Finite Group Databasebeta

← #13078261

Subgroups — #13078261

Order 1408.

524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#535C211yesmaximal, characteristic, complemented
2#10623361C211yesmaximal, characteristic, complemented
3C2×#67001C211yesmaximal, characteristic, complemented
4C22×#4323C211yesmaximal, characteristic, complemented
5#10622828C211yesmaximal, characteristic, complemented
6#10622652C214yesmaximal, complemented
7#10622651C214yesmaximal, complemented
8#10622614C211yesmaximal, characteristic, complemented
9#10622611C211yesmaximal, characteristic, complemented
10C2×C11×#41C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C22×D44C2211yescharacteristic
13C11×#127—21no—
14C11×#124—21no—
15C11×#121C2214yescomplemented
16C11×#120—22no—
17C11×#117C2211yescharacteristic
18#67001—24no—
19#67000—21no—
20#66993—21no—
21#66990—22no—
22C2×#4323—24no—
23C2×#4323C2212yes—
24C2×#4323C2212yes—
25#66983C2214yescomplemented
26#66979C2211yescharacteristic
27C2×#4318C2211yescharacteristic
28C2×#4318C2212yescomplemented
29C22×C11⋊C8C2211yescharacteristic
30C22×C11⋊C8C2212yescomplemented
31#66896C2214yescomplemented
32#66873C2214yescomplemented
33#66872C2212yescomplemented
34#66871C2212yescomplemented
35C24×C11—21no—
36C23×D11—21no—
37C11×#41—22no—
38C11×#41—22no—
39C2×Q8×C11D411yescharacteristic
40C2×D4×C11—24no—
41C2×D4×C11—22no—
42C2×D4×C11—21no—
43C2×D4×C11—22no—
44C2×D4×C11D412yes—
45C2×D4×C11D411yescharacteristic
46C2×D4×C11C2312yes—
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C2×C22⋊D11—24no—
50C2×D44—21no—
51C2×D44—22no—
52C2×D44—22no—
53C2×D44C2312yes—
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—21no—
56C11×C22⋊C4—24no—
57C42×C11—21no—
58C22⋊Dic11—21no—
59#4323—24no—
60#4323—24no—
61(C2×D11)⋊C4—24no—
62C4⋊Dic11C2312yes—
63C4×Dic11—21no—
64#4318—24no—
65#4318—22no—
66C2×C11⋊C8—24no—
67C2×C11⋊C8D414yescomplemented
68C2×C11⋊C8C2312yes—
69C2×C11⋊C8C2311yescharacteristic
70C2×C11⋊C8C2311yescharacteristic
71#3058—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—42no—
74C23×C11—82no—
75C23×C11C2×D412yes—
76C23×C11C2×D411yescharacteristic
77C22×D11—22no—
78C22×D11—42no—
79C22×D11—82no—
80Q8×C11—22no—
81D4×C11—24no—
82D4×C11—22no—
83D4×C11—22no—
84D4×C11—22no—
85D4×C11—42no—
86D4×C11—84no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11#4112yes—
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—84no—
96C2×Dic11—22no—
97D44—22no—
98D44—22no—
99D44—42no—
100C11⋊C8—22no—
101C11⋊C8C2×D412yes—
102C11⋊C8C2×D412yes—
103C22×D8—111no—
104C2×#131—111no—
105#535—111no—
106#535D1111yescharacteristic, complemented
107#469—114no—
108#466—114no—
109#427—111no—
110#418—111no—
111#418—111no—
112C22×C11—22no—
113C22×C11—22no—
114C22×C11—24no—
115C22×C11—42no—
116C22×C11—44no—
117C22×C11—84no—
118C22×C11#12112yes—
119C22×C11C22×D411yescharacteristic
120C2×D11—42no—
121C2×D11—44no—
122C2×D11—84no—
123C4×C11—22no—
124C4×C11—42no—
125C4×C11#12112yes—
126C4×C11C22×D411yescharacteristic
127C4×C11C2×#4111yescharacteristic
128Dic11—42no—
129C2×#41C2×D1111yescharacteristic
130C22×D4—111no—
131C22×D4C2×D1111yescharacteristic
132C2×D8—112no—
133C2×D8—112no—
134C2×D8—224no—
135#131—224no—
136C2×M16—111no—
137C2×M16—112no—
138C22×C8—111no—
139C22×C8—112no—
140#127—21no—
141#127—221no—
142#124—21no—
143#124—221no—
144#121—114no—
145#121C2×D1114yescomplemented
146#120—22no—
147#120—222no—
148#117—111no—
149#117C2×D1111yescharacteristic
150#107—112no—
151#106—112no—
152#102—114no—
153#102—114no—
154C2×C11—22no—
155C2×C11—42no—
156C2×C11—82no—
157C2×C11C2×#12111yescharacteristic
158C2×C11#57612yes—
159D11—82no—
160C24—21no—
161C24—221no—
162#41—22no—
163#41—22no—
164C2×Q8C22⋊D1111yescharacteristic
165C2×D4—24no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—21no—
169C2×D4—112no—
170C2×D4—224no—
171C2×D4—222no—
172C2×D4—222no—
173C2×D4—221no—
174C2×D4C22⋊D1112yes—
175C2×D4C22⋊D1111yescharacteristic
176C2×D4C22×D1112yes—
177C22×C4C22×D1112yes—
178C22×C4C22×D1111yescharacteristic
179D8—224no—
180D8—224no—
181M16—224no—
182M16—222no—
183C2×C8—114no—
184C2×C8—111no—
185C2×C8—111no—
186C2×C8—112no—
187C2×C8—224no—
188C4⋊C4—112no—
189C4⋊C4C22×D1112yes—
190C22⋊C4—21no—
191C22⋊C4—24no—
192C22⋊C4—221no—
193C22⋊C4—224no—
194C42—21no—
195C42—221no—
196C11#305811yescharacteristic, complemented, Sylow
197C23—22no—
198C23—42no—
199C23—82no—
200C23—222no—
201C23—442no—
202C23—882no—
203C23C2×C22⋊D1112yes—
204C23C2×C22⋊D1111yescharacteristic
205Q8—22no—
206D4—24no—
207D4—22no—
208D4—22no—
209D4—22no—
210D4—42no—
211D4—84no—
212D4—222no—
213D4—222no—
214D4—442no—
215D4—884no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—222no—
220C2×C4D4×D1112yes—
221C2×C4#434112yes—
222C2×C4C2×C22⋊D1112yes—
223C2×C4C2×C22⋊D1111yescharacteristic
224C2×C4C23×D1111yescharacteristic
225C8—112no—
226C8—112no—
227C8—222no—
228C22—22no—
229C22—22no—
230C22—24no—
231C22—42no—
232C22—44no—
233C22—84no—
234C22—442no—
235C22—444no—
236C22—884no—
237C22#6699212yes—
238C22C22×C22⋊D1111yescharacteristic
239C4—22no—
240C4—42no—
241C4—442no—
242C4#6699212yes—
243C4C2×D4×D1111yescharacteristic
244C4C2×#434111yescharacteristic
245C2—22no—
246C2—42no—
247C2—82no—
248C2—882no—
249C2C2×#6699211yescharacteristic
250C2#1062336612yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3058
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C11×#535C2semidirect
2. #10623361C2semidirect
3. C2×#67001C2semidirect
4. C22×#4323C2semidirect
5. #10622828C2semidirect
6. #10622652C2semidirect
7. #10622651C2semidirect
8. #10622614C2semidirect
9. #10622611C2semidirect
15. C11×#121C22semidirect
25. #66983C22semidirect
28. C2×#4318C22semidirect
30. C22×C11⋊C8C22semidirect
31. #66896C22semidirect
32. #66873C22semidirect
33. #66872C22semidirect
34. #66871C22semidirect
67. C2×C11⋊C8D4semidirect
106. #535D11semidirect
145. #121C2×D11semidirect
196. C11#3058semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106233612
C2×#670012
C22×#43232
#106228282
#106226522
#106226512
#106226142
#106226112
#305811