Finite Group Databasebeta

← #25010401

Subgroups — #25010401

Order 11008.

356 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 69 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#19146316C211yesmaximal, characteristic
2#19136823C211yesmaximal, characteristic, complemented
3#19136732C211yesmaximal, characteristic, complemented
4#19133985C211yesmaximal, characteristic, complemented
5#19132643C211yesmaximal, characteristic, complemented
6#19132551C211yesmaximal, characteristic, complemented
7C43×#1331C211yesmaximal, characteristic, complemented
8C2×#13063344—21no—
9#14583553—21no—
10#14583304C2211yescharacteristic
11#14583279C2211yescharacteristic
12#14583141—21no—
13#14583105—21no—
14#14583104—21no—
15#14583062—22no—
16C8×D172C2211yescharacteristic
17#14582724—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582704—22no—
20#14582700—21no—
21#14582646—21no—
22C4×D8×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621900—22no—
26#13063344—42no—
27#13063344—42no—
28C2×Dic172—21no—
29C2×Dic172D412yes—
30C2×#10621873—41no—
31C2×#10621883—22no—
32C2×C8×D43—21no—
33#13063325—21no—
34#13063325—21no—
35#13063309—42no—
36#13063305—22no—
37#13063299—41no—
38C4×D172D411yescharacteristic
39C2×C4⋊Dic43—41no—
40C2×C43⋊C16—21no—
41#13063259—21no—
42#13063259—21no—
43C4⋊(C43⋊C8)D411yescharacteristic
44#13063250—41no—
45#13063248—22no—
46(C2×D43)⋊C8—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—
57C22×Dic43—42no—
58#10621900—44no—
59#10621900—82no—
60C2×D172D811yescharacteristic
61C2×C4×D43—21no—
62C2×Dic86—22no—
63C2×Dic86—41no—
64D8×C43—21no—
65D8×C43SD1612yescomplemented
66C2×C8×C43—41no—
67C2×C8×C43C2×D411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C4⋊C4×C43—21no—
70C22⋊C4×C43—41no—
71C42×C43C2×D411yescharacteristic
72#10621883—44no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—42no—
75C4⋊Dic43—42no—
76C4⋊Dic43—41no—
77C4⋊Dic43—41no—
78C4⋊Dic43—41no—
79C4⋊Dic43—41no—
80C4⋊Dic43D811yescharacteristic
81C2×C43⋊C8—21no—
82Dic172—42no—
83Dic172—41no—
84Dic172—41no—
85#10621873—82no—
86C8×D43—41no—
87C8×D43—41no—
88C16×C43—41no—
89C43⋊C16—41no—
90C23×C43—41no—
91C22×D43—21no—
92D4×C43—22no—
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—
101C2×Dic43—21no—
102C2×Dic43—42no—
103C2×Dic43—84no—
104C2×Dic43—81no—
105D172—21no—
106D172—21no—
107C4×D43—41no—
108C4×D43—41no—
109Dic86—42no—
110Dic86—42no—
111Dic86—81no—
112Dic86—81no—
113C8×C43—21no—
114C8×C43—81no—
115C8×C43C2×SD1611yescharacteristic
116C8×C43AGL(1,ℤ/8)11yescharacteristic
117C43⋊C8—41no—
118#12371—431nomaximal, Sylow
119C22×C43—42no—
120C22×C43—81no—
121C22×C43—81no—
122C22×C43#44711yescharacteristic
123C2×D43—41no—
124C2×D43—41no—
125C2×D43—41no—
126C4×C43—21no—
127C4×C43—81no—
128C4×C43#45011yescharacteristic
129C4×C43#45511yescharacteristic
130C4×C43#50811yescharacteristic
131C4×C43#50911yescharacteristic
132Dic43—41no—
133Dic43—82no—
134Dic43—161no—
135#3283—431no—
136#2241—431no—
137#2224—431no—
138#1673—431no—
139#1362—431no—
140#1331D4311yescharacteristic, complemented
141D4⋊C16—431no—
142C2×C43—82no—
143C2×C43#163911yescharacteristic
144C2×C43#218611yescharacteristic
145C2×C43#219511yescharacteristic
146D43—81no—
147C2×#135—861no—
148#547—861no—
149#500—431no—
150#494—431no—
151#467—861no—
152#461—861no—
153#461—861no—
154#452—862no—
155C4×D8C2×D4311yescharacteristic
156C8×D4—431no—
157#366—861no—
158C4⋊C16—431no—
159#358—862no—
160#357—861no—
161C4×C16C2×D4311yescharacteristic
162#335C2×D4311yescharacteristic
163#332—861no—
164C43#1237111yescharacteristic, complemented, Sylow
165C2×#41—862no—
166#135—1722no—
167#135—1722no—
168C2×Q16—432no—
169C2×Q16—861no—
170C2×SD16—862no—
171C2×SD16—1721no—
172C2×D8D17211yescharacteristic
173C22×C8—861no—
174C4⋊Q8—861no—
175C4⋊Q8—861no—
176#123—1722no—
177C22⋊Q8—862no—
178#121—1721no—
179C4×D4—21no—
180C4×D4—431no—
181C2×C4⋊C4—1721no—
182C2×C16—21no—
183C2×C16—861no—
184#107—861no—
185#107—861no—
186#107D17211yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—431no—
189#103—862no—
190#103—1721no—
191#102—21no—
192C22⋊C8—861no—
193C4×C8C22×D4311yescharacteristic
194#41—3442no—
195#41—1724no—
196C2×Q8—862no—
197C2×Q8—1721no—
198C2×D4—21no—
199C2×D4—431no—
200C2×D4—1722no—
201C22×C4—41no—
202C22×C4—861no—
203C22×C4—1722no—
204Q16—1722no—
205Q16—1721no—
206Q16—1721no—
207SD16—3442no—
208SD16—1724no—
209D8—21no—
210D8#1062187312yescomplemented
211C2×C8—41no—
212C2×C8—861no—
213C2×C8—1721no—
214C2×C8—1721no—
215C2×C8C2×D17211yescharacteristic
216C2×C8D4×D4311yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—431no—
219C4⋊C4—1722no—
220C4⋊C4—1721no—
221C4⋊C4—1721no—
222C4⋊C4—1721no—
223C4⋊C4—1721no—
224C22⋊C4—41no—
225C22⋊C4—861no—
226C22⋊C4—1722no—
227C42D4×D4311yescharacteristic
228C16—41no—
229C16—1721no—
230C23—41no—
231C23—861no—
232Q8—3441no—
233Q8—3441no—
234Q8—1722no—
235Q8—1722no—
236D4—22no—
237D4—41no—
238D4—861no—
239D4—861no—
240D4—3444no—
241C2×C4—41no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—861no—
245C2×C4—3444no—
246C2×C4—3441no—
247C2×C4—1722no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4#1306329511yescharacteristic
251C2×C4D8×D4311yescharacteristic
252C2×C4#1306335211yescharacteristic
253C8—21no—
254C8—81no—
255C8—1721no—
256C8C2×#1062187311yescharacteristic
257C8#1306335311yescharacteristic
258C22—42no—
259C22—81no—
260C22—81no—
261C22—1721no—
262C22—1721no—
263C22—1721no—
264C22#1458303411yescharacteristic
265C4—21no—
266C4—81no—
267C4—3442no—
268C4—1721no—
269C4—6881no—
270C4#1458305211yescharacteristic
271C4#1458307811yescharacteristic
272C4#1458333011yescharacteristic
273C4#1458333311yescharacteristic
274C2—82no—
275C2—3441no—
276C2#1913377711yescharacteristic
277C2#1913651911yescharacteristic
278C2#1913657411yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1331C2
socleC22×C43#447
prime radical#19146316C2
hypercenter#1331D43
hypocenterC43#12371
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. #19136823C2semidirect
3. #19136732C2semidirect
4. #19133985C2semidirect
5. #19132643C2semidirect
6. #19132551C2semidirect
7. C43×#1331C2semidirect
65. D8×C43SD16semidirect
140. #1331D43semidirect
164. C43#12371semidirect
210. D8#10621873semidirect

Maximal subgroups

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

subgroupindex
#191463162
#191368232
#191367322
#191339852
#191326432
#191325512
C43×#13312
#1237143