Finite Group Databasebeta

← #13072929

Subgroups — #13072929

Order 1408.

584 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D11C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C11×#380C211yesmaximal, characteristic, complemented
4#10622825C211yesmaximal, characteristic, complemented
5#10622600C211yesmaximal, characteristic, complemented
6#10622598C211yesmaximal, characteristic, complemented
7#10622586C211yesmaximal, characteristic, complemented
8#10622569C212yesmaximal
9#10622562C212yesmaximal, complemented
10#10622281C212yesmaximal, complemented
11#10622271C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2212yes—
21C4×C22⋊D11—24no—
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31C4⋊C4×D11—24no—
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—22no—
47C2×C22⋊D11—22no—
48C2×C22⋊D11Q814yes—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C2×C4×D11—24no—
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—42no—
58C2×C4×D11—42no—
59C2×C4×D11D414yes—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—22no—
62C11×C22⋊C4—42no—
63C22⋊Dic11—22no—
64C22⋊Dic11—42no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—24no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70Dic11⋊C4—24no—
71Dic11⋊C4—22no—
72Dic11⋊C4—42no—
73C4×Dic11—22no—
74#2487—111nomaximal, Sylow
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11C2×Q812yes—
82C23×C11C2411yescharacteristic
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11C2×D412yes—
88C22×D11C2×Q812yes—
89C22×D11#4112yes—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—44no—
100C2×C4×C11C2×D412yes—
101C2×C4×C11#4112yes—
102C2×C4×C11#4112yes—
103C22⋊D11—28no—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11C2×D412yes—
118C2×Dic11C2×Q812yes—
119C4×D11—28no—
120C4×D11—48no—
121C2×C4×D4—111no—
122C22×C4⋊C4—111no—
123#400—112no—
124#399—112no—
125#389—111no—
126#389—111no—
127#386—112no—
128#385—112no—
129#380—111no—
130#380—111no—
131#380D1111yescharacteristic, complemented
132C22×C11—22no—
133C22×C11—22no—
134C22×C11—22no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11C22×D411yescharacteristic
140C22×C11C22×Q811yescharacteristic
141C22×C11C2×#4111yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11C2×#4111yescharacteristic
144C22×C11H(5,𝔽2)11yescharacteristic
145C22×C11H(5,𝔽2)11yescharacteristic
146C2×D11—22no—
147C2×D11—22no—
148C2×D11—22no—
149C2×D11—22no—
150C2×D11—22no—
151C2×D11—22no—
152C2×D11C22⋊Q814yes—
153C4×C11—41no—
154C4×C11—42no—
155C4×C11—42no—
156C4×C11#12314yes—
157Dic11—22no—
158Dic11—22no—
159Dic11—42no—
160Dic11—41no—
161Dic11—42no—
162C22×D4—111no—
163C23×C4—111no—
164C23×C4—112no—
165C23×C4C2×D1111yescharacteristic
166C4×D4—224no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—112no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—112no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—224no—
174C2×C4⋊C4C2×D1111yescharacteristic
175C2×C4⋊C4C2×D1111yescharacteristic
176C2×C22⋊C4—111no—
177C2×C22⋊C4—111no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4C2×D1112yes—
181C2×C42—111no—
182#95—112no—
183#95—112no—
184#95—112no—
185#95—112no—
186#95C2×D1112yes—
187C2×C11—42no—
188C2×C11C2×C22⋊Q811yescharacteristic
189C2×C11C2×#12311yescharacteristic
190C2×C11#53511yescharacteristic
191C2×C11#55311yescharacteristic
192C2×C11#55311yescharacteristic
193C2×C11#55411yescharacteristic
194C2×C11#55411yescharacteristic
195D11—24no—
196C24—111no—
197C24C22×D1111yescharacteristic
198C2×D4—114no—
199C2×D4—222no—
200C2×D4—222no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—111no—
205C22×C4—111no—
206C22×C4—114no—
207C22×C4—112no—
208C22×C4—112no—
209C22×C4—111no—
210C22×C4—224no—
211C22×C4—222no—
212C22×C4—222no—
213C22×C4—442no—
214C22×C4—442no—
215C22×C4C22×D1111yescharacteristic
216C22×C4C22×D1112yes—
217C22×C4C22×D1112yes—
218C22×C4C22×D1111yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—224no—
222C4⋊C4—222no—
223C4⋊C4—222no—
224C4⋊C4—222no—
225C4⋊C4—442no—
226C4⋊C4—442no—
227C22⋊C4—42no—
228C22⋊C4—222no—
229C22⋊C4—224no—
230C22⋊C4—222no—
231C22⋊C4—442no—
232C42—222no—
233C11#248711yescharacteristic, complemented, Sylow
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—112no—
241C23—112no—
242C23—112no—
243C23—221no—
244C23—221no—
245C23—221no—
246C23—221no—
247C23Q8×D1112yes—
248C23C23×D1111yescharacteristic
249D4—228no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—44no—
260C2×C4—112no—
261C2×C4—112no—
262C2×C4—221no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—221no—
266C2×C4—228no—
267C2×C4—222no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—448no—
277C2×C4#433912yes—
278C2×C4D4×D1112yes—
279C2×C4#434112yes—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22—114no—
288C22—222no—
289C22—222no—
290C22—222no—
291C22—222no—
292C22—222no—
293C22—222no—
294C22C2×#433911yescharacteristic
295C22C2×D4×D1111yescharacteristic
296C22C2×#434111yescharacteristic
297C22#6703711yescharacteristic
298C22C2×Q8×D1111yescharacteristic
299C22#41×D1111yescharacteristic
300C22#6704211yescharacteristic
301C4—41no—
302C4—42no—
303C4—42no—
304C4—222no—
305C4—222no—
306C4—442no—
307C4—442no—
308C4—441no—
309C4#6693614yes—
310C2—42no—
311C2—224no—
312C2C2×#6693611yescharacteristic
313C2#1062304211yescharacteristic
314C2#1062306111yescharacteristic
315C2#1062313811yescharacteristic
316C2#1062314511yescharacteristic
317C2D11×C22⋊Q811yescharacteristic
318C2#1062316611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC22×C22⋊D11C22
hypercenter#380D11
hypocenterC11#2487
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D11C2semidirect
3. C11×#380C2semidirect
4. #10622825C2semidirect
5. #10622600C2semidirect
6. #10622598C2semidirect
7. #10622586C2semidirect
9. #10622562C2semidirect
10. #10622281C2semidirect
11. #10622271C2semidirect
131. #380D11semidirect
233. C11#2487semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D112
C2×C4⋊C4×D112
C11×#3802
#106228252
#106226002
#106225982
#106225862
#106225692
#106225622
#106222812
#106222712
#248711