Finite Group Databasebeta

← #13079742

Subgroups — #13079742

Order 1408.

404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#10623127C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic, complemented
3C11×#481C211yesmaximal, characteristic, complemented
4#10622647C211yesmaximal, characteristic, complemented
5#10622581C211yesmaximal, characteristic, complemented
6#10622483C212yesmaximal, complemented
7#10622468C212yesmaximal, complemented
8#10622374C212yesmaximal, complemented
9#10622373C212yesmaximal, complemented
10#10622348C211yesmaximal, characteristic, complemented
11#10622331C211yesmaximal, characteristic, complemented
12C2×#4341—21no—
13C22×Dic22—21no—
14C11×#121C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#66993C2211yescharacteristic
17#66992—21no—
18D4×Dic11C2211yescharacteristic
19#66983C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4—21no—
22C2×C4×Dic11C2211yescharacteristic
23#66946C2211yescharacteristic
24#66941—21no—
25#66941—21no—
26#66941C2211yescharacteristic
27#66941C2212yes—
28#66941C2212yes—
29#66938—21no—
30(C22⋊D11)⋊C4—21no—
31C11×#106C2212yes—
32C11×#102C2212yes—
33C11×C22⋊C8C2211yescharacteristic
34#66896C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36#66885C2212yes—
37#66881C2212yes—
38Dic11⋊C8C2212yes—
39C8×Dic11C2212yes—
40#66873C2212yes—
41#66872C2212yes—
42#66872C2212yes—
43C2×D4×C11—21no—
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—21no—
48C2×C22⋊D11—21no—
49C2×C22⋊D11—21no—
50C22×Dic11—21no—
51C22×Dic11—21no—
52C22×Dic11D411yescharacteristic
53C22×Dic11D411yescharacteristic
54#4341—44no—
55C2×D44C2311yescharacteristic
56C2×C4×D11—21no—
57C2×Dic22—21no—
58C2×Dic22—22no—
59C2×Dic22—22no—
60C2×Dic22—44no—
61C2×C8×C11C2312yes—
62C11×C4⋊C4—21no—
63C11×C4⋊C4C2311yescharacteristic
64C11×C4⋊C4C2312yes—
65C11×C22⋊C4—21no—
66C22⋊Dic11—21no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11C2311yescharacteristic
71C4⋊Dic11C2312yes—
72Dic11⋊C4—21no—
73Dic11⋊C4—22no—
74Dic11⋊C4—22no—
75C4×Dic11D411yescharacteristic
76C4×Dic11D411yescharacteristic
77C4×Dic11C2311yescharacteristic
78C4×Dic11C2311yescharacteristic
79C2×C11⋊C8C2312yes—
80#3227—111nomaximal, Sylow
81C23×C11—21no—
82C23×C11C2×D411yescharacteristic
83C22×D11—21no—
84D4×C11—22no—
85D4×C11—42no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—42no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2411yescharacteristic
92C22⋊D11—42no—
93C22⋊D11—42no—
94C22⋊D11—42no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11SD1614yes—
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104C2×Dic11C2×D411yescharacteristic
105D44—22no—
106C4×D11—42no—
107Dic22—44no—
108Dic22—42no—
109Dic22—44no—
110C8×C11—22no—
111C11⋊C8—22no—
112#532—111no—
113C2×C4⋊Q8—111no—
114#498—112no—
115#486—112no—
116#481—111no—
117#481—111no—
118#481—111no—
119#481D1111yescharacteristic, complemented
120#476—112no—
121#476—112no—
122#431—111no—
123C22×C11—21no—
124C22×C11—21no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11—41no—
128C22×C11C2×SD1612yes—
129C22×C11C22×D411yescharacteristic
130C2×D11—41no—
131C2×D11—41no—
132C2×D11—41no—
133C4×C11—21no—
134C4×C11—41no—
135C4×C11—42no—
136C4×C112−1+412yes—
137Dic11—21no—
138Dic11—41no—
139Dic11—42no—
140Dic11C2×SD1612yes—
141Dic11C2×SD1612yes—
142Dic11AGL(1,ℤ/8)12yes—
143C2×#41—221no—
144C22×Q8—221no—
145C4⋊Q8—112no—
146C4⋊Q8—112no—
147C4⋊Q8—111no—
148C4⋊Q8—221no—
149C4⋊Q8—221no—
150#127—111no—
151#124—221no—
152#121—111no—
153#121—221no—
154#121C2×D1111yescharacteristic
155C4×D4—111no—
156C4×D4—111no—
157C4×D4—221no—
158C2×C4⋊C4—111no—
159C2×C4⋊C4—221no—
160C2×C4⋊C4C2×D1111yescharacteristic
161C2×C42—111no—
162#106—112no—
163#106—112no—
164#106—112no—
165#106C2×D1112yes—
166C4⋊C8—112no—
167#102—112no—
168#102—112no—
169#102—112no—
170#102C2×D1112yes—
171C22⋊C8—111no—
172C22⋊C8C2×D1111yescharacteristic
173C4×C8—112no—
174C2×C11—22no—
175C2×C11—81no—
176C2×C11#53611yescharacteristic
177C2×C11C22×SD1611yescharacteristic
178C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
179D11—81no—
180#41—444no—
181C2×Q8—221no—
182C2×Q8—222no—
183C2×Q8—222no—
184C2×Q8—444no—
185C2×D4—21no—
186C2×D4—111no—
187C2×D4—221no—
188C2×D4—221no—
189C2×D4—221no—
190C2×D4C22×D1111yescharacteristic
191C22×C4—21no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4—221no—
195C22×C4—221no—
196C22×C4—221no—
197C22×C4C22×D1111yescharacteristic
198C2×C8—112no—
199C2×C8C22×D1112yes—
200C4⋊C4—21no—
201C4⋊C4—112no—
202C4⋊C4—111no—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4C22×D1112yes—
208C4⋊C4C22×D1111yescharacteristic
209C22⋊C4—21no—
210C22⋊C4—221no—
211C22⋊C4—221no—
212C22⋊C4—221no—
213C42—111no—
214C42—111no—
215C42—111no—
216C42—111no—
217C11#322711yescharacteristic, complemented, Sylow
218C23—21no—
219C23—221no—
220C23D4×D1111yescharacteristic
221Q8—444no—
222Q8—442no—
223Q8—444no—
224D4—22no—
225D4—42no—
226D4—222no—
227D4—442no—
228D4—442no—
229D4—442no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—114no—
235C2×C4—111no—
236C2×C4—111no—
237C2×C4—111no—
238C2×C4—111no—
239C2×C4—222no—
240C2×C4—221no—
241C2×C4—222no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4D4×D1111yescharacteristic
246C2×C4C23×D1111yescharacteristic
247C8—22no—
248C8—222no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—441no—
255C22—441no—
256C22—441no—
257C22SD16×D1112yes—
258C22C2×D4×D1111yescharacteristic
259C4—21no—
260C4—41no—
261C4—42no—
262C4—112no—
263C4—112no—
264C4—112no—
265C4—221no—
266C4—441no—
267C4—442no—
268C4#6704312yes—
269C2—22no—
270C2—81no—
271C2—881no—
272C2#1062317911yescharacteristic
273C2C2×SD16×D1111yescharacteristic
274C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#481C2
socleC22×C11C22×D4
prime radical#10623127C2
hypercenter#481D11
hypocenterC11#3227
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
3. C11×#481C2semidirect
4. #10622647C2semidirect
5. #10622581C2semidirect
6. #10622483C2semidirect
7. #10622468C2semidirect
8. #10622374C2semidirect
9. #10622373C2semidirect
10. #10622348C2semidirect
11. #10622331C2semidirect
119. #481D11semidirect
217. C11#3227semidirect

Maximal subgroups

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

subgroupindex
#106231272
C2×#669412
C11×#4812
#106226472
#106225812
#106224832
#106224682
#106223742
#106223732
#106223482
#106223312
#322711