Finite Group Databasebeta

← #13080850

Subgroups — #13080850

Order 1408.

448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623248C211yesmaximal, characteristic
2#10623115C211yesmaximal, characteristic, complemented
3C11×#460C211yesmaximal, characteristic, complemented
4#10622787C212yesmaximal, complemented
5#10622782C212yesmaximal, complemented
6#10622683C211yesmaximal, characteristic, complemented
7C4×#4325C211yesmaximal, characteristic, complemented
8#10622459C211yesmaximal, characteristic, complemented
9#10622451C211yesmaximal, characteristic, complemented
10#10622397C212yesmaximal, complemented
11#10622383C212yesmaximal, complemented
12C2×D4×D11—21no—
13C2×D4×D11C2212yes—
14C2×C11×SD16C2212yescomplemented
15C11×#127C2211yescharacteristic
16C4×Q8×C11C2211yescharacteristic, complemented
17#66999C2212yescomplemented
18C2×#4325C2211yescharacteristic
19#66991—21no—
20#66991C2212yes—
21#66990—22no—
22C2×#4313C2212yescomplemented
23#66951—22no—
24#66945C2212yescomplemented
25#66928—21no—
26C4×D44C2211yescharacteristic
27C4×D44C2211yescharacteristic
28#66922C2211yescharacteristic, complemented
29C4×Dic22—21no—
30C11×C4⋊C8C2211yescharacteristic, complemented
31C11×#102C2212yescomplemented
32#66899C2211yescharacteristic, complemented
33#66896C2212yescomplemented
34#66896C2212yescomplemented
35#66885C2212yes—
36(C2×D11)⋊C8C2212yescomplemented
37#66882C2212yescomplemented
38#66873C2211yescharacteristic
39#66872C2211yescharacteristic, complemented
40C4×C11⋊C8C2211yescharacteristic, complemented
41C23×D11—22no—
42C2×Q8×C11C2311yescharacteristic
43C2×D4×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11C2312yes—
46C2×C22⋊D11—22no—
47C2×C22⋊D11—22no—
48D4×D11—24no—
49D4×D11—42no—
50D4×D11—44no—
51C2×D44D411yescharacteristic
52C2×D44C2311yescharacteristic
53C2×C4×D11—21no—
54C2×C4×D11C2312yes—
55C2×Dic22—21no—
56C11×SD16—42no—
57C2×C8×C11C2312yes—
58C11×C4⋊C4—21no—
59C11×C4⋊C4C2311yescharacteristic
60C42×C11—21no—
61C42×C11C2311yescharacteristic
62C22⋊Dic11—22no—
63#4325—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4D412yes—
68C4⋊Dic11—21no—
69C4⋊Dic11D411yescharacteristic
70C4⋊Dic11C2311yescharacteristic
71C4⋊Dic11C2312yes—
72Dic11⋊C4—22no—
73C4×Dic11—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76#4313—42no—
77#3324—111nomaximal, Sylow
78C23×C11—22no—
79C22×D11—21no—
80C22×D11—44no—
81C22×D11—44no—
82C22×D11—82no—
83C22×D11C2×D412yes—
84Q8×C11—21no—
85Q8×C11—21no—
86D4×C11—22no—
87D4×C11—22no—
88D4×C11—42no—
89D4×C11—81no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—44no—
96C22⋊D11—44no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11C2×D412yes—
100D44—22no—
101D44—21no—
102D44#4112yes—
103C4×D11—22no—
104C4×D11—22no—
105C4×D11—42no—
106Dic22—42no—
107C8×C11—22no—
108C11⋊C8—21no—
109C11⋊C8—21no—
110#556—111no—
111D42—111no—
112#486—111no—
113#482—112no—
114#474—111no—
115#468—112no—
116#460D1111yescharacteristic, complemented
117#450—112no—
118C4×SD16—111no—
119#436—111no—
120#418—112no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11C22×D411yescharacteristic
125C2×D11—22no—
126C2×D11—22no—
127C2×D11—22no—
128C2×D11—22no—
129C2×D11—41no—
130C2×D11—41no—
131C2×D11—88no—
132C4×C11—21no—
133C4×C11—41no—
134C4×C11—41no—
135C4×C11AGL(1,ℤ/8)12yes—
136C4×C11C2×#4111yescharacteristic
137C4×C11H(5,𝔽2)11yescharacteristic
138Dic11—22no—
139Dic11—42no—
140Dic11—41no—
141C22×D4—112no—
142C22×D4—221no—
143C2×SD16—111no—
144C2×SD16C2×D1112yescomplemented
145C2×M16—112no—
146C4⋊Q8—111no—
147#127C2×D1111yescharacteristic
148#126—222no—
149#124—221no—
150C22⋊Q8—112no—
151#121—112no—
152#121—221no—
153#120—222no—
154C4×Q8—221no—
155C4×Q8C2×D1111yescharacteristic, complemented
156C4×D4—111no—
157C4×D4—111no—
158#117—112no—
159#107—112no—
160#106—111no—
161C4⋊C8C2×D1111yescharacteristic, complemented
162#103—111no—
163#102—112no—
164#102—112no—
165#102—112no—
166#102—111no—
167#102C2×D1112yescomplemented
168C22⋊C8—112no—
169C4×C8—111no—
170C2×C11—82no—
171C2×C11#54611yescharacteristic
172C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C11#57711yescharacteristic
174D11—42no—
175D11—42no—
176C24—222no—
177C2×Q8—221no—
178C2×Q8C22×D1111yescharacteristic
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—111no—
182C2×D4—111no—
183C2×D4—222no—
184C2×D4—224no—
185C2×D4—222no—
186C2×D4—442no—
187C2×D4—444no—
188C2×D4C22×D1112yes—
189C22×C4—112no—
190C22×C4—221no—
191SD16—42no—
192SD16—222no—
193M16—442no—
194C2×C8—111no—
195C2×C8—111no—
196C2×C8C22×D1112yes—
197C4⋊C4—21no—
198C4⋊C4—111no—
199C4⋊C4—112no—
200C4⋊C4—111no—
201C4⋊C4—222no—
202C4⋊C4—221no—
203C4⋊C4C22×D1111yescharacteristic
204C22⋊C4—112no—
205C22⋊C4—222no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4—221no—
209C42—21no—
210C42—222no—
211C42C22×D1111yescharacteristic
212C11#332411yescharacteristic, complemented, Sylow
213C23—22no—
214C23—112no—
215C23—221no—
216C23—444no—
217C23—444no—
218C23—882no—
219Q8—21no—
220Q8—21no—
221Q8—442no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—81no—
226D4—112no—
227D4—222no—
228D4—221no—
229D4—444no—
230D4—444no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—112no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—221no—
238C2×C4—442no—
239C2×C4D4×D1111yescharacteristic
240C2×C4D4×D1111yescharacteristic
241C2×C4C23×D1111yescharacteristic
242C8—22no—
243C8—221no—
244C8—221no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—222no—
249C22—222no—
250C22—222no—
251C22—222no—
252C22—441no—
253C22—441no—
254C22—888no—
255C22C2×D4×D1111yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—222no—
260C4—441no—
261C4—442no—
262C4#6696712yes—
263C4#6703711yescharacteristic
264C4#41×D1111yescharacteristic
265C2—82no—
266C2—442no—
267C2—442no—
268C2#1062314311yescharacteristic
269C2C2×#6696711yescharacteristic
270C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#460C2
socleC22×C11C22×D4
prime radical#10623248C2
hypercenter#460D11
hypocenterC11#3324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10623115C2semidirect
3. C11×#460C2semidirect
4. #10622787C2semidirect
5. #10622782C2semidirect
6. #10622683C2semidirect
7. C4×#4325C2semidirect
8. #10622459C2semidirect
9. #10622451C2semidirect
10. #10622397C2semidirect
11. #10622383C2semidirect
14. C2×C11×SD16C22semidirect
16. C4×Q8×C11C22semidirect
17. #66999C22semidirect
22. C2×#4313C22semidirect
24. #66945C22semidirect
28. #66922C22semidirect
30. C11×C4⋊C8C22semidirect
31. C11×#102C22semidirect
32. #66899C22semidirect
33. #66896C22semidirect
34. #66896C22semidirect
36. (C2×D11)⋊C8C22semidirect
37. #66882C22semidirect
39. #66872C22semidirect
40. C4×C11⋊C8C22semidirect
116. #460D11semidirect
144. C2×SD16C2×D11semidirect
155. C4×Q8C2×D11semidirect
161. C4⋊C8C2×D11semidirect
167. #102C2×D11semidirect
212. C11#3324semidirect

Maximal subgroups

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

subgroupindex
#106232482
#106231152
C11×#4602
#106227872
#106227822
#106226832
C4×#43252
#106224592
#106224512
#106223972
#106223832
#332411