Finite Group Databasebeta

← #13079794

Subgroups — #13079794

Order 1408.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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, complemented
2#10623088C211yesmaximal, characteristic
3C11×#476C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622620C211yesmaximal, characteristic, complemented
6#10622480C212yesmaximal, complemented
7#10622471C212yesmaximal, complemented
8#10622464C211yesmaximal, characteristic, complemented
9#10622446C211yesmaximal, characteristic, complemented
10#10622392C212yesmaximal
11#10622381C212yesmaximal, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C4×D4×C11C2211yescharacteristic
14#66999—21no—
15Q8×Dic11—21no—
16#66991C2211yescharacteristic
17#66989C2211yescharacteristic
18C4×C22⋊D11—21no—
19#66979—21no—
20#66950—21no—
21#66950C2211yescharacteristic
22#66945C2212yes—
23#66943C2211yescharacteristic
24#66943C2212yes—
25#66940—21no—
26#66936—21no—
27#66932—21no—
28C42×D11C2211yescharacteristic
29#66922C2211yescharacteristic
30C4×Dic22C2211yescharacteristic
31C11×#106C2212yes—
32C11×C4⋊C8C2211yescharacteristic
33C11×#102C2212yes—
34#66896C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66881C2212yes—
37#66880C2212yes—
38C8×Dic11C2212yes—
39#66874C2212yes—
40#66871C2212yes—
41#66871C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11—21no—
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C2×C22⋊D11—21no—
47C2×C4×D11D411yescharacteristic
48C2×C4×D11D411yescharacteristic
49C2×C4×D11C2311yescharacteristic
50C2×Dic22—21no—
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2311yescharacteristic
55C11×C4⋊C4C2312yes—
56C11×C22⋊C4—21no—
57C42×C11C2311yescharacteristic
58C22⋊Dic11—21no—
59C22⋊Dic11—21no—
60C22⋊Dic11—21no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11—21no—
65C4⋊Dic11—22no—
66C4⋊Dic11—21no—
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2312yes—
69Dic11⋊C4—21no—
70Dic11⋊C4—22no—
71Dic11⋊C4—21no—
72C4×Dic11—22no—
73C4×Dic11—21no—
74C4×Dic11D411yescharacteristic
75C4×Dic11D411yescharacteristic
76C4×Dic11C2311yescharacteristic
77C2×C11⋊C8C2312yes—
78#3233—111nomaximal, Sylow
79C23×C11—21no—
80C22×D11C2×D411yescharacteristic
81Q8×C11—42no—
82D4×C11—21no—
83D4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—42no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C22⋊D11—42no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11C2×D411yescharacteristic
95C2×Dic11C2×D411yescharacteristic
96C2×Dic11C2×D411yescharacteristic
97C4×D11—22no—
98C4×D11—21no—
99C4×D11—21no—
100C4×D11—41no—
101Dic22—21no—
102Dic22—21no—
103Dic22—42no—
104C8×C11—22no—
105C11⋊C8—22no—
106#533—111no—
107#529—111no—
108#499—112no—
109#488—112no—
110#485—112no—
111#482—112no—
112#477—111no—
113#476D1111yescharacteristic, complemented
114#475—111no—
115#474—111no—
116#431—111no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11C22×D411yescharacteristic
121C2×D11—21no—
122C2×D11—21no—
123C2×D11—21no—
124C4×C11—21no—
125C4×C11—41no—
126C4×C11—42no—
127C4×C11#13512yes—
128C4×C112−1+411yescharacteristic
129C4×C112−1+411yescharacteristic
130Dic11—21no—
131Dic11—21no—
132Dic11—21no—
133Dic11—41no—
134Dic11—42no—
135Dic11—41no—
136C4⋊Q8—111no—
137C4⋊Q8C2×D1111yescharacteristic
138#126—221no—
139#125—111no—
140#125—112no—
141#124—111no—
142#123—221no—
143C22⋊Q8—111no—
144C22⋊Q8—221no—
145C22⋊Q8—221no—
146#121—111no—
147C4×Q8—111no—
148C4×Q8—221no—
149C4×Q8—221no—
150C4×D4—221no—
151C4×D4C2×D1111yescharacteristic
152#117—112no—
153#117—221no—
154C2×C42—111no—
155#107—112no—
156#107—112no—
157#106—112no—
158#106C2×D1112yes—
159C4⋊C8—111no—
160C4⋊C8C2×D1111yescharacteristic
161#103—112no—
162#103—112no—
163#102—112no—
164#102C2×D1112yes—
165C22⋊C8—112no—
166C4×C8—112no—
167C2×C11—81no—
168C2×C11#53611yescharacteristic
169C2×C11C2×#13511yescharacteristic
170C2×C11#57511yescharacteristic
171D11—41no—
172C2×Q8—21no—
173C2×Q8—111no—
174C2×Q8—221no—
175C2×D4—221no—
176C2×D4C22×D1111yescharacteristic
177C22×C4—21no—
178C22×C4—111no—
179C22×C4—111no—
180C22×C4—111no—
181C2×C8—112no—
182C2×C8C22×D1112yes—
183C4⋊C4—21no—
184C4⋊C4—112no—
185C4⋊C4—111no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4C22×D1112yes—
194C4⋊C4C22×D1111yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—222no—
197C22⋊C4—221no—
198C22⋊C4—221no—
199C22⋊C4—221no—
200C22⋊C4—221no—
201C42—111no—
202C42—111no—
203C42—111no—
204C42—222no—
205C42—221no—
206C42C22×D1111yescharacteristic
207C11#323311yescharacteristic, complemented, Sylow
208C23—21no—
209C23—111no—
210Q8—42no—
211Q8—221no—
212Q8—221no—
213Q8—442no—
214D4—21no—
215D4—21no—
216D4—442no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—111no—
221C2×C4—111no—
222C2×C4—111no—
223C2×C4—222no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—222no—
229C2×C4—441no—
230C2×C4D4×D1111yescharacteristic
231C2×C4D4×D1111yescharacteristic
232C2×C4C23×D1111yescharacteristic
233C8—22no—
234C8—222no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—221no—
239C22—221no—
240C22—221no—
241C22C2×D4×D1111yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—221no—
246C4—221no—
247C4—221no—
248C4—442no—
249C4—441no—
250C4—441no—
251C4#6696912yes—
252C4#6704011yescharacteristic
253C4#6704311yescharacteristic
254C2—81no—
255C2—441no—
256C2#1062315911yescharacteristic
257C2C2×#6696911yescharacteristic
258C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#476C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#476D11
hypocenterC11#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#476C2semidirect
4. #10622704C2semidirect
5. #10622620C2semidirect
6. #10622480C2semidirect
7. #10622471C2semidirect
8. #10622464C2semidirect
9. #10622446C2semidirect
11. #10622381C2semidirect
113. #476D11semidirect
207. C11#3233semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106230882
C11×#4762
#106227042
#106226202
#106224802
#106224712
#106224642
#106224462
#106223922
#106223812
#323311