Finite Group Databasebeta

← #27208281

Subgroups — #27208281

Order 13184.

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

normal subgroups only

This group has 370 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#20268592C212yesmaximal, complemented
2#20268227C212yesmaximal, complemented
3#20268225C214yesmaximal, complemented
4#20268223C211yesmaximal, characteristic, complemented
5#20268220C212yesmaximal, complemented
6D16×D103C212yesmaximal, complemented
7#20268207C211yesmaximal, characteristic, complemented
8C2×D16×C103C211yesmaximal, characteristic, complemented
9#15693066—22no—
10#15693047—22no—
11#15693045—24no—
12#15693043C2212yescomplemented
13#15693040C2214yescomplemented
14D8×D103C2214yescomplemented
15#15693027C2211yescharacteristic
16Dic824C2211yescharacteristic, complemented
17#15692966C2212yescomplemented
18#15692965C2214yescomplemented
19D1648C2211yescharacteristic, complemented
20#15692962C2214yescomplemented
21#15692961C2211yescharacteristic, complemented
22#15692960C2212yescomplemented
23C16×D103C2212yescomplemented
24C2×D8×C103C2212yescomplemented
25D16×C103C2212yescomplemented
26D16×C103C2212yescomplemented
27C2×C16×C103C2211yescharacteristic, complemented
28#13110105—22no—
29#13110105D411yescharacteristic
30#13110104—24no—
31#13110104—42no—
32C2×C22⋊D103—44no—
33D4×D103—24no—
34D4×D103—42no—
35Dic412C2312yes—
36#13110094—22no—
37#13110093—24no—
38D824C2312yes—
39#13110090—24no—
40#13110089D411yescharacteristic
41#13110088D412yes—
42C8×D103C2312yes—
43C103⋊C16C2312yes—
44C2×D4×C103—22no—
45D8×C103—22no—
46D8×C103C2314yes—
47C2×C8×C103C2311yescharacteristic
48C16×C103C2311yescharacteristic
49C16×C103C2311yescharacteristic
50C23×C103—42no—
51C22×D103—44no—
52D4×C103—24no—
53D4×C103—42no—
54C2×C4×C103C2×D411yescharacteristic
55C22⋊D103—42no—
56C22⋊D103—44no—
57C22⋊D103—44no—
58C22⋊D103D812yes—
59C2×Dic103—44no—
60D412—22no—
61D412D811yescharacteristic
62C4×D103—42no—
63C4×D103C2×D412yes—
64Dic206—22no—
65Dic206D811yescharacteristic
66C8×C103C2×D411yescharacteristic
67C8×C103C2411yescharacteristic
68C103⋊C8C2×D412yes—
69C22×C103—44no—
70C22×C103—162no—
71C22×C103C2×D811yescharacteristic
72C2×D103—42no—
73C2×D103—164no—
74C2×D103C2×D812yes—
75C4×C103C2×D811yescharacteristic
76C4×C103C22×D411yescharacteristic
77Dic103—42no—
78Dic103C2×D812yes—
79C2×C103—21no—
80C2×C103—84no—
81C2×C103C22×D811yescharacteristic
82D103—22no—
83D103—82no—
84#3415—1031nomaximal, Sylow
85C103#341511yescharacteristic, complemented, Sylow
86#576—1032no—
87#509—1032no—
88#509—1034no—
89#508—1032no—
90#508—1031no—
91C2×D16—1032no—
92C2×D16D10311yescharacteristic, complemented
93#504—1031no—
94H(5,𝔽2)—2062no—
95AGL(1,ℤ/8)—2064no—
96AGL(1,ℤ/8)—2062no—
97#135—1034no—
98#135—1032no—
99C2×D8—1034no—
100C2×D8C2×D10312yescomplemented
101#131—1031no—
102Q32—1031no—
103SD32—1034no—
104SD32—1032no—
105D16—1034no—
106D16—1031no—
107D16C2×D10312yescomplemented
108D16C2×D10312yescomplemented
109M32—1031no—
110M32—1032no—
111C2×C16—1032no—
112C2×C16C2×D10311yescharacteristic, complemented
113#41—1031no—
114#41—4122no—
115#41—2064no—
116#41—2062no—
117C2×D4—22no—
118C2×D4—4122no—
119C2×D4—4124no—
120C2×D4—2064no—
121Q16—1032no—
122SD16—2064no—
123SD16—2062no—
124D8—22no—
125D8—1032no—
126D8—2064no—
127D8C22×D10314yes—
128M16—1031no—
129M16—1032no—
130C2×C8—1032no—
131C2×C8C22×D10311yescharacteristic
132C16—1032no—
133C16C22×D10311yescharacteristic
134C16C22×D10311yescharacteristic
135C23—42no—
136C23—4124no—
137Q8—1031no—
138Q8—2062no—
139D4—24no—
140D4—42no—
141D4—1032no—
142D4—1031no—
143D4—4124no—
144D4—4124no—
145D4—4122no—
146D4—2062no—
147C2×C4—1032no—
148C2×C4—4124no—
149C2×C4—4122no—
150C2×C4D4×D10311yescharacteristic
151C8—1032no—
152C8D4×D10311yescharacteristic
153C8C23×D10311yescharacteristic
154C22—44no—
155C22—162no—
156C22—1032no—
157C22—16484no—
158C22—4122no—
159C22D8×D10311yescharacteristic
160C4—1032no—
161C4—4122no—
162C4D8×D10311yescharacteristic
163C4C2×D4×D10311yescharacteristic
164C2—21no—
165C2—84no—
166C2—8242no—
167C2—2062no—
168C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC2C2×D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
FittingC2×D16×C103C2
socleC2×C103C22×D8
hypercenterC2×D16D103
hypocenterC103#3415
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #20268592C2semidirect
2. #20268227C2semidirect
3. #20268225C2semidirect
4. #20268223C2semidirect
5. #20268220C2semidirect
6. D16×D103C2semidirect
7. #20268207C2semidirect
8. C2×D16×C103C2semidirect
12. #15693043C22semidirect
13. #15693040C22semidirect
14. D8×D103C22semidirect
16. Dic824C22semidirect
17. #15692966C22semidirect
18. #15692965C22semidirect
19. D1648C22semidirect
20. #15692962C22semidirect
21. #15692961C22semidirect
22. #15692960C22semidirect
23. C16×D103C22semidirect
24. C2×D8×C103C22semidirect
25. D16×C103C22semidirect
26. D16×C103C22semidirect
27. C2×C16×C103C22semidirect
85. C103#3415semidirect
92. C2×D16D103semidirect
100. C2×D8C2×D103semidirect
107. D16C2×D103semidirect
108. D16C2×D103semidirect
112. C2×C16C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202685922
#202682272
#202682252
#202682232
#202682202
D16×D1032
#202682072
C2×D16×C1032
#3415103