Finite Group Databasebeta

← #13073528

Subgroups — #13073528

Order 1408.

788 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 161 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×#66992C212yesmaximal, complemented
2C2×#66937C212yesmaximal, complemented
3C2×(C22⋊D11)⋊C4C212yesmaximal, complemented
4C11×#394C211yesmaximal, characteristic, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622589C211yesmaximal, characteristic, complemented
7#10622574C212yesmaximal, complemented
8#10622555C212yesmaximal, complemented
9#10622280C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C22⋊D11C2212yes—
13C23×Dic11C2212yes—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20#66992—28no—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29#66937—28no—
30(C22⋊D11)⋊C4—28no—
31C11×#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C24×C11C2312yes—
35C23×D11C2312yes—
36C2×D4×C11—24no—
37C2×D4×C11—41no—
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—24no—
43C2×C22⋊D11—24no—
44C2×C22⋊D11—24no—
45C2×C22⋊D11—24no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11D418yescomplemented
48C22×Dic11—24no—
49C22×Dic11—24no—
50C22×Dic11—24no—
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C22×Dic11C2312yes—
54C2×D44—24no—
55C2×D44—41no—
56C2×C4×D11—24no—
57C2×C4×D11—24no—
58C2×C4×D11—24no—
59C11×C4⋊C4—41no—
60C11×C22⋊C4—24no—
61C11×C22⋊C4—24no—
62C22⋊Dic11—24no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66C4⋊Dic11—41no—
67Dic11⋊C4—24no—
68Dic11⋊C4—24no—
69Dic11⋊C4—24no—
70C4×Dic11D414yescomplemented
71#2537—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11C2×D414yes—
79C23×C11C2411yescharacteristic
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11C2×D414yes—
87D4×C11—44no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11C2×D412yes—
98C22⋊D11—216no—
99C22⋊D11—48no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—48no—
107C2×Dic11C2×D414yes—
108C2×Dic11C2×D414yes—
109C2×Dic11#4114yes—
110D44—44no—
111C4×D11—48no—
112C2×#121—112no—
113C2×#121—112no—
114C2×C4×D4—112no—
115#394—111no—
116#394—112no—
117#394D1111yescharacteristic, complemented
118#384—111no—
119#380—112no—
120#380—112no—
121C22×C11—24no—
122C22×C11—24no—
123C22×C11—24no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11C22×D411yescharacteristic
129C22×C11C22×D412yes—
130C22×C11C2×#4112yes—
131C22×C11H(5,𝔽2)11yescharacteristic
132C22×C112−1+411yescharacteristic
133C2×D11—24no—
134C2×D11—24no—
135C2×D11—24no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—42no—
139C2×D11—42no—
140C4×C11—22no—
141C4×C11—42no—
142C4×C11—41no—
143C4×C11—41no—
144Dic11—42no—
145Dic11—42no—
146Dic11#12118yescomplemented
147C22×D4—112no—
148C22×D4—112no—
149C22×D4—111no—
150C22×D4C2×D1111yescharacteristic
151C23×C4—112no—
152C23×C4—112no—
153#121—228no—
154#121—228no—
155C4×D4—228no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4—111no—
160C2×C4⋊C4C2×D1111yescharacteristic
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4C2×D1112yes—
166C2×C22⋊C4C2×D1112yes—
167C2×C42—111no—
168#95—111no—
169#95—112no—
170#95C2×D1111yescharacteristic
171C2×C11—44no—
172C2×C11C2×#12112yes—
173C2×C11#53711yescharacteristic
174C2×C11D4211yescharacteristic
175C2×C11#54712yes—
176C2×C11#55511yescharacteristic
177D11—44no—
178C24—112no—
179C24C22×D1112yes—
180C2×D4—24no—
181C2×D4—41no—
182C2×D4—118no—
183C2×D4—224no—
184C2×D4—224no—
185C2×D4—224no—
186C2×D4—224no—
187C2×D4—224no—
188C2×D4—441no—
189C2×D4—442no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—112no—
193C22×C4—224no—
194C22×C4—224no—
195C22×C4—224no—
196C22×C4—224no—
197C22×C4—224no—
198C22×C4—224no—
199C22×C4C22×D1112yes—
200C22×C4C22×D1111yescharacteristic
201C22×C4C22×D1111yescharacteristic
202C22×C4C22×D1111yescharacteristic
203C4⋊C4—41no—
204C4⋊C4—224no—
205C4⋊C4—224no—
206C4⋊C4—224no—
207C4⋊C4—441no—
208C22⋊C4—24no—
209C22⋊C4—24no—
210C22⋊C4—224no—
211C22⋊C4—224no—
212C22⋊C4—224no—
213C22⋊C4—224no—
214C42—114no—
215C11#253711yescharacteristic, complemented, Sylow
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—114no—
223C23—222no—
224C23—222no—
225C23—222no—
226C23—222no—
227C23—222no—
228C23—222no—
229C23D4×D1114yes—
230C23C23×D1111yescharacteristic
231D4—44no—
232D4—2216no—
233D4—444no—
234D4—448no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—114no—
245C2×C4—114no—
246C2×C4—114no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—448no—
254C2×C4—448no—
255C2×C4D4×D1112yes—
256C22—24no—
257C22—24no—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—224no—
264C22—224no—
265C22—224no—
266C22—442no—
267C22—442no—
268C22—442no—
269C22—442no—
270C22C2×D4×D1112yes—
271C22C2×D4×D1111yescharacteristic
272C22#6703711yescharacteristic
273C22#41×D1112yes—
274C22#6704311yescharacteristic
275C4—22no—
276C4—41no—
277C4—41no—
278C4—42no—
279C4—118no—
280C4—442no—
281C4—442no—
282C2—44no—
283C2—444no—
284C2#1062312111yescharacteristic
285C2#1062312811yescharacteristic
286C2D11×#12112yes—
287C2#1062318612yes—
288C2#1062320111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
hypercenter#394D11
hypocenterC11#2537
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#66992C2semidirect
2. C2×#66937C2semidirect
3. C2×(C22⋊D11)⋊C4C2semidirect
4. C11×#394C2semidirect
5. #10622604C2semidirect
6. #10622589C2semidirect
7. #10622574C2semidirect
8. #10622555C2semidirect
9. #10622280C2semidirect
47. C2×C22⋊D11D4semidirect
70. C4×Dic11D4semidirect
117. #394D11semidirect
146. Dic11#121semidirect
215. C11#2537semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C2×#669372
C2×(C22⋊D11)⋊C42
C11×#3942
#106226042
#106225892
#106225742
#106225552
#106222802
#253711