Finite Group Databasebeta

← #13073561

Subgroups — #13073561

Order 1408.

948 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 177 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×#66993C211yesmaximal, characteristic, complemented
2C2×#66993C211yesmaximal, characteristic, complemented
3C2×#66946C211yesmaximal, characteristic, complemented
4C2×#66937C214yesmaximal, complemented
5C2×#66927C211yesmaximal, characteristic, complemented
6C11×#390C211yesmaximal, characteristic, complemented
7#10622601C211yesmaximal, characteristic, complemented
8#10622573C214yesmaximal, complemented
9C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C22⋊D11C2214yes—
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic
15C22×D44C2214yes—
16C22×D44C2211yescharacteristic
17C22×C4×D11C2212yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2214yes—
20C2×C42×C11C2211yescharacteristic
21#66993—24no—
22#66993—24no—
23C2×(C2×D11)⋊C4C2214yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28#66946—24no—
29#66937—216no—
30#66927—24no—
31C11⋊#95C2212yes—
32C24×C11C2312yes—
33C23×D11C2312yes—
34C23×D11C2312yes—
35C2×D4×C11—22no—
36C2×D4×C11—22no—
37C2×D4×C11—22no—
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11—28no—
42C2×C22⋊D11—28no—
43C2×C22⋊D11—24no—
44C2×C22⋊D11—24no—
45C2×C22⋊D11—28no—
46C2×C22⋊D11—44no—
47C2×C22⋊D11—44no—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C2×D44—28no—
52C2×D44—22no—
53C2×D44—22no—
54C2×D44—28no—
55C2×D44—22no—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44—44no—
59C2×D44D414yescomplemented
60C2×C4×D11—28no—
61C2×C4×D11—24no—
62C11×C4⋊C4—22no—
63C11×C22⋊C4—28no—
64C42×C11—22no—
65(C2×D11)⋊C4—28no—
66(C2×D11)⋊C4—24no—
67Dic11⋊C4D418yescomplemented
68C4×Dic11—22no—
69C4×Dic11D414yescomplemented
70#2541—111nomaximal, Sylow
71C23×C11—24no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—24no—
76C23×C11C2411yescharacteristic
77C22×D11—22no—
78C22×D11—24no—
79C22×D11—22no—
80C22×D11—24no—
81C22×D11—24no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—24no—
86C22×D11C2×D414yes—
87D4×C11—44no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—24no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D414yes—
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2×D412yes—
95C2×C4×C11#4112yes—
96C22⋊D11—416no—
97C22⋊D11—48no—
98C22⋊D11—48no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11C2×D412yes—
103C2×Dic11C2×D414yes—
104C2×Dic11C2×D412yes—
105C2×Dic11C2×D414yes—
106D44—28no—
107D44—416no—
108D44—44no—
109C4×D11—48no—
110C2×#127—111no—
111C2×#127—111no—
112C2×#127—111no—
113C2×#121—114no—
114C2×C4×D4—111no—
115#392—114no—
116#390—111no—
117#390D1111yescharacteristic, complemented
118C4×C4⋊C4—111no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—44no—
123C22×C11—44no—
124C22×C11C22×D411yescharacteristic
125C22×C11C22×D411yescharacteristic
126C22×C11C22×D412yes—
127C22×C11C2×#4111yescharacteristic
128C22×C11H(5,𝔽2)12yes—
129C2×D11—24no—
130C2×D11—28no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—44no—
134C2×D11—42no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—44no—
138C2×D11—44no—
139C4×C11—24no—
140C4×C11—42no—
141C4×C11#12114yescomplemented
142Dic11—22no—
143Dic11—24no—
144Dic11#12714yescomplemented
145C22×D4—112no—
146C22×D4—114no—
147C22×D4—112no—
148C22×D4—111no—
149C22×D4—111no—
150C22×D4—114no—
151C22×D4C2×D1111yescharacteristic
152C23×C4—112no—
153#127—224no—
154#127—224no—
155#127—224no—
156#121—2216no—
157C4×D4—224no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4C2×D1111yescharacteristic
160C2×C22⋊C4—112no—
161C2×C22⋊C4—114no—
162C2×C22⋊C4C2×D1114yes—
163C2×C42—111no—
164C2×C42—111no—
165C2×C42C2×D1111yescharacteristic
166#95—112no—
167C2×C11—82no—
168C2×C11C2×#12111yescharacteristic
169C2×C11C2×#12711yescharacteristic
170C2×C11#53511yescharacteristic
171C2×C11D4212yes—
172C2×C11#55012yes—
173D11—44no—
174D11—82no—
175C24—112no—
176C24—112no—
177C24C22×D1112yes—
178C2×D4—22no—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4—114no—
182C2×D4—228no—
183C2×D4—228no—
184C2×D4—228no—
185C2×D4—224no—
186C2×D4—224no—
187C2×D4—228no—
188C2×D4—222no—
189C2×D4—222no—
190C2×D4—222no—
191C2×D4—228no—
192C2×D4—222no—
193C2×D4—222no—
194C2×D4—444no—
195C2×D4—444no—
196C2×D4—444no—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—112no—
200C22×C4—224no—
201C22×C4—228no—
202C22×C4C22×D1112yes—
203C22×C4C22×D1112yes—
204C22×C4C22×D1111yescharacteristic
205C4⋊C4—22no—
206C4⋊C4—118no—
207C22⋊C4—28no—
208C22⋊C4—224no—
209C22⋊C4—228no—
210C42—22no—
211C42—114no—
212C42—222no—
213C11#254111yescharacteristic, complemented, Sylow
214C23—22no—
215C23—24no—
216C23—22no—
217C23—22no—
218C23—24no—
219C23—114no—
220C23—222no—
221C23—222no—
222C23—224no—
223C23—224no—
224C23—222no—
225C23—224no—
226C23—222no—
227C23—222no—
228C23—224no—
229C23C23×D1111yescharacteristic
230D4—44no—
231D4—228no—
232D4—4416no—
233D4—448no—
234D4—4416no—
235D4—448no—
236D4—444no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—112no—
242C2×C4—114no—
243C2×C4—112no—
244C2×C4—114no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—448no—
249C2×C4#433912yes—
250C2×C4D4×D1114yes—
251C2×C4D4×D1112yes—
252C2×C4D4×D1112yes—
253C22—42no—
254C22—42no—
255C22—44no—
256C22—44no—
257C22—42no—
258C22—224no—
259C22—228no—
260C22—442no—
261C22—444no—
262C22—442no—
263C22—442no—
264C22—442no—
265C22—444no—
266C22—444no—
267C22—442no—
268C22C2×#433911yescharacteristic
269C22C2×D4×D1111yescharacteristic
270C22C2×D4×D1112yes—
271C22C2×D4×D1111yescharacteristic
272C22#6704212yes—
273C4—24no—
274C4—42no—
275C4—114no—
276C4—224no—
277C4—222no—
278C4#6693714yescomplemented
279C2—82no—
280C2—444no—
281C2—882no—
282C2C2×#6693711yescharacteristic
283C2#1062308412yes—
284C2#1062314012yes—
285C2#1062320511yescharacteristic
286C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
hypercenter#390D11
hypocenterC11#2541
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66993C2semidirect
2. C2×#66993C2semidirect
3. C2×#66946C2semidirect
4. C2×#66937C2semidirect
5. C2×#66927C2semidirect
6. C11×#390C2semidirect
7. #10622601C2semidirect
8. #10622573C2semidirect
9. C4×Dic11⋊C4C2semidirect
59. C2×D44D4semidirect
67. Dic11⋊C4D4semidirect
69. C4×Dic11D4semidirect
117. #390D11semidirect
141. C4×C11#121semidirect
144. Dic11#127semidirect
213. C11#2541semidirect
278. C4#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669462
C2×#669372
C2×#669272
C11×#3902
#106226012
#106225732
C4×Dic11⋊C42
#254111