Finite Group Databasebeta

← #13079445

Subgroups — #13079445

Order 1408.

414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623137C211yesmaximal, characteristic
2C2×#66950C211yesmaximal, characteristic, complemented
3C11×#481C211yesmaximal, characteristic, complemented
4#10622653C211yesmaximal, characteristic, complemented
5#10622583C211yesmaximal, characteristic, complemented
6#10622481C212yesmaximal, complemented
7#10622480C212yesmaximal, complemented
8#10622396C212yesmaximal, complemented
9#10622393C212yesmaximal, complemented
10#10622352C211yesmaximal, characteristic, complemented
11#10622339C211yesmaximal, characteristic, complemented
12C2×#4341C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C11×#121C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#66991C2211yescharacteristic
18#66990—21no—
19D4×Dic11—21no—
20C2×#4324C2212yescomplemented
21C2×(C2×D11)⋊C4—21no—
22C2×C4⋊Dic11—21no—
23#66977C2211yescharacteristic
24C2×Dic44C2212yescomplemented
25C2×#4313C2212yes—
26#66950—21no—
27#66950—21no—
28#66950C2212yes—
29#66950C2211yescharacteristic
30#66950C2212yes—
31#66945C2211yescharacteristic
32#66936—21no—
33(C22⋊D11)⋊C4—21no—
34C11×#106C2212yescomplemented
35C11×#102C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic
37C22⋊(C11⋊C8)C2211yescharacteristic
38(C2×D11)⋊C8C2212yes—
39#66880C2212yescomplemented
40#66874C2212yescomplemented
41#66874C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11D411yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—21no—
49C2×C22⋊D11—21no—
50C22×Dic11—21no—
51C22×Dic11—21no—
52C22×Dic11D411yescharacteristic
53#4341—42no—
54C2×C4×D11—42no—
55C2×C4×D11D411yescharacteristic
56C2×C4×D11D411yescharacteristic
57C2×C4×D11C2311yescharacteristic
58C2×C4×D11C2311yescharacteristic
59C2×Dic22—21no—
60C2×Dic22—42no—
61C2×Dic22C2311yescharacteristic
62C2×Dic22C2312yes—
63C2×C8×C11C2312yes—
64C11×C4⋊C4—21no—
65C11×C4⋊C4C2312yes—
66C11×C4⋊C4C2311yescharacteristic
67C11×C22⋊C4—21no—
68C22⋊Dic11—21no—
69C22⋊Dic11—21no—
70#4324—42no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—21no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75C4⋊Dic11—21no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11C2311yescharacteristic
79Dic11⋊C4—21no—
80C4×Dic11—21no—
81C2×C11⋊C8C2312yes—
82Dic44—42no—
83#4313—42no—
84#3196—111nomaximal, Sylow
85C23×C11—21no—
86C23×C11C2×D411yescharacteristic
87C22×D11—22no—
88C22×D11—41no—
89C22×D11—41no—
90C22×D11C2×D411yescharacteristic
91C22×D11C2×D411yescharacteristic
92D4×C11—22no—
93D4×C11—42no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—42no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C22⋊D11—42no—
101C22⋊D11—42no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11C2×D411yescharacteristic
109C2×Dic11C2×D411yescharacteristic
110C4×D11—22no—
111C4×D11—22no—
112C4×D11—41no—
113C4×D11—41no—
114Dic22—22no—
115Dic22—22no—
116Dic22—22no—
117Dic22—42no—
118C8×C11—22no—
119C11⋊C8—22no—
120#525—111no—
121C2×C22⋊Q8—111no—
122#485—112no—
123#484—111no—
124#481D1111yescharacteristic, complemented
125#470—112no—
126#468—112no—
127#452—112no—
128#451—111no—
129#448—111no—
130#407—111no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11#13712yes—
137C22×C11C22×D411yescharacteristic
138C2×D11—21no—
139C2×D11—21no—
140C2×D11—21no—
141C2×D11—21no—
142C2×D11—21no—
143C2×D11—21no—
144C2×D11—44no—
145C4×C11—21no—
146C4×C11—41no—
147C4×C11—42no—
148C4×C11H(5,𝔽2)12yes—
149Dic11—21no—
150Dic11—21no—
151Dic11—42no—
152Dic11—41no—
153Dic11—41no—
154C2×#41—111no—
155C22×Q8—111no—
156C23×C4—111no—
157C2×Q16—112no—
158C2×SD16—112no—
159C2×M16—112no—
160#123—221no—
161C22⋊Q8—111no—
162C22⋊Q8—112no—
163C22⋊Q8—112no—
164C22⋊Q8—111no—
165C22⋊Q8—221no—
166C22⋊Q8—221no—
167#121—111no—
168#121C2×D1111yescharacteristic
169#120—221no—
170C4×D4—221no—
171C4×D4—221no—
172#117—111no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4C2×D1111yescharacteristic
175C2×C22⋊C4—221no—
176#107—112no—
177#106C2×D1112yescomplemented
178#103—112no—
179#103—112no—
180#103—112no—
181#102C2×D1112yescomplemented
182C22⋊C8—111no—
183C22⋊C8—112no—
184C22⋊C8C2×D1111yescharacteristic
185C2×C11—22no—
186C2×C11—81no—
187C2×C11#53411yescharacteristic
188C2×C11C2×#13711yescharacteristic
189C2×C11#57511yescharacteristic
190D11—41no—
191D11—41no—
192C24—111no—
193#41—442no—
194C2×Q8—112no—
195C2×Q8—111no—
196C2×Q8—221no—
197C2×Q8—442no—
198C2×D4—21no—
199C2×D4—221no—
200C2×D4—221no—
201C2×D4C22×D1111yescharacteristic
202C22×C4—21no—
203C22×C4—111no—
204C22×C4—111no—
205C22×C4—111no—
206C22×C4—111no—
207C22×C4—111no—
208C22×C4—221no—
209C22×C4—221no—
210C22×C4—442no—
211C22×C4C22×D1111yescharacteristic
212Q16—442no—
213SD16—442no—
214M16—442no—
215C2×C8—112no—
216C2×C8C22×D1112yes—
217C4⋊C4—21no—
218C4⋊C4—111no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—221no—
222C4⋊C4—221no—
223C4⋊C4C22×D1112yes—
224C4⋊C4C22×D1111yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—222no—
227C22⋊C4—222no—
228C22⋊C4—221no—
229C22⋊C4—221no—
230C22⋊C4—221no—
231C22⋊C4—221no—
232C42—221no—
233C11#319611yescharacteristic, complemented, Sylow
234C23—21no—
235C23—111no—
236C23—111no—
237C23—222no—
238C23—441no—
239C23—441no—
240C23D4×D1111yescharacteristic
241Q8—222no—
242Q8—222no—
243Q8—222no—
244Q8—442no—
245D4—22no—
246D4—42no—
247D4—442no—
248D4—442no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—111no—
254C2×C4—111no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—221no—
258C2×C4—221no—
259C2×C4—222no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4D4×D1111yescharacteristic
266C2×C4C23×D1111yescharacteristic
267C8—22no—
268C8—222no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—221no—
275C22—221no—
276C22—221no—
277C22—221no—
278C22—221no—
279C22—221no—
280C22—444no—
281C22#6696812yes—
282C22C2×D4×D1111yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—221no—
287C4—221no—
288C4—441no—
289C4—441no—
290C4—442no—
291C4#6704212yes—
292C2—22no—
293C2—81no—
294C2—441no—
295C2—441no—
296C2#1062318411yescharacteristic
297C2C2×#6696811yescharacteristic
298C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#481C2
socleC22×C11C22×D4
prime radical#10623137C2
hypercenter#481D11
hypocenterC11#3196
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×#66950C2semidirect
3. C11×#481C2semidirect
4. #10622653C2semidirect
5. #10622583C2semidirect
6. #10622481C2semidirect
7. #10622480C2semidirect
8. #10622396C2semidirect
9. #10622393C2semidirect
10. #10622352C2semidirect
11. #10622339C2semidirect
20. C2×#4324C22semidirect
24. C2×Dic44C22semidirect
34. C11×#106C22semidirect
35. C11×#102C22semidirect
39. #66880C22semidirect
40. #66874C22semidirect
41. #66874C22semidirect
42. #66871C22semidirect
124. #481D11semidirect
177. #106C2×D11semidirect
181. #102C2×D11semidirect
233. C11#3196semidirect

Maximal subgroups

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

subgroupindex
#106231372
C2×#669502
C11×#4812
#106226532
#106225832
#106224812
#106224802
#106223962
#106223932
#106223522
#106223392
#319611