Finite Group Databasebeta

← #13079577

Subgroups — #13079577

Order 1408.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#529C211yesmaximal, characteristic, complemented
2C2×#66928C211yesmaximal, characteristic, complemented
3#10622681C212yesmaximal, complemented
4#10622672C212yesmaximal, complemented
5#10622663C211yesmaximal, characteristic, complemented
6#10622659C211yesmaximal, characteristic, complemented
7#10622653C211yesmaximal, characteristic, complemented
8#10622649C211yesmaximal, characteristic
9#10622641C212yesmaximal, complemented
10#10622629C212yesmaximal, complemented
11#10622538C211yesmaximal, characteristic, complemented
12C22×D44C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C11×#126—21no—
15C11×#125C2211yescharacteristic, complemented
16C11×#124C2211yescharacteristic, complemented
17C11×#123—21no—
18C11×C22⋊Q8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic, complemented
21C4×D4×C11—21no—
22C4×D4×C11C2211yescharacteristic, complemented
23C11×#117—21no—
24C2×C42×C11C2211yescharacteristic
25C2×#4326C2212yescomplemented
26C2×#4325C2212yes—
27C2×#4324C2212yescomplemented
28C2×#4323C2212yes—
29C2×(C2×D11)⋊C4—21no—
30C2×(C2×D11)⋊C4—21no—
31#66928—21no—
32#66928—21no—
33#66928C2212yes—
34#66928C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66874C2212yescomplemented
38#66874C2212yescomplemented
39#66873C2212yes—
40#66873C2212yes—
41C4⋊(C11⋊C8)C2212yescomplemented
42C4×C11⋊C8C2212yescomplemented
43C23×D11—21no—
44C2×Q8×C11C2311yescharacteristic
45C2×D4×C11—21no—
46C2×D4×C11C2311yescharacteristic
47C22×C4×C11—21no—
48C22×C4×C11D411yescharacteristic
49C22×C4×C11D411yescharacteristic
50C22×C4×C11C2311yescharacteristic
51C22×Dic11—21no—
52C2×D44—21no—
53C2×D44—42no—
54C2×D44C2312yes—
55C2×Dic22—21no—
56C2×Dic22—42no—
57C2×Dic22C2312yes—
58C11×C4⋊C4—21no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—21no—
62C11×C4⋊C4C2311yescharacteristic
63C11×C4⋊C4C2311yescharacteristic
64C11×C22⋊C4—21no—
65C11×C22⋊C4—21no—
66C11×C22⋊C4—21no—
67C11×C22⋊C4—21no—
68C11×C22⋊C4—21no—
69C42×C11—21no—
70C42×C11D411yescharacteristic
71C42×C11D411yescharacteristic
72C42×C11C2311yescharacteristic
73C42×C11C2311yescharacteristic
74#4326—42no—
75#4325—42no—
76#4324—42no—
77#4323—42no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4—22no—
82C2×C11⋊C8C2312yes—
83C2×C11⋊C8C2312yes—
84#3211—111nomaximal, Sylow
85C23×C11—21no—
86C23×C11C2×D411yescharacteristic
87C22×D11—22no—
88C22×D11—42no—
89C22×D11—42no—
90C22×D11—42no—
91Q8×C11—22no—
92D4×C11—22no—
93D4×C11—42no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11C2×D411yescharacteristic
104C2×C4×C11C2×D411yescharacteristic
105C2×C4×C11C2×D411yescharacteristic
106C2×C4×C11C2411yescharacteristic
107C2×Dic11—22no—
108C2×Dic11—42no—
109D44—22no—
110D44—22no—
111D44—42no—
112Dic22—22no—
113Dic22—22no—
114Dic22—42no—
115C11⋊C8—22no—
116C11⋊C8—22no—
117#529D1111yescharacteristic, complemented
118C2×#124—111no—
119#495—112no—
120#488—112no—
121#464—112no—
122#463—112no—
123#451—111no—
124#450—111no—
125#448—111no—
126#447—111no—
127#431—111no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11#13512yes—
134C22×C11C22×D411yescharacteristic
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—84no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11H(5,𝔽2)12yes—
148Dic11—42no—
149C22×Q8—111no—
150C22×D4—111no—
151C2×Q16—112no—
152C2×SD16—112no—
153C2×SD16—112no—
154C2×D8—112no—
155#126—21no—
156#125C2×D1111yescharacteristic, complemented
157#124—112no—
158#124—112no—
159#124—221no—
160#124—221no—
161#124C2×D1111yescharacteristic, complemented
162#123—21no—
163C22⋊Q8C2×D1111yescharacteristic
164#121C2×D1111yescharacteristic
165C4×Q8C2×D1111yescharacteristic, complemented
166C4×D4—21no—
167C4×D4C2×D1111yescharacteristic, complemented
168#117—21no—
169C2×C22⋊C4—221no—
170C2×C22⋊C4—221no—
171C2×C42C2×D1111yescharacteristic
172C4⋊C8—112no—
173#103—112no—
174#103—112no—
175#102—112no—
176#102—112no—
177C22⋊C8—111no—
178C22⋊C8—111no—
179C4×C8—112no—
180C2×C11—22no—
181C2×C11—81no—
182C2×C11#53511yescharacteristic
183C2×C11C2×#13511yescharacteristic
184C2×C11#57511yescharacteristic
185D11—82no—
186C24—221no—
187C2×Q8—112no—
188C2×Q8—221no—
189C2×Q8—442no—
190C2×Q8C22×D1111yescharacteristic
191C2×D4—21no—
192C2×D4—112no—
193C2×D4—221no—
194C2×D4—442no—
195C2×D4C22×D1111yescharacteristic
196C22×C4—21no—
197C22×C4—221no—
198C22×C4C22⋊D1111yescharacteristic
199C22×C4C22⋊D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201Q16—442no—
202SD16—442no—
203SD16—442no—
204D8—442no—
205C2×C8—112no—
206C2×C8—112no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4C22×D1111yescharacteristic
212C4⋊C4C22×D1111yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—21no—
218C22⋊C4—222no—
219C22⋊C4—222no—
220C22⋊C4—222no—
221C22⋊C4—222no—
222C42—21no—
223C42C22⋊D1111yescharacteristic
224C42C22⋊D1111yescharacteristic
225C42C22×D1111yescharacteristic
226C42C22×D1111yescharacteristic
227C11#321111yescharacteristic, complemented, Sylow
228C23—21no—
229C23—222no—
230C23—442no—
231C23—442no—
232C23—442no—
233C23C2×C22⋊D1111yescharacteristic
234Q8—22no—
235Q8—222no—
236Q8—222no—
237Q8—442no—
238D4—22no—
239D4—42no—
240D4—222no—
241D4—222no—
242D4—442no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—222no—
251C2×C4—442no—
252C2×C4C2×C22⋊D1111yescharacteristic
253C2×C4C2×C22⋊D1111yescharacteristic
254C2×C4C2×C22⋊D1111yescharacteristic
255C2×C4C2×C22⋊D1111yescharacteristic
256C2×C4C2×C22⋊D1111yescharacteristic
257C2×C4C23×D1111yescharacteristic
258C8—222no—
259C8—222no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—442no—
266C22—442no—
267C22—442no—
268C22—884no—
269C22#6700312yes—
270C22C22×C22⋊D1111yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—442no—
280C4#6704212yes—
281C2—22no—
282C2—81no—
283C2—882no—
284C2C2×#6700311yescharacteristic
285C2#1062335311yescharacteristic
286C2#1062336111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#529C2
socleC22×C11C22×D4
prime radical#10622649C2
hypercenter#529D11
hypocenterC11#3211
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C11×#529C2semidirect
2. C2×#66928C2semidirect
3. #10622681C2semidirect
4. #10622672C2semidirect
5. #10622663C2semidirect
6. #10622659C2semidirect
7. #10622653C2semidirect
9. #10622641C2semidirect
10. #10622629C2semidirect
11. #10622538C2semidirect
15. C11×#125C22semidirect
16. C11×#124C22semidirect
20. C4×Q8×C11C22semidirect
22. C4×D4×C11C22semidirect
25. C2×#4326C22semidirect
27. C2×#4324C22semidirect
37. #66874C22semidirect
38. #66874C22semidirect
41. C4⋊(C11⋊C8)C22semidirect
42. C4×C11⋊C8C22semidirect
117. #529D11semidirect
156. #125C2×D11semidirect
161. #124C2×D11semidirect
165. C4×Q8C2×D11semidirect
167. C4×D4C2×D11semidirect
227. C11#3211semidirect

Maximal subgroups

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

subgroupindex
C11×#5292
C2×#669282
#106226812
#106226722
#106226632
#106226592
#106226532
#106226492
#106226412
#106226292
#106225382
#321111