Finite Group Databasebeta

← #13072282

Subgroups — #13072282

Order 1408.

780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 181 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×C22⋊Dic11C212yesmaximal
2C2×#66931C212yesmaximal, complemented
3C11×#379C211yesmaximal, characteristic
4#10622563C212yesmaximal, complemented
5#10622562C211yesmaximal, characteristic, complemented
6#10622561C212yesmaximal, complemented
7#10622560C211yesmaximal, characteristic, complemented
8#10622559C212yesmaximal, complemented
9#10622555C212yesmaximal, complemented
10C25×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C23×Dic11C2212yes—
13C22×Dic22C2211yescharacteristic, complemented
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic11—28no—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C4⋊Dic11C2212yescomplemented
24C2×C4⋊Dic11C2211yescharacteristic, complemented
25C2×Dic11⋊C4C2212yescomplemented
26C2×Dic11⋊C4C2212yescomplemented
27C2×Dic11⋊C4C2212yescomplemented
28#66931—28no—
29C11⋊#95C2211yescharacteristic, complemented
30C11⋊#95C2212yescomplemented
31C11⋊#95C2211yescharacteristic, complemented
32C11⋊#95C2212yescomplemented
33C24×C11—24no—
34C24×C11—24no—
35C24×C11—41no—
36C24×C11—41no—
37C24×C11Q814yescomplemented
38C24×C11C2311yescharacteristic
39C24×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×Dic11—24no—
44C22×Dic11—24no—
45C22×Dic11—24no—
46C22×Dic11—24no—
47C22×Dic11—42no—
48C22×Dic11—42no—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C2×Dic22—24no—
54C2×Dic22—41no—
55C11×C22⋊C4—24no—
56C11×C22⋊C4—24no—
57C11×C22⋊C4—41no—
58C11×C22⋊C4—41no—
59C22⋊Dic11—24no—
60C22⋊Dic11—24no—
61C22⋊Dic11—24no—
62C22⋊Dic11D418yes—
63C4⋊Dic11—24no—
64C4⋊Dic11—41no—
65Dic11⋊C4—24no—
66Dic11⋊C4—24no—
67Dic11⋊C4—42no—
68#2437—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—216no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—44no—
79C23×C11—44no—
80C23×C11—48no—
81C23×C11—44no—
82C23×C11C2×D414yes—
83C23×C11C2×Q812yes—
84C23×C11C2×Q814yes—
85C23×C11#4114yes—
86C23×C11C2411yescharacteristic
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—48no—
105C2×Dic11—48no—
106C2×Dic11C2×D414yes—
107C2×Dic11C2×D414yes—
108Dic22—44no—
109C2×C22⋊Q8—112no—
110C22×C22⋊C4—112no—
111#399—111no—
112#396—112no—
113#393—111no—
114#385—112no—
115#385—112no—
116#380—112no—
117#379D1111yescharacteristic
118C22×C11—24no—
119C22×C11—24no—
120C22×C11—24no—
121C22×C11—24no—
122C22×C11—24no—
123C22×C11—24no—
124C22×C11—24no—
125C22×C11—22no—
126C22×C11—416no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11—41no—
130C22×C11C22⋊Q818yescomplemented
131C22×C11C22×D412yes—
132C22×C11C22×Q811yescharacteristic
133C22×C11C2×#4112yes—
134C22×C11H(5,𝔽2)11yescharacteristic
135C22×C11H(5,𝔽2)11yescharacteristic
136C4×C11—41no—
137C4×C11—42no—
138C4×C11—41no—
139Dic11—24no—
140Dic11—24no—
141Dic11—42no—
142Dic11—42no—
143C25C2×D1111yescharacteristic
144C22×Q8—111no—
145C23×C4—112no—
146C23×C4—112no—
147C22⋊Q8—228no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—111no—
153C2×C22⋊C4—112no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—228no—
158C2×C22⋊C4C2×D1112yes—
159C2×C22⋊C4C2×D1112yes—
160C2×C22⋊C4C2×D1111yescharacteristic
161C2×C22⋊C4C2×D1111yescharacteristic
162#95—111no—
163#95—112no—
164#95—112no—
165#95—111no—
166C2×C11—28no—
167C2×C11—42no—
168C2×C11C2×C22⋊Q812yes—
169C2×C11#54311yescharacteristic
170C2×C11D4211yescharacteristic
171C2×C11#54612yes—
172C2×C11#55111yescharacteristic
173C24—24no—
174C24—24no—
175C24—41no—
176C24—41no—
177C24Dic2214yescomplemented
178C24C22×D1111yescharacteristic
179C24C22×D1112yes—
180C2×Q8—224no—
181C2×Q8—441no—
182C22×C4—112no—
183C22×C4—112no—
184C22×C4—112no—
185C22×C4—112no—
186C22×C4—224no—
187C22×C4—224no—
188C22×C4—224no—
189C22×C4—224no—
190C22×C4—442no—
191C22×C4—442no—
192C22×C4C22×D1111yescharacteristic
193C22×C4C22×D1112yes—
194C22×C4C22×D1111yescharacteristic
195C4⋊C4—224no—
196C4⋊C4—224no—
197C4⋊C4—224no—
198C4⋊C4—442no—
199C4⋊C4—441no—
200C22⋊C4—24no—
201C22⋊C4—24no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—118no—
205C22⋊C4—224no—
206C22⋊C4—224no—
207C22⋊C4—224no—
208C11#243711yescharacteristic, complemented, Sylow
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—216no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—21no—
218C23—44no—
219C23—44no—
220C23—44no—
221C23—48no—
222C23C2×Dic2212yes—
223C23C2×Dic2214yes—
224C23D4×D1114yes—
225C23#434114yes—
226C23C23×D1111yescharacteristic
227Q8—444no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—114no—
236C2×C4—114no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—448no—
248C2×C4—448no—
249C22—24no—
250C22—24no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—416no—
258C22—41no—
259C22—41no—
260C22—42no—
261C22#6693118yescomplemented
262C22C22×Dic2211yescharacteristic
263C22C2×D4×D1112yes—
264C22C2×#434112yes—
265C22#6703711yescharacteristic
266C22#6703711yescharacteristic
267C4—41no—
268C4—41no—
269C4—42no—
270C4—224no—
271C4—224no—
272C4—442no—
273C4—442no—
274C2—28no—
275C2—42no—
276C2C2×#6693112yes—
277C2#1062301411yescharacteristic
278C2#1062311811yescharacteristic
279C2#1062312111yescharacteristic
280C2#1062312212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
prime radicalC25×C11C22
hypercenter#379D11
hypocenterC11#2437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#66931C2semidirect
4. #10622563C2semidirect
5. #10622562C2semidirect
6. #10622561C2semidirect
7. #10622560C2semidirect
8. #10622559C2semidirect
9. #10622555C2semidirect
13. C22×Dic22C22semidirect
23. C2×C4⋊Dic11C22semidirect
24. C2×C4⋊Dic11C22semidirect
25. C2×Dic11⋊C4C22semidirect
26. C2×Dic11⋊C4C22semidirect
27. C2×Dic11⋊C4C22semidirect
29. C11⋊#95C22semidirect
30. C11⋊#95C22semidirect
31. C11⋊#95C22semidirect
32. C11⋊#95C22semidirect
37. C24×C11Q8semidirect
130. C22×C11C22⋊Q8semidirect
177. C24Dic22semidirect
208. C11#2437semidirect
261. C22#66931semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Dic112
C2×#669312
C11×#3792
#106225632
#106225622
#106225612
#106225602
#106225592
#106225552
#243711