Finite Group Databasebeta

← #16782426

Subgroups — #16782426

Order 3328.

422 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 148 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#13130772C212yesmaximal
2#13130757C214yesmaximal
3C82×D13C211yesmaximal, characteristic
4C2×#88102—24no—
5#11719059C2214yes—
6C4×C8×D13C2212yes—
7C4×C8×D13C2211yescharacteristic
8#11718265—28no—
9C82×C13C411yescharacteristic, complemented
10C8×#1055C412yescomplemented
11C8×#1055C411yescharacteristic, complemented
12C2×C4⋊#261—28no—
13C2×C4⋊#261—24no—
14C2×C8×D13D414yes—
15C2×C8×D13D412yes—
16C42×D13C2311yescharacteristic
17#88102—48no—
18C4×C8×C13C2×C412yes—
19C4×C8×C13C2×C411yescharacteristic
20C8×Dic13Q814yes—
21C8×Dic13Q812yes—
22C4×#1055C2×C412yes—
23C4×#1055C2×C411yescharacteristic
24#8816—131nomaximal, Sylow
25C22×#261—44no—
26C2×C4×D13C2×D411yescharacteristic
27C2×C4×D13C2×D412yes—
28C4⋊#261—48no—
29C4⋊#261—416no—
30C2×C8×C13C4⋊C414yes—
31C2×C8×C13C4⋊C412yes—
32C42×C13C22×C411yescharacteristic
33C4×Dic13C2×Q811yescharacteristic
34C4×Dic13C2×Q812yes—
35C2×#1055C4⋊C414yes—
36C2×#1055C4⋊C412yes—
37C8×D13—28no—
38C8×D13D814yes—
39C8×D13Q1614yes—
40#1845—132no—
41#1834—134no—
42C2×C82—131no—
43C22×D13#12711yescharacteristic
44C2×#261—84no—
45C2×#261—88no—
46C2×C4×C13C2×C4⋊C411yescharacteristic
47C2×C4×C13C2×C4⋊C412yes—
48C2×Dic13C4⋊Q812yes—
49C2×Dic13C4⋊Q811yescharacteristic
50C4×D13C2×D812yes—
51C4×D13C2×Q1612yes—
52C4×D13#13518yes—
53C8×C13—24no—
54C8×C13#10714yes—
55#1055—24no—
56#1055#10714yes—
57C2×#107—264no—
58C2×C4×C8—132no—
59C2×C4×C8—131no—
60#384—134no—
61#340—268no—
62C82—132no—
63C82—131no—
64C82#26111yescharacteristic, complemented
65C22×C13#38411yescharacteristic
66C2×D13#49311yescharacteristic
67C2×D13#49411yescharacteristic
68C2×D13#49514yes—
69#261—164no—
70C4×C13C2×#10712yes—
71C4×C13#42714yes—
72Dic13#49914yes—
73Dic13#50012yes—
74C22×C8—132no—
75C22×C8—134no—
76C2×C4⋊C4—268no—
77C2×C4⋊C4—264no—
78C2×C42—131no—
79#107—528no—
80C4×C8—132no—
81C4×C8—134no—
82C4×C8—131no—
83C4×C8—132no—
84C4×C8C2×#26112yes—
85C4×C8C2×#26111yescharacteristic
86C2×C13#184511yescharacteristic
87C2×C13#184612yes—
88D13#170912yes—
89D13#171012yes—
90C22×C4—131no—
91C22×C4—132no—
92C22×C4—524no—
93C2×C8—132no—
94C2×C8—134no—
95C2×C8—134no—
96C2×C8—134no—
97C2×C8—268no—
98C2×C8C4⋊#26114yes—
99C2×C8C4⋊#26112yes—
100C4⋊C4—528no—
101C4⋊C4—5216no—
102C42—131no—
103C42—132no—
104C42C22×#26111yescharacteristic
105C13#881611yescharacteristic, complemented, Sylow
106C23—131no—
107C2×C4—131no—
108C2×C4—132no—
109C2×C4—132no—
110C2×C4—132no—
111C2×C4—138no—
112C2×C4—1044no—
113C2×C4—1048no—
114C2×C4C2×C4⋊#26111yescharacteristic
115C2×C4C2×C4⋊#26112yes—
116C8—24no—
117C8—134no—
118C8—264no—
119C8#8810214yes—
120C22—131no—
121C22—131no—
122C22—134no—
123C22#1171905911yescharacteristic
124C4—132no—
125C4—134no—
126C4—2084no—
127C4C2×#8810212yes—
128C4#1171909214yes—
129C2—132no—
130C2—132no—
131C2#1313077211yescharacteristic
132C2#1313077312yes—
subgroupG/H
centerC22#11719059
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC82×C13C4
socleC22×C13#384
prime radicalC22×D13#127
cosocleC42×D13C23
hypercenterC82#261
hypocenterC13#8816
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82

Complements

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

NH ≅ G/Ntype
9. C82×C13C4semidirect
10. C8×#1055C4semidirect
11. C8×#1055C4semidirect
64. C82#261semidirect
105. C13#8816semidirect

Maximal subgroups

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

subgroupindex
#131307722
#131307572
C82×D132
#881613