Finite Group Databasebeta

← #442×D103 #27203933

Subgroups — #442×D103 #27203933

Order 13184.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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
2C4×D4×D103C212yesmaximal, complemented
3#20267904C211yesmaximal, characteristic, complemented
4#20267903C211yesmaximal, characteristic, complemented
5#20267902C211yesmaximal, characteristic, complemented
6#20267901C212yesmaximal, complemented
7#20267900C212yesmaximal, complemented
8#106×D103C211yesmaximal, characteristic, complemented
9#102×D103C212yesmaximal, complemented
10#97×D103C211yesmaximal, characteristic, complemented
11#442×C103C211yesmaximal, characteristic, complemented
12C2×D4×D103C2212yes—
13C22×C4×D103—22no—
14C2×D824C2211yescharacteristic
15C2×#13110090C2212yes—
16D8×D103C418yescomplemented
17C2×C8×D103C2211yescharacteristic
18C2×C8×D103C2211yescharacteristic
19C4×D412C2212yescomplemented
20D4×Dic103C2212yescomplemented
21#15692983C2212yescomplemented
22C4×C22⋊D103—22no—
23(C22⋊D103)⋊C4—22no—
24C4⋊C4×D103C2212yes—
25C22⋊C4×D103—22no—
26C42×D103C2211yescharacteristic
27#15692953C2211yescharacteristic, complemented
28#15692952C2212yescomplemented
29#15692943C2212yescomplemented
30#15692942C2212yescomplemented
31#15692941C2212yescomplemented
32#15692932C2211yescharacteristic, complemented
33#15692931C2211yescharacteristic, complemented
34#15692931C2211yescharacteristic, 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×D103—22no—
49C2×C4×D103—48no—
50C2×C4×D103D412yes—
51C2×C4×D103C2311yescharacteristic
52D824C2×C414yescomplemented
53#13110090C2×C418yescomplemented
54C2×C103⋊C8C2311yescharacteristic
55C2×C103⋊C8C2311yescharacteristic
56C8×D103—22no—
57C8×D103C2×C414yescomplemented
58C4⋊Dic103C2312yes—
59Dic103⋊C4—22no—
60C22⋊Dic103—22no—
61(C2×D103)⋊C4—22no—
62(C2×D103)⋊C4—22no—
63C4×Dic103D412yes—
64C4×Dic103C2311yescharacteristic
65C2×D4×C103C2312yes—
66C22×C4×C103—22no—
67D8×C103C2×C414yescomplemented
68C2×C8×C103C2311yescharacteristic
69C2×C8×C103C2311yescharacteristic
70C4⋊C4×C103C2312yes—
71C22⋊C4×C103—22no—
72C42×C103C2311yescharacteristic
73C23×C103—22no—
74C22×D103—22no—
75C22×D103—28no—
76C22×D103—44no—
77C22×D103—44no—
78C22×D103C2×D411yescharacteristic
79D4×C103—22no—
80D4×C103C22×C414yescomplemented
81C2×C4×C103—22no—
82C2×C4×C103—44no—
83C2×C4×C103C2×D412yes—
84C2×C4×C103C2411yescharacteristic
85C22⋊D103—28no—
86C2×Dic103—22no—
87C2×Dic103—44no—
88C2×Dic103C2×D412yes—
89C2×Dic103C2×D411yescharacteristic
90D412—22no—
91D412C22×C414yescomplemented
92C4×D103—24no—
93C4×D103—44no—
94C4×D103—44no—
95C4×D103—44no—
96C4×D103C22×C412yes—
97C4×D103#4112yes—
98C8×C103—21no—
99C8×C103C22×C412yescomplemented
100C103⋊C8—21no—
101C103⋊C8C22×C412yescomplemented
102C22×C103—24no—
103C22×C103—42no—
104C22×C103—42no—
105C22×C103C22×D411yescharacteristic
106C2×D103—24no—
107C2×D103—42no—
108C2×D103—42no—
109C2×D103—416no—
110C2×D103C4×D412yes—
111C2×D103AGL(1,ℤ/8)14yes—
112C4×C103—22no—
113C4×C103—42no—
114C4×C103C23×C411yescharacteristic
115C4×C103C2×#4111yescharacteristic
116Dic103—22no—
117Dic103—42no—
118Dic103C4×D412yes—
119C2×C103—44no—
120C2×C103C2×C4×D411yescharacteristic
121C2×C103C2×AGL(1,ℤ/8)12yes—
122D103—44no—
123D103#44214yesdirect product factor
124C2×#442—1031nomaximal, Sylow
125C103C2×#44211yescharacteristic, complemented, Sylow
126C22×D8—1031no—
127C2×C4×D4—1032no—
128#442—1031no—
129#442—1032no—
130#442—1031no—
131#442—1032no—
132#442—1031no—
133#442D10311yescharacteristic, direct product factor
134C2×#106—1031no—
135C2×#102—1032no—
136C2×#97—1031no—
137C22×D4—1032no—
138C23×C4—2062no—
139C2×D8—1032no—
140C2×D8—1038no—
141C2×D8—1031no—
142C2×D8C2×D10311yescharacteristic
143C22×C8—1031no—
144C22×C8—1031no—
145C4×D4—1032no—
146C4×D4—1032no—
147C4×D4—1032no—
148C4×D4—2062no—
149C4×D4—2062no—
150C4×D4C2×D10312yescomplemented
151C2×C4⋊C4—1032no—
152C2×C22⋊C4—2062no—
153C2×C42—1031no—
154#106—1031no—
155#106—1032no—
156#106C2×D10311yescharacteristic, complemented
157#102—1032no—
158#102—1032no—
159#102—1032no—
160#102C2×D10312yescomplemented
161#97—1031no—
162#97—1031no—
163#97—1031no—
164#97C2×D10311yescharacteristic, complemented
165C24—2062no—
166C2×D4—1038no—
167C2×D4—1032no—
168C2×D4—2064no—
169C2×D4—2062no—
170C2×D4C22×D10312yes—
171C22×C4—22no—
172C22×C4—1031no—
173C22×C4—1032no—
174C22×C4—4128no—
175C22×C4—2062no—
176C22×C4—2062no—
177C22×C4—2062no—
178C22×C4—2062no—
179D8—1038no—
180D8—1034no—
181D8C4×D10314yescomplemented
182C2×C8—1031no—
183C2×C8—1034no—
184C2×C8—1031no—
185C2×C8—2062no—
186C2×C8C22×D10311yescharacteristic
187C2×C8C22×D10311yescharacteristic
188C4⋊C4—1032no—
189C4⋊C4—2062no—
190C4⋊C4C22×D10312yes—
191C22⋊C4—22no—
192C22⋊C4—2062no—
193C22⋊C4—2062no—
194C22⋊C4—2062no—
195C42—1032no—
196C42—1031no—
197C42C22×D10311yescharacteristic
198C23—22no—
199C23—1031no—
200C23—4124no—
201C23—4124no—
202C23—2068no—
203C23—2062no—
204D4—22no—
205D4—1034no—
206D4—2068no—
207D4—2062no—
208D4C2×C4×D10314yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—1031no—
212C2×C4—1032no—
213C2×C4—1032no—
214C2×C4—1032no—
215C2×C4—4124no—
216C2×C4—4124no—
217C2×C4—4124no—
218C2×C4—4124no—
219C2×C4—2064no—
220C2×C4—2062no—
221C2×C4D4×D10312yes—
222C2×C4C23×D10311yescharacteristic
223C8—21no—
224C8—1032no—
225C8—2061no—
226C8C2×C4×D10312yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—1034no—
231C22—1032no—
232C22—41216no—
233C22—4122no—
234C22—4122no—
235C22—2064no—
236C22C2×D4×D10311yescharacteristic
237C4—22no—
238C4—42no—
239C4—1032no—
240C4—4122no—
241C4—2062no—
242C4C22×C4×D10311yescharacteristic
243C4#41×D10311yescharacteristic
244C2—44no—
245C2—1034no—
246C2—4124no—
247C2C4×D4×D10311yescharacteristic
248C2AGL(1,ℤ/8)×D10312yes—
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
hypocenterC103C2×#442
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. C4×D4×D103C2semidirect
3. #20267904C2semidirect
4. #20267903C2semidirect
5. #20267902C2semidirect
6. #20267901C2semidirect
7. #20267900C2semidirect
8. #106×D103C2semidirect
9. #102×D103C2semidirect
10. #97×D103C2semidirect
11. #442×C103C2semidirect
16. D8×D103C4semidirect
19. C4×D412C22semidirect
20. D4×Dic103C22semidirect
21. #15692983C22semidirect
27. #15692953C22semidirect
28. #15692952C22semidirect
29. #15692943C22semidirect
30. #15692942C22semidirect
31. #15692941C22semidirect
32. #15692932C22semidirect
33. #15692931C22semidirect
34. #15692931C22semidirect
36. C4×D4×C103C22semidirect
37. #106×C103C22semidirect
38. #102×C103C22semidirect
39. #97×C103C22semidirect
44. D4×D103C2×C4semidirect
52. D824C2×C4semidirect
53. #13110090C2×C4semidirect
57. C8×D103C2×C4semidirect
67. D8×C103C2×C4semidirect
80. D4×C103C22×C4semidirect
91. D412C22×C4semidirect
99. C8×C103C22×C4semidirect
101. C103⋊C8C22×C4semidirect
123. D103#442direct (N × H)
125. C103C2×#442semidirect
133. #442D103direct (N × H)
150. C4×D4C2×D103semidirect
156. #106C2×D103semidirect
160. #102C2×D103semidirect
164. #97C2×D103semidirect
181. D8C4×D103semidirect
208. D4C2×C4×D103semidirect
226. C8C2×C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1032
C4×D4×D1032
#202679042
#202679032
#202679022
#202679012
#202679002
#106×D1032
#102×D1032
#97×D1032
#442×C1032
C2×#442103