Finite Group Databasebeta

← #13079809

Subgroups — #13079809

Order 1408.

366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 111 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#10623247C211yesmaximal, characteristic
2#10623219C211yesmaximal, characteristic, complemented
3C11×#490C211yesmaximal, characteristic, complemented
4#10622684C211yesmaximal, characteristic, complemented
5#10622678C211yesmaximal, characteristic, complemented
6#10622397C212yesmaximal, complemented
7#10622392C212yesmaximal, complemented
8#10622374C212yesmaximal, complemented
9#10622372C212yesmaximal, complemented
10#10622318C211yesmaximal, characteristic, complemented
11#10622315C211yesmaximal, characteristic, complemented
12C2×#4341—21no—
13C11×#127C2211yescharacteristic
14C11×#125C2211yescharacteristic
15#66991—21no—
16#66991C2212yes—
17#66989—21no—
18D4×Dic11—21no—
19D4×Dic11C2212yes—
20#66949—21no—
21#66949—21no—
22#66945C2211yescharacteristic
23#66945C2211yescharacteristic
24#66941C2211yescharacteristic
25#66941C2211yescharacteristic
26#66940—21no—
27#66940—21no—
28C42×D11C2211yescharacteristic
29#66923C2211yescharacteristic
30#66922C2211yescharacteristic
31C11×#102C2212yes—
32C11×#102C2212yes—
33C11×#97C2211yescharacteristic
34#66896C2212yes—
35#66896C2212yes—
36(C2×D11)⋊C8C2212yes—
37#66882C2212yes—
38#66881C2212yes—
39Dic11⋊C8C2212yes—
40#66872C2212yes—
41#66871C2212yes—
42#66867C2211yescharacteristic
43C2×D4×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11C2312yes—
46C2×C22⋊D11—22no—
47C22×Dic11—22no—
48#4341—44no—
49C2×C4×D11D411yescharacteristic
50C2×C4×D11D411yescharacteristic
51C2×C4×D11C2311yescharacteristic
52C2×Dic22—21no—
53C2×Dic22—21no—
54C2×Dic22—21no—
55C2×C8×C11C2312yes—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2311yescharacteristic
59C11×C4⋊C4C2311yescharacteristic
60C42×C11C2311yescharacteristic
61C22⋊Dic11—22no—
62C22⋊Dic11—22no—
63(C2×D11)⋊C4—21no—
64(C2×D11)⋊C4—21no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2312yes—
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73C4×Dic11—21no—
74C4×Dic11—21no—
75C4×Dic11D411yescharacteristic
76C4×Dic11D411yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79#3235—111nomaximal, Sylow
80C23×C11—22no—
81C22×D11C2×D411yescharacteristic
82D4×C11—24no—
83D4×C11—42no—
84D4×C11—42no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C22⋊D11—44no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—44no—
95C2×Dic11C2×D411yescharacteristic
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98C4×D11—22no—
99C4×D11—22no—
100C4×D11—41no—
101Dic22—42no—
102Dic22—42no—
103Dic22—42no—
104C8×C11—22no—
105C11⋊C8—22no—
106#533—111no—
107#532—111no—
108#501—111no—
109#501—111no—
110#490—111no—
111#490D1111yescharacteristic, complemented
112#482—112no—
113#482—112no—
114#476—112no—
115#474—112no—
116#432—111no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11C22×D411yescharacteristic
121C2×D11—21no—
122C2×D11—21no—
123C2×D11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—41no—
127C4×C11—41no—
128C4×C112−1+412yes—
129Dic11—21no—
130Dic11—21no—
131Dic11—41no—
132Dic11—42no—
133Dic11—41no—
134Dic11AGL(1,ℤ/8)12yes—
135C2×#41—221no—
136C4⋊Q8—111no—
137C4⋊Q8—111no—
138C4⋊Q8—111no—
139#127C2×D1111yescharacteristic
140#125—111no—
141#125C2×D1111yescharacteristic
142#124—221no—
143C22⋊Q8—221no—
144C22⋊Q8—221no—
145#121—112no—
146#121—221no—
147C4×Q8—221no—
148C4×Q8—221no—
149C4×D4—112no—
150C4×D4—221no—
151#117—111no—
152#117—111no—
153C2×C42—111no—
154#107—112no—
155#107—112no—
156#106—112no—
157#106—112no—
158C4⋊C8—112no—
159#102—112no—
160#102—112no—
161#102C2×D1112yes—
162#102C2×D1112yes—
163C22⋊C8—112no—
164#97—111no—
165#97C2×D1111yescharacteristic
166C2×C11—82no—
167C2×C11#53611yescharacteristic
168C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C11#57511yescharacteristic
170D11—41no—
171#41—444no—
172C2×Q8—221no—
173C2×Q8—221no—
174C2×Q8—221no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—222no—
178C2×D4C22×D1112yes—
179C22×C4—111no—
180C22×C4—111no—
181C22×C4—111no—
182C22×C4—222no—
183C2×C8—112no—
184C2×C8C22×D1112yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—111no—
188C4⋊C4—111no—
189C4⋊C4—112no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4C22×D1111yescharacteristic
196C4⋊C4C22×D1111yescharacteristic
197C22⋊C4—221no—
198C22⋊C4—221no—
199C22⋊C4—222no—
200C22⋊C4—222no—
201C42—111no—
202C42—111no—
203C42—111no—
204C42—221no—
205C42—221no—
206C42C22×D1111yescharacteristic
207C11#323511yescharacteristic, complemented, Sylow
208C23—22no—
209C23—111no—
210Q8—442no—
211Q8—442no—
212Q8—442no—
213D4—24no—
214D4—42no—
215D4—42no—
216D4—444no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—111no—
220C2×C4—111no—
221C2×C4—111no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—222no—
227C2×C4—441no—
228C2×C4—444no—
229C2×C4D4×D1111yescharacteristic
230C2×C4D4×D1111yescharacteristic
231C2×C4C23×D1111yescharacteristic
232C8—22no—
233C8—222no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—221no—
238C22—221no—
239C22—221no—
240C22C2×D4×D1111yescharacteristic
241C4—21no—
242C4—21no—
243C4—41no—
244C4—41no—
245C4—112no—
246C4—221no—
247C4—221no—
248C4—442no—
249C4—441no—
250C4—441no—
251C4#6704312yes—
252C2—82no—
253C2—441no—
254C2#1062320611yescharacteristic
255C2D11×AGL(1,ℤ/8)11yescharacteristic
256C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#490C2
socleC22×C11C22×D4
prime radical#10623247C2
hypercenter#490D11
hypocenterC11#3235
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #10623219C2semidirect
3. C11×#490C2semidirect
4. #10622684C2semidirect
5. #10622678C2semidirect
6. #10622397C2semidirect
7. #10622392C2semidirect
8. #10622374C2semidirect
9. #10622372C2semidirect
10. #10622318C2semidirect
11. #10622315C2semidirect
111. #490D11semidirect
207. C11#3235semidirect

Maximal subgroups

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

subgroupindex
#106232472
#106232192
C11×#4902
#106226842
#106226782
#106223972
#106223922
#106223742
#106223722
#106223182
#106223152
#323511