Finite Group Databasebeta

← #13079942

Subgroups — #13079942

Order 1408.

398 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#529C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic, complemented
3#10622679C212yesmaximal, complemented
4#10622670C212yesmaximal, complemented
5#10622661C212yesmaximal, complemented
6#10622651C212yesmaximal, complemented
7#10622640C211yesmaximal, characteristic, complemented
8#10622634C211yesmaximal, characteristic, complemented
9#10622628C211yesmaximal, characteristic, complemented
10#10622621C211yesmaximal, characteristic, complemented
11C2×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
12C2×#4339—21no—
13C11×#126—21no—
14C11×#125C2211yescharacteristic
15C11×#124C2211yescharacteristic
16C11×#123—21no—
17C11×C22⋊Q8C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×D4×C11—21no—
21C4×D4×C11C2211yescharacteristic
22C11×#117—21no—
23C2×C42×C11C2211yescharacteristic
24C2×#4325C2212yes—
25C2×#4323C2212yes—
26#66983—21no—
27#66983C2212yes—
28C22×C11⋊C8C2212yes—
29#66928—21no—
30#66927C2211yescharacteristic
31C4×D44—21no—
32C4×D44C2212yes—
33#66922C2211yescharacteristic
34#66899C2212yes—
35#66896C2212yes—
36#66873C2212yes—
37#66873C2212yes—
38#66872C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C4⋊(C11⋊C8)C2211yescharacteristic
42C4⋊(C11⋊C8)C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11D411yescharacteristic
48C22×C4×C11D411yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—22no—
51#4339—44no—
52C2×D44—21no—
53C2×D44—21no—
54C2×D44C2312yes—
55C2×C4×D11—22no—
56C2×Dic22—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4C2311yescharacteristic
62C11×C4⋊C4C2311yescharacteristic
63C11×C22⋊C4—21no—
64C11×C22⋊C4—21no—
65C11×C22⋊C4—21no—
66C11×C22⋊C4—21no—
67C11×C22⋊C4—21no—
68C42×C11—21no—
69C42×C11D411yescharacteristic
70C42×C11D411yescharacteristic
71C42×C11C2311yescharacteristic
72C42×C11C2311yescharacteristic
73#4325—42no—
74#4323—42no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77C4⋊Dic11—21no—
78C4⋊Dic11C2312yes—
79C2×C11⋊C8—42no—
80C2×C11⋊C8C2312yes—
81C2×C11⋊C8C2312yes—
82#3247—111nomaximal, Sylow
83C23×C11—21no—
84C23×C11C2×D411yescharacteristic
85C22×D11—22no—
86Q8×C11—21no—
87Q8×C11—21no—
88D4×C11—21no—
89D4×C11—21no—
90D4×C11—42no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—42no—
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11C2×D411yescharacteristic
104C2×C4×C11C2411yescharacteristic
105C22⋊D11—44no—
106C2×Dic11—22no—
107D44—22no—
108D44—22no—
109D44—42no—
110D44—42no—
111C4×D11—44no—
112Dic22—42no—
113C11⋊C8—22no—
114C11⋊C8—22no—
115#532—111no—
116#529D1111yescharacteristic, complemented
117#478—112no—
118#477—111no—
119#476—111no—
120#466—112no—
121#465—112no—
122#463—112no—
123#460—111no—
124#459—111no—
125C2×C4⋊C8—111no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11—41no—
131C22×C11AGL(1,ℤ/8)12yes—
132C22×C11C22×D411yescharacteristic
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—42no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11—41no—
143C4×C11#13512yes—
144C4×C11H(5,𝔽2)11yescharacteristic
145C4×C112−1+411yescharacteristic
146Dic11—42no—
147C2×#41—221no—
148C2×SD16—112no—
149C2×D8—112no—
150C22×C8—112no—
151C4⋊Q8—111no—
152#127—111no—
153#126—21no—
154#125C2×D1111yescharacteristic
155#124—221no—
156#124C2×D1111yescharacteristic
157#123—21no—
158C22⋊Q8C2×D1111yescharacteristic
159#121—112no—
160#121—221no—
161#121C2×D1111yescharacteristic
162C4×Q8C2×D1111yescharacteristic
163C4×D4—21no—
164C4×D4—112no—
165C4×D4—221no—
166C4×D4C2×D1111yescharacteristic
167#117—21no—
168C2×C42C2×D1111yescharacteristic
169#107—112no—
170#106—112no—
171C4⋊C8—111no—
172C4⋊C8—111no—
173C4⋊C8—112no—
174#103—112no—
175#102—112no—
176#102—112no—
177#102—112no—
178C2×C11—22no—
179C2×C11—81no—
180C2×C11#53711yescharacteristic
181C2×C11C2×#13511yescharacteristic
182C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
183D11—82no—
184#41—444no—
185C2×Q8—221no—
186C2×Q8C22×D1111yescharacteristic
187C2×D4—21no—
188C2×D4—112no—
189C2×D4—222no—
190C2×D4—221no—
191C2×D4—221no—
192C2×D4C22×D1111yescharacteristic
193C22×C4—21no—
194C22×C4—222no—
195C22×C4C22⋊D1111yescharacteristic
196C22×C4C22⋊D1111yescharacteristic
197C22×C4C22×D1111yescharacteristic
198SD16—442no—
199D8—442no—
200C2×C8—112no—
201C2×C8—112no—
202C2×C8—442no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—112no—
208C4⋊C4—221no—
209C4⋊C4C22×D1111yescharacteristic
210C4⋊C4C22×D1111yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—222no—
217C22⋊C4—222no—
218C42—21no—
219C42C22⋊D1111yescharacteristic
220C42C22⋊D1111yescharacteristic
221C42C22×D1111yescharacteristic
222C42C22×D1111yescharacteristic
223C11#324711yescharacteristic, complemented, Sylow
224C23—21no—
225C23—222no—
226C23C2×C22⋊D1111yescharacteristic
227Q8—21no—
228Q8—21no—
229Q8—442no—
230D4—21no—
231D4—21no—
232D4—42no—
233D4—222no—
234D4—222no—
235D4—442no—
236D4—444no—
237D4—442no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—222no—
247C2×C4—444no—
248C2×C4C2×C22⋊D1111yescharacteristic
249C2×C4C2×C22⋊D1111yescharacteristic
250C2×C4C2×C22⋊D1111yescharacteristic
251C2×C4C2×C22⋊D1111yescharacteristic
252C2×C4C2×C22⋊D1111yescharacteristic
253C2×C4C23×D1111yescharacteristic
254C8—222no—
255C8—222no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—442no—
262C22—442no—
263C22—442no—
264C22#6700212yes—
265C22C22×C22⋊D1111yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—442no—
274C4#6700312yes—
275C4#6704211yescharacteristic
276C4#6704311yescharacteristic
277C2—22no—
278C2—81no—
279C2—882no—
280C2C2×#6700211yescharacteristic
281C2C2×#6700311yescharacteristic
282C2#1062336411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#529C2
socleC22×C11C22×D4
hypercenter#529D11
hypocenterC11#3247
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. #10623008C2semidirect
3. #10622679C2semidirect
4. #10622670C2semidirect
5. #10622661C2semidirect
6. #10622651C2semidirect
7. #10622640C2semidirect
8. #10622634C2semidirect
9. #10622628C2semidirect
10. #10622621C2semidirect
11. C2×C4⋊(C11⋊C8)C2semidirect
116. #529D11semidirect
223. C11#3247semidirect

Maximal subgroups

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

subgroupindex
C11×#5292
#106230082
#106226792
#106226702
#106226612
#106226512
#106226402
#106226342
#106226282
#106226212
C2×C4⋊(C11⋊C8)2
#324711