Finite Group Databasebeta

← #13074420

Subgroups — #13074420

Order 1408.

668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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×#66999C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D11C211yesmaximal, characteristic
3C11×#393C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic, complemented
5#10622568C212yesmaximal
6#10622562C211yesmaximal, characteristic, complemented
7#10622561C212yesmaximal, complemented
8#10622290C211yesmaximal, characteristic, complemented
9#10622289C212yesmaximal, complemented
10#10622281C212yesmaximal, complemented
11#10622280C211yesmaximal, characteristic, complemented
12C24×D11C2211yescharacteristic
13C22×Q8×C11C2211yescharacteristic, complemented
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20#66999—24no—
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×C4⋊Dic11C2211yescharacteristic, complemented
28C2×C4⋊Dic11C2212yescomplemented
29C2×Dic11⋊C4C2212yescomplemented
30C2×Dic11⋊C4C2212yescomplemented
31C2×Dic11⋊C4C2212yescomplemented
32C22⋊C4×D11—24no—
33C11×#95C2211yescharacteristic, complemented
34C11×#95C2212yescomplemented
35C11⋊#95C2211yescharacteristic, complemented
36C11⋊#95C2212yescomplemented
37C24×C11C2311yescharacteristic
38C23×D11—22no—
39C23×D11—22no—
40C23×D11—42no—
41C23×D11—42no—
42C23×D11Q814yescomplemented
43C23×D11C2311yescharacteristic
44C23×D11C2311yescharacteristic
45C2×Q8×C11—22no—
46C2×Q8×C11—42no—
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2312yes—
50C22×C4×C11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C2×C4×D11—22no—
56C2×C4×D11—42no—
57C2×C4×D11—42no—
58C2×C4×D11D414yes—
59C11×C22⋊C4—22no—
60C11×C22⋊C4—42no—
61C22⋊Dic11—22no—
62C22⋊Dic11—42no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69C4⋊Dic11—22no—
70C4⋊Dic11—42no—
71Dic11⋊C4—24no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74#2626—111nomaximal, Sylow
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11C2×Q812yes—
80C23×C11C2411yescharacteristic
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—28no—
88C22×D11—48no—
89C22×D11—44no—
90C22×D11—44no—
91C22×D11—48no—
92C22×D11C2×D412yes—
93C22×D11C2×Q812yes—
94C22×D11C2×Q812yes—
95C22×D11#4112yes—
96Q8×C11—44no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11C2×D412yes—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11C2×D412yes—
117C4×D11—44no—
118C4×D11—44no—
119C2×C22⋊Q8—111no—
120C22×C22⋊C4—111no—
121#399—111no—
122#399—111no—
123#396—112no—
124#396—112no—
125#393—111no—
126#393D1111yescharacteristic, complemented
127#385—112no—
128#380—111no—
129#379—112no—
130C22×C11—22no—
131C22×C11—24no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—42no—
135C22×C11C22×D411yescharacteristic
136C22×C11C22×Q811yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C11H(5,𝔽2)12yes—
139C22×C11H(5,𝔽2)12yes—
140C2×D11—22no—
141C2×D11—22no—
142C2×D11—24no—
143C2×D11—24no—
144C2×D11—22no—
145C2×D11—24no—
146C2×D11—416no—
147C2×D11—41no—
148C2×D11—41no—
149C2×D11—42no—
150C2×D11C22⋊Q814yes—
151C4×C11—22no—
152C4×C11—42no—
153C4×C11—41no—
154C4×C11—42no—
155Dic11—22no—
156Dic11—41no—
157Dic11—42no—
158Dic11—42no—
159C25—111no—
160C22×Q8C2×D1111yescharacteristic, complemented
161C23×C4—111no—
162C23×C4—111no—
163C22⋊Q8—224no—
164C2×C4⋊C4—112no—
165C2×C4⋊C4—111no—
166C2×C4⋊C4—112no—
167C2×C4⋊C4—112no—
168C2×C4⋊C4—112no—
169C2×C22⋊C4—111no—
170C2×C22⋊C4—111no—
171C2×C22⋊C4—111no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4—224no—
178C2×C22⋊C4C2×D1111yescharacteristic
179C2×C22⋊C4C2×D1112yes—
180#95—111no—
181#95—112no—
182#95C2×D1111yescharacteristic, complemented
183#95C2×D1112yescomplemented
184C2×C11—42no—
185C2×C11C2×C22⋊Q811yescharacteristic
186C2×C11#53411yescharacteristic
187C2×C11#53511yescharacteristic
188C2×C11#53812yes—
189C2×C11#54312yes—
190D11—24no—
191D11—42no—
192C24—111no—
193C24—111no—
194C24—114no—
195C24—222no—
196C24—222no—
197C24—442no—
198C24—442no—
199C24C22×D1111yescharacteristic
200C2×Q8—22no—
201C2×Q8—42no—
202C22×C4—111no—
203C22×C4—114no—
204C22×C4—112no—
205C22×C4—111no—
206C22×C4—112no—
207C22×C4—222no—
208C22×C4—442no—
209C22×C4—442no—
210C22×C4C22×D1112yes—
211C22×C4C22×D1112yes—
212C22×C4C22×D1111yescharacteristic
213C22×C4C22×D1111yescharacteristic
214C4⋊C4—224no—
215C4⋊C4—222no—
216C4⋊C4—442no—
217C4⋊C4—442no—
218C4⋊C4—442no—
219C22⋊C4—22no—
220C22⋊C4—42no—
221C22⋊C4—222no—
222C22⋊C4—224no—
223C22⋊C4—224no—
224C22⋊C4—222no—
225C22⋊C4—222no—
226C22⋊C4—442no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C11#262611yescharacteristic, complemented, Sylow
230C23—21no—
231C23—22no—
232C23—21no—
233C23—22no—
234C23—112no—
235C23—112no—
236C23—112no—
237C23—112no—
238C23—228no—
239C23—222no—
240C23—222no—
241C23—221no—
242C23—222no—
243C23—221no—
244C23—222no—
245C23—448no—
246C23—444no—
247C23—444no—
248C23—448no—
249C23Q8×D1112yes—
250C23C23×D1111yescharacteristic
251Q8—44no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—112no—
262C2×C4—222no—
263C2×C4—221no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—444no—
272C2×C4—444no—
273C2×C4D4×D1112yes—
274C22—22no—
275C22—24no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—114no—
280C22—222no—
281C22—224no—
282C22—222no—
283C22—224no—
284C22—222no—
285C22—224no—
286C22—4416no—
287C22—441no—
288C22—441no—
289C22—442no—
290C22C2×D4×D1111yescharacteristic
291C22#6703712yes—
292C22C2×Q8×D1111yescharacteristic
293C22#41×D1111yescharacteristic
294C22#6704212yes—
295C4—22no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—222no—
300C4—441no—
301C4—442no—
302C4—442no—
303C2—42no—
304C2—224no—
305C2—442no—
306C2#1062312011yescharacteristic
307C2D11×C22⋊Q811yescharacteristic
308C2#1062316512yes—
309C2#1062320511yescharacteristic
310C2#1062320912yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC24×D11C22
hypercenter#393D11
hypocenterC11#2626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
3. C11×#393C2semidirect
4. #10622844C2semidirect
6. #10622562C2semidirect
7. #10622561C2semidirect
8. #10622290C2semidirect
9. #10622289C2semidirect
10. #10622281C2semidirect
11. #10622280C2semidirect
13. C22×Q8×C11C22semidirect
27. C2×C4⋊Dic11C22semidirect
28. C2×C4⋊Dic11C22semidirect
29. C2×Dic11⋊C4C22semidirect
30. C2×Dic11⋊C4C22semidirect
31. C2×Dic11⋊C4C22semidirect
33. C11×#95C22semidirect
34. C11×#95C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
42. C23×D11Q8semidirect
126. #393D11semidirect
160. C22×Q8C2×D11semidirect
182. #95C2×D11semidirect
183. #95C2×D11semidirect
229. C11#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C22⋊C4×D112
C11×#3932
#106228442
#106225682
#106225622
#106225612
#106222902
#106222892
#106222812
#106222802
#262611