Finite Group Databasebeta

← #25010394

Subgroups — #25010394

Order 11008.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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
1Q16×D172C211yesmaximal, characteristic
2#19136823C211yesmaximal, characteristic, complemented
3#19136737C211yesmaximal, characteristic, complemented
4#19133985C211yesmaximal, characteristic
5#19132643C211yesmaximal, characteristic, complemented
6#19132551C211yesmaximal, characteristic
7C43×#1332C211yesmaximal, characteristic, complemented
8C2×Q16×D43—21no—
9Q8×D172—21no—
10#14583304C2211yescharacteristic
11#14583279C2211yescharacteristic
12#14583141—21no—
13#14583109—21no—
14#14583105—21no—
15#14583056—22no—
16C8×D172C2211yescharacteristic
17#14582726—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582704—22no—
20#14582703—21no—
21#14582646—21no—
22C4×Q16×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Q8×D43—22no—
26C2×Dic172—21no—
27C2×Dic172D412yes—
28C2×#10621885—22no—
29Q16×D43—42no—
30Q16×D43—42no—
31C2×#10621873—41no—
32C2×C8×D43—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—41no—
36#13063305—22no—
37#13063305—42no—
38C4×D172—41no—
39C4×D172D411yescharacteristic
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×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—
55Q8×D43—44no—
56Q8×D43—82no—
57C2×D172D811yescharacteristic
58C2×C4×D43—21no—
59C2×C4×D43—42no—
60C2×Dic86—22no—
61C2×Dic86—42no—
62C2×Dic86—41no—
63Q16×C43—21no—
64Q16×C43SD1612yescomplemented
65C2×C8×C43—41no—
66C2×C8×C43C2×D411yescharacteristic
67C2×C8×C43C2×D411yescharacteristic
68C4⋊C4×C43—21no—
69C4⋊C4×C43—41no—
70C42×C43—41no—
71C42×C43C2×D411yescharacteristic
72#10621885—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—
90C22×D43—21no—
91Q8×C43—22no—
92Q8×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43#12011yescharacteristic
96C2×C4×C43C2×D811yescharacteristic
97C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
98C2×Dic43—21no—
99C2×Dic43—42no—
100C2×Dic43—81no—
101D172—21no—
102D172SD3212yes—
103C4×D43—41no—
104C4×D43—41no—
105C4×D43—84no—
106Dic86—42no—
107Dic86—42no—
108Dic86—84no—
109Dic86—81no—
110Dic86—81no—
111C8×C43—21no—
112C8×C43—81no—
113C8×C43C2×SD1611yescharacteristic
114C8×C43AGL(1,ℤ/8)11yescharacteristic
115C43⋊C8—41no—
116#12370—431nomaximal, Sylow
117C22×C43#44711yescharacteristic
118C2×D43—22no—
119C2×D43—41no—
120C2×D43—41no—
121C4×C43—21no—
122C4×C43—42no—
123C4×C43—81no—
124C4×C43#45011yescharacteristic
125C4×C43#45511yescharacteristic
126C4×C43C2×SD3211yescharacteristic
127C4×C43#51011yescharacteristic
128Dic43—41no—
129Dic43—82no—
130Dic43—161no—
131D4×Q16—431no—
132#2241—431no—
133#2225—431no—
134#1673—431no—
135#1362—431no—
136#1332D4311yescharacteristic, complemented
137D4⋊C16—431no—
138C2×C43#163911yescharacteristic
139C2×C43#218511yescharacteristic
140C2×C43#219511yescharacteristic
141D43—42no—
142C22×Q16—861no—
143D4×Q8—861no—
144#500—431no—
145#494—431no—
146#467—861no—
147#462—861no—
148#461—861no—
149#451—862no—
150C4×Q16C2×D4311yescharacteristic
151C8×D4—431no—
152#367—861no—
153C4⋊C16—431no—
154#358—862no—
155#358—861no—
156C4×C16C2×D4311yescharacteristic
157#335C2×D4311yescharacteristic
158#332—861no—
159C43#1237011yescharacteristic, complemented, Sylow
160C22×Q8—862no—
161C2×Q16—432no—
162C2×Q16—862no—
163C2×Q16—861no—
164C2×Q16—1722no—
165C2×Q16—1722no—
166C2×Q16D17211yescharacteristic
167C2×SD16—1721no—
168C22×C8—861no—
169C4⋊Q8—861no—
170C4⋊Q8—861no—
171C4⋊Q8—1721no—
172C22⋊Q8—862no—
173C22⋊Q8—1722no—
174C4×Q8—21no—
175C4×D4—431no—
176C4×D4—1721no—
177C2×C16—21no—
178C2×C16—861no—
179#107—861no—
180#107—861no—
181#107D17211yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—431no—
184#103—21no—
185#103—862no—
186#103—1721no—
187C22⋊C8—861no—
188C4×C8C22×D4311yescharacteristic
189C2×Q8—21no—
190C2×Q8—862no—
191C2×Q8—3442no—
192C2×Q8—1722no—
193C2×Q8—1724no—
194C2×Q8—1721no—
195C2×D4—431no—
196C22×C4—861no—
197C22×C4—1722no—
198Q16—21no—
199Q16—1722no—
200Q16—1724no—
201Q16—1721no—
202Q16—1721no—
203Q16#1062187312yescomplemented
204SD16—3442no—
205C2×C8—41no—
206C2×C8—861no—
207C2×C8—1721no—
208C2×C8—1721no—
209C2×C8C2×D17211yescharacteristic
210C2×C8D4×D4311yescharacteristic
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—431no—
214C4⋊C4—1722no—
215C4⋊C4—1721no—
216C4⋊C4—1721no—
217C4⋊C4—1721no—
218C4⋊C4—1721no—
219C22⋊C4—861no—
220C22⋊C4—1722no—
221C42—41no—
222C42D4×D4311yescharacteristic
223C16—41no—
224C16—1721no—
225C23—861no—
226Q8—22no—
227Q8—41no—
228Q8—3444no—
229Q8—3441no—
230Q8—3441no—
231Q8—1722no—
232Q8—1722no—
233D4—432no—
234D4—861no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—861no—
238C2×C4—3444no—
239C2×C4—3441no—
240C2×C4—1722no—
241C2×C4—1721no—
242C2×C4—1721no—
243C2×C4#1306329511yescharacteristic
244C2×C4D8×D4311yescharacteristic
245C2×C4#1306335211yescharacteristic
246C8—21no—
247C8—81no—
248C8—1721no—
249C8C2×#1062187311yescharacteristic
250C8#1306335311yescharacteristic
251C22—862no—
252C22—1721no—
253C22—1721no—
254C22#1458303411yescharacteristic
255C4—21no—
256C4—42no—
257C4—81no—
258C4—3442no—
259C4—1721no—
260C4—6881no—
261C4#1458305211yescharacteristic
262C4#1458307811yescharacteristic
263C4SD32×D4311yescharacteristic
264C4#1458334111yescharacteristic
265C2—1722no—
266C2#1913377711yescharacteristic
267C2#1913651311yescharacteristic
268C2#1913657411yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1332C2
socleC22×C43#447
prime radicalC2×D172D8
hypercenter#1332D43
hypocenterC43#12370
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
2. #19136823C2semidirect
3. #19136737C2semidirect
5. #19132643C2semidirect
7. C43×#1332C2semidirect
64. Q16×C43SD16semidirect
136. #1332D43semidirect
159. C43#12370semidirect
203. Q16#10621873semidirect

Maximal subgroups

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

subgroupindex
Q16×D1722
#191368232
#191367372
#191339852
#191326432
#191325512
C43×#13322
#1237043