Finite Group Databasebeta

← #13073502

Subgroups — #13073502

Order 1408.

800 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C11C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic
3C2×#66988C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#10622826C212yesmaximal, complemented
6#10622825C211yesmaximal, characteristic, complemented
7#10622607C212yesmaximal, complemented
8#10622574C212yesmaximal, complemented
9#10622568C211yesmaximal, characteristic, complemented
10#10622556C211yesmaximal, characteristic, complemented
11#10622553C212yesmaximal, complemented
12C24×D11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C23×C4×C11C2211yescharacteristic, complemented
16C22×C22⋊D11C2212yes—
17C23×Dic11C2211yescharacteristic
18C4×D4×C11—24no—
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic, complemented
22C2×C42×C11C2211yescharacteristic, complemented
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2212yescomplemented
26#66990—24no—
27#66988—24no—
28C2×(C2×D11)⋊C4—24no—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×(C2×D11)⋊C4C2212yes—
33C2×(C2×D11)⋊C4C2212yes—
34C2×C4⋊Dic11C2212yescomplemented
35C2×Dic11⋊C4C2212yescomplemented
36C11⋊#95C2212yescomplemented
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×C11D414yes—
50C22×C4×C11—22no—
51C22×C4×C11—42no—
52C22×C4×C11—42no—
53C22×C4×C11D414yescomplemented
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C2×C22⋊D11—24no—
60C2×C22⋊D11—24no—
61C2×C22⋊D11—42no—
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C22×Dic11C2312yes—
66C22×Dic11C2312yes—
67C22×Dic11C2312yes—
68C11×C4⋊C4—22no—
69C11×C22⋊C4—22no—
70C11×C22⋊C4—22no—
71C42×C11—22no—
72C22⋊Dic11—22no—
73C22⋊Dic11—24no—
74C22⋊Dic11—22no—
75(C2×D11)⋊C4—24no—
76(C2×D11)⋊C4—24no—
77(C2×D11)⋊C4—24no—
78(C2×D11)⋊C4—24no—
79(C2×D11)⋊C4—42no—
80C4⋊Dic11—42no—
81Dic11⋊C4—24no—
82#2534—111nomaximal, Sylow
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—21no—
86C23×C11—22no—
87C23×C11—21no—
88C23×C11—22no—
89C23×C11C2×D412yes—
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—28no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11C2×D412yes—
118C2×C4×C11C2×D412yes—
119C2×C4×C11C2×D412yes—
120C22⋊D11—48no—
121C2×Dic11—22no—
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×#123—111no—
132C2×#120—111no—
133C2×C4×D4D1111yescharacteristic, complemented
134C22×C22⋊C4—111no—
135#396—112no—
136#394—112no—
137#388—112no—
138#386—112no—
139#381—111no—
140#380—111no—
141#379—111no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—24no—
145C22×C11—24no—
146C22×C11—22no—
147C22×C11—24no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—42no—
151C22×C11#12114yes—
152C22×C11C22×D411yescharacteristic
153C22×C11C22×D411yescharacteristic
154C22×C11C2×#4111yescharacteristic
155C22×C11C2×#4112yes—
156C22×C11H(5,𝔽2)12yes—
157C2×D11—24no—
158C2×D11—24no—
159C2×D11—24no—
160C2×D11—416no—
161C2×D11—42no—
162C2×D11—42no—
163C2×D11—42no—
164C2×D11—42no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—41no—
169C4×C11—41no—
170Dic11—42no—
171Dic11—42no—
172Dic11—42no—
173C25—111no—
174C22×D4—112no—
175C22×D4C2×D1111yescharacteristic
176C23×C4—111no—
177C23×C4C2×D1111yescharacteristic
178C23×C4C2×D1111yescharacteristic, complemented
179#123—224no—
180#120—224no—
181C4×D4—24no—
182C2×C4⋊C4—112no—
183C2×C4⋊C4—112no—
184C2×C4⋊C4C2×D1111yescharacteristic, complemented
185C2×C22⋊C4—111no—
186C2×C22⋊C4—111no—
187C2×C22⋊C4—112no—
188C2×C22⋊C4—112no—
189C2×C22⋊C4—112no—
190C2×C22⋊C4—112no—
191C2×C22⋊C4—112no—
192C2×C22⋊C4—112no—
193C2×C22⋊C4—224no—
194C2×C22⋊C4C2×D1111yescharacteristic
195C2×C22⋊C4C2×D1111yescharacteristic, complemented
196C2×C42C2×D1111yescharacteristic, complemented
197#95—112no—
198#95—112no—
199#95—112no—
200C2×C11—24no—
201C2×C11—42no—
202C2×C11C2×#12111yescharacteristic
203C2×C11#52511yescharacteristic
204C2×C11#53411yescharacteristic
205C2×C11#54612yes—
206C2×C11#55112yes—
207D11—44no—
208C24—112no—
209C24—224no—
210C24—222no—
211C24—222no—
212C24—222no—
213C24—442no—
214C24C22×D1111yescharacteristic
215C24C22×D1111yescharacteristic
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—224no—
219C2×D4—224no—
220C2×D4—442no—
221C2×D4D4414yes—
222C22×C4—22no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—112no—
226C22×C4—112no—
227C22×C4—112no—
228C22×C4—222no—
229C22×C4—222no—
230C22×C4—222no—
231C22×C4C22⋊D1114yescomplemented
232C22×C4C22×D1111yescharacteristic
233C22×C4C22×D1111yescharacteristic
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1111yescharacteristic
236C22×C4C22×D1111yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—224no—
239C4⋊C4—442no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—224no—
243C22⋊C4—222no—
244C22⋊C4—222no—
245C22⋊C4—224no—
246C22⋊C4—224no—
247C22⋊C4—224no—
248C22⋊C4—224no—
249C22⋊C4—442no—
250C42—22no—
251C11#253411yescharacteristic, complemented, Sylow
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—21no—
258C23—114no—
259C23—228no—
260C23—222no—
261C23—222no—
262C23—222no—
263C23—222no—
264C23—222no—
265C23—222no—
266C23—448no—
267C23—448no—
268C23—444no—
269C23—444no—
270C23C2×D4412yes—
271C23C2×D4412yes—
272C23#433912yes—
273C23C2×C22⋊D1112yes—
274C23C23×D1111yescharacteristic
275D4—28no—
276D4—448no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—222no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—222no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—444no—
297C2×C4C2×D4412yes—
298C2×C4C2×C22⋊D1112yes—
299C2×C4C2×C22⋊D1112yes—
300C22—22no—
301C22—24no—
302C22—24no—
303C22—22no—
304C22—22no—
305C22—24no—
306C22—41no—
307C22—42no—
308C22—41no—
309C22—224no—
310C22—224no—
311C22—224no—
312C22—4416no—
313C22—442no—
314C22—442no—
315C22—442no—
316C22—442no—
317C22#6698314yes—
318C22C22×D4411yescharacteristic
319C22C2×#433911yescharacteristic
320C22#6703712yes—
321C22#41×D1112yes—
322C22C22×C22⋊D1111yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—41no—
327C4—41no—
328C4—442no—
329C4—442no—
330C4—442no—
331C2—24no—
332C2—42no—
333C2—444no—
334C2#1062308512yes—
335C2#1062308712yes—
336C2C2×#6698311yescharacteristic
337C2#1062333511yescharacteristic
338C2#1062335911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC2×#66990C2
hypercenterC2×C4×D4D11
hypocenterC11#2534
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C11C2semidirect
3. C2×#66988C2semidirect
4. C22×(C2×D11)⋊C4C2semidirect
5. #10622826C2semidirect
6. #10622825C2semidirect
7. #10622607C2semidirect
8. #10622574C2semidirect
9. #10622568C2semidirect
10. #10622556C2semidirect
11. #10622553C2semidirect
15. C23×C4×C11C22semidirect
19. C2×C11×C4⋊C4C22semidirect
21. C2×C11×C22⋊C4C22semidirect
22. C2×C42×C11C22semidirect
25. C2×C22⋊Dic11C22semidirect
34. C2×C4⋊Dic11C22semidirect
35. C2×Dic11⋊C4C22semidirect
36. C11⋊#95C22semidirect
37. C11⋊#95C22semidirect
38. C11⋊#95C22semidirect
53. C22×C4×C11D4semidirect
133. C2×C4×D4D11semidirect
178. C23×C4C2×D11semidirect
184. C2×C4⋊C4C2×D11semidirect
195. C2×C22⋊C4C2×D11semidirect
196. C2×C42C2×D11semidirect
231. C22×C4C22⋊D11semidirect
251. C11#2534semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669902
C2×#669882
C22×(C2×D11)⋊C42
#106228262
#106228252
#106226072
#106225742
#106225682
#106225562
#106225532
#253411