Finite Group Databasebeta

← #13073045

Subgroups — #13073045

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
1C11×#380C211yesmaximal, characteristic
2#10622825C211yesmaximal, characteristic
3C4×C22⋊Dic11C211yesmaximal, characteristic
4#10622598C211yesmaximal, characteristic, complemented
5#10622589C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#10622586C211yesmaximal, characteristic, complemented
8#10622561C212yesmaximal
9#10622557C212yesmaximal
10#10622272C212yesmaximal, complemented
11#10622265C212yesmaximal, 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×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2212yes—
28C11×#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
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×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C11×C22⋊C4—42no—
52C22⋊Dic11—22no—
53C22⋊Dic11—42no—
54C22⋊Dic11Q814yes—
55C4⋊Dic11—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11—42no—
58Dic11⋊C4—24no—
59Dic11⋊C4—42no—
60Dic11⋊C4—42no—
61C4×Dic11—22no—
62C4×Dic11—22no—
63C4×Dic11—42no—
64#2497—111nomaximal, Sylow
65C23×C11—21no—
66C23×C11—21no—
67C23×C11—21no—
68C23×C11—21no—
69C23×C11—21no—
70C23×C11—21no—
71C23×C11C2×Q812yes—
72C23×C11C2411yescharacteristic
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—44no—
83C2×C4×C11#4112yes—
84C2×C4×C11#4112yes—
85C2×C4×C11#4112yes—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11C2×Q812yes—
102C2×Dic11C2×Q812yes—
103C2×Dic11#4112yes—
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#380D1111yescharacteristic
113C4×C4⋊C4—111no—
114C4×C22⋊C4—111no—
115C22×C11—22no—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11C22×Q811yescharacteristic
123C22×C11C2×#4111yescharacteristic
124C22×C11C2×#4111yescharacteristic
125C22×C11C2×#4111yescharacteristic
126C22×C11C2×#4111yescharacteristic
127C22×C11H(5,𝔽2)11yescharacteristic
128C22×C11H(5,𝔽2)11yescharacteristic
129C4×C11—41no—
130C4×C11—42no—
131C4×C11—42no—
132C4×C11#12614yes—
133Dic11—22no—
134Dic11—22no—
135Dic11—22no—
136Dic11—42no—
137Dic11—41no—
138Dic11—42no—
139C23×C4C2×D1111yescharacteristic
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⋊C4C2×D1112yes—
152C2×C42—111no—
153C2×C42—111no—
154C2×C42—112no—
155#95—111no—
156#95—111no—
157#95—112no—
158#95—112no—
159#95—112no—
160#95—112no—
161#95C2×D1112yes—
162C2×C11—42no—
163C2×C11C2×#12611yescharacteristic
164C2×C11#53311yescharacteristic
165C2×C11#54011yescharacteristic
166C2×C11#55311yescharacteristic
167C2×C11#55411yescharacteristic
168C2×C11#55411yescharacteristic
169C2×C11#55511yescharacteristic
170C24C22×D1111yescharacteristic
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—111no—
177C22×C4—111no—
178C22×C4—112no—
179C22×C4—112no—
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1112yes—
182C22×C4C22×D1112yes—
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—42no—
193C22⋊C4—114no—
194C22⋊C4—222no—
195C22⋊C4—442no—
196C42—222no—
197C42—222no—
198C42—442no—
199C11#249711yescharacteristic, complemented, Sylow
200C23—21no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23—21no—
205C23—21no—
206C23Q8×D1112yes—
207C23C23×D1111yescharacteristic
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—44no—
218C2×C4—112no—
219C2×C4—112no—
220C2×C4—112no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—221no—
236C2×C4#433912yes—
237C2×C4#434112yes—
238C2×C4#434112yes—
239C22—22no—
240C22—22no—
241C22—22no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22C2×#433911yescharacteristic
247C22C2×#434111yescharacteristic
248C22C2×#434111yescharacteristic
249C22#6703711yescharacteristic
250C22C2×Q8×D1111yescharacteristic
251C22#41×D1111yescharacteristic
252C22#6704211yescharacteristic
253C4—41no—
254C4—42no—
255C4—42no—
256C4—222no—
257C4—222no—
258C4—222no—
259C4—441no—
260C4—442no—
261C4—442no—
262C4#6693214yes—
263C2—42no—
264C2C2×#6693211yescharacteristic
265C2#1062304211yescharacteristic
266C2#1062306311yescharacteristic
267C2#1062314511yescharacteristic
268C2#1062315011yescharacteristic
269C2#1062315311yescharacteristic
270C2#1062316611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC24×C11C23
hypercenter#380D11
hypocenterC11#2497
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
4. #10622598C2semidirect
5. #10622589C2semidirect
6. C4⋊C4×Dic11C2semidirect
7. #10622586C2semidirect
10. #10622272C2semidirect
11. #10622265C2semidirect
199. C11#2497semidirect

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
#106225892
C4⋊C4×Dic112
#106225862
#106225612
#106225572
#106222722
#106222652
#249711