Finite Group Databasebeta

← #13080967

Subgroups — #13080967

Order 1408.

388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C11×#554C211yesmaximal, characteristic, complemented
2#10623086C211yesmaximal, characteristic
3#10622697C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5#10622661C212yesmaximal, complemented
6#10622656C212yesmaximal, complemented
7C4×#4325C211yesmaximal, characteristic, complemented
8#10622633C211yesmaximal, characteristic, complemented
9D4×C11⋊C8C211yesmaximal, characteristic, complemented
10#10622581C212yesmaximal, complemented
11C2×#66872C212yesmaximal, complemented
12C2×#4341—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#125—21no—
15C11×C22⋊Q8—22no—
16C11×C22⋊Q8C2212yes—
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11—21no—
19C4×D4×C11C2211yescharacteristic
20C2×C11×C4⋊C4C2212yes—
21C2×#4325C2211yescharacteristic
22#66983C2212yes—
23C2×C4⋊Dic11C2212yes—
24C22×C11⋊C8C2212yes—
25#66950—21no—
26#66939—22no—
27C4×D44C2211yescharacteristic
28#66922C2211yescharacteristic
29#66899C2212yes—
30#66899C2211yescharacteristic
31C22⋊(C11⋊C8)C2212yes—
32#66873C2211yescharacteristic
33#66873C2212yes—
34#66872C2211yescharacteristic
35#66872C2212yes—
36#66872C2212yes—
37#66872C2212yes—
38#66872C2212yes—
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2311yescharacteristic
43C2×D4×C11D411yescharacteristic
44C22×C4×C11—22no—
45C22×C4×C11C2312yes—
46C2×C22⋊D11—22no—
47C22×Dic11—22no—
48#4341—44no—
49C2×D44C2311yescharacteristic
50C2×C4×D11—21no—
51C2×Dic22—21no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4D411yescharacteristic
57C11×C4⋊C4C2311yescharacteristic
58C11×C4⋊C4C2312yes—
59C11×C22⋊C4—22no—
60C11×C22⋊C4D412yes—
61C42×C11—21no—
62C42×C11C2311yescharacteristic
63#4325—22no—
64(C2×D11)⋊C4—21no—
65(C2×D11)⋊C4—22no—
66C4⋊Dic11—21no—
67C4⋊Dic11—22no—
68C4⋊Dic11C2312yes—
69C4⋊Dic11C2311yescharacteristic
70C2×C11⋊C8—24no—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2312yes—
73C2×C11⋊C8C2311yescharacteristic
74#3335—111nomaximal, Sylow
75C23×C11C2×D412yes—
76C22×D11—21no—
77Q8×C11—21no—
78Q8×C11—21no—
79Q8×C11—81no—
80D4×C11SD1614yescomplemented
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—82no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D412yes—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2411yescharacteristic
91C22⋊D11—44no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—44no—
95D44—21no—
96D44—21no—
97C4×D11—42no—
98Dic22—42no—
99C11⋊C8—22no—
100C11⋊C8—21no—
101C11⋊C8#4112yescomplemented
102#554D1111yescharacteristic, complemented
103#547—111no—
104#498—111no—
105#483—112no—
106#481—112no—
107#476—111no—
108#475—111no—
109#465—112no—
110C4×SD16—111no—
111C8×D4—111no—
112C2×#106—112no—
113C22×C11—22no—
114C22×C11—22no—
115C22×C11C2×SD1614yes—
116C22×C11C22×D411yescharacteristic
117C2×D11—41no—
118C2×D11—41no—
119C2×D11—41no—
120C4×C11—22no—
121C4×C11—21no—
122C4×C11—41no—
123C4×C11—41no—
124C4×C11—42no—
125C4×C11C2×SD1612yes—
126C4×C11C2×#4111yescharacteristic
127C4×C112−1+411yescharacteristic
128Dic11—42no—
129Dic11—41no—
130C2×#41—221no—
131C2×SD16—111no—
132C22×C8—112no—
133C4⋊Q8—111no—
134C4⋊Q8C2×D1111yescharacteristic
135#125—21no—
136#123—222no—
137C22⋊Q8—22no—
138C22⋊Q8—221no—
139C22⋊Q8C2×D1112yes—
140#121—112no—
141C4×Q8C2×D1111yescharacteristic
142C4×D4—21no—
143C4×D4—111no—
144C4×D4C2×D1111yescharacteristic
145C2×C4⋊C4—112no—
146C2×C4⋊C4C2×D1112yes—
147#106—111no—
148#106—112no—
149#106—112no—
150#106—112no—
151#106—112no—
152C4⋊C8—111no—
153#103—111no—
154#103—112no—
155#102—111no—
156#102—112no—
157C22⋊C8—112no—
158C4×C8—111no—
159C2×C11—24no—
160C2×C11#54711yescharacteristic
161C2×C11C22×SD1611yescharacteristic
162C2×C11#57711yescharacteristic
163D11—81no—
164#41—444no—
165C2×Q8—21no—
166C2×Q8—221no—
167C2×Q8C22×D1111yescharacteristic
168C2×D4—111no—
169C2×D4—222no—
170C2×D4C22⋊D1111yescharacteristic
171C22×C4—22no—
172C22×C4—222no—
173C22×C4—221no—
174C22×C4C22×D1112yes—
175SD16—222no—
176C2×C8—111no—
177C2×C8—111no—
178C2×C8—112no—
179C2×C8—224no—
180C4⋊C4—22no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—22no—
184C4⋊C4—111no—
185C4⋊C4—112no—
186C4⋊C4—222no—
187C4⋊C4—221no—
188C4⋊C4C22⋊D1111yescharacteristic
189C4⋊C4C22×D1111yescharacteristic
190C4⋊C4C22×D1112yes—
191C22⋊C4—22no—
192C22⋊C4—221no—
193C22⋊C4—222no—
194C22⋊C4C22⋊D1112yes—
195C42—21no—
196C42C22×D1111yescharacteristic
197C11#333511yescharacteristic, complemented, Sylow
198C23—221no—
199C23C2×C22⋊D1112yes—
200Q8—21no—
201Q8—21no—
202Q8—81no—
203Q8—442no—
204D4—221no—
205D4—221no—
206D4—444no—
207D4#432514yescomplemented
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—82no—
214C2×C4—221no—
215C2×C4—222no—
216C2×C4—444no—
217C2×C4—442no—
218C2×C4C2×C22⋊D1111yescharacteristic
219C2×C4C2×C22⋊D1112yes—
220C2×C4C2×C22⋊D1111yescharacteristic
221C2×C4C23×D1111yescharacteristic
222C8—112no—
223C8—222no—
224C8—221no—
225C22—22no—
226C22—22no—
227C22—441no—
228C22—441no—
229C22—441no—
230C22C2×#432514yes—
231C22C22×C22⋊D1111yescharacteristic
232C4—22no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—42no—
237C4—441no—
238C4—442no—
239C4C2×#432512yes—
240C4#41×D1111yescharacteristic
241C4#6704311yescharacteristic
242C2—24no—
243C2—881no—
244C2C22×#432511yescharacteristic
245C2#1062335511yescharacteristic
246C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#554C2
socleC22×C11C22×D4
prime radical#10623086C2
hypercenter#554D11
hypocenterC11#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C11×#554C2semidirect
3. #10622697C2semidirect
4. #10622692C2semidirect
5. #10622661C2semidirect
6. #10622656C2semidirect
7. C4×#4325C2semidirect
8. #10622633C2semidirect
9. D4×C11⋊C8C2semidirect
10. #10622581C2semidirect
11. C2×#66872C2semidirect
80. D4×C11SD16semidirect
101. C11⋊C8#41semidirect
102. #554D11semidirect
197. C11#3335semidirect
207. D4#4325semidirect

Maximal subgroups

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

subgroupindex
C11×#5542
#106230862
#106226972
#106226922
#106226612
#106226562
C4×#43252
#106226332
D4×C11⋊C82
#106225812
C2×#668722
#333511