Finite Group Databasebeta

← #30595032

Subgroups — #30595032

Order 15616.

144 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460766C211yesmaximal, characteristic
2#21460727C211yesmaximal, characteristic
3#21447395C211yesmaximal, characteristic
4#16840765—21no—
5#16840658—21no—
6#16839811C411yescharacteristic
7#16839785C2211yescharacteristic
8#16839532—21no—
9#16839521—21no—
10C61×H(3,ℤ/4)C411yescharacteristic
11C2×#11758217—22no—
12#14519851—41no—
13#14519844—41no—
14C4⋊#92420—41no—
15C2×#11758194—21no—
16C2×#11758194D411yescharacteristic
17C2×C4×Dic61D411yescharacteristic
18#14519713—41no—
19#14519706—41no—
20C2×M16×C61C2×C411yescharacteristic
21#117×C61—21no—
22C22×C4×C61C22⋊C411yescharacteristic
23C22×Dic61—21no—
24#11758217—82no—
25C2×#92420—42no—
26M16×C61—41no—
27C2×C8×C61—21no—
28C4⋊C4×C61—41no—
29C22⋊C4×C61—41no—
30C42×C61—41no—
31C4×Dic61—21no—
32C4×Dic61SD1611yescharacteristic
33C4×Dic61Q1611yescharacteristic
34#11758194—41no—
35#11758194—41no—
36#11758194—41no—
37C2×#92418—21no—
38C2×#92418—41no—
39#11758187—81no—
40C23×C61#10411yescharacteristic
41C2×C4×C61—21no—
42C2×C4×C61—21no—
43C2×C4×C61—81no—
44C2×C4×C61#9911yescharacteristic
45C2×C4×C61#10311yescharacteristic
46C2×Dic61—21no—
47C2×Dic61—21no—
48C2×Dic61—41no—
49C2×Dic61—41no—
50#92420—82no—
51C8×C61—41no—
52#92418—41no—
53#92418—81no—
54#7440—611nomaximal, Sylow
55C22×C61—21no—
56C22×C61—41no—
57C22×C61#32811yescharacteristic
58C4×C61—21no—
59C4×C61—161no—
60C4×C61#35211yescharacteristic
61C4×C61#35511yescharacteristic
62Dic61—21no—
63Dic61—21no—
64Dic61—41no—
65#2102—611no—
66#1327—611no—
67#1309—611no—
68C2×C61—21no—
69C2×C61—41no—
70C2×C61#135311yescharacteristic
71#430—611no—
72#423—611no—
73#423—1221no—
74#349—1221no—
75#344—1221no—
76#339—1221no—
77H(3,ℤ/4)#692311yescharacteristic
78C61#744011yescharacteristic, complemented, Sylow
79C2×M16—611no—
80C2×M16—1222no—
81C2×M16—1221no—
82C2×M16C2×#692311yescharacteristic
83#117—21no—
84C2×C42—611no—
85M32—2441no—
86#108—2441no—
87C4⋊C8—2441no—
88C4⋊C8—2441no—
89C4⋊C8—2441no—
90C22×C4—1221no—
91C22×C4C22⋊#692311yescharacteristic
92M16—41no—
93M16—4882no—
94M16—2441no—
95M16—2441no—
96M16—2441no—
97C2×C8—21no—
98C2×C8—1221no—
99C2×C8—2441no—
100C2×C8—2442no—
101C4⋊C4—41no—
102C22⋊C4—41no—
103C42—41no—
104C42—611no—
105C42—611no—
106C42—1221no—
107C16—4881no—
108C23#1451984111yescharacteristic
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—81no—
112C2×C4—1221no—
113C2×C4—1221no—
114C2×C4—2441no—
115C2×C4—2441no—
116C2×C4#1451983611yescharacteristic
117C2×C4#1451984011yescharacteristic
118C8—41no—
119C8—4882no—
120C8—4881no—
121C8—2441no—
122C22—21no—
123C22—41no—
124C22#1684061511yescharacteristic
125C4—21no—
126C4—161no—
127C4—1221no—
128C4—1221no—
129C4—2441no—
130C4#1684066511yescharacteristic
131C4#1684067111yescharacteristic
132C2—21no—
133C2—41no—
134C2#2146081711yescharacteristic
subgroupG/H
centerC2#21460817
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×H(3,ℤ/4)C4
socleC2×C61#1353
prime radicalC23×C61#104
cosocle#16839785C22
hypercenterH(3,ℤ/4)#6923
hypocenterC61#7440
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
78. C61#7440semidirect

Maximal subgroups

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

subgroupindex
#214607662
#214607272
#214473952
#744061