Finite Group Databasebeta

← #13079451

Subgroups — #13079451

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#10623158C211yesmaximal, characteristic
2C2×#66950C211yesmaximal, characteristic, complemented
3C11×#484C211yesmaximal, characteristic, complemented
4#10622663C211yesmaximal, characteristic, complemented
5#10622581C211yesmaximal, characteristic, complemented
6#10622501C212yesmaximal, complemented
7#10622499C212yesmaximal, complemented
8#10622429C212yesmaximal, complemented
9#10622423C212yesmaximal, complemented
10#10622351C211yesmaximal, characteristic, complemented
11#10622339C211yesmaximal, characteristic, complemented
12C2×#4343C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C11×C22⋊Q8C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#66999C2211yescharacteristic
18C2×#4326C2212yescomplemented
19#66983C2211yescharacteristic
20C2×(C2×D11)⋊C4—21no—
21C2×C4⋊Dic11—21no—
22C2×#4314C2212yescomplemented
23C2×#4313C2212yes—
24#66950—21no—
25#66950—21no—
26#66950C2212yes—
27#66950C2212yes—
28#66948C2211yescharacteristic
29#66947—21no—
30#66946—21no—
31#66945C2211yescharacteristic
32#66935—21no—
33(C22⋊D11)⋊C4—21no—
34C11×#107C2212yescomplemented
35C11×#103C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic
37C22⋊(C11⋊C8)C2211yescharacteristic
38(C2×D11)⋊C8C2212yes—
39#66880C2212yescomplemented
40#66874C2212yescomplemented
41#66873C2212yescomplemented
42#66872C2212yescomplemented
43C23×D11D411yescharacteristic
44C2×Q8×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—21no—
48C22×Dic11—21no—
49C22×Dic11D411yescharacteristic
50#4343—42no—
51C2×D44—21no—
52C2×D44—21no—
53C2×D44C2311yescharacteristic
54C2×C4×D11—21no—
55C2×C4×D11—42no—
56C2×C4×D11D411yescharacteristic
57C2×C4×D11D411yescharacteristic
58C2×C4×D11C2311yescharacteristic
59C2×C4×D11C2311yescharacteristic
60C2×Dic22—21no—
61C2×Dic22—42no—
62C2×Dic22C2312yes—
63C2×C8×C11C2312yes—
64C11×C4⋊C4—21no—
65C11×C4⋊C4—21no—
66C11×C4⋊C4C2312yes—
67C11×C4⋊C4C2311yescharacteristic
68C11×C22⋊C4—21no—
69#4326—42no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—21no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—21no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11C2311yescharacteristic
79Dic11⋊C4—21no—
80C4×Dic11—21no—
81C2×C11⋊C8C2312yes—
82#4314—42no—
83#4313—42no—
84#3196—111nomaximal, Sylow
85C23×C11C2×D411yescharacteristic
86C22×D11—22no—
87C22×D11—21no—
88C22×D11—41no—
89C22×D11—41no—
90C22×D11C2×D411yescharacteristic
91C22×D11C2×D411yescharacteristic
92Q8×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—42no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C22⋊D11—42no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—41no—
104C2×Dic11—42no—
105C2×Dic11C2×D411yescharacteristic
106C2×Dic11C2×D411yescharacteristic
107D44—22no—
108D44—42no—
109D44—42no—
110C4×D11—22no—
111C4×D11—22no—
112C4×D11—41no—
113C4×D11—41no—
114C4×D11—42no—
115Dic22—22no—
116Dic22—22no—
117Dic22—42no—
118C8×C11—22no—
119C11⋊C8—22no—
120#525—111no—
121C2×C22⋊Q8—111no—
122#485—112no—
123#484D1111yescharacteristic, complemented
124#481—111no—
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#13712yes—
134C22×C11C22×D411yescharacteristic
135C2×D11—21no—
136C2×D11—21no—
137C2×D11—21no—
138C2×D11—21no—
139C2×D11—21no—
140C2×D11—21no—
141C2×D11—44no—
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—41no—
145C4×C11—21no—
146C4×C11—41no—
147C4×C11—42no—
148C4×C11—41no—
149C4×C11H(5,𝔽2)12yes—
150Dic11—21no—
151Dic11—21no—
152Dic11—42no—
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—221no—
165C22⋊Q8—221no—
166C22⋊Q8C2×D1111yescharacteristic
167#121—111no—
168#121—111no—
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#107C2×D1112yescomplemented
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#53411yescharacteristic
187C2×C11C2×#13711yescharacteristic
188C2×C11#57511yescharacteristic
189D11—41no—
190D11—41no—
191D11—81no—
192C24—111no—
193#41—442no—
194C2×Q8—112no—
195C2×Q8—221no—
196C2×Q8—442no—
197C2×Q8C22×D1111yescharacteristic
198C2×D4—111no—
199C2×D4—221no—
200C2×D4—221no—
201C2×D4—221no—
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—21no—
219C4⋊C4—111no—
220C4⋊C4—222no—
221C4⋊C4—222no—
222C4⋊C4—221no—
223C4⋊C4C22×D1112yes—
224C4⋊C4C22×D1111yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—221no—
227C22⋊C4—222no—
228C22⋊C4—222no—
229C22⋊C4—221no—
230C22⋊C4—221no—
231C22⋊C4—221no—
232C42—221no—
233C11#319611yescharacteristic, complemented, Sylow
234C23—111no—
235C23—111no—
236C23—222no—
237C23—221no—
238C23—441no—
239C23—441no—
240C23D4×D1111yescharacteristic
241Q8—22no—
242Q8—222no—
243Q8—222no—
244Q8—442no—
245D4—222no—
246D4—442no—
247D4—442no—
248D4—442no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—111no—
255C2×C4—111no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—221no—
259C2×C4—222no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—442no—
263C2×C4—441no—
264C2×C4—442no—
265C2×C4D4×D1111yescharacteristic
266C2×C4C23×D1111yescharacteristic
267C8—22no—
268C8—222no—
269C22—21no—
270C22—21no—
271C22—221no—
272C22—221no—
273C22—221no—
274C22—221no—
275C22—221no—
276C22—221no—
277C22—444no—
278C22—441no—
279C22—441no—
280C22—441no—
281C22#6697112yes—
282C22C2×D4×D1111yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—41no—
287C4—221no—
288C4—221no—
289C4—441no—
290C4—442no—
291C4#6704212yes—
292C2—22no—
293C2—441no—
294C2—441no—
295C2—881no—
296C2#1062318411yescharacteristic
297C2C2×#6697111yescharacteristic
298C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#484C2
socleC22×C11C22×D4
prime radical#10623158C2
hypercenter#484D11
hypocenterC11#3196
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#66950C2semidirect
3. C11×#484C2semidirect
4. #10622663C2semidirect
5. #10622581C2semidirect
6. #10622501C2semidirect
7. #10622499C2semidirect
8. #10622429C2semidirect
9. #10622423C2semidirect
10. #10622351C2semidirect
11. #10622339C2semidirect
18. C2×#4326C22semidirect
22. C2×#4314C22semidirect
34. C11×#107C22semidirect
35. C11×#103C22semidirect
39. #66880C22semidirect
40. #66874C22semidirect
41. #66873C22semidirect
42. #66872C22semidirect
123. #484D11semidirect
176. #107C2×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
#106231582
C2×#669502
C11×#4842
#106226632
#106225812
#106225012
#106224992
#106224292
#106224232
#106223512
#106223392
#319611