Finite Group Databasebeta

← #22581217

Subgroups — #22581217

Order 8896.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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, complemented
2#17984870C211yesmaximal, characteristic
3C2×#14555774C211yesmaximal, characteristic, complemented
4#17984848C211yesmaximal, characteristic, complemented
5#17984760C211yesmaximal, characteristic, complemented
6#17984758C211yesmaximal, characteristic, complemented
7#108×C139C211yesmaximal, characteristic, complemented
8#14555785C2211yescharacteristic
9C2×Dic278C2211yescharacteristic
10C2×D556C2211yescharacteristic
11Dic556—21no—
12#14555774—21no—
13#14555774—21no—
14#14555774—21no—
15#14555774—21no—
16D1112—21no—
17#14555769C2211yescharacteristic
18#14555768—21no—
19C8×D139—21no—
20M16×C139C2211yescharacteristic
21M16×C139C2211yescharacteristic
22C2×C8×C139C2211yescharacteristic
23C22×D139—21no—
24Dic278—21no—
25Dic278—21no—
26Dic278D411yescharacteristic
27D556—21no—
28D556—21no—
29D556D411yescharacteristic
30C22⋊D139—21no—
31C2×Dic139—21no—
32C4×D139—21no—
33C139⋊C8—21no—
34C2×C4×C139C2311yescharacteristic
35C8×C139—21no—
36C8×C139—21no—
37C8×C139D411yescharacteristic
38C8×C139D411yescharacteristic
39C22×C139#4111yescharacteristic
40C2×D139—21no—
41C2×D139—41no—
42C2×D139—81no—
43C4×C139C2×D411yescharacteristic
44C4×C139C2×D411yescharacteristic
45Dic139—21no—
46Dic139—41no—
47C2×C139—21no—
48C2×C139#12111yescharacteristic
49D139—41no—
50D139—81no—
51C139#47111yescharacteristic, complemented, Sylow
52#471—1391nomaximal, Sylow
53#137—1391no—
54AGL(1,ℤ/8)—1391no—
55C2×SD16—1391no—
56#131—1391no—
57#108D13911yescharacteristic, complemented
58#101—1391no—
59#100—1391no—
60#41—1391no—
61C2×Q8—1391no—
62C2×D4—1391no—
63Q16—2781no—
64SD16—2781no—
65SD16—2781no—
66SD16—2781no—
67SD16—2781no—
68D8—2781no—
69M16—2781no—
70M16—1391no—
71M16C2×D13911yescharacteristic
72M16C2×D13911yescharacteristic
73C2×C8—2781no—
74C2×C8C2×D13911yescharacteristic
75C23—2781no—
76Q8—2781no—
77Q8—2781no—
78Q8—1391no—
79D4—2781no—
80D4—2781no—
81D4—2781no—
82D4—1391no—
83C2×C4—2781no—
84C2×C4—2781no—
85C2×C4C22×D13911yescharacteristic
86C8—21no—
87C8—21no—
88C8—2781no—
89C8D55611yescharacteristic
90C8D55611yescharacteristic
91C22—2781no—
92C22—5561no—
93C22—11121no—
94C22#1455578611yescharacteristic
95C4—2781no—
96C4—5561no—
97C4D4×D13911yescharacteristic
98C4C2×D55611yescharacteristic
99C2—21no—
100C2—5561no—
101C2—11121no—
102C2#1798481711yescharacteristic
subgroupG/H
centerC2#17984817
commutatorC2×C4×C139C23
FrattiniC2×C4C22×D139
Fitting#108×C139C2
socleC2×C139#121
hypercenter#108D139
hypocenterC139#471
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #17984875C2semidirect
3. C2×#14555774C2semidirect
4. #17984848C2semidirect
5. #17984760C2semidirect
6. #17984758C2semidirect
7. #108×C139C2semidirect
51. C139#471semidirect
57. #108D139semidirect