Finite Group Databasebeta

← #13078611

Subgroups — #13078611

Order 1408.

492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×D4×Dic11C211yesmaximal, characteristic, complemented
2#10623127C211yesmaximal, characteristic, complemented
3C11×#447C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622763C212yesmaximal, complemented
6D8×Dic11C212yesmaximal, complemented
7#10622646C211yesmaximal, characteristic, complemented
8#10622372C212yesmaximal, complemented
9#10622369C212yesmaximal, complemented
10#10622349C211yesmaximal, characteristic, complemented
11#10622331C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×Dic11—21no—
14C2×#4341—21no—
15C2×C11×D8C2212yes—
16C11×#121C2211yescharacteristic
17C2×C22⋊Dic11—21no—
18#66993C2211yescharacteristic, complemented
19#66992—21no—
20D4×Dic11—21no—
21D4×Dic11—21no—
22D4×Dic11C2212yes—
23D4×Dic11C2212yes—
24D4×Dic11C2211yescharacteristic, complemented
25C2×#4323C2212yes—
26#66983C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29#66946C2211yescharacteristic, complemented
30#66941C2211yescharacteristic, complemented
31#66938—21no—
32(C22⋊D11)⋊C4—21no—
33C11×#102C2212yes—
34C11×C22⋊C8C2211yescharacteristic
35#66896C2212yes—
36#66896C2212yescomplemented
37C22⋊(C11⋊C8)C2211yescharacteristic
38#66885C2212yescomplemented
39#66882C2212yescomplemented
40Dic11⋊C8C2212yescomplemented
41C8×Dic11C2212yescomplemented
42#66871C2212yescomplemented
43C24×C11—21no—
44C2×D4×C11—24no—
45C2×D4×C11—21no—
46C2×D4×C11—21no—
47C2×D4×C11C2311yescharacteristic
48C2×D4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—21no—
51C2×C22⋊D11—21no—
52C2×C22⋊D11—21no—
53C22×Dic11—21no—
54C22×Dic11—22no—
55C22×Dic11—22no—
56C22×Dic11—21no—
57C22×Dic11—44no—
58C22×Dic11D411yescharacteristic
59C22×Dic11D411yescharacteristic
60#4341—44no—
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×Dic22—21no—
64C11×D8—24no—
65C2×C8×C11C2312yes—
66C11×C4⋊C4C2311yescharacteristic
67C11×C22⋊C4—21no—
68C22⋊Dic11—21no—
69C22⋊Dic11—22no—
70C22⋊Dic11—22no—
71#4323—24no—
72(C2×D11)⋊C4—21no—
73(C2×D11)⋊C4—21no—
74C4⋊Dic11—21no—
75C4⋊Dic11C2312yes—
76C4⋊Dic11C2311yescharacteristic
77Dic11⋊C4—21no—
78C4×Dic11D411yescharacteristic
79C4×Dic11D411yescharacteristic
80C4×Dic11C2311yescharacteristic
81C4×Dic11C2311yescharacteristic
82C2×C11⋊C8C2312yes—
83#3100—111nomaximal, Sylow
84C23×C11—24no—
85C23×C11—22no—
86C23×C11—21no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11C2×D411yescharacteristic
90C22×D11—21no—
91D4×C11—24no—
92D4×C11—22no—
93D4×C11—22no—
94D4×C11—42no—
95D4×C11#4114yescomplemented
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C22⋊D11—42no—
101C22⋊D11—42no—
102C22⋊D11—42no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—44no—
109C2×Dic11—44no—
110C2×Dic11D814yescomplemented
111C2×Dic11C2×D411yescharacteristic
112C2×Dic11C2×D411yescharacteristic
113C2×Dic11C2×D411yescharacteristic
114C2×Dic11C2×D411yescharacteristic
115D44—22no—
116C4×D11—42no—
117Dic22—42no—
118C8×C11—22no—
119C11⋊C8—22no—
120#532—111no—
121C2×C4×D4—111no—
122#480—111no—
123#480—111no—
124#474—112no—
125#459—112no—
126#447—111no—
127#447D1111yescharacteristic, complemented
128C4×D8—112no—
129C4×D8—112no—
130#431—111no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—24no—
134C22×C11—48no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11C2×D812yes—
141C22×C11C22×D411yescharacteristic
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—41no—
145C4×C11—21no—
146C4×C11—41no—
147C4×C11C2×#4112yes—
148Dic11—21no—
149Dic11—21no—
150Dic11—41no—
151Dic11—42no—
152Dic11C2×D812yes—
153Dic11C2×D812yes—
154C2×#41—221no—
155C22×D4C2×D1111yescharacteristic
156C23×C4—221no—
157C2×D8—112no—
158C2×D8C2×D1112yes—
159C4⋊Q8—111no—
160#127—111no—
161#124—221no—
162#121—111no—
163#121—221no—
164#121C2×D1111yescharacteristic
165C4×D4—112no—
166C4×D4—112no—
167C4×D4—111no—
168C4×D4—111no—
169C4×D4—221no—
170C4×D4—221no—
171C4×D4—221no—
172C2×C4⋊C4—111no—
173C2×C22⋊C4—221no—
174C2×C42—111no—
175#107—112no—
176#107—112no—
177C4⋊C8—112no—
178#102—112no—
179#102—112no—
180#102—112no—
181#102C2×D1112yes—
182C22⋊C8—111no—
183C22⋊C8C2×D1111yescharacteristic
184C4×C8—112no—
185C2×C11—22no—
186C2×C11—44no—
187C2×C11—81no—
188C2×C11#52511yescharacteristic
189C2×C11C22×D811yescharacteristic
190C2×C11#57511yescharacteristic
191D11—81no—
192C24—21no—
193#41—444no—
194C2×Q8—221no—
195C2×D4—24no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—111no—
199C2×D4—221no—
200C2×D4—221no—
201C2×D4—221no—
202C2×D4C22×D1111yescharacteristic
203C2×D4C22×D1112yes—
204C22×C4—111no—
205C22×C4—111no—
206C22×C4—221no—
207C22×C4—222no—
208C22×C4—222no—
209C22×C4—221no—
210C22×C4—221no—
211C22×C4—444no—
212C22×C4C22×D1111yescharacteristic
213D8—24no—
214D8—224no—
215C2×C8—112no—
216C2×C8C22×D1112yes—
217C4⋊C4—112no—
218C4⋊C4—111no—
219C4⋊C4—221no—
220C4⋊C4—221no—
221C4⋊C4C22×D1111yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—221no—
224C22⋊C4—222no—
225C22⋊C4—222no—
226C22⋊C4—221no—
227C22⋊C4—221no—
228C42—111no—
229C42—111no—
230C42—111no—
231C42—111no—
232C11#310011yescharacteristic, complemented, Sylow
233C23—24no—
234C23—22no—
235C23—21no—
236C23—42no—
237C23—42no—
238C23—221no—
239C23D4×D1111yescharacteristic
240Q8—442no—
241D4—24no—
242D4—22no—
243D4—22no—
244D4—42no—
245D4—222no—
246D4—442no—
247D4—442no—
248D4—442no—
249D4#434114yescomplemented
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—114no—
253C2×C4—111no—
254C2×C4—111no—
255C2×C4—111no—
256C2×C4—111no—
257C2×C4—222no—
258C2×C4—221no—
259C2×C4—442no—
260C2×C4—444no—
261C2×C4—444no—
262C2×C4—442no—
263C2×C4—441no—
264C2×C4—442no—
265C2×C4D4×D1111yescharacteristic
266C2×C4C23×D1111yescharacteristic
267C8—22no—
268C8—222no—
269C22—21no—
270C22—21no—
271C22—24no—
272C22—48no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—441no—
279C22—441no—
280C22—441no—
281C22D8×D1112yes—
282C22C2×D4×D1111yescharacteristic
283C4—21no—
284C4—41no—
285C4—112no—
286C4—112no—
287C4—221no—
288C4—221no—
289C4—442no—
290C4—441no—
291C4C2×#434112yes—
292C2—22no—
293C2—44no—
294C2—81no—
295C2—881no—
296C2#1062311711yescharacteristic
297C2C2×D8×D1111yescharacteristic
298C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#447C2
socleC22×C11C22×D4
hypercenter#447D11
hypocenterC11#3100
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic11C2semidirect
2. #10623127C2semidirect
3. C11×#447C2semidirect
4. #10622830C2semidirect
5. #10622763C2semidirect
6. D8×Dic11C2semidirect
7. #10622646C2semidirect
8. #10622372C2semidirect
9. #10622369C2semidirect
10. #10622349C2semidirect
11. #10622331C2semidirect
18. #66993C22semidirect
24. D4×Dic11C22semidirect
29. #66946C22semidirect
30. #66941C22semidirect
36. #66896C22semidirect
38. #66885C22semidirect
39. #66882C22semidirect
40. Dic11⋊C8C22semidirect
41. C8×Dic11C22semidirect
42. #66871C22semidirect
95. D4×C11#41semidirect
110. C2×Dic11D8semidirect
127. #447D11semidirect
232. C11#3100semidirect
249. D4#4341semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
#106231272
C11×#4472
#106228302
#106227632
D8×Dic112
#106226462
#106223722
#106223692
#106223492
#106223312
#310011