Finite Group Databasebeta

← #13078613

Subgroups — #13078613

Order 1408.

492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#10623127C211yesmaximal, characteristic, complemented
2C2×#66946C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622649C211yesmaximal, characteristic, complemented
5#10622580C211yesmaximal, characteristic, complemented
6#10622503C212yesmaximal, complemented
7#10622485C212yesmaximal, complemented
8#10622399C212yesmaximal, complemented
9#10622369C212yesmaximal, complemented
10#10622345C211yesmaximal, characteristic, complemented
11#10622331C211yesmaximal, characteristic, complemented
12C2×#4341—21no—
13C22×D44C2211yescharacteristic
14C22×C4×D11—21no—
15C11×#121C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#66993C2211yescharacteristic, complemented
18#66992—21no—
19D4×Dic11C2211yescharacteristic, complemented
20C2×#4323C2212yes—
21#66983C2211yescharacteristic
22C2×(C2×D11)⋊C4—21no—
23C2×C4×Dic11C2211yescharacteristic
24C2×D88C2212yes—
25#66946—21no—
26#66946—21no—
27#66946C2212yes—
28#66946C2212yes—
29#66946C2211yescharacteristic, complemented
30#66941C2211yescharacteristic, complemented
31#66938—21no—
32(C22⋊D11)⋊C4—21no—
33C11×#107C2212yescomplemented
34C11×#102C2212yescomplemented
35C11×C22⋊C8C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66885C2212yes—
38Dic11⋊C8C2212yescomplemented
39C8×Dic11C2212yescomplemented
40#66873C2212yes—
41#66873C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11—21no—
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—21no—
49C2×C22⋊D11—21no—
50C2×C22⋊D11—21no—
51C22×Dic11—21no—
52C22×Dic11D411yescharacteristic
53C22×Dic11D411yescharacteristic
54#4341—44no—
55C2×D44—24no—
56C2×D44—21no—
57C2×D44C2311yescharacteristic
58C2×D44C2312yes—
59C2×C4×D11—21no—
60C2×C4×D11—22no—
61C2×C4×D11—22no—
62C2×C4×D11—44no—
63C2×Dic22—21no—
64C2×C8×C11C2312yes—
65C11×C4⋊C4—21no—
66C11×C4⋊C4C2312yes—
67C11×C4⋊C4C2311yescharacteristic
68C11×C22⋊C4—21no—
69C22⋊Dic11—21no—
70#4323—24no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—21no—
75C4⋊Dic11C2311yescharacteristic
76Dic11⋊C4—21no—
77C4×Dic11D411yescharacteristic
78C4×Dic11D411yescharacteristic
79C4×Dic11C2311yescharacteristic
80C4×Dic11C2311yescharacteristic
81C2×C11⋊C8C2312yes—
82D88—24no—
83#3100—111nomaximal, Sylow
84C23×C11—21no—
85C23×C11C2×D411yescharacteristic
86C22×D11—24no—
87C22×D11—22no—
88C22×D11—21no—
89C22×D11—42no—
90C22×D11—42no—
91D4×C11—22no—
92D4×C11—42no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2411yescharacteristic
99C22⋊D11—42no—
100C22⋊D11—42no—
101C22⋊D11—42no—
102C2×Dic11—21no—
103C2×Dic11—41no—
104C2×Dic11—42no—
105C2×Dic11D814yescomplemented
106C2×Dic11C2×D411yescharacteristic
107C2×Dic11C2×D411yescharacteristic
108C2×Dic11C2×D411yescharacteristic
109C2×Dic11C2×D411yescharacteristic
110D44—24no—
111D44—22no—
112D44—22no—
113D44#4114yescomplemented
114C4×D11—44no—
115C4×D11—44no—
116C4×D11—42no—
117Dic22—42no—
118C8×C11—22no—
119C11⋊C8—22no—
120#532—111no—
121C2×C4×D4—111no—
122#480—111no—
123#480D1111yescharacteristic, complemented
124#474—112no—
125#459—112no—
126#447—111no—
127#447—111no—
128C4×D8—112no—
129C4×D8—112no—
130#431—111no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11C2×D812yes—
137C22×C11C22×D411yescharacteristic
138C2×D11—24no—
139C2×D11—48no—
140C2×D11—42no—
141C2×D11—42no—
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—41no—
145C4×C11—21no—
146C4×C11—42no—
147C4×C11—41no—
148C4×C11C2×#4112yes—
149Dic11—21no—
150Dic11—21no—
151Dic11—41no—
152Dic11C2×D812yes—
153Dic11C2×D812yes—
154C2×#41—221no—
155C22×D4—111no—
156C23×C4—221no—
157C2×D8—112no—
158C2×D8—112no—
159C4⋊Q8—111no—
160#127—111no—
161#124—221no—
162#121—111no—
163#121—221no—
164#121C2×D1111yescharacteristic
165C4×D4—111no—
166C4×D4—112no—
167C4×D4—112no—
168C4×D4—111no—
169C4×D4—221no—
170C4×D4—221no—
171C4×D4—221no—
172C2×C4⋊C4C2×D1111yescharacteristic
173C2×C22⋊C4—221no—
174C2×C42—111no—
175#107—112no—
176#107C2×D1112yescomplemented
177C4⋊C8—112no—
178#102—112no—
179#102—112no—
180#102—112no—
181#102C2×D1112yescomplemented
182C22⋊C8—111no—
183C22⋊C8C2×D1111yescharacteristic
184C4×C8—112no—
185C2×C11—22no—
186C2×C11—81no—
187C2×C11#52511yescharacteristic
188C2×C11C22×D811yescharacteristic
189C2×C11#57511yescharacteristic
190D11—44no—
191D11—81no—
192C24—221no—
193#41—444no—
194C2×Q8—221no—
195C2×D4—21no—
196C2×D4—112no—
197C2×D4—111no—
198C2×D4—224no—
199C2×D4—221no—
200C2×D4—221no—
201C2×D4—221no—
202C2×D4—221no—
203C2×D4C22×D1111yescharacteristic
204C22×C4—21no—
205C22×C4—111no—
206C22×C4—111no—
207C22×C4—222no—
208C22×C4—222no—
209C22×C4—221no—
210C22×C4—221no—
211C22×C4—444no—
212C22×C4C22×D1111yescharacteristic
213D8—224no—
214D8—224no—
215C2×C8—112no—
216C2×C8C22×D1112yes—
217C4⋊C4—21no—
218C4⋊C4—111no—
219C4⋊C4—221no—
220C4⋊C4C22×D1111yescharacteristic
221C4⋊C4C22×D1112yes—
222C22⋊C4—21no—
223C22⋊C4—222no—
224C22⋊C4—222no—
225C22⋊C4—221no—
226C22⋊C4—221no—
227C22⋊C4—221no—
228C42—111no—
229C42—111no—
230C42—111no—
231C42—111no—
232C11#310011yescharacteristic, complemented, Sylow
233C23—21no—
234C23—224no—
235C23—222no—
236C23—221no—
237C23—442no—
238C23—442no—
239C23D4×D1111yescharacteristic
240Q8—442no—
241D4—22no—
242D4—42no—
243D4—114no—
244D4—224no—
245D4—222no—
246D4—222no—
247D4—442no—
248D4—442no—
249D4—442no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—114no—
255C2×C4—111no—
256C2×C4—111no—
257C2×C4—111no—
258C2×C4—111no—
259C2×C4—221no—
260C2×C4—444no—
261C2×C4—444no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—441no—
265C2×C4D4×D1111yescharacteristic
266C2×C4C23×D1111yescharacteristic
267C8—22no—
268C8—222no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—224no—
275C22—448no—
276C22—442no—
277C22—442no—
278C22—441no—
279C22—441no—
280C22—441no—
281C22D8×D1112yes—
282C22C2×D4×D1111yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—112no—
287C4—112no—
288C4—221no—
289C4—221no—
290C4—441no—
291C4#41×D1112yes—
292C2—22no—
293C2—81no—
294C2—444no—
295C2—881no—
296C2#1062318711yescharacteristic
297C2C2×D8×D1111yescharacteristic
298C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
hypercenter#480D11
hypocenterC11#3100
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #10623127C2semidirect
2. C2×#66946C2semidirect
3. C11×#480C2semidirect
4. #10622649C2semidirect
5. #10622580C2semidirect
6. #10622503C2semidirect
7. #10622485C2semidirect
8. #10622399C2semidirect
9. #10622369C2semidirect
10. #10622345C2semidirect
11. #10622331C2semidirect
17. #66993C22semidirect
19. D4×Dic11C22semidirect
29. #66946C22semidirect
30. #66941C22semidirect
33. C11×#107C22semidirect
34. C11×#102C22semidirect
38. Dic11⋊C8C22semidirect
39. C8×Dic11C22semidirect
41. #66873C22semidirect
42. #66871C22semidirect
105. C2×Dic11D8semidirect
113. D44#41semidirect
123. #480D11semidirect
176. #107C2×D11semidirect
181. #102C2×D11semidirect
232. C11#3100semidirect

Maximal subgroups

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

subgroupindex
#106231272
C2×#669462
C11×#4802
#106226492
#106225802
#106225032
#106224852
#106223992
#106223692
#106223452
#106223312
#310011