Finite Group Databasebeta

← #13072916

Subgroups — #13072916

Order 1408.

540 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66945C211yesmaximal, characteristic, complemented
2C2×C4×D44C211yesmaximal, characteristic
3C11×#389C211yesmaximal, characteristic, complemented
4#10622606C212yesmaximal, complemented
5#10622603C212yesmaximal, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622600C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622285C212yesmaximal
11#10622268C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2212yes—
30#66945—24no—
31C4×D44—24no—
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48C2×D44—22no—
49C2×D44—22no—
50C2×D44—22no—
51C2×C4×D11—22no—
52C2×C4×D11—22no—
53C2×C4×D11—22no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11D414yes—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—42no—
60C42×C11—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70Dic11⋊C4—24no—
71C4×Dic11—24no—
72#2485—111nomaximal, Sylow
73C23×C11C2411yescharacteristic
74C22×D11—21no—
75C22×D11—21no—
76C22×D11—21no—
77C22×D11—21no—
78C22×D11—21no—
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11C2×D412yes—
87C22×D11#4112yes—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11C2×D412yes—
100C2×C4×C11#4112yes—
101C2×C4×C11#4112yes—
102C2×C4×C11#4112yes—
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—22no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11C2×D412yes—
115D44—28no—
116C4×D11—28no—
117C4×D11—44no—
118C2×C4×D4—111no—
119C2×#117—111no—
120#397—112no—
121#394—112no—
122#389—111no—
123#389D1111yescharacteristic, complemented
124#388—112no—
125#387—112no—
126#380—111no—
127#380—111no—
128#380—111no—
129C22×C11C22×D411yescharacteristic
130C22×C11C2×#4111yescharacteristic
131C22×C11C2×#4111yescharacteristic
132C22×C11C2×#4111yescharacteristic
133C22×C11C2×#4111yescharacteristic
134C22×C11H(5,𝔽2)11yescharacteristic
135C22×C112−1+411yescharacteristic
136C2×D11—22no—
137C2×D11—22no—
138C2×D11—22no—
139C2×D11—22no—
140C2×D11—22no—
141C2×D11—22no—
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—41no—
145C2×D11—41no—
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—41no—
149C2×D11—41no—
150C4×C11—22no—
151C4×C11—42no—
152C4×C11—41no—
153C4×C11—42no—
154C4×C11#12314yes—
155Dic11—22no—
156Dic11—41no—
157Dic11—42no—
158Dic11—42no—
159C22×D4—111no—
160C23×C4—111no—
161C23×C4—111no—
162C4×D4—224no—
163#117—224no—
164C2×C4⋊C4—111no—
165C2×C4⋊C4—111no—
166C2×C4⋊C4—111no—
167C2×C4⋊C4—112no—
168C2×C4⋊C4C2×D1111yescharacteristic
169C2×C4⋊C4C2×D1111yescharacteristic
170C2×C4⋊C4C2×D1112yes—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—111no—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C42—112no—
178C2×C42C2×D1111yescharacteristic
179#95—112no—
180#95—112no—
181#95—112no—
182#95—112no—
183#95C2×D1112yes—
184C2×C11C2×#12311yescharacteristic
185C2×C11#52511yescharacteristic
186C2×C11#53711yescharacteristic
187C2×C11#55211yescharacteristic
188C2×C11#55311yescharacteristic
189C2×C11#55511yescharacteristic
190C2×C11#55611yescharacteristic
191D11—42no—
192D11—42no—
193C24—111no—
194C24—111no—
195C2×D4—222no—
196C2×D4—222no—
197C2×D4—222no—
198C22×C4—111no—
199C22×C4—114no—
200C22×C4—111no—
201C22×C4—112no—
202C22×C4—112no—
203C22×C4—222no—
204C22×C4—222no—
205C22×C4—222no—
206C22×C4—222no—
207C22×C4—222no—
208C22×C4C22×D1112yes—
209C22×C4C22×D1111yescharacteristic
210C22×C4C22×D1112yes—
211C22×C4C22×D1111yescharacteristic
212C22×C4C22×D1111yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—42no—
216C4⋊C4—222no—
217C4⋊C4—222no—
218C4⋊C4—224no—
219C4⋊C4—222no—
220C22⋊C4—222no—
221C22⋊C4—224no—
222C22⋊C4—222no—
223C22⋊C4—224no—
224C22⋊C4—442no—
225C22⋊C4—442no—
226C42—22no—
227C42—224no—
228C11#248511yescharacteristic, complemented, Sylow
229C23—112no—
230C23—112no—
231C23—221no—
232C23—221no—
233C23—221no—
234C23—221no—
235C23—221no—
236C23—221no—
237C23—221no—
238C23—221no—
239C23—221no—
240C23—221no—
241C23—221no—
242C23—221no—
243C23C23×D1111yescharacteristic
244D4—228no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—112no—
257C2×C4—221no—
258C2×C4—221no—
259C2×C4—228no—
260C2×C4—221no—
261C2×C4—222no—
262C2×C4—221no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—221no—
268C2×C4—222no—
269C2×C4—444no—
270C2×C4#433912yes—
271C2×C4D4×D1112yes—
272C2×C4#434312yes—
273C2×C4#434312yes—
274C22—222no—
275C22—222no—
276C22—222no—
277C22—222no—
278C22—222no—
279C22—222no—
280C22—441no—
281C22—441no—
282C22—441no—
283C22—441no—
284C22—441no—
285C22—441no—
286C22—441no—
287C22—441no—
288C22C2×#433911yescharacteristic
289C22C2×D4×D1111yescharacteristic
290C22#6703711yescharacteristic
291C22C2×#434311yescharacteristic
292C22C2×#434311yescharacteristic
293C22#41×D1111yescharacteristic
294C22#6704311yescharacteristic
295C4—22no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—222no—
300C4—442no—
301C4—441no—
302C4—442no—
303C4#6694714yes—
304C2—442no—
305C2—442no—
306C2C2×#6694711yescharacteristic
307C2#1062308911yescharacteristic
308C2#1062311511yescharacteristic
309C2#1062313911yescharacteristic
310C2#1062315811yescharacteristic
311C2#1062322511yescharacteristic
312C2#1062326511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC22×D44C22
hypercenter#389D11
hypocenterC11#2485
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#66945C2semidirect
3. C11×#389C2semidirect
4. #10622606C2semidirect
5. #10622603C2semidirect
6. #10622600C2semidirect
7. #10622600C2semidirect
8. #10622600C2semidirect
9. #10622541C2semidirect
11. #10622268C2semidirect
123. #389D11semidirect
228. C11#2485semidirect

Maximal subgroups

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

subgroupindex
C2×#669452
C2×C4×D442
C11×#3892
#106226062
#106226032
#106226002
#106225412
#106222852
#106222682
#248511