Finite Group Databasebeta

← #13072891

Subgroups — #13072891

Order 1408.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#66945C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D11C211yesmaximal, characteristic
3C11×#399C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622603C212yesmaximal, complemented
6#10622602C212yesmaximal, complemented
7#10622568C212yesmaximal
8#10622566C211yesmaximal, characteristic, complemented
9#10622558C212yesmaximal, complemented
10#10622287C211yesmaximal, characteristic, complemented
11#10622277C211yesmaximal, characteristic, complemented
12C24×D11C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic, complemented
16C2×C11×C4⋊C4C2212yescomplemented
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2212yes—
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×Dic11⋊C4C2212yescomplemented
29C2×C4×Dic11C2212yescomplemented
30#66945—24no—
31C22⋊C4×D11—24no—
32C11×#95C2211yescharacteristic, complemented
33C11⋊#95C2212yescomplemented
34C11⋊#95C2211yescharacteristic, complemented
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C24×C11C2311yescharacteristic
38C23×D11—22no—
39C23×D11—22no—
40C23×D11—22no—
41C23×D11—24no—
42C23×D11—42no—
43C23×D11C2311yescharacteristic
44C23×D11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C2×C4×D11—22no—
54C2×C4×D11—24no—
55C2×C4×D11—42no—
56C2×C4×D11D414yes—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—42no—
59C11×C22⋊C4—22no—
60C11×C22⋊C4—42no—
61C22⋊Dic11—22no—
62C22⋊Dic11—24no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—42no—
69C4⋊Dic11—22no—
70Dic11⋊C4—42no—
71C4×Dic11—24no—
72#2482—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11#4112yes—
78C23×C11C2411yescharacteristic
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—22no—
82C22×D11—28no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—48no—
88C22×D11—48no—
89C22×D11—44no—
90C22×D11—44no—
91C22×D11C2×D412yes—
92C22×D11#4112yes—
93C22×D11#4114yes—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11C2×D412yes—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11C2×D412yes—
114C4×D11—28no—
115C4×D11—44no—
116C2×#117—111no—
117C22×C22⋊C4—111no—
118#399—111no—
119#399D1111yescharacteristic, complemented
120#397—111no—
121#397—111no—
122#388—112no—
123#388—112no—
124#385—112no—
125#381—111no—
126#379—112no—
127C22×C11—22no—
128C22×C11—24no—
129C22×C11—41no—
130C22×C11—41no—
131C22×C11—42no—
132C22×C11C22×D411yescharacteristic
133C22×C11C2×#4111yescharacteristic
134C22×C11C2×#4112yes—
135C22×C11C2×#4111yescharacteristic
136C22×C11H(5,𝔽2)12yes—
137C2×D11—22no—
138C2×D11—22no—
139C2×D11—24no—
140C2×D11—24no—
141C2×D11—22no—
142C2×D11—24no—
143C2×D11—416no—
144C2×D11—41no—
145C2×D11—41no—
146C2×D11—42no—
147C2×D11#12314yes—
148C4×C11—22no—
149C4×C11—42no—
150C4×C11—41no—
151C4×C11—42no—
152Dic11—22no—
153Dic11—42no—
154Dic11—41no—
155Dic11—42no—
156C25—111no—
157C23×C4—111no—
158C23×C4—111no—
159#117—224no—
160C2×C4⋊C4—111no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4C2×D1111yescharacteristic, complemented
163C2×C4⋊C4C2×D1112yescomplemented
164C2×C22⋊C4—111no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—111no—
167C2×C22⋊C4—111no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—224no—
173C2×C22⋊C4C2×D1111yescharacteristic
174C2×C22⋊C4C2×D1112yes—
175C2×C42—112no—
176#95—112no—
177#95—111no—
178#95—112no—
179#95—112no—
180#95C2×D1111yescharacteristic, complemented
181C2×C11—42no—
182C2×C11C2×#12311yescharacteristic
183C2×C11#52511yescharacteristic
184C2×C11#53511yescharacteristic
185C2×C11#55112yes—
186C2×C11#55112yes—
187D11—24no—
188D11—42no—
189C24—111no—
190C24—111no—
191C24—222no—
192C24—222no—
193C24—224no—
194C24—222no—
195C24—442no—
196C24C22×D1111yescharacteristic
197C22×C4—111no—
198C22×C4—114no—
199C22×C4—112no—
200C22×C4—112no—
201C22×C4—111no—
202C22×C4—224no—
203C22×C4—222no—
204C22×C4—442no—
205C22×C4C22×D1112yes—
206C22×C4C22×D1111yescharacteristic
207C22×C4C22×D1112yes—
208C22×C4C22×D1111yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—42no—
211C4⋊C4—222no—
212C4⋊C4—442no—
213C22⋊C4—22no—
214C22⋊C4—42no—
215C22⋊C4—222no—
216C22⋊C4—224no—
217C22⋊C4—224no—
218C22⋊C4—224no—
219C22⋊C4—222no—
220C22⋊C4—224no—
221C22⋊C4—222no—
222C22⋊C4—442no—
223C42—224no—
224C11#248211yescharacteristic, complemented, Sylow
225C23—21no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—112no—
230C23—114no—
231C23—112no—
232C23—228no—
233C23—222no—
234C23—221no—
235C23—221no—
236C23—221no—
237C23—222no—
238C23—221no—
239C23—222no—
240C23—448no—
241C23—444no—
242C23—448no—
243C23—444no—
244C23#434312yes—
245C23C23×D1111yescharacteristic
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—112no—
256C2×C4—228no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—221no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—444no—
267C2×C4D4×D1112yes—
268C22—22no—
269C22—24no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—114no—
274C22—222no—
275C22—222no—
276C22—224no—
277C22—224no—
278C22—222no—
279C22—224no—
280C22—4416no—
281C22—441no—
282C22—442no—
283C22—441no—
284C22C2×D4×D1111yescharacteristic
285C22#6703712yes—
286C22C2×#434311yescharacteristic
287C22#41×D1111yescharacteristic
288C22#41×D1112yes—
289C4—22no—
290C4—41no—
291C4—42no—
292C4—42no—
293C4—222no—
294C4—441no—
295C4—442no—
296C4—442no—
297C2—42no—
298C2—224no—
299C2—442no—
300C2#1062315811yescharacteristic
301C2#1062316812yes—
302C2D11×#12311yescharacteristic
303C2#1062319012yes—
304C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC24×D11C22
hypercenter#399D11
hypocenterC11#2482
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66945C2semidirect
3. C11×#399C2semidirect
4. #10622605C2semidirect
5. #10622603C2semidirect
6. #10622602C2semidirect
8. #10622566C2semidirect
9. #10622558C2semidirect
10. #10622287C2semidirect
11. #10622277C2semidirect
15. C2×C11×C4⋊C4C22semidirect
16. C2×C11×C4⋊C4C22semidirect
27. C2×C4⋊Dic11C22semidirect
28. C2×Dic11⋊C4C22semidirect
29. C2×C4×Dic11C22semidirect
32. C11×#95C22semidirect
33. C11⋊#95C22semidirect
34. C11⋊#95C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
119. #399D11semidirect
162. C2×C4⋊C4C2×D11semidirect
163. C2×C4⋊C4C2×D11semidirect
180. #95C2×D11semidirect
224. C11#2482semidirect

Maximal subgroups

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

subgroupindex
C2×#669452
C2×C22⋊C4×D112
C11×#3992
#106226052
#106226032
#106226022
#106225682
#106225662
#106225582
#106222872
#106222772
#248211