Finite Group Databasebeta

← #13071195

Subgroups — #13071195

Order 1408.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×D4×D11C211yesmaximal, characteristic
2C2×#66945C211yesmaximal, characteristic, complemented
3C2×#66925C211yesmaximal, characteristic, complemented
4C11×#390C211yesmaximal, characteristic, complemented
5#10622834C211yesmaximal, characteristic, complemented
6#10622601C211yesmaximal, characteristic, complemented
7#10622570C214yesmaximal, complemented
8#10622568C214yesmaximal, complemented
9#10622552C211yesmaximal, characteristic, complemented
10C24×D11C2212yes—
11C22×D4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C2×D4×D11—24no—
14C2×D4×D11—24no—
15C2×D4×D11C418yescomplemented
16C22×D44C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic, complemented
19C2×C11×C22⋊C4C2214yescomplemented
20C2×C42×C11C2211yescharacteristic, complemented
21C2×C22⋊Dic11C2214yescomplemented
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2214yescomplemented
25C2×(C2×D11)⋊C4C2214yescomplemented
26C2×C4⋊Dic11C2211yescharacteristic, complemented
27C2×Dic11⋊C4C2212yescomplemented
28C2×C4×Dic11C2211yescharacteristic, complemented
29C2×C4×Dic11C2212yescomplemented
30#66945—24no—
31#66925—24no—
32C24×C11C2312yes—
33C23×D11—24no—
34C23×D11—24no—
35C23×D11—44no—
36C23×D11—44no—
37C23×D11C2×C418yes—
38C23×D11C2312yes—
39C23×D11C2311yescharacteristic
40C2×D4×C11—22no—
41C2×D4×C11—22no—
42C2×D4×C11C2×C414yes—
43C22×C4×C11C2312yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11C2×C418yes—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52D4×D11—232no—
53C2×D44—22no—
54C2×D44—22no—
55C2×D44C2×C414yes—
56C2×C4×D11C2×C414yes—
57C2×C4×D11D414yes—
58C2×C4×D11D414yes—
59C11×C4⋊C4—22no—
60C11×C22⋊C4—44no—
61C42×C11—22no—
62C22⋊Dic11—44no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—44no—
66(C2×D11)⋊C4—44no—
67C4⋊Dic11—22no—
68Dic11⋊C4—24no—
69C4×Dic11—24no—
70C4×Dic11—22no—
71#2309—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—24no—
75C23×C11—24no—
76C23×C11C22×C414yes—
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—24no—
83C22×D11—24no—
84C22×D11—216no—
85C22×D11—416no—
86C22×D11—48no—
87C22×D11—416no—
88C22×D11—48no—
89C22×D11C22×C414yes—
90C22×D11C22×C412yes—
91C22×D11C2×D412yes—
92C22×D11C2×D412yes—
93D4×C11—28no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—24no—
98C2×C4×C11—22no—
99C2×C4×C11C22×C412yes—
100C2×C4×C11C2×D412yes—
101C2×C4×C11C2×D412yes—
102C22⋊D11—216no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—24no—
107C2×Dic11—22no—
108C2×Dic11C22×C412yes—
109C2×Dic11C2×D412yes—
110C2×Dic11C2×D412yes—
111D44—28no—
112C4×D11C22⋊C4116yescomplemented
113C23×D4—111no—
114C2×#117—111no—
115C2×#117—111no—
116#390—111no—
117#390—111no—
118#390—114no—
119#390—111no—
120#390D1111yescharacteristic, complemented
121#379—114no—
122C22×C11—24no—
123C22×C11—28no—
124C22×C11—42no—
125C22×C11—44no—
126C22×C11—42no—
127C22×C11C23×C411yescharacteristic
128C22×C11C22×D411yescharacteristic
129C22×C11C22×D411yescharacteristic
130C22×C11H(5,𝔽2)12yes—
131C22×C11H(5,𝔽2)12yes—
132C2×D11—24no—
133C2×D11—22no—
134C2×D11—24no—
135C2×D11—22no—
136C2×D11—24no—
137C2×D11—28no—
138C2×D11—432no—
139C2×D11—42no—
140C2×D11—44no—
141C2×D11—42no—
142C2×D11C2×C22⋊C414yes—
143C4×C11—42no—
144C4×C11—42no—
145C4×C11C2×C22⋊C414yes—
146Dic11—42no—
147Dic11—42no—
148Dic11C2×C22⋊C414yes—
149C25—112no—
150C22×D4—112no—
151C22×D4—118no—
152C22×D4—111no—
153C22×D4—224no—
154C22×D4—224no—
155C22×D4C2×D1111yescharacteristic
156C23×C4—111no—
157#117—224no—
158#117—224no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—111no—
161C2×C4⋊C4C2×D1111yescharacteristic, complemented
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—114no—
165C2×C22⋊C4—114no—
166C2×C22⋊C4—114no—
167C2×C22⋊C4C2×D1114yescomplemented
168C2×C42—112no—
169C2×C42—111no—
170C2×C42C2×D1111yescharacteristic, complemented
171C2×C11—44no—
172C2×C11C22×C22⋊C411yescharacteristic
173C2×C11#51812yes—
174C2×C11#53511yescharacteristic
175C2×C11#53512yes—
176C2×C11#53511yescharacteristic
177D11—24no—
178D11—44no—
179C24—111no—
180C24—112no—
181C24—118no—
182C24—224no—
183C24—224no—
184C24—444no—
185C24—444no—
186C24C22×D1112yes—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—118no—
190C2×D4—114no—
191C2×D4—2232no—
192C2×D4—224no—
193C2×D4—224no—
194C2×D4—222no—
195C2×D4—222no—
196C2×D4C4×D1114yes—
197C22×C4—111no—
198C22×C4—114no—
199C22×C4—114no—
200C22×C4—114no—
201C22×C4—112no—
202C22×C4—112no—
203C22×C4C22×D1112yes—
204C22×C4C22×D1112yes—
205C22×C4C22×D1111yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—224no—
208C4⋊C4—222no—
209C22⋊C4—44no—
210C22⋊C4—224no—
211C22⋊C4—224no—
212C22⋊C4—444no—
213C22⋊C4—444no—
214C22⋊C4—444no—
215C42—22no—
216C42—224no—
217C42—222no—
218C11#230911yescharacteristic, complemented, Sylow
219C23—22no—
220C23—22no—
221C23—24no—
222C23—24no—
223C23—112no—
224C23—112no—
225C23—112no—
226C23—114no—
227C23—2216no—
228C23—222no—
229C23—222no—
230C23—222no—
231C23—222no—
232C23—224no—
233C23—224no—
234C23—4416no—
235C23—448no—
236C23—4416no—
237C23—448no—
238C23C2×C4×D1114yes—
239C23C23×D1111yescharacteristic
240D4—28no—
241D4—2216no—
242D4—228no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—112no—
249C2×C4—112no—
250C2×C4—112no—
251C2×C4—1116no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—224no—
257C2×C4C2×C4×D1112yes—
258C2×C4D4×D1112yes—
259C2×C4D4×D1112yes—
260C22—24no—
261C22—28no—
262C22—42no—
263C22—44no—
264C22—42no—
265C22—114no—
266C22—222no—
267C22—224no—
268C22—224no—
269C22—222no—
270C22—224no—
271C22—228no—
272C22—4432no—
273C22—442no—
274C22—444no—
275C22—442no—
276C22C22×C4×D1111yescharacteristic
277C22C2×D4×D1111yescharacteristic
278C22C2×D4×D1111yescharacteristic
279C22#6703712yes—
280C22#6704212yes—
281C4—42no—
282C4—42no—
283C4—114no—
284C4—442no—
285C4—442no—
286C4C22⋊C4×D1114yes—
287C2—44no—
288C2—224no—
289C2—444no—
290C2C2×C22⋊C4×D1111yescharacteristic
291C2#1062307612yes—
292C2#1062313812yes—
293C2#1062320511yescharacteristic
294C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#390C2
socle, cosocleC23×C11C24
prime radicalC22×D4×D11C2
hypercenter#390D11
hypocenterC11#2309
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66945C2semidirect
3. C2×#66925C2semidirect
4. C11×#390C2semidirect
5. #10622834C2semidirect
6. #10622601C2semidirect
7. #10622570C2semidirect
8. #10622568C2semidirect
9. #10622552C2semidirect
15. C2×D4×D11C4semidirect
18. C2×C11×C4⋊C4C22semidirect
19. C2×C11×C22⋊C4C22semidirect
20. C2×C42×C11C22semidirect
21. C2×C22⋊Dic11C22semidirect
24. C2×(C2×D11)⋊C4C22semidirect
25. C2×(C2×D11)⋊C4C22semidirect
26. C2×C4⋊Dic11C22semidirect
27. C2×Dic11⋊C4C22semidirect
28. C2×C4×Dic11C22semidirect
29. C2×C4×Dic11C22semidirect
112. C4×D11C22⋊C4semidirect
120. #390D11semidirect
161. C2×C4⋊C4C2×D11semidirect
167. C2×C22⋊C4C2×D11semidirect
170. C2×C42C2×D11semidirect
218. C11#2309semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D112
C2×#669452
C2×#669252
C11×#3902
#106228342
#106226012
#106225702
#106225682
#106225522
#230911