Finite Group Databasebeta

← #22580955

Subgroups — #22580955

Order 8896.

162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14555785C211yesmaximal, characteristic
2C2×C4⋊Dic139C211yesmaximal, characteristic, complemented
3#17984767C212yesmaximal, complemented
4#17984764C212yesmaximal, complemented
5C2×M16×C139C211yesmaximal, characteristic, complemented
6#14555785—22no—
7#14555785C414yescomplemented
8C2×Dic278C2211yescharacteristic
9C2×D556C2211yescharacteristic
10C2×C22⋊D139—21no—
11C22×Dic139—21no—
12C2×C4×D139—21no—
13C4⋊Dic139—21no—
14C4⋊Dic139C2212yes—
15C22×C4×C139C2211yescharacteristic
16M16×C139—22no—
17C2×C8×C139C2212yes—
18C22×D139—21no—
19Dic278—21no—
20Dic278C2×C412yescomplemented
21D556—21no—
22D556C2×C412yescomplemented
23C22⋊D139—24no—
24C2×Dic139—21no—
25C2×Dic139—22no—
26C2×Dic139—42no—
27C4×D139—24no—
28C23×C139D411yescharacteristic
29C2×C4×C139C2×C412yes—
30C2×C4×C139D412yes—
31C2×C4×C139D411yescharacteristic
32C2×C4×C139C2311yescharacteristic
33C8×C139—22no—
34C22×C139—21no—
35C22×C139—21no—
36C22×C139C22⋊C412yes—
37C22×C139C2×D411yescharacteristic
38C2×D139—22no—
39C2×D139—41no—
40C2×D139—41no—
41C4×C139C22⋊C412yes—
42C4×C139C22×C411yescharacteristic
43C4×C139C2×D411yescharacteristic
44Dic139—22no—
45Dic139—42no—
46C2×C139—22no—
47C2×C139C2×C22⋊C411yescharacteristic
48C2×C139AGL(1,ℤ/8)11yescharacteristic
49C2×C139#13711yescharacteristic
50D139—42no—
51C139#41711yescharacteristic, complemented, Sylow
52#417—1391nomaximal, Sylow
53C2×#41—1391no—
54C2×M16D13911yescharacteristic, complemented
55C2×C4⋊C4—1391no—
56#103—1392no—
57#102—1392no—
58#41—2782no—
59#41—1394no—
60C2×Q8—1391no—
61C2×D4—2781no—
62C2×D4—1391no—
63C22×C4—2781no—
64C22×C4—2781no—
65C22×C4C2×D13911yescharacteristic
66M16—22no—
67C2×C8C2×D13912yes—
68C4⋊C4—2781no—
69C4⋊C4—1392no—
70C23—2781no—
71C23D55611yescharacteristic
72Q8—2781no—
73Q8—1392no—
74D4—2784no—
75D4—2781no—
76D4—1392no—
77C2×C4—2781no—
78C2×C4—2784no—
79C2×C4—2782no—
80C2×C4—5562no—
81C2×C4C4×D13912yes—
82C2×C4C22⋊D13912yes—
83C2×C4D55611yescharacteristic
84C2×C4C22×D13911yescharacteristic
85C8—22no—
86C22—21no—
87C22—21no—
88C22—2782no—
89C22—5561no—
90C22—5561no—
91C22(C2×D139)⋊C412yes—
92C22C2×D55611yescharacteristic
93C4—2782no—
94C4—5562no—
95C4(C2×D139)⋊C412yes—
96C4C2×C4×D13911yescharacteristic
97C4C2×C22⋊D13911yescharacteristic
98C2—22no—
99C2—5562no—
100C2C2×(C2×D139)⋊C411yescharacteristic
101C2#1798487011yescharacteristic
102C2#1798487511yescharacteristic
subgroupG/H
centerC22C2×D556
commutatorC4×C139C22×C4
FrattiniC2×C4C22×D139
FittingC2×M16×C139C2
socleC22×C139C2×D4
hypercenterC2×M16D139
hypocenterC139#417
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Dic139C2semidirect
3. #17984767C2semidirect
4. #17984764C2semidirect
5. C2×M16×C139C2semidirect
7. #14555785C4semidirect
20. Dic278C2×C4semidirect
22. D556C2×C4semidirect
51. C139#417semidirect
54. C2×M16D139semidirect