Finite Group Databasebeta

← #15765885

Subgroups — #15765885

Order 3328.

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 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#13119117C213yesmaximal
2#13114908C213yesmaximal
3C13×#1304C211yesmaximal, characteristic
4C22×C22⋊Dic13C2213yes—
5C13×#379C2213yes—
6#11718908C2211yescharacteristic
7#11718614—26no—
8#11718611—26no—
9#11718604—26no—
10#11718119—26no—
11C25×C13C2311yescharacteristic
12C23×Dic13D416yes—
13C2×C13×C22⋊C4—26no—
14C2×C13×C22⋊C4D416yes—
15C2×C22⋊Dic13—26no—
16C2×C22⋊Dic13—26no—
17C2×C22⋊Dic13—23no—
18C2×C22⋊Dic13—23no—
19C2×C22⋊Dic13—23no—
20C2×C4⋊Dic13—26no—
21#88071—26no—
22#88071—212no—
23#10339—131nomaximal, Sylow
24C24×C13—46no—
25C24×C13C2×D413yes—
26C24×C13C2×D413yes—
27C24×C13#4111yescharacteristic
28C22×C4×C13—26no—
29C22×Dic13—26no—
30C22×Dic13—26no—
31C22×Dic13—26no—
32C22×Dic13—412no—
33C22×Dic13—41no—
34C13×C22⋊C4—412no—
35C13×C22⋊C4—46no—
36C22⋊Dic13—43no—
37C22⋊Dic13—46no—
38C22⋊Dic13—43no—
39C22⋊Dic13—46no—
40C4⋊Dic13—86no—
41#2483—133no—
42#1819—133no—
43#1304D1311yescharacteristic
44C23×C13—212no—
45C23×C13—26no—
46C23×C13—43no—
47C23×C13—46no—
48C23×C13—43no—
49C23×C13—88no—
50C23×C13#12013yes—
51C23×C13#12113yes—
52C23×C13#12711yescharacteristic
53C2×C4×C13—412no—
54C2×C4×C13—46no—
55C2×Dic13—412no—
56C2×Dic13—46no—
57C2×Dic13—412no—
58C2×Dic13—86no—
59C2×Dic13—83no—
60C22×C22⋊C4—133no—
61#397—266no—
62#385—266no—
63#381—266no—
64#379—131no—
65#379C2×D1313yes—
66#342—266no—
67C22×C13—26no—
68C22×C13—26no—
69C22×C13—23no—
70C22×C13—23no—
71C22×C13—412no—
72C22×C13—86no—
73C22×C13—82no—
74C22×C13#39211yescharacteristic
75C22×C13#45816yes—
76C4×C13—86no—
77Dic13—86no—
78Dic13—161no—
79C25C22×D1311yescharacteristic
80C23×C4—136no—
81C2×C4⋊C4—266no—
82C2×C22⋊C4—26no—
83C2×C22⋊C4—263no—
84C2×C22⋊C4—266no—
85C2×C22⋊C4—266no—
86C2×C22⋊C4—263no—
87C2×C22⋊C4—263no—
88C2×C22⋊C4D5216yes—
89#95—266no—
90#95—2612no—
91C2×C13—26no—
92C2×C13—41no—
93C2×C13—43no—
94C2×C13#202213yes—
95C24—46no—
96C24C2×D5213yes—
97C24D4×D1313yes—
98C24#613111yescharacteristic
99C22×C4—26no—
100C22×C4—266no—
101C22×C4—266no—
102C22×C4—266no—
103C22×C4—5212no—
104C22×C4—521no—
105C4⋊C4—1046no—
106C22⋊C4—412no—
107C22⋊C4—46no—
108C22⋊C4—523no—
109C22⋊C4—523no—
110C22⋊C4—526no—
111C22⋊C4—526no—
112C13#1033911yescharacteristic, complemented, Sylow
113C23—212no—
114C23—26no—
115C23—43no—
116C23—46no—
117C23—43no—
118C23—88no—
119C23#8812811yescharacteristic
120C23#8813613yes—
121C23#8814913yes—
122C2×C4—412no—
123C2×C4—46no—
124C2×C4—5212no—
125C2×C4—5212no—
126C2×C4—526no—
127C2×C4—1046no—
128C2×C4—1043no—
129C22—26no—
130C22—23no—
131C22—26no—
132C22—23no—
133C22—412no—
134C22—86no—
135C22—82no—
136C22#1171833211yescharacteristic
137C22#1171840316yes—
138C4—86no—
139C4—1046no—
140C4—2081no—
141C2—26no—
142C2—41no—
143C2—43no—
144C2#1311596813yes—
subgroupG/H
centerC22#11718332
commutator, prime radical, cosocleC25×C13C23
FrattiniC25C22×D13
FittingC13×#1304C2
socleC22×C13#392
hypercenter#1304D13
hypocenterC13#10339
LCSG ▷ C25×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
112. C13#10339semidirect

Maximal subgroups

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

subgroupindex
#131191172
#131149082
C13×#13042
#1033913