Finite Group Databasebeta

← #13074317

Subgroups — #13074317

Order 1408.

476 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 135 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×#66945C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic
5#10622596C211yesmaximal, characteristic, complemented
6#10622287C211yesmaximal, characteristic
7#10622282C212yesmaximal
8#10622281C212yesmaximal
9#10622268C212yesmaximal, complemented
10#10622261C211yesmaximal, characteristic, complemented
11#10622260C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C4C2211yescharacteristic
16C2×(C2×D11)⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28#66945—24no—
29#66943—24no—
30C11×#95C2212yes—
31C11×#95C2211yescharacteristic
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C2×C4×D11—22no—
49C2×C4×D11—22no—
50C2×C4×D11—22no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—22no—
57C4⋊Dic11—24no—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60Dic11⋊C4—24no—
61Dic11⋊C4—24no—
62Dic11⋊C4—24no—
63C4×Dic11—22no—
64C4×Dic11—24no—
65C4×Dic11D414yes—
66#2611—111nomaximal, Sylow
67C23×C11C2411yescharacteristic
68C22×D11—21no—
69C22×D11—22no—
70C22×D11—21no—
71C22×D11—22no—
72C22×D11#4112yes—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D412yes—
85C2×C4×C11#4112yes—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—22no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11C2×D412yes—
97C2×Dic11C2×D412yes—
98C2×Dic11#4114yes—
99C4×D11—28no—
100C2×#125—111no—
101C2×#117—111no—
102#400D1111yescharacteristic, complemented
103#399—111no—
104#398—111no—
105#397—111no—
106#389—112no—
107#388—112no—
108#387—112no—
109#385—112no—
110#376—111no—
111C22×C11C22×D411yescharacteristic
112C22×C11C2×#4111yescharacteristic
113C22×C11C2×#4111yescharacteristic
114C22×C11C2×#4112yes—
115C22×C112−1+412yes—
116C2×D11—22no—
117C2×D11—24no—
118C2×D11—41no—
119C2×D11—41no—
120C2×D11—42no—
121C4×C11—22no—
122C4×C11—22no—
123C4×C11—42no—
124C4×C11—41no—
125C4×C11—42no—
126Dic11—22no—
127Dic11—22no—
128Dic11—24no—
129Dic11—42no—
130Dic11—41no—
131C23×C4—111no—
132#125—224no—
133#117—224no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4C2×D1111yescharacteristic
141C2×C4⋊C4C2×D1111yescharacteristic
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—111no—
151#95—112no—
152#95—112no—
153#95C2×D1111yescharacteristic
154#95C2×D1112yes—
155#95C2×D1112yes—
156C2×C11#52511yescharacteristic
157C2×C11#53211yescharacteristic
158C2×C11#53611yescharacteristic
159C2×C11#55212yes—
160C2×C11#55212yes—
161D11—42no—
162C24—111no—
163C22×C4—112no—
164C22×C4—111no—
165C22×C4—111no—
166C22×C4—111no—
167C22×C4—112no—
168C22×C4—222no—
169C22×C4—222no—
170C22×C4—222no—
171C22×C4C22×D1112yes—
172C22×C4C22×D1111yescharacteristic
173C22×C4C22×D1112yes—
174C22×C4C22×D1111yescharacteristic
175C22×C4C22×D1111yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—222no—
179C4⋊C4—224no—
180C4⋊C4—224no—
181C4⋊C4—224no—
182C4⋊C4—222no—
183C4⋊C4—224no—
184C22⋊C4—222no—
185C22⋊C4—224no—
186C22⋊C4—224no—
187C22⋊C4—222no—
188C42—114no—
189C42—222no—
190C42—224no—
191C11#261111yescharacteristic, complemented, Sylow
192C23—112no—
193C23—221no—
194C23—221no—
195C23—222no—
196C23—222no—
197C23C23×D1111yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—112no—
210C2×C4—112no—
211C2×C4—114no—
212C2×C4—228no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—222no—
216C2×C4—221no—
217C2×C4—222no—
218C2×C4—221no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4D4×D1112yes—
224C2×C4#434312yes—
225C22—224no—
226C22—222no—
227C22—441no—
228C22—441no—
229C22—442no—
230C22C2×D4×D1111yescharacteristic
231C22C2×#434311yescharacteristic
232C22#41×D1111yescharacteristic
233C22#41×D1112yes—
234C22#6704312yes—
235C4—22no—
236C4—22no—
237C4—42no—
238C4—41no—
239C4—42no—
240C4—222no—
241C4—222no—
242C4—224no—
243C4—442no—
244C4—441no—
245C2—442no—
246C2#1062315811yescharacteristic
247C2#1062317911yescharacteristic
248C2#1062319911yescharacteristic
249C2#1062322512yes—
250C2#1062323912yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC23×D11C23
hypercenter#400D11
hypocenterC11#2611
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
3. C11×#400C2semidirect
5. #10622596C2semidirect
9. #10622268C2semidirect
10. #10622261C2semidirect
11. #10622260C2semidirect
102. #400D11semidirect
191. C11#2611semidirect

Maximal subgroups

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

subgroupindex
C2×#669452
C2×#669432
C11×#4002
#106226052
#106225962
#106222872
#106222822
#106222812
#106222682
#106222612
#106222602
#261111