Finite Group Databasebeta

← #27205940

Subgroups — #27205940

Order 13184.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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#121×D103C212yesmaximal, complemented
2#20268111C212yesmaximal, complemented
3#20268108C212yesmaximal, complemented
4#20268044C211yesmaximal, characteristic, complemented
5#20268042C212yesmaximal, complemented
6#20267926C212yesmaximal, complemented
7#20267923C212yesmaximal, complemented
8#20267754C211yesmaximal, characteristic, complemented
9#469×C103C211yesmaximal, characteristic, complemented
10C2×D4×D103—22no—
11C2×D4×D103C2212yescomplemented
12C22×C4×D103C2211yescharacteristic
13C2×D824C2211yescharacteristic, complemented
14C2×#13110090C2212yescomplemented
15C2×#13110089C2211yescharacteristic, complemented
16#15692996C2212yes—
17#15692995C2212yescomplemented
18#15692994—22no—
19#15692993—22no—
20#15692992C2212yes—
21C4⋊C4×D103C2212yescomplemented
22C22⋊C4×D103—22no—
23#15692953C2211yescharacteristic, complemented
24#15692952C2212yescomplemented
25#15692943C2212yescomplemented
26#15692942C2212yescomplemented
27#15692941C2212yescomplemented
28(C2×D103)⋊C8C2212yescomplemented
29(C2×D103)⋊C8C2212yescomplemented
30C2×D8×C103C2211yescharacteristic, complemented
31C2×M16×C103C2211yescharacteristic, complemented
32#121×C103C2212yescomplemented
33#106×C103C2211yescharacteristic, complemented
34#102×C103C2212yescomplemented
35C23×D103—22no—
36C23×D103D411yescharacteristic
37C2×D412—22no—
38C2×D412C2312yes—
39C2×C22⋊D103—22no—
40C2×C22⋊D103—22no—
41C2×C22⋊D103—22no—
42D4×D103—42no—
43D4×D103—42no—
44D4×D103—48no—
45C22×Dic103D411yescharacteristic
46C2×C4×D103—22no—
47C2×C4×D103—41no—
48C2×C4×D103—41no—
49C2×C4×D103D412yes—
50C2×C4×D103C2312yes—
51D824—41no—
52#13110090—42no—
53#13110089—41no—
54C2×C103⋊C8C2312yes—
55C4⋊Dic103C2312yes—
56Dic103⋊C4—22no—
57C22⋊Dic103—22no—
58(C2×D103)⋊C4—22no—
59(C2×D103)⋊C4—22no—
60C2×D4×C103—22no—
61C2×D4×C103C2312yes—
62C22×C4×C103C2311yescharacteristic
63D8×C103—41no—
64M16×C103—41no—
65C2×C8×C103C2311yescharacteristic
66C2×C8×C103C2311yescharacteristic
67C4⋊C4×C103C2312yes—
68C22⋊C4×C103—22no—
69C23×C103—22no—
70C23×C103C2×D411yescharacteristic
71C22×D103—24no—
72C22×D103—22no—
73C22×D103—41no—
74C22×D103—44no—
75C22×D103—44no—
76C22×D103—44no—
77C22×D103C2×D412yes—
78D4×C103—22no—
79D4×C103—22no—
80D4×C103—44no—
81C2×C4×C103—21no—
82C2×C4×C103—21no—
83C2×C4×C103—22no—
84C2×C4×C103C2×D411yescharacteristic
85C2×C4×C103C2411yescharacteristic
86C22⋊D103—44no—
87C22⋊D103—44no—
88C22⋊D103—44no—
89C2×Dic103—22no—
90C2×Dic103—41no—
91C2×Dic103C2×D412yes—
92D412—22no—
93D412—22no—
94D412—44no—
95C4×D103—22no—
96C4×D103—22no—
97C4×D103—42no—
98C4×D103—44no—
99C8×C103—21no—
100C8×C103—21no—
101C103⋊C8—22no—
102C22×C103—21no—
103C22×C103—22no—
104C22×C103—42no—
105C22×C103—42no—
106C22×C103—42no—
107C22×C103C22×D411yescharacteristic
108C2×D103—22no—
109C2×D103—22no—
110C2×D103—44no—
111C2×D103—42no—
112C2×D103—42no—
113C2×D103—42no—
114C2×D103—88no—
115C2×D103AGL(1,ℤ/8)14yes—
116C4×C103—21no—
117C4×C103—42no—
118C4×C103H(5,𝔽2)11yescharacteristic
119C4×C103H(5,𝔽2)11yescharacteristic
120Dic103—22no—
121Dic103—42no—
122C2×C103—41no—
123C2×C103—82no—
124C2×C103#53411yescharacteristic
125C2×C103C2×AGL(1,ℤ/8)12yes—
126D103—24no—
127D103—82no—
128#3192—1031nomaximal, Sylow
129C103#319211yescharacteristic, complemented, Sylow
130C2×#121—1032no—
131#481—1032no—
132#481—1032no—
133#469—1031no—
134#469—1032no—
135#469D10311yescharacteristic, complemented
136#447—1032no—
137#447—1032no—
138#407—1031no—
139C22×D4—1032no—
140C22×D4—2062no—
141C23×C4—1031no—
142C2×D8—1032no—
143C2×D8—1031no—
144C2×D8C2×D10311yescharacteristic, complemented
145C2×M16—1031no—
146C2×M16C2×D10311yescharacteristic, complemented
147#121—1032no—
148#121—1032no—
149#121—1032no—
150#121—2062no—
151#121—2062no—
152#121C2×D10312yescomplemented
153C2×C4⋊C4—1032no—
154C2×C22⋊C4—2062no—
155#106—1031no—
156#106—1032no—
157#106C2×D10311yescharacteristic, complemented
158#102—1032no—
159#102—1032no—
160#102—1032no—
161#102C2×D10312yescomplemented
162C22⋊C8—1032no—
163C22⋊C8—1032no—
164C24—1031no—
165C24—2062no—
166C2×D4—22no—
167C2×D4—1032no—
168C2×D4—4128no—
169C2×D4—4122no—
170C2×D4—4122no—
171C2×D4—2062no—
172C2×D4—2062no—
173C2×D4—2062no—
174C2×D4—2062no—
175C2×D4C22×D10312yes—
176C22×C4—1031no—
177C22×C4—1032no—
178C22×C4—1032no—
179C22×C4—4121no—
180C22×C4—4121no—
181C22×C4—2062no—
182C22×C4C22×D10311yescharacteristic
183D8—41no—
184D8—4121no—
185D8—4122no—
186M16—41no—
187M16—4121no—
188C2×C8—1032no—
189C2×C8C22×D10311yescharacteristic
190C2×C8C22×D10311yescharacteristic
191C4⋊C4—1032no—
192C4⋊C4—2062no—
193C4⋊C4C22×D10312yes—
194C22⋊C4—22no—
195C22⋊C4—2062no—
196C22⋊C4—2062no—
197C22⋊C4—2062no—
198C23—22no—
199C23—1032no—
200C23—4121no—
201C23—4124no—
202C23—4124no—
203C23—4124no—
204C23—2064no—
205C23—2062no—
206C23D4×D10311yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—4124no—
211D4—4124no—
212D4—4124no—
213D4—4124no—
214D4—2062no—
215D4—2062no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—1032no—
220C2×C4—4122no—
221C2×C4—4124no—
222C2×C4—4121no—
223C2×C4—2062no—
224C2×C4—2062no—
225C2×C4—2062no—
226C2×C4D4×D10311yescharacteristic
227C2×C4C23×D10311yescharacteristic
228C8—21no—
229C8—21no—
230C8—2062no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—8248no—
237C22—1034no—
238C22—4124no—
239C22—4122no—
240C22—4122no—
241C22—4122no—
242C22—2062no—
243C22—2062no—
244C22C2×D4×D10311yescharacteristic
245C4—21no—
246C4—42no—
247C4—4122no—
248C4—2062no—
249C4#1569306611yescharacteristic
250C4#1569306711yescharacteristic
251C2—41no—
252C2—82no—
253C2—8242no—
254C2—2064no—
255C2#2026834911yescharacteristic
256C2AGL(1,ℤ/8)×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#469×C103C2
socleC22×C103C22×D4
hypercenter#469D103
hypocenterC103#3192
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D103C2semidirect
2. #20268111C2semidirect
3. #20268108C2semidirect
4. #20268044C2semidirect
5. #20268042C2semidirect
6. #20267926C2semidirect
7. #20267923C2semidirect
8. #20267754C2semidirect
9. #469×C103C2semidirect
11. C2×D4×D103C22semidirect
13. C2×D824C22semidirect
14. C2×#13110090C22semidirect
15. C2×#13110089C22semidirect
17. #15692995C22semidirect
21. C4⋊C4×D103C22semidirect
23. #15692953C22semidirect
24. #15692952C22semidirect
25. #15692943C22semidirect
26. #15692942C22semidirect
27. #15692941C22semidirect
28. (C2×D103)⋊C8C22semidirect
29. (C2×D103)⋊C8C22semidirect
30. C2×D8×C103C22semidirect
31. C2×M16×C103C22semidirect
32. #121×C103C22semidirect
33. #106×C103C22semidirect
34. #102×C103C22semidirect
129. C103#3192semidirect
135. #469D103semidirect
144. C2×D8C2×D103semidirect
146. C2×M16C2×D103semidirect
152. #121C2×D103semidirect
157. #106C2×D103semidirect
161. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#121×D1032
#202681112
#202681082
#202680442
#202680422
#202679262
#202679232
#202677542
#469×C1032
#3192103