Finite Group Databasebeta

← #23765621

Subgroups — #23765621

Order 10112.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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#19098822C211yesmaximal, characteristic
2#19098610C211yesmaximal, characteristic
3#19098385C211yesmaximal, characteristic, complemented
4#19098380C211yesmaximal, characteristic, complemented
5#19098378C211yesmaximal, characteristic, complemented
6#19098344C211yesmaximal, characteristic
7#365×C79C211yesmaximal, characteristic, complemented
8C2×Dic316C2211yescharacteristic
9C2×#11929607C2211yescharacteristic
10M16×D79—21no—
11#14579141—21no—
12#14579101C2211yescharacteristic
13#14579097C2211yescharacteristic
14#14579096—21no—
15#14579084—21no—
16M32×C79C2211yescharacteristic
17#108×C79C2211yescharacteristic
18#106×C79C2211yescharacteristic
19C2×Dic158—21no—
20C2×C4×D79D411yescharacteristic
21Dic316—21no—
22Dic316—21no—
23#11929608—21no—
24#11929607—21no—
25#11929607—21no—
26#11929607—41no—
27C2×C79⋊C8D411yescharacteristic
28C8×D79—41no—
29C4⋊Dic79—41no—
30(C2×D79)⋊C4—41no—
31C79⋊C16—21no—
32M16×C79—21no—
33C2×C8×C79C2311yescharacteristic
34C4⋊C4×C79—21no—
35C16×C79—21no—
36C22×D79SD1611yescharacteristic
37C2×C4×C79—41no—
38C2×C4×C79C2×D411yescharacteristic
39C2×Dic79—41no—
40C2×Dic79SD1611yescharacteristic
41C4×D79—21no—
42C4×D79—21no—
43Dic158—41no—
44Dic158—41no—
45C8×C79—41no—
46C8×C79#4111yescharacteristic
47C8×C79#4111yescharacteristic
48C79⋊C8—21no—
49C79⋊C8—41no—
50C22×C79C2×SD1611yescharacteristic
51C2×D79—21no—
52C2×D79—41no—
53C4×C79—81no—
54C4×C79#12311yescharacteristic
55C4×C79AGL(1,ℤ/8)11yescharacteristic
56Dic79—21no—
57Dic79—81no—
58C2×C79—21no—
59C2×C79#48111yescharacteristic
60D79—41no—
61#2239—791nomaximal, Sylow
62C79#223911yescharacteristic, complemented, Sylow
63#470—791no—
64#430—791no—
65#365—791no—
66#365D7911yescharacteristic, complemented
67#362—791no—
68#362—791no—
69#349—791no—
70C2×Q16—791no—
71C2×M16—791no—
72C2×M16—1581no—
73C22⋊Q8—1581no—
74M32—791no—
75M32C2×D7911yescharacteristic
76#108—791no—
77#108—1581no—
78#108C2×D7911yescharacteristic
79#106C2×D7911yescharacteristic
80#103—1581no—
81C2×Q8—1581no—
82C22×C4—791no—
83Q16—1581no—
84Q16—1581no—
85M16—21no—
86M16—3161no—
87M16—1581no—
88M16—1581no—
89M16—1581no—
90C2×C8—3161no—
91C2×C8—791no—
92C2×C8C22×D7911yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—3161no—
95C22⋊C4—3161no—
96C16—21no—
97C16—1581no—
98C23—791no—
99Q8—3161no—
100Q8—3161no—
101C2×C4—41no—
102C2×C4—3161no—
103C2×C4—791no—
104C2×C4—1581no—
105C2×C4—1581no—
106C2×C4D4×D7911yescharacteristic
107C8—41no—
108C8—3161no—
109C8—1581no—
110C8#1192962411yescharacteristic
111C8#1192962511yescharacteristic
112C22—3161no—
113C22—1581no—
114C22SD16×D7911yescharacteristic
115C4—81no—
116C4—6321no—
117C4—1581no—
118C4#1457914611yescharacteristic
119C4#1457918811yescharacteristic
120C2—21no—
121C2—3161no—
122C2#1909888311yescharacteristic
subgroupG/H
centerC2#19098883
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#365×C79C2
socleC2×C79#481
prime radicalC22×D79SD16
hypercenter#365D79
hypocenterC79#2239
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
3. #19098385C2semidirect
4. #19098380C2semidirect
5. #19098378C2semidirect
7. #365×C79C2semidirect
62. C79#2239semidirect
66. #365D79semidirect