110C2×Dic43—82no—
111C2×Dic43—81no—
112Dic86—41no—
113Dic86—41no—
114C8×C43—21no—
115C8×C43—21no—
116C8×C43—81no—
117C43⋊C8—41no—
118#12309—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—41no—
121C22×C43—81no—
122C22×C43—81no—
123C22×C43—81no—
124C22×C43#45011yescharacteristic
125C4×C43—21no—
126C4×C43—81no—
127C4×C43#45411yescharacteristic
128C4×C43#45811yescharacteristic
129Dic43—41no—
130Dic43—41no—
131Dic43—81no—
132Dic43—81no—
133Dic43—161no—
134#3256—431no—
135#2239—431no—
136#2238D4311yescharacteristic
137#2102—431no—
138#1340—431no—
139#1339—431no—
140#1327—431no—
141C2×C43—21no—
142C2×C43—41no—
143C2×C43—161no—
144C2×C43#161611yescharacteristic
145#529—861no—
146#479—861no—
147#478—861no—
148#470—431no—
149#469C2×D4311yescharacteristic
150#468—861no—
151#464—861no—
152#463—861no—
153#430C2×D4311yescharacteristic
154#423—431no—
155#365—21no—
156#365—861no—
157#362—861no—
158#361—21no—
159#349—431no—
160#349C2×D4311yescharacteristic
161#344—861no—
162#339—861no—
163H(3,ℤ/4)—431no—
164C43#1230911yescharacteristic, complemented, Sylow
165C2×Q16—431no—
166C2×SD16—861no—
167C2×D8C22⋊D4311yescharacteristic
168C2×M16—21no—
169C2×M16—431no—
170C2×M16C22×D4311yescharacteristic
171#126—1721no—
172#125—861no—
173#124—861no—
174#123—1721no—
175C22⋊Q8—861no—
176#121—21no—
177C4×Q8—861no—
178C4×D4—861no—
179C4×D4—1721no—
180#117—861no—
181#117—1721no—
182C2×C42—431no—
183M32—21no—
184M32—861no—
185#108—21no—
186#108—21no—
187#107—861no—
188#106—431no—
189#106C22⋊D4311yescharacteristic
190C4⋊C8—861no—
191C4⋊C8—861no—
192#103—861no—
193#103—861no—
194#102—21no—
195#102—861no—
196C2×Q8—861no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—861no—
200C22×C4—1721no—
201C22×C4D4×D4311yescharacteristic
202Q16—1721no—
203SD16—3441no—
204D8—41no—
205M16—41no—
206M16—41no—
207M16—41no—
208M16—1721no—
209C2×C8—41no—
210C2×C8—861no—
211C2×C8D4×D4311yescharacteristic
212C2×C8C2×C22⋊D4311yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—861no—
215C4⋊C4—1721no—
216C4⋊C4—1721no—
217C4⋊C4—1721no—
218C4⋊C4—1721no—
219C4⋊C4—1721no—
220C22⋊C4—41no—
221C22⋊C4—1721no—
222C22⋊C4—1721no—
223C22⋊C4—1721no—
224C22⋊C4—1721no—
225C22⋊C4—1721no—
226C42—431no—
227C42—431no—
228C42—861no—
229C42—1721no—
230C42—1721no—
231C16—41no—
232C16—1721no—
233C23—41no—
234C23#1306335211yescharacteristic
235Q8—1721no—
236Q8—1721no—
237D4—41no—
238D4—41no—
239D4—82no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—861no—
244C2×C4—861no—
245C2×C4—3442no—
246C2×C4—3441no—
247C2×C4—3441no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4#1306329311yescharacteristic
251C2×C4SD16×D4311yescharacteristic
252C8—21no—
253C8—21no—
254C8—81no—
255C8—1721no—
256C22—21no—
257C22—41no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22#1458304811yescharacteristic
262C4—21no—
263C4—81no—
264C4—3441no—
265C4—3441no—
266C4—1721no—
267C4—1721no—
268C4—6881no—
269C4#1458307011yescharacteristic
270C4#1458308811yescharacteristic
271C2—21no—
272C2—41no—
273C2—161no—
274C2#1913363011yescharacteristic
subgroupG/H
centerC2#19133630
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#2238C2
socleC2×C43#1616
prime radicalC43×#469C22
hypercenter#2238D43
hypocenterC43#12309
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2238

Complements

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

NH ≅ G/Ntype
2. #19136814C2semidirect
3. #19136169C2semidirect
4. #19132584C2semidirect
6. #19132545C2semidirect
164. C43#12309semidirect

Maximal subgroups

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

subgroupindex
#191459902
#191368142
#191361692
#191325842
#191325802
#191325452
C43×#22382
#1230943