Finite Group Databasebeta

← #27204371

Subgroups — #27204371

Order 13184.

994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15693047C212yesmaximal, complemented
2#20268302C211yesmaximal, characteristic, complemented
3#20267942C214yesmaximal, complemented
4#20267925C214yesmaximal, complemented
5#20267796C212yesmaximal, complemented
6#20267755C211yesmaximal, characteristic, complemented
7C23×D4×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic, complemented
9#15693047—28no—
10C2×#13110093C2214yescomplemented
11C2×#13110090C2214yescomplemented
12C2×#13110089C2212yescomplemented
13#15693004—21no—
14#15693000C2212yescomplemented
15#15692995C2212yescomplemented
16#15692990—21no—
17C4×C22⋊D103—22no—
18#15692980C2211yescharacteristic, complemented
19#15692942C2218yescomplemented
20C22⋊(C103⋊C8)C2214yescomplemented
21C25×C103—21no—
22C22×D4×C103—28no—
23C22×D4×C103—22no—
24C22×D4×C103—21no—
25C22×D4×C103C2214yes—
26C22×D4×C103C2212yes—
27C23×C4×C103C2211yescharacteristic
28#13110105—24no—
29C2×Dic206C2311yescharacteristic, complemented
30C2×D412C2311yescharacteristic, complemented
31C2×C22⋊D103—21no—
32C2×C22⋊D103—22no—
33C2×C4×D103—21no—
34#13110093—28no—
35#13110090—28no—
36#13110089—24no—
37C2×C103⋊C8C2314yescomplemented
38C4⋊Dic103C2312yescomplemented
39Dic103⋊C4—22no—
40C22⋊Dic103—21no—
41C22⋊Dic103—22no—
42(C2×D103)⋊C4—22no—
43C4×Dic103—21no—
44C24×C103—28no—
45C24×C103—24no—
46C24×C103—22no—
47C24×C103—48no—
48C24×C103D411yescharacteristic
49C2×D4×C103—28no—
50C2×D4×C103—216no—
51C2×D4×C103—216no—
52C2×D4×C103—24no—
53C2×D4×C103—22no—
54C2×D4×C103—24no—
55C2×D4×C103D418yescomplemented
56C2×D4×C103C2314yes—
57C22×C4×C103—24no—
58C22×C4×C103D412yes—
59C22×C4×C103D411yescharacteristic
60C22×C4×C103C2312yes—
61C22×C4×C103C2311yescharacteristic
62C23×C103—22no—
63C23×C103—24no—
64C23×C103—216no—
65C23×C103—28no—
66C23×C103—24no—
67C23×C103—432no—
68C23×C103—48no—
69C23×C103—48no—
70C23×C103—48no—
71C23×C103C2×D411yescharacteristic
72C23×C103C2×D412yes—
73C22×D103—21no—
74D4×C103—216no—
75D4×C103—28no—
76D4×C103—24no—
77D4×C103C2×D418yes—
78C2×C4×C103—22no—
79C2×C4×C103—24no—
80C2×C4×C103—24no—
81C2×C4×C103C2×D412yes—
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103C2×D414yes—
84C2×C4×C103C2411yescharacteristic
85C22⋊D103—42no—
86C22⋊D103—44no—
87C2×Dic103—22no—
88C2×Dic103—21no—
89D412—22no—
90C4×D103—42no—
91Dic206—22no—
92C103⋊C8—24no—
93C22×C103—28no—
94C22×C103—22no—
95C22×C103—22no—
96C22×C103—22no—
97C22×C103—28no—
98C22×C103—416no—
99C22×C103—432no—
100C22×C103—48no—
101C22×C103#12012yes—
102C22×C103AGL(1,ℤ/8)14yescomplemented
103C22×C103C22×D411yescharacteristic
104C2×D103—41no—
105C2×D103—42no—
106C4×C103—22no—
107C4×C103#12012yes—
108C4×C103C22×D412yes—
109Dic103—41no—
110Dic103—42no—
111C2×C103—22no—
112C2×C103—24no—
113C2×C103—48no—
114C2×C103C2×#12011yescharacteristic
115C2×C103C2×AGL(1,ℤ/8)12yes—
116D103—81no—
117#3003—1031nomaximal, Sylow
118C103#300311yescharacteristic, complemented, Sylow
119C23×D4D10311yescharacteristic, complemented
120C2×AGL(1,ℤ/8)—1032no—
121#525—1031no—
122#450—1034no—
123#447—1034no—
124#418—1032no—
125#407—1031no—
126C25—21no—
127C2×#41—1031no—
128C22×D4—28no—
129C22×D4—22no—
130C22×D4—21no—
131C22×D4C2×D10314yes—
132C22×D4C2×D10312yes—
133C23×C4C2×D10311yescharacteristic
134AGL(1,ℤ/8)—2068no—
135C2×SD16—1034no—
136C2×D8—1034no—
137C2×M16—1032no—
138#123—2061no—
139C22⋊Q8—1032no—
140#121—1032no—
141#120—2061no—
142C4×D4—2062no—
143#117—1031no—
144#102—1038no—
145C22⋊C8—1034no—
146C24—28no—
147C24—24no—
148C24—22no—
149C24—48no—
150C24C22⋊D10311yescharacteristic
151#41—2064no—
152C2×Q8—1031no—
153C2×D4—28no—
154C2×D4—216no—
155C2×D4—216no—
156C2×D4—24no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—1031no—
160C2×D4—2062no—
161C2×D4—2061no—
162C2×D4C22⋊D10318yescomplemented
163C2×D4C22×D10314yes—
164C22×C4—24no—
165C22×C4—2061no—
166C22×C4C22⋊D10312yes—
167C22×C4C22⋊D10311yescharacteristic
168C22×C4C22×D10312yes—
169C22×C4C22×D10311yescharacteristic
170SD16—2068no—
171D8—2068no—
172M16—2064no—
173C2×C8—1034no—
174C4⋊C4—1032no—
175C4⋊C4—2062no—
176C22⋊C4—2061no—
177C22⋊C4—2062no—
178C22⋊C4—2062no—
179C42—2061no—
180C23—22no—
181C23—24no—
182C23—216no—
183C23—24no—
184C23—28no—
185C23—432no—
186C23—48no—
187C23—48no—
188C23—48no—
189C23—2061no—
190C23C2×C22⋊D10311yescharacteristic
191C23C2×C22⋊D10312yes—
192Q8—2062no—
193D4—216no—
194D4—24no—
195D4—28no—
196D4—4122no—
197D4—4124no—
198D4—2062no—
199D4C2×C22⋊D10318yes—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—4122no—
204C2×C4—2062no—
205C2×C4—2061no—
206C2×C4C2×C22⋊D10312yes—
207C2×C4C2×C22⋊D10314yes—
208C2×C4C2×C22⋊D10311yescharacteristic
209C2×C4C23×D10311yescharacteristic
210C8—2064no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—28no—
216C22—416no—
217C22—432no—
218C22—48no—
219C22—4122no—
220C22—4121no—
221C22#1569299012yes—
222C22#1569304714yescomplemented
223C22C22×C22⋊D10311yescharacteristic
224C4—22no—
225C4—4122no—
226C4—4121no—
227C4#1569299012yes—
228C4C22×C22⋊D10312yes—
229C2—22no—
230C2—24no—
231C2—48no—
232C2—8241no—
233C2C2×#1569299011yescharacteristic
234C2C2×#1569304712yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC23×D4×C103C2
socleC22×C103C22×D4
hypercenterC23×D4D103
hypocenterC103#3003
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#15693047C2semidirect
2. #20268302C2semidirect
3. #20267942C2semidirect
4. #20267925C2semidirect
5. #20267796C2semidirect
6. #20267755C2semidirect
7. C23×D4×C103C2semidirect
8. C2×#13110105C22semidirect
10. C2×#13110093C22semidirect
11. C2×#13110090C22semidirect
12. C2×#13110089C22semidirect
14. #15693000C22semidirect
15. #15692995C22semidirect
18. #15692980C22semidirect
19. #15692942C22semidirect
20. C22⋊(C103⋊C8)C22semidirect
29. C2×Dic206C23semidirect
30. C2×D412C23semidirect
37. C2×C103⋊C8C23semidirect
38. C4⋊Dic103C23semidirect
55. C2×D4×C103D4semidirect
102. C22×C103AGL(1,ℤ/8)semidirect
118. C103#3003semidirect
119. C23×D4D103semidirect
162. C2×D4C22⋊D103semidirect
222. C22#15693047semidirect

Maximal subgroups

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

subgroupindex
C2×#156930472
#202683022
#202679422
#202679252
#202677962
#202677552
C23×D4×C1032
#3003103