Finite Group Databasebeta

← #13073018

Subgroups — #13073018

Order 1408.

412 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#380C211yesmaximal, characteristic
2#10622825C211yesmaximal, characteristic
3C4×C22⋊Dic11C211yesmaximal, characteristic
4#10622598C211yesmaximal, characteristic, complemented
5#10622590C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#10622586C211yesmaximal, characteristic, complemented
8#10622566C212yesmaximal
9#10622557C212yesmaximal
10C11⋊#401C212yesmaximal, complemented
11#10622268C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24C2×C4×Dic11C2211yescharacteristic
25C2×C4×Dic11C2212yes—
26C11×#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C24×C11C2311yescharacteristic
36C22×C4×C11—22no—
37C22×C4×C11—22no—
38C22×C4×C11—22no—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C11×C22⋊C4—42no—
52C22⋊Dic11—22no—
53C22⋊Dic11—24no—
54C22⋊Dic11—22no—
55C4⋊Dic11—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11—42no—
58Dic11⋊C4—24no—
59C4×Dic11—22no—
60C4×Dic11—22no—
61C4×Dic11—42no—
62#2494—111nomaximal, Sylow
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—21no—
67C23×C11—21no—
68C23×C11—21no—
69C23×C11#4112yes—
70C23×C11C2411yescharacteristic
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—44no—
81C2×C4×C11#4112yes—
82C2×C4×C11#4112yes—
83C2×C4×C11#4112yes—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11#4112yes—
102#401—112no—
103#397—112no—
104#389—111no—
105#389—111no—
106#388—112no—
107#387—112no—
108#382—111no—
109#380—111no—
110#380D1111yescharacteristic
111C4×C4⋊C4—111no—
112C4×C22⋊C4—111no—
113C22×C11—22no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11C2×#4111yescharacteristic
121C22×C11C2×#4111yescharacteristic
122C22×C11C2×#4111yescharacteristic
123C22×C11C2×#4111yescharacteristic
124C22×C11C2×#4111yescharacteristic
125C22×C11H(5,𝔽2)11yescharacteristic
126C22×C112−1+411yescharacteristic
127C4×C11—41no—
128C4×C11—42no—
129C4×C11—42no—
130C4×C11#12614yes—
131Dic11—22no—
132Dic11—42no—
133Dic11—41no—
134Dic11—41no—
135Dic11—42no—
136Dic11—41no—
137C23×C4C2×D1111yescharacteristic
138C2×C4⋊C4—111no—
139C2×C4⋊C4—111no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4C2×D1111yescharacteristic
143C2×C4⋊C4C2×D1111yescharacteristic
144C2×C22⋊C4—111no—
145C2×C22⋊C4—111no—
146C2×C22⋊C4—112no—
147C2×C22⋊C4C2×D1112yes—
148C2×C42—111no—
149C2×C42—111no—
150C2×C42—112no—
151#95—111no—
152#95—111no—
153#95—112no—
154#95—112no—
155#95—112no—
156#95—112no—
157#95—112no—
158#95—112no—
159#95C2×D1112yes—
160C2×C11—42no—
161C2×C11C2×#12611yescharacteristic
162C2×C11#52911yescharacteristic
163C2×C11#54211yescharacteristic
164C2×C11#55211yescharacteristic
165C2×C11#55311yescharacteristic
166C2×C11#55311yescharacteristic
167C2×C11#55611yescharacteristic
168C24C22×D1111yescharacteristic
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—111no—
173C22×C4—111no—
174C22×C4—111no—
175C22×C4—112no—
176C22×C4—111no—
177C22×C4—112no—
178C22×C4C22×D1111yescharacteristic
179C22×C4C22×D1112yes—
180C22×C4C22×D1112yes—
181C22×C4C22×D1111yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—224no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—442no—
188C22⋊C4—42no—
189C22⋊C4—222no—
190C22⋊C4—222no—
191C22⋊C4—224no—
192C42—222no—
193C42—222no—
194C42—442no—
195C11#249411yescharacteristic, complemented, Sylow
196C23—21no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—21no—
202C23#434312yes—
203C23C23×D1111yescharacteristic
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—44no—
214C2×C4—112no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—221no—
218C2×C4—221no—
219C2×C4—222no—
220C2×C4—221no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4#433912yes—
233C2×C4#434112yes—
234C2×C4#434112yes—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22C2×#433911yescharacteristic
243C22C2×#434111yescharacteristic
244C22C2×#434111yescharacteristic
245C22#6703711yescharacteristic
246C22C2×#434311yescharacteristic
247C22#41×D1111yescharacteristic
248C22#6704311yescharacteristic
249C4—41no—
250C4—42no—
251C4—42no—
252C4—222no—
253C4—441no—
254C4—442no—
255C4—441no—
256C4—442no—
257C4—441no—
258C4#6693214yes—
259C2—42no—
260C2C2×#6693211yescharacteristic
261C2#1062304511yescharacteristic
262C2#1062306411yescharacteristic
263C2#1062313411yescharacteristic
264C2#1062314511yescharacteristic
265C2#1062315511yescharacteristic
266C2#1062317311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC24×C11C23
hypercenter#380D11
hypocenterC11#2494
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
4. #10622598C2semidirect
5. #10622590C2semidirect
6. C4⋊C4×Dic11C2semidirect
7. #10622586C2semidirect
10. C11⋊#401C2semidirect
11. #10622268C2semidirect
195. C11#2494semidirect

Maximal subgroups

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

subgroupindex
C11×#3802
#106228252
C4×C22⋊Dic112
#106225982
#106225902
C4⋊C4×Dic112
#106225862
#106225662
#106225572
C11⋊#4012
#106222682
#249411