Finite Group Databasebeta

← #13069080

Subgroups — #13069080

Order 1408.

390 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 101 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×#121C211yesmaximal, characteristic
2C22×#4318C211yesmaximal, characteristic, complemented
3C2×#66897C212yesmaximal, complemented
4#10622820C211yesmaximal, characteristic, complemented
5#10622168C212yesmaximal, complemented
6C22×D4×C11C412yes—
7C22×D4×C11C2211yescharacteristic
8C23×C4×C11C2211yescharacteristic
9C11×#121—21no—
10C11×#121—21no—
11C11×#121—21no—
12C11×#121—21no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C412yes—
15C2×#4318—21no—
16C2×#4318—24no—
17C2×#4318C2212yes—
18C2×#4318C2212yes—
19C22×C11⋊C8—21no—
20#66897—24no—
21C22⋊(C11⋊C8)—21no—
22C22⋊(C11⋊C8)—21no—
23C24×C11C2×C411yescharacteristic
24C24×C11C2×C412yes—
25C2×D4×C11—22no—
26C2×D4×C11—22no—
27C2×D4×C11—22no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—22no—
31C2×D4×C11—44no—
32C22×C4×C11—22no—
33C22×C4×C11—22no—
34C22×C4×C11C2×C411yescharacteristic
35C22×C4×C11C2×C412yes—
36C22×C4×C11D411yescharacteristic
37C22×C4×C11D411yescharacteristic
38C22×C4×C11D411yescharacteristic
39C22×C4×C11D411yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C11×C4⋊C4—21no—
42C11×C4⋊C4—21no—
43C11×C22⋊C4—22no—
44C11×C22⋊C4—22no—
45#4318—24no—
46#4318—22no—
47#4318—22no—
48#4318—22no—
49#4318D414yescomplemented
50C2×C11⋊C8—24no—
51C2×C11⋊C8—22no—
52C2×C11⋊C8—22no—
53#1900—111nomaximal, Sylow
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—22no—
57C23×C11—24no—
58C23×C11—41no—
59C23×C11—42no—
60C23×C11—42no—
61C23×C11C22⋊C411yescharacteristic
62C23×C11C22⋊C411yescharacteristic
63C23×C11C22×C411yescharacteristic
64D4×C11—44no—
65D4×C11—44no—
66D4×C11—41no—
67D4×C11—42no—
68D4×C11—41no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—42no—
78C2×C4×C11C22⋊C411yescharacteristic
79C2×C4×C11C22⋊C411yescharacteristic
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11#4112yes—
84C11⋊C8—24no—
85C11⋊C8—42no—
86C22×M16—111no—
87C2×#121D1111yescharacteristic
88C2×#100—112no—
89#407—111no—
90#343—112no—
91C22×C11—21no—
92C22×C11—21no—
93C22×C11—21no—
94C22×C11—21no—
95C22×C11—21no—
96C22×C11—21no—
97C22×C11—21no—
98C22×C11—44no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—84no—
103C22×C11#10012yescomplemented
104C22×C11C2×C22⋊C411yescharacteristic
105C22×C11C4×D412yes—
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—42no—
109C4×C11#12011yescharacteristic
110C4×C11#12112yes—
111C4×C11#12311yescharacteristic
112C22×D4Dic1112yes—
113C22×D4C2×D1111yescharacteristic
114C23×C4C2×D1111yescharacteristic
115C2×M16—112no—
116C2×M16—112no—
117C2×M16—224no—
118C2×M16—221no—
119C22×C8—221no—
120#121—21no—
121#121—21no—
122#121—21no—
123#121—21no—
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C22⋊C4Dic1112yes—
126#100—224no—
127C22⋊C8—221no—
128C22⋊C8—221no—
129C2×C11—22no—
130C2×C11—22no—
131C2×C11—41no—
132C2×C11—82no—
133C2×C11#38611yescharacteristic
134C2×C11C2×#10011yescharacteristic
135C2×C11#41311yescharacteristic
136C24C2×Dic1111yescharacteristic
137C24C2×Dic1112yes—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—44no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4C2×Dic1111yescharacteristic
148C22×C4C2×Dic1112yes—
149C22×C4C22⋊D1111yescharacteristic
150C22×C4C22⋊D1111yescharacteristic
151C22×C4C22⋊D1111yescharacteristic
152C22×C4C22⋊D1111yescharacteristic
153C22×C4C22×D1111yescharacteristic
154M16—114no—
155M16—224no—
156M16—222no—
157M16—222no—
158M16—222no—
159C2×C8—224no—
160C2×C8—222no—
161C2×C8—222no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C11#190011yescharacteristic, complemented, Sylow
167C23—22no—
168C23—22no—
169C23—22no—
170C23—24no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23C22⋊Dic1111yescharacteristic
175C23C22⋊Dic1111yescharacteristic
176C23C22×Dic1111yescharacteristic
177D4—44no—
178D4—44no—
179D4—41no—
180D4—41no—
181D4—42no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4C22⋊Dic1111yescharacteristic
192C2×C4C22⋊Dic1111yescharacteristic
193C2×C4D4×D1112yes—
194C2×C4#434112yes—
195C2×C4C2×C22⋊D1111yescharacteristic
196C2×C4C2×C22⋊D1111yescharacteristic
197C8—224no—
198C8—442no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—44no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—84no—
211C22#6689712yescomplemented
212C22D4×Dic1112yes—
213C22C2×C22⋊Dic1111yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4#6698811yescharacteristic
218C4#6699011yescharacteristic
219C4#6699212yes—
220C2—22no—
221C2—22no—
222C2—41no—
223C2—82no—
224C2C2×#6689711yescharacteristic
225C2#1062283311yescharacteristic
226C2#1062285011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic11
commutatorC23×C11C22×C4
FrattiniC22×C4C22×D11
Fitting, prime radicalC2×C11×#121C2
socleC22×C11C2×C22⋊C4
cosocleC22×C4×C11C23
hypercenterC2×#121D11
hypocenterC11#1900
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C22×#4318C2semidirect
3. C2×#66897C2semidirect
4. #10622820C2semidirect
5. #10622168C2semidirect
49. #4318D4semidirect
103. C22×C11#100semidirect
166. C11#1900semidirect
211. C22#66897semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C22×#43182
C2×#668972
#106228202
#106221682
#190011