Finite Group Databasebeta

← #13073196

Subgroups — #13073196

Order 1408.

496 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66929C212yesmaximal, complemented
2C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3#10622601C211yesmaximal, characteristic
4#10622601C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic, complemented
6#10622586C211yesmaximal, characteristic, complemented
7#10622553C212yesmaximal, complemented
8#10622552C211yesmaximal, characteristic
9C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
10#10622289C212yesmaximal, complemented
11#10622288C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31#66929—28no—
32C11×#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C23×D11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2311yescharacteristic
43C22×Dic11C2312yes—
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C2×D44—22no—
48C2×D44—22no—
49C2×D44—22no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—22no—
52C42×C11—24no—
53C42×C11—22no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4—24no—
58(C2×D11)⋊C4—42no—
59(C2×D11)⋊C4—42no—
60C4⋊Dic11—22no—
61Dic11⋊C4—24no—
62Dic11⋊C4—24no—
63Dic11⋊C4—22no—
64Dic11⋊C4—42no—
65Dic11⋊C4D414yescomplemented
66C4×Dic11—22no—
67C4×Dic11—22no—
68#2512—111nomaximal, Sylow
69C23×C11C2411yescharacteristic
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11C2×D412yes—
89C2×C4×C11#4112yes—
90C2×C4×C11#4112yes—
91C2×C4×C11#4112yes—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11C2×D412yes—
105C2×Dic11C2×D412yes—
106C2×Dic11#4112yes—
107D44—44no—
108C2×#126—112no—
109#397—112no—
110#396—112no—
111#390—111no—
112#390—111no—
113#390—111no—
114#389—111no—
115#388—112no—
116#384—111no—
117C4×C4⋊C4—111no—
118C4×C4⋊C4D1111yescharacteristic, complemented
119C22×C11C22×D411yescharacteristic
120C22×C11C2×#4111yescharacteristic
121C22×C11C2×#4111yescharacteristic
122C22×C11C2×#4111yescharacteristic
123C22×C11C2×#4111yescharacteristic
124C22×C11H(5,𝔽2)11yescharacteristic
125C22×C112−1+411yescharacteristic
126C2×D11—42no—
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—42no—
132C2×D11—42no—
133C4×C11—22no—
134C4×C11—42no—
135C4×C11—42no—
136C4×C11—41no—
137C4×C11#12614yescomplemented
138Dic11—22no—
139Dic11—22no—
140Dic11—22no—
141Dic11—41no—
142Dic11—42no—
143C22×D4—111no—
144#126—228no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—111no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C4⋊C4C2×D1111yescharacteristic
153C2×C22⋊C4—112no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C42—111no—
160C2×C42—111no—
161C2×C42C2×D1112yes—
162C2×C42C2×D1111yescharacteristic
163#95—111no—
164#95—111no—
165#95—112no—
166#95C2×D1112yes—
167C2×C11C2×#12611yescharacteristic
168C2×C11#53211yescharacteristic
169C2×C11#54211yescharacteristic
170C2×C11#54711yescharacteristic
171C2×C11#55011yescharacteristic
172C2×C11#55311yescharacteristic
173C2×C11#55611yescharacteristic
174D11—82no—
175C24—112no—
176C2×D4—222no—
177C2×D4—222no—
178C2×D4—222no—
179C22×C4—111no—
180C22×C4—111no—
181C22×C4—111no—
182C22×C4—111no—
183C22×C4—112no—
184C22×C4C22×D1111yescharacteristic
185C22×C4C22×D1112yes—
186C22×C4C22×D1112yes—
187C22×C4C22×D1111yescharacteristic
188C22×C4C22×D1111yescharacteristic
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—114no—
192C4⋊C4—224no—
193C4⋊C4—224no—
194C4⋊C4—222no—
195C4⋊C4—222no—
196C4⋊C4—442no—
197C22⋊C4—224no—
198C22⋊C4—224no—
199C22⋊C4—224no—
200C22⋊C4—224no—
201C22⋊C4—442no—
202C22⋊C4—442no—
203C42—22no—
204C42—24no—
205C42—222no—
206C42—222no—
207C11#251211yescharacteristic, complemented, Sylow
208C23—222no—
209C23—222no—
210C23—222no—
211C23—222no—
212C23—222no—
213C23—222no—
214C23—222no—
215C23C23×D1111yescharacteristic
216D4—444no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—112no—
229C2×C4—112no—
230C2×C4—112no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4—221no—
237C2×C4—221no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—221no—
241C2×C4—221no—
242C2×C4—222no—
243C2×C4#433912yes—
244C2×C4#433912yes—
245C2×C4#433912yes—
246C2×C4D4×D1112yes—
247C22—442no—
248C22—442no—
249C22—442no—
250C22—442no—
251C22—442no—
252C22—442no—
253C22—442no—
254C22C2×#433911yescharacteristic
255C22C2×#433911yescharacteristic
256C22C2×#433911yescharacteristic
257C22C2×D4×D1111yescharacteristic
258C22#6704011yescharacteristic
259C22#41×D1111yescharacteristic
260C22#6704211yescharacteristic
261C4—22no—
262C4—41no—
263C4—42no—
264C4—42no—
265C4—222no—
266C4—222no—
267C4—222no—
268C4—442no—
269C4—441no—
270C4#6692914yescomplemented
271C2—882no—
272C2C2×#6692911yescharacteristic
273C2#1062303811yescharacteristic
274C2#1062306111yescharacteristic
275C2#1062307911yescharacteristic
276C2#1062308411yescharacteristic
277C2#1062309911yescharacteristic
278C2#1062311311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
prime radicalC22×D44C22
hypercenterC4×C4⋊C4D11
hypocenterC11#2512
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#66929C2semidirect
2. C4×C11×C4⋊C4C2semidirect
5. #10622589C2semidirect
6. #10622586C2semidirect
7. #10622553C2semidirect
9. C4×Dic11⋊C4C2semidirect
10. #10622289C2semidirect
11. #10622288C2semidirect
65. Dic11⋊C4D4semidirect
118. C4×C4⋊C4D11semidirect
137. C4×C11#126semidirect
207. C11#2512semidirect
270. C4#66929semidirect

Maximal subgroups

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

subgroupindex
C2×#669292
C4×C11×C4⋊C42
#106226012
#106225892
#106225862
#106225532
#106225522
C4×Dic11⋊C42
#106222892
#106222882
#251211