Finite Group Databasebeta

← #30595263

Subgroups — #30595263

Order 15616.

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

normal subgroups only

This group has 158 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, complemented
2#21460822C211yesmaximal, characteristic, complemented
3#21445114C211yesmaximal, characteristic
4#16840667—21no—
5#16840654—21no—
6#16840510C411yescharacteristic, complemented
7#16840151—21no—
8#16840128C2211yescharacteristic
9#16839501—21no—
10C61×#330C411yescharacteristic, complemented
11#14519851—41no—
12#14519836—41no—
13C2×#11758190—41no—
14C2×D488—41no—
15#14519774D411yescharacteristic
16#14519765—21no—
17#14519762—41no—
18#14519755—41no—
19#14519752—41no—
20#14519697—41no—
21#14519688D411yescharacteristic
22#125×C61C2×C411yescharacteristic
23#97×C61—21no—
24C2×D244—21no—
25C2×D244—21no—
26C2×D244—41no—
27C2×D244—41no—
28C2×C4×D61—41no—
29C2×Dic122—21no—
30C22⋊#6923—81no—
31C2×C8×C61—41no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—41no—
34C42×C61C22⋊C411yescharacteristic
35#11758198—41no—
36#11758198—41no—
37#11758198—41no—
38#11758196—41no—
39C2×#92418—21no—
40D488—82no—
41#11758190—82no—
42#11758187—42no—
43C22×D61—41no—
44C22×D61—41no—
45C2×#6923—161no—
46C2×C4×C61—21no—
47C2×C4×C61—41no—
48C2×C4×C61#9911yescharacteristic
49C2×Dic61—41no—
50D244—81no—
51D244—81no—
52D244—81no—
53D244—81no—
54D244—161no—
55C4×D61—161no—
56Dic122—81no—
57C8×C61—42no—
58#92418—41no—
59#7523—611nomaximal, Sylow
60C22×C61AΣL(1,𝔽16)11yescharacteristic
61C2×D61—81no—
62C2×D61—81no—
63C2×D61—81no—
64C2×D61—81no—
65C2×D61—161no—
66#6923—321no—
67C4×C61—21no—
68C4×C61—41no—
69C4×C61—81no—
70Dic61—81no—
71#1656—611no—
72#1412—611no—
73#1355—611no—
74C2×C61—21no—
75C2×C61#140411yescharacteristic
76D61—161no—
77D61—161no—
78#562—611no—
79#496—1221no—
80#490—611no—
81#353—1221no—
82#347—1221no—
83#330#692311yescharacteristic, complemented
84#329—1221no—
85C61#752311yescharacteristic, complemented, Sylow
86C2×SD16—2441no—
87C2×D8—2441no—
88#127—611no—
89#125C2×#692311yescharacteristic
90#124—1221no—
91#123—2441no—
92C22⋊Q8—2441no—
93#121—2441no—
94M32—2441no—
95#102—2441no—
96#99—2441no—
97#97—21no—
98#97—611no—
99C2×Q8—1221no—
100C2×D4—1221no—
101C2×D4—1221no—
102C2×D4—2441no—
103C2×D4—2441no—
104C22×C4—2441no—
105SD16—4882no—
106D8—4882no—
107C2×C8—41no—
108C2×C8—1221no—
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—2441no—
112C22⋊C4—4881no—
113C22⋊C4—2441no—
114C22⋊C4—2441no—
115C22⋊C4—2441no—
116C42C22⋊#692311yescharacteristic
117C16—2442no—
118C23—2441no—
119C23—2441no—
120Q8—4881no—
121D4—9761no—
122D4—4881no—
123D4—4881no—
124D4—4881no—
125D4—4881no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—9761no—
129C2×C4—9761no—
130C2×C4—2441no—
131C2×C4#1451983611yescharacteristic
132C8—42no—
133C8—2441no—
134C22—9761no—
135C22—4881no—
136C22—4881no—
137C22—4881no—
138C22—4881no—
139C22#1684066311yescharacteristic
140C4—21no—
141C4—41no—
142C4—81no—
143C4—19521no—
144C4—4881no—
145C2—21no—
146C2—9761no—
147C2—9761no—
148C2#2146094311yescharacteristic
subgroupG/H
centerC2#21460943
commutator#125×C61C2×C4
Frattini#125C2×#6923
FittingC61×#330C4
socleC2×C61#1404
prime radical#21445114C2
cosocle#16840128C22
hypercenter#330#6923
hypocenterC61#7523
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
1. #21460958C2semidirect
2. #21460822C2semidirect
6. #16840510C4semidirect
10. C61×#330C4semidirect
83. #330#6923semidirect
85. C61#7523semidirect

Maximal subgroups

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

subgroupindex
#214609582
#214608222
#214451142
#752361