Finite Group Databasebeta

← #25010137

Subgroups — #25010137

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#19147609C211yesmaximal, characteristic
2#19136642C211yesmaximal, characteristic, complemented
3#19133962C211yesmaximal, characteristic, complemented
4#19132641C211yesmaximal, characteristic
5#19132575C211yesmaximal, characteristic, complemented
6#19132560C211yesmaximal, characteristic, complemented
7C43×#2248C211yesmaximal, characteristic
8#14583635—21no—
9C2×#13063271—21no—
10#14583282—21no—
11#14583181—21no—
12#14583112—22no—
13#14583096—21no—
14C8×Dic86C2211yescharacteristic
15C4×Dic172C2211yescharacteristic
16D8×Dic43—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582703—21no—
19#14582652C2211yescharacteristic
20#14582645—21no—
21C2×SD32×C43—22no—
22C43×#494C2211yescharacteristic
23C43×#493C2211yescharacteristic
24C4×C16×C43C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×#10621883—22no—
27#13063312—22no—
28#13063312—41no—
29#13063306—42no—
30C4×Dic86—21no—
31C4×Dic86D411yescharacteristic
32D4×Dic43—22no—
33D4×Dic43—41no—
34#13063271—42no—
35C2×C43⋊C16—21no—
36#13063259D411yescharacteristic
37#13063256—41no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063250—21no—
42#13063248—41no—
43#13063246—22no—
44C8×Dic43—21no—
45C2×Q16×C43—21no—
46C2×Q16×C43—21no—
47C2×D8×C43—21no—
48C2×D8×C43D412yes—
49C4⋊Q8×C43—21no—
50#127×C43—21no—
51SD32×C43—44no—
52C2×C16×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—41no—
55C2×D4×C43—22no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C22×Dic43—42no—
59C2×Dic86—21no—
60C2×Dic86D811yescharacteristic
61Q16×C43—42no—
62Q16×C43—41no—
63Q16×C43—41no—
64D8×C43—42no—
65D8×C43—41no—
66D8×C43—41no—
67C2×C8×C43C2×D411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C42×C43C2×D411yescharacteristic
72C22⋊Dic43—42no—
73C22⋊Dic43—42no—
74C22⋊Dic43—42no—
75#10621883—82no—
76C4⋊Dic43—21no—
77C4⋊Dic43D811yescharacteristic
78Dic43⋊C4—21no—
79Dic43⋊C4—41no—
80C4×Dic43—21no—
81C4×Dic43—41no—
82C2×C43⋊C8—21no—
83C2×C43⋊C8—41no—
84Dic172—21no—
85Dic172—21no—
86C16×C43—22no—
87C43⋊C16—41no—
88C23×C43—42no—
89Q8×C43—81no—
90Q8×C43—81no—
91D4×C43—42no—
92D4×C43—42no—
93D4×C43—81no—
94D4×C43—81no—
95D4×C43—161no—
96C2×C4×C43—81no—
97C2×C4×C43#12011yescharacteristic
98C2×C4×C43C2×D811yescharacteristic
99C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—162no—
105Dic86—21no—
106Dic86—21no—
107Dic86—41no—
108Dic86—41no—
109C8×C43—21no—
110C8×C43#13511yescharacteristic
111C8×C43AGL(1,ℤ/8)11yescharacteristic
112C43⋊C8—41no—
113C43⋊C8—81no—
114#12333—431nomaximal, Sylow
115C22×C43—82no—
116C22×C43—82no—
117C22×C43—82no—
118C22×C43#44711yescharacteristic
119C4×C43—21no—
120C4×C43—161no—
121C4×C43#44911yescharacteristic
122C4×C43#45311yescharacteristic
123C4×C43#50811yescharacteristic
124C4×C43#51011yescharacteristic
125Dic43—41no—
126Dic43—41no—
127Dic43—81no—
128Dic43—81no—
129#3396—431no—
130#2248D4311yescharacteristic
131#2209—431no—
132#1670—431no—
133#1361—431no—
134Q8⋊C16—431no—
135#1332—431no—
136C2×C43—162no—
137C2×C43#162111yescharacteristic
138C2×C43#218911yescharacteristic
139C2×C43#219411yescharacteristic
140#559—861no—
141C2×Q32—861no—
142C2×SD32—22no—
143#495—861no—
144#494C2×D4311yescharacteristic
145#493C2×D4311yescharacteristic
146#475—861no—
147#463—862no—
148#460—861no—
149C8×Q8—431no—
150C4×Q16—431no—
151C4×D8—861no—
152C4⋊C16—431no—
153#358—861no—
154C4×C16C2×D4311yescharacteristic
155#335—431no—
156#332—861no—
157C43#1233311yescharacteristic, complemented, Sylow
158C2×Q16—21no—
159C2×Q16—21no—
160C2×Q16—431no—
161C2×SD16—862no—
162C2×D8—21no—
163C2×D8C22⋊D4312yes—
164C4⋊Q8—21no—
165#127—21no—
166#124—862no—
167#124—1721no—
168#123—1722no—
169C4×Q8—431no—
170C4×Q8—861no—
171C4×D4—862no—
172C4×D4—1721no—
173Q32—1722no—
174SD32—44no—
175C2×C16—21no—
176C2×C16—861no—
177#107—431no—
178#106—1721no—
179C4⋊C8—431no—
180C4⋊C8—861no—
181C4⋊C8—861no—
182#103—861no—
183#103—1721no—
184#102—862no—
185C4×C8—861no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—41no—
188C2×Q8—431no—
189C2×Q8—861no—
190C2×D4—22no—
191C2×D4—41no—
192C2×D4—41no—
193C22×C4—1722no—
194Q16—42no—
195Q16—41no—
196Q16—41no—
197Q16—861no—
198Q16—861no—
199SD16—3442no—
200D8—42no—
201D8—41no—
202D8—41no—
203C2×C8—861no—
204C2×C8—1721no—
205C2×C8D4×D4311yescharacteristic
206C2×C8C2×C22⋊D4311yescharacteristic
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—861no—
212C4⋊C4—1721no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—861no—
217C42—1721no—
218C42D4×D4311yescharacteristic
219C16—22no—
220C16—1721no—
221C23—42no—
222Q8—81no—
223Q8—81no—
224Q8—861no—
225Q8—861no—
226Q8—1721no—
227Q8—1721no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—161no—
233C2×C4—81no—
234C2×C4—861no—
235C2×C4—861no—
236C2×C4—1721no—
237C2×C4—1721no—
238C2×C4—6882no—
239C2×C4#1306329311yescharacteristic
240C2×C4D8×D4311yescharacteristic
241C2×C4#1306334911yescharacteristic
242C8—21no—
243C8—3441no—
244C8—1721no—
245C8#1306334411yescharacteristic
246C8#1306334911yescharacteristic
247C22—82no—
248C22—82no—
249C22—82no—
250C22#1458303111yescharacteristic
251C4—21no—
252C4—161no—
253C4—3441no—
254C4—3441no—
255C4—1721no—
256C4—1721no—
257C4#1458304111yescharacteristic
258C4#1458306611yescharacteristic
259C4#1458333011yescharacteristic
260C4#1458333811yescharacteristic
261C2—162no—
262C2#1913365711yescharacteristic
263C2#1913653211yescharacteristic
264C2#1913656511yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2248C2
socleC22×C43#447
prime radicalC43×#493C22
hypercenter#2248D43
hypocenterC43#12333
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
2. #19136642C2semidirect
3. #19133962C2semidirect
5. #19132575C2semidirect
6. #19132560C2semidirect
157. C43#12333semidirect

Maximal subgroups

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

subgroupindex
#191476092
#191366422
#191339622
#191326412
#191325752
#191325602
C43×#22482
#1233343