Finite Group Databasebeta

← #16786496

Subgroups — #16786496

Order 3328.

702 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 154 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
1D13⋊#430C213yesmaximal
2#13130498C213yesmaximal
3D13×#338C211yesmaximal, characteristic
4C22×C4×#261C2211yescharacteristic
5C2×D13⋊M16C2213yes—
6C2×M16×D13C2213yes—
7#11719100—212no—
8D13⋊#108—26no—
9(C2×#261)⋊C8—26no—
10C13×#338C411yescharacteristic, complemented
11#11718152C413yescomplemented
12C23×#261Q812yes—
13C22×C4×D13C2311yescharacteristic
14C2×#6122—23no—
15C2×C4×#261—23no—
16C2×C4×#261—23no—
17D13⋊M16—26no—
18D13⋊M16—26no—
19C2×#6118D416yes—
20C2×D13⋊C8—23no—
21C2×C13×M16C2×C413yes—
22C2×#6099C2×C413yes—
23M16×D13—26no—
24M16×D13—26no—
25C2×#6094Q816yes—
26C2×C8×D13D416yes—
27#88104—212no—
28#88103—212no—
29#11338—131nomaximal, Sylow
30C23×D13C2×Q811yescharacteristic
31C22×#261—26no—
32C22×#261—44no—
33C22×C4×C13C22×C411yescharacteristic
34C22×Dic13#4111yescharacteristic
35C2×C4×D13C2×D413yes—
36C2×C4×D13C2×D413yes—
37C2×C4×D13C2×Q813yes—
38C2×C4×D13#4113yes—
39#6122—46no—
40C2×#1057—26no—
41C4×#261—43no—
42C4×#261—41no—
43#6118—212no—
44D13⋊C8—43no—
45D13⋊C8—43no—
46C13×M16—26no—
47C2×C8×C13C4⋊C416yes—
48#6099—26no—
49C2×#1055C4⋊C416yes—
50#6094—212no—
51C8×D13—26no—
52C8×D13—26no—
53C2×#430—133no—
54C2×#338—131no—
55#1728—133no—
56C23×C13C4×Q811yescharacteristic
57C22×D13—42no—
58C22×D13C22⋊Q813yes—
59C22×D13C4⋊Q813yes—
60C2×#261—212no—
61C2×#261—46no—
62C2×#261—42no—
63C2×C4×C13C2×C4⋊C413yes—
64C2×C4×C13C4×D413yes—
65C2×Dic13#12113yes—
66C2×Dic13#12513yes—
67C4×D13#12013yes—
68C4×D13C22⋊Q816yes—
69C4×D13#12313yes—
70C4×D13#12711yescharacteristic
71C4×D13C4⋊Q813yes—
72#1057—46no—
73C8×C13—26no—
74#1055—26no—
75C22×M16—133no—
76C22×M16—133no—
77C22×C42—131no—
78#430—2612no—
79C2×#108—266no—
80#338—133no—
81#338#26111yescharacteristic, complemented
82#336—266no—
83C22×C13—41no—
84C22×C13#38913yes—
85C2×D13—26no—
86C2×D13—43no—
87C2×D13#39513yes—
88C2×D13#39911yescharacteristic
89#261—44no—
90C4×C13#38411yescharacteristic
91C4×C13#38513yes—
92Dic13#39211yescharacteristic
93Dic13#39813yes—
94C23×C4—131no—
95C23×C4—132no—
96C2×M16—133no—
97C2×M16—136no—
98C2×M16—136no—
99C2×M16—266no—
100C2×M16—266no—
101C2×M16—263no—
102C2×M16—266no—
103C2×M16—266no—
104C2×M16C2×#26113yes—
105C22×C8—136no—
106C22×C8—263no—
107C2×C42—263no—
108C2×C42—263no—
109#108—2612no—
110#108—2612no—
111C2×C13—23no—
112C2×C13#144411yescharacteristic
113D13—23no—
114D13#209112yes—
115C24—131no—
116C22×C4—131no—
117C22×C4—133no—
118C22×C4—133no—
119C22×C4—133no—
120C22×C4—133no—
121C22×C4—266no—
122C22×C4—524no—
123C22×C4C22×#26111yescharacteristic
124M16—26no—
125M16—2612no—
126M16—266no—
127M16—2612no—
128M16—526no—
129C2×C8—136no—
130C2×C8—266no—
131C2×C8—266no—
132C2×C8—266no—
133C2×C8—523no—
134C2×C8—523no—
135C2×C8C4⋊#26116yes—
136C42—521no—
137C42—523no—
138C13#1133811yescharacteristic, complemented, Sylow
139C23—133no—
140C23—133no—
141C23—522no—
142C23Q8×#26111yescharacteristic
143C2×C4—133no—
144C2×C4—133no—
145C2×C4—131no—
146C2×C4—133no—
147C2×C4—133no—
148C2×C4—133no—
149C2×C4—136no—
150C2×C4—2612no—
151C2×C4—522no—
152C2×C4—526no—
153C2×C4C2×C4⋊#26113yes—
154C2×C4D4×#26113yes—
155C8—26no—
156C8—266no—
157C8—526no—
158C22—41no—
159C22—131no—
160C22—133no—
161C22—266no—
162C22—523no—
163C22#1171908313yes—
164C4—131no—
165C4—133no—
166C4—524no—
167C4#1171905911yescharacteristic
168C4#1171907013yes—
169C2—23no—
170C2—132no—
171C2—263no—
172C2#1313002411yescharacteristic
subgroupG/H
centerC4#11719059
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#338C4
socleC2×C13#1444
prime radicalC23×D13C2×Q8
cosocleC22×C4×D13C23
hypercenter#338#261
hypocenterC13#11338
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #338

Complements

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

NH ≅ G/Ntype
10. C13×#338C4semidirect
11. #11718152C4semidirect
81. #338#261semidirect
138. C13#11338semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4302
#131304982
D13×#3382
#1133813