Finite Group Databasebeta

← #13072334

Subgroups — #13072334

Order 1408.

520 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊C4C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3#10622825C212yesmaximal
4#10622825C211yesmaximal, characteristic
5#10622823C212yesmaximal
6C4×C22⋊Dic11C211yesmaximal, characteristic
7#10622599C212yesmaximal, complemented
8#10622598C211yesmaximal, characteristic, complemented
9#10622597C212yesmaximal, complemented
10#10622590C211yesmaximal, characteristic, complemented
11#10622586C211yesmaximal, characteristic, complemented
12C23×C4×C11C2212yes—
13C23×C4×C11C2211yescharacteristic
14C2×C11×C4⋊C4—24no—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2212yes—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29#66943—24no—
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—24no—
41C22×C4×C11—24no—
42C22×C4×C11—42no—
43C22×C4×C11Q814yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C11×C4⋊C4—24no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4D414yes—
57C22⋊Dic11—22no—
58C22⋊Dic11—22no—
59C22⋊Dic11—24no—
60C4⋊Dic11—24no—
61C4⋊Dic11—22no—
62C4⋊Dic11—22no—
63C4⋊Dic11—42no—
64Dic11⋊C4—24no—
65Dic11⋊C4—42no—
66C4×Dic11—22no—
67C4×Dic11—22no—
68#2442—111nomaximal, Sylow
69C23×C11—21no—
70C23×C11—21no—
71C23×C11—21no—
72C23×C11—21no—
73C23×C11C2×Q812yes—
74C23×C11#4112yes—
75C23×C11#4112yes—
76C23×C11C2411yescharacteristic
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—28no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—48no—
86C2×C4×C11C2×D414yes—
87C2×C4×C11C2×D412yes—
88C2×C4×C11C2×Q812yes—
89C2×C4×C11C2×Q812yes—
90C2×C4×C11#4112yes—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×#125—111no—
110C22×C4⋊C4D1111yescharacteristic
111#400—112no—
112#398—112no—
113#389—111no—
114#389—111no—
115#385—112no—
116#382—111no—
117#380—112no—
118#380—111no—
119C4×C22⋊C4—111no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—22no—
126C22×C11#12514yescomplemented
127C22×C11C22×D411yescharacteristic
128C22×C11C22×Q811yescharacteristic
129C22×C11C2×#4111yescharacteristic
130C22×C11C2×#4111yescharacteristic
131C22×C11C2×#4111yescharacteristic
132C22×C11H(5,𝔽2)11yescharacteristic
133C22×C112−1+411yescharacteristic
134C4×C11—22no—
135C4×C11—24no—
136C4×C11—42no—
137C4×C11C22⋊Q814yes—
138Dic11—41no—
139Dic11—41no—
140Dic11—42no—
141Dic11—41no—
142Dic11—41no—
143Dic11—42no—
144C23×C4C2×D1112yes—
145C23×C4C2×D1111yescharacteristic
146#125—224no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—111no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—111no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4C2×D1111yescharacteristic
155C2×C4⋊C4C2×D1112yes—
156C2×C4⋊C4C2×D1111yescharacteristic
157C2×C22⋊C4—111no—
158C2×C22⋊C4—111no—
159C2×C22⋊C4—112no—
160C2×C42—111no—
161C2×C42—111no—
162#95—111no—
163#95—111no—
164#95—112no—
165#95—112no—
166#95—112no—
167#95—112no—
168#95—112no—
169C2×C11—24no—
170C2×C11C2×C22⋊Q811yescharacteristic
171C2×C11C2×#12511yescharacteristic
172C2×C11#54411yescharacteristic
173C2×C11#54611yescharacteristic
174C2×C11#54811yescharacteristic
175C2×C11#55211yescharacteristic
176C2×C11#55311yescharacteristic
177C24C22×D1111yescharacteristic
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—24no—
181C22×C4—24no—
182C22×C4—42no—
183C22×C4—111no—
184C22×C4—111no—
185C22×C4—111no—
186C22×C4—112no—
187C22×C4—112no—
188C22×C4—111no—
189C22×C4Dic2214yes—
190C22×C4C22×D1112yes—
191C22×C4C22×D1111yescharacteristic
192C22×C4C22×D1112yes—
193C22×C4C22×D1111yescharacteristic
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—222no—
197C4⋊C4—224no—
198C4⋊C4—224no—
199C4⋊C4—222no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4C22⋊D1114yes—
203C22⋊C4—222no—
204C22⋊C4—222no—
205C22⋊C4—224no—
206C42—222no—
207C42—222no—
208C11#244211yescharacteristic, complemented, Sylow
209C23—21no—
210C23—21no—
211C23—21no—
212C23—21no—
213C23C2×Dic2212yes—
214C23#434112yes—
215C23#434312yes—
216C23C23×D1111yescharacteristic
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—28no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—48no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—222no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—222no—
236C2×C4—221no—
237C2×C4—222no—
238C2×C4—221no—
239C2×C4—221no—
240C2×C4—222no—
241C2×C4—221no—
242C2×C4—221no—
243C2×C4—222no—
244C2×C4C2×Dic2212yes—
245C2×C4C2×Dic2212yes—
246C2×C4#433912yes—
247C2×C4C2×C22⋊D1114yes—
248C2×C4C2×C22⋊D1112yes—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22#6694314yescomplemented
256C22C22×Dic2211yescharacteristic
257C22C2×#433911yescharacteristic
258C22C2×#434111yescharacteristic
259C22#6703711yescharacteristic
260C22C2×#434311yescharacteristic
261C22#6704011yescharacteristic
262C22C22×C22⋊D1111yescharacteristic
263C4—22no—
264C4—24no—
265C4—42no—
266C4—441no—
267C4—441no—
268C4—442no—
269C4—441no—
270C4—441no—
271C4—442no—
272C4#6697714yes—
273C2—24no—
274C2C2×#6694311yescharacteristic
275C2#1062303111yescharacteristic
276C2#1062304411yescharacteristic
277C2#1062304511yescharacteristic
278C2C2×#6697711yescharacteristic
279C2#1062333711yescharacteristic
280C2#1062334811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×C4⋊C4C2
prime radicalC24×C11C23
hypercenterC22×C4⋊C4D11
hypocenterC11#2442
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
7. #10622599C2semidirect
8. #10622598C2semidirect
9. #10622597C2semidirect
10. #10622590C2semidirect
11. #10622586C2semidirect
126. C22×C11#125semidirect
208. C11#2442semidirect
255. C22#66943semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C42
C2×#669432
#106228252
#106228232
C4×C22⋊Dic112
#106225992
#106225982
#106225972
#106225902
#106225862
#244211