Finite Group Databasebeta

← #23765716

Subgroups — #23765716

Order 10112.

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

normal subgroups only

This group has 104 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#19098992C211yesmaximal, characteristic
2Q32×D79C211yesmaximal, characteristic, complemented
3Dic1264C211yesmaximal, characteristic, complemented
4#19098403C211yesmaximal, characteristic, complemented
5#19098401C211yesmaximal, characteristic, complemented
6#19098396C211yesmaximal, characteristic, complemented
7SD64×C79C211yesmaximal, characteristic, complemented
8#14579180—21no—
9Q16×D79—21no—
10Dic632C2211yescharacteristic
11Dic632C2211yescharacteristic
12#14579107—21no—
13#14579105—21no—
14C16×D79C2211yescharacteristic
15C79⋊C32C2211yescharacteristic
16Q32×C79C2211yescharacteristic
17D16×C79C2211yescharacteristic
18C32×C79C2211yescharacteristic
19#11929623—41no—
20Q8×D79—41no—
21Dic316—21no—
22Dic316—21no—
23#11929614—41no—
24#11929612—41no—
25C8×D79D411yescharacteristic
26C79⋊C16D411yescharacteristic
27Q16×C79—21no—
28D8×C79—21no—
29C16×C79C2311yescharacteristic
30Q8×C79—41no—
31D4×C79—41no—
32C22⋊D79—81no—
33C2×Dic79—81no—
34C4×D79—81no—
35C4×D79D811yescharacteristic
36Dic158—41no—
37Dic158—41no—
38Dic158—81no—
39C8×C79C2×D411yescharacteristic
40C79⋊C8D811yescharacteristic
41C22×C79—81no—
42C2×D79D1611yescharacteristic
43C4×C79—81no—
44C4×C79C2×D811yescharacteristic
45Dic79—81no—
46Dic79—81no—
47Dic79D1611yescharacteristic
48C2×C79—161no—
49C2×C79C2×D1611yescharacteristic
50D79—21no—
51#2264—791nomaximal, Sylow
52C79#226411yescharacteristic, complemented, Sylow
53#508—791no—
54C2×Q32—791no—
55Q64—791no—
56Q64—791no—
57SD64—791no—
58SD64D7911yescharacteristic, complemented
59M64—791no—
60#135—1581no—
61C2×Q16—1581no—
62Q32—791no—
63Q32—791no—
64Q32—1581no—
65Q32C2×D7911yescharacteristic
66SD32—1581no—
67D16C2×D7911yescharacteristic
68C2×C16—791no—
69C32—791no—
70C32C2×D7911yescharacteristic
71#41—3161no—
72C2×Q8—3161no—
73Q16—21no—
74Q16—3161no—
75Q16—1581no—
76Q16—1581no—
77SD16—3161no—
78D8—21no—
79C2×C8—791no—
80C16—791no—
81C16C22×D7911yescharacteristic
82Q8—41no—
83Q8—3161no—
84Q8—3161no—
85Q8—6321no—
86D4—41no—
87D4—6321no—
88C2×C4—791no—
89C2×C4—6321no—
90C2×C4—6321no—
91C8—791no—
92C8D4×D7911yescharacteristic
93C22—81no—
94C22—791no—
95C4—81no—
96C4—791no—
97C4—6321no—
98C4—6321no—
99C4D8×D7911yescharacteristic
100C2—161no—
101C2—1581no—
102C2D16×D7911yescharacteristic
subgroupG/H
centerC2D16×D79
commutator, cosocleC16×C79C23
FrattiniC16C22×D79
FittingSD64×C79C2
socleC2×C79C2×D16
prime radical#19098992C2
hypercenterSD64D79
hypocenterC79#2264
LCSG ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64

Complements

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

NH ≅ G/Ntype
2. Q32×D79C2semidirect
3. Dic1264C2semidirect
4. #19098403C2semidirect
5. #19098401C2semidirect
6. #19098396C2semidirect
7. SD64×C79C2semidirect
52. C79#2264semidirect
58. SD64D79semidirect