Finite Group Databasebeta

← #13074950

Subgroups — #13074950

Order 1408.

1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#120C211yesmaximal, characteristic, complemented
2C2×#67006C212yesmaximal, complemented
3C2×#66990C212yesmaximal, complemented
4C2×#66990C211yesmaximal, characteristic, complemented
5#10622835C212yesmaximal, complemented
6#10622834C211yesmaximal, characteristic, complemented
7#10622574C212yesmaximal, complemented
8#10622572C212yesmaximal, complemented
9#10622570C212yesmaximal, complemented
10C25×C11C2211yescharacteristic, complemented
11C24×D11C2211yescharacteristic, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2212yes—
17C11×#120—24no—
18C2×C11×C22⋊C4C2212yescomplemented
19C2×C11×C22⋊C4C2211yescharacteristic, complemented
20#67006—28no—
21C2×C22⋊Dic11C2212yescomplemented
22C2×C22⋊Dic11C2211yescharacteristic, complemented
23C2×C22⋊Dic11C2212yescomplemented
24C2×C22⋊Dic11C2212yescomplemented
25C2×C22⋊Dic11C2212yescomplemented
26#66990—24no—
27#66990—28no—
28C2×(C2×D11)⋊C4C2212yescomplemented
29C2×(C2×D11)⋊C4C2212yescomplemented
30C2×(C2×D11)⋊C4C2212yescomplemented
31C2×C4⋊Dic11C2211yescharacteristic, complemented
32C2×Dic11⋊C4C2212yescomplemented
33C2×C4×Dic11C2211yescharacteristic, complemented
34C11⋊#95C2212yescomplemented
35C24×C11—24no—
36C24×C11—22no—
37C24×C11—42no—
38C24×C11—41no—
39C24×C11—41no—
40C24×C11C2311yescharacteristic
41C24×C11C2311yescharacteristic
42C24×C11C2312yes—
43C23×D11—22no—
44C23×D11—24no—
45C23×D11—41no—
46C23×D11—42no—
47C23×D11—41no—
48C23×D11C2312yes—
49C2×D4×C11—24no—
50C2×D4×C11—24no—
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11—42no—
54C2×D4×C11D414yescomplemented
55C22×C4×C11C2312yes—
56C22×C4×C11C2311yescharacteristic
57C2×C22⋊D11—24no—
58C2×C22⋊D11—24no—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—24no—
61C2×C22⋊D11—42no—
62C2×C22⋊D11—42no—
63C2×C22⋊D11—42no—
64C2×C22⋊D11—42no—
65C2×C22⋊D11D418yescomplemented
66C22×Dic11C2312yes—
67C22×Dic11C2312yes—
68C22×Dic11C2312yes—
69C11×C22⋊C4—22no—
70C11×C22⋊C4—24no—
71C22⋊Dic11—24no—
72C22⋊Dic11—24no—
73C22⋊Dic11—24no—
74C22⋊Dic11—22no—
75C22⋊Dic11—24no—
76(C2×D11)⋊C4—24no—
77(C2×D11)⋊C4—24no—
78(C2×D11)⋊C4—24no—
79C4⋊Dic11—41no—
80Dic11⋊C4—42no—
81C4×Dic11—41no—
82#2679—111nomaximal, Sylow
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—22no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—22no—
97C23×C11—48no—
98C23×C11—44no—
99C23×C11—44no—
100C23×C11—48no—
101C23×C11—44no—
102C23×C11C2×D414yes—
103C23×C11C2×D412yes—
104C23×C11C2×D412yes—
105C23×C11C2411yescharacteristic
106C22×D11—22no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—22no—
110C22×D11—22no—
111C22×D11—22no—
112C22×D11—44no—
113C22×D11—48no—
114C22×D11—48no—
115C22×D11—44no—
116C22×D11—44no—
117C22×D11C2×D414yes—
118D4×C11—44no—
119D4×C11—48no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11C2×D412yes—
126C22⋊D11—48no—
127C22⋊D11—48no—
128C22⋊D11—48no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11C2×D414yes—
138C2×#120—112no—
139C2×#120—112no—
140C2×#120—111no—
141C2×#120D1111yescharacteristic, complemented
142#394—112no—
143#394—112no—
144#394—112no—
145#390—111no—
146#390—112no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—24no—
150C22×C11—24no—
151C22×C11—24no—
152C22×C11—24no—
153C22×C11—24no—
154C22×C11—416no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—41no—
160C22×C11—42no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—42no—
165C22×C11C22×D412yes—
166C22×C11C22×D411yescharacteristic
167C22×C11H(5,𝔽2)11yescharacteristic
168C22×C11H(5,𝔽2)12yes—
169C22×C11H(5,𝔽2)11yescharacteristic
170C2×D11—24no—
171C2×D11—24no—
172C2×D11—24no—
173C2×D11—416no—
174C2×D11—42no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C4×C11—22no—
179C4×C11—42no—
180Dic11—24no—
181Dic11—42no—
182Dic11—42no—
183C25—111no—
184C25C2×D1111yescharacteristic, complemented
185C22×D4—112no—
186C22×D4—112no—
187C22×D4—112no—
188C22×D4C2×D1112yes—
189C22×D4C2×D1111yescharacteristic
190#120—24no—
191#120—228no—
192#120—228no—
193#120—224no—
194C2×C4⋊C4—112no—
195C2×C4⋊C4—111no—
196C2×C22⋊C4—112no—
197C2×C22⋊C4—112no—
198C2×C22⋊C4—112no—
199C2×C22⋊C4—112no—
200C2×C22⋊C4—111no—
201C2×C22⋊C4—112no—
202C2×C22⋊C4—112no—
203C2×C22⋊C4—112no—
204C2×C22⋊C4C2×D1112yescomplemented
205C2×C22⋊C4C2×D1111yescharacteristic, complemented
206C2×C42—111no—
207#95—112no—
208C2×C11—42no—
209C2×C11—42no—
210C2×C11—44no—
211C2×C11#53411yescharacteristic
212C2×C11#53412yes—
213C2×C11D4212yes—
214C2×C11D4211yescharacteristic
215C2×C11H(3,𝔽4)11yescharacteristic
216D11—44no—
217C24—24no—
218C24—22no—
219C24—42no—
220C24—41no—
221C24—41no—
222C24—112no—
223C24—224no—
224C24—222no—
225C24—442no—
226C24—441no—
227C24—441no—
228C24C22×D1112yes—
229C24C22×D1111yescharacteristic
230C24C22×D1111yescharacteristic
231C2×D4—24no—
232C2×D4—24no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4—42no—
236C2×D4—118no—
237C2×D4—224no—
238C2×D4—224no—
239C2×D4—224no—
240C2×D4—224no—
241C2×D4—442no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—442no—
245C2×D4C22⋊D1114yescomplemented
246C22×C4—112no—
247C22×C4—112no—
248C22×C4—112no—
249C22×C4C22×D1112yes—
250C22×C4C22×D1111yescharacteristic
251C4⋊C4—442no—
252C4⋊C4—441no—
253C22⋊C4—22no—
254C22⋊C4—24no—
255C22⋊C4—224no—
256C22⋊C4—224no—
257C22⋊C4—224no—
258C22⋊C4—224no—
259C22⋊C4—224no—
260C22⋊C4—224no—
261C22⋊C4—222no—
262C22⋊C4—224no—
263C42—441no—
264C11#267911yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—21no—
273C23—21no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—48no—
280C23—44no—
281C23—44no—
282C23—48no—
283C23—44no—
284C23—114no—
285C23—222no—
286C23—222no—
287C23—222no—
288C23—222no—
289C23—222no—
290C23—222no—
291C23—448no—
292C23—444no—
293C23—444no—
294C23—448no—
295C23—444no—
296C23D4×D1114yes—
297C23C2×C22⋊D1112yes—
298C23C2×C22⋊D1112yes—
299C23C23×D1111yescharacteristic
300D4—44no—
301D4—48no—
302D4—448no—
303D4—448no—
304D4—448no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—114no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4C2×C22⋊D1112yes—
320C22—24no—
321C22—24no—
322C22—24no—
323C22—22no—
324C22—22no—
325C22—24no—
326C22—24no—
327C22—416no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—224no—
339C22—224no—
340C22—224no—
341C22—4416no—
342C22—442no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22C2×D4×D1112yes—
347C22#6703712yes—
348C22#6703711yescharacteristic
349C22#6703711yescharacteristic
350C22C22×C22⋊D1111yescharacteristic
351C4—22no—
352C4—42no—
353C4—224no—
354C4—442no—
355C4—442no—
356C2—44no—
357C2—42no—
358C2—42no—
359C2—444no—
360C2#1062312012yes—
361C2#1062312111yescharacteristic
362C2#1062312511yescharacteristic
363C2D4×C22⋊D1112yes—
364C2#1062333511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#120C2
hypercenterC2×#120D11
hypocenterC11#2679
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C11×#120C2semidirect
2. C2×#67006C2semidirect
3. C2×#66990C2semidirect
4. C2×#66990C2semidirect
5. #10622835C2semidirect
6. #10622834C2semidirect
7. #10622574C2semidirect
8. #10622572C2semidirect
9. #10622570C2semidirect
10. C25×C11C22semidirect
11. C24×D11C22semidirect
18. C2×C11×C22⋊C4C22semidirect
19. C2×C11×C22⋊C4C22semidirect
21. C2×C22⋊Dic11C22semidirect
22. C2×C22⋊Dic11C22semidirect
23. C2×C22⋊Dic11C22semidirect
24. C2×C22⋊Dic11C22semidirect
25. C2×C22⋊Dic11C22semidirect
28. C2×(C2×D11)⋊C4C22semidirect
29. C2×(C2×D11)⋊C4C22semidirect
30. C2×(C2×D11)⋊C4C22semidirect
31. C2×C4⋊Dic11C22semidirect
32. C2×Dic11⋊C4C22semidirect
33. C2×C4×Dic11C22semidirect
34. C11⋊#95C22semidirect
54. C2×D4×C11D4semidirect
65. C2×C22⋊D11D4semidirect
141. C2×#120D11semidirect
184. C25C2×D11semidirect
204. C2×C22⋊C4C2×D11semidirect
205. C2×C22⋊C4C2×D11semidirect
245. C2×D4C22⋊D11semidirect
264. C11#2679semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1202
C2×#670062
C2×#669902
#106228352
#106228342
#106225742
#106225722
#106225702
#267911