Finite Group Databasebeta

← #25010136

Subgroups — #25010136

Order 11008.

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

normal subgroups only

This group has 362 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#19147569C211yesmaximal, characteristic
2#19136851C211yesmaximal, characteristic, complemented
3#19136640C211yesmaximal, characteristic, complemented
4#19133966C211yesmaximal, characteristic, complemented
5#19132640C211yesmaximal, characteristic, complemented
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1331C211yesmaximal, characteristic, complemented
8#14583570—21no—
9C2×#13063270—22no—
10C2×#13063269—21no—
11#14583279C2211yescharacteristic
12#14583276C2211yescharacteristic
13#14583274—21no—
14#14583185—21no—
15#14583094—21no—
16#14583093—22no—
17C8×Dic86C2211yescharacteristic
18#14582981—21no—
19C4⋊(C43⋊C16)C2211yescharacteristic
20#14582702—21no—
21#14582644—21no—
22C4×D8×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621898—41no—
26C2×Dic172—21no—
27C2×Dic172—21no—
28C2×D344—21no—
29C2×D344D412yes—
30C2×#10621882—22no—
31#13063325—21no—
32#13063322—21no—
33#13063321—22no—
34#13063299—41no—
35#13063298—42no—
36C4×Dic86D411yescharacteristic
37#13063287—22no—
38#13063270—44no—
39#13063269—42no—
40C2×C43⋊C16—21no—
41#13063257—41no—
42C4⋊(C43⋊C8)D411yescharacteristic
43Dic43⋊C8—21no—
44#13063250—41no—
45#13063245—22no—
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×C22⋊D43—42no—
57C2×C22⋊D43—42no—
58#10621898—82no—
59#10621898—82no—
60C2×D172—22no—
61C2×D172—41no—
62C2×D172—41no—
63C2×C4×D43—42no—
64C2×Dic86—41no—
65C2×Dic86D811yescharacteristic
66D8×C43—21no—
67D8×C43—21no—
68C2×C8×C43—41no—
69C2×C8×C43C2×D411yescharacteristic
70C2×C8×C43C2×D411yescharacteristic
71C4⋊C4×C43—21no—
72C22⋊C4×C43—41no—
73C42×C43C2×D411yescharacteristic
74#10621882—82no—
75(C2×D43)⋊C4—42no—
76C4⋊Dic43—41no—
77C4⋊Dic43—41no—
78C4⋊Dic43D811yescharacteristic
79Dic43⋊C4—21no—
80C4×Dic43—21no—
81C2×C43⋊C8—21no—
82Dic172—42no—
83Dic172—41no—
84Dic172—41no—
85D344—42no—
86D344—41no—
87D344—41no—
88C16×C43—22no—
89C43⋊C16—41no—
90C23×C43—41no—
91C22×D43—42no—
92D4×C43—41no—
93D4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—81no—
96C2×C4×C43—81no—
97C2×C4×C43#12011yescharacteristic
98C2×C4×C43C2×D811yescharacteristic
99C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
100C22⋊D43—84no—
101C22⋊D43—162no—
102C2×Dic43—21no—
103C2×Dic43—21no—
104C2×Dic43—81no—
105D172—42no—
106D172—42no—
107D172—81no—
108D172—81no—
109D172—161no—
110C4×D43—84no—
111Dic86—21no—
112Dic86—81no—
113Dic86—81no—
114Dic86SD3212yescomplemented
115C8×C43—21no—
116C8×C43—81no—
117C8×C43#13511yescharacteristic
118C8×C43AGL(1,ℤ/8)11yescharacteristic
119C43⋊C8—41no—
120#12332—431nomaximal, Sylow
121C22×C43—81no—
122C22×C43—81no—
123C22×C43—81no—
124C22×C43#44711yescharacteristic
125C2×D43—82no—
126C2×D43—82no—
127C2×D43—82no—
128C4×C43—21no—
129C4×C43—81no—
130C4×C43#44911yescharacteristic
131C4×C43#45311yescharacteristic
132C4×C43C2×SD3211yescharacteristic
133C4×C43#50911yescharacteristic
134Dic43—22no—
135Dic43—41no—
136Dic43—161no—
137#3391—431no—
138#2248—431no—
139#2208—431no—
140#1670—431no—
141#1361—431no—
142Q8⋊C16—431no—
143#1331D4311yescharacteristic, complemented
144C2×C43—161no—
145C2×C43#162111yescharacteristic
146C2×C43#218711yescharacteristic
147C2×C43#219411yescharacteristic
148D43—162no—
149#550—861no—
150C2×SD32—862no—
151C2×SD32—861no—
152#494—431no—
153#493—431no—
154#493—861no—
155#475—861no—
156#459—862no—
157#459—861no—
158C8×Q8—431no—
159C4×D8—861no—
160C4×D8C2×D4311yescharacteristic
161C4⋊C16—431no—
162#358—861no—
163C4×C16C2×D4311yescharacteristic
164#335C2×D4311yescharacteristic
165#332—861no—
166C43#1233211yescharacteristic, complemented, Sylow
167C2×#41—1721no—
168C2×Q16—861no—
169C2×Q16—861no—
170C2×D8—432no—
171C2×D8—862no—
172C2×D8—861no—
173C2×D8D17211yescharacteristic
174C4⋊Q8—861no—
175#127—862no—
176#127—861no—
177#121—1722no—
178#121—1721no—
179C4×Q8—431no—
180C4×D4—21no—
181C4×D4—862no—
182SD32—1724no—
183SD32—1722no—
184C2×C16—21no—
185C2×C16—861no—
186#107D17211yescharacteristic
187#106—1721no—
188C4⋊C8—21no—
189C4⋊C8—431no—
190C4⋊C8—861no—
191#103—1721no—
192#102—21no—
193#102—862no—
194C4×C8—861no—
195C4×C8C22×D4311yescharacteristic
196#41—3442no—
197#41—3442no—
198C2×Q8—431no—
199C2×Q8—1721no—
200C2×D4—21no—
201C2×D4—862no—
202C2×D4—1722no—
203C2×D4—1722no—
204C2×D4—1721no—
205C2×D4—1721no—
206C22×C4—41no—
207C22×C4—1722no—
208Q16—1722no—
209Q16—1721no—
210Q16—1721no—
211D8—21no—
212D8—21no—
213D8—3442no—
214D8—1722no—
215D8—1721no—
216D8—1721no—
217C2×C8—41no—
218C2×C8—861no—
219C2×C8C2×D17211yescharacteristic
220C2×C8D4×D4311yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—431no—
223C4⋊C4—861no—
224C4⋊C4—1721no—
225C4⋊C4—1721no—
226C22⋊C4—41no—
227C22⋊C4—1722no—
228C42—861no—
229C42D4×D4311yescharacteristic
230C16—22no—
231C16—1721no—
232C23—41no—
233C23—1722no—
234Q8—432no—
235Q8—861no—
236Q8—3441no—
237Q8—3441no—
238D4—41no—
239D4—41no—
240D4—3444no—
241D4—3441no—
242D4—3441no—
243D4—1722no—
244D4—1722no—
245D4—6881no—
246D4—6882no—
247C2×C4—41no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—861no—
251C2×C4—861no—
252C2×C4—3444no—
253C2×C4—3441no—
254C2×C4#1306329511yescharacteristic
255C2×C4D8×D4311yescharacteristic
256C2×C4#1306335211yescharacteristic
257C8—21no—
258C8—81no—
259C8—1721no—
260C8#1306334711yescharacteristic
261C8#1306335311yescharacteristic
262C22—81no—
263C22—81no—
264C22—81no—
265C22—3442no—
266C22—3442no—
267C22—3442no—
268C22#1458303411yescharacteristic
269C4—21no—
270C4—81no—
271C4—862no—
272C4—1721no—
273C4—6881no—
274C4#1458304611yescharacteristic
275C4#1458306811yescharacteristic
276C4SD32×D4311yescharacteristic
277C4#1458333311yescharacteristic
278C2—161no—
279C2—6882no—
280C2#1913366311yescharacteristic
281C2#1913652511yescharacteristic
282C2#1913656711yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1331C2
socleC22×C43#447
prime radical#19147569C2
hypercenter#1331D43
hypocenterC43#12332
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
2. #19136851C2semidirect
3. #19136640C2semidirect
4. #19133966C2semidirect
5. #19132640C2semidirect
6. #19132575C2semidirect
7. C43×#1331C2semidirect
114. Dic86SD32semidirect
143. #1331D43semidirect
166. C43#12332semidirect

Maximal subgroups

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

subgroupindex
#191475692
#191368512
#191366402
#191339662
#191326402
#191325752
C43×#13312
#1233243