Finite Group Databasebeta

← #27205608

Subgroups — #27205608

Order 13184.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15693052C212yesmaximal, complemented
2C2×#15693047C212yesmaximal, complemented
3#20268341C211yesmaximal, characteristic, complemented
4#20268186C212yesmaximal, complemented
5#20268181C212yesmaximal, complemented
6#20268173C214yesmaximal, complemented
7C4×#13110089C211yesmaximal, characteristic, complemented
8C2×#124×C103C211yesmaximal, characteristic, complemented
9C2×#13110105C2212yes—
10#15693052—28no—
11#15693047—28no—
12C2×#13110095C2214yescomplemented
13C2×#13110093C2214yes—
14C2×#13110092C2214yescomplemented
15C2×#13110090C2214yes—
16C2×#13110089C2212yes—
17#15693021C2211yescharacteristic, complemented
18#15693018C2211yescharacteristic, complemented
19#15693009C2212yescomplemented
20#15692995—22no—
21C4×D412—22no—
22#15692932C2212yescomplemented
23C4×C103⋊C8C2212yescomplemented
24C22×Q8×C103C2211yescharacteristic
25C22×D4×C103C2211yescharacteristic
26#124×C103—22no—
27#124×C103C2212yes—
28#124×C103C2212yes—
29C2×C22⋊C4×C103—22no—
30C2×C42×C103C2211yescharacteristic
31#13110105—24no—
32#13110105—24no—
33C2×Dic206C2312yes—
34C2×D412—22no—
35C2×D412C2312yes—
36C2×C22⋊D103—22no—
37C2×C4×D103—22no—
38#13110095—28no—
39#13110093—28no—
40#13110092—28no—
41#13110090—28no—
42#13110089D418yescomplemented
43C2×C103⋊C8C2314yes—
44C4⋊Dic103—22no—
45(C2×D103)⋊C4—24no—
46C24×C103—21no—
47C2×Q8×C103—21no—
48C2×Q8×C103—24no—
49C2×Q8×C103C2312yes—
50C2×D4×C103—24no—
51C2×D4×C103—21no—
52C2×D4×C103C2312yes—
53C22×C4×C103—21no—
54C22×C4×C103D412yes—
55C22×C4×C103C2311yescharacteristic
56C22⋊C4×C103—24no—
57C22⋊C4×C103—24no—
58C42×C103D412yes—
59C42×C103C2311yescharacteristic
60C42×C103C2311yescharacteristic
61C23×C103—22no—
62C23×C103—44no—
63C23×C103—42no—
64C23×C103C2×D411yescharacteristic
65C22×D103—22no—
66Q8×C103—24no—
67Q8×C103—42no—
68D4×C103—24no—
69D4×C103—42no—
70C2×C4×C103—22no—
71C2×C4×C103—42no—
72C2×C4×C103—42no—
73C2×C4×C103C2×D414yes—
74C2×C4×C103C2×D412yes—
75C2×C4×C103C2×D412yes—
76C2×C4×C103C2×D411yescharacteristic
77C2×C4×C103C2411yescharacteristic
78C22⋊D103—44no—
79C2×Dic103—22no—
80D412—22no—
81D412—22no—
82D412—44no—
83C4×D103—44no—
84Dic206—22no—
85Dic206—22no—
86C103⋊C8C2×D418yes—
87C22×C103—22no—
88C22×C103—42no—
89C22×C103—44no—
90C22×C103—84no—
91C22×C103#12712yes—
92C22×C103C22×D411yescharacteristic
93C2×D103—42no—
94C2×D103—44no—
95C4×C103—22no—
96C4×C103—22no—
97C4×C103—42no—
98C4×C103#12712yes—
99C4×C103C22×D412yes—
100Dic103—42no—
101C2×C103—22no—
102C2×C103—82no—
103C2×C103C2×#12711yescharacteristic
104C2×C103#57512yes—
105D103—82no—
106#3153—1031nomaximal, Sylow
107C103#315311yescharacteristic, complemented, Sylow
108C2×#137—1032no—
109C2×AGL(1,ℤ/8)—1032no—
110#532—1031no—
111C2×#124D10311yescharacteristic, complemented
112#497—1032no—
113#496—1032no—
114#495—1034no—
115C4×M16—1031no—
116C2×#41—1032no—
117C22×Q8C2×D10311yescharacteristic
118C22×D4C2×D10311yescharacteristic
119#137—2068no—
120AGL(1,ℤ/8)—2068no—
121C2×Q16—1034no—
122C2×SD16—1034no—
123C2×SD16—1034no—
124C2×D8—1034no—
125C2×M16—1032no—
126C4⋊Q8—1031no—
127#127—1031no—
128#124—22no—
129#124—1032no—
130#124C2×D10312yes—
131#124C2×D10312yes—
132#121—2062no—
133C4×D4—2062no—
134C2×C22⋊C4—22no—
135C2×C42C2×D10311yescharacteristic
136#97—1032no—
137C4×C8—1032no—
138C24—21no—
139#41—2064no—
140#41—2064no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—1032no—
144C2×Q8C22×D10312yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—1032no—
148C2×D4—2062no—
149C2×D4—2062no—
150C2×D4C22×D10312yes—
151C22×C4—21no—
152C22×C4—2062no—
153C22×C4C22⋊D10312yes—
154C22×C4C22×D10311yescharacteristic
155Q16—2068no—
156SD16—2068no—
157SD16—2068no—
158D8—2068no—
159M16—1038no—
160C2×C8—1034no—
161C4⋊C4—2062no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—2064no—
165C42C22⋊D10312yes—
166C42C22×D10311yescharacteristic
167C42C22×D10311yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—2062no—
172C23C2×C22⋊D10311yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—2062no—
176Q8—2062no—
177D4—24no—
178D4—42no—
179D4—4124no—
180D4—4124no—
181D4—2062no—
182D4—2062no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—4124no—
187C2×C4—2062no—
188C2×C4D4×D10314yes—
189C2×C4C2×C22⋊D10312yes—
190C2×C4C2×C22⋊D10312yes—
191C2×C4C2×C22⋊D10311yescharacteristic
192C2×C4C23×D10311yescharacteristic
193C8—1038no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—4122no—
199C22—4124no—
200C22#1569301712yes—
201C22C22×C22⋊D10311yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—4122no—
206C4#1569301712yes—
207C4C2×D4×D10312yes—
208C2—22no—
209C2—82no—
210C2—8242no—
211C2C2×#1569301711yescharacteristic
212C2#2026858912yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#124×C103C2
socleC22×C103C22×D4
hypercenterC2×#124D103
hypocenterC103#3153
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#15693052C2semidirect
2. C2×#15693047C2semidirect
3. #20268341C2semidirect
4. #20268186C2semidirect
5. #20268181C2semidirect
6. #20268173C2semidirect
7. C4×#13110089C2semidirect
8. C2×#124×C103C2semidirect
12. C2×#13110095C22semidirect
14. C2×#13110092C22semidirect
17. #15693021C22semidirect
18. #15693018C22semidirect
19. #15693009C22semidirect
22. #15692932C22semidirect
23. C4×C103⋊C8C22semidirect
42. #13110089D4semidirect
107. C103#3153semidirect
111. C2×#124D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930522
C2×#156930472
#202683412
#202681862
#202681812
#202681732
C4×#131100892
C2×#124×C1032
#3153103