Finite Group Databasebeta

← #25010277

Subgroups — #25010277

Order 11008.

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

normal subgroups only

This group has 298 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#19147488C211yesmaximal, characteristic, complemented
2#19136632C211yesmaximal, characteristic
3#19133952C211yesmaximal, characteristic
4#19132650C211yesmaximal, characteristic, complemented
5#19132575C211yesmaximal, characteristic, complemented
6#19132560C211yesmaximal, characteristic, complemented
7C43×#2240C211yesmaximal, characteristic
8#14583624—21no—
9C2×#13063269—21no—
10#14583300—21no—
11#14583205—22no—
12#14583181—21no—
13#14583096—21no—
14C8×Dic86C2211yescharacteristic
15C4×Dic172C2211yescharacteristic
16#14582993—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582700—21no—
19#14582652C2211yescharacteristic
20#14582643—21no—
21C43×#500C2211yescharacteristic
22C43×#493C2211yescharacteristic
23C43×#357—22no—
24C4×C16×C43C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×#10621883—41no—
27#13063323—41no—
28#13063316—22no—
29#13063315—42no—
30Q8×Dic43—41no—
31C4×Dic86—21no—
32C4×Dic86D411yescharacteristic
33#13063290—22no—
34#13063269—42no—
35C2×C43⋊C16—21no—
36#13063259D411yescharacteristic
37#13063256—22no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063250—21no—
42#13063248—22no—
43#13063246—41no—
44C8×Dic43—21no—
45C2×D8×C43—21no—
46C2×D8×C43—21no—
47C4⋊Q8×C43—21no—
48#127×C43—21no—
49C2×C16×C43—21no—
50#107×C43—21no—
51#107×C43D412yes—
52C4×C8×C43C2311yescharacteristic
53C2×Q8×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×Dic86—21no—
58C2×Dic86D811yescharacteristic
59D8×C43—42no—
60D8×C43—41no—
61D8×C43—41no—
62C2×C8×C43C2×D411yescharacteristic
63C2×C8×C43C2×D411yescharacteristic
64C4⋊C4×C43—22no—
65C4⋊C4×C43—41no—
66C42×C43C2×D411yescharacteristic
67#10621883—82no—
68C4⋊Dic43—21no—
69C4⋊Dic43—42no—
70C4⋊Dic43D811yescharacteristic
71Dic43⋊C4—21no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74Dic43⋊C4—41no—
75C4×Dic43—21no—
76C4×Dic43—42no—
77C4×Dic43—41no—
78C2×C43⋊C8—21no—
79C2×C43⋊C8—41no—
80Dic172—21no—
81Dic172SD1612yescomplemented
82C16×C43—41no—
83C43⋊C16—41no—
84C23×C43—81no—
85Q8×C43—81no—
86Q8×C43—81no—
87D4×C43—81no—
88D4×C43—81no—
89D4×C43—81no—
90D4×C43—81no—
91D4×C43—161no—
92C2×C4×C43—42no—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43C2×D811yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C2×Dic43—21no—
97C2×Dic43—21no—
98C2×Dic43—41no—
99C2×Dic43—41no—
100Dic86—22no—
101Dic86—21no—
102Dic86—21no—
103Dic86—41no—
104C8×C43—21no—
105C8×C43C2×SD1611yescharacteristic
106C8×C43#13711yescharacteristic
107C43⋊C8—41no—
108C43⋊C8—81no—
109#12353—431nomaximal, Sylow
110C22×C43—161no—
111C22×C43—161no—
112C22×C43—161no—
113C22×C43#44711yescharacteristic
114C4×C43—21no—
115C4×C43—82no—
116C4×C43#44811yescharacteristic
117C4×C43#45411yescharacteristic
118C4×C43#50811yescharacteristic
119C4×C43#50911yescharacteristic
120Dic43—42no—
121Dic43—41no—
122Dic43—41no—
123Dic43—81no—
124#3383—431no—
125#2240D4311yescharacteristic
126#2207—431no—
127#1668—431no—
128#1364—431no—
129Q8⋊C16—431no—
130#1332—431no—
131C2×C43—321no—
132C2×C43#162711yescharacteristic
133C2×C43#218611yescharacteristic
134C2×C43#219311yescharacteristic
135#557—861no—
136C2×SD32—861no—
137#500C2×D4311yescharacteristic
138#499—861no—
139#493C2×D4311yescharacteristic
140#479—862no—
141#475—861no—
142#460—861no—
143C8×Q8—431no—
144C4×Q16—431no—
145C4×Q16—861no—
146C4⋊C16—431no—
147#357—22no—
148#357—861no—
149C4×C16C2×D4311yescharacteristic
150#335—431no—
151#331—861no—
152C43#1235311yescharacteristic, complemented, Sylow
153C2×Q16—431no—
154C2×SD16—1721no—
155C2×D8—21no—
156C2×D8—21no—
157C4⋊Q8—21no—
158C4⋊Q8—1721no—
159#127—21no—
160#125—862no—
161#125—1722no—
162C4×Q8—431no—
163C4×Q8—862no—
164C4×Q8—861no—
165C4×Q8—1721no—
166SD32—1722no—
167C2×C16—21no—
168C2×C16—861no—
169#107—21no—
170#107—431no—
171#107C22⋊D4312yes—
172#106—862no—
173C4⋊C8—431no—
174C4⋊C8—861no—
175C4⋊C8—861no—
176#103—862no—
177#103—861no—
178#102—1721no—
179C4×C8—861no—
180C4×C8C22×D4311yescharacteristic
181C2×Q8—41no—
182C2×Q8—431no—
183C2×Q8—861no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—41no—
187Q16—432no—
188Q16—861no—
189SD16—3442no—
190D8—42no—
191D8—41no—
192D8—41no—
193C2×C8—861no—
194C2×C8—1721no—
195C2×C8D4×D4311yescharacteristic
196C2×C8C2×C22⋊D4311yescharacteristic
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—431no—
200C4⋊C4—861no—
201C4⋊C4—861no—
202C4⋊C4—1722no—
203C4⋊C4—1722no—
204C4⋊C4—1722no—
205C4⋊C4—1721no—
206C42—861no—
207C42—1722no—
208C42—1721no—
209C42D4×D4311yescharacteristic
210C16—41no—
211C16—1721no—
212C23—81no—
213Q8—81no—
214Q8—81no—
215Q8—861no—
216Q8—861no—
217Q8—862no—
218Q8—1721no—
219D4—81no—
220D4—81no—
221D4—81no—
222D4—81no—
223D4—161no—
224C2×C4—42no—
225C2×C4—861no—
226C2×C4—861no—
227C2×C4—1721no—
228C2×C4—1721no—
229C2×C4#1306329311yescharacteristic
230C2×C4D8×D4311yescharacteristic
231C2×C4#1306334911yescharacteristic
232C8—21no—
233C8—3441no—
234C8—1721no—
235C8SD16×D4311yescharacteristic
236C8#1306335411yescharacteristic
237C22—161no—
238C22—161no—
239C22—161no—
240C22#1458303111yescharacteristic
241C4—21no—
242C4—82no—
243C4—3441no—
244C4—1721no—
245C4—1721no—
246C4—1722no—
247C4#1458303611yescharacteristic
248C4#1458307111yescharacteristic
249C4#1458332811yescharacteristic
250C4#1458333311yescharacteristic
251C2—321no—
252C2#1913369511yescharacteristic
253C2#1913651511yescharacteristic
254C2#1913655811yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2240C2
socleC22×C43#447
prime radicalC43×#493C22
hypercenter#2240D43
hypocenterC43#12353
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #19147488C2semidirect
4. #19132650C2semidirect
5. #19132575C2semidirect
6. #19132560C2semidirect
81. Dic172SD16semidirect
152. C43#12353semidirect

Maximal subgroups

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

subgroupindex
#191474882
#191366322
#191339522
#191326502
#191325752
#191325602
C43×#22402
#1235343