Finite Group Databasebeta

← #13079442

Subgroups — #13079442

Order 1408.

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

normal subgroups only

This group has 414 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×#525C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3#10622852C212yesmaximal, complemented
4#10622820C211yesmaximal, characteristic, complemented
5#10622665C212yesmaximal, complemented
6#10622663C211yesmaximal, characteristic, complemented
7#10622657C211yesmaximal, characteristic, complemented
8#10622655C212yesmaximal, complemented
9#10622653C211yesmaximal, characteristic, complemented
10#10622647C211yesmaximal, characteristic, complemented
11#10622609C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C11×#123—21no—
16C11×C22⋊Q8C2211yescharacteristic
17C11×C22⋊Q8C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C11×#121C2211yescharacteristic
20C11×#120—21no—
21C4×D4×C11—21no—
22C4×D4×C11—21no—
23C11×#117C2211yescharacteristic
24C2×C22⋊Dic11—21no—
25C2×#4326C2212yescomplemented
26C2×#4324C2212yescomplemented
27C2×C4⋊Dic11C2211yescharacteristic
28#66977—21no—
29#66977—21no—
30#66977C2212yes—
31#66977C2212yes—
32C2×Dic11⋊C4—21no—
33C2×#4318C2212yes—
34#66899C2212yescomplemented
35#66896C2212yescomplemented
36C22⋊(C11⋊C8)C2212yes—
37C22⋊(C11⋊C8)C2211yescharacteristic
38C22⋊(C11⋊C8)C2211yescharacteristic
39#66874C2212yescomplemented
40#66874C2212yescomplemented
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C24×C11D411yescharacteristic
44C11×#41—42no—
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11—21no—
47C2×D4×C11—21no—
48C2×D4×C11—21no—
49C2×D4×C11C2311yescharacteristic
50C22×C4×C11—21no—
51C22×C4×C11—42no—
52C22×C4×C11D411yescharacteristic
53C22×C4×C11D411yescharacteristic
54C22×C4×C11D411yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×Dic11—21no—
59C22×Dic11—21no—
60C2×Dic22—21no—
61C2×Dic22—42no—
62C2×Dic22C2312yes—
63C11×C4⋊C4—21no—
64C11×C4⋊C4—21no—
65C11×C4⋊C4C2311yescharacteristic
66C11×C4⋊C4C2311yescharacteristic
67C11×C22⋊C4—21no—
68C11×C22⋊C4—21no—
69C11×C22⋊C4—21no—
70C11×C22⋊C4—21no—
71C11×C22⋊C4—21no—
72C42×C11—21no—
73C22⋊Dic11—22no—
74C22⋊Dic11—22no—
75#4326—42no—
76#4324—42no—
77C4⋊Dic11—21no—
78C4⋊Dic11C2312yes—
79Dic11⋊C4—22no—
80Dic11⋊C4—22no—
81#4318—42no—
82C2×C11⋊C8C2312yes—
83C2×C11⋊C8C2312yes—
84#3196—111nomaximal, Sylow
85C23×C11—22no—
86C23×C11—21no—
87C23×C11—41no—
88C23×C11—41no—
89C23×C11C2×D411yescharacteristic
90C23×C11C2×D411yescharacteristic
91C23×C11C2×D411yescharacteristic
92Q8×C11—22no—
93D4×C11—22no—
94D4×C11—42no—
95D4×C11—42no—
96D4×C11—42no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11C2×D411yescharacteristic
108C2×C4×C11C2×D411yescharacteristic
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2411yescharacteristic
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115Dic22—22no—
116Dic22—22no—
117Dic22—42no—
118C11⋊C8—22no—
119C11⋊C8—22no—
120#525D1111yescharacteristic
121C2×C22⋊Q8—111no—
122#485—112no—
123#484—111no—
124#481—111no—
125#470—112no—
126#468—112no—
127#452—112no—
128#451—111no—
129#448—111no—
130#407—111no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—44no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11#13712yes—
144C22×C11C22×D411yescharacteristic
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11H(5,𝔽2)12yes—
152Dic11—42no—
153Dic11—42no—
154C2×#41C2×D1111yescharacteristic
155C22×Q8—111no—
156C23×C4C2×D1111yescharacteristic
157C2×Q16—112no—
158C2×SD16—112no—
159C2×M16—112no—
160#123—21no—
161C22⋊Q8—112no—
162C22⋊Q8—112no—
163C22⋊Q8—221no—
164C22⋊Q8—221no—
165C22⋊Q8C2×D1111yescharacteristic
166C22⋊Q8C2×D1111yescharacteristic
167#121C2×D1111yescharacteristic
168#121C2×D1111yescharacteristic
169#120—21no—
170C4×D4—21no—
171C4×D4—21no—
172#117C2×D1111yescharacteristic
173C2×C4⋊C4—111no—
174C2×C4⋊C4—221no—
175C2×C22⋊C4—221no—
176#107—112no—
177#106—112no—
178#103—112no—
179#103—112no—
180#103—112no—
181#102—112no—
182C22⋊C8—111no—
183C22⋊C8—111no—
184C22⋊C8—112no—
185C2×C11—22no—
186C2×C11—41no—
187C2×C11—41no—
188C2×C11—81no—
189C2×C11#53411yescharacteristic
190C2×C11C2×#13711yescharacteristic
191C2×C11#57511yescharacteristic
192C24C22⋊D1111yescharacteristic
193#41—42no—
194C2×Q8—112no—
195C2×Q8—221no—
196C2×Q8—442no—
197C2×Q8C22×D1111yescharacteristic
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4C22×D1111yescharacteristic
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—221no—
205C22×C4—221no—
206C22×C4C22⋊D1111yescharacteristic
207C22×C4C22⋊D1111yescharacteristic
208C22×C4C22⋊D1111yescharacteristic
209C22×C4C22×D1111yescharacteristic
210C22×C4C22×D1111yescharacteristic
211C22×C4C22×D1111yescharacteristic
212Q16—442no—
213SD16—442no—
214M16—442no—
215C2×C8—112no—
216C2×C8—112no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—112no—
220C4⋊C4—221no—
221C4⋊C4—222no—
222C4⋊C4—222no—
223C4⋊C4C22×D1111yescharacteristic
224C4⋊C4C22×D1111yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—222no—
231C22⋊C4—222no—
232C42—21no—
233C11#319611yescharacteristic, complemented, Sylow
234C23—22no—
235C23—21no—
236C23—41no—
237C23—41no—
238C23C2×C22⋊D1111yescharacteristic
239C23C2×C22⋊D1111yescharacteristic
240C23C2×C22⋊D1111yescharacteristic
241Q8—22no—
242Q8—222no—
243Q8—222no—
244Q8—442no—
245D4—22no—
246D4—42no—
247D4—42no—
248D4—42no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4C2×C22⋊D1111yescharacteristic
264C2×C4C2×C22⋊D1111yescharacteristic
265C2×C4C2×C22⋊D1111yescharacteristic
266C2×C4C23×D1111yescharacteristic
267C8—222no—
268C8—222no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—44no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22#6700412yes—
282C22C22×C22⋊D1111yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—442no—
290C4—442no—
291C4#6703712yes—
292C2—22no—
293C2—41no—
294C2—41no—
295C2—81no—
296C2#1062333511yescharacteristic
297C2#1062335311yescharacteristic
298C2C2×#6700411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#525C2
socleC22×C11C22×D4
hypercenter#525D11
hypocenterC11#3196
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
3. #10622852C2semidirect
4. #10622820C2semidirect
5. #10622665C2semidirect
6. #10622663C2semidirect
7. #10622657C2semidirect
8. #10622655C2semidirect
9. #10622653C2semidirect
10. #10622647C2semidirect
11. #10622609C2semidirect
25. C2×#4326C22semidirect
26. C2×#4324C22semidirect
34. #66899C22semidirect
35. #66896C22semidirect
39. #66874C22semidirect
40. #66874C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
233. C11#3196semidirect

Maximal subgroups

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

subgroupindex
C11×#5252
C2×#669772
#106228522
#106228202
#106226652
#106226632
#106226572
#106226552
#106226532
#106226472
#106226092
#319611