Finite Group Databasebeta

← #30595262

Subgroups — #30595262

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#21460959C211yesmaximal, characteristic, complemented
2#21460822C211yesmaximal, characteristic, complemented
3#21445112C211yesmaximal, characteristic
4#16840667—21no—
5#16840654—21no—
6#16840152—21no—
7#16840128C2211yescharacteristic
8#16839504C411yescharacteristic, complemented
9#16839502—21no—
10C61×#562C411yescharacteristic, complemented
11#14519851—41no—
12#14519836—41no—
13C2×#11758201—41no—
14C2×#11758199—41no—
15#14519774D411yescharacteristic
16#14519697—41no—
17#14519688—21no—
18#14519688D411yescharacteristic
19#125×C61C2×C411yescharacteristic
20#124×C61—21no—
21#123×C61—41no—
22C22⋊Q8×C61—41no—
23#121×C61—41no—
24C2×Q8×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—41no—
27C22×C4×C61—41no—
28C2×D244—21no—
29C2×D244—41no—
30C22⋊#6923—81no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—41no—
33C4⋊C4×C61—41no—
34C22⋊C4×C61—41no—
35C22⋊C4×C61—41no—
36C22⋊C4×C61—41no—
37C42×C61C22⋊C411yescharacteristic
38#11758201—82no—
39#11758199—82no—
40C2×#92418—21no—
41C2×#92418—41no—
42#11758187—42no—
43C23×C61—41no—
44C22×D61—41no—
45C2×#6923—161no—
46Q8×C61—81no—
47D4×C61—81no—
48D4×C61—161no—
49C2×C4×C61—21no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61—161no—
53C2×C4×C61#9911yescharacteristic
54D244—81no—
55D244—81no—
56D244—81no—
57#92418—41no—
58#92418—42no—
59#7523—611nomaximal, Sylow
60C22×C61—81no—
61C22×C61—81no—
62C22×C61—81no—
63C22×C61AΣL(1,𝔽16)11yescharacteristic
64C2×D61—81no—
65C2×D61—161no—
66#6923—321no—
67C4×C61—21no—
68C4×C61—41no—
69C4×C61—81no—
70C4×C61—81no—
71#1656—611no—
72#1412—611no—
73#1355—611no—
74C2×C61—21no—
75C2×C61—161no—
76C2×C61#140411yescharacteristic
77D61—161no—
78#562#692311yescharacteristic, complemented
79#496—1221no—
80#490—611no—
81#353—1221no—
82#347—1221no—
83#330—611no—
84#329—1221no—
85C61#752311yescharacteristic, complemented, Sylow
86C2×SD16—2441no—
87C2×D8—2441no—
88#127—611no—
89#125C2×#692311yescharacteristic
90#124—21no—
91#123—41no—
92C22⋊Q8—41no—
93#121—41no—
94M32—2441no—
95#102—2441no—
96#99—2441no—
97#97—611no—
98#97—1221no—
99C2×Q8—21no—
100C2×D4—21no—
101C2×D4—41no—
102C2×D4—1221no—
103C2×D4—2441no—
104C22×C4—41no—
105SD16—4882no—
106D8—4882no—
107C2×C8—1221no—
108C2×C8—2441no—
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C22⋊C4—41no—
113C22⋊C4—41no—
114C22⋊C4—41no—
115C22⋊C4—4881no—
116C42C22⋊#692311yescharacteristic
117C16—2442no—
118C23—41no—
119C23—2441no—
120Q8—81no—
121D4—81no—
122D4—161no—
123D4—4881no—
124D4—4881no—
125D4—4881no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—161no—
130C2×C4—9761no—
131C2×C4#1451983511yescharacteristic
132C8—2441no—
133C8—2442no—
134C22—81no—
135C22—81no—
136C22—81no—
137C22—9761no—
138C22—4881no—
139C22#1684066211yescharacteristic
140C4—21no—
141C4—41no—
142C4—81no—
143C4—81no—
144C4—19521no—
145C2—21no—
146C2—161no—
147C2—9761no—
148C2#2146094211yescharacteristic
subgroupG/H
centerC2#21460942
commutator#125×C61C2×C4
Frattini#125C2×#6923
FittingC61×#562C4
socleC2×C61#1404
prime radical#21445112C2
cosocle#16840128C22
hypercenter#562#6923
hypocenterC61#7523
LCSG ▷ #125×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #21460959C2semidirect
2. #21460822C2semidirect
8. #16839504C4semidirect
10. C61×#562C4semidirect
78. #562#6923semidirect
85. C61#7523semidirect

Maximal subgroups

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

subgroupindex
#214609592
#214608222
#214451122
#752361