Finite Group Databasebeta

← #27203993

Subgroups — #27203993

Order 13184.

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×D103C211yesmaximal, characteristic
2#20268263C212yesmaximal, complemented
3#20267904C211yesmaximal, characteristic, complemented
4#20267903C211yesmaximal, characteristic, complemented
5#20267902C211yesmaximal, characteristic, complemented
6C4×#13110090C212yesmaximal, complemented
7#20267871C212yesmaximal, complemented
8#20267826C211yesmaximal, characteristic, complemented
9#20267794C212yesmaximal, complemented
10#20267748C211yesmaximal, characteristic, complemented
11#442×C103C211yesmaximal, characteristic, complemented
12C2×D4×D103C2212yes—
13C2×D824C2211yescharacteristic
14C2×#13110090C2212yes—
15D8×D103C418yescomplemented
16C2×#13110088C2211yescharacteristic
17C2×C8×D103C2211yescharacteristic
18C4×D412C2212yescomplemented
19D4×Dic103C2212yescomplemented
20#15692983C2212yescomplemented
21C4×C22⋊D103—22no—
22(C22⋊D103)⋊C4—22no—
23#15692979C2212yes—
24#15692978C2211yescharacteristic
25C2×(C2×D103)⋊C4—22no—
26C22⋊C4×D103—22no—
27#15692954C2212yescomplemented
28#15692953C2211yescharacteristic, complemented
29#15692943C2212yescomplemented
30#15692942C2212yescomplemented
31#15692941C2212yescomplemented
32#15692931C2211yescharacteristic, complemented
33C4×C103⋊C8C2211yescharacteristic, complemented
34C8×Dic103C2211yescharacteristic, complemented
35C2×D8×C103C2211yescharacteristic
36C4×D4×C103C2212yescomplemented
37#106×C103C2211yescharacteristic, complemented
38#102×C103C2212yescomplemented
39#97×C103C2211yescharacteristic, complemented
40C23×D103—22no—
41C2×D412C2312yes—
42C2×C22⋊D103—22no—
43D4×D103—24no—
44D4×D103C2×C418yescomplemented
45C22×Dic103—22no—
46C2×C4×D103—22no—
47C2×C4×D103—22no—
48C2×C4×D103C2311yescharacteristic
49D824C2×C414yescomplemented
50#13110090C2×C418yescomplemented
51#13110088—22no—
52C2×C103⋊C8C2311yescharacteristic
53C2×C103⋊C8C2311yescharacteristic
54C8×D103C2×C414yescomplemented
55C4⋊Dic103C2312yes—
56Dic103⋊C4D412yes—
57C22⋊Dic103—22no—
58(C2×D103)⋊C4—22no—
59(C2×D103)⋊C4—22no—
60(C2×D103)⋊C4—22no—
61(C2×D103)⋊C4D412yes—
62C4×Dic103—22no—
63C4×Dic103C2311yescharacteristic
64C2×D4×C103C2312yes—
65C22×C4×C103—22no—
66D8×C103C2×C414yescomplemented
67C2×C8×C103C2311yescharacteristic
68C2×C8×C103C2311yescharacteristic
69C4⋊C4×C103C2312yes—
70C22⋊C4×C103—22no—
71C42×C103C2311yescharacteristic
72C23×C103—22no—
73C22×D103—22no—
74C22×D103—28no—
75C22×D103—82no—
76C22×D103—82no—
77C22×D103C2×D411yescharacteristic
78D4×C103—22no—
79D4×C103C22×C414yes—
80C2×C4×C103—22no—
81C2×C4×C103—82no—
82C2×C4×C103C2×D412yes—
83C2×C4×C103C2411yescharacteristic
84C22⋊D103—28no—
85C2×Dic103—22no—
86C2×Dic103—82no—
87C2×Dic103C2×D412yes—
88C2×Dic103C2×D411yescharacteristic
89D412—22no—
90D412C22×C414yes—
91C4×D103—82no—
92C4×D103—82no—
93C4×D103C22×C412yes—
94C4×D103#4112yes—
95C8×C103—21no—
96C8×C103C22×C412yes—
97C103⋊C8—21no—
98C103⋊C8C22×C412yes—
99C22×C103—24no—
100C22×C103—42no—
101C22×C103—42no—
102C22×C103C22×D411yescharacteristic
103C2×D103—22no—
104C2×D103—24no—
105C2×D103—42no—
106C2×D103—42no—
107C2×D103—88no—
108C2×D103C4×D412yes—
109C4×C103—22no—
110C4×C103—42no—
111C4×C103C23×C411yescharacteristic
112C4×C103C2×#4111yescharacteristic
113Dic103—22no—
114Dic103—42no—
115Dic103C4×D412yes—
116C2×C103—44no—
117C2×C103C2×C4×D411yescharacteristic
118C2×C103#57612yes—
119D103—22no—
120D103—44no—
121#2948—1031nomaximal, Sylow
122C103#294811yescharacteristic, complemented, Sylow
123C22×D8—1031no—
124#518—1032no—
125#442—1031no—
126#442—1031no—
127#442—1031no—
128#442D10311yescharacteristic, complemented
129C4×D8—1032no—
130C4×D8—1032no—
131#427—1031no—
132#418—1032no—
133#405—1031no—
134C22×D4—1032no—
135C2×D8—1032no—
136C2×D8—1038no—
137C2×D8—1031no—
138C2×D8C2×D10311yescharacteristic
139C2×M16—1031no—
140C22×C8—1031no—
141C4×D4—1032no—
142C4×D4—1032no—
143C4×D4—1032no—
144C4×D4—2062no—
145C4×D4—2062no—
146C4×D4C2×D10312yescomplemented
147#117—1031no—
148#117—1032no—
149C2×C22⋊C4—2062no—
150C2×C22⋊C4—2062no—
151#107—1032no—
152#106—1031no—
153#106C2×D10311yescharacteristic, complemented
154#102—1032no—
155#102—1032no—
156#102—1032no—
157#102C2×D10312yescomplemented
158#97—1031no—
159#97C2×D10311yescharacteristic, complemented
160C4×C8—1031no—
161C4×C8—1031no—
162C24—2062no—
163C2×D4—1038no—
164C2×D4—1032no—
165C2×D4—2064no—
166C2×D4—2062no—
167C2×D4C22×D10312yes—
168C22×C4—22no—
169C22×C4—1031no—
170C22×C4—2062no—
171C22×C4—2062no—
172C22×C4—2062no—
173D8—1038no—
174D8—1034no—
175D8C4×D10314yescomplemented
176M16—2062no—
177C2×C8—1031no—
178C2×C8—1034no—
179C2×C8—1031no—
180C2×C8C22×D10311yescharacteristic
181C2×C8C22×D10311yescharacteristic
182C4⋊C4—1032no—
183C4⋊C4—1032no—
184C4⋊C4C22×D10312yes—
185C22⋊C4—22no—
186C22⋊C4—1032no—
187C22⋊C4—2062no—
188C22⋊C4—2062no—
189C22⋊C4—2062no—
190C22⋊C4—2062no—
191C42—1031no—
192C42—2062no—
193C42C22×D10311yescharacteristic
194C23—22no—
195C23—8242no—
196C23—8242no—
197C23—1031no—
198C23—2068no—
199C23—2062no—
200D4—22no—
201D4—1034no—
202D4—2068no—
203D4—2062no—
204D4C2×C4×D10314yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—8242no—
208C2×C4—8242no—
209C2×C4—8242no—
210C2×C4—1031no—
211C2×C4—1032no—
212C2×C4—1032no—
213C2×C4—1032no—
214C2×C4—2062no—
215C2×C4D4×D10312yes—
216C2×C4C23×D10311yescharacteristic
217C8—21no—
218C8—1032no—
219C8—2061no—
220C8C2×C4×D10312yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—8248no—
225C22—1032no—
226C22—4122no—
227C22—4122no—
228C22—2064no—
229C22—2062no—
230C22C2×D4×D10311yescharacteristic
231C4—22no—
232C4—42no—
233C4—1032no—
234C4—4122no—
235C4—2062no—
236C4C22×C4×D10311yescharacteristic
237C4#41×D10311yescharacteristic
238C2—44no—
239C2—4124no—
240C2—2062no—
241C2C4×D4×D10311yescharacteristic
242C2#2026859512yes—
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#442×C103C2
socleC22×C103C22×D4
prime radicalC2×D8×D103C2
cosocleC2×C4×C103C24
hypercenter#442D103
hypocenterC103#2948
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #20268263C2semidirect
3. #20267904C2semidirect
4. #20267903C2semidirect
5. #20267902C2semidirect
6. C4×#13110090C2semidirect
7. #20267871C2semidirect
8. #20267826C2semidirect
9. #20267794C2semidirect
10. #20267748C2semidirect
11. #442×C103C2semidirect
15. D8×D103C4semidirect
18. C4×D412C22semidirect
19. D4×Dic103C22semidirect
20. #15692983C22semidirect
27. #15692954C22semidirect
28. #15692953C22semidirect
29. #15692943C22semidirect
30. #15692942C22semidirect
31. #15692941C22semidirect
32. #15692931C22semidirect
33. C4×C103⋊C8C22semidirect
34. C8×Dic103C22semidirect
36. C4×D4×C103C22semidirect
37. #106×C103C22semidirect
38. #102×C103C22semidirect
39. #97×C103C22semidirect
44. D4×D103C2×C4semidirect
49. D824C2×C4semidirect
50. #13110090C2×C4semidirect
54. C8×D103C2×C4semidirect
66. D8×C103C2×C4semidirect
122. C103#2948semidirect
128. #442D103semidirect
146. C4×D4C2×D103semidirect
153. #106C2×D103semidirect
157. #102C2×D103semidirect
159. #97C2×D103semidirect
175. D8C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1032
#202682632
#202679042
#202679032
#202679022
C4×#131100902
#202678712
#202678262
#202677942
#202677482
#442×C1032
#2948103