Finite Group Databasebeta

← #13073043

Subgroups — #13073043

Order 1408.

428 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
2#10622600C211yesmaximal, characteristic
3#10622600C211yesmaximal, characteristic
4#10622589C211yesmaximal, characteristic, complemented
5#10622586C211yesmaximal, characteristic, complemented
6#10622553C212yesmaximal
7C4×(C2×D11)⋊C4C211yesmaximal, characteristic
8#10622546C212yesmaximal, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622289C212yesmaximal
11#10622271C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16C2×C42×C11C2212yes—
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28C11×#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C23×D11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C2×C4×D11—22no—
47C2×C4×D11—22no—
48C2×C4×D11—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C42×C11—22no—
52C42×C11—42no—
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—42no—
55(C2×D11)⋊C4—42no—
56(C2×D11)⋊C4Q814yes—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59Dic11⋊C4—24no—
60Dic11⋊C4—42no—
61Dic11⋊C4—42no—
62Dic11⋊C4—42no—
63C4×Dic11—22no—
64#2497—111nomaximal, Sylow
65C23×C11C2411yescharacteristic
66C22×D11—21no—
67C22×D11—21no—
68C22×D11—21no—
69C22×D11—21no—
70C22×D11—21no—
71C22×D11—21no—
72C22×D11C2×Q812yes—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×Q812yes—
85C2×C4×C11#4112yes—
86C2×C4×C11#4112yes—
87C2×C4×C11#4112yes—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11C2×Q812yes—
102C2×Dic11#4112yes—
103C4×D11—44no—
104#400—112no—
105#396—112no—
106#389—111no—
107#389—111no—
108#388—112no—
109#387—112no—
110#384—111no—
111#380—111no—
112#380—111no—
113C4×C4⋊C4D1111yescharacteristic, complemented
114C4×C22⋊C4—111no—
115C22×C11C22×Q811yescharacteristic
116C22×C11C2×#4111yescharacteristic
117C22×C11C2×#4111yescharacteristic
118C22×C11C2×#4111yescharacteristic
119C22×C11C2×#4111yescharacteristic
120C22×C11H(5,𝔽2)11yescharacteristic
121C22×C11H(5,𝔽2)11yescharacteristic
122C2×D11—22no—
123C2×D11—22no—
124C2×D11—22no—
125C2×D11—41no—
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—41no—
129C4×C11—22no—
130C4×C11—42no—
131C4×C11—42no—
132C4×C11—41no—
133C4×C11#12614yes—
134Dic11—22no—
135Dic11—22no—
136Dic11—41no—
137Dic11—42no—
138Dic11—42no—
139C23×C4—111no—
140C2×C4⋊C4—111no—
141C2×C4⋊C4—111no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4C2×D1111yescharacteristic
147C2×C4⋊C4C2×D1111yescharacteristic
148C2×C22⋊C4—111no—
149C2×C22⋊C4—111no—
150C2×C22⋊C4—112no—
151C2×C22⋊C4—112no—
152C2×C42—111no—
153C2×C42C2×D1111yescharacteristic
154C2×C42C2×D1112yes—
155#95—111no—
156#95—111no—
157#95—112no—
158#95—112no—
159#95—112no—
160#95—112no—
161#95C2×D1112yes—
162C2×C11C2×#12611yescharacteristic
163C2×C11#53311yescharacteristic
164C2×C11#54011yescharacteristic
165C2×C11#55311yescharacteristic
166C2×C11#55411yescharacteristic
167C2×C11#55411yescharacteristic
168C2×C11#55511yescharacteristic
169D11—42no—
170C24—111no—
171C22×C4—111no—
172C22×C4—111no—
173C22×C4—111no—
174C22×C4—112no—
175C22×C4—112no—
176C22×C4—222no—
177C22×C4—222no—
178C22×C4—222no—
179C22×C4C22×D1112yes—
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1112yes—
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1111yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—224no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—442no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C22⋊C4—114no—
193C22⋊C4—222no—
194C22⋊C4—442no—
195C22⋊C4—442no—
196C42—22no—
197C42—42no—
198C42—222no—
199C11#249711yescharacteristic, complemented, Sylow
200C23—112no—
201C23—221no—
202C23—221no—
203C23—221no—
204C23—221no—
205C23—221no—
206C23—221no—
207C23C23×D1111yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—112no—
220C2×C4—112no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—444no—
235C2×C4#433912yes—
236C2×C4#433912yes—
237C2×C4#433912yes—
238C2×C4Q8×D1112yes—
239C22—222no—
240C22—222no—
241C22—222no—
242C22—441no—
243C22—441no—
244C22—441no—
245C22—441no—
246C22C2×#433911yescharacteristic
247C22C2×#433911yescharacteristic
248C22C2×#433911yescharacteristic
249C22#6703711yescharacteristic
250C22C2×Q8×D1111yescharacteristic
251C22#41×D1111yescharacteristic
252C22#6704211yescharacteristic
253C4—22no—
254C4—41no—
255C4—42no—
256C4—42no—
257C4—222no—
258C4—222no—
259C4—441no—
260C4—442no—
261C4—442no—
262C4#6692914yes—
263C2—442no—
264C2C2×#6692911yescharacteristic
265C2#1062304211yescharacteristic
266C2#1062306311yescharacteristic
267C2#1062308911yescharacteristic
268C2#1062309311yescharacteristic
269C2#1062310911yescharacteristic
270C2#1062311011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
prime radicalC23×D11C23
hypercenterC4×C4⋊C4D11
hypocenterC11#2497
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C4×C11×C4⋊C4C2semidirect
4. #10622589C2semidirect
5. #10622586C2semidirect
8. #10622546C2semidirect
9. #10622541C2semidirect
11. #10622271C2semidirect
113. C4×C4⋊C4D11semidirect
199. C11#2497semidirect

Maximal subgroups

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

subgroupindex
C4×C11×C4⋊C42
#106226002
#106225892
#106225862
#106225532
C4×(C2×D11)⋊C42
#106225462
#106225412
#106222892
#106222712
#249711