Finite Group Databasebeta

← #13130740

Subgroups — #13130740

Order 1664.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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×C4⋊C4×D13C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic
3D13⋊(C22⋊C8)C211yesmaximal, characteristic
4#11718246C214yesmaximal, complemented
5C22×C4×D13—21no—
6C22×C4×D13C2211yescharacteristic
7C2×C22⋊#261—21no—
8C2×C4⋊#261C2212yes—
9C2×D13⋊C8C2212yes—
10C2×C13×C4⋊C4C411yescharacteristic, complemented
11C2×C4⋊Dic13C411yescharacteristic, complemented
12C2×#6101—21no—
13C4⋊C4×D13—21no—
14C4⋊C4×D13—21no—
15C4⋊C4×D13C412yescomplemented
16C4⋊C4×D13C2212yes—
17C22⋊#1057—21no—
18(C2×#261)⋊C4—21no—
19#88111—21no—
20C23×D13D411yescharacteristic
21C22×#261—22no—
22C22×C4×C13—21no—
23C22×C4×C13C2×C411yescharacteristic
24C22×Dic13—21no—
25C22×Dic13D411yescharacteristic
26C2×C4×D13—24no—
27C2×C4×D13—22no—
28C2×C4×D13—22no—
29C2×C4×D13—44no—
30C2×C4×D13C2×C411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13C2311yescharacteristic
34C22⋊#261—42no—
35C2×#1057—22no—
36C4⋊#261—24no—
37D13⋊C8—24no—
38C13×C4⋊C4—21no—
39C13×C4⋊C4C2×C412yes—
40C4⋊Dic13—21no—
41C4⋊Dic13C2×C412yes—
42#6101—22no—
43#6101—22no—
44#1824—131nomaximal, Sylow
45C23×C13C22⋊C411yescharacteristic
46C22×D13—22no—
47C22×D13—22no—
48C22×D13C22⋊C411yescharacteristic
49C22×D13SD1612yes—
50C22×D13Q1612yes—
51C22×D13C2×D411yescharacteristic
52C2×#261—42no—
53C2×#261—42no—
54C2×#261—42no—
55C2×C4×C13—22no—
56C2×C4×C13—22no—
57C2×C4×C13—42no—
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22×C411yescharacteristic
60C2×Dic13—22no—
61C2×Dic13—22no—
62C2×Dic13—42no—
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C2×D411yescharacteristic
65C4×D13—22no—
66C4×D13—22no—
67C4×D13—22no—
68C4×D13—44no—
69C4×D13—44no—
70C4×D13#4114yes—
71#1057—42no—
72C22×C4⋊C4—131no—
73C2×C22⋊C8—131no—
74#380—131no—
75#340—134no—
76C22×C13—21no—
77C22×C13—21no—
78C22×C13#10312yes—
79C22×C13C2×C22⋊C411yescharacteristic
80C2×D13—21no—
81C2×D13—21no—
82C2×D13—24no—
83C2×D13—24no—
84C2×D13#10312yes—
85C2×D13#12312yes—
86C2×D13C2×SD1611yescharacteristic
87C2×D13C2×Q1611yescharacteristic
88C2×D13AGL(1,ℤ/8)12yes—
89#261—82no—
90C4×C13—21no—
91C4×C13—42no—
92C4×C13#11712yes—
93Dic13—21no—
94Dic13—42no—
95Dic13#12312yes—
96C23×C4—131no—
97C23×C4—261no—
98C22×C8—132no—
99C2×C4⋊C4—131no—
100C2×C4⋊C4—132no—
101C2×C4⋊C4—132no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—261no—
104C2×C4⋊C4—261no—
105C2×C4⋊C4—261no—
106C2×C4⋊C4#26111yescharacteristic, complemented
107C2×C22⋊C4—261no—
108C22⋊C8—261no—
109C22⋊C8—261no—
110#95—261no—
111C2×C13—22no—
112C2×C13#38111yescharacteristic
113C2×C13C2×#10311yescharacteristic
114C2×C13#41811yescharacteristic
115D13—22no—
116D13#48112yes—
117D13#48412yes—
118C24—131no—
119C22×C4—21no—
120C22×C4—131no—
121C22×C4—131no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4—131no—
125C22×C4—264no—
126C22×C4—262no—
127C22×C4—262no—
128C22×C4—261no—
129C22×C4—262no—
130C22×C4—524no—
131C22×C4C2×#26111yescharacteristic
132C2×C8—262no—
133C2×C8—264no—
134C4⋊C4—21no—
135C4⋊C4—132no—
136C4⋊C4—262no—
137C4⋊C4—262no—
138C4⋊C4—264no—
139C4⋊C4—261no—
140C4⋊C4C2×#26112yes—
141C22⋊C4—522no—
142C13#182411yescharacteristic, complemented, Sylow
143C23—131no—
144C23—132no—
145C23—132no—
146C23—131no—
147C23—262no—
148C23—262no—
149C23C22⋊#26111yescharacteristic
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—131no—
154C2×C4—134no—
155C2×C4—131no—
156C2×C4—262no—
157C2×C4—262no—
158C2×C4—262no—
159C2×C4—262no—
160C2×C4—262no—
161C2×C4—524no—
162C2×C4—524no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4—522no—
167C2×C4C22⋊#26111yescharacteristic
168C2×C4C22×#26111yescharacteristic
169C8—522no—
170C22—21no—
171C22—21no—
172C22—132no—
173C22—132no—
174C22—131no—
175C22—131no—
176C22—132no—
177C22—264no—
178C22—264no—
179C22—261no—
180C22—261no—
181C22#8811712yes—
182C22C2×C22⋊#26111yescharacteristic
183C4—21no—
184C4—42no—
185C4—132no—
186C4—261no—
187C4—522no—
188C4—1042no—
189C4#8823712yes—
190C2—22no—
191C2—132no—
192C2—132no—
193C2—262no—
194C2#1171913511yescharacteristic
195C2#1171913811yescharacteristic
196C2C2×#8811711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1824
LCSG ▷ C2×C4×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
4. #11718246C2semidirect
10. C2×C13×C4⋊C4C4semidirect
11. C2×C4⋊Dic13C4semidirect
15. C4⋊C4×D13C4semidirect
106. C2×C4⋊C4#261semidirect
142. C13#1824semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D132
#117191362
D13⋊(C22⋊C8)2
#117182462
#182413