Finite Group Databasebeta

← #13079797

Subgroups — #13079797

Order 1408.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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#10623010C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic, complemented
3C11×#431C211yesmaximal, characteristic, complemented
4#10622464C211yesmaximal, characteristic, complemented
5#10622463C211yesmaximal, characteristic, complemented
6#10622459C211yesmaximal, characteristic, complemented
7#10622455C211yesmaximal, characteristic, complemented
8#10622350C212yesmaximal
9#10622336C212yesmaximal, complemented
10#10622310C212yesmaximal, complemented
11#10622296C212yesmaximal, complemented
12C2×C42×C11C2211yescharacteristic
13#66983C2211yescharacteristic
14#66982—21no—
15C4×C22⋊D11—21no—
16#66979C2212yes—
17#66977—21no—
18#66977—21no—
19#66977C2211yescharacteristic
20#66929—21no—
21#66928C2211yescharacteristic
22C4×D44C2211yescharacteristic
23#66925—21no—
24#66923C2212yes—
25#66923C2211yescharacteristic
26#66922C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22—21no—
29C4×Dic22—21no—
30C4×Dic22C2211yescharacteristic
31C11×C4⋊C8C2211yescharacteristic
32C11×C4⋊C8C2211yescharacteristic
33C11×C22⋊C8C2212yes—
34C4×C8×C11C2212yes—
35#66885C2212yes—
36#66885C2212yes—
37#66882C2212yes—
38#66882C2212yes—
39#66881C2212yes—
40#66881C2212yes—
41#66880C2212yes—
42#66880C2212yes—
43C22×C4×C11D411yescharacteristic
44C22×C4×C11D411yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C2×D44C2311yescharacteristic
48C2×C4×D11—21no—
49C2×Dic22—21no—
50C2×Dic22—21no—
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2312yes—
53C2×C8×C11C2312yes—
54C42×C11D411yescharacteristic
55C42×C11D411yescharacteristic
56C42×C11C2311yescharacteristic
57C42×C11C2311yescharacteristic
58C22⋊Dic11—22no—
59C22⋊Dic11—21no—
60(C2×D11)⋊C4—21no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—21no—
64C4⋊Dic11—21no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2312yes—
67C4⋊Dic11C2312yes—
68C4⋊Dic11C2311yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76C4×Dic11—22no—
77C4×Dic11—21no—
78#3233—111nomaximal, Sylow
79C23×C11C2×D411yescharacteristic
80C22×D11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—41no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2411yescharacteristic
91C22⋊D11—42no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97D44—21no—
98D44—21no—
99C4×D11—42no—
100Dic22—21no—
101Dic22—21no—
102Dic22—42no—
103Dic22—42no—
104C8×C11—22no—
105C8×C11—22no—
106#533—111no—
107#529—111no—
108#499—112no—
109#488—112no—
110#485—112no—
111#482—112no—
112#477—111no—
113#476—111no—
114#475—111no—
115#474—111no—
116#431D1111yescharacteristic, complemented
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11C22×D411yescharacteristic
121C2×D11—41no—
122C2×D11—41no—
123C2×D11—41no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11#13512yes—
129C4×C112−1+411yescharacteristic
130C4×C112−1+411yescharacteristic
131Dic11—41no—
132Dic11—42no—
133Dic11—41no—
134Dic11—42no—
135Dic11—41no—
136C4⋊Q8—111no—
137C4⋊Q8—111no—
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—111no—
151C4×D4—221no—
152#117—112no—
153#117—221no—
154C2×C42C2×D1111yescharacteristic
155#107—112no—
156#107—112no—
157#106—112no—
158#106—112no—
159C4⋊C8C2×D1111yescharacteristic
160C4⋊C8C2×D1111yescharacteristic
161#103—112no—
162#103—112no—
163#102—112no—
164#102—112no—
165C22⋊C8C2×D1112yes—
166C4×C8C2×D1112yes—
167C2×C11—41no—
168C2×C11#53611yescharacteristic
169C2×C11C2×#13511yescharacteristic
170C2×C11#57511yescharacteristic
171D11—81no—
172C2×Q8—111no—
173C2×Q8—221no—
174C2×Q8—221no—
175C2×D4—111no—
176C2×D4—221no—
177C22×C4—221no—
178C22×C4D4411yescharacteristic
179C22×C4D4411yescharacteristic
180C22×C4C22×D1111yescharacteristic
181C2×C8C22×D1112yes—
182C2×C8C22×D1112yes—
183C4⋊C4—112no—
184C4⋊C4—112no—
185C4⋊C4—111no—
186C4⋊C4—111no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C22⋊C4—222no—
196C22⋊C4—221no—
197C22⋊C4—221no—
198C22⋊C4—221no—
199C22⋊C4—221no—
200C22⋊C4—221no—
201C42—222no—
202C42—221no—
203C42D4411yescharacteristic
204C42D4411yescharacteristic
205C42C22×D1111yescharacteristic
206C42C22×D1111yescharacteristic
207C11#323311yescharacteristic, complemented, Sylow
208C23—221no—
209C23C2×D4411yescharacteristic
210Q8—221no—
211Q8—221no—
212Q8—442no—
213Q8—442no—
214D4—221no—
215D4—221no—
216D4—442no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—221no—
226C2×C4—442no—
227C2×C4C2×D4411yescharacteristic
228C2×C4C2×D4411yescharacteristic
229C2×C4C2×D4411yescharacteristic
230C2×C4C2×D4411yescharacteristic
231C2×C4C2×D4411yescharacteristic
232C2×C4C23×D1111yescharacteristic
233C8—22no—
234C8—22no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—441no—
239C22—441no—
240C22—441no—
241C22C22×D4411yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—441no—
247C4—442no—
248C4—441no—
249C4—442no—
250C4—441no—
251C4#6695712yes—
252C4#6704311yescharacteristic
253C4#6704311yescharacteristic
254C2—41no—
255C2—881no—
256C2#1062305711yescharacteristic
257C2C2×#6695711yescharacteristic
258C2#1062327911yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#431C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#431D11
hypocenterC11#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #10623001C2semidirect
3. C11×#431C2semidirect
4. #10622464C2semidirect
5. #10622463C2semidirect
6. #10622459C2semidirect
7. #10622455C2semidirect
9. #10622336C2semidirect
10. #10622310C2semidirect
11. #10622296C2semidirect
116. #431D11semidirect
207. C11#3233semidirect

Maximal subgroups

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

subgroupindex
#106230102
#106230012
C11×#4312
#106224642
#106224632
#106224592
#106224552
#106223502
#106223362
#106223102
#106222962
#323311