Finite Group Databasebeta

← #22581227

Subgroups — #22581227

Order 8896.

100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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#17984875C211yesmaximal, characteristic
2#17984873C211yesmaximal, characteristic
3C2×#14555775C211yesmaximal, characteristic, complemented
4#17984850C211yesmaximal, characteristic
5#17984777C211yesmaximal, characteristic, complemented
6#17984760C211yesmaximal, characteristic, complemented
7#101×C139C211yesmaximal, characteristic, complemented
8#14555785C2211yescharacteristic
9C2×Dic278C2211yescharacteristic
10Dic556—21no—
11#14555775—21no—
12#14555775—21no—
13#14555775—21no—
14#14555774—21no—
15#14555772—21no—
16#14555769C2211yescharacteristic
17#14555768—21no—
18C2×C139⋊C8C2211yescharacteristic
19C8×D139—21no—
20C2×Q8×C139C2211yescharacteristic
21M16×C139C2211yescharacteristic
22M16×C139C2211yescharacteristic
23Dic278—21no—
24Dic278—21no—
25Dic278D411yescharacteristic
26D556D411yescharacteristic
27C22⋊D139—21no—
28C2×Dic139—21no—
29C4×D139—21no—
30C139⋊C8—21no—
31C139⋊C8D411yescharacteristic
32C139⋊C8D411yescharacteristic
33Q8×C139—21no—
34Q8×C139—21no—
35C2×C4×C139—21no—
36C2×C4×C139C2311yescharacteristic
37C8×C139—21no—
38C8×C139—21no—
39C22×C139#4111yescharacteristic
40C2×D139—21no—
41C4×C139—41no—
42C4×C139C2×D411yescharacteristic
43C4×C139C2×D411yescharacteristic
44Dic139—21no—
45Dic139—41no—
46C2×C139—21no—
47C2×C139#12111yescharacteristic
48D139—41no—
49C139#47311yescharacteristic, complemented, Sylow
50#473—1391nomaximal, Sylow
51#137—1391no—
52#137—1391no—
53C2×Q16—1391no—
54#131—1391no—
55#108—1391no—
56#101—1391no—
57#101D13911yescharacteristic, complemented
58#41—1391no—
59C2×Q8—1391no—
60C2×Q8C2×D13911yescharacteristic
61Q16—2781no—
62Q16—2781no—
63Q16—2781no—
64Q16—2781no—
65SD16—2781no—
66SD16—2781no—
67M16—2781no—
68M16—1391no—
69M16C2×D13911yescharacteristic
70M16C2×D13911yescharacteristic
71C2×C8—2781no—
72C2×C8—1391no—
73Q8—21no—
74Q8—21no—
75Q8—2781no—
76Q8—2781no—
77Q8—1391no—
78D4—2781no—
79D4—1391no—
80C2×C4—21no—
81C2×C4—2781no—
82C2×C4—2781no—
83C2×C4C22×D13911yescharacteristic
84C8—21no—
85C8—21no—
86C8—2781no—
87C8—1391no—
88C8—1391no—
89C22—2781no—
90C22#1455578511yescharacteristic
91C4—41no—
92C4—2781no—
93C4—5561no—
94C4D4×D13911yescharacteristic
95C4D4×D13911yescharacteristic
96C2—21no—
97C2—5561no—
98C2#1798481511yescharacteristic
subgroupG/H
centerC2#17984815
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#101×C139C2
socleC2×C139#121
hypercenter#101D139
hypocenterC139#473
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. C2×#14555775C2semidirect
5. #17984777C2semidirect
6. #17984760C2semidirect
7. #101×C139C2semidirect
49. C139#473semidirect
57. #101D139semidirect