Finite Group Databasebeta

← #13079770

Subgroups — #13079770

Order 1408.

326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623259C211yesmaximal, characteristic
2#10623259C211yesmaximal, characteristic
3C11×#487C211yesmaximal, characteristic, complemented
4#10622694C211yesmaximal, characteristic, complemented
5#10622691C211yesmaximal, characteristic, complemented
6#10622428C214yesmaximal
7#10622412C214yesmaximal, complemented
8#10622298C211yesmaximal, characteristic
9#10622293C211yesmaximal, characteristic, complemented
10C11×C4⋊Q8C2211yescharacteristic
11C11×C4⋊Q8C2211yescharacteristic
12#66999—21no—
13#66999C2212yes—
14Q8×Dic11—21no—
15Q8×Dic11C2212yes—
16#66950—21no—
17#66950—21no—
18#66945—21no—
19#66945C2212yes—
20#66943—21no—
21#66943C2212yes—
22#66940—21no—
23#66940—21no—
24C42×D11C2211yescharacteristic
25#66922C2211yescharacteristic
26#66922C2211yescharacteristic
27C11×#103C2214yes—
28C4×C8×C11C2211yescharacteristic
29#66899C2214yes—
30(C2×D11)⋊C8C2212yes—
31#66881C2214yes—
32Dic11⋊C8C2212yes—
33#66871C2214yes—
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11C2312yes—
37C2×C4×D11D411yescharacteristic
38C2×C4×D11D411yescharacteristic
39C2×C4×D11C2311yescharacteristic
40C2×Dic22—21no—
41C2×Dic22—21no—
42C2×C8×C11C2312yes—
43C11×C4⋊C4—21no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4C2312yes—
47C42×C11C2311yescharacteristic
48(C2×D11)⋊C4—22no—
49(C2×D11)⋊C4—22no—
50C4⋊Dic11—22no—
51C4⋊Dic11—22no—
52C4⋊Dic11—21no—
53C4⋊Dic11—21no—
54C4⋊Dic11C2312yes—
55C4⋊Dic11C2312yes—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58C4×Dic11—22no—
59C4×Dic11—22no—
60C4×Dic11D411yescharacteristic
61C4×Dic11D411yescharacteristic
62C4×Dic11C2311yescharacteristic
63C2×C11⋊C8C2312yes—
64#3231—111nomaximal, Sylow
65C22×D11C2×D411yescharacteristic
66Q8×C11—24no—
67Q8×C11—42no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2411yescharacteristic
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11C2×D411yescharacteristic
76C2×Dic11C2×D411yescharacteristic
77C2×Dic11C2×D411yescharacteristic
78C4×D11—22no—
79C4×D11—22no—
80C4×D11—22no—
81Dic22—42no—
82Dic22—42no—
83C8×C11—22no—
84C11⋊C8—22no—
85#533—111no—
86#533—111no—
87#500—111no—
88#498—111no—
89#487—111no—
90#487D1111yescharacteristic, complemented
91#485—114no—
92#479—114no—
93#431—111no—
94C22×C11C22×D411yescharacteristic
95C2×D11—21no—
96C2×D11—21no—
97C2×D11—21no—
98C4×C11—42no—
99C4×C11—42no—
100C4×C11#13512yes—
101C4×C11#13712yes—
102C4×C112−1+412yes—
103Dic11—21no—
104Dic11—21no—
105Dic11—21no—
106Dic11—42no—
107Dic11—42no—
108C4⋊Q8—111no—
109C4⋊Q8—111no—
110C4⋊Q8C2×D1111yescharacteristic
111C4⋊Q8C2×D1111yescharacteristic
112#125—112no—
113#125—221no—
114C22⋊Q8—112no—
115C22⋊Q8—221no—
116C22⋊Q8—221no—
117C22⋊Q8—221no—
118C4×Q8—112no—
119C4×Q8—221no—
120C4×Q8—221no—
121C4×Q8—221no—
122#117—112no—
123#117—221no—
124C2×C42—111no—
125#107—114no—
126#106—114no—
127C4⋊C8—112no—
128#103—114no—
129#103C2×D1114yes—
130C22⋊C8—112no—
131C4×C8—111no—
132C4×C8C2×D1111yescharacteristic
133C2×C11#53611yescharacteristic
134C2×C11C2×#13511yescharacteristic
135C2×C11C2×#13711yescharacteristic
136D11—41no—
137C2×Q8—21no—
138C2×Q8—221no—
139C2×Q8—221no—
140C2×Q8C22×D1112yes—
141C22×C4—111no—
142C22×C4—111no—
143C22×C4—111no—
144C2×C8—112no—
145C2×C8C22×D1112yes—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—112no—
150C4⋊C4—112no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—222no—
154C4⋊C4—222no—
155C4⋊C4—221no—
156C4⋊C4—221no—
157C4⋊C4C22×D1112yes—
158C22⋊C4—222no—
159C22⋊C4—222no—
160C42—111no—
161C42—111no—
162C42—111no—
163C42—222no—
164C42—222no—
165C42C22×D1111yescharacteristic
166C11#323111yescharacteristic, complemented, Sylow
167C23—111no—
168Q8—24no—
169Q8—42no—
170Q8—442no—
171Q8—442no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—111no—
175C2×C4—111no—
176C2×C4—111no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4D4×D1111yescharacteristic
183C2×C4D4×D1111yescharacteristic
184C2×C4C23×D1111yescharacteristic
185C8—22no—
186C8—222no—
187C22—221no—
188C22—221no—
189C22—221no—
190C22C2×D4×D1111yescharacteristic
191C4—42no—
192C4—42no—
193C4—221no—
194C4—221no—
195C4—221no—
196C4—442no—
197C4—442no—
198C4#6696912yes—
199C4#6697112yes—
200C4#6704312yes—
201C2—441no—
202C2#1062320611yescharacteristic
203C2C2×#6696911yescharacteristic
204C2C2×#6697111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#487D11
hypocenterC11#3231
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C11×#487C2semidirect
4. #10622694C2semidirect
5. #10622691C2semidirect
7. #10622412C2semidirect
9. #10622293C2semidirect
90. #487D11semidirect
166. C11#3231semidirect

Maximal subgroups

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

subgroupindex
#106232592
C11×#4872
#106226942
#106226912
#106224282
#106224122
#106222982
#106222932
#323111