Finite Group Databasebeta

← #30595276

Subgroups — #30595276

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#21460825C211yesmaximal, characteristic
3#21445148C211yesmaximal, characteristic
4#16840673—21no—
5#16840654—21no—
6C61⋊#564C411yescharacteristic
7#16840171—21no—
8#16840132C2211yescharacteristic
9#16839503—21no—
10C61×#330C411yescharacteristic
11#14519851—41no—
12#14519838—41no—
13#14519777D411yescharacteristic
14#14519769—21no—
15#14519768—41no—
16#14519767—41no—
17#14519767—41no—
18#14519711—41no—
19#14519709—41no—
20#14519700—41no—
21#14519688D411yescharacteristic
22#125×C61C2×C411yescharacteristic
23#97×C61—21no—
24C2×Dic122—21no—
25#11758217—81no—
26C2×C8×C61—41no—
27C4⋊C4×C61—21no—
28C4⋊C4×C61—41no—
29C42×C61C22⋊C411yescharacteristic
30C4⋊Dic61—21no—
31C4⋊Dic61—21no—
32C4⋊Dic61—41no—
33C4⋊Dic61—41no—
34#11758196—41no—
35#11758196—41no—
36#11758196—41no—
37#11758196—41no—
38C4×Dic61—41no—
39C2×#92418—21no—
40#11758187—42no—
41C2×C4×C61—21no—
42C2×C4×C61—41no—
43C2×C4×C61#9911yescharacteristic
44C2×Dic61—41no—
45C2×Dic61—41no—
46C2×Dic61—41no—
47Dic122—81no—
48#92420—161no—
49C8×C61—42no—
50#92418—41no—
51#7526—611nomaximal, Sylow
52C22×C61AΣL(1,𝔽16)11yescharacteristic
53C4×C61—21no—
54C4×C61—41no—
55C4×C61—81no—
56Dic61—81no—
57Dic61—81no—
58Dic61—81no—
59#1663—611no—
60#1413—611no—
61#1356—611no—
62C2×C61—21no—
63C2×C61#140411yescharacteristic
64#564—611no—
65#501—1221no—
66#491—611no—
67#356—1221no—
68#347—1221no—
69#330—1221no—
70#330#692311yescharacteristic
71C61#752611yescharacteristic, complemented, Sylow
72C4⋊Q8—611no—
73#125—1221no—
74#125—2441no—
75#125—2441no—
76#125—2441no—
77#125C2×#692311yescharacteristic
78M32—2441no—
79#107—2441no—
80#106—2441no—
81#103—2441no—
82#101—2441no—
83#97—21no—
84#97—611no—
85C2×Q8—1221no—
86M16—4881no—
87C2×C8—41no—
88C2×C8—1221no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—1221no—
92C4⋊C4—1221no—
93C4⋊C4—2441no—
94C4⋊C4—2441no—
95C4⋊C4—2441no—
96C4⋊C4—2441no—
97C4⋊C4—2441no—
98C4⋊C4—2441no—
99C42—2441no—
100C42C22⋊#692311yescharacteristic
101C16—2442no—
102Q8—4881no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—2441no—
106C2×C4—2441no—
107C2×C4—2441no—
108C2×C4#1451983611yescharacteristic
109C8—42no—
110C8—9761no—
111C8—2441no—
112C22#1684066311yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—4881no—
117C4—4881no—
118C4—4881no—
119C2—21no—
120C2#2146094311yescharacteristic
subgroupG/H
centerC2#21460943
commutator#125×C61C2×C4
Frattini#125C2×#6923
FittingC61×#330C4
socleC2×C61#1404
prime radicalC22×C61AΣL(1,𝔽16)
cosocle#16840132C22
hypercenter#330#6923
hypocenterC61#7526
LCSG ▷ #125×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #330

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
#214608252
#214451482
#752661