Finite Group Databasebeta

← #13080937

Subgroups — #13080937

Order 1408.

430 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 123 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×#547C211yesmaximal, characteristic, complemented
2#10623084C211yesmaximal, characteristic, complemented
3#10622707C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5#10622652C212yesmaximal, complemented
6#10622650C212yesmaximal, complemented
7C4×#4324C211yesmaximal, characteristic, complemented
8#10622628C211yesmaximal, characteristic, complemented
9#10622625C211yesmaximal, characteristic, complemented
10#10622581C212yesmaximal, complemented
11#10622579C212yesmaximal, complemented
12C2×C11×#41—21no—
13C2×#4339C2212yes—
14C11×C4⋊Q8C2211yescharacteristic
15C11×#123—22no—
16C11×C22⋊Q8—21no—
17C11×#121C2212yes—
18C4×D4×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20C2×C11×C4⋊C4C2212yes—
21#66993—21no—
22C2×#4324C2211yescharacteristic
23C2×#4323C2212yes—
24#66983C2212yes—
25C2×#4318C2212yes—
26#66946—21no—
27#66937—22no—
28#66927C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30#66896C2211yescharacteristic
31C22⋊(C11⋊C8)C2212yes—
32#66874C2211yescharacteristic
33#66874C2212yes—
34#66873C2212yes—
35#66873C2212yes—
36#66873C2212yes—
37#66872C2211yescharacteristic
38#66872C2212yes—
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C11×#41—44no—
42C2×Q8×C11—21no—
43C2×D4×C11—22no—
44C2×D4×C11D411yescharacteristic
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—22no—
47C22×C4×C11—21no—
48C22×C4×C11C2312yes—
49C2×C22⋊D11—22no—
50C2×C22⋊D11—22no—
51#4339—24no—
52#4339—42no—
53C2×D44—21no—
54C2×D44—21no—
55C2×D44C2312yes—
56C2×C4×D11—22no—
57C2×Dic22C2311yescharacteristic
58C11×C4⋊C4—22no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4D411yescharacteristic
61C11×C4⋊C4C2311yescharacteristic
62C11×C4⋊C4C2312yes—
63C11×C22⋊C4—21no—
64C11×C22⋊C4—22no—
65C11×C22⋊C4D412yes—
66C42×C11C2311yescharacteristic
67#4324—22no—
68#4323—42no—
69(C2×D11)⋊C4—22no—
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—21no—
72C4×Dic11—21no—
73#4318—42no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2312yes—
77#3332—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11C2×D412yes—
80C22×D11—22no—
81Q8×C11—42no—
82D4×C11—22no—
83D4×C11—21no—
84D4×C11—21no—
85D4×C11—44no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—44no—
91C2×C4×C11—42no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2411yescharacteristic
96C22⋊D11—44no—
97C22⋊D11—82no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100D44—22no—
101D44—22no—
102D44—42no—
103D44—81no—
104C4×D11—44no—
105Dic22—21no—
106Dic22#4112yescomplemented
107C11⋊C8—21no—
108C11⋊C8—21no—
109C11⋊C8—22no—
110#550—111no—
111#547D1111yescharacteristic, complemented
112#486—111no—
113#481—112no—
114#475—111no—
115#469—112no—
116#459—111no—
117#449—112no—
118C4×SD16—111no—
119#436—111no—
120#417—112no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11C22×D411yescharacteristic
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—42no—
131C4×C11—22no—
132C4×C11—21no—
133C4×C11—41no—
134C4×C11—42no—
135C4×C11AGL(1,ℤ/8)12yes—
136C4×C11C2×#4111yescharacteristic
137C4×C11H(5,𝔽2)11yescharacteristic
138Dic11—22no—
139Dic11—41no—
140C2×#41—21no—
141C2×#41—112no—
142C2×SD16—111no—
143C2×D8—112no—
144C2×M16—112no—
145C4⋊Q8C2×D1111yescharacteristic
146#127—111no—
147#127—221no—
148#123—22no—
149C22⋊Q8—21no—
150#121—112no—
151#121—222no—
152#121C2×D1112yes—
153C4×Q8—111no—
154C4×D4—221no—
155C4×D4C2×D1111yescharacteristic
156C4×D4C2×D1111yescharacteristic
157C2×C4⋊C4C2×D1112yes—
158#106—111no—
159#106—112no—
160C4⋊C8—111no—
161#103—111no—
162#103—112no—
163#102—111no—
164#102—112no—
165#102—112no—
166#102—112no—
167C22⋊C8—112no—
168C4×C8—111no—
169C2×C11—42no—
170C2×C11—81no—
171C2×C11#54611yescharacteristic
172C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C11#57711yescharacteristic
174D11—82no—
175#41—44no—
176#41—224no—
177#41—442no—
178C2×Q8—21no—
179C2×Q8—111no—
180C2×D4—22no—
181C2×D4—112no—
182C2×D4—222no—
183C2×D4—222no—
184C2×D4—221no—
185C2×D4—221no—
186C2×D4C22⋊D1111yescharacteristic
187C2×D4C22×D1111yescharacteristic
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—222no—
191C22×C4C22×D1112yes—
192SD16—222no—
193D8—442no—
194M16—442no—
195C2×C8—111no—
196C2×C8—111no—
197C2×C8—112no—
198C4⋊C4—22no—
199C4⋊C4—21no—
200C4⋊C4—111no—
201C4⋊C4—221no—
202C4⋊C4C22⋊D1111yescharacteristic
203C4⋊C4C22×D1111yescharacteristic
204C4⋊C4C22×D1112yes—
205C22⋊C4—21no—
206C22⋊C4—22no—
207C22⋊C4—222no—
208C22⋊C4C22⋊D1112yes—
209C42—221no—
210C42C22×D1111yescharacteristic
211C11#333211yescharacteristic, complemented, Sylow
212C23—21no—
213C23—222no—
214C23C2×C22⋊D1112yes—
215Q8—42no—
216Q8—112no—
217Q8—221no—
218D4—22no—
219D4—21no—
220D4—21no—
221D4—44no—
222D4—222no—
223D4—222no—
224D4—444no—
225D4—442no—
226D4—881no—
227D4—882no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4—444no—
237C2×C4C2×C22⋊D1111yescharacteristic
238C2×C4C2×C22⋊D1112yes—
239C2×C4C2×C22⋊D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—221no—
242C8—221no—
243C8—222no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—442no—
251C22—442no—
252C22—442no—
253C22C22×C22⋊D1111yescharacteristic
254C4—22no—
255C4—21no—
256C4—41no—
257C4—42no—
258C4—222no—
259C4—441no—
260C4#6698512yes—
261C4#41×D1111yescharacteristic
262C4#6704211yescharacteristic
263C2—42no—
264C2—81no—
265C2—882no—
266C2C2×#6698511yescharacteristic
267C2#1062336011yescharacteristic
268C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#547C2
socleC22×C11C22×D4
hypercenter#547D11
hypocenterC11#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C11×#547C2semidirect
2. #10623084C2semidirect
3. #10622707C2semidirect
4. #10622701C2semidirect
5. #10622652C2semidirect
6. #10622650C2semidirect
7. C4×#4324C2semidirect
8. #10622628C2semidirect
9. #10622625C2semidirect
10. #10622581C2semidirect
11. #10622579C2semidirect
106. Dic22#41semidirect
111. #547D11semidirect
211. C11#3332semidirect

Maximal subgroups

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

subgroupindex
C11×#5472
#106230842
#106227072
#106227012
#106226522
#106226502
C4×#43242
#106226282
#106226252
#106225812
#106225792
#333211