Finite Group Databasebeta

← #23762796

Subgroups — #23762796

Order 10112.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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#19098850C212yesmaximal
2C8×D316C211yesmaximal, characteristic
3#19098316C211yesmaximal, characteristic, complemented
4#19098312C212yesmaximal, complemented
5#500×C79C211yesmaximal, characteristic, complemented
6C2×C8×D79—21no—
7C4×D316C2211yescharacteristic
8#14579092—22no—
9C4⋊(C79⋊C8)C2211yescharacteristic
10C4⋊(C79⋊C8)C2212yes—
11#14579081—22no—
12(C2×D79)⋊C8—21no—
13C4⋊Q8×C79C2212yes—
14#107×C79—21no—
15#107×C79—21no—
16C4×C8×C79C2211yescharacteristic
17C2×D316D411yescharacteristic
18C2×C4×D79—21no—
19C2×C79⋊C8—21no—
20C2×C79⋊C8—22no—
21C8×D79—42no—
22C4⋊Dic79D411yescharacteristic
23(C2×D79)⋊C4—21no—
24C2×Q8×C79—22no—
25C2×C8×C79D411yescharacteristic
26C2×C8×C79D411yescharacteristic
27C4⋊C4×C79—22no—
28C4⋊C4×C79—22no—
29C42×C79C2311yescharacteristic
30C22×D79—21no—
31Q8×C79—82no—
32C2×C4×C79—42no—
33C2×C4×C79C2×D411yescharacteristic
34C2×C4×C79C2×D411yescharacteristic
35C2×C4×C79#4111yescharacteristic
36C2×Dic79—21no—
37D316—21no—
38D316Q1612yes—
39C4×D79—41no—
40C4×D79—41no—
41C8×C79—21no—
42C8×C79SD1612yes—
43C79⋊C8—41no—
44C79⋊C8—42no—
45C22×C79#12111yescharacteristic
46C2×D79—22no—
47C2×D79—41no—
48C2×D79—41no—
49C4×C79—21no—
50C4×C79—82no—
51C4×C79C2×SD1611yescharacteristic
52C4×C79C2×Q1611yescharacteristic
53C4×C79#13511yescharacteristic
54C4×C79#13711yescharacteristic
55Dic79—41no—
56C2×C79#46111yescharacteristic
57C2×C79#46711yescharacteristic
58C2×C79#47211yescharacteristic
59D79—42no—
60#1675—791nomaximal, Sylow
61C79#167511yescharacteristic, complemented, Sylow
62#500D7911yescharacteristic, complemented
63#476—792no—
64C8×D4—791no—
65#335—791no—
66#333—792no—
67C22×C8—1581no—
68C4⋊Q8C2×D7912yes—
69C4×D4—791no—
70#107—21no—
71#107—21no—
72#106—1582no—
73C4⋊C8—791no—
74C4⋊C8—792no—
75#102—1582no—
76C22⋊C8—1581no—
77C4×C8C2×D7911yescharacteristic
78C2×Q8—22no—
79C2×D4—791no—
80C22×C4—1581no—
81C2×C8—3162no—
82C2×C8—1582no—
83C2×C8—1581no—
84C2×C8C22⋊D7911yescharacteristic
85C2×C8C22⋊D7911yescharacteristic
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—791no—
89C22⋊C4—1581no—
90C42C22×D7911yescharacteristic
91C23—1581no—
92Q8—82no—
93D4—792no—
94D4—1581no—
95C2×C4—42no—
96C2×C4—3161no—
97C2×C4—3161no—
98C2×C4—1581no—
99C2×C4D4×D7911yescharacteristic
100C2×C4C2×C22⋊D7911yescharacteristic
101C2×C4#1192962311yescharacteristic
102C8—21no—
103C8—3161no—
104C8—3162no—
105C8#1192961112yes—
106C22—3161no—
107C22—3161no—
108C22—1582no—
109C22#1457913211yescharacteristic
110C4—21no—
111C4—82no—
112C4—3161no—
113C4C2×#1192961111yescharacteristic
114C4Q16×D7911yescharacteristic
115C4#1457918411yescharacteristic
116C4#1457919211yescharacteristic
117C2—3162no—
118C2#1909876511yescharacteristic
119C2#1909880111yescharacteristic
120C2#1909883011yescharacteristic
subgroupG/H
centerC22#14579132
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#500×C79C2
socleC22×C79#121
prime radicalC2×D316D4
hypercenter#500D79
hypocenterC79#1675
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #19098316C2semidirect
4. #19098312C2semidirect
5. #500×C79C2semidirect
61. C79#1675semidirect
62. #500D79semidirect