Finite Group Databasebeta

← #13074489

Subgroups — #13074489

Order 1408.

512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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×#66943C211yesmaximal, characteristic, complemented
2C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C11×#397C211yesmaximal, characteristic, complemented
4#10622606C211yesmaximal, characteristic, complemented
5#10622572C212yesmaximal
6#10622563C212yesmaximal, complemented
7#10622562C211yesmaximal, characteristic, complemented
8#10622290C211yesmaximal, characteristic, complemented
9#10622281C212yesmaximal, complemented
10#10622270C212yesmaximal, complemented
11#10622264C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2212yes—
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29#66943—24no—
30(C22⋊D11)⋊C4—24no—
31C11×#95C2211yescharacteristic
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C2×C22⋊D11—22no—
44C2×C22⋊D11—22no—
45C2×C22⋊D11—22no—
46C22×Dic11—22no—
47C22×Dic11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C2×C4×D11—22no—
54C2×C4×D11—42no—
55C11×C4⋊C4—22no—
56C11×C22⋊C4—24no—
57C11×C22⋊C4—22no—
58C22⋊Dic11—42no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—42no—
62C4⋊Dic11—24no—
63C4⋊Dic11—22no—
64C4⋊Dic11—42no—
65Dic11⋊C4—22no—
66Dic11⋊C4—24no—
67Dic11⋊C4—42no—
68C4×Dic11D414yes—
69#2633—111nomaximal, Sylow
70C23×C11—21no—
71C23×C11—21no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11#4112yes—
75C23×C11C2411yescharacteristic
76C22×D11—21no—
77C22×D11—21no—
78C22×D11—22no—
79C22×D11—22no—
80C22×D11#4112yes—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11C2×D412yes—
91C22⋊D11—28no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—44no—
104C2×Dic11C2×D412yes—
105C2×Dic11C2×D412yes—
106C4×D11—44no—
107C2×#125—111no—
108C2×C4×D4—111no—
109#399—111no—
110#399—111no—
111#398—112no—
112#397—111no—
113#397D1111yescharacteristic, complemented
114#394—112no—
115#385—112no—
116#385—112no—
117#383—111no—
118C22×C11—22no—
119C22×C11—24no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11—42no—
123C22×C11C22×D411yescharacteristic
124C22×C11C2×#4111yescharacteristic
125C22×C11C2×#4111yescharacteristic
126C22×C11H(5,𝔽2)12yes—
127C22×C112−1+412yes—
128C2×D11—22no—
129C2×D11—24no—
130C2×D11—41no—
131C2×D11—41no—
132C2×D11—42no—
133C4×C11—22no—
134C4×C11—42no—
135C4×C11—41no—
136C4×C11—42no—
137Dic11—22no—
138Dic11—22no—
139Dic11—42no—
140Dic11—41no—
141Dic11—42no—
142C22×D4—111no—
143C23×C4—111no—
144C23×C4—111no—
145#125—224no—
146C4×D4—224no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—111no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4C2×D1111yescharacteristic
154C2×C22⋊C4—111no—
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4C2×D1111yescharacteristic
159C2×C22⋊C4C2×D1112yes—
160C2×C42—111no—
161#95—112no—
162#95—112no—
163#95—111no—
164#95—112no—
165#95C2×D1111yescharacteristic
166#95C2×D1112yes—
167C2×C11—42no—
168C2×C11#52511yescharacteristic
169C2×C11#53511yescharacteristic
170C2×C11#53611yescharacteristic
171C2×C11#53912yes—
172C2×C11#53912yes—
173D11—42no—
174C24—111no—
175C24C22×D1111yescharacteristic
176C2×D4—222no—
177C2×D4—222no—
178C2×D4—222no—
179C22×C4—111no—
180C22×C4—111no—
181C22×C4—112no—
182C22×C4—111no—
183C22×C4—112no—
184C22×C4—222no—
185C22×C4—222no—
186C22×C4—442no—
187C22×C4—442no—
188C22×C4C22×D1112yes—
189C22×C4C22×D1112yes—
190C22×C4C22×D1111yescharacteristic
191C22×C4C22×D1111yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—222no—
194C4⋊C4—224no—
195C4⋊C4—224no—
196C4⋊C4—222no—
197C4⋊C4—442no—
198C4⋊C4—442no—
199C22⋊C4—24no—
200C22⋊C4—22no—
201C22⋊C4—224no—
202C22⋊C4—222no—
203C22⋊C4—442no—
204C22⋊C4—442no—
205C42—114no—
206C11#263311yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—112no—
212C23—221no—
213C23—221no—
214C23—222no—
215C23—222no—
216C23#434112yes—
217C23C23×D1111yescharacteristic
218D4—228no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—112no—
229C2×C4—112no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—221no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—444no—
242C2×C4—444no—
243C2×C4D4×D1112yes—
244C22—22no—
245C22—24no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22—224no—
250C22—222no—
251C22—441no—
252C22—442no—
253C22—441no—
254C22C2×D4×D1111yescharacteristic
255C22C2×#434111yescharacteristic
256C22#41×D1111yescharacteristic
257C22#6704212yes—
258C22#6704312yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—41no—
263C4—222no—
264C4—222no—
265C4—442no—
266C4—441no—
267C4—442no—
268C2—42no—
269C2—442no—
270C2#1062313711yescharacteristic
271C2#1062317911yescharacteristic
272C2#1062319612yes—
273C2#1062320511yescharacteristic
274C2#1062323812yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC22×C22⋊D11C22
hypercenter#397D11
hypocenterC11#2633
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#66943C2semidirect
3. C11×#397C2semidirect
4. #10622606C2semidirect
6. #10622563C2semidirect
7. #10622562C2semidirect
8. #10622290C2semidirect
9. #10622281C2semidirect
10. #10622270C2semidirect
11. #10622264C2semidirect
113. #397D11semidirect
206. C11#2633semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×(C22⋊D11)⋊C42
C11×#3972
#106226062
#106225722
#106225632
#106225622
#106222902
#106222812
#106222702
#106222642
#263311