Finite Group Databasebeta

← #13072002

Subgroups — #13072002

Order 1408.

786 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic
3C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4C2×#66979C211yesmaximal, characteristic, complemented
5#10622833C211yesmaximal, characteristic, complemented
6#10622607C212yesmaximal, complemented
7#10622603C212yesmaximal, complemented
8#10622574C212yesmaximal, complemented
9#10622570C212yesmaximal, complemented
10#10622568C211yesmaximal, characteristic, complemented
11#10622559C211yesmaximal, characteristic, complemented
12C24×D11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C23×Dic11C2211yescharacteristic
17C11×#123—24no—
18C2×C11×C4⋊C4C2211yescharacteristic, complemented
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic, complemented
22C2×C11×C22⋊C4C2211yescharacteristic, complemented
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2212yescomplemented
26#66990—24no—
27C2×(C2×D11)⋊C4—24no—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×(C2×D11)⋊C4C2212yes—
33#66979—24no—
34C2×C4⋊Dic11C2212yescomplemented
35C2×Dic11⋊C4C2212yescomplemented
36C2×C4×Dic11C2212yescomplemented
37C11⋊#95C2212yescomplemented
38C11⋊#95C2212yescomplemented
39C24×C11C2311yescharacteristic
40C24×C11C2311yescharacteristic
41C23×D11—22no—
42C23×D11—24no—
43C23×D11—22no—
44C23×D11—22no—
45C23×D11—42no—
46C23×D11C2312yes—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11D414yescomplemented
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C2×C22⋊D11—24no—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—42no—
61C22×Dic11—22no—
62C22×Dic11—42no—
63C22×Dic11C2312yes—
64C22×Dic11C2312yes—
65C22×Dic11C2312yes—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—22no—
68C11×C22⋊C4—22no—
69C11×C22⋊C4—22no—
70C11×C22⋊C4—22no—
71C22⋊Dic11—22no—
72C22⋊Dic11—42no—
73C22⋊Dic11D414yes—
74(C2×D11)⋊C4—24no—
75(C2×D11)⋊C4—24no—
76(C2×D11)⋊C4—24no—
77(C2×D11)⋊C4—24no—
78(C2×D11)⋊C4—42no—
79C4⋊Dic11—24no—
80Dic11⋊C4—42no—
81C4×Dic11—24no—
82#2411—111nomaximal, Sylow
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—22no—
88C23×C11—21no—
89C23×C11—22no—
90C23×C11C2×D412yes—
91C23×C11C2×D412yes—
92C23×C11#4112yes—
93C23×C11C2411yescharacteristic
94C22×D11—28no—
95C22×D11—22no—
96C22×D11—22no—
97C22×D11—22no—
98C22×D11—22no—
99C22×D11—22no—
100C22×D11—22no—
101C22×D11—48no—
102C22×D11—48no—
103C22×D11—44no—
104C22×D11—44no—
105C22×D11#4114yes—
106D4×C11—44no—
107C2×C4×C11—28no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11C2×D412yes—
120C2×C4×C11C2×D412yes—
121C22⋊D11—48no—
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—44no—
131C2×Dic11C2×D414yes—
132C2×#123D1111yescharacteristic, complemented
133C2×#120—111no—
134C2×#117—111no—
135C22×C22⋊C4—111no—
136#396—112no—
137#394—112no—
138#390—112no—
139#388—112no—
140#386—111no—
141#385—111no—
142#379—111no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—24no—
146C22×C11—24no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11#12114yes—
153C22×C11C22×D411yescharacteristic
154C22×C11C22×D411yescharacteristic
155C22×C11C2×#4111yescharacteristic
156C22×C11C2×#4112yes—
157C22×C11H(5,𝔽2)12yes—
158C2×D11—24no—
159C2×D11—24no—
160C2×D11—24no—
161C2×D11—416no—
162C2×D11—42no—
163C2×D11—42no—
164C2×D11—42no—
165C2×D11—42no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171Dic11—24no—
172Dic11—42no—
173Dic11—42no—
174C25—111no—
175C22×D4—112no—
176C22×D4C2×D1111yescharacteristic
177C23×C4—111no—
178C23×C4C2×D1111yescharacteristic
179#123—24no—
180#120—224no—
181#117—224no—
182C2×C4⋊C4—112no—
183C2×C4⋊C4—112no—
184C2×C4⋊C4C2×D1111yescharacteristic, complemented
185C2×C4⋊C4C2×D1111yescharacteristic, complemented
186C2×C22⋊C4—111no—
187C2×C22⋊C4—111no—
188C2×C22⋊C4—112no—
189C2×C22⋊C4—112no—
190C2×C22⋊C4—112no—
191C2×C22⋊C4—112no—
192C2×C22⋊C4—112no—
193C2×C22⋊C4—112no—
194C2×C22⋊C4—224no—
195C2×C22⋊C4C2×D1111yescharacteristic
196C2×C22⋊C4C2×D1111yescharacteristic, complemented
197C2×C22⋊C4C2×D1111yescharacteristic, complemented
198C2×C42—112no—
199#95—112no—
200#95—112no—
201C2×C11—24no—
202C2×C11—81no—
203C2×C11C2×#12111yescharacteristic
204C2×C11#52511yescharacteristic
205C2×C11#53511yescharacteristic
206C2×C11#54612yes—
207C2×C11#55112yes—
208D11—44no—
209C24—112no—
210C24—224no—
211C24—222no—
212C24—222no—
213C24—222no—
214C24—442no—
215C24C22×D1111yescharacteristic
216C24C22×D1111yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—224no—
221C2×D4—224no—
222C2×D4—442no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—112no—
226C22×C4—112no—
227C22×C4—112no—
228C22×C4—222no—
229C22×C4—442no—
230C22×C4C22⋊D1114yescomplemented
231C22×C4C22×D1111yescharacteristic
232C22×C4C22×D1111yescharacteristic
233C22×C4C22×D1111yescharacteristic
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1111yescharacteristic
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—224no—
239C4⋊C4—442no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—114no—
244C22⋊C4—224no—
245C22⋊C4—224no—
246C22⋊C4—222no—
247C22⋊C4—224no—
248C22⋊C4—224no—
249C22⋊C4—442no—
250C22⋊C4—442no—
251C42—224no—
252C11#241111yescharacteristic, complemented, Sylow
253C23—22no—
254C23—22no—
255C23—21no—
256C23—21no—
257C23—22no—
258C23—22no—
259C23—21no—
260C23—114no—
261C23—228no—
262C23—222no—
263C23—222no—
264C23—222no—
265C23—222no—
266C23—222no—
267C23—222no—
268C23—448no—
269C23—448no—
270C23—444no—
271C23—444no—
272C23D4×D1112yes—
273C23#434112yes—
274C23C2×C22⋊D1112yes—
275C23C23×D1111yescharacteristic
276D4—44no—
277D4—448no—
278C2×C4—28no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—114no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—222no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—222no—
297C2×C4—222no—
298C2×C4—222no—
299C2×C4—444no—
300C2×C4C2×C22⋊D1112yes—
301C2×C4C2×C22⋊D1112yes—
302C22—22no—
303C22—22no—
304C22—24no—
305C22—24no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—42no—
310C22—42no—
311C22—224no—
312C22—224no—
313C22—224no—
314C22—4416no—
315C22—442no—
316C22—442no—
317C22—442no—
318C22—442no—
319C22#6699214yes—
320C22C2×D4×D1111yescharacteristic
321C22C2×#434111yescharacteristic
322C22#41×D1112yes—
323C22#6704212yes—
324C22C22×C22⋊D1111yescharacteristic
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—224no—
331C4—442no—
332C4—442no—
333C2—24no—
334C2—81no—
335C2—444no—
336C2#1062318512yes—
337C2#1062318912yes—
338C2C2×#6699211yescharacteristic
339C2#1062335911yescharacteristic
340C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#123C2
prime radicalC2×#66990C2
hypercenterC2×#123D11
hypocenterC11#2411
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
3. C22×(C2×D11)⋊C4C2semidirect
4. C2×#66979C2semidirect
5. #10622833C2semidirect
6. #10622607C2semidirect
7. #10622603C2semidirect
8. #10622574C2semidirect
9. #10622570C2semidirect
10. #10622568C2semidirect
11. #10622559C2semidirect
18. C2×C11×C4⋊C4C22semidirect
19. C2×C11×C4⋊C4C22semidirect
21. C2×C11×C22⋊C4C22semidirect
22. C2×C11×C22⋊C4C22semidirect
25. C2×C22⋊Dic11C22semidirect
34. C2×C4⋊Dic11C22semidirect
35. C2×Dic11⋊C4C22semidirect
36. C2×C4×Dic11C22semidirect
37. C11⋊#95C22semidirect
38. C11⋊#95C22semidirect
52. C22×C4×C11D4semidirect
132. C2×#123D11semidirect
184. C2×C4⋊C4C2×D11semidirect
185. C2×C4⋊C4C2×D11semidirect
196. C2×C22⋊C4C2×D11semidirect
197. C2×C22⋊C4C2×D11semidirect
230. C22×C4C22⋊D11semidirect
252. C11#2411semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×#669902
C22×(C2×D11)⋊C42
C2×#669792
#106228332
#106226072
#106226032
#106225742
#106225702
#106225682
#106225592
#241111