Finite Group Databasebeta

← #27208282

Subgroups — #27208282

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#20268593C212yesmaximal, complemented
2#20268228C214yesmaximal, complemented
3#20268226C212yesmaximal, complemented
4#20268224C212yesmaximal, complemented
5C2×D1648C211yesmaximal, characteristic, complemented
6D16×D103C212yesmaximal, complemented
7#20268207C211yesmaximal, characteristic, complemented
8#508×C103C211yesmaximal, characteristic, complemented
9#15693067—22no—
10#15693048—24no—
11#15693046—22no—
12#15693044C2214yescomplemented
13C2×D824C2212yescomplemented
14D8×D103C2214yescomplemented
15#15693027C2211yescharacteristic
16#15692964C2214yescomplemented
17D1648C2212yescomplemented
18D1648C2212yescomplemented
19#15692962C2214yescomplemented
20#15692961C2211yescharacteristic, complemented
21#15692960C2212yescomplemented
22C16×D103C2212yescomplemented
23#135×C103C2212yescomplemented
24Q32×C103C2211yescharacteristic, complemented
25SD32×C103C2212yescomplemented
26D16×C103C2211yescharacteristic, complemented
27C2×C16×C103C2211yescharacteristic, complemented
28#13110106—24no—
29#13110105—42no—
30#13110105D411yescharacteristic
31C2×D412—22no—
32C2×D412—42no—
33D4×D103—24no—
34D4×D103—44no—
35#13110092—24no—
36D824—22no—
37D824C2314yes—
38#13110090—24no—
39#13110089D411yescharacteristic
40#13110088D412yes—
41C8×D103C2312yes—
42C103⋊C16C2312yes—
43#41×C103—22no—
44Q16×C103C2312yes—
45SD16×C103—22no—
46D8×C103C2312yes—
47C2×C8×C103C2311yescharacteristic
48C16×C103C2311yescharacteristic
49C16×C103C2311yescharacteristic
50C22×D103—42no—
51C22×D103—44no—
52Q8×C103—22no—
53D4×C103—22no—
54D4×C103—42no—
55C2×C4×C103—42no—
56C2×C4×C103C2×D411yescharacteristic
57C22⋊D103—44no—
58C22⋊D103D812yes—
59D412—24no—
60D412—44no—
61D412—42no—
62D412D811yescharacteristic
63C4×D103—44no—
64C4×D103C2×D412yes—
65Dic206D811yescharacteristic
66C8×C103C2×D411yescharacteristic
67C8×C103C2411yescharacteristic
68C103⋊C8C2×D412yes—
69C22×C103—42no—
70C22×C103C2×D811yescharacteristic
71C2×D103—44no—
72C2×D103—164no—
73C2×D103—162no—
74C2×D103C2×D812yes—
75C4×C103—42no—
76C4×C103C2×D811yescharacteristic
77C4×C103C22×D411yescharacteristic
78Dic103C2×D812yes—
79C2×C103—21no—
80C2×C103—82no—
81C2×C103C22×D811yescharacteristic
82D103—22no—
83D103—84no—
84#3415—1031nomaximal, Sylow
85C103#341511yescharacteristic, complemented, Sylow
86#576—1032no—
87#509—1032no—
88#509—1034no—
89#508—1032no—
90#508D10311yescharacteristic, complemented
91C2×D16—1032no—
92C2×D16—1031no—
93#504—1031no—
94H(5,𝔽2)—2062no—
95AGL(1,ℤ/8)—2064no—
96AGL(1,ℤ/8)—2062no—
97#135—1034no—
98#135C2×D10312yescomplemented
99C2×D8—1034no—
100C2×D8—1032no—
101#131—1031no—
102Q32C2×D10311yescharacteristic, complemented
103SD32—1034no—
104SD32C2×D10312yescomplemented
105D16—1034no—
106D16—1032no—
107D16—1032no—
108D16C2×D10311yescharacteristic, complemented
109M32—1031no—
110M32—1032no—
111C2×C16—1032no—
112C2×C16C2×D10311yescharacteristic, complemented
113#41—22no—
114#41—1031no—
115#41—4122no—
116#41—2064no—
117C2×D4—4122no—
118C2×D4—4124no—
119C2×D4—2064no—
120C2×D4—2062no—
121Q16C22×D10312yes—
122SD16—22no—
123SD16—2064no—
124D8—1034no—
125D8—2064no—
126D8—2062no—
127D8C22×D10312yes—
128M16—1031no—
129M16—1032no—
130C2×C8—1032no—
131C2×C8C22×D10311yescharacteristic
132C16—1032no—
133C16C22×D10311yescharacteristic
134C16C22×D10311yescharacteristic
135C23—4124no—
136C23—4122no—
137Q8—22no—
138Q8—1031no—
139D4—22no—
140D4—42no—
141D4—1032no—
142D4—1031no—
143D4—4124no—
144D4—4124no—
145D4—4122no—
146D4—2064no—
147C2×C4—42no—
148C2×C4—1032no—
149C2×C4—4124no—
150C2×C4D4×D10311yescharacteristic
151C8—1032no—
152C8D4×D10311yescharacteristic
153C8C23×D10311yescharacteristic
154C22—42no—
155C22—1032no—
156C22—16482no—
157C22—16484no—
158C22—4124no—
159C22D8×D10311yescharacteristic
160C4—42no—
161C4—1032no—
162C4D8×D10311yescharacteristic
163C4C2×D4×D10311yescharacteristic
164C2—21no—
165C2—82no—
166C2—8244no—
167C2—2062no—
168C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC2C2×D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
Fitting#508×C103C2
socleC2×C103C22×D8
hypercenter#508D103
hypocenterC103#3415
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #20268593C2semidirect
2. #20268228C2semidirect
3. #20268226C2semidirect
4. #20268224C2semidirect
5. C2×D1648C2semidirect
6. D16×D103C2semidirect
7. #20268207C2semidirect
8. #508×C103C2semidirect
12. #15693044C22semidirect
13. C2×D824C22semidirect
14. D8×D103C22semidirect
16. #15692964C22semidirect
17. D1648C22semidirect
18. D1648C22semidirect
19. #15692962C22semidirect
20. #15692961C22semidirect
21. #15692960C22semidirect
22. C16×D103C22semidirect
23. #135×C103C22semidirect
24. Q32×C103C22semidirect
25. SD32×C103C22semidirect
26. D16×C103C22semidirect
27. C2×C16×C103C22semidirect
85. C103#3415semidirect
90. #508D103semidirect
98. #135C2×D103semidirect
102. Q32C2×D103semidirect
104. SD32C2×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
#202685932
#202682282
#202682262
#202682242
C2×D16482
D16×D1032
#202682072
#508×C1032
#3415103