Finite Group Databasebeta

← #13074188

Subgroups — #13074188

Order 1408.

492 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#66945C211yesmaximal, characteristic
3C11×#395C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic
5#10622603C212yesmaximal
6#10622596C211yesmaximal, characteristic, complemented
7#10622594C212yesmaximal, complemented
8#10622287C211yesmaximal, characteristic
9#10622281C212yesmaximal
10#10622268C212yesmaximal, complemented
11#10622264C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16Q8×Dic11—24no—
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28#66945—24no—
29C11×#95C2211yescharacteristic
30C11×#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C2×Q8×C11—22no—
39C2×Q8×C11—24no—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×C4×D11—22no—
51C2×C4×D11—22no—
52C2×C4×D11—22no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—24no—
55(C2×D11)⋊C4—22no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—24no—
59C4⋊Dic11—22no—
60C4⋊Dic11—24no—
61C4⋊Dic11—22no—
62Dic11⋊C4—24no—
63C4×Dic11—22no—
64C4×Dic11—24no—
65C4×Dic11D414yes—
66#2599—111nomaximal, Sylow
67C23×C11C2411yescharacteristic
68C22×D11—21no—
69C22×D11—22no—
70C22×D11—21no—
71C22×D11—22no—
72C22×D11#4112yes—
73Q8×C11—28no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D412yes—
85C2×C4×C11#4114yes—
86C2×C4×C11#4112yes—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11C2×D412yes—
99C2×Dic11C2×D412yes—
100C4×D11—28no—
101C2×C4×Q8—111no—
102C2×#117—111no—
103#398—111no—
104#397—111no—
105#395D1111yescharacteristic, complemented
106#393—111no—
107#388—112no—
108#387—112no—
109#387—112no—
110#385—112no—
111#383—111no—
112C22×C11C22×D411yescharacteristic
113C22×C11C2×#4112yes—
114C22×C11C2×#4111yescharacteristic
115C22×C11C2×#4111yescharacteristic
116C22×C112−1+412yes—
117C2×D11—22no—
118C2×D11—24no—
119C2×D11—41no—
120C2×D11—41no—
121C2×D11—42no—
122C4×C11—22no—
123C4×C11—24no—
124C4×C11—22no—
125C4×C11—41no—
126C4×C11—42no—
127Dic11—22no—
128Dic11—22no—
129Dic11—42no—
130Dic11—41no—
131Dic11—42no—
132C22×Q8C2×D1111yescharacteristic
133C23×C4—111no—
134C4×Q8—224no—
135#117—224no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—112no—
138C2×C4⋊C4—111no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4C2×D1111yescharacteristic
141C2×C4⋊C4C2×D1112yes—
142C2×C22⋊C4—111no—
143C2×C22⋊C4—111no—
144C2×C22⋊C4—112no—
145C2×C22⋊C4—112no—
146C2×C42—111no—
147C2×C42—111no—
148C2×C42—112no—
149#95—112no—
150#95—112no—
151#95—111no—
152#95—112no—
153#95—112no—
154#95—112no—
155#95C2×D1111yescharacteristic
156#95C2×D1112yes—
157C2×C11#52511yescharacteristic
158C2×C11#52511yescharacteristic
159C2×C11#53611yescharacteristic
160C2×C11#55212yes—
161C2×C11#55612yes—
162D11—42no—
163C24—111no—
164C2×Q8—22no—
165C2×Q8—24no—
166C22×C4—111no—
167C22×C4—111no—
168C22×C4—112no—
169C22×C4—111no—
170C22×C4—112no—
171C22×C4—222no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4C22×D1112yes—
175C22×C4C22×D1111yescharacteristic
176C22×C4C22×D1111yescharacteristic
177C22×C4C22×D1112yes—
178C22×C4C22×D1111yescharacteristic
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—222no—
182C4⋊C4—224no—
183C4⋊C4—222no—
184C4⋊C4—224no—
185C22⋊C4—222no—
186C22⋊C4—224no—
187C22⋊C4—222no—
188C22⋊C4—224no—
189C42—114no—
190C42—222no—
191C42—224no—
192C11#259911yescharacteristic, complemented, Sylow
193C23—112no—
194C23—221no—
195C23—222no—
196C23—221no—
197C23—222no—
198C23C23×D1111yescharacteristic
199Q8—28no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—112no—
211C2×C4—112no—
212C2×C4—228no—
213C2×C4—221no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4D4×D1112yes—
225C2×C4#434114yes—
226C2×C4#434312yes—
227C22—222no—
228C22—224no—
229C22—441no—
230C22—442no—
231C22—441no—
232C22C2×D4×D1111yescharacteristic
233C22C2×#434112yes—
234C22C2×#434311yescharacteristic
235C22#6704012yes—
236C22#41×D1111yescharacteristic
237C4—22no—
238C4—24no—
239C4—22no—
240C4—41no—
241C4—42no—
242C4—222no—
243C4—222no—
244C4—441no—
245C4—442no—
246C4—442no—
247C2—442no—
248C2#1062311711yescharacteristic
249C2#1062315811yescharacteristic
250C2#1062317012yes—
251C2#1062325511yescharacteristic
252C2#1062326312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC23×D11C23
hypercenter#395D11
hypocenterC11#2599
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic11C2semidirect
3. C11×#395C2semidirect
6. #10622596C2semidirect
7. #10622594C2semidirect
10. #10622268C2semidirect
11. #10622264C2semidirect
105. #395D11semidirect
192. C11#2599semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
C2×#669452
C11×#3952
#106228442
#106226032
#106225962
#106225942
#106222872
#106222812
#106222682
#106222642
#259911