Finite Group Databasebeta

← #13080841

Subgroups — #13080841

Order 1408.

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

normal subgroups only

This group has 448 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×#556C211yesmaximal, characteristic, complemented
2D4×D44C211yesmaximal, characteristic
3#10622701C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622662C212yesmaximal, complemented
6#10622659C212yesmaximal, complemented
7#10622640C211yesmaximal, characteristic, complemented
8C4×#4325C211yesmaximal, characteristic, complemented
9#10622625C211yesmaximal, characteristic, complemented
10#10622616C212yesmaximal, complemented
11#10622614C212yesmaximal, complemented
12C2×D4×D11—21no—
13C22×D44C2212yes—
14C11×C4⋊Q8C2211yescharacteristic, complemented
15C11×#126—22no—
16C11×#124—21no—
17C11×C22⋊Q8C2212yescomplemented
18C4×Q8×C11—21no—
19C4×Q8×C11C2211yescharacteristic, complemented
20C4×D4×C11C2211yescharacteristic
21C11×#117C2212yescomplemented
22C2×#4325C2211yescharacteristic
23C2×#4325C2212yescomplemented
24#66983C2212yes—
25C2×#4318C2212yescomplemented
26#66948—21no—
27#66935—22no—
28#66927C2211yescharacteristic
29C4×D44C2211yescharacteristic
30#66899C2211yescharacteristic, complemented
31C22⋊(C11⋊C8)C2212yescomplemented
32#66873C2211yescharacteristic
33#66873C2212yes—
34#66873C2212yescomplemented
35#66873C2212yescomplemented
36#66873C2212yescomplemented
37#66872C2211yescharacteristic, complemented
38#66871C2212yescomplemented
39C4⋊(C11⋊C8)C2211yescharacteristic, complemented
40C4×C11⋊C8C2211yescharacteristic, complemented
41C23×D11—22no—
42C2×Q8×C11—21no—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11D411yescharacteristic
45C22×C4×C11C2312yes—
46C2×C22⋊D11—22no—
47D4×D11—44no—
48C2×D44—24no—
49C2×D44—21no—
50C2×D44—22no—
51C2×D44—21no—
52C2×D44—42no—
53C2×D44C2312yes—
54C2×D44C2311yescharacteristic
55C2×C4×D11—21no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4D411yescharacteristic
60C11×C4⋊C4C2312yes—
61C11×C4⋊C4C2311yescharacteristic
62C11×C22⋊C4—22no—
63C11×C22⋊C4—22no—
64C11×C22⋊C4D412yes—
65C42×C11—22no—
66C42×C11—21no—
67C42×C11C2311yescharacteristic
68#4325—22no—
69#4325—42no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—22no—
72C4⋊Dic11C2311yescharacteristic
73#4318—42no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2312yes—
77#3324—111nomaximal, Sylow
78C23×C11C2×D412yes—
79C22×D11—21no—
80C22×D11—22no—
81C22×D11—44no—
82C22×D11—44no—
83C22×D11—82no—
84Q8×C11—21no—
85Q8×C11—21no—
86Q8×C11—42no—
87D4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2411yescharacteristic
97C22⋊D11—44no—
98C2×Dic11—21no—
99D44—22no—
100D44—21no—
101D44—22no—
102D44—44no—
103D44—42no—
104D44—81no—
105D44#4112yes—
106C4×D11—42no—
107C11⋊C8—21no—
108C11⋊C8—21no—
109C11⋊C8—22no—
110#556D1111yescharacteristic, complemented
111D42—111no—
112#486—111no—
113#482—112no—
114#474—111no—
115#468—112no—
116#460—111no—
117#450—112no—
118C4×SD16—111no—
119#436—111no—
120#418—112no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11C22×D411yescharacteristic
125C2×D11—22no—
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—88no—
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—41no—
135C4×C11—42no—
136C4×C11—41no—
137C4×C11AGL(1,ℤ/8)12yes—
138C4×C11C2×#4111yescharacteristic
139C4×C11H(5,𝔽2)11yescharacteristic
140Dic11—41no—
141C22×D4—112no—
142C22×D4—221no—
143C2×SD16—111no—
144C2×SD16—112no—
145C2×M16—112no—
146C4⋊Q8C2×D1111yescharacteristic, complemented
147#127—111no—
148#126—22no—
149#124—21no—
150C22⋊Q8C2×D1112yescomplemented
151#121—112no—
152#121—221no—
153#120—222no—
154C4×Q8—21no—
155C4×Q8C2×D1111yescharacteristic, complemented
156C4×D4—111no—
157C4×D4C2×D1111yescharacteristic
158#117C2×D1112yescomplemented
159#107—112no—
160#106—111no—
161C4⋊C8—111no—
162#103—111no—
163#102—111no—
164#102—112no—
165#102—112no—
166#102—112no—
167#102—112no—
168C22⋊C8—112no—
169C4×C8—111no—
170C2×C11—42no—
171C2×C11#54611yescharacteristic
172C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C11#57711yescharacteristic
174D11—42no—
175D11—82no—
176C24—222no—
177C2×Q8—21no—
178C2×Q8C22×D1111yescharacteristic
179C2×D4—111no—
180C2×D4—112no—
181C2×D4—224no—
182C2×D4—222no—
183C2×D4—222no—
184C2×D4—221no—
185C2×D4—221no—
186C2×D4—442no—
187C2×D4—444no—
188C2×D4C22⋊D1111yescharacteristic
189C22×C4—221no—
190C22×C4C22×D1112yes—
191SD16—222no—
192SD16—442no—
193M16—442no—
194C2×C8—111no—
195C2×C8—111no—
196C2×C8—112no—
197C4⋊C4—22no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—111no—
201C4⋊C4C22⋊D1111yescharacteristic
202C4⋊C4C22×D1111yescharacteristic
203C4⋊C4C22×D1112yes—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—221no—
207C22⋊C4—222no—
208C22⋊C4C22⋊D1112yes—
209C42—22no—
210C42—21no—
211C42C22×D1111yescharacteristic
212C11#332411yescharacteristic, complemented, Sylow
213C23—221no—
214C23—222no—
215C23—444no—
216C23—444no—
217C23—882no—
218C23C2×C22⋊D1112yes—
219Q8—21no—
220Q8—21no—
221Q8—42no—
222D4—22no—
223D4—112no—
224D4—222no—
225D4—221no—
226D4—222no—
227D4—444no—
228D4—444no—
229D4—442no—
230D4—881no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—221no—
237C2×C4—442no—
238C2×C4C2×C22⋊D1112yes—
239C2×C4C2×C22⋊D1111yescharacteristic
240C2×C4C2×C22⋊D1111yescharacteristic
241C2×C4C23×D1111yescharacteristic
242C8—221no—
243C8—221no—
244C8—222no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—222no—
249C22—441no—
250C22—441no—
251C22—442no—
252C22—442no—
253C22—442no—
254C22—888no—
255C22C22×C22⋊D1111yescharacteristic
256C4—22no—
257C4—21no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—441no—
262C4#6700212yes—
263C4#41×D1111yescharacteristic
264C4#6704211yescharacteristic
265C2—42no—
266C2—442no—
267C2—882no—
268C2C2×#6700211yescharacteristic
269C2#1062336011yescharacteristic
270C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radicalD4×D44C2
hypercenter#556D11
hypocenterC11#3324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C11×#556C2semidirect
3. #10622701C2semidirect
4. #10622700C2semidirect
5. #10622662C2semidirect
6. #10622659C2semidirect
7. #10622640C2semidirect
8. C4×#4325C2semidirect
9. #10622625C2semidirect
10. #10622616C2semidirect
11. #10622614C2semidirect
14. C11×C4⋊Q8C22semidirect
17. C11×C22⋊Q8C22semidirect
19. C4×Q8×C11C22semidirect
21. C11×#117C22semidirect
23. C2×#4325C22semidirect
25. C2×#4318C22semidirect
30. #66899C22semidirect
31. C22⋊(C11⋊C8)C22semidirect
34. #66873C22semidirect
35. #66873C22semidirect
36. #66873C22semidirect
37. #66872C22semidirect
38. #66871C22semidirect
39. C4⋊(C11⋊C8)C22semidirect
40. C4×C11⋊C8C22semidirect
110. #556D11semidirect
146. C4⋊Q8C2×D11semidirect
150. C22⋊Q8C2×D11semidirect
155. C4×Q8C2×D11semidirect
158. #117C2×D11semidirect
212. C11#3324semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
D4×D442
#106227012
#106227002
#106226622
#106226592
#106226402
C4×#43252
#106226252
#106226162
#106226142
#332411