Finite Group Databasebeta

← #13072612

Subgroups — #13072612

Order 1408.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×C22⋊D11C212yesmaximal, complemented
2C2×#66949C212yesmaximal, complemented
3C11×#385C211yesmaximal, characteristic, complemented
4#10622603C212yesmaximal, complemented
5#10622573C211yesmaximal, characteristic
6#10622572C212yesmaximal, complemented
7#10622560C211yesmaximal, characteristic, complemented
8#10622278C212yesmaximal, complemented
9#10622265C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×D44C2211yescharacteristic
13C22×C4×D11C2212yes—
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic11C2212yes—
19C4×C22⋊D11—28no—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2212yes—
27#66949—28no—
28C11×#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C24×C11C2311yescharacteristic
34C23×D11C2312yes—
35C22×C4×C11—24no—
36C22×C4×C11—41no—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C2×C22⋊D11—24no—
42C2×C22⋊D11—24no—
43C2×C22⋊D11—24no—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×D44—24no—
48C2×D44—41no—
49C2×C4×D11—24no—
50C2×C4×D11—24no—
51C2×C4×D11—42no—
52C2×Dic22—24no—
53C2×Dic22—41no—
54C11×C4⋊C4—24no—
55C11×C22⋊C4—22no—
56C11×C22⋊C4—41no—
57C22⋊Dic11—24no—
58(C2×D11)⋊C4—24no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—24no—
62Dic11⋊C4—24no—
63Dic11⋊C4D418yescomplemented
64C4×Dic11—24no—
65#2463—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—21no—
69C23×C11—21no—
70C23×C11#4112yes—
71C23×C11C2411yescharacteristic
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11#4114yes—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—44no—
89C2×C4×C11C2×D414yes—
90C22⋊D11—216no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11C2×D414yes—
99C2×Dic11C2×D414yes—
100D44—44no—
101C4×D11—48no—
102Dic22—44no—
103C2×C22⋊Q8—112no—
104C2×C4×D4—112no—
105#394—112no—
106#393—111no—
107#392—111no—
108#388—112no—
109#387—112no—
110#386—112no—
111#385D1111yescharacteristic, complemented
112C22×C11—24no—
113C22×C11—22no—
114C22×C11—41no—
115C22×C11—42no—
116C22×C11—41no—
117C22×C11C22×D412yes—
118C22×C11C2×#4111yescharacteristic
119C22×C11C2×#4112yes—
120C22×C11H(5,𝔽2)11yescharacteristic
121C22×C112−1+411yescharacteristic
122C2×D11—24no—
123C2×D11—24no—
124C2×D11—24no—
125C2×D11—42no—
126C2×D11—42no—
127C2×D11—42no—
128C2×D11—42no—
129C4×C11—24no—
130C4×C11—42no—
131C4×C11—41no—
132C4×C11—41no—
133Dic11—24no—
134Dic11—24no—
135Dic11—42no—
136C22×Q8—111no—
137C22×D4—112no—
138C22×D4—111no—
139C23×C4—112no—
140C23×C4C2×D1111yescharacteristic
141C22⋊Q8—228no—
142C4×D4—228no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4C2×D1112yes—
146C2×C22⋊C4—112no—
147C2×C22⋊C4—112no—
148C2×C22⋊C4—112no—
149C2×C22⋊C4—112no—
150C2×C22⋊C4—112no—
151C2×C22⋊C4C2×D1111yescharacteristic
152C2×C22⋊C4C2×D1111yescharacteristic
153C2×C42—112no—
154#95—112no—
155#95—111no—
156#95—112no—
157#95—111no—
158#95C2×D1112yes—
159C2×C11—42no—
160C2×C11#52512yes—
161C2×C11#53911yescharacteristic
162C2×C11D4211yescharacteristic
163C2×C11#54812yes—
164C2×C11#55111yescharacteristic
165D11—44no—
166C24—112no—
167C24C22×D1111yescharacteristic
168C2×Q8—224no—
169C2×Q8—441no—
170C2×D4—224no—
171C2×D4—224no—
172C2×D4—224no—
173C2×D4—224no—
174C2×D4—441no—
175C22×C4—24no—
176C22×C4—41no—
177C22×C4—112no—
178C22×C4—112no—
179C22×C4—112no—
180C22×C4—224no—
181C22×C4—224no—
182C22×C4—442no—
183C22×C4C22×D1111yescharacteristic
184C22×C4C22×D1112yes—
185C22×C4C22×D1111yescharacteristic
186C22×C4C22×D1112yes—
187C4⋊C4—24no—
188C4⋊C4—118no—
189C4⋊C4—224no—
190C22⋊C4—22no—
191C22⋊C4—41no—
192C22⋊C4—224no—
193C22⋊C4—224no—
194C22⋊C4—224no—
195C22⋊C4—224no—
196C22⋊C4—224no—
197C42—224no—
198C11#246311yescharacteristic, complemented, Sylow
199C23—22no—
200C23—21no—
201C23—21no—
202C23—22no—
203C23—114no—
204C23—222no—
205C23—222no—
206C23—222no—
207C23—222no—
208C23—222no—
209C23—222no—
210C23#433912yes—
211C23C23×D1111yescharacteristic
212Q8—444no—
213D4—2216no—
214D4—444no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—44no—
225C2×C4—114no—
226C2×C4—114no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—448no—
235C2×C4D4×D1114yes—
236C22—22no—
237C22—24no—
238C22—41no—
239C22—42no—
240C22—41no—
241C22—224no—
242C22—224no—
243C22—224no—
244C22—442no—
245C22—442no—
246C22—442no—
247C22—442no—
248C22C2×#433911yescharacteristic
249C22C2×D4×D1112yes—
250C22#6703711yescharacteristic
251C22#6704011yescharacteristic
252C22#41×D1112yes—
253C4—24no—
254C4—42no—
255C4—41no—
256C4—41no—
257C4—224no—
258C4—224no—
259C4—442no—
260C2—42no—
261C2—444no—
262C2#1062304611yescharacteristic
263C2#1062307812yes—
264C2#1062312111yescharacteristic
265C2#1062316412yes—
266C2#1062319011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radical#10622573C2
hypercenter#385D11
hypocenterC11#2463
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D11C2semidirect
2. C2×#66949C2semidirect
3. C11×#385C2semidirect
4. #10622603C2semidirect
6. #10622572C2semidirect
7. #10622560C2semidirect
8. #10622278C2semidirect
9. #10622265C2semidirect
63. Dic11⋊C4D4semidirect
111. #385D11semidirect
198. C11#2463semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D112
C2×#669492
C11×#3852
#106226032
#106225732
#106225722
#106225602
#106222782
#106222652
#246311