Finite Group Databasebeta

← #13071995

Subgroups — #13071995

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×#117C211yesmaximal, characteristic, complemented
2C2×#66982C211yesmaximal, characteristic, complemented
3C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic
5#10622607C212yesmaximal, complemented
6#10622604C212yesmaximal, complemented
7#10622571C211yesmaximal, characteristic, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622563C211yesmaximal, characteristic, complemented
10#10622553C212yesmaximal, complemented
11#10622552C212yesmaximal, complemented
12C24×D11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C23×Dic11C2211yescharacteristic
16C22×D44C2212yes—
17C11×#117—24no—
18C2×C11×C4⋊C4C2212yescomplemented
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C42×C11C2212yescomplemented
22C2×C22⋊Dic11C2211yescharacteristic
23#66982—24no—
24C2×(C2×D11)⋊C4—24no—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
31C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
32C2×(C2×D11)⋊C4C2212yescomplemented
33C2×C4⋊Dic11C2212yescomplemented
34C2×Dic11⋊C4C2211yescharacteristic, complemented
35C2×Dic11⋊C4C2211yescharacteristic, complemented
36#66935—24no—
37C11⋊#95C2212yescomplemented
38C11⋊#95C2212yescomplemented
39C24×C11C2311yescharacteristic
40C23×D11—22no—
41C23×D11—24no—
42C23×D11—22no—
43C23×D11—22no—
44C23×D11—42no—
45C23×D11C2311yescharacteristic
46C23×D11C2312yes—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11D414yescomplemented
50C22×C4×C11C2312yes—
51C22×C4×C11C2312yes—
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C2×C22⋊D11—22no—
55C2×C22⋊D11—22no—
56C2×C22⋊D11—22no—
57C22×Dic11—22no—
58C22×Dic11—42no—
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2312yes—
62C22×Dic11C2311yescharacteristic
63C2×D44—24no—
64C2×D44—24no—
65C2×D44—42no—
66C11×C4⋊C4—24no—
67C11×C22⋊C4—22no—
68C11×C22⋊C4D414yes—
69C42×C11—24no—
70C22⋊Dic11—22no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—24no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4—42no—
78(C2×D11)⋊C4—42no—
79C4⋊Dic11—42no—
80Dic11⋊C4—22no—
81Dic11⋊C4—22no—
82#2411—111nomaximal, Sylow
83C23×C11—22no—
84C23×C11—22no—
85C23×C11C2×D412yes—
86C23×C11C2×D412yes—
87C23×C11#4112yes—
88C23×C11C2411yescharacteristic
89C22×D11—28no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11—22no—
95C22×D11—22no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—22no—
99C22×D11—21no—
100C22×D11—22no—
101C22×D11—48no—
102C22×D11—48no—
103C22×D11—44no—
104C22×D11—44no—
105C22×D11#4114yes—
106C2×C4×C11—28no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11C2×D412yes—
117C2×C4×C11C2×D412yes—
118C2×C4×C11C2×D414yes—
119C22⋊D11—44no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—22no—
124C2×Dic11—21no—
125C2×Dic11—22no—
126C2×Dic11—21no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—44no—
131D44—48no—
132C2×#123—111no—
133C2×#120—111no—
134C2×#117D1111yescharacteristic, complemented
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#12114yes—
148C22×C11C22×D411yescharacteristic
149C22×C11C22×D411yescharacteristic
150C22×C11C2×#4111yescharacteristic
151C22×C11C2×#4112yes—
152C22×C11H(5,𝔽2)12yes—
153C2×D11—24no—
154C2×D11—24no—
155C2×D11—24no—
156C2×D11—416no—
157C2×D11—42no—
158C2×D11—42no—
159C2×D11—42no—
160C2×D11—42no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—42no—
165C2×D11—42no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—24no—
169C4×C11—42no—
170Dic11—41no—
171Dic11—41no—
172Dic11—41no—
173Dic11—42no—
174C25—111no—
175C22×D4—111no—
176C22×D4—112no—
177C23×C4—111no—
178C23×C4C2×D1111yescharacteristic
179#123—224no—
180#120—224no—
181#117—24no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4C2×D1112yescomplemented
186C2×C22⋊C4—111no—
187C2×C22⋊C4—112no—
188C2×C22⋊C4—112no—
189C2×C22⋊C4—112no—
190C2×C22⋊C4—111no—
191C2×C22⋊C4—111no—
192C2×C22⋊C4—112no—
193C2×C22⋊C4—112no—
194C2×C22⋊C4—112no—
195C2×C22⋊C4—224no—
196C2×C22⋊C4C2×D1111yescharacteristic
197C2×C22⋊C4C2×D1111yescharacteristic
198C2×C42C2×D1112yescomplemented
199#95—112no—
200#95—112no—
201C2×C11—24no—
202C2×C11C2×#12111yescharacteristic
203C2×C11#52511yescharacteristic
204C2×C11#53511yescharacteristic
205C2×C11#54612yes—
206C2×C11#55112yes—
207D11—44no—
208D11—81no—
209C24—112no—
210C24—111no—
211C24—224no—
212C24—222no—
213C24—222no—
214C24—222no—
215C24—442no—
216C24C22×D1111yescharacteristic
217C2×D4—224no—
218C2×D4—222no—
219C2×D4—222no—
220C2×D4—222no—
221C2×D4—224no—
222C2×D4—442no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—111no—
226C22×C4—112no—
227C22×C4—111no—
228C22×C4—111no—
229C22×C4—222no—
230C22×C4—442no—
231C22×C4D4414yescomplemented
232C22×C4C22×D1112yes—
233C22×C4C22×D1111yescharacteristic
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1112yes—
236C4⋊C4—24no—
237C4⋊C4—222no—
238C4⋊C4—222no—
239C4⋊C4—442no—
240C22⋊C4—22no—
241C22⋊C4—224no—
242C22⋊C4—222no—
243C22⋊C4—224no—
244C22⋊C4—224no—
245C22⋊C4—222no—
246C22⋊C4—222no—
247C22⋊C4—224no—
248C22⋊C4—442no—
249C22⋊C4—442no—
250C22⋊C4C22⋊D1114yes—
251C42—24no—
252C11#241111yescharacteristic, complemented, Sylow
253C23—22no—
254C23—22no—
255C23—114no—
256C23—228no—
257C23—222no—
258C23—222no—
259C23—222no—
260C23—222no—
261C23—222no—
262C23—222no—
263C23—221no—
264C23—221no—
265C23—222no—
266C23—222no—
267C23—221no—
268C23—448no—
269C23—448no—
270C23—444no—
271C23—444no—
272C23C2×D4412yes—
273C23#433912yes—
274C23C2×C22⋊D1112yes—
275C23C23×D1111yescharacteristic
276D4—448no—
277D4—444no—
278C2×C4—28no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—222no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—222no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—222no—
297C2×C4—221no—
298C2×C4—444no—
299C2×C4C2×D4412yes—
300C2×C4C2×D4412yes—
301C2×C4C2×C22⋊D1114yes—
302C22—22no—
303C22—22no—
304C22—24no—
305C22—24no—
306C22—224no—
307C22—224no—
308C22—224no—
309C22—4416no—
310C22—442no—
311C22—442no—
312C22—442no—
313C22—442no—
314C22—441no—
315C22—441no—
316C22—442no—
317C22—441no—
318C22—442no—
319C22#6698314yes—
320C22C22×D4411yescharacteristic
321C22C2×#433911yescharacteristic
322C22#41×D1112yes—
323C22#6704212yes—
324C22C22×C22⋊D1111yescharacteristic
325C4—22no—
326C4—22no—
327C4—24no—
328C4—42no—
329C4—441no—
330C4—442no—
331C4—441no—
332C4—441no—
333C2—24no—
334C2—444no—
335C2—881no—
336C2#1062305511yescharacteristic
337C2#1062305611yescharacteristic
338C2#1062305812yes—
339C2C2×#6698311yescharacteristic
340C2#1062336012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#117C2
prime radicalC2×#66935C2
hypercenterC2×#117D11
hypocenterC11#2411
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C11×#117C2semidirect
2. C2×#66982C2semidirect
3. C22×(C2×D11)⋊C4C2semidirect
5. #10622607C2semidirect
6. #10622604C2semidirect
7. #10622571C2semidirect
8. #10622568C2semidirect
9. #10622563C2semidirect
10. #10622553C2semidirect
11. #10622552C2semidirect
18. C2×C11×C4⋊C4C22semidirect
21. C2×C42×C11C22semidirect
30. C2×(C2×D11)⋊C4C22semidirect
31. C2×(C2×D11)⋊C4C22semidirect
32. C2×(C2×D11)⋊C4C22semidirect
33. C2×C4⋊Dic11C22semidirect
34. C2×Dic11⋊C4C22semidirect
35. C2×Dic11⋊C4C22semidirect
37. C11⋊#95C22semidirect
38. C11⋊#95C22semidirect
49. C22×C4×C11D4semidirect
134. C2×#117D11semidirect
185. C2×C4⋊C4C2×D11semidirect
198. C2×C42C2×D11semidirect
231. C22×C4D44semidirect
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×#1172
C2×#669822
C22×(C2×D11)⋊C42
C2×#669352
#106226072
#106226042
#106225712
#106225682
#106225632
#106225532
#106225522
#241111