Finite Group Databasebeta

← #30595265

Subgroups — #30595265

Order 15616.

134 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 22 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#21460958C211yesmaximal, characteristic
2#21460823C211yesmaximal, characteristic
3#21445121C211yesmaximal, characteristic
4#16840667—21no—
5#16840654—21no—
6#16840128—21no—
7#16840128C2211yescharacteristic
8#16839504—21no—
9#16839504C411yescharacteristic, complemented
10C61×#564C411yescharacteristic, complemented
11#14519851—41no—
12#14519836—41no—
13#14519774D411yescharacteristic
14#14519697—41no—
15#14519697—41no—
16#14519697—41no—
17#14519688—21no—
18#14519688D411yescharacteristic
19#125×C61—21no—
20#125×C61—41no—
21#125×C61—41no—
22#125×C61—41no—
23#125×C61C2×C411yescharacteristic
24C2×D244—21no—
25C2×D244—41no—
26C22⋊#6923—81no—
27C4⋊C4×C61—21no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—21no—
30C4⋊C4×C61—41no—
31C4⋊C4×C61—41no—
32C4⋊C4×C61—41no—
33C4⋊C4×C61—41no—
34C4⋊C4×C61—41no—
35C4⋊C4×C61—41no—
36C42×C61—41no—
37C42×C61C22⋊C411yescharacteristic
38C2×#92418—21no—
39C2×#92418—41no—
40#11758187—42no—
41C22×D61—41no—
42C2×#6923—161no—
43C2×C4×C61—21no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61#9911yescharacteristic
48D244—81no—
49D244—82no—
50#92418—41no—
51#92418—81no—
52#7524—611nomaximal, Sylow
53C22×C61AΣL(1,𝔽16)11yescharacteristic
54C2×D61—81no—
55C2×D61—161no—
56#6923—321no—
57C4×C61—21no—
58C4×C61—41no—
59C4×C61—81no—
60C4×C61—81no—
61C4×C61—81no—
62#1658—611no—
63#1412—611no—
64#1355—611no—
65C2×C61—21no—
66C2×C61#140411yescharacteristic
67D61—161no—
68#564#692311yescharacteristic, complemented
69#490—611no—
70#490—1221no—
71#353—1221no—
72#347—1221no—
73#330—611no—
74#330—1221no—
75C61#752411yescharacteristic, complemented, Sylow
76#127—611no—
77#125—21no—
78#125—41no—
79#125—41no—
80#125—41no—
81#125C2×#692311yescharacteristic
82M32—2441no—
83#102—2441no—
84#102—2441no—
85#102—2441no—
86#99—2441no—
87#97—611no—
88#97—1221no—
89C2×D4—1221no—
90C2×D4—2441no—
91C2×C8—1221no—
92C2×C8—2441no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C4⋊C4—41no—
101C4⋊C4—41no—
102C22⋊C4—4881no—
103C42—41no—
104C42C22⋊#692311yescharacteristic
105C16—2442no—
106C23—2441no—
107D4—4881no—
108D4—4882no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—9761no—
114C2×C4#1451983511yescharacteristic
115C8—4881no—
116C8—2441no—
117C22—9761no—
118C22—4881no—
119C22#1684066211yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—81no—
124C4—81no—
125C4—19521no—
126C2—21no—
127C2—9761no—
128C2#2146094211yescharacteristic
subgroupG/H
centerC2#21460942
commutator#125×C61C2×C4
Frattini#125C2×#6923
FittingC61×#564C4
socleC2×C61#1404
prime radical#14519774D4
cosocle#16840128C22
hypercenter#564#6923
hypocenterC61#7524
LCSG ▷ #125×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #564

Complements

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

NH ≅ G/Ntype
9. #16839504C4semidirect
10. C61×#564C4semidirect
68. #564#6923semidirect
75. C61#7524semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214609582
#214608232
#214451212
#752461