Finite Group Databasebeta

← #22581210

Subgroups — #22581210

Order 8896.

110 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 39 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×#14555775C211yesmaximal, characteristic, complemented
2C2×#14555768C211yesmaximal, characteristic
3#17984822C211yesmaximal, characteristic
4#17984818C211yesmaximal, characteristic
5#17984773C211yesmaximal, characteristic, complemented
6#17984767C211yesmaximal, characteristic, complemented
7#103×C139C211yesmaximal, characteristic, complemented
8C2×Dic278C2211yescharacteristic
9C2×C4×D139C2211yescharacteristic
10#14555775—22no—
11#14555768—22no—
12C2×C139⋊C8C2211yescharacteristic
13C4⋊Dic139—21no—
14C4⋊Dic139C2211yescharacteristic
15Dic139⋊C4—21no—
16(C2×D139)⋊C4—21no—
17(C2×D139)⋊C4—21no—
18C2×Q8×C139C2211yescharacteristic
19C2×C8×C139C2211yescharacteristic
20C4⋊C4×C139C2211yescharacteristic
21C22×D139D411yescharacteristic
22Dic278—21no—
23Dic278—21no—
24C2×Dic139—21no—
25C2×Dic139—21no—
26C2×Dic139D411yescharacteristic
27C4×D139—21no—
28C4×D139—21no—
29C139⋊C8D412yes—
30Q8×C139—21no—
31Q8×C139—21no—
32C2×C4×C139—21no—
33C2×C4×C139—21no—
34C2×C4×C139C2311yescharacteristic
35C8×C139—21no—
36C22×C139C2×D411yescharacteristic
37C2×D139—21no—
38C2×D139—21no—
39C2×D139—21no—
40C4×C139—41no—
41C4×C139—41no—
42C4×C139C2×D411yescharacteristic
43C4×C139#4111yescharacteristic
44Dic139—21no—
45Dic139—41no—
46Dic139—41no—
47C2×C139#12111yescharacteristic
48C2×C139#13711yescharacteristic
49C2×C139#13711yescharacteristic
50D139—41no—
51C139#47011yescharacteristic, complemented, Sylow
52#470—1391nomaximal, Sylow
53C2×Q16—1391no—
54C2×M16—1391no—
55C22⋊Q8—1391no—
56C22⋊Q8—1391no—
57#106—1391no—
58#103—1391no—
59#103D13911yescharacteristic, complemented
60C2×Q8—1391no—
61C2×Q8C2×D13911yescharacteristic
62C22×C4—1391no—
63Q16—2782no—
64M16—2782no—
65C2×C8—1391no—
66C2×C8C2×D13911yescharacteristic
67C4⋊C4—2781no—
68C4⋊C4—2781no—
69C4⋊C4—1391no—
70C4⋊C4C2×D13911yescharacteristic
71C22⋊C4—2781no—
72C22⋊C4—2781no—
73C23—1391no—
74Q8—21no—
75Q8—21no—
76Q8—2781no—
77Q8—2781no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—2781no—
81C2×C4—2781no—
82C2×C4—2781no—
83C2×C4—2781no—
84C2×C4—1391no—
85C2×C4C22×D13911yescharacteristic
86C8—21no—
87C8—1392no—
88C22—2781no—
89C22—2781no—
90C22—2781no—
91C22D4×D13911yescharacteristic
92C4—41no—
93C4—41no—
94C4—2781no—
95C4—5561no—
96C4—5561no—
97C4D4×D13911yescharacteristic
98C4#1455578511yescharacteristic
99C2—5561no—
100C2#1798481511yescharacteristic
101C2#1798487111yescharacteristic
102C2#1798487411yescharacteristic
subgroupG/H
centerC22D4×D139
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#103×C139C2
socleC22×C139C2×D4
hypercenter#103D139
hypocenterC139#470
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#14555775C2semidirect
5. #17984773C2semidirect
6. #17984767C2semidirect
7. #103×C139C2semidirect
51. C139#470semidirect
59. #103D139semidirect