Finite Group Databasebeta

← #13077902

Subgroups — #13077902

Order 1408.

732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×C11×2−1+4C211yesmaximal, characteristic, complemented
2#10623361C211yesmaximal, characteristic, complemented
3C2×#67002C211yesmaximal, characteristic, complemented
4C22×#4325C211yesmaximal, characteristic, complemented
5#10622851C214yesmaximal, complemented
6#10622847C211yesmaximal, characteristic, complemented
7#10622846C211yesmaximal, characteristic, complemented
8#10622840C214yesmaximal, complemented
9#10622838C211yesmaximal, characteristic, complemented
10C11×2−1+4—24no—
11C11×2−1+4—24no—
12C2×C11×#41—22no—
13C2×C11×#41—21no—
14C2×C11×#41C2211yescharacteristic
15C2×C11×#41C2211yescharacteristic
16C2×C11×#41C2212yescomplemented
17C22×Q8×C11—21no—
18C22×Q8×C11C2211yescharacteristic
19C22×Q8×C11C2212yescomplemented
20C22×D44C2211yescharacteristic
21#67002—24no—
22#67000—21no—
23C2×#4325—24no—
24C2×#4325C2214yes—
25C2×#4325C2212yes—
26#66993—21no—
27#66990—22no—
28C2×#4323C2212yes—
29#66983C2214yes—
30#66979C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32C22×C11⋊C8C2211yescharacteristic
33#66899C2214yescomplemented
34#66899C2212yescomplemented
35#66896C2212yescomplemented
36C22⋊(C11⋊C8)C2214yescomplemented
37C23×D11—21no—
38C11×#41—216no—
39C11×#41—28no—
40C11×#41—24no—
41C11×#41—24no—
42C11×#41—22no—
43C11×#41—22no—
44C11×#41—22no—
45C11×#41D414yescomplemented
46C2×Q8×C11—28no—
47C2×Q8×C11—24no—
48C2×Q8×C11—24no—
49C2×Q8×C11—21no—
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11D411yescharacteristic
53C2×Q8×C11D414yescomplemented
54C2×Q8×C11C2312yes—
55C2×Q8×C11C2311yescharacteristic
56C2×D4×C11—21no—
57C2×D4×C11—22no—
58C2×D4×C11D412yes—
59C2×D4×C11D411yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11C2312yes—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—24no—
68C2×D44—21no—
69C2×D44—22no—
70C2×D44—22no—
71C2×D44C2312yes—
72C22⋊Dic11—21no—
73#4325—28no—
74#4325—24no—
75#4323—24no—
76(C2×D11)⋊C4—24no—
77C4⋊Dic11C2312yes—
78C4×Dic11—21no—
79#4318—22no—
80C2×C11⋊C8—22no—
81C2×C11⋊C8C2312yes—
82C2×C11⋊C8C2312yes—
83#3010—111nomaximal, Sylow
84C23×C11—21no—
85C23×C11C2×D412yes—
86C23×C11C2×D411yescharacteristic
87C22×D11—22no—
88C22×D11—42no—
89C22×D11—82no—
90Q8×C11—28no—
91Q8×C11—22no—
92Q8×C11—24no—
93Q8×C11—21no—
94Q8×C11—22no—
95Q8×C11C2×D412yes—
96Q8×C11C2×D414yes—
97D4×C11—28no—
98D4×C11—24no—
99D4×C11—24no—
100D4×C11—22no—
101D4×C11—21no—
102D4×C11C2×D412yes—
103C2×C4×C11—28no—
104C2×C4×C11—28no—
105C2×C4×C11—24no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—24no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11C2×D412yes—
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2×D412yes—
114C2×C4×C11C2×D412yes—
115C2×C4×C11C2411yescharacteristic
116C22⋊D11—84no—
117C2×Dic11—22no—
118D44—22no—
119D44—22no—
120D44—42no—
121C11⋊C8—22no—
122C11⋊C8—22no—
123C2×2−1+4D1111yescharacteristic, complemented
124C2×AGL(1,ℤ/8)—111no—
125C22×SD16—111no—
126#535—111no—
127#449—114no—
128#448—114no—
129#419—111no—
130#416—111no—
131#408—111no—
132C22×C11—22no—
133C22×C11—22no—
134C22×C11—22no—
135C22×C11—24no—
136C22×C11—42no—
137C22×C11#12012yes—
138C22×C11C22×D411yescharacteristic
139C2×D11—42no—
140C2×D11—44no—
141C2×D11—84no—
142C4×C11—24no—
143C4×C11—22no—
144C4×C11—22no—
145C4×C11#12012yes—
146C4×C11C22×D411yescharacteristic
147C4×C11C22×D411yescharacteristic
148Dic11—42no—
1492−1+4—24no—
1502−1+4—24no—
151C2×#41—22no—
152C2×#41—21no—
153C2×#41C2×D1111yescharacteristic
154C2×#41C2×D1111yescharacteristic
155C2×#41C2×D1112yescomplemented
156C22×Q8—21no—
157C22×Q8C2×D1111yescharacteristic
158C22×Q8C2×D1112yescomplemented
159C22×D4—111no—
160AGL(1,ℤ/8)—224no—
161C2×SD16—114no—
162C2×SD16—112no—
163C2×SD16—224no—
164C2×D8—112no—
165C2×M16—111no—
166C22×C8—111no—
167#127—221no—
168#124—221no—
169#121—114no—
170#120—222no—
171#117—111no—
172#103—112no—
173#103—114no—
174#102—112no—
175C22⋊C8—114no—
176C2×C11—22no—
177C2×C11—42no—
178C2×C11—42no—
179C2×C11C2×#12011yescharacteristic
180C2×C11#57712yes—
181D11—82no—
182C24—221no—
183#41—216no—
184#41—28no—
185#41—24no—
186#41—24no—
187#41—22no—
188#41—22no—
189#41—22no—
190#41C22⋊D1114yescomplemented
191C2×Q8—28no—
192C2×Q8—24no—
193C2×Q8—24no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8C22⋊D1111yescharacteristic
198C2×Q8C22⋊D1114yescomplemented
199C2×Q8C22×D1112yes—
200C2×Q8C22×D1111yescharacteristic
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—112no—
204C2×D4—224no—
205C2×D4—222no—
206C2×D4—222no—
207C2×D4—221no—
208C2×D4C22⋊D1112yes—
209C2×D4C22⋊D1111yescharacteristic
210C2×D4C22×D1111yescharacteristic
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4C22×D1112yes—
216C22×C4C22×D1111yescharacteristic
217SD16—228no—
218SD16—224no—
219D8—224no—
220M16—222no—
221C2×C8—112no—
222C2×C8—112no—
223C2×C8—222no—
224C4⋊C4—112no—
225C22⋊C4—221no—
226C22⋊C4—224no—
227C42—221no—
228C11#301011yescharacteristic, complemented, Sylow
229C23—21no—
230C23—222no—
231C23—442no—
232C23—882no—
233C23C2×C22⋊D1112yes—
234C23C2×C22⋊D1111yescharacteristic
235Q8—28no—
236Q8—22no—
237Q8—24no—
238Q8—21no—
239Q8—22no—
240Q8C2×C22⋊D1112yes—
241Q8C2×C22⋊D1114yes—
242D4—28no—
243D4—24no—
244D4—24no—
245D4—22no—
246D4—21no—
247D4—222no—
248D4—222no—
249D4—442no—
250D4—884no—
251D4C2×C22⋊D1112yes—
252C2×C4—28no—
253C2×C4—28no—
254C2×C4—24no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—24no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—222no—
261C2×C4C2×C22⋊D1112yes—
262C2×C4C2×C22⋊D1111yescharacteristic
263C2×C4C2×C22⋊D1112yes—
264C2×C4C2×C22⋊D1112yes—
265C2×C4C23×D1111yescharacteristic
266C8—222no—
267C8—222no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—22no—
272C22—42no—
273C22—444no—
274C22—442no—
275C22—884no—
276C22#6700612yes—
277C22C22×C22⋊D1111yescharacteristic
278C4—24no—
279C4—22no—
280C4—22no—
281C4—442no—
282C4#6700612yes—
283C4C22×C22⋊D1111yescharacteristic
284C4C22×C22⋊D1111yescharacteristic
285C2—22no—
286C2—42no—
287C2—42no—
288C2—882no—
289C2#1062336812yes—
290C2C2×#6700611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×2−1+4C2
socleC22×C11C22×D4
hypercenterC2×2−1+4D11
hypocenterC11#3010
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C11×2−1+4C2semidirect
2. #10623361C2semidirect
3. C2×#67002C2semidirect
4. C22×#4325C2semidirect
5. #10622851C2semidirect
6. #10622847C2semidirect
7. #10622846C2semidirect
8. #10622840C2semidirect
9. #10622838C2semidirect
16. C2×C11×#41C22semidirect
19. C22×Q8×C11C22semidirect
33. #66899C22semidirect
34. #66899C22semidirect
35. #66896C22semidirect
36. C22⋊(C11⋊C8)C22semidirect
45. C11×#41D4semidirect
53. C2×Q8×C11D4semidirect
123. C2×2−1+4D11semidirect
155. C2×#41C2×D11semidirect
158. C22×Q8C2×D11semidirect
190. #41C22⋊D11semidirect
198. C2×Q8C22⋊D11semidirect
228. C11#3010semidirect

Maximal subgroups

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

subgroupindex
C2×C11×2−1+42
#106233612
C2×#670022
C22×#43252
#106228512
#106228472
#106228462
#106228402
#106228382
#301011