Finite Group Databasebeta

← #30595248

Subgroups — #30595248

Order 15616.

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

normal subgroups only

This group has 162 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#21460950C211yesmaximal, characteristic
2#21460827C211yesmaximal, characteristic
3#21444879C211yesmaximal, characteristic
4#16840685—21no—
5#16840667—21no—
6#16840498C411yescharacteristic, complemented
7#16840138C2211yescharacteristic
8#16839963—21no—
9#16839492—21no—
10C61×#331C411yescharacteristic, complemented
11#14519851—41no—
12#14519836—41no—
13C2×#11758190—41no—
14C2×#11758199—41no—
15#14519774D411yescharacteristic
16#14519764—41no—
17#14519758—41no—
18C4×Dic122—21no—
19D4×Dic61—41no—
20#14519699—41no—
21C4×#92418D411yescharacteristic
22#127×C61C2×C411yescharacteristic
23C4⋊C8×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—41no—
26C22×Dic61—41no—
27C2×D244—21no—
28C2×D244—41no—
29C2×Dic122—21no—
30C22⋊#6923—81no—
31C2×C8×C61—41no—
32C42×C61C22⋊C411yescharacteristic
33C22⋊Dic61—42no—
34C22⋊Dic61—41no—
35#11758199—81no—
36#11758199—81no—
37C4⋊Dic61—21no—
38#11758196—41no—
39C4×Dic61—41no—
40C2×#92418—21no—
41#11758190—82no—
42#11758187—81no—
43C23×C61—41no—
44C22×D61—41no—
45C2×#6923—161no—
46D4×C61—81no—
47D4×C61—81no—
48D4×C61—81no—
49C2×C4×C61—21no—
50C2×C4×C61#9911yescharacteristic
51C2×Dic61—41no—
52C2×Dic61—41no—
53C2×Dic61—161no—
54D244—81no—
55D244—81no—
56D244—81no—
57Dic122—41no—
58Dic122—41no—
59C8×C61—81no—
60#92418—21no—
61#92418—21no—
62#7516—611nomaximal, Sylow
63C22×C61—82no—
64C22×C61—81no—
65C22×C61AΣL(1,𝔽16)11yescharacteristic
66C2×D61—81no—
67C2×D61—161no—
68#6923—321no—
69C4×C61—21no—
70C4×C61—21no—
71C4×C61—21no—
72Dic61—81no—
73Dic61—81no—
74#1620—611no—
75#1408—611no—
76#1357—611no—
77C2×C61—21no—
78C2×C61—161no—
79C2×C61#140211yescharacteristic
80D61—161no—
81#559—611no—
82#493—611no—
83#460—1221no—
84#364—1221no—
85#353—1221no—
86#331#692311yescharacteristic, complemented
87Q8⋊C8—1221no—
88C61#751611yescharacteristic, complemented, Sylow
89C2×SD16—2441no—
90C2×D8—2441no—
91#127—611no—
92#127C2×#692311yescharacteristic
93#124—2441no—
94#123—2441no—
95C4×Q8—1221no—
96C4×D4—2441no—
97M32—2441no—
98C4⋊C8—21no—
99#102—2441no—
100#99—2441no—
101C4×C8—611no—
102C2×Q8—1221no—
103C2×D4—21no—
104C2×D4—41no—
105C2×D4—1221no—
106C2×D4—2441no—
107C22×C4—2441no—
108SD16—4882no—
109D8—4881no—
110D8—4881no—
111C2×C8—41no—
112C2×C8—1221no—
113C4⋊C4—1221no—
114C4⋊C4—2441no—
115C22⋊C4—4881no—
116C22⋊C4—2442no—
117C22⋊C4—2441no—
118C42—2441no—
119C42C22⋊#692311yescharacteristic
120C16—4881no—
121C23—41no—
122C23—2441no—
123Q8—2441no—
124Q8—2441no—
125D4—81no—
126D4—81no—
127D4—81no—
128D4—4881no—
129D4—4881no—
130D4—4881no—
131C2×C4—21no—
132C2×C4—9761no—
133C2×C4—9761no—
134C2×C4—2441no—
135C2×C4—2441no—
136C2×C4#1451983611yescharacteristic
137C8—81no—
138C8—1221no—
139C8—1221no—
140C22—82no—
141C22—81no—
142C22—9761no—
143C22—4881no—
144C22#1684066311yescharacteristic
145C4—21no—
146C4—21no—
147C4—21no—
148C4—19521no—
149C4—4881no—
150C4—4881no—
151C2—21no—
152C2—161no—
153C2—9761no—
154C2#2146093911yescharacteristic
subgroupG/H
centerC2#21460939
commutator#127×C61C2×C4
Frattini#127C2×#6923
FittingC61×#331C4
socleC2×C61#1402
prime radical, cosocle#16840138C22
hypercenter#331#6923
hypocenterC61#7516
LCSG ▷ #127×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
6. #16840498C4semidirect
10. C61×#331C4semidirect
86. #331#6923semidirect
88. C61#7516semidirect

Maximal subgroups

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

subgroupindex
#214609502
#214608272
#214448792
#751661