Finite Group Databasebeta

← #30595295

Subgroups — #30595295

Order 15616.

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

normal subgroups only

This group has 138 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#21460955C211yesmaximal, characteristic
2#21460953C211yesmaximal, characteristic
3#21445421C211yesmaximal, characteristic
4#16840673—21no—
5#16840667—21no—
6#16840135C2211yescharacteristic
7#16840112—21no—
8#16840110—21no—
9C8×#92418C411yescharacteristic, complemented
10C61×#498C411yescharacteristic, complemented
11#14519838—41no—
12#14519836—41no—
13C2×#11758190—41no—
14#14519777D411yescharacteristic
15#14519774D411yescharacteristic
16#14519701—42no—
17#14519697—42no—
18C4×#92418—21no—
19C4⋊Q8×C61—21no—
20#106×C61—41no—
21C4×C8×C61C2×C411yescharacteristic
22C2×Q8×C61—41no—
23C2×D244—21no—
24C2×D244—41no—
25C2×Dic122—21no—
26C22⋊#6923—81no—
27#11758217—81no—
28C2×C8×C61—21no—
29C4⋊C4×C61—41no—
30C4⋊C4×C61—41no—
31C42×C61C22⋊C411yescharacteristic
32C4⋊Dic61—41no—
33C2×#92418—22no—
34#11758190—82no—
35C22×D61—41no—
36C2×#6923—161no—
37Q8×C61—82no—
38C2×C4×C61—21no—
39C2×C4×C61—81no—
40C2×C4×C61#9911yescharacteristic
41C2×Dic61—41no—
42D244—81no—
43D244—82no—
44Dic122—81no—
45#92420—161no—
46C8×C61—22no—
47#92418—42no—
48#7536—611nomaximal, Sylow
49C22×C61#35311yescharacteristic
50C2×D61—81no—
51C2×D61—161no—
52#6923—321no—
53C4×C61—22no—
54C4×C61—21no—
55C4×C61—161no—
56Dic61—81no—
57#1708—611no—
58#1410—611no—
59#1409—611no—
60C2×C61—21no—
61C2×C61#140911yescharacteristic
62D61—161no—
63#498#692311yescharacteristic, complemented
64#492—611no—
65#487—1221no—
66#486—1221no—
67#356—1221no—
68#353—1221no—
69C82—611no—
70C61#753611yescharacteristic, complemented, Sylow
71C2×SD16—2441no—
72C4⋊Q8—21no—
73C4⋊Q8—611no—
74#127—611no—
75#106—41no—
76#103—2442no—
77#102—2442no—
78#101—2441no—
79#99—2441no—
80C4×C8—1221no—
81C4×C8C2×#692311yescharacteristic
82C2×Q8—41no—
83C2×Q8—1221no—
84C2×D4—1221no—
85C2×D4—2441no—
86SD16—4882no—
87M16—4881no—
88C2×C8—21no—
89C2×C8—1222no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—2441no—
93C22⋊C4—4881no—
94C42C22⋊#692311yescharacteristic
95C23—2441no—
96Q8—82no—
97Q8—4881no—
98D4—4882no—
99D4—4881no—
100C2×C4—21no—
101C2×C4—81no—
102C2×C4—9761no—
103C2×C4—2441no—
104C2×C4#1451983511yescharacteristic
105C8—22no—
106C8—9761no—
107C8—2442no—
108C22—9761no—
109C22—4881no—
110C22#1684066611yescharacteristic
111C4—22no—
112C4—21no—
113C4—161no—
114C4—19521no—
115C4—4881no—
116C2—21no—
117C2—9761no—
118C2#2146095211yescharacteristic
subgroupG/H
centerC2#21460952
commutatorC4×C8×C61C2×C4
FrattiniC4×C8C2×#6923
FittingC61×#498C4
socleC2×C61#1409
prime radical#14519774D4
cosocle#16840135C22
hypercenter#498#6923
hypocenterC61#7536
LCSG ▷ C4×C8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
9. C8×#92418C4semidirect
10. C61×#498C4semidirect
63. #498#6923semidirect
70. C61#7536semidirect

Maximal subgroups

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

subgroupindex
#214609552
#214609532
#214454212
#753661