Finite Group Databasebeta

← #13079614

Subgroups — #13079614

Order 1408.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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#10623259C211yesmaximal, characteristic, complemented
2D11×#124C211yesmaximal, characteristic
3C11×#497C211yesmaximal, characteristic, complemented
4#10622799C212yesmaximal, complemented
5#10622798C212yesmaximal, complemented
6#10622782C212yesmaximal
7#10622779C212yesmaximal, complemented
8#10622699C211yesmaximal, characteristic, complemented
9#10622668C211yesmaximal, characteristic, complemented
10#10622327C211yesmaximal, characteristic, complemented
11#10622318C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic
13C2×D4×D11C2211yescharacteristic
14C2×C11×Q16C2212yescomplemented
15C2×C11×SD16C2212yes—
16C11×C4⋊Q8C2211yescharacteristic, complemented
17C11×#124C2211yescharacteristic
18#67000C2211yescharacteristic
19#66999C2212yes—
20Q8×Dic11C2212yescomplemented
21C2×#4326C2212yescomplemented
22C2×#4325C2212yes—
23#66989C2211yescharacteristic
24#66950—21no—
25#66945—21no—
26#66943—21no—
27#66940—21no—
28#66938—21no—
29#66938—21no—
30C22⋊C4×D11—21no—
31C22⋊C4×D11—21no—
32#66928C2211yescharacteristic
33C42×D11C2211yescharacteristic
34#66922C2211yescharacteristic, complemented
35C11×#97C2211yescharacteristic, complemented
36#66899C2212yescomplemented
37#66896C2212yes—
38#66885C2212yes—
39(C2×D11)⋊C8C2212yes—
40#66880C2212yescomplemented
41Dic11⋊C8C2212yescomplemented
42#66867C2211yescharacteristic, complemented
43C23×D11—21no—
44C2×Q8×C11C2311yescharacteristic
45C2×Q8×C11C2312yes—
46C2×D4×C11C2311yescharacteristic
47C2×C22⋊D11—21no—
48Q8×D11—42no—
49D4×D11—42no—
50C2×D44C2311yescharacteristic
51C2×C4×D11—21no—
52C2×C4×D11D411yescharacteristic
53C2×C4×D11D411yescharacteristic
54C2×C4×D11C2311yescharacteristic
55C2×Dic22—21no—
56C2×Dic22—21no—
57C2×Dic22C2311yescharacteristic
58C11×Q16—42no—
59C11×SD16—42no—
60C2×C8×C11C2312yes—
61C11×C4⋊C4—21no—
62C11×C4⋊C4—21no—
63C11×C22⋊C4—21no—
64C11×C22⋊C4—21no—
65C42×C11C2311yescharacteristic
66C22⋊Dic11—21no—
67C22⋊Dic11—21no—
68#4326—42no—
69#4325—42no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—21no—
74(C2×D11)⋊C4—21no—
75C4⋊Dic11—22no—
76C4⋊Dic11—21no—
77C4⋊Dic11C2312yes—
78Dic11⋊C4—22no—
79C4×Dic11—22no—
80C4×Dic11D411yescharacteristic
81C4×Dic11D411yescharacteristic
82C4×Dic11C2311yescharacteristic
83C2×C11⋊C8C2312yes—
84#3215—111nomaximal, Sylow
85C23×C11—21no—
86C22×D11—21no—
87C22×D11—42no—
88C22×D11—42no—
89C22×D11—42no—
90C22×D11C2×D411yescharacteristic
91Q8×C11—22no—
92Q8×C11—22no—
93Q8×C11—22no—
94D4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C22⋊D11—42no—
101C2×Dic11—22no—
102C2×Dic11—21no—
103C2×Dic11C2×D411yescharacteristic
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106D44—22no—
107C4×D11—22no—
108C4×D11—22no—
109C4×D11—41no—
110C4×D11—42no—
111Dic22—22no—
112Dic22—42no—
113Dic22—42no—
114C8×C11—22no—
115C11⋊C8—22no—
116#533—111no—
117C2×#124—111no—
118#497—111no—
119#497D1111yescharacteristic, complemented
120#489—111no—
121#489—111no—
122#464—112no—
123#464—112no—
124#451—112no—
125#450—112no—
126#432—111no—
127C22×C11—41no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11C22×D411yescharacteristic
131C2×D11—21no—
132C2×D11—21no—
133C2×D11—41no—
134C2×D11—41no—
135C2×D11—41no—
136C2×D11—84no—
137C2×D11#13712yes—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—42no—
141C4×C11—41no—
142C4×C11H(5,𝔽2)12yes—
143Dic11—21no—
144Dic11—21no—
145Dic11—21no—
146Dic11—41no—
147Dic11—42no—
148C22×Q8—111no—
149C22×D4—111no—
150C2×Q16—112no—
151C2×Q16C2×D1112yescomplemented
152C2×SD16—112no—
153C2×SD16C2×D1112yes—
154C4⋊Q8—111no—
155C4⋊Q8C2×D1111yescharacteristic, complemented
156#125—221no—
157#124—111no—
158#124—111no—
159#124—111no—
160#124—221no—
161#124—221no—
162#124C2×D1111yescharacteristic
163C22⋊Q8—112no—
164C22⋊Q8—221no—
165C4×Q8—112no—
166C4×Q8—221no—
167#117—221no—
168C2×C22⋊C4—221no—
169C2×C22⋊C4—221no—
170C2×C42—111no—
171C4⋊C8—112no—
172#103—112no—
173#103—112no—
174#102—112no—
175#102—112no—
176C22⋊C8—112no—
177#97—111no—
178#97C2×D1111yescharacteristic, complemented
179C2×C11—81no—
180C2×C11#53511yescharacteristic
181C2×C11C2×#13711yescharacteristic
182C2×C11#57511yescharacteristic
183D11—22no—
184D11—81no—
185C24—221no—
186C2×Q8—111no—
187C2×Q8—221no—
188C2×Q8—221no—
189C2×Q8—442no—
190C2×Q8C22×D1111yescharacteristic
191C2×Q8C22×D1112yes—
192C2×D4—111no—
193C2×D4—221no—
194C2×D4—442no—
195C2×D4C22×D1111yescharacteristic
196C22×C4—111no—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—221no—
200Q16—42no—
201Q16—442no—
202SD16—42no—
203SD16—442no—
204C2×C8—112no—
205C2×C8C22×D1112yes—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—112no—
209C4⋊C4—222no—
210C4⋊C4—222no—
211C4⋊C4—221no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—221no—
215C22⋊C4—221no—
216C22⋊C4—222no—
217C22⋊C4—221no—
218C22⋊C4—221no—
219C22⋊C4—221no—
220C22⋊C4—221no—
221C42—111no—
222C42—111no—
223C42—111no—
224C42—222no—
225C42C22×D1111yescharacteristic
226C11#321511yescharacteristic, complemented, Sylow
227C23—21no—
228C23—111no—
229C23—221no—
230C23—442no—
231C23—442no—
232C23—442no—
233Q8—22no—
234Q8—22no—
235Q8—22no—
236Q8—222no—
237Q8—442no—
238Q8—442no—
239D4—22no—
240D4—222no—
241D4—442no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—111no—
245C2×C4—111no—
246C2×C4—111no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—221no—
251C2×C4—441no—
252C2×C4—442no—
253C2×C4D4×D1111yescharacteristic
254C2×C4D4×D1111yescharacteristic
255C2×C4C23×D1111yescharacteristic
256C8—22no—
257C8—222no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—112no—
262C22—221no—
263C22—221no—
264C22—441no—
265C22—441no—
266C22—441no—
267C22—884no—
268C22C2×D4×D1111yescharacteristic
269C4—21no—
270C4—21no—
271C4—41no—
272C4—42no—
273C4—221no—
274C4—221no—
275C4—221no—
276C4—441no—
277C4—442no—
278C4#6703712yes—
279C2—81no—
280C2—222no—
281C2—881no—
282C2#1062324611yescharacteristic
283C2D11×#13711yescharacteristic
284C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#497C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
hypercenter#497D11
hypocenterC11#3215
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#497C2semidirect
4. #10622799C2semidirect
5. #10622798C2semidirect
7. #10622779C2semidirect
8. #10622699C2semidirect
9. #10622668C2semidirect
10. #10622327C2semidirect
11. #10622318C2semidirect
14. C2×C11×Q16C22semidirect
16. C11×C4⋊Q8C22semidirect
20. Q8×Dic11C22semidirect
21. C2×#4326C22semidirect
34. #66922C22semidirect
35. C11×#97C22semidirect
36. #66899C22semidirect
40. #66880C22semidirect
41. Dic11⋊C8C22semidirect
42. #66867C22semidirect
119. #497D11semidirect
151. C2×Q16C2×D11semidirect
155. C4⋊Q8C2×D11semidirect
178. #97C2×D11semidirect
226. C11#3215semidirect

Maximal subgroups

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

subgroupindex
#106232592
D11×#1242
C11×#4972
#106227992
#106227982
#106227822
#106227792
#106226992
#106226682
#106223272
#106223182
#321511