Finite Group Databasebeta

← #30595274

Subgroups — #30595274

Order 15616.

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

normal subgroups only

This group has 126 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#21460962C211yesmaximal, characteristic
2#21460826C211yesmaximal, characteristic
3#21445147C211yesmaximal, characteristic
4#16840673—21no—
5#16840654—21no—
6#16840172—21no—
7#16840132C2211yescharacteristic
8#16839504—21no—
9#16839504C411yescharacteristic
10C61×#564C411yescharacteristic
11#14519851—41no—
12#14519838—41no—
13#14519777D411yescharacteristic
14#14519710—41no—
15#14519708—41no—
16#14519700—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×Dic122—21no—
25#11758217—81no—
26C4⋊C4×C61—21no—
27C4⋊C4×C61—21no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—41no—
30C4⋊C4×C61—41no—
31C4⋊C4×C61—41no—
32C4⋊C4×C61—41no—
33C4⋊C4×C61—41no—
34C4⋊C4×C61—41no—
35C42×C61—41no—
36C42×C61C22⋊C411yescharacteristic
37C4⋊Dic61—41no—
38C2×#92418—21no—
39C2×#92418—41no—
40#11758187—42no—
41C2×C4×C61—21no—
42C2×C4×C61—41no—
43C2×C4×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61#9911yescharacteristic
46C2×Dic61—41no—
47Dic122—81no—
48#92420—161no—
49#92418—41no—
50#92418—42no—
51#7526—611nomaximal, Sylow
52C22×C61AΣL(1,𝔽16)11yescharacteristic
53C4×C61—21no—
54C4×C61—41no—
55C4×C61—81no—
56C4×C61—81no—
57C4×C61—81no—
58Dic61—81no—
59#1663—611no—
60#1413—611no—
61#1356—611no—
62C2×C61—21no—
63C2×C61#140411yescharacteristic
64#564#692311yescharacteristic
65#501—1221no—
66#491—611no—
67#356—1221no—
68#347—1221no—
69#330—611no—
70#330—1221no—
71C61#752611yescharacteristic, complemented, Sylow
72C4⋊Q8—611no—
73#125—21no—
74#125—41no—
75#125—41no—
76#125—41no—
77#125C2×#692311yescharacteristic
78M32—2441no—
79#107—2441no—
80#106—2441no—
81#103—2441no—
82#101—2441no—
83#97—611no—
84#97—1221no—
85C2×Q8—1221no—
86M16—4881no—
87C2×C8—1221no—
88C2×C8—2441no—
89C4⋊C4—21no—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—2441no—
99C42—41no—
100C42C22⋊#692311yescharacteristic
101C16—2442no—
102Q8—4881no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—2441no—
108C2×C4#1451983511yescharacteristic
109C8—9761no—
110C8—2441no—
111C8—2442no—
112C22#1684066211yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—81no—
117C4—81no—
118C4—4881no—
119C2—21no—
120C2#2146094211yescharacteristic
subgroupG/H
centerC2#21460942
commutator#125×C61C2×C4
Frattini#125C2×#6923
FittingC61×#564C4
socleC2×C61#1404
prime radicalC22×C61AΣL(1,𝔽16)
cosocle#16840132C22
hypercenter#564#6923
hypocenterC61#7526
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
71. C61#7526semidirect

Maximal subgroups

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

subgroupindex
#214609622
#214608262
#214451472
#752661