Finite Group Databasebeta

← #13079775

Subgroups — #13079775

Order 1408.

326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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×#533C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic
3#10622706C211yesmaximal, characteristic, complemented
4#10622706C211yesmaximal, characteristic, complemented
5#10622692C211yesmaximal, characteristic, complemented
6#10622691C211yesmaximal, characteristic, complemented
7#10622676C214yesmaximal, complemented
8#10622609C214yesmaximal
9#10622538C211yesmaximal, characteristic
10C11×C4⋊Q8C2211yescharacteristic
11C11×C4⋊Q8C2211yescharacteristic
12C11×#125C2212yes—
13C11×C22⋊Q8—21no—
14C11×C22⋊Q8—21no—
15C4×Q8×C11—21no—
16C4×Q8×C11—21no—
17C11×#117C2212yes—
18C2×C42×C11C2211yescharacteristic
19#66979—21no—
20#66977—21no—
21#66977C2212yes—
22#66923—21no—
23#66922C2211yescharacteristic
24#66922C2211yescharacteristic
25C4×Dic22—21no—
26C4×Dic22C2212yes—
27C22⋊(C11⋊C8)C2212yes—
28#66874C2214yes—
29#66874C2214yes—
30#66872C2214yes—
31#66871C2214yes—
32C4⋊(C11⋊C8)C2212yes—
33C4×C11⋊C8C2211yescharacteristic
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11—21no—
37C22×C4×C11D411yescharacteristic
38C22×C4×C11D411yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C2×Dic22—21no—
41C2×Dic22C2312yes—
42C11×C4⋊C4—22no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4C2312yes—
47C11×C4⋊C4C2312yes—
48C11×C22⋊C4—22no—
49C42×C11—22no—
50C42×C11D411yescharacteristic
51C42×C11D411yescharacteristic
52C42×C11C2311yescharacteristic
53C42×C11C2311yescharacteristic
54C22⋊Dic11—22no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61C4×Dic11—22no—
62C2×C11⋊C8C2312yes—
63C2×C11⋊C8C2312yes—
64#3231—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66Q8×C11—42no—
67Q8×C11—42no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2411yescharacteristic
79C2×Dic11—22no—
80C2×Dic11—22no—
81Dic22—24no—
82Dic22—42no—
83C11⋊C8—22no—
84C11⋊C8—22no—
85#533—111no—
86#533D1111yescharacteristic
87#500—111no—
88#498—111no—
89#487—111no—
90#487—111no—
91#485—114no—
92#479—114no—
93#431—111no—
94C22×C11—21no—
95C22×C11—21no—
96C22×C11—21no—
97C22×C11C22×D411yescharacteristic
98C4×C11—21no—
99C4×C11—21no—
100C4×C11—21no—
101C4×C11—42no—
102C4×C11—42no—
103C4×C11#13512yes—
104C4×C11#13712yes—
105C4×C112−1+412yes—
106Dic11—42no—
107Dic11—42no—
108C4⋊Q8—111no—
109C4⋊Q8—111no—
110C4⋊Q8C2×D1111yescharacteristic
111C4⋊Q8C2×D1111yescharacteristic
112#125—221no—
113#125C2×D1112yes—
114C22⋊Q8—21no—
115C22⋊Q8—21no—
116C22⋊Q8—112no—
117C22⋊Q8—221no—
118C4×Q8—21no—
119C4×Q8—21no—
120C4×Q8—112no—
121C4×Q8—221no—
122#117—221no—
123#117C2×D1112yes—
124C2×C42C2×D1111yescharacteristic
125#107—114no—
126#106—114no—
127C4⋊C8—112no—
128#103—114no—
129#103—114no—
130C22⋊C8—112no—
131C4×C8—111no—
132C4×C8—111no—
133C2×C11—41no—
134C2×C11#53611yescharacteristic
135C2×C11C2×#13511yescharacteristic
136C2×C11C2×#13711yescharacteristic
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—112no—
140C2×Q8—221no—
141C22×C4C22⋊D1111yescharacteristic
142C22×C4C22⋊D1111yescharacteristic
143C22×C4C22×D1111yescharacteristic
144C2×C8—112no—
145C2×C8—112no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—112no—
151C4⋊C4—221no—
152C4⋊C4—221no—
153C4⋊C4—222no—
154C4⋊C4—222no—
155C4⋊C4—221no—
156C4⋊C4C22×D1112yes—
157C4⋊C4C22×D1112yes—
158C22⋊C4—22no—
159C22⋊C4—222no—
160C42—22no—
161C42—222no—
162C42C22⋊D1111yescharacteristic
163C42C22⋊D1111yescharacteristic
164C42C22×D1111yescharacteristic
165C42C22×D1111yescharacteristic
166C11#323111yescharacteristic, complemented, Sylow
167C23C2×C22⋊D1111yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—224no—
171Q8—442no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4C2×C22⋊D1111yescharacteristic
180C2×C4C2×C22⋊D1111yescharacteristic
181C2×C4C2×C22⋊D1111yescharacteristic
182C2×C4C2×C22⋊D1111yescharacteristic
183C2×C4C2×C22⋊D1111yescharacteristic
184C2×C4C23×D1111yescharacteristic
185C8—222no—
186C8—222no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22C22×C22⋊D1111yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—442no—
197C4—442no—
198C4#6700312yes—
199C4#6700412yes—
200C4#6704012yes—
201C2—41no—
202C2#1062334711yescharacteristic
203C2C2×#6700311yescharacteristic
204C2C2×#6700411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#533D11
hypocenterC11#3231
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #10622706C2semidirect
4. #10622706C2semidirect
5. #10622692C2semidirect
6. #10622691C2semidirect
7. #10622676C2semidirect
166. C11#3231semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230012
#106227062
#106226922
#106226912
#106226762
#106226092
#106225382
#323111