Finite Group Databasebeta

← #13130113

Subgroups — #13130113

Order 1664.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C2×#88149C211yesmaximal, characteristic
2#11719127C211yesmaximal, characteristic, complemented
3D13⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#11718287C214yesmaximal, complemented
5C22×D52C412yes—
6C22×D52C411yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×#6118—21no—
9C2×D13⋊C8—21no—
10C2×C13×C4⋊C4C411yescharacteristic
11C2×#6103C2212yes—
12#88149—21no—
13#88149—21no—
14#88149—21no—
15#88149—21no—
16C22⋊#1057C2212yes—
17C22⋊#1057C2212yes—
18#88111—21no—
19#88111—21no—
20C23×D13C2×C411yescharacteristic
21C23×D13C2×C412yes—
22C22×C4×C13C2×C412yes—
23C22×C4×C13C2×C411yescharacteristic
24C22×Dic13C2311yescharacteristic
25C2×D52—22no—
26C2×D52—22no—
27C2×D52—21no—
28C2×D52—21no—
29C2×D52—42no—
30C2×D52—44no—
31C2×C4×D13—42no—
32C2×C4×D13D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×#1057—22no—
37C2×#1057—22no—
38#6118—42no—
39D13⋊C8—42no—
40C13×C4⋊C4—21no—
41C13×C4⋊C4—21no—
42#6103—22no—
43#6103—22no—
44#1471—131nomaximal, Sylow
45C23×C13C22×C411yescharacteristic
46C22×D13—22no—
47C22×D13—22no—
48C22×D13—22no—
49C22×D13—24no—
50C22×D13—41no—
51C22×D13—42no—
52C22×D13—42no—
53C22×D13C22⋊C411yescharacteristic
54C22×D13C22⋊C411yescharacteristic
55C2×C4×C13—22no—
56C2×C4×C13—22no—
57C2×C4×C13—42no—
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22⋊C411yescharacteristic
60C2×Dic13—41no—
61C2×Dic13C2×D411yescharacteristic
62C2×Dic13C2×D411yescharacteristic
63D52—42no—
64D52—44no—
65D52—44no—
66D52—42no—
67C4×D13—22no—
68C4×D13—22no—
69C4×D13—41no—
70C4×D13—41no—
71#1057—42no—
72#1057—42no—
73C2×#121—131no—
74#407—131no—
75C2×C22⋊C8—131no—
76#323—134no—
77C22×C13—21no—
78C22×C13—21no—
79C22×C13C2×C22⋊C411yescharacteristic
80C22×C13#13112yes—
81C2×D13—21no—
82C2×D13—21no—
83C2×D13—21no—
84C2×D13—21no—
85C2×D13—21no—
86C2×D13—44no—
87C2×D13—42no—
88C2×D13—42no—
89C2×D13—42no—
90C2×D13—84no—
91C2×D13#10012yes—
92C4×C13—21no—
93C4×C13—42no—
94C4×C13#9912yes—
95Dic13—21no—
96Dic13—21no—
97C22×D4—132no—
98C22×D4—131no—
99C23×C4—131no—
100C2×M16—261no—
101C22×C8—261no—
102#121—261no—
103#121—261no—
104#121—261no—
105#121—261no—
106C2×C4⋊C4#26111yescharacteristic
107C2×C22⋊C4—132no—
108C22⋊C8—132no—
109C22⋊C8—132no—
110C22⋊C8—261no—
111C22⋊C8—261no—
112C2×C13—22no—
113C2×C13#40811yescharacteristic
114C2×C13C2×#9911yescharacteristic
115C2×C13C2×#10011yescharacteristic
116D13—22no—
117D13—41no—
118D13—82no—
119C24—131no—
120C24—132no—
121C2×D4—262no—
122C2×D4—262no—
123C2×D4—261no—
124C2×D4—261no—
125C2×D4—522no—
126C2×D4—524no—
127C22×C4—131no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—131no—
131C22×C4—131no—
132C22×C4—522no—
133C22×C4C2×#26112yes—
134C22×C4C2×#26111yescharacteristic
135M16—522no—
136C2×C8—262no—
137C2×C8—262no—
138C2×C8—522no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C22⋊C4—262no—
142C22⋊C4—262no—
143C13#147111yescharacteristic, complemented, Sylow
144C23—131no—
145C23—131no—
146C23—262no—
147C23—262no—
148C23—262no—
149C23—264no—
150C23—521no—
151C23—522no—
152C23—522no—
153C23C22×#26111yescharacteristic
154D4—522no—
155D4—524no—
156D4—524no—
157D4—522no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—521no—
166C2×C4—521no—
167C2×C4—521no—
168C2×C4C22⋊#26111yescharacteristic
169C2×C4C22⋊#26111yescharacteristic
170C8—522no—
171C8—522no—
172C22—21no—
173C22—21no—
174C22—132no—
175C22—261no—
176C22—261no—
177C22—261no—
178C22—261no—
179C22—261no—
180C22—524no—
181C22—522no—
182C22—522no—
183C22—522no—
184C22—1044no—
185C22#8824012yes—
186C22C2×C22⋊#26111yescharacteristic
187C4—21no—
188C4—42no—
189C4—261no—
190C4—261no—
191C4#8810712yes—
192C2—22no—
193C2—262no—
194C2—521no—
195C2—1042no—
196C2C2×#8810711yescharacteristic
197C2D13⋊#10011yescharacteristic
198C2#1171915911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#88149C2
cosocleC22×Dic13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1471
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11719127C2semidirect
3. D13⋊(C22⋊C8)C2semidirect
4. #11718287C2semidirect
143. C13#1471semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
#117191272
D13⋊(C22⋊C8)2
#117182872
#147113