Finite Group Databasebeta

← #13079443

Subgroups — #13079443

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
1C2×#66999C211yesmaximal, characteristic, complemented
2#10623137C211yesmaximal, characteristic
3C11×#448C211yesmaximal, characteristic, complemented
4#10622841C211yesmaximal, characteristic, complemented
5#10622787C212yesmaximal, complemented
6#10622786C212yesmaximal, complemented
7#10622647C211yesmaximal, characteristic, complemented
8#10622429C212yesmaximal, complemented
9#10622427C212yesmaximal, complemented
10#10622339C211yesmaximal, characteristic, complemented
11#10622335C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×#4341C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C2×C11×SD16C2212yescomplemented
16C11×#121C2211yescharacteristic
17#66999—21no—
18#66999—21no—
19#66999C2212yes—
20#66999C2212yes—
21C2×#4326C2212yescomplemented
22#66991C2211yescharacteristic
23#66990—21no—
24D4×Dic11—21no—
25C2×(C2×D11)⋊C4—21no—
26C2×C4⋊Dic11C2211yescharacteristic
27#66977C2211yescharacteristic
28C2×Dic11⋊C4—21no—
29C2×#4313C2212yes—
30#66950C2211yescharacteristic
31#66945C2211yescharacteristic
32#66936—21no—
33(C22⋊D11)⋊C4—21no—
34C11×#103C2212yescomplemented
35C11×C22⋊C8C2211yescharacteristic
36#66899C2212yescomplemented
37#66896C2212yescomplemented
38C22⋊(C11⋊C8)C2211yescharacteristic
39(C2×D11)⋊C8C2212yes—
40#66882C2212yescomplemented
41#66880C2212yescomplemented
42#66872C2212yescomplemented
43C23×D11D411yescharacteristic
44C2×Q8×C11—21no—
45C2×Q8×C11—42no—
46C2×Q8×C11C2312yes—
47C2×D4×C11—21no—
48C2×D4×C11C2311yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—21no—
52C2×C22⋊D11—21no—
53C22×Dic11—21no—
54C22×Dic11—21no—
55C22×Dic11D411yescharacteristic
56#4341—42no—
57C2×C4×D11—42no—
58C2×C4×D11D411yescharacteristic
59C2×C4×D11D411yescharacteristic
60C2×C4×D11C2311yescharacteristic
61C2×C4×D11C2311yescharacteristic
62C2×Dic22C2311yescharacteristic
63C11×SD16—42no—
64C2×C8×C11C2312yes—
65C11×C4⋊C4C2311yescharacteristic
66C11×C22⋊C4—21no—
67C22⋊Dic11—21no—
68C22⋊Dic11—21no—
69#4326—42no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76C4⋊Dic11C2312yes—
77C4⋊Dic11C2311yescharacteristic
78Dic11⋊C4—22no—
79Dic11⋊C4—22no—
80Dic11⋊C4—21no—
81C4×Dic11—21no—
82C2×C11⋊C8C2312yes—
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
92Q8×C11—22no—
93Q8×C11—22no—
94Q8×C11—42no—
95D4×C11—22no—
96D4×C11—42no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—42no—
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2411yescharacteristic
103C22⋊D11—42no—
104C22⋊D11—42no—
105C2×Dic11—21no—
106C2×Dic11—22no—
107C2×Dic11—21no—
108C2×Dic11—41no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11C2×D411yescharacteristic
112C2×Dic11C2×D411yescharacteristic
113C4×D11—22no—
114C4×D11—22no—
115C4×D11—41no—
116C4×D11—41no—
117Dic22—22no—
118C8×C11—22no—
119C11⋊C8—22no—
120#525—111no—
121C2×C22⋊Q8—111no—
122#485—112no—
123#484—111no—
124#481—111no—
125#470—112no—
126#468—112no—
127#452—112no—
128#451—111no—
129#448D1111yescharacteristic, complemented
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—42no—
147C4×C11—41no—
148C4×C11H(5,𝔽2)12yes—
149Dic11—21no—
150Dic11—21no—
151Dic11—41no—
152Dic11—42no—
153Dic11—41no—
154C2×#41—111no—
155C22×Q8C2×D1111yescharacteristic
156C23×C4—111no—
157C2×Q16—112no—
158C2×SD16C2×D1112yescomplemented
159C2×M16—112no—
160#123—221no—
161C22⋊Q8—112no—
162C22⋊Q8—112no—
163C22⋊Q8—111no—
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—111no—
174C2×C4⋊C4—221no—
175C2×C22⋊C4—221no—
176#107—112no—
177#106—112no—
178#103—112no—
179#103—112no—
180#103C2×D1112yescomplemented
181#102—112no—
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—21no—
195C2×Q8—42no—
196C2×Q8—111no—
197C2×Q8C22×D1112yes—
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—42no—
214M16—442no—
215C2×C8—112no—
216C2×C8C22×D1112yes—
217C4⋊C4—112no—
218C4⋊C4—111no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—221no—
222C4⋊C4—221no—
223C4⋊C4—221no—
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—22no—
242Q8—22no—
243Q8—42no—
244Q8—222no—
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—222no—
259C2×C4—221no—
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—442no—
289C4—441no—
290C4—441no—
291C4#6703712yes—
292C2—22no—
293C2—81no—
294C2—441no—
295C2—441no—
296C2#1062312011yescharacteristic
297C2C2×#6696811yescharacteristic
298C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#448C2
socleC22×C11C22×D4
prime radical#10623137C2
hypercenter#448D11
hypocenterC11#3196
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
3. C11×#448C2semidirect
4. #10622841C2semidirect
5. #10622787C2semidirect
6. #10622786C2semidirect
7. #10622647C2semidirect
8. #10622429C2semidirect
9. #10622427C2semidirect
10. #10622339C2semidirect
11. #10622335C2semidirect
15. C2×C11×SD16C22semidirect
21. C2×#4326C22semidirect
34. C11×#103C22semidirect
36. #66899C22semidirect
37. #66896C22semidirect
40. #66882C22semidirect
41. #66880C22semidirect
42. #66872C22semidirect
129. #448D11semidirect
158. C2×SD16C2×D11semidirect
180. #103C2×D11semidirect
233. C11#3196semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
#106231372
C11×#4482
#106228412
#106227872
#106227862
#106226472
#106224292
#106224272
#106223392
#106223352
#319611