Finite Group Databasebeta

← #25010143

Subgroups — #25010143

Order 11008.

324 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147605C211yesmaximal, characteristic
2#19136851C211yesmaximal, characteristic
3#19136645C211yesmaximal, characteristic, complemented
4#19133966C211yesmaximal, characteristic, complemented
5#19132640C211yesmaximal, characteristic
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1332C211yesmaximal, characteristic, complemented
8#14583634—21no—
9C2×#13063271—21no—
10C2×#13063270—22no—
11#14583284—21no—
12#14583279C2211yescharacteristic
13#14583276C2211yescharacteristic
14#14583185—21no—
15#14583117—22no—
16#14583099—21no—
17C8×Dic86C2211yescharacteristic
18#14582981—21no—
19C4⋊(C43⋊C16)C2211yescharacteristic
20#14582702—21no—
21#14582644—21no—
22C4×Q16×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—21no—
26C2×Dic172—21no—
27C2×#10621884—22no—
28C2×D344—21no—
29C2×D344D412yes—
30#13063325—21no—
31#13063322—21no—
32#13063314—22no—
33#13063313—41no—
34#13063310—42no—
35C4×Dic86D411yescharacteristic
36C4×D172—41no—
37#13063287—22no—
38#13063271—42no—
39#13063270—44no—
40C2×C43⋊C16—21no—
41#13063257—41no—
42C4⋊(C43⋊C8)D411yescharacteristic
43Dic43⋊C8—21no—
44#13063250—41no—
45#13063245—22no—
46C8×Dic43—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—
55C2×D172—22no—
56C2×D172—41no—
57C2×D172—41no—
58C2×C4×D43—42no—
59C2×Dic86—41no—
60C2×Dic86D811yescharacteristic
61Q16×C43—21no—
62Q16×C43—21no—
63C2×C8×C43—41no—
64C2×C8×C43C2×D411yescharacteristic
65C2×C8×C43C2×D411yescharacteristic
66C4⋊C4×C43—21no—
67C4⋊C4×C43—41no—
68C42×C43—41no—
69C42×C43C2×D411yescharacteristic
70#10621884—82no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—42no—
73(C2×D43)⋊C4—42no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76C4⋊Dic43D811yescharacteristic
77Dic43⋊C4—21no—
78C4×Dic43—21no—
79C2×C43⋊C8—21no—
80Dic172—42no—
81Dic172—41no—
82Dic172—41no—
83D344—42no—
84D344—41no—
85D344—41no—
86C16×C43—22no—
87C43⋊C16—41no—
88C22×D43—42no—
89Q8×C43—41no—
90Q8×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43C2×D811yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C2×Dic43—21no—
97C2×Dic43—21no—
98C2×Dic43—81no—
99D172—42no—
100D172—42no—
101D172—81no—
102D172—81no—
103D172—161no—
104C4×D43—162no—
105Dic86—21no—
106Dic86—21no—
107Dic86—81no—
108Dic86—81no—
109C8×C43—21no—
110C8×C43—81no—
111C8×C43#13511yescharacteristic
112C8×C43AGL(1,ℤ/8)11yescharacteristic
113C43⋊C8—41no—
114#12333—431nomaximal, Sylow
115C22×C43#44711yescharacteristic
116C2×D43—82no—
117C2×D43—82no—
118C2×D43—82no—
119C4×C43—21no—
120C4×C43—81no—
121C4×C43—81no—
122C4×C43#44911yescharacteristic
123C4×C43#45311yescharacteristic
124C4×C43#50811yescharacteristic
125C4×C43#51011yescharacteristic
126Dic43—41no—
127Dic43—41no—
128Dic43—161no—
129#3396—431no—
130#2248—431no—
131#2209—431no—
132#1670—431no—
133#1361—431no—
134Q8⋊C16—431no—
135#1332D4311yescharacteristic, complemented
136C2×C43#162111yescharacteristic
137C2×C43#218911yescharacteristic
138C2×C43#219411yescharacteristic
139D43—162no—
140#559—861no—
141C2×Q32—861no—
142C2×SD32—862no—
143#495—861no—
144#494—431no—
145#493—431no—
146#475—861no—
147#463—862no—
148#460—861no—
149C8×Q8—431no—
150C4×Q16C2×D4311yescharacteristic
151C4×D8—861no—
152C4⋊C16—431no—
153#358—861no—
154C4×C16C2×D4311yescharacteristic
155#335C2×D4311yescharacteristic
156#332—861no—
157C43#1233311yescharacteristic, complemented, Sylow
158C2×Q16—861no—
159C2×Q16—861no—
160C2×Q16D17211yescharacteristic
161C2×SD16—862no—
162C2×D8—432no—
163C2×D8—861no—
164C4⋊Q8—861no—
165#127—861no—
166#124—862no—
167#124—1721no—
168#123—1722no—
169C4×Q8—21no—
170C4×Q8—431no—
171C4×D4—862no—
172C4×D4—1721no—
173Q32—1722no—
174SD32—1724no—
175C2×C16—21no—
176C2×C16—861no—
177#107D17211yescharacteristic
178#106—1721no—
179C4⋊C8—21no—
180C4⋊C8—431no—
181C4⋊C8—861no—
182#103—21no—
183#103—1721no—
184#102—862no—
185C4×C8—861no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—21no—
188C2×Q8—431no—
189C2×Q8—1721no—
190C2×D4—862no—
191C2×D4—1721no—
192C2×D4—1721no—
193C22×C4—1722no—
194Q16—21no—
195Q16—21no—
196Q16—1722no—
197Q16—1721no—
198Q16—1721no—
199SD16—3442no—
200D8—1722no—
201D8—1721no—
202D8—1721no—
203C2×C8—41no—
204C2×C8—861no—
205C2×C8C2×D17211yescharacteristic
206C2×C8D4×D4311yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—1721no—
212C4⋊C4—1721no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—41no—
217C42—861no—
218C42D4×D4311yescharacteristic
219C16—22no—
220C16—1721no—
221C23—1722no—
222Q8—41no—
223Q8—41no—
224Q8—861no—
225Q8—861no—
226Q8—3441no—
227Q8—3441no—
228D4—3441no—
229D4—3441no—
230D4—1722no—
231D4—1722no—
232D4—6881no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—861no—
236C2×C4—861no—
237C2×C4—3441no—
238C2×C4—6882no—
239C2×C4#1306329511yescharacteristic
240C2×C4D8×D4311yescharacteristic
241C2×C4#1306335211yescharacteristic
242C8—21no—
243C8—81no—
244C8—1721no—
245C8#1306334711yescharacteristic
246C8#1306335311yescharacteristic
247C22—3442no—
248C22—3442no—
249C22—3442no—
250C22#1458303411yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—1721no—
255C4—1721no—
256C4—6881no—
257C4#1458304611yescharacteristic
258C4#1458306811yescharacteristic
259C4#1458333011yescharacteristic
260C4#1458334111yescharacteristic
261C2—6882no—
262C2#1913366311yescharacteristic
263C2#1913653811yescharacteristic
264C2#1913656711yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1332C2
socleC22×C43#447
prime radical#14583276C22
hypercenter#1332D43
hypocenterC43#12333
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
3. #19136645C2semidirect
4. #19133966C2semidirect
6. #19132575C2semidirect
7. C43×#1332C2semidirect
135. #1332D43semidirect
157. C43#12333semidirect

Maximal subgroups

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

subgroupindex
#191476052
#191368512
#191366452
#191339662
#191326402
#191325752
C43×#13322
#1233343