Finite Group Databasebeta

← #13074825

Subgroups — #13074825

Order 1408.

816 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66948C212yesmaximal, complemented
2C2×#66935C212yesmaximal, complemented
3C11×#399C211yesmaximal, characteristic, complemented
4#10622606C212yesmaximal, complemented
5#10622604C212yesmaximal, complemented
6#10622573C211yesmaximal, characteristic, complemented
7#10622569C212yesmaximal, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622278C212yesmaximal, complemented
10C24×D11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×D44C2212yes—
13C22×D44C2212yes—
14C22×D44C2211yescharacteristic, complemented
15C22×C4×D11C2212yescomplemented
16C2×C11×C4⋊C4C2212yescomplemented
17C2×C11×C4⋊C4C2211yescharacteristic, complemented
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yescomplemented
26C2×(C2×D11)⋊C4C2212yescomplemented
27#66948—28no—
28#66935—28no—
29C11×#95C2211yescharacteristic, complemented
30C11⋊#95C2212yescomplemented
31C11⋊#95C2212yescomplemented
32C11⋊#95C2211yescharacteristic, complemented
33C24×C11C2311yescharacteristic
34C23×D11—22no—
35C23×D11—24no—
36C23×D11—42no—
37C23×D11—41no—
38C23×D11—41no—
39C23×D11C2312yes—
40C23×D11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C2×C22⋊D11—24no—
46C2×C22⋊D11—24no—
47C2×C22⋊D11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C2×D44—24no—
51C2×D44—24no—
52C2×D44—24no—
53C2×D44—42no—
54C2×D44—42no—
55C2×D44—42no—
56C2×D44—41no—
57C2×D44D418yescomplemented
58C2×C4×D11—24no—
59C2×C4×D11—42no—
60C2×C4×D11—42no—
61C11×C4⋊C4—24no—
62C11×C4⋊C4—41no—
63C11×C22⋊C4—24no—
64C11×C22⋊C4—41no—
65C22⋊Dic11—41no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—42no—
72#2668—111nomaximal, Sylow
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—22no—
77C23×C11#4112yes—
78C23×C11C2411yescharacteristic
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—44no—
92C22×D11—48no—
93C22×D11—48no—
94C22×D11—44no—
95C22×D11—44no—
96C22×D11C2×D414yes—
97C22×D11C2×D414yes—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11C2×D414yes—
108C22⋊D11—48no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115D44—48no—
116D44—48no—
117D44—44no—
118C4×D11—48no—
119C2×#121—112no—
120C2×#120—112no—
121#399D1111yescharacteristic, complemented
122#397—112no—
123#394—112no—
124#392—111no—
125#386—112no—
126#386—112no—
127#379—111no—
128C22×C11—22no—
129C22×C11—24no—
130C22×C11—42no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11C22×D412yes—
134C22×C11C2×#4111yescharacteristic
135C22×C11H(5,𝔽2)11yescharacteristic
136C22×C11H(5,𝔽2)11yescharacteristic
137C22×C11H(5,𝔽2)12yes—
138C2×D11—24no—
139C2×D11—24no—
140C2×D11—24no—
141C2×D11—24no—
142C2×D11—24no—
143C2×D11—24no—
144C2×D11—416no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C4×C11—24no—
154C4×C11—42no—
155C4×C11—41no—
156C4×C11—41no—
157Dic11—42no—
158Dic11—42no—
159C25—111no—
160C22×D4—112no—
161C22×D4—112no—
162C22×D4—112no—
163C22×D4—111no—
164C23×C4—112no—
165#121—228no—
166#120—228no—
167C2×C4⋊C4C2×D1112yescomplemented
168C2×C4⋊C4C2×D1111yescharacteristic, complemented
169C2×C22⋊C4—112no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4C2×D1112yes—
177C2×C22⋊C4C2×D1111yescharacteristic
178#95—112no—
179#95—112no—
180#95—111no—
181#95C2×D1111yescharacteristic, complemented
182C2×C11—42no—
183C2×C11#53412yes—
184C2×C11#53811yescharacteristic
185C2×C11D4211yescharacteristic
186C2×C11#54612yes—
187C2×C11#56011yescharacteristic
188D11—44no—
189D11—44no—
190C24—112no—
191C24—112no—
192C24—224no—
193C24—222no—
194C24—441no—
195C24—441no—
196C24—442no—
197C24C22×D1111yescharacteristic
198C2×D4—118no—
199C2×D4—224no—
200C2×D4—224no—
201C2×D4—224no—
202C2×D4—224no—
203C2×D4—224no—
204C2×D4—442no—
205C2×D4—442no—
206C2×D4—441no—
207C2×D4—442no—
208C2×D4—442no—
209C22×C4—112no—
210C22×C4—112no—
211C22×C4—224no—
212C22×C4—442no—
213C22×C4—442no—
214C22×C4C22×D1112yes—
215C22×C4C22×D1111yescharacteristic
216C22×C4C22×D1111yescharacteristic
217C22×C4C22×D1112yes—
218C4⋊C4—24no—
219C4⋊C4—41no—
220C22⋊C4—24no—
221C22⋊C4—41no—
222C22⋊C4—224no—
223C22⋊C4—224no—
224C22⋊C4—224no—
225C22⋊C4—224no—
226C22⋊C4—442no—
227C22⋊C4—442no—
228C22⋊C4—441no—
229C11#266811yescharacteristic, complemented, Sylow
230C23—22no—
231C23—21no—
232C23—21no—
233C23—22no—
234C23—114no—
235C23—114no—
236C23—222no—
237C23—222no—
238C23—222no—
239C23—222no—
240C23—222no—
241C23—222no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23—222no—
246C23—222no—
247C23—222no—
248C23—448no—
249C23—444no—
250C23—444no—
251C23—448no—
252C23—444no—
253C23#434312yes—
254C23C23×D1111yescharacteristic
255D4—448no—
256D4—444no—
257D4—448no—
258D4—448no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—448no—
275C2×C4D4×D1114yes—
276C22—24no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—224no—
282C22—224no—
283C22—224no—
284C22—224no—
285C22—224no—
286C22—224no—
287C22—4416no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22—442no—
293C22—442no—
294C22—442no—
295C22—442no—
296C22C2×D4×D1112yes—
297C22#6703711yescharacteristic
298C22C2×#434311yescharacteristic
299C22#6704212yes—
300C22#6704211yescharacteristic
301C4—24no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—442no—
306C4—442no—
307C2—42no—
308C2—444no—
309C2—444no—
310C2#1062316112yes—
311C2#1062317511yescharacteristic
312C2#1062318412yes—
313C2#1062319711yescharacteristic
314C2#1062324811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
hypercenter#399D11
hypocenterC11#2668
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66935C2semidirect
3. C11×#399C2semidirect
4. #10622606C2semidirect
5. #10622604C2semidirect
6. #10622573C2semidirect
7. #10622569C2semidirect
8. #10622568C2semidirect
9. #10622278C2semidirect
14. C22×D44C22semidirect
15. C22×C4×D11C22semidirect
16. C2×C11×C4⋊C4C22semidirect
17. C2×C11×C4⋊C4C22semidirect
25. C2×(C2×D11)⋊C4C22semidirect
26. C2×(C2×D11)⋊C4C22semidirect
29. C11×#95C22semidirect
30. C11⋊#95C22semidirect
31. C11⋊#95C22semidirect
32. C11⋊#95C22semidirect
57. C2×D44D4semidirect
121. #399D11semidirect
167. C2×C4⋊C4C2×D11semidirect
168. C2×C4⋊C4C2×D11semidirect
181. #95C2×D11semidirect
229. C11#2668semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669352
C11×#3992
#106226062
#106226042
#106225732
#106225692
#106225682
#106222782
#266811