Finite Group Databasebeta

← #30595290

Subgroups — #30595290

Order 15616.

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

normal subgroups only

This group has 156 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#21460951C211yesmaximal, characteristic
2#21460951C211yesmaximal, characteristic
3#21445447C211yesmaximal, characteristic
4#16840667—21no—
5#16840667—21no—
6#16840160C411yescharacteristic, complemented
7#16840139C2211yescharacteristic
8#16840135—21no—
9#16840109—21no—
10C61×#322C411yescharacteristic, complemented
11#14519836—41no—
12#14519836—41no—
13C2×#11758190—42no—
14C2×D488—41no—
15#14519777—21no—
16#14519774D411yescharacteristic
17#14519774D411yescharacteristic
18#14519709—41no—
19#14519699—42no—
20C4×C8×C61—21no—
21C4×C8×C61C2×C411yescharacteristic
22C2×D244—21no—
23C2×D244—21no—
24C2×D244—41no—
25C2×D244—41no—
26C2×Dic122—41no—
27C22⋊#6923—81no—
28C22⋊#6923—81no—
29C2×C8×C61—21no—
30C2×C8×C61—22no—
31C42×C61C22⋊C411yescharacteristic
32C4⋊Dic61—41no—
33C4⋊Dic61—41no—
34D488—82no—
35#11758190—84no—
36C22×D61—41no—
37C22×D61—41no—
38C2×#6923—161no—
39C2×#6923—161no—
40C2×C4×C61—21no—
41C2×C4×C61#9911yescharacteristic
42C2×Dic61—81no—
43D244—81no—
44D244—81no—
45D244—82no—
46D244—82no—
47Dic122—82no—
48C8×C61—22no—
49C8×C61—42no—
50#7533—611nomaximal, Sylow
51C22×C61#35311yescharacteristic
52C2×D61—81no—
53C2×D61—81no—
54C2×D61—161no—
55C2×D61—161no—
56#6923—321no—
57#6923—321no—
58C4×C61—22no—
59C4×C61—21no—
60Dic61—161no—
61#1715—611no—
62#1408—611no—
63#1408—611no—
64C2×C61—21no—
65C2×C61#140911yescharacteristic
66D61—161no—
67D61—161no—
68#498—611no—
69#493—611no—
70#492—1221no—
71#486—1221no—
72#353—1221no—
73#353—1221no—
74#322#692311yescharacteristic, complemented
75C61#753311yescharacteristic, complemented, Sylow
76C2×SD16—2442no—
77C2×D8—2441no—
78C4⋊Q8—1221no—
79#127—611no—
80#127—611no—
81#106—2441no—
82#102—2442no—
83#99—2441no—
84#99—2441no—
85C4×C8—21no—
86C4×C8C2×#692311yescharacteristic
87C2×Q8—2441no—
88C2×D4—1221no—
89C2×D4—1221no—
90C2×D4—2441no—
91C2×D4—2441no—
92SD16—4884no—
93D8—4882no—
94C2×C8—21no—
95C2×C8—22no—
96C4⋊C4—2441no—
97C4⋊C4—2441no—
98C22⋊C4—4881no—
99C22⋊C4—4881no—
100C42C22⋊#692311yescharacteristic
101C23—2441no—
102C23—2441no—
103Q8—4882no—
104D4—4882no—
105D4—4882no—
106D4—4881no—
107D4—4881no—
108C2×C4—21no—
109C2×C4—9761no—
110C2×C4—9761no—
111C2×C4—4881no—
112C2×C4#1451983611yescharacteristic
113C8—22no—
114C8—42no—
115C22—9761no—
116C22—9761no—
117C22—4881no—
118C22—4881no—
119C22#1684066711yescharacteristic
120C4—22no—
121C4—21no—
122C4—19521no—
123C4—19521no—
124C4—9761no—
125C2—21no—
126C2—9761no—
127C2—9761no—
128C2#2146095311yescharacteristic
subgroupG/H
centerC2#21460953
commutatorC4×C8×C61C2×C4
FrattiniC4×C8C2×#6923
FittingC61×#322C4
socleC2×C61#1409
prime radical, cosocle#16840139C22
hypercenter#322#6923
hypocenterC61#7533
LCSG ▷ C4×C8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
6. #16840160C4semidirect
10. C61×#322C4semidirect
74. #322#6923semidirect
75. C61#7533semidirect

Maximal subgroups

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

subgroupindex
#214609512
#214454472
#753361