Finite Group Databasebeta

← #13072110

Subgroups — #13072110

Order 1408.

596 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66983C211yesmaximal, characteristic
2C2×#66946C211yesmaximal, characteristic, complemented
3C11×#380C211yesmaximal, characteristic, complemented
4C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#10622601C211yesmaximal, characteristic, complemented
6#10622598C211yesmaximal, characteristic, complemented
7#10622590C211yesmaximal, characteristic, complemented
8#10622574C212yesmaximal, complemented
9#10622569C212yesmaximal, complemented
10#10622287C212yesmaximal, complemented
11#10622277C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic
21#66983—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30#66946—24no—
31C11×#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2312yes—
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—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—42no—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C2×D44—22no—
55C2×D44—22no—
56C2×D44D414yes—
57C2×C4×D11—24no—
58C2×C4×D11—24no—
59C2×C4×D11—42no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—22no—
62C11×C22⋊C4—42no—
63C22⋊Dic11—22no—
64C22⋊Dic11—22no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69C4⋊Dic11—22no—
70C4⋊Dic11—42no—
71C4×Dic11—22no—
72C4×Dic11—22no—
73#2420—111nomaximal, Sylow
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11#4112yes—
81C23×C11C2411yescharacteristic
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11C2×D414yes—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—44no—
99C2×C4×C11C2×D412yes—
100C2×C4×C11#4112yes—
101C2×C4×C11#4112yes—
102C22⋊D11—48no—
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—22no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11#4112yes—
118D44—28no—
119C4×D11—48no—
120C2×#121—111no—
121C2×C4×D4—111no—
122#397—112no—
123#394—112no—
124#390—111no—
125#389—111no—
126#386—112no—
127#382—111no—
128#381—112no—
129#380D1111yescharacteristic, complemented
130C4×C22⋊C4—111no—
131C22×C11—22no—
132C22×C11—22no—
133C22×C11—22no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11C22×D411yescharacteristic
139C22×C11C2×#4111yescharacteristic
140C22×C11C2×#4111yescharacteristic
141C22×C11C2×#4111yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11H(5,𝔽2)11yescharacteristic
144C22×C11H(5,𝔽2)11yescharacteristic
145C2×D11—24no—
146C2×D11—24no—
147C2×D11—24no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C4×C11—41no—
153C4×C11—42no—
154C4×C11—42no—
155C4×C11#12314yes—
156Dic11—22no—
157Dic11—41no—
158Dic11—42no—
159Dic11—41no—
160Dic11—41no—
161C22×D4—112no—
162C22×D4—111no—
163C23×C4—112no—
164C23×C4C2×D1111yescharacteristic
165#121—224no—
166C4×D4—224no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—112no—
169C2×C4⋊C4C2×D1111yescharacteristic
170C2×C4⋊C4C2×D1111yescharacteristic
171C2×C22⋊C4—111no—
172C2×C22⋊C4—111no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4C2×D1112yes—
178C2×C42—111no—
179C2×C42—111no—
180#95—111no—
181#95—111no—
182#95—112no—
183#95—112no—
184#95—112no—
185#95C2×D1112yes—
186C2×C11—42no—
187C2×C11C2×#12311yescharacteristic
188C2×C11#52911yescharacteristic
189C2×C11#54011yescharacteristic
190C2×C11#54611yescharacteristic
191C2×C11#54611yescharacteristic
192C2×C11#55311yescharacteristic
193C2×C11#55511yescharacteristic
194D11—44no—
195C24—112no—
196C24C22×D1111yescharacteristic
197C2×D4—114no—
198C2×D4—224no—
199C2×D4—224no—
200C2×D4—222no—
201C2×D4—222no—
202C2×D4—442no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—111no—
207C22×C4—111no—
208C22×C4—111no—
209C22×C4—112no—
210C22×C4—111no—
211C22×C4—224no—
212C22×C4—224no—
213C22×C4—442no—
214C22×C4C22×D1111yescharacteristic
215C22×C4C22×D1112yes—
216C22×C4C22×D1112yes—
217C22×C4C22×D1111yescharacteristic
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—222no—
221C4⋊C4—442no—
222C22⋊C4—42no—
223C22⋊C4—224no—
224C22⋊C4—224no—
225C22⋊C4—222no—
226C22⋊C4—222no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C42—222no—
230C42—222no—
231C11#242011yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—114no—
239C23—222no—
240C23—222no—
241C23—222no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23#434312yes—
246C23C23×D1111yescharacteristic
247D4—228no—
248D4—448no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—44no—
259C2×C4—112no—
260C2×C4—221no—
261C2×C4—221no—
262C2×C4—221no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—222no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—222no—
274C2×C4—448no—
275C2×C4#433912yes—
276C2×C4D4×D1112yes—
277C2×C4#434112yes—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—224no—
286C22—224no—
287C22—224no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22C2×#433911yescharacteristic
293C22C2×D4×D1111yescharacteristic
294C22C2×#434111yescharacteristic
295C22#6703711yescharacteristic
296C22C2×#434311yescharacteristic
297C22#41×D1111yescharacteristic
298C22#6704211yescharacteristic
299C4—41no—
300C4—42no—
301C4—42no—
302C4—222no—
303C4—441no—
304C4—441no—
305C4—442no—
306C4—441no—
307C4#6693614yes—
308C2—42no—
309C2—444no—
310C2C2×#6693611yescharacteristic
311C2#1062304511yescharacteristic
312C2#1062306311yescharacteristic
313C2#1062314311yescharacteristic
314C2#1062315011yescharacteristic
315C2#1062315511yescharacteristic
316C2#1062316111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC2×#66983C2
hypercenter#380D11
hypocenterC11#2420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#66946C2semidirect
3. C11×#380C2semidirect
4. C4×C22⋊Dic11C2semidirect
5. #10622601C2semidirect
6. #10622598C2semidirect
7. #10622590C2semidirect
8. #10622574C2semidirect
9. #10622569C2semidirect
10. #10622287C2semidirect
11. #10622277C2semidirect
129. #380D11semidirect
231. C11#2420semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×#669462
C11×#3802
C4×C22⋊Dic112
#106226012
#106225982
#106225902
#106225742
#106225692
#106222872
#106222772
#242011