Finite Group Databasebeta

← #13080849

Subgroups — #13080849

Order 1408.

448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623115C211yesmaximal, characteristic, complemented
2D4×D44C211yesmaximal, characteristic
3C4×C11×SD16C211yesmaximal, characteristic, complemented
4#10622782C212yesmaximal, complemented
5#10622640C211yesmaximal, characteristic, complemented
6#10622620C211yesmaximal, characteristic, complemented
7#10622479C212yesmaximal, complemented
8#10622425C212yesmaximal, complemented
9#10622383C212yesmaximal, complemented
10#10622307C211yesmaximal, characteristic, complemented
11#10622301C211yesmaximal, characteristic, complemented
12C2×D4×D11C2212yes—
13C22×D44—21no—
14C2×C11×SD16C2211yescharacteristic
15C4×Q8×C11C2211yescharacteristic, complemented
16C4×D4×C11C2211yescharacteristic
17#66999C2212yescomplemented
18C2×#4325C2212yescomplemented
19#66983—21no—
20C2×#4313C2212yescomplemented
21#66951—22no—
22#66948C2212yes—
23#66945C2212yescomplemented
24#66935—22no—
25#66928—21no—
26#66927C2211yescharacteristic
27C4×D44C2211yescharacteristic
28#66922C2211yescharacteristic, complemented
29C4×Dic22—21no—
30C11×#106C2211yescharacteristic, complemented
31C11×#103C2211yescharacteristic, complemented
32C11×#102C2211yescharacteristic
33C4×C8×C11C2211yescharacteristic, complemented
34#66896C2212yes—
35#66885C2212yescomplemented
36#66885C2212yescomplemented
37(C2×D11)⋊C8C2212yescomplemented
38#66873C2212yescomplemented
39#66871C2212yescomplemented
40C4⋊(C11⋊C8)C2211yescharacteristic, complemented
41C23×D11—22no—
42C2×Q8×C11C2311yescharacteristic
43C2×D4×C11C2311yescharacteristic
44C22×C4×C11—21no—
45C2×C22⋊D11—22no—
46D4×D11—24no—
47D4×D11—42no—
48C2×D44—22no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44—44no—
52C2×D44D411yescharacteristic
53C2×D44C2312yes—
54C2×C4×D11C2312yes—
55C2×Dic22—21no—
56C11×SD16—22no—
57C2×C8×C11C2311yescharacteristic
58C2×C8×C11C2311yescharacteristic
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2311yescharacteristic
61C11×C4⋊C4C2311yescharacteristic
62C11×C22⋊C4—21no—
63C42×C11—21no—
64C42×C11C2311yescharacteristic
65#4325—42no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4D412yes—
70C4⋊Dic11—21no—
71C4⋊Dic11D411yescharacteristic
72C4⋊Dic11C2312yes—
73Dic11⋊C4—22no—
74C4×Dic11—22no—
75C2×C11⋊C8C2312yes—
76#4313—42no—
77#3324—111nomaximal, Sylow
78C23×C11—21no—
79C22×D11—22no—
80C22×D11—44no—
81C22×D11—44no—
82C22×D11—82no—
83C22×D11C2×D412yes—
84Q8×C11—21no—
85Q8×C11—21no—
86D4×C11—21no—
87D4×C11#4112yes—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—42no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—44no—
96C2×Dic11—22no—
97C2×Dic11C2×D412yes—
98D44—22no—
99D44—22no—
100D44—22no—
101D44—44no—
102D44—42no—
103D44—81no—
104C4×D11—22no—
105C4×D11—22no—
106Dic22—42no—
107C8×C11—21no—
108C8×C11—21no—
109C11⋊C8—22no—
110#556—111no—
111D42—111no—
112#486—111no—
113#482—112no—
114#474—111no—
115#468—112no—
116#460—111no—
117#450—112no—
118C4×SD16D1111yescharacteristic, complemented
119#436—111no—
120#418—112no—
121C22×C11—22no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11C22×D411yescharacteristic
125C2×D11—22no—
126C2×D11—22no—
127C2×D11—22no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—88no—
132C4×C11—21no—
133C4×C11—41no—
134C4×C11—41no—
135C4×C11—41no—
136C4×C11AGL(1,ℤ/8)12yes—
137C4×C11C2×#4111yescharacteristic
138C4×C11H(5,𝔽2)11yescharacteristic
139Dic11—22no—
140Dic11—42no—
141C22×D4—112no—
142C22×D4—221no—
143C2×SD16—112no—
144C2×SD16C2×D1111yescharacteristic
145C2×M16—112no—
146C4⋊Q8—111no—
147#127—111no—
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×D4C2×D1111yescharacteristic
158#117—112no—
159#107—112no—
160#106C2×D1111yescharacteristic, complemented
161C4⋊C8—111no—
162#103C2×D1111yescharacteristic, complemented
163#102—112no—
164#102—112no—
165#102—112no—
166#102—112no—
167#102C2×D1111yescharacteristic
168C22⋊C8—112no—
169C4×C8C2×D1111yescharacteristic, complemented
170C2×C11—42no—
171C2×C11#54611yescharacteristic
172C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C11#57711yescharacteristic
174D11—42no—
175D11—82no—
176C24—222no—
177C2×Q8—221no—
178C2×Q8C22×D1111yescharacteristic
179C2×D4—111no—
180C2×D4—112no—
181C2×D4—222no—
182C2×D4—222no—
183C2×D4—224no—
184C2×D4—221no—
185C2×D4—221no—
186C2×D4—444no—
187C2×D4—442no—
188C2×D4C22×D1111yescharacteristic
189C22×C4—21no—
190C22×C4—112no—
191SD16—22no—
192SD16—442no—
193M16—442no—
194C2×C8—112no—
195C2×C8C22×D1111yescharacteristic
196C2×C8C22×D1111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—111no—
199C4⋊C4—112no—
200C4⋊C4—222no—
201C4⋊C4—221no—
202C4⋊C4C22×D1111yescharacteristic
203C4⋊C4C22×D1111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—112no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4—222no—
209C42—21no—
210C42—222no—
211C42C22×D1111yescharacteristic
212C11#332411yescharacteristic, complemented, Sylow
213C23—21no—
214C23—112no—
215C23—222no—
216C23—444no—
217C23—444no—
218C23—882no—
219Q8—21no—
220Q8—21no—
221Q8—442no—
222D4—21no—
223D4—222no—
224D4—222no—
225D4—222no—
226D4—444no—
227D4—444no—
228D4—442no—
229D4—881no—
230D4#433912yes—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—112no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4D4×D1111yescharacteristic
240C2×C4D4×D1111yescharacteristic
241C2×C4C23×D1111yescharacteristic
242C8—21no—
243C8—21no—
244C8—222no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—222no—
249C22—222no—
250C22—222no—
251C22—442no—
252C22—442no—
253C22—442no—
254C22—888no—
255C22C2×D4×D1111yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—222no—
261C4—442no—
262C4#6696712yes—
263C4C2×#433911yescharacteristic
264C4#6704211yescharacteristic
265C2—42no—
266C2—442no—
267C2—882no—
268C2#1062308111yescharacteristic
269C2C2×#6696711yescharacteristic
270C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
prime radicalD4×D44C2
hypercenterC4×SD16D11
hypocenterC11#3324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10623115C2semidirect
3. C4×C11×SD16C2semidirect
4. #10622782C2semidirect
5. #10622640C2semidirect
6. #10622620C2semidirect
7. #10622479C2semidirect
8. #10622425C2semidirect
9. #10622383C2semidirect
10. #10622307C2semidirect
11. #10622301C2semidirect
15. C4×Q8×C11C22semidirect
17. #66999C22semidirect
18. C2×#4325C22semidirect
20. C2×#4313C22semidirect
23. #66945C22semidirect
28. #66922C22semidirect
30. C11×#106C22semidirect
31. C11×#103C22semidirect
33. C4×C8×C11C22semidirect
35. #66885C22semidirect
36. #66885C22semidirect
37. (C2×D11)⋊C8C22semidirect
38. #66873C22semidirect
39. #66871C22semidirect
40. C4⋊(C11⋊C8)C22semidirect
118. C4×SD16D11semidirect
155. C4×Q8C2×D11semidirect
160. #106C2×D11semidirect
162. #103C2×D11semidirect
169. C4×C8C2×D11semidirect
212. C11#3324semidirect

Maximal subgroups

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

subgroupindex
#106231152
D4×D442
C4×C11×SD162
#106227822
#106226402
#106226202
#106224792
#106224252
#106223832
#106223072
#106223012
#332411