Finite Group Databasebeta

← #13074579

Subgroups — #13074579

Order 1408.

420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C11×#389C211yesmaximal, characteristic, complemented
2#10622607C212yesmaximal, complemented
3#10622606C212yesmaximal, complemented
4#10622601C211yesmaximal, characteristic
5#10622601C211yesmaximal, characteristic
6#10622598C211yesmaximal, characteristic, complemented
7#10622586C211yesmaximal, characteristic, complemented
8#10622552C211yesmaximal, characteristic
9#10622545C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal, complemented
11#10622287C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28C11×#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C23×D11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2311yescharacteristic
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C2×D44—22no—
47C2×D44—22no—
48C2×D44—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—42no—
52C42×C11—22no—
53(C2×D11)⋊C4—42no—
54(C2×D11)⋊C4—42no—
55(C2×D11)⋊C4—42no—
56(C2×D11)⋊C4—42no—
57(C2×D11)⋊C4—42no—
58(C2×D11)⋊C4—42no—
59C4⋊Dic11—22no—
60C4⋊Dic11—42no—
61Dic11⋊C4—42no—
62C4×Dic11—22no—
63C4×Dic11—22no—
64#2644—111nomaximal, Sylow
65C23×C11C2411yescharacteristic
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11#4112yes—
86C2×C4×C11#4112yes—
87C2×C4×C11#4112yes—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103D44—44no—
104#397—112no—
105#397—112no—
106#397—112no—
107#396—112no—
108#390—111no—
109#390—111no—
110#390—111no—
111#389—111no—
112#389—111no—
113#389D1111yescharacteristic, complemented
114#376—111no—
115C22×C11C2×#4111yescharacteristic
116C22×C11C2×#4111yescharacteristic
117C22×C11C2×#4111yescharacteristic
118C22×C11H(5,𝔽2)11yescharacteristic
119C22×C11H(5,𝔽2)11yescharacteristic
120C22×C11H(5,𝔽2)11yescharacteristic
121C22×C112−1+411yescharacteristic
122C2×D11—42no—
123C2×D11—42no—
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—42no—
127C2×D11—42no—
128C2×D11—42no—
129C4×C11—42no—
130C4×C11—41no—
131C4×C11—42no—
132C4×C11—41no—
133C4×C11#12614yes—
134Dic11—41no—
135Dic11—41no—
136Dic11—42no—
137Dic11—41no—
138Dic11—41no—
139C22×D4—111no—
140C2×C4⋊C4—111no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4C2×D1111yescharacteristic
144C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4—112no—
152C2×C42—111no—
153C2×C42—111no—
154C2×C42C2×D1111yescharacteristic
155#95—111no—
156#95—111no—
157#95—111no—
158#95—111no—
159#95—112no—
160#95—112no—
161#95C2×D1112yes—
162C2×C11C2×#12611yescharacteristic
163C2×C11#54011yescharacteristic
164C2×C11#54011yescharacteristic
165C2×C11#54011yescharacteristic
166C2×C11#54211yescharacteristic
167C2×C11#54211yescharacteristic
168C2×C11#54211yescharacteristic
169D11—82no—
170C24—112no—
171C2×D4—222no—
172C2×D4—222no—
173C2×D4—222no—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—111no—
177C22×C4—111no—
178C22×C4—112no—
179C22×C4C22×D1111yescharacteristic
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1112yes—
182C22×C4C22×D1112yes—
183C22×C4C22×D1111yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—222no—
188C4⋊C4—442no—
189C4⋊C4—442no—
190C22⋊C4—442no—
191C22⋊C4—442no—
192C22⋊C4—442no—
193C22⋊C4—442no—
194C22⋊C4—442no—
195C22⋊C4—442no—
196C42—22no—
197C42—222no—
198C42—222no—
199C11#264411yescharacteristic, complemented, Sylow
200C23—222no—
201C23—222no—
202C23—222no—
203C23—222no—
204C23—222no—
205C23—222no—
206C23—222no—
207C23C23×D1111yescharacteristic
208D4—444no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—222no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4#433912yes—
237C2×C4#434112yes—
238C2×C4#434312yes—
239C22—442no—
240C22—442no—
241C22—442no—
242C22—442no—
243C22—442no—
244C22—442no—
245C22—442no—
246C22C2×#433911yescharacteristic
247C22C2×#434111yescharacteristic
248C22#6703711yescharacteristic
249C22C2×#434311yescharacteristic
250C22#6704011yescharacteristic
251C22#6704211yescharacteristic
252C22#6704211yescharacteristic
253C4—42no—
254C4—41no—
255C4—42no—
256C4—41no—
257C4—441no—
258C4—441no—
259C4—441no—
260C4—441no—
261C4—442no—
262C4#6695114yes—
263C2—882no—
264C2C2×#6695111yescharacteristic
265C2#1062309311yescharacteristic
266C2#1062311311yescharacteristic
267C2#1062315011yescharacteristic
268C2#1062317411yescharacteristic
269C2#1062322911yescharacteristic
270C2#1062326411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC22×D44C22
hypercenter#389D11
hypocenterC11#2644
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C11×#389C2semidirect
2. #10622607C2semidirect
3. #10622606C2semidirect
6. #10622598C2semidirect
7. #10622586C2semidirect
9. #10622545C2semidirect
10. #10622288C2semidirect
11. #10622287C2semidirect
113. #389D11semidirect
199. C11#2644semidirect

Maximal subgroups

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

subgroupindex
C11×#3892
#106226072
#106226062
#106226012
#106225982
#106225862
#106225522
#106225452
#106222882
#106222872
#264411