Finite Group Databasebeta

← #13078740

Subgroups — #13078740

Order 1408.

424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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#10623256C211yesmaximal, characteristic
2C4×Q8×D11C211yesmaximal, characteristic, complemented
3C11×#477C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622640C211yesmaximal, characteristic, complemented
6#10622502C212yesmaximal, complemented
7#10622495C212yesmaximal, complemented
8#10622461C211yesmaximal, characteristic, complemented
9#10622448C211yesmaximal, characteristic, complemented
10#10622430C212yesmaximal, complemented
11#10622419C212yesmaximal, complemented
12C2×#4343—21no—
13C2×Q8×D11C2211yescharacteristic
14C11×C4⋊Q8C2211yescharacteristic
15C4×Q8×C11C2211yescharacteristic
16#67000—21no—
17Q8×Dic11C2211yescharacteristic
18C2×#4325C2212yes—
19C2×#4314C2212yes—
20#66948—21no—
21#66948C2212yes—
22#66946—21no—
23#66946C2212yes—
24C4⋊C4×D11—21no—
25C4⋊C4×D11C2211yescharacteristic
26#66940—21no—
27#66940C2211yescharacteristic
28#66927C2211yescharacteristic
29C42×D11—21no—
30C42×D11C2211yescharacteristic
31C4×Dic22—21no—
32C4×Dic22C2211yescharacteristic
33C11×#107C2212yes—
34C11×C4⋊C8C2211yescharacteristic
35C11×#103C2212yes—
36#66885C2212yes—
37(C2×D11)⋊C8C2212yes—
38#66879C2212yes—
39#66874C2212yes—
40#66873C2212yes—
41#66871C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11—21no—
44C2×Q8×C11C2311yescharacteristic
45#4343—44no—
46Q8×D11—22no—
47Q8×D11—22no—
48C2×D44—22no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44C2312yes—
52C2×C4×D11—22no—
53C2×C4×D11—21no—
54C2×C4×D11—21no—
55C2×C4×D11D411yescharacteristic
56C2×C4×D11D411yescharacteristic
57C2×C4×D11C2311yescharacteristic
58C2×Dic22—21no—
59C2×Dic22C2311yescharacteristic
60C2×C8×C11C2312yes—
61C11×C4⋊C4—21no—
62C11×C4⋊C4—21no—
63C11×C4⋊C4C2312yes—
64C11×C4⋊C4C2311yescharacteristic
65C42×C11—21no—
66C42×C11C2311yescharacteristic
67#4325—24no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70C4⋊Dic11—21no—
71C4⋊Dic11C2311yescharacteristic
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75C4×Dic11—21no—
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11D411yescharacteristic
79C4×Dic11D411yescharacteristic
80C4×Dic11C2311yescharacteristic
81C2×C11⋊C8C2312yes—
82#4314—24no—
83#3112—111nomaximal, Sylow
84C22×D11—22no—
85C22×D11C2×D411yescharacteristic
86Q8×C11—21no—
87Q8×C11—42no—
88Q8×C11#4112yescomplemented
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11C2×D411yescharacteristic
98C2×Dic11C2×D411yescharacteristic
99C2×Dic11C2×D411yescharacteristic
100D44—22no—
101D44—22no—
102D44—42no—
103D44—44no—
104D44—42no—
105C4×D11—24no—
106C4×D11—22no—
107C4×D11—22no—
108C4×D11—21no—
109C4×D11—21no—
110C4×D11—44no—
111C4×D11—42no—
112Dic22—24no—
113Dic22—21no—
114Dic22#4112yescomplemented
115C8×C11—22no—
116C11⋊C8—22no—
117#532—111no—
118C2×C4×Q8—111no—
119#480—112no—
120#477—111no—
121#477D1111yescharacteristic, complemented
122#460—111no—
123#460—111no—
124#448—112no—
125#440—112no—
126#440—112no—
127#432—111no—
128C22×C11C22×D411yescharacteristic
129C2×D11—21no—
130C2×D11—21no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11AGL(1,ℤ/8)12yes—
135C4×C11—22no—
136C4×C11—21no—
137C4×C11—42no—
138C4×C11—41no—
139C4×C11#13712yes—
140C4×C11C2×#4111yescharacteristic
141C4×C11C2×#4111yescharacteristic
142Dic11—21no—
143Dic11—22no—
144Dic11—21no—
145Dic11—21no—
146Dic11—41no—
147C2×#41—221no—
148C22×Q8—111no—
149C2×SD16—112no—
150C2×SD16—112no—
151C4⋊Q8C2×D1111yescharacteristic
152#127—111no—
153#124—221no—
154#121—112no—
155#121—221no—
156C4×Q8—111no—
157C4×Q8—111no—
158C4×Q8—111no—
159C4×Q8—221no—
160C4×Q8—221no—
161C4×Q8C2×D1111yescharacteristic
162C4×D4—112no—
163C4×D4—221no—
164C2×C4⋊C4—111no—
165C2×C4⋊C4—221no—
166C2×C42—111no—
167C2×C42—221no—
168#107—112no—
169#107C2×D1112yes—
170C4⋊C8—111no—
171C4⋊C8C2×D1111yescharacteristic
172#103—112no—
173#103C2×D1112yes—
174#102—112no—
175#102—112no—
176C22⋊C8—112no—
177#97—112no—
178C2×C11#52511yescharacteristic
179C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C11C2×#13711yescharacteristic
181D11—22no—
182D11—82no—
183#41—444no—
184C2×Q8—21no—
185C2×Q8—111no—
186C2×Q8—221no—
187C2×Q8—222no—
188C2×Q8—222no—
189C2×Q8C22×D1111yescharacteristic
190C2×D4—112no—
191C2×D4—222no—
192C2×D4—221no—
193C2×D4—221no—
194C22×C4—111no—
195C22×C4—111no—
196C22×C4—111no—
197C22×C4—222no—
198C22×C4—221no—
199C22×C4—221no—
200SD16—224no—
201SD16—224no—
202C2×C8—112no—
203C2×C8C22×D1112yes—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—111no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4C22×D1111yescharacteristic
212C4⋊C4C22×D1112yes—
213C22⋊C4—222no—
214C22⋊C4—222no—
215C42—21no—
216C42—111no—
217C42—111no—
218C42—111no—
219C42—221no—
220C42—221no—
221C42—221no—
222C42C22×D1111yescharacteristic
223C11#311211yescharacteristic, complemented, Sylow
224C23—111no—
225C23—222no—
226Q8—21no—
227Q8—42no—
228Q8—112no—
229Q8—224no—
230Q8—221no—
231Q8#434312yescomplemented
232D4—222no—
233D4—222no—
234D4—442no—
235D4—444no—
236D4—442no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—111no—
241C2×C4—111no—
242C2×C4—111no—
243C2×C4—222no—
244C2×C4—224no—
245C2×C4—221no—
246C2×C4—222no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—444no—
251C2×C4—442no—
252C2×C4D4×D1111yescharacteristic
253C2×C4D4×D1111yescharacteristic
254C2×C4C23×D1111yescharacteristic
255C8—22no—
256C8—222no—
257C22—112no—
258C22—221no—
259C22—221no—
260C22—442no—
261C22—442no—
262C22—442no—
263C22C2×D4×D1111yescharacteristic
264C4—21no—
265C4—22no—
266C4—42no—
267C4—41no—
268C4—221no—
269C4—221no—
270C4—221no—
271C4—222no—
272C4—441no—
273C4#6697112yes—
274C4C2×#434311yescharacteristic
275C4#41×D1111yescharacteristic
276C2—222no—
277C2—882no—
278C2#1062315811yescharacteristic
279C2C2×#6697111yescharacteristic
280C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radical#10623256C2
hypercenter#477D11
hypocenterC11#3112
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D11C2semidirect
3. C11×#477C2semidirect
4. #10622704C2semidirect
5. #10622640C2semidirect
6. #10622502C2semidirect
7. #10622495C2semidirect
8. #10622461C2semidirect
9. #10622448C2semidirect
10. #10622430C2semidirect
11. #10622419C2semidirect
88. Q8×C11#41semidirect
114. Dic22#41semidirect
121. #477D11semidirect
223. C11#3112semidirect
231. Q8#4343semidirect

Maximal subgroups

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

subgroupindex
#106232562
C4×Q8×D112
C11×#4772
#106227042
#106226402
#106225022
#106224952
#106224612
#106224482
#106224302
#106224192
#311211