Finite Group Databasebeta

← #30598775

Subgroups — #30598775

Order 15616.

910 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461714C216yesmaximal
2C22×#14519771C211yesmaximal, characteristic
3#16840703C2214yes—
4#16840640—212no—
5C2×#14519771—212no—
6C22×#11758196C413yescomplemented
7C22×#11758198C2213yes—
8C22×C42×C61C411yescharacteristic, complemented
9C2×C22⋊#6923—212no—
10C24×D61C2311yescharacteristic
11C23×Dic61C2×C413yes—
12#14519771—232no—
13C2×#11758196—26no—
14C2×#11758196—26no—
15C2×#11758196—26no—
16C2×#11758198—26no—
17C2×#11758198—26no—
18C2×#11758198D4112yes—
19C23×C4×C61C2×C413yes—
20C2×C42×C61—26no—
21C24×C61C22×C411yescharacteristic
22C23×D61—46no—
23C23×D61C2×D416yes—
24C22×#6923—44no—
25C22×C4×C61—23no—
26C22×C4×C61—23no—
27C22×C4×C61—46no—
28C22×C4×C61C22⋊C416yes—
29C22×Dic61—23no—
30C22×Dic61—23no—
31C22×Dic61—46no—
32C22×Dic61C22⋊C416yes—
33C22⋊#6923—424no—
34C42×C61—28no—
35#11758198—224no—
36#11758196—224no—
37C23×C61—26no—
38C23×C61C2×C22⋊C413yes—
39C22×D61—212no—
40C22×D61—46no—
41C22×D61—46no—
42C22×D61—88no—
43C22×D61#12014yes—
44C2×#6923—812no—
45C2×C4×C61—26no—
46C2×C4×C61—46no—
47C2×C4×C61—46no—
48C2×C4×C61—46no—
49C2×Dic61—26no—
50C2×Dic61—46no—
51C2×Dic61—46no—
52C2×Dic61—46no—
53#8545—611nomaximal, Sylow
54C22×C61—28no—
55C22×C61—23no—
56C22×C61—23no—
57C22×C61#37911yescharacteristic
58C22×C61#41016yes—
59C2×D61—212no—
60C2×D61—812no—
61#6923—164no—
62C4×C61—46no—
63Dic61—46no—
64C22×#126—611no—
65#1819—616no—
66C2×C61—26no—
67C2×C61#178213yes—
68D61—44no—
69C2×#126—12212no—
70C22×C4⋊C4—613no—
71C22×C22⋊C4—613no—
72C22×C42#692311yescharacteristic, complemented
73#379—614no—
74#342—12212no—
75C61#854511yescharacteristic, complemented, Sylow
76C25—611no—
77C23×C4—613no—
78C23×C4C2×#692313yes—
79#126—12232no—
80C2×C4⋊C4—1226no—
81C2×C4⋊C4—1226no—
82C2×C4⋊C4—1226no—
83C2×C22⋊C4—6112no—
84C2×C22⋊C4—1226no—
85C2×C22⋊C4—1226no—
86C2×C22⋊C4—12212no—
87C2×C42—26no—
88C24—616no—
89C24—2446no—
90C24C22×#692311yescharacteristic
91C22×C4—23no—
92C22×C4—23no—
93C22×C4—46no—
94C22×C4—616no—
95C22×C4—1223no—
96C22×C4—1223no—
97C22×C4—2444no—
98C22×C4—2446no—
99C22×C4C22⋊#692316yes—
100C4⋊C4—12224no—
101C22⋊C4—12224no—
102C22⋊C4—24424no—
103C42—28no—
104C23—26no—
105C23—614no—
106C23—12212no—
107C23—4888no—
108C23—2446no—
109C23—2446no—
110C23C2×C22⋊#692313yes—
111C2×C4—26no—
112C2×C4—46no—
113C2×C4—46no—
114C2×C4—46no—
115C2×C4—1226no—
116C2×C4—48812no—
117C2×C4—2446no—
118C2×C4—2446no—
119C2×C4—2446no—
120C22—28no—
121C22—23no—
122C22—23no—
123C22—12212no—
124C22—48812no—
125C22#1684070311yescharacteristic
126C22#1684074116yes—
127C4—46no—
128C4—9764no—
129C4—2446no—
130C2—26no—
131C2—2444no—
132C2#2146164813yes—
subgroupG/H
centerC22#16840703
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C42×C61C4
socleC22×C61#379
prime radical, cosocleC24×D61C23
hypercenterC22×C42#6923
hypocenterC61#8545
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
6. C22×#11758196C4semidirect
8. C22×C42×C61C4semidirect
72. C22×C42#6923semidirect
75. C61#8545semidirect

Maximal subgroups

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

subgroupindex
#214617142
C22×#145197712
#854561