Finite Group Databasebeta

← #13077465

Subgroups — #13077465

Order 1408.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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
1C2×D8×D11C211yesmaximal, characteristic
2#10623076C212yesmaximal, complemented
3C11×#442C211yesmaximal, characteristic, complemented
4#10622765C211yesmaximal, characteristic, complemented
5C4×#4323C212yesmaximal, complemented
6#10622482C211yesmaximal, characteristic, complemented
7#10622473C211yesmaximal, characteristic, complemented
8#10622383C212yesmaximal, complemented
9#10622369C212yesmaximal, complemented
10#10622324C211yesmaximal, characteristic, complemented
11#10622321C211yesmaximal, characteristic, complemented
12C2×D4×D11C2212yes—
13C2×C11×D8C2211yescharacteristic
14C4×D4×C11C2212yescomplemented
15D4×Dic11C2212yescomplemented
16C2×#4323C2212yes—
17C4×C22⋊D11—22no—
18C2×(C2×D11)⋊C4—22no—
19D8×D11C418yescomplemented
20C2×D88C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22C2×C8×D11C2211yescharacteristic
23#66946C2212yescomplemented
24#66945C2212yes—
25(C22⋊D11)⋊C4—22no—
26C22⋊C4×D11—22no—
27C4×D44C2212yescomplemented
28#66925C2211yescharacteristic
29C11×#106C2211yescharacteristic, complemented
30C11×#102C2212yescomplemented
31C11×#97C2211yescharacteristic, complemented
32#66896C2212yescomplemented
33#66885C2212yescomplemented
34#66881C2211yescharacteristic, complemented
35#66879C2211yescharacteristic, complemented
36C8×Dic11C2211yescharacteristic, complemented
37#66873C2212yescomplemented
38#66871C2212yescomplemented
39C4×C11⋊C8C2211yescharacteristic, complemented
40C23×D11—22no—
41C2×D4×C11C2312yes—
42C22×C4×C11—22no—
43C2×C22⋊D11—22no—
44C22×Dic11—22no—
45D4×D11—24no—
46D4×D11C2×C418yescomplemented
47C2×D44C2312yes—
48C2×C4×D11—22no—
49C2×C4×D11—22no—
50C2×C4×D11C2311yescharacteristic
51C11×D8C2×C414yescomplemented
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—22no—
56C42×C11C2311yescharacteristic
57C22⋊Dic11—22no—
58#4323C2×C418yescomplemented
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4D412yes—
63C4⋊Dic11C2312yes—
64Dic11⋊C4D412yes—
65C4×Dic11—22no—
66C4×Dic11C2311yescharacteristic
67C2×C11⋊C8C2311yescharacteristic
68C2×C11⋊C8C2311yescharacteristic
69D88C2×C414yescomplemented
70#4313—22no—
71C8×D11C2×C414yescomplemented
72#2948—111nomaximal, Sylow
73C23×C11—22no—
74C22×D11—22no—
75C22×D11—28no—
76C22×D11—82no—
77C22×D11—82no—
78C22×D11C2×D411yescharacteristic
79D4×C11—22no—
80D4×C11C22×C414yes—
81C2×C4×C11—22no—
82C2×C4×C11—82no—
83C2×C4×C11C2×D412yes—
84C2×C4×C11C2411yescharacteristic
85C22⋊D11—28no—
86C2×Dic11—22no—
87C2×Dic11—82no—
88C2×Dic11C2×D412yes—
89C2×Dic11C2×D411yescharacteristic
90D44—22no—
91D44C22×C414yes—
92C4×D11—82no—
93C4×D11—82no—
94C4×D11C22×C412yes—
95C4×D11#4112yes—
96C8×C11—21no—
97C8×C11C22×C412yes—
98C11⋊C8—21no—
99C11⋊C8C22×C412yes—
100C22×D8—111no—
101#518—112no—
102#442—111no—
103#442—111no—
104#442—111no—
105#442D1111yescharacteristic, complemented
106C4×D8—112no—
107C4×D8—112no—
108#427—111no—
109#418—112no—
110#405—111no—
111C22×C11—24no—
112C22×C11—42no—
113C22×C11—42no—
114C22×C11C22×D411yescharacteristic
115C2×D11—22no—
116C2×D11—24no—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—88no—
120C2×D11C4×D412yes—
121C4×C11—22no—
122C4×C11—42no—
123C4×C11C23×C411yescharacteristic
124C4×C11C2×#4111yescharacteristic
125Dic11—22no—
126Dic11—42no—
127Dic11C4×D412yes—
128C22×D4—112no—
129C2×D8—112no—
130C2×D8—118no—
131C2×D8—111no—
132C2×D8C2×D1111yescharacteristic
133C2×M16—111no—
134C22×C8—111no—
135C4×D4—112no—
136C4×D4—112no—
137C4×D4—112no—
138C4×D4—222no—
139C4×D4—222no—
140C4×D4C2×D1112yescomplemented
141#117—111no—
142#117—112no—
143C2×C22⋊C4—222no—
144C2×C22⋊C4—222no—
145#107—112no—
146#106—111no—
147#106C2×D1111yescharacteristic, complemented
148#102—112no—
149#102—112no—
150#102—112no—
151#102C2×D1112yescomplemented
152#97—111no—
153#97C2×D1111yescharacteristic, complemented
154C4×C8—111no—
155C4×C8—111no—
156C2×C11—44no—
157C2×C11C2×C4×D411yescharacteristic
158C2×C11#57612yes—
159D11—22no—
160D11—44no—
161C24—222no—
162C2×D4—118no—
163C2×D4—112no—
164C2×D4—224no—
165C2×D4—222no—
166C2×D4C22×D1112yes—
167C22×C4—22no—
168C22×C4—111no—
169C22×C4—222no—
170C22×C4—222no—
171C22×C4—222no—
172D8—118no—
173D8—114no—
174D8C4×D1114yescomplemented
175M16—222no—
176C2×C8—111no—
177C2×C8—114no—
178C2×C8—111no—
179C2×C8C22×D1111yescharacteristic
180C2×C8C22×D1111yescharacteristic
181C4⋊C4—112no—
182C4⋊C4—112no—
183C4⋊C4C22×D1112yes—
184C22⋊C4—22no—
185C22⋊C4—112no—
186C22⋊C4—222no—
187C22⋊C4—222no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C42—111no—
191C42—222no—
192C42C22×D1111yescharacteristic
193C11#294811yescharacteristic, complemented, Sylow
194C23—22no—
195C23—111no—
196C23—228no—
197C23—222no—
198C23—882no—
199C23—882no—
200D4—22no—
201D4—114no—
202D4—228no—
203D4—222no—
204D4C2×C4×D1114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—111no—
208C2×C4—112no—
209C2×C4—112no—
210C2×C4—112no—
211C2×C4—222no—
212C2×C4—882no—
213C2×C4—882no—
214C2×C4—882no—
215C2×C4D4×D1112yes—
216C2×C4C23×D1111yescharacteristic
217C8—21no—
218C8—112no—
219C8—221no—
220C8C2×C4×D1112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—112no—
225C22—222no—
226C22—224no—
227C22—442no—
228C22—442no—
229C22—888no—
230C22C2×D4×D1111yescharacteristic
231C4—22no—
232C4—42no—
233C4—112no—
234C4—222no—
235C4—442no—
236C4C22×C4×D1111yescharacteristic
237C4#41×D1111yescharacteristic
238C2—44no—
239C2—222no—
240C2—444no—
241C2C4×D4×D1111yescharacteristic
242C2#1062330512yes—
subgroupG/H
centerC22C2×D4×D11
commutatorC4×C11C23×C4
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
prime radicalC2×D8×D11C2
cosocleC2×C4×C11C24
hypercenter#442D11
hypocenterC11#2948
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #10623076C2semidirect
3. C11×#442C2semidirect
4. #10622765C2semidirect
5. C4×#4323C2semidirect
6. #10622482C2semidirect
7. #10622473C2semidirect
8. #10622383C2semidirect
9. #10622369C2semidirect
10. #10622324C2semidirect
11. #10622321C2semidirect
14. C4×D4×C11C22semidirect
15. D4×Dic11C22semidirect
19. D8×D11C4semidirect
23. #66946C22semidirect
27. C4×D44C22semidirect
29. C11×#106C22semidirect
30. C11×#102C22semidirect
31. C11×#97C22semidirect
32. #66896C22semidirect
33. #66885C22semidirect
34. #66881C22semidirect
35. #66879C22semidirect
36. C8×Dic11C22semidirect
37. #66873C22semidirect
38. #66871C22semidirect
39. C4×C11⋊C8C22semidirect
46. D4×D11C2×C4semidirect
51. C11×D8C2×C4semidirect
58. #4323C2×C4semidirect
69. D88C2×C4semidirect
71. C8×D11C2×C4semidirect
105. #442D11semidirect
140. C4×D4C2×D11semidirect
147. #106C2×D11semidirect
151. #102C2×D11semidirect
153. #97C2×D11semidirect
174. D8C4×D11semidirect
193. C11#2948semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D112
#106230762
C11×#4422
#106227652
C4×#43232
#106224822
#106224732
#106223832
#106223692
#106223242
#106223212
#294811