Finite Group Databasebeta

← #25010283

Subgroups — #25010283

Order 11008.

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

normal subgroups only

This group has 298 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#19147484C211yesmaximal, characteristic, complemented
2#19136819C211yesmaximal, characteristic
3#19136635C211yesmaximal, characteristic
4#19133956C211yesmaximal, characteristic
5#19132651C211yesmaximal, characteristic, complemented
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1332C211yesmaximal, characteristic, complemented
8#14583628—21no—
9C2×#13063268—21no—
10#14583304C2211yescharacteristic
11#14583300—21no—
12#14583276C2211yescharacteristic
13#14583208—22no—
14#14583184—21no—
15#14583100—21no—
16C8×Dic86C2211yescharacteristic
17Q16×Dic43—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582701—22no—
20#14582699—21no—
21#14582642—21no—
22C4×Q16×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621873—41no—
26C2×D344—21no—
27C2×D344—21no—
28#13063325—21no—
29#13063325—41no—
30#13063322—21no—
31#13063316—22no—
32#13063316—42no—
33Q8×Dic43—22no—
34C4×Dic86—41no—
35C4×Dic86D411yescharacteristic
36#13063268—42no—
37C2×C43⋊C16—21no—
38#13063259—21no—
39#13063259D412yes—
40#13063256—22no—
41C4⋊(C43⋊C8)D411yescharacteristic
42Dic43⋊C8—21no—
43#13063249—22no—
44#13063247—41no—
45C8×Dic43—21no—
46C2×Q16×C43D411yescharacteristic
47C4×Q8×C43—21no—
48C2×C16×C43—21no—
49#107×C43D411yescharacteristic
50C4⋊C8×C43—21no—
51#103×C43—21no—
52C4×C8×C43C2311yescharacteristic
53C2×Q8×C43—21no—
54C2×D172—41no—
55C2×D172—41no—
56C2×D172—41no—
57C2×Dic86—41no—
58C2×Dic86D811yescharacteristic
59Q16×C43—21no—
60Q16×C43SD1612yescomplemented
61C2×C8×C43—41no—
62C2×C8×C43C2×D411yescharacteristic
63C2×C8×C43C2×D411yescharacteristic
64C4⋊C4×C43—21no—
65C4⋊C4×C43—41no—
66C42×C43—41no—
67C42×C43C2×D411yescharacteristic
68C4⋊Dic43—22no—
69C4⋊Dic43—42no—
70C4⋊Dic43—42no—
71C4⋊Dic43—41no—
72C4⋊Dic43D811yescharacteristic
73Dic43⋊C4—21no—
74Dic43⋊C4—42no—
75C4×Dic43—21no—
76C4×Dic43—42no—
77C2×C43⋊C8—21no—
78D344—42no—
79D344—41no—
80D344—41no—
81#10621873—82no—
82C16×C43—41no—
83C43⋊C16—41no—
84C22×D43—81no—
85Q8×C43—22no—
86Q8×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43#12011yescharacteristic
90C2×C4×C43C2×D811yescharacteristic
91C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
92C2×Dic43—21no—
93C2×Dic43—21no—
94C2×Dic43—42no—
95D172—81no—
96D172—81no—
97D172—81no—
98D172—81no—
99D172—161no—
100Dic86—21no—
101Dic86—21no—
102Dic86—81no—
103Dic86—81no—
104C8×C43—21no—
105C8×C43—81no—
106C8×C43C2×SD1611yescharacteristic
107C8×C43#13711yescharacteristic
108C43⋊C8—41no—
109#12353—431nomaximal, Sylow
110C22×C43#44711yescharacteristic
111C2×D43—161no—
112C2×D43—161no—
113C2×D43—161no—
114C4×C43—21no—
115C4×C43—42no—
116C4×C43—81no—
117C4×C43#44811yescharacteristic
118C4×C43#45411yescharacteristic
119C4×C43#50811yescharacteristic
120C4×C43#50911yescharacteristic
121Dic43—41no—
122Dic43—41no—
123Dic43—82no—
124#3383—431no—
125#2240—431no—
126#2207—431no—
127#1668—431no—
128#1364—431no—
129Q8⋊C16—431no—
130#1332D4311yescharacteristic, complemented
131C2×C43#162711yescharacteristic
132C2×C43#218611yescharacteristic
133C2×C43#219311yescharacteristic
134D43—321no—
135#557—861no—
136C2×SD32—861no—
137#500—431no—
138#499—861no—
139#493—431no—
140#479—862no—
141#475—861no—
142#460—861no—
143C8×Q8—431no—
144C4×Q16—861no—
145C4×Q16C2×D4311yescharacteristic
146C4⋊C16—431no—
147#357—862no—
148#357—861no—
149C4×C16C2×D4311yescharacteristic
150#335C2×D4311yescharacteristic
151#331—861no—
152C43#1235311yescharacteristic, complemented, Sylow
153C2×Q16D17211yescharacteristic
154C2×SD16—1721no—
155C2×D8—861no—
156C2×D8—861no—
157C4⋊Q8—861no—
158C4⋊Q8—1721no—
159#127—861no—
160#125—862no—
161#125—1722no—
162C4×Q8—21no—
163C4×Q8—431no—
164C4×Q8—862no—
165C4×Q8—1721no—
166SD32—1722no—
167C2×C16—21no—
168C2×C16—861no—
169#107—432no—
170#107—861no—
171#107D17211yescharacteristic
172#106—862no—
173C4⋊C8—21no—
174C4⋊C8—431no—
175C4⋊C8—861no—
176#103—21no—
177#103—862no—
178#102—1721no—
179C4×C8—861no—
180C4×C8C22×D4311yescharacteristic
181C2×Q8—21no—
182C2×Q8—431no—
183C2×Q8—1721no—
184C2×D4—1721no—
185C2×D4—1721no—
186C2×D4—1721no—
187Q16—21no—
188Q16#1062187312yescomplemented
189SD16—3442no—
190D8—1722no—
191D8—1721no—
192D8—1721no—
193C2×C8—41no—
194C2×C8—861no—
195C2×C8C2×D17211yescharacteristic
196C2×C8D4×D4311yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—41no—
199C4⋊C4—431no—
200C4⋊C4—861no—
201C4⋊C4—862no—
202C4⋊C4—1722no—
203C4⋊C4—1722no—
204C4⋊C4—1722no—
205C4⋊C4—1721no—
206C42—41no—
207C42—861no—
208C42—1722no—
209C42D4×D4311yescharacteristic
210C16—41no—
211C16—1721no—
212C23—3441no—
213Q8—22no—
214Q8—41no—
215Q8—861no—
216Q8—861no—
217Q8—3441no—
218Q8—3441no—
219D4—3441no—
220D4—3441no—
221D4—3441no—
222D4—3441no—
223D4—6881no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—861no—
227C2×C4—861no—
228C2×C4—1722no—
229C2×C4#1306329511yescharacteristic
230C2×C4D8×D4311yescharacteristic
231C2×C4#1306335211yescharacteristic
232C8—21no—
233C8—81no—
234C8—1721no—
235C8C2×#1062187311yescharacteristic
236C8#1306335811yescharacteristic
237C22—6881no—
238C22—6881no—
239C22—6881no—
240C22#1458303411yescharacteristic
241C4—21no—
242C4—42no—
243C4—81no—
244C4—3442no—
245C4—1721no—
246C4—1721no—
247C4#1458304011yescharacteristic
248C4#1458307311yescharacteristic
249C4#1458333211yescharacteristic
250C4#1458333611yescharacteristic
251C2—13761no—
252C2#1913370111yescharacteristic
253C2#1913652111yescharacteristic
254C2#1913656011yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1332C2
socleC22×C43#447
prime radical#14583276C22
hypercenter#1332D43
hypocenterC43#12353
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
1. #19147484C2semidirect
5. #19132651C2semidirect
6. #19132575C2semidirect
7. C43×#1332C2semidirect
60. Q16×C43SD16semidirect
130. #1332D43semidirect
152. C43#12353semidirect
188. Q16#10621873semidirect

Maximal subgroups

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

subgroupindex
#191474842
#191368192
#191366352
#191339562
#191326512
#191325752
C43×#13322
#1235343