Finite Group Databasebeta

← #24984106

Subgroups — #24984106

Order 11008.

282 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 41 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#19135677C211yesmaximal, characteristic
2#19132527C211yesmaximal, characteristic
3C43×#1393C211yesmaximal, characteristic
4C22×#10621883—21no—
5C2×#13063325C411yescharacteristic, complemented
6C2×#13063248—21no—
7#14582654C411yescharacteristic, complemented
8#14582625—21no—
9C2×#99×C43—21no—
10C43×#390C2211yescharacteristic
11C22×Dic86—21no—
12C2×#10621883—42no—
13C2×#10621883—42no—
14C2×#10621883—41no—
15C2×#10621883—41no—
16C22×C43⋊C8—21no—
17#13063325—42no—
18C2×C4⋊Dic43—41no—
19#13063248—42no—
20C22⋊(C43⋊C8)—41no—
21C22×D4×C43D411yescharacteristic
22C2×C4⋊C4×C43D411yescharacteristic
23C2×C22⋊C4×C43—41no—
24C2×C22⋊C4×C43—41no—
25C2×C42×C43C2×C411yescharacteristic
26#99×C43—22no—
27#99×C43—41no—
28C24×C43—21no—
29C2×D4×C43—21no—
30C2×D4×C43—41no—
31C2×D4×C43—41no—
32C2×D4×C43D811yescharacteristic
33C2×D4×C43SD1611yescharacteristic
34C22×C4×C43—21no—
35C22×C4×C43—21no—
36C22×C4×C43—81no—
37C22×C4×C43C22⋊C411yescharacteristic
38C22×Dic43—41no—
39C2×Dic86—22no—
40C2×Dic86—41no—
41C2×Dic86—41no—
42C2×Dic86—41no—
43C2×Dic86—41no—
44C2×Dic86—41no—
45C4⋊C4×C43—41no—
46C22⋊C4×C43—42no—
47C22⋊C4×C43—81no—
48C22⋊C4×C43—82no—
49C42×C43—41no—
50#10621883—44no—
51#10621883—44no—
52C4⋊Dic43—42no—
53C4⋊Dic43—42no—
54C2×C43⋊C8—22no—
55C2×C43⋊C8—41no—
56C2×C43⋊C8—41no—
57C2×C43⋊C8—81no—
58C23×C43—21no—
59C23×C43—21no—
60C23×C43—41no—
61C23×C43—41no—
62C23×C43—81no—
63C23×C43—81no—
64C23×C43#9911yescharacteristic
65D4×C43—41no—
66D4×C43—41no—
67D4×C43—81no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—22no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43—81no—
75C2×C4×C43—82no—
76C2×C4×C43—161no—
77C2×C4×C43—161no—
78C2×C4×C43#10211yescharacteristic
79C2×C4×C43#10411yescharacteristic
80C2×Dic43—42no—
81C2×Dic43—81no—
82C2×Dic43—81no—
83Dic86—42no—
84Dic86—42no—
85Dic86—81no—
86Dic86—81no—
87C43⋊C8—42no—
88C43⋊C8—161no—
89#7403—431nomaximal, Sylow
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—41no—
93C22×C43—41no—
94C22×C43—81no—
95C22×C43—81no—
96C22×C43—81no—
97C22×C43—81no—
98C22×C43—161no—
99C22×C43#32711yescharacteristic
100C22×C43AΣL(1,𝔽16)11yescharacteristic
101C22×C43#35311yescharacteristic
102C4×C43—21no—
103C4×C43—21no—
104C4×C43—42no—
105C4×C43—81no—
106C4×C43—162no—
107Dic43—82no—
108#2013—431no—
109#1393D4311yescharacteristic
110#1318—431no—
111C2×C43—21no—
112C2×C43—21no—
113C2×C43—81no—
114C2×C43—81no—
115C2×C43#134311yescharacteristic
116C2×C43#140711yescharacteristic
117C2×C43#140911yescharacteristic
118C22×SD16—861no—
119C2×C4⋊Q8—431no—
120C2×#103—861no—
121C2×#99—21no—
122#390C2×D4311yescharacteristic
123#336—431no—
124#324—861no—
125C43#740311yescharacteristic, complemented, Sylow
126C22×Q8—861no—
127C22×D4C22⋊D4311yescharacteristic
128C2×SD16—1722no—
129C2×SD16—1722no—
130C2×SD16—1721no—
131C2×SD16—1721no—
132C22×C8—861no—
133C4⋊Q8—1722no—
134C2×C4⋊C4—1721no—
135C2×C4⋊C4D17211yescharacteristic
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C42C4×D4311yescharacteristic
139#103—1722no—
140#99—22no—
141#99—41no—
142C22⋊C8—1721no—
143C24—21no—
144C2×Q8—862no—
145C2×Q8—1721no—
146C2×Q8—1721no—
147C2×Q8—1721no—
148C2×Q8—1721no—
149C2×Q8—1721no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4#1062188211yescharacteristic
154C2×D4#1062188411yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—81no—
158C22×C4—1721no—
159C22×C4(C2×D43)⋊C411yescharacteristic
160SD16—1724no—
161SD16—1724no—
162C2×C8—862no—
163C2×C8—3441no—
164C2×C8—1721no—
165C2×C8—1721no—
166C4⋊C4—41no—
167C4⋊C4—1722no—
168C4⋊C4—1722no—
169C22⋊C4—42no—
170C22⋊C4—82no—
171C22⋊C4—81no—
172C42—41no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23—81no—
178C23—81no—
179C23#1306323911yescharacteristic
180Q8—3441no—
181Q8—3441no—
182Q8—1722no—
183Q8—1722no—
184D4—41no—
185D4—41no—
186D4—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—82no—
195C2×C4—161no—
196C2×C4—161no—
197C2×C4—3441no—
198C2×C4—3441no—
199C2×C4—1722no—
200C2×C4#1306324511yescharacteristic
201C2×C4#1306325311yescharacteristic
202C8—1722no—
203C8—6881no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—161no—
213C22#1458263211yescharacteristic
214C22#1458268511yescharacteristic
215C22#1458269111yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—81no—
220C4—162no—
221C4—3442no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2#1913259111yescharacteristic
227C2#1913275411yescharacteristic
228C2#1913275911yescharacteristic
subgroupG/H
centerC22#14582691
commutatorC2×C42×C43C2×C4
Frattini#390C2×D43
FittingC43×#1393C2
socleC22×C43#353
prime radicalC22×D4×C43D4
cosocleC43×#390C22
hypercenter#1393D43
hypocenterC43#7403
LCSG ▷ C2×C42×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1393

Complements

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

NH ≅ G/Ntype
5. C2×#13063325C4semidirect
7. #14582654C4semidirect
125. C43#7403semidirect

Maximal subgroups

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

subgroupindex
#191356772
#191325272
C43×#13932
#740343