Finite Group Databasebeta

← #13080847

Subgroups — #13080847

Order 1408.

448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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
1D42×C11C211yesmaximal, characteristic
2#10623073C211yesmaximal, characteristic, complemented
3#10622831C212yesmaximal, complemented
4#10622828C212yesmaximal, complemented
5#10622688C211yesmaximal, characteristic, complemented
6#10622683C211yesmaximal, characteristic, complemented
7#10622655C212yesmaximal, complemented
8#10622648C212yesmaximal, complemented
9C4×#4324C211yesmaximal, characteristic, complemented
10#10622625C211yesmaximal, characteristic, complemented
11#10622620C211yesmaximal, characteristic, complemented
12C22×D4×C11—21no—
13C22×D4×C11C2212yes—
14C11×#127C2211yescharacteristic
15C11×#121—21no—
16C11×#121C2212yes—
17C11×#120—22no—
18C4×D4×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66989—21no—
21C2×#4324C2211yescharacteristic
22C2×#4324C2212yescomplemented
23#66979C2212yescomplemented
24#66977C2212yescomplemented
25C2×#4318C2212yescomplemented
26#66940—21no—
27#66932—22no—
28#66922C2211yescharacteristic, complemented
29C4×Dic22C2211yescharacteristic, complemented
30#66896C2211yescharacteristic
31#66896C2212yes—
32#66896C2212yescomplemented
33#66896C2212yescomplemented
34#66896C2212yescomplemented
35C22⋊(C11⋊C8)C2212yescomplemented
36#66874C2211yescharacteristic, complemented
37#66872C2211yescharacteristic, complemented
38#66871C2212yescomplemented
39C4⋊(C11⋊C8)C2211yescharacteristic, complemented
40C4×C11⋊C8C2211yescharacteristic, complemented
41C24×C11—22no—
42C2×D4×C11—24no—
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—21no—
46C2×D4×C11—21no—
47C2×D4×C11—42no—
48C2×D4×C11—44no—
49C2×D4×C11D411yescharacteristic
50C2×D4×C11C2312yes—
51C2×D4×C11C2311yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11C2312yes—
54C2×Dic22—21no—
55C2×Dic22C2311yescharacteristic
56C11×C4⋊C4D411yescharacteristic
57C11×C4⋊C4C2311yescharacteristic
58C11×C22⋊C4—21no—
59C11×C22⋊C4—22no—
60C11×C22⋊C4D412yes—
61C42×C11C2311yescharacteristic
62C22⋊Dic11—22no—
63C22⋊Dic11—22no—
64#4324—22no—
65#4324—42no—
66C4⋊Dic11—21no—
67C4⋊Dic11C2312yes—
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—22no—
71C4×Dic11—21no—
72C4×Dic11—22no—
73#4318—42no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2312yes—
77#3324—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11—22no—
80C23×C11—44no—
81C23×C11—44no—
82C23×C11—82no—
83C23×C11C2×D412yes—
84D4×C11—22no—
85D4×C11—22no—
86D4×C11—21no—
87D4×C11—22no—
88D4×C11—44no—
89D4×C11—44no—
90D4×C11—42no—
91D4×C11—81no—
92D4×C11#4112yes—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—42no—
97C2×C4×C11C2×D412yes—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2411yescharacteristic
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—22no—
104Dic22—21no—
105Dic22—21no—
106Dic22—42no—
107C11⋊C8—21no—
108C11⋊C8—21no—
109C11⋊C8—22no—
110#556—111no—
111D42D1111yescharacteristic
112#486—111no—
113#482—112no—
114#474—111no—
115#468—112no—
116#460—111no—
117#450—112no—
118C4×SD16—111no—
119#436—111no—
120#418—112no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—88no—
131C22×C11C22×D411yescharacteristic
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—41no—
135C4×C11AGL(1,ℤ/8)12yes—
136C4×C11C2×#4111yescharacteristic
137C4×C11H(5,𝔽2)11yescharacteristic
138Dic11—41no—
139Dic11—42no—
140Dic11—41no—
141C22×D4—21no—
142C22×D4C2×D1112yes—
143C2×SD16—111no—
144C2×SD16—112no—
145C2×M16—112no—
146C4⋊Q8—111no—
147#127C2×D1111yescharacteristic
148#126—222no—
149#124—221no—
150C22⋊Q8—112no—
151#121—21no—
152#121C2×D1112yes—
153#120—22no—
154C4×Q8—111no—
155C4×Q8—221no—
156C4×D4C2×D1111yescharacteristic
157C4×D4C2×D1111yescharacteristic
158#117—112no—
159#107—112no—
160#106—111no—
161C4⋊C8—111no—
162#103—111no—
163#102—111no—
164#102—112no—
165#102—112no—
166#102—112no—
167#102—112no—
168C22⋊C8—112no—
169C4×C8—111no—
170C2×C11—42no—
171C2×C11—42no—
172C2×C11—82no—
173C2×C11#54611yescharacteristic
174C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C11#57711yescharacteristic
176C24—22no—
177C2×Q8—111no—
178C2×Q8—221no—
179C2×D4—24no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—42no—
185C2×D4—44no—
186C2×D4C22⋊D1111yescharacteristic
187C2×D4C22×D1112yes—
188C2×D4C22×D1111yescharacteristic
189C22×C4—21no—
190C22×C4C22×D1112yes—
191SD16—222no—
192SD16—442no—
193M16—442no—
194C2×C8—111no—
195C2×C8—111no—
196C2×C8—112no—
197C4⋊C4—111no—
198C4⋊C4—112no—
199C4⋊C4—221no—
200C4⋊C4—222no—
201C4⋊C4—221no—
202C4⋊C4C22⋊D1111yescharacteristic
203C4⋊C4C22×D1111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—22no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4C22⋊D1112yes—
209C42—222no—
210C42—221no—
211C42C22×D1111yescharacteristic
212C11#332411yescharacteristic, complemented, Sylow
213C23—21no—
214C23—22no—
215C23—44no—
216C23—44no—
217C23—82no—
218C23C2×C22⋊D1112yes—
219Q8—221no—
220Q8—221no—
221Q8—442no—
222D4—22no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#434112yes—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—221no—
236C2×C4—222no—
237C2×C4—221no—
238C2×C4C2×C22⋊D1112yes—
239C2×C4C2×C22⋊D1111yescharacteristic
240C2×C4C2×C22⋊D1111yescharacteristic
241C2×C4C23×D1111yescharacteristic
242C8—221no—
243C8—221no—
244C8—222no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—88no—
255C22C22×C22⋊D1111yescharacteristic
256C4—22no—
257C4—21no—
258C4—41no—
259C4—442no—
260C4—441no—
261C4—441no—
262C4#6698512yes—
263C4C2×#434111yescharacteristic
264C4#6703711yescharacteristic
265C2—42no—
266C2—42no—
267C2—82no—
268C2C2×#6698511yescharacteristic
269C2#1062333711yescharacteristic
270C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalD42×C11C2
socleC22×C11C22×D4
hypercenterD42D11
hypocenterC11#3324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
2. #10623073C2semidirect
3. #10622831C2semidirect
4. #10622828C2semidirect
5. #10622688C2semidirect
6. #10622683C2semidirect
7. #10622655C2semidirect
8. #10622648C2semidirect
9. C4×#4324C2semidirect
10. #10622625C2semidirect
11. #10622620C2semidirect
22. C2×#4324C22semidirect
23. #66979C22semidirect
24. #66977C22semidirect
25. C2×#4318C22semidirect
28. #66922C22semidirect
29. C4×Dic22C22semidirect
32. #66896C22semidirect
33. #66896C22semidirect
34. #66896C22semidirect
35. C22⋊(C11⋊C8)C22semidirect
36. #66874C22semidirect
37. #66872C22semidirect
38. #66871C22semidirect
39. C4⋊(C11⋊C8)C22semidirect
40. C4×C11⋊C8C22semidirect
212. C11#3324semidirect

Maximal subgroups

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

subgroupindex
D42×C112
#106230732
#106228312
#106228282
#106226882
#106226832
#106226552
#106226482
C4×#43242
#106226252
#106226202
#332411