Finite Group Databasebeta

← #13079426

Subgroups — #13079426

Order 1408.

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

normal subgroups only

This group has 466 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, complemented
2C2×#66983C211yesmaximal, characteristic, complemented
3#10622851C212yesmaximal, complemented
4#10622820C211yesmaximal, characteristic, complemented
5#10622662C212yesmaximal, complemented
6#10622659C211yesmaximal, characteristic, complemented
7#10622656C211yesmaximal, characteristic, complemented
8#10622652C212yesmaximal, complemented
9#10622649C211yesmaximal, characteristic, complemented
10#10622646C211yesmaximal, characteristic, complemented
11#10622616C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic, complemented
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11—21no—
15C22×D44C2211yescharacteristic
16C11×#123—21no—
17C11×C22⋊Q8C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic, complemented
19C11×#121C2211yescharacteristic
20C11×#121C2211yescharacteristic, complemented
21C11×#120—21no—
22C4×D4×C11—21no—
23C4×D4×C11—21no—
24C11×#117C2211yescharacteristic, complemented
25C2×#4325C2212yescomplemented
26C2×#4323C2212yescomplemented
27#66983—21no—
28#66983—21no—
29#66983C2212yes—
30#66983C2212yes—
31C2×(C2×D11)⋊C4—21no—
32C2×C4⋊Dic11C2211yescharacteristic
33C2×#4318C2212yescomplemented
34#66899C2212yescomplemented
35#66896C2212yescomplemented
36C22⋊(C11⋊C8)C2211yescharacteristic
37C22⋊(C11⋊C8)C2211yescharacteristic
38C22⋊(C11⋊C8)C2212yescomplemented
39#66873C2212yescomplemented
40#66873C2212yescomplemented
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C24×C11D411yescharacteristic
44C23×D11—21no—
45C11×#41—42no—
46C2×Q8×C11C2311yescharacteristic
47C2×D4×C11—21no—
48C2×D4×C11—21no—
49C2×D4×C11—21no—
50C2×D4×C11C2311yescharacteristic
51C22×C4×C11—21no—
52C22×C4×C11—42no—
53C22×C4×C11D411yescharacteristic
54C22×C4×C11D411yescharacteristic
55C22×C4×C11D411yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C2×C22⋊D11—22no—
60C2×C22⋊D11—22no—
61C2×C22⋊D11—44no—
62C22×Dic11—21no—
63C2×D44—21no—
64C2×D44—42no—
65C2×D44C2312yes—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4C2311yescharacteristic
69C11×C4⋊C4C2311yescharacteristic
70C11×C22⋊C4—21no—
71C11×C22⋊C4—21no—
72C11×C22⋊C4—21no—
73C11×C22⋊C4—21no—
74C11×C22⋊C4—21no—
75C42×C11—21no—
76#4325—42no—
77#4323—42no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—22no—
80C4⋊Dic11—21no—
81C4⋊Dic11C2312yes—
82#4318—42no—
83C2×C11⋊C8C2312yes—
84C2×C11⋊C8C2312yes—
85#3194—111nomaximal, Sylow
86C23×C11—22no—
87C23×C11—21no—
88C23×C11—41no—
89C23×C11—41no—
90C23×C11C2×D411yescharacteristic
91C23×C11C2×D411yescharacteristic
92C23×C11C2×D411yescharacteristic
93C22×D11—22no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97Q8×C11—22no—
98D4×C11—22no—
99D4×C11—42no—
100D4×C11—42no—
101D4×C11—42no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—42no—
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2411yescharacteristic
116C22⋊D11—44no—
117C22⋊D11—44no—
118C2×Dic11—22no—
119C2×Dic11—42no—
120D44—22no—
121D44—22no—
122D44—42no—
123C11⋊C8—22no—
124C11⋊C8—22no—
125#525D1111yescharacteristic, complemented
126C2×#121—111no—
127#483—111no—
128#482—112no—
129#480—111no—
130#469—112no—
131#468—112no—
132#450—111no—
133#449—112no—
134#447—111no—
135#407—111no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—44no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11AGL(1,ℤ/8)12yes—
149C22×C11C22×D411yescharacteristic
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—84no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11H(5,𝔽2)12yes—
161Dic11—42no—
162C2×#41C2×D1111yescharacteristic, complemented
163C22×D4—111no—
164C22×D4—221no—
165C23×C4C2×D1111yescharacteristic
166C2×SD16—112no—
167C2×D8—112no—
168C2×M16—112no—
169#123—21no—
170C22⋊Q8C2×D1111yescharacteristic
171C22⋊Q8C2×D1111yescharacteristic, complemented
172#121—112no—
173#121—112no—
174#121—221no—
175#121—221no—
176#121C2×D1111yescharacteristic
177#121C2×D1111yescharacteristic, complemented
178#120—21no—
179C4×D4—21no—
180C4×D4—21no—
181#117C2×D1111yescharacteristic, complemented
182C2×C4⋊C4—111no—
183C2×C22⋊C4—221no—
184#107—112no—
185#106—112no—
186#103—112no—
187#102—112no—
188#102—112no—
189#102—112no—
190C22⋊C8—111no—
191C22⋊C8—111no—
192C22⋊C8—112no—
193C2×C11—22no—
194C2×C11—41no—
195C2×C11—41no—
196C2×C11—81no—
197C2×C11#53411yescharacteristic
198C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C11#57511yescharacteristic
200D11—82no—
201C24—221no—
202C24C22⋊D1111yescharacteristic
203#41—42no—
204C2×Q8C22×D1111yescharacteristic
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—112no—
209C2×D4—222no—
210C2×D4—222no—
211C2×D4—221no—
212C2×D4—442no—
213C2×D4—444no—
214C2×D4C22×D1111yescharacteristic
215C22×C4—21no—
216C22×C4—42no—
217C22×C4—221no—
218C22×C4C22⋊D1111yescharacteristic
219C22×C4C22⋊D1111yescharacteristic
220C22×C4C22⋊D1111yescharacteristic
221C22×C4C22×D1111yescharacteristic
222C22×C4C22×D1111yescharacteristic
223C22×C4C22×D1111yescharacteristic
224SD16—442no—
225D8—442no—
226M16—442no—
227C2×C8—112no—
228C2×C8—112no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—112no—
232C4⋊C4—221no—
233C4⋊C4C22×D1111yescharacteristic
234C4⋊C4C22×D1111yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—222no—
241C22⋊C4—222no—
242C42—21no—
243C11#319411yescharacteristic, complemented, Sylow
244C23—22no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—222no—
249C23—442no—
250C23—442no—
251C23—442no—
252C23C2×C22⋊D1111yescharacteristic
253C23C2×C22⋊D1111yescharacteristic
254C23C2×C22⋊D1111yescharacteristic
255Q8—22no—
256D4—22no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—222no—
261D4—222no—
262D4—442no—
263D4—444no—
264D4—444no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—222no—
276C2×C4—442no—
277C2×C4C2×C22⋊D1111yescharacteristic
278C2×C4C2×C22⋊D1111yescharacteristic
279C2×C4C2×C22⋊D1111yescharacteristic
280C2×C4C23×D1111yescharacteristic
281C8—222no—
282C8—222no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—442no—
296C22—442no—
297C22—442no—
298C22—884no—
299C22#6700212yes—
300C22C22×C22⋊D1111yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—442no—
308C4#6703712yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—81no—
313C2—882no—
314C2#1062333511yescharacteristic
315C2C2×#6700211yescharacteristic
316C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#525C2
socleC22×C11C22×D4
hypercenter#525D11
hypocenterC11#3194
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
1. C11×#525C2semidirect
2. C2×#66983C2semidirect
3. #10622851C2semidirect
4. #10622820C2semidirect
5. #10622662C2semidirect
6. #10622659C2semidirect
7. #10622656C2semidirect
8. #10622652C2semidirect
9. #10622649C2semidirect
10. #10622646C2semidirect
11. #10622616C2semidirect
12. C2×C11×#41C22semidirect
18. C11×C22⋊Q8C22semidirect
20. C11×#121C22semidirect
24. C11×#117C22semidirect
25. C2×#4325C22semidirect
26. C2×#4323C22semidirect
33. C2×#4318C22semidirect
34. #66899C22semidirect
35. #66896C22semidirect
38. C22⋊(C11⋊C8)C22semidirect
39. #66873C22semidirect
40. #66873C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
125. #525D11semidirect
162. C2×#41C2×D11semidirect
171. C22⋊Q8C2×D11semidirect
177. #121C2×D11semidirect
181. #117C2×D11semidirect
243. C11#3194semidirect

Maximal subgroups

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

subgroupindex
C11×#5252
C2×#669832
#106228512
#106228202
#106226622
#106226592
#106226562
#106226522
#106226492
#106226462
#106226162
#319411