Finite Group Databasebeta

← #23765573

Subgroups — #23765573

Order 10112.

120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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#19098681C211yesmaximal, characteristic
2#19098385C212yesmaximal, complemented
3#19098384C211yesmaximal, characteristic, complemented
4#19098372C212yesmaximal
5#499×C79C211yesmaximal, characteristic, complemented
6#14579183C2211yescharacteristic
7#14579167—21no—
8#14579101C2212yes—
9#14579097C2211yescharacteristic
10#14579089—21no—
11#125×C79—21no—
12#107×C79—21no—
13#106×C79C2212yes—
14C4×C8×C79C2211yescharacteristic
15#11929624—21no—
16Dic316Q811yescharacteristic
17#11929613—21no—
18D632Q811yescharacteristic
19#11929608—21no—
20#11929607—41no—
21C8×D79—41no—
22C79⋊C16—22no—
23C2×C8×C79D411yescharacteristic
24C2×C8×C79C2311yescharacteristic
25C4⋊C4×C79—22no—
26C4⋊C4×C79—42no—
27C42×C79D411yescharacteristic
28C2×C4×C79—21no—
29C2×C4×C79—42no—
30C2×C4×C79C2×D411yescharacteristic
31C22⋊D79—41no—
32D316—21no—
33C4×D79—41no—
34Dic158—21no—
35C8×C79SD1611yescharacteristic
36C8×C79SD1611yescharacteristic
37C8×C79C2×Q811yescharacteristic
38C8×C79#4111yescharacteristic
39C79⋊C8—41no—
40C22×C79AGL(1,ℤ/8)11yescharacteristic
41C2×D79—41no—
42C4×C79—41no—
43C4×C79—82no—
44C4×C79C22⋊Q811yescharacteristic
45C4×C79C2×SD1611yescharacteristic
46Dic79—41no—
47C2×C79—21no—
48C2×C79#47611yescharacteristic
49D79—81no—
50#2231—791nomaximal, Sylow
51C79#223111yescharacteristic, complemented, Sylow
52#499D7911yescharacteristic, complemented
53#443—791no—
54#365—792no—
55#364—791no—
56#360—792no—
57#135—791no—
58#131—1581no—
59#125—21no—
60M32—792no—
61#108—791no—
62#107—21no—
63#106C2×D7912yes—
64#104—1581no—
65C4×C8C2×D7911yescharacteristic
66#41—1581no—
67Q16—791no—
68SD16—1581no—
69D8—791no—
70M16—3161no—
71M16—1581no—
72C2×C8—3161no—
73C2×C8C22⋊D7911yescharacteristic
74C2×C8C22×D7911yescharacteristic
75C4⋊C4—22no—
76C4⋊C4—42no—
77C42C22⋊D7911yescharacteristic
78C16—1582no—
79Q8—1581no—
80D4—3161no—
81D4—1581no—
82C2×C4—21no—
83C2×C4—42no—
84C2×C4—3161no—
85C2×C4C2×C22⋊D7911yescharacteristic
86C8—3161no—
87C8#1192961111yescharacteristic
88C8#1192961111yescharacteristic
89C8Q8×D7911yescharacteristic
90C8#1192962511yescharacteristic
91C22—3161no—
92C22#1457918711yescharacteristic
93C4—41no—
94C4—82no—
95C4—3161no—
96C4#1457913711yescharacteristic
97C4C2×#1192961111yescharacteristic
98C2—21no—
99C2—6321no—
100C2#1909885011yescharacteristic
subgroupG/H
centerC2#19098850
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#499×C79C2
socleC2×C79#476
prime radical#14579183C22
hypercenter#499D79
hypocenterC79#2231
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #19098385C2semidirect
3. #19098384C2semidirect
5. #499×C79C2semidirect
51. C79#2231semidirect
52. #499D79semidirect