Finite Group Databasebeta

← #13073215

Subgroups — #13073215

Order 1408.

440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 137 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×#390C211yesmaximal, characteristic
2#10622834C211yesmaximal, characteristic
3#10622834C211yesmaximal, characteristic
4C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5#10622586C211yesmaximal, characteristic, complemented
6#10622565C212yesmaximal, complemented
7#10622565C212yesmaximal, complemented
8#10622558C212yesmaximal, complemented
9#10622557C212yesmaximal, complemented
10#10622549C211yesmaximal, characteristic, complemented
11C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28C2×C4×Dic11C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C24×C11C2312yes—
36C2×D4×C11—22no—
37C2×D4×C11—22no—
38C2×D4×C11—22no—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C11×C4⋊C4—22no—
50C11×C22⋊C4—42no—
51C11×C22⋊C4—42no—
52C42×C11—22no—
53C22⋊Dic11—24no—
54C22⋊Dic11—24no—
55C22⋊Dic11—42no—
56C22⋊Dic11—42no—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—42no—
62C4×Dic11—22no—
63C4×Dic11—22no—
64C4×Dic11—42no—
65#2513—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11C2411yescharacteristic
74D4×C11—44no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11#4112yes—
85C2×C4×C11#4112yes—
86C2×C4×C11#4112yes—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11#4112yes—
104C2×Dic11#4112yes—
105#397—112no—
106#397—112no—
107#390—111no—
108#390—111no—
109#390D1111yescharacteristic
110#389—111no—
111#388—112no—
112#388—112no—
113#382—111no—
114C4×C4⋊C4—111no—
115C4×C4⋊C4—111no—
116C22×C11—42no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11C2×#4111yescharacteristic
124C22×C11C2×#4111yescharacteristic
125C22×C11C2×#4111yescharacteristic
126C22×C11C2×#4111yescharacteristic
127C22×C11C2×#4111yescharacteristic
128C22×C11H(5,𝔽2)11yescharacteristic
129C22×C11H(5,𝔽2)11yescharacteristic
130C4×C11—42no—
131C4×C11—41no—
132C4×C11—41no—
133C4×C11#12614yes—
134Dic11—22no—
135Dic11—22no—
136Dic11—41no—
137Dic11—41no—
138Dic11—42no—
139Dic11—42no—
140C22×D4C2×D1111yescharacteristic
141C2×C4⋊C4—111no—
142C2×C4⋊C4—111no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4C2×D1111yescharacteristic
147C2×C22⋊C4—112no—
148C2×C22⋊C4—112no—
149C2×C22⋊C4—112no—
150C2×C22⋊C4—112no—
151C2×C22⋊C4C2×D1112yes—
152C2×C22⋊C4C2×D1112yes—
153C2×C42—111no—
154C2×C42—111no—
155C2×C42—112no—
156C2×C42C2×D1111yescharacteristic
157#95—111no—
158#95—112no—
159#95—111no—
160#95—112no—
161#95—112no—
162#95—112no—
163C2×C11—82no—
164C2×C11C2×#12611yescharacteristic
165C2×C11#52911yescharacteristic
166C2×C11#54011yescharacteristic
167C2×C11#55311yescharacteristic
168C2×C11#55511yescharacteristic
169C2×C11#55911yescharacteristic
170C2×C11#55911yescharacteristic
171C24C22×D1112yes—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—22no—
175C22×C4—111no—
176C22×C4—111no—
177C22×C4—112no—
178C22×C4—111no—
179C22×C4—112no—
180C22×C4—111no—
181C22×C4C22×D1111yescharacteristic
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1112yes—
184C22×C4C22×D1111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—442no—
191C22⋊C4—42no—
192C22⋊C4—42no—
193C22⋊C4—224no—
194C22⋊C4—224no—
195C22⋊C4—442no—
196C22⋊C4—442no—
197C42—22no—
198C42—222no—
199C42—222no—
200C42—442no—
201C11#251311yescharacteristic, complemented, Sylow
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23C23×D1111yescharacteristic
210D4—44no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—112no—
221C2×C4—112no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—221no—
238C2×C4#433912yes—
239C2×C4#434112yes—
240C2×C4#434112yes—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×#433911yescharacteristic
249C22C2×#434111yescharacteristic
250C22C2×#434111yescharacteristic
251C22#6703711yescharacteristic
252C22#6703711yescharacteristic
253C22#41×D1111yescharacteristic
254C22#41×D1111yescharacteristic
255C4—42no—
256C4—41no—
257C4—41no—
258C4—222no—
259C4—222no—
260C4—441no—
261C4—442no—
262C4—442no—
263C4—441no—
264C4#6693214yes—
265C2—82no—
266C2C2×#6693211yescharacteristic
267C2#1062309011yescharacteristic
268C2#1062309011yescharacteristic
269C2#1062314511yescharacteristic
270C2#1062314711yescharacteristic
271C2#1062321111yescharacteristic
272C2#1062325011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2513
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic11C2semidirect
5. #10622586C2semidirect
6. #10622565C2semidirect
7. #10622565C2semidirect
8. #10622558C2semidirect
9. #10622557C2semidirect
10. #10622549C2semidirect
11. C4×Dic11⋊C4C2semidirect
201. C11#2513semidirect

Maximal subgroups

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

subgroupindex
C11×#3902
#106228342
C4⋊C4×Dic112
#106225862
#106225652
#106225582
#106225572
#106225492
C4×Dic11⋊C42
#251311