Finite Group Databasebeta

← #13079943

Subgroups — #13079943

Order 1408.

398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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#10623010C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic, complemented
3C2×C11×C4⋊C8C211yesmaximal, characteristic, complemented
4#10622728C212yesmaximal, complemented
5#10622727C212yesmaximal, complemented
6#10622463C211yesmaximal, characteristic, complemented
7#10622461C211yesmaximal, characteristic, complemented
8#10622460C212yesmaximal, complemented
9#10622457C212yesmaximal, complemented
10#10622456C211yesmaximal, characteristic, complemented
11#10622455C211yesmaximal, characteristic, complemented
12C2×#4339—21no—
13C22×C8×C11C2212yes—
14C2×C42×C11C2211yescharacteristic
15#66983—21no—
16#66983C2212yes—
17#66983C2211yescharacteristic
18#66982—21no—
19C4×C22⋊D11—21no—
20#66977C2211yescharacteristic
21C2×D88C2212yes—
22C2×#4314C2212yes—
23#66929—21no—
24#66928—21no—
25#66928C2211yescharacteristic
26#66927C2211yescharacteristic
27C4×D44—21no—
28C4×D44C2212yes—
29C4×D44C2211yescharacteristic
30#66925—21no—
31#66923C2211yescharacteristic
32#66922C2211yescharacteristic
33C4×Dic22C2211yescharacteristic
34C11×C4⋊C8C2211yescharacteristic
35C11×C4⋊C8C2211yescharacteristic
36C11×C4⋊C8C2212yes—
37#66885C2212yes—
38#66885C2212yes—
39#66885C2212yes—
40#66882C2212yes—
41#66881C2212yes—
42#66880C2212yes—
43C22×C4×C11D411yescharacteristic
44C22×C4×C11D411yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C2×C22⋊D11—22no—
48#4339—44no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44C2312yes—
52C2×D44C2311yescharacteristic
53C2×C4×D11—21no—
54C2×C4×D11—22no—
55C2×Dic22—21no—
56C2×Dic22C2311yescharacteristic
57C2×C8×C11—42no—
58C2×C8×C11C2312yes—
59C2×C8×C11C2312yes—
60C42×C11D411yescharacteristic
61C42×C11D411yescharacteristic
62C42×C11C2311yescharacteristic
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65(C2×D11)⋊C4—21no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11C2312yes—
73C4⋊Dic11C2311yescharacteristic
74C4⋊Dic11C2311yescharacteristic
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80D88—42no—
81#4314—42no—
82#3247—111nomaximal, Sylow
83C23×C11C2×D411yescharacteristic
84C22×D11—21no—
85C22×D11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2411yescharacteristic
96C22⋊D11—44no—
97C22⋊D11—42no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—22no—
102D44—22no—
103D44—21no—
104D44—22no—
105D44—21no—
106D44—42no—
107D44—42no—
108C4×D11—44no—
109C4×D11—42no—
110Dic22—21no—
111Dic22—21no—
112Dic22—42no—
113C8×C11—22no—
114C8×C11—22no—
115#532—111no—
116#529—111no—
117#478—112no—
118#477—111no—
119#476—111no—
120#466—112no—
121#465—112no—
122#463—112no—
123#460—111no—
124#459—111no—
125C2×C4⋊C8D1111yescharacteristic, complemented
126C22×C11—21no—
127C22×C11—21no—
128C22×C11AGL(1,ℤ/8)12yes—
129C22×C11C22×D411yescharacteristic
130C2×D11—41no—
131C2×D11—42no—
132C2×D11—41no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—41no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11#13512yes—
141C4×C11H(5,𝔽2)11yescharacteristic
142C4×C112−1+411yescharacteristic
143Dic11—41no—
144Dic11—41no—
145Dic11—42no—
146Dic11—41no—
147C2×#41—221no—
148C2×SD16—112no—
149C2×D8—112no—
150C22×C8C2×D1112yes—
151C4⋊Q8—111no—
152#127—111no—
153#126—221no—
154#125—111no—
155#124—111no—
156#124—221no—
157#123—221no—
158C22⋊Q8—111no—
159#121—111no—
160#121—112no—
161#121—221no—
162C4×Q8—111no—
163C4×D4—111no—
164C4×D4—112no—
165C4×D4—221no—
166C4×D4—221no—
167#117—221no—
168C2×C42C2×D1111yescharacteristic
169#107—112no—
170#106—112no—
171C4⋊C8C2×D1111yescharacteristic
172C4⋊C8C2×D1111yescharacteristic
173C4⋊C8C2×D1112yes—
174#103—112no—
175#102—112no—
176#102—112no—
177#102—112no—
178C2×C11—22no—
179C2×C11#53711yescharacteristic
180C2×C11C2×#13511yescharacteristic
181C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
182D11—81no—
183D11—82no—
184#41—444no—
185C2×Q8—111no—
186C2×Q8—221no—
187C2×D4—111no—
188C2×D4—112no—
189C2×D4—221no—
190C2×D4—222no—
191C2×D4—221no—
192C2×D4—221no—
193C22×C4—221no—
194C22×C4—222no—
195C22×C4D4411yescharacteristic
196C22×C4D4411yescharacteristic
197C22×C4C22×D1111yescharacteristic
198SD16—442no—
199D8—442no—
200C2×C8—42no—
201C2×C8C22×D1112yes—
202C2×C8C22×D1112yes—
203C4⋊C4—111no—
204C4⋊C4—111no—
205C4⋊C4—112no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C22⋊C4—221no—
212C22⋊C4—221no—
213C22⋊C4—221no—
214C22⋊C4—222no—
215C22⋊C4—221no—
216C22⋊C4—222no—
217C22⋊C4—221no—
218C42—221no—
219C42D4411yescharacteristic
220C42D4411yescharacteristic
221C42C22×D1111yescharacteristic
222C42C22×D1111yescharacteristic
223C11#324711yescharacteristic, complemented, Sylow
224C23—221no—
225C23—222no—
226C23C2×D4411yescharacteristic
227Q8—221no—
228Q8—221no—
229Q8—442no—
230D4—221no—
231D4—222no—
232D4—221no—
233D4—222no—
234D4—442no—
235D4—444no—
236D4—442no—
237D4—442no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—221no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4—222no—
246C2×C4—444no—
247C2×C4—442no—
248C2×C4C2×D4411yescharacteristic
249C2×C4C2×D4411yescharacteristic
250C2×C4C2×D4411yescharacteristic
251C2×C4C2×D4411yescharacteristic
252C2×C4C2×D4411yescharacteristic
253C2×C4C23×D1111yescharacteristic
254C8—22no—
255C8—22no—
256C22—21no—
257C22—21no—
258C22—441no—
259C22—442no—
260C22—442no—
261C22—441no—
262C22—441no—
263C22—442no—
264C22#6696112yes—
265C22C22×D4411yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—441no—
271C4—442no—
272C4—441no—
273C4—441no—
274C4#6695712yes—
275C4#6703711yescharacteristic
276C4#6704011yescharacteristic
277C2—22no—
278C2—881no—
279C2—882no—
280C2#1062304111yescharacteristic
281C2C2×#6695711yescharacteristic
282C2C2×#6696111yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×C4⋊C8C2
socleC22×C11C22×D4
hypercenterC2×C4⋊C8D11
hypocenterC11#3247
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10623010C2semidirect
2. #10623008C2semidirect
3. C2×C11×C4⋊C8C2semidirect
4. #10622728C2semidirect
5. #10622727C2semidirect
6. #10622463C2semidirect
7. #10622461C2semidirect
8. #10622460C2semidirect
9. #10622457C2semidirect
10. #10622456C2semidirect
11. #10622455C2semidirect
125. C2×C4⋊C8D11semidirect
223. C11#3247semidirect

Maximal subgroups

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

subgroupindex
#106230102
#106230082
C2×C11×C4⋊C82
#106227282
#106227272
#106224632
#106224612
#106224602
#106224572
#106224562
#106224552
#324711