Finite Group Databasebeta

← #13079583

Subgroups — #13079583

Order 1408.

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

normal subgroups only

This group has 410 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#10623010C211yesmaximal, characteristic, complemented
2C2×#66928C211yesmaximal, characteristic, complemented
3C11×#431C211yesmaximal, characteristic, complemented
4#10622458C212yesmaximal, complemented
5#10622457C212yesmaximal, complemented
6#10622352C211yesmaximal, characteristic, complemented
7#10622351C211yesmaximal, characteristic, complemented
8#10622345C211yesmaximal, characteristic
9#10622344C211yesmaximal, characteristic, complemented
10#10622310C212yesmaximal, complemented
11#10622309C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15#66983C2211yescharacteristic
16#66982—21no—
17C4×C22⋊D11—21no—
18C2×(C2×D11)⋊C4—21no—
19C2×(C2×D11)⋊C4—21no—
20#66977C2211yescharacteristic
21C2×Dic44C2212yescomplemented
22C2×D88C2212yes—
23C2×#4314C2212yes—
24C2×#4314C2212yescomplemented
25#66929—21no—
26#66928—21no—
27#66928—21no—
28#66928C2212yes—
29#66928C2212yes—
30#66928C2211yescharacteristic, complemented
31C4×D44C2211yescharacteristic, complemented
32#66925—21no—
33#66923C2211yescharacteristic, complemented
34C4×Dic22C2211yescharacteristic, complemented
35C11×C4⋊C8C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic
37C11×C22⋊C8C2211yescharacteristic
38C4×C8×C11C2212yescomplemented
39#66885C2212yes—
40#66885C2212yes—
41#66880C2212yescomplemented
42#66880C2212yescomplemented
43C23×D11—21no—
44C22×C4×C11D411yescharacteristic
45C22×C4×C11D411yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—21no—
48C22×Dic11—21no—
49C2×D44—21no—
50C2×D44—42no—
51C2×D44C2312yes—
52C2×D44C2311yescharacteristic
53C2×C4×D11—21no—
54C2×Dic22—21no—
55C2×Dic22—42no—
56C2×Dic22C2312yes—
57C2×Dic22C2311yescharacteristic
58C2×C8×C11C2312yes—
59C2×C8×C11C2312yes—
60C42×C11D411yescharacteristic
61C42×C11D411yescharacteristic
62C42×C11C2311yescharacteristic
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65(C2×D11)⋊C4—21no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4—22no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—21no—
73C4⋊Dic11C2311yescharacteristic
74C4⋊Dic11C2311yescharacteristic
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80Dic44—42no—
81D88—42no—
82#4314—42no—
83#4314—42no—
84#3211—111nomaximal, Sylow
85C23×C11C2×D411yescharacteristic
86C22×D11—21no—
87C22×D11—22no—
88C22×D11—42no—
89C22×D11—42no—
90C22×D11—42no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—41no—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C22⋊D11—42no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—42no—
106D44—22no—
107D44—22no—
108D44—22no—
109D44—42no—
110C4×D11—42no—
111Dic22—22no—
112Dic22—22no—
113Dic22—22no—
114Dic22—42no—
115C8×C11—22no—
116C8×C11—22no—
117#529—111no—
118C2×#124—111no—
119#495—112no—
120#488—112no—
121#464—112no—
122#463—112no—
123#451—111no—
124#450—111no—
125#448—111no—
126#447—111no—
127#431D1111yescharacteristic, complemented
128C22×C11—21no—
129C22×C11—21no—
130C22×C11#13512yes—
131C22×C11C22×D411yescharacteristic
132C2×D11—42no—
133C2×D11—41no—
134C2×D11—42no—
135C2×D11—41no—
136C2×D11—42no—
137C2×D11—41no—
138C2×D11—84no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11H(5,𝔽2)12yes—
145Dic11—42no—
146Dic11—41no—
147Dic11—41no—
148Dic11—41no—
149C22×Q8—111no—
150C22×D4—111no—
151C2×Q16—112no—
152C2×SD16—112no—
153C2×SD16—112no—
154C2×D8—112no—
155#126—221no—
156#125—111no—
157#124—112no—
158#124—112no—
159#124—111no—
160#124—221no—
161#124—221no—
162#123—221no—
163C22⋊Q8—111no—
164#121—111no—
165C4×Q8—111no—
166C4×D4—111no—
167C4×D4—221no—
168#117—221no—
169C2×C22⋊C4—221no—
170C2×C22⋊C4—221no—
171C2×C42C2×D1111yescharacteristic
172C4⋊C8C2×D1112yescomplemented
173#103—112no—
174#103—112no—
175#102—112no—
176#102—112no—
177C22⋊C8C2×D1111yescharacteristic
178C22⋊C8C2×D1111yescharacteristic
179C4×C8C2×D1112yescomplemented
180C2×C11—22no—
181C2×C11#53511yescharacteristic
182C2×C11C2×#13511yescharacteristic
183C2×C11#57511yescharacteristic
184D11—81no—
185D11—82no—
186C24—221no—
187C2×Q8—112no—
188C2×Q8—111no—
189C2×Q8—221no—
190C2×Q8—442no—
191C2×D4—112no—
192C2×D4—111no—
193C2×D4—221no—
194C2×D4—221no—
195C2×D4—442no—
196C22×C4—221no—
197C22×C4—221no—
198C22×C4D4411yescharacteristic
199C22×C4D4411yescharacteristic
200C22×C4C22×D1111yescharacteristic
201Q16—442no—
202SD16—442no—
203SD16—442no—
204D8—442no—
205C2×C8C22×D1112yes—
206C2×C8C22×D1112yes—
207C4⋊C4—111no—
208C4⋊C4—111no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—221no—
213C22⋊C4—221no—
214C22⋊C4—222no—
215C22⋊C4—222no—
216C22⋊C4—222no—
217C22⋊C4—222no—
218C22⋊C4—221no—
219C22⋊C4—221no—
220C22⋊C4—221no—
221C22⋊C4—221no—
222C42—221no—
223C42D4411yescharacteristic
224C42D4411yescharacteristic
225C42C22×D1111yescharacteristic
226C42C22×D1111yescharacteristic
227C11#321111yescharacteristic, complemented, Sylow
228C23—221no—
229C23—222no—
230C23—442no—
231C23—442no—
232C23—442no—
233C23C2×D4411yescharacteristic
234Q8—222no—
235Q8—222no—
236Q8—222no—
237Q8—442no—
238D4—222no—
239D4—222no—
240D4—222no—
241D4—442no—
242D4—442no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—222no—
249C2×C4—221no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4C2×D4411yescharacteristic
253C2×C4C2×D4411yescharacteristic
254C2×C4C2×D4411yescharacteristic
255C2×C4C2×D4411yescharacteristic
256C2×C4C2×D4411yescharacteristic
257C2×C4C23×D1111yescharacteristic
258C8—22no—
259C8—22no—
260C22—21no—
261C22—21no—
262C22—441no—
263C22—442no—
264C22—441no—
265C22—442no—
266C22—442no—
267C22—441no—
268C22—884no—
269C22#6695712yes—
270C22C22×D4411yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—441no—
277C4—441no—
278C4—442no—
279C4—441no—
280C4#6704212yes—
281C2—22no—
282C2—882no—
283C2—881no—
284C2#1062305611yescharacteristic
285C2C2×#6695711yescharacteristic
286C2#1062327911yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#431C2
socleC22×C11C22×D4
prime radical#10622345C2
hypercenter#431D11
hypocenterC11#3211
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #10623010C2semidirect
2. C2×#66928C2semidirect
3. C11×#431C2semidirect
4. #10622458C2semidirect
5. #10622457C2semidirect
6. #10622352C2semidirect
7. #10622351C2semidirect
9. #10622344C2semidirect
10. #10622310C2semidirect
11. #10622309C2semidirect
21. C2×Dic44C22semidirect
24. C2×#4314C22semidirect
30. #66928C22semidirect
31. C4×D44C22semidirect
33. #66923C22semidirect
34. C4×Dic22C22semidirect
35. C11×C4⋊C8C22semidirect
38. C4×C8×C11C22semidirect
41. #66880C22semidirect
42. #66880C22semidirect
127. #431D11semidirect
172. C4⋊C8C2×D11semidirect
179. C4×C8C2×D11semidirect
227. C11#3211semidirect

Maximal subgroups

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

subgroupindex
#106230102
C2×#669282
C11×#4312
#106224582
#106224572
#106223522
#106223512
#106223452
#106223442
#106223102
#106223092
#321111