Finite Group Databasebeta

← #13078221

Subgroups — #13078221

Order 1408.

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

normal subgroups only

This group has 500 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
1C2×C11×#135C211yesmaximal, characteristic, complemented
2#10623359C212yesmaximal, complemented
3C22×#4313C211yesmaximal, characteristic, complemented
4#10622846C212yesmaximal, complemented
5#10622802C212yesmaximal, complemented
6#10622787C214yesmaximal, complemented
7#10622772C212yesmaximal, complemented
8#10622719C211yesmaximal, characteristic, complemented
9C2×C11×#41C2212yes—
10C22×C4×D11C2211yescharacteristic
11C11×#135—24no—
12C2×C11×Q16C2211yescharacteristic, complemented
13C2×C11×SD16C2212yescomplemented
14C2×C11×D8C2211yescharacteristic, complemented
15C22×C8×C11C2211yescharacteristic
16#66999C2214yes—
17#66991C2214yes—
18#66990—22no—
19#66988—22no—
20C4×C22⋊D11—24no—
21#66979C2212yes—
22C22×C11⋊C8C2211yescharacteristic
23C2×#4313—24no—
24C2×#4313C2212yes—
25C2×#4313C2212yes—
26#66899C2214yescomplemented
27#66896C2214yescomplemented
28#66882C2212yescomplemented
29#66881C2212yescomplemented
30C23×D11D411yescharacteristic
31C11×#41—24no—
32C11×#41—24no—
33C2×Q8×C11C2312yes—
34C2×D4×C11—22no—
35C2×D4×C11C2312yes—
36C22×C4×C11—22no—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—24no—
39C22×Dic11D411yescharacteristic
40C2×C4×D11—22no—
41C2×C4×D11—22no—
42C2×C4×D11D412yes—
43C2×C4×D11C2312yes—
44C11×Q16—22no—
45C11×SD16—24no—
46C11×D8—22no—
47C2×C8×C11D414yescomplemented
48C2×C8×C11C2311yescharacteristic
49C2×C8×C11C2311yescharacteristic
50C22⋊Dic11—24no—
51C22⋊Dic11—22no—
52(C2×D11)⋊C4—24no—
53C4⋊Dic11C2314yes—
54Dic11⋊C4—24no—
55C4×Dic11—22no—
56C2×C11⋊C8—22no—
57C2×C11⋊C8C2312yes—
58#4313—24no—
59#4313—24no—
60#3054—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11C2×D411yescharacteristic
63C22×D11—22no—
64C22×D11—42no—
65C22×D11C2×D412yes—
66Q8×C11—22no—
67Q8×C11—22no—
68D4×C11—22no—
69D4×C11—22no—
70D4×C11—44no—
71C2×C4×C11—22no—
72C2×C4×C11—44no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D412yes—
75C2×C4×C11#4112yes—
76C2×C4×C11C2411yescharacteristic
77C22⋊D11—48no—
78C2×Dic11—22no—
79C2×Dic11—24no—
80C2×Dic11C2×D412yes—
81C4×D11—24no—
82C4×D11—22no—
83C4×D11—22no—
84C8×C11C2×D412yes—
85C8×C11C2×D412yes—
86C11⋊C8—22no—
87C2×#135D1111yescharacteristic, complemented
88C22×M16—111no—
89#525—112no—
90#470—112no—
91#469—112no—
92#468—114no—
93#427—111no—
94#416—112no—
95C22×C11—22no—
96C22×C11—42no—
97C22×C11—44no—
98C22×C11#12112yes—
99C22×C11C22×D411yescharacteristic
100C2×D11—22no—
101C2×D11—24no—
102C2×D11—44no—
103C4×C11—42no—
104C4×C11#12112yes—
105C4×C11C22×D411yescharacteristic
106C4×C11C2×#4111yescharacteristic
107Dic11—22no—
108Dic11—44no—
109C2×#41C2×D1112yes—
110C23×C4—111no—
111#135—24no—
112C2×Q16C2×D1111yescharacteristic, complemented
113C2×SD16C2×D1112yescomplemented
114C2×D8C2×D1111yescharacteristic, complemented
115C2×M16—112no—
116C2×M16—112no—
117C2×M16—224no—
118C22×C8—111no—
119C22×C8C2×D1111yescharacteristic
120#123—222no—
121C22⋊Q8—114no—
122#121—114no—
123#120—222no—
124C4×D4—224no—
125#117—112no—
126#107—112no—
127#106—112no—
128#103—114no—
129#102—114no—
130C2×C11—22no—
131C2×C11—82no—
132C2×C11C2×#12111yescharacteristic
133C2×C11#57512yes—
134D11—42no—
135C24—111no—
136#41—24no—
137#41—24no—
138C2×Q8C22×D1112yes—
139C2×D4—22no—
140C2×D4—224no—
141C2×D4C22×D1112yes—
142C22×C4—22no—
143C22×C4—111no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—222no—
147C22×C4—222no—
148C22×C4C22×D1111yescharacteristic
149Q16—22no—
150SD16—24no—
151D8—22no—
152M16—224no—
153M16—224no—
154C2×C8—112no—
155C2×C8—222no—
156C2×C8C22⋊D1114yescomplemented
157C2×C8C22×D1111yescharacteristic
158C2×C8C22×D1111yescharacteristic
159C4⋊C4—114no—
160C4⋊C4—224no—
161C22⋊C4—224no—
162C22⋊C4—224no—
163C22⋊C4—222no—
164C42—222no—
165C11#305411yescharacteristic, complemented, Sylow
166C23—22no—
167C23—112no—
168C23—222no—
169C23—442no—
170C23D4×D1111yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—448no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—112no—
180C2×C4—222no—
181C2×C4—224no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—224no—
185C2×C4D4×D1111yescharacteristic
186C2×C4#434112yes—
187C2×C4C2×C22⋊D1112yes—
188C2×C4C23×D1111yescharacteristic
189C8—222no—
190C8C2×C22⋊D1112yes—
191C8C2×C22⋊D1112yes—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—224no—
196C22—222no—
197C22—444no—
198C22#6699112yes—
199C22C2×D4×D1111yescharacteristic
200C4—42no—
201C4—222no—
202C4—444no—
203C4#6699112yes—
204C4C2×#434111yescharacteristic
205C4C22×C22⋊D1111yescharacteristic
206C2—22no—
207C2—82no—
208C2—442no—
209C2#1062329912yes—
210C2C2×#6699111yescharacteristic
subgroupG/H
centerC2×C4D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#135C2
socleC22×C11C22×D4
hypercenterC2×#135D11
hypocenterC11#3054
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C11×#135C2semidirect
2. #10623359C2semidirect
3. C22×#4313C2semidirect
4. #10622846C2semidirect
5. #10622802C2semidirect
6. #10622787C2semidirect
7. #10622772C2semidirect
8. #10622719C2semidirect
12. C2×C11×Q16C22semidirect
13. C2×C11×SD16C22semidirect
14. C2×C11×D8C22semidirect
26. #66899C22semidirect
27. #66896C22semidirect
28. #66882C22semidirect
29. #66881C22semidirect
47. C2×C8×C11D4semidirect
87. C2×#135D11semidirect
112. C2×Q16C2×D11semidirect
113. C2×SD16C2×D11semidirect
114. C2×D8C2×D11semidirect
156. C2×C8C22⋊D11semidirect
165. C11#3054semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1352
#106233592
C22×#43132
#106228462
#106228022
#106227872
#106227722
#106227192
#305411