Finite Group Databasebeta

← #13130093

Subgroups — #13130093

Order 1664.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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×D52C211yesmaximal, characteristic
2#11719127C212yesmaximal, complemented
3#11718287C212yesmaximal, complemented
4#11718285C212yesmaximal, complemented
5C22×D52C411yescharacteristic
6C22×C4×D13C411yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×#6118—22no—
9C2×C42×C13C411yescharacteristic
10C2×#6103C411yescharacteristic
11C2×#6103C2211yescharacteristic
12C2×C4⋊Dic13C2211yescharacteristic
13C4×D52—22no—
14C4×D52—22no—
15C22⋊#1057C2214yes—
16#88111—22no—
17C23×D13C2×C411yescharacteristic
18C23×D13C2×C411yescharacteristic
19C22×C4×C13C2×C411yescharacteristic
20C22×C4×C13C2×C411yescharacteristic
21C22×C4×C13C2×C411yescharacteristic
22C22×Dic13C2×C411yescharacteristic
23C22×Dic13C2311yescharacteristic
24C2×D52—22no—
25C2×D52—22no—
26C2×D52—22no—
27C2×C4×D13—21no—
28C2×C4×D13—21no—
29C2×C4×D13—42no—
30C2×C4×D13—42no—
31C2×C4×D13D412yes—
32C2×C4×D13D412yes—
33C2×#1057—24no—
34#6118—44no—
35C42×C13—21no—
36C42×C13—21no—
37#6103—22no—
38#6103—22no—
39C4⋊Dic13—22no—
40#1465—131nomaximal, Sylow
41C23×C13C22×C411yescharacteristic
42C22×D13—21no—
43C22×D13—21no—
44C22×D13—21no—
45C22×D13—21no—
46C22×D13—41no—
47C22×D13—41no—
48C22×D13—41no—
49C22×D13—41no—
50C22×D13C22⋊C412yes—
51C22×D13M1612yescomplemented
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13—22no—
55C2×C4×C13—21no—
56C2×C4×C13—41no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13M1612yescomplemented
60C2×Dic13—21no—
61C2×Dic13—41no—
62C2×Dic13—41no—
63C2×Dic13C2×D412yes—
64D52—28no—
65C4×D13—24no—
66C4×D13—42no—
67C4×D13—42no—
68C4×D13—42no—
69#1057—44no—
70C2×C4×D4—131no—
71#407—132no—
72#324—132no—
73#323—132no—
74C22×C13—21no—
75C22×C13—21no—
76C22×C13C2×C22⋊C411yescharacteristic
77C22×C13C2×M1611yescharacteristic
78C22×C13C2×M1611yescharacteristic
79C2×D13—22no—
80C2×D13—22no—
81C2×D13—22no—
82C2×D13—22no—
83C2×D13—42no—
84C2×D13—42no—
85C2×D13—42no—
86C2×D13—41no—
87C2×D13—41no—
88C2×D13—42no—
89C4×C13—22no—
90C4×C13—21no—
91C4×C13—41no—
92C4×C13#9912yes—
93Dic13—22no—
94Dic13—41no—
95C22×D4—131no—
96C23×C4—131no—
97C23×C4—131no—
98C2×M16—262no—
99C4×D4—262no—
100C4×D4—262no—
101C2×C4⋊C4—131no—
102C2×C22⋊C4—131no—
103C2×C22⋊C4—131no—
104C2×C42#26111yescharacteristic
105C22⋊C8—134no—
106C22⋊C8—262no—
107C2×C13—21no—
108C2×C13—21no—
109C2×C13#40711yescharacteristic
110C2×C13C2×#9911yescharacteristic
111C2×C13#41311yescharacteristic
112D13—42no—
113D13—42no—
114C24—131no—
115C24—131no—
116C2×D4—262no—
117C2×D4—262no—
118C2×D4—262no—
119C22×C4—131no—
120C22×C4—132no—
121C22×C4—132no—
122C22×C4—131no—
123C22×C4—261no—
124C22×C4—261no—
125C22×C4—522no—
126C22×C4—522no—
127C22×C4C2×#26111yescharacteristic
128C22×C4C2×#26111yescharacteristic
129C22×C4C2×#26111yescharacteristic
130M16—524no—
131C2×C8—264no—
132C4⋊C4—262no—
133C22⋊C4—262no—
134C22⋊C4—262no—
135C42—21no—
136C42—21no—
137C13#146511yescharacteristic, complemented, Sylow
138C23—132no—
139C23—132no—
140C23—261no—
141C23—261no—
142C23—261no—
143C23—261no—
144C23—521no—
145C23—521no—
146C23—521no—
147C23—521no—
148C23C22×#26111yescharacteristic
149D4—268no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—132no—
156C2×C4—264no—
157C2×C4—261no—
158C2×C4—522no—
159C2×C4—522no—
160C2×C4—521no—
161C2×C4—522no—
162C2×C4—521no—
163C2×C4#611812yescomplemented
164C2×C4C22⋊#26111yescharacteristic
165C2×C4C22⋊#26111yescharacteristic
166C8—524no—
167C22—21no—
168C22—21no—
169C22—262no—
170C22—262no—
171C22—262no—
172C22—262no—
173C22—522no—
174C22—522no—
175C22—522no—
176C22—522no—
177C22—521no—
178C22—521no—
179C22C2×#611811yescharacteristic
180C22D13⋊M1611yescharacteristic
181C22C2×C22⋊#26111yescharacteristic
182C4—21no—
183C4—22no—
184C4—41no—
185C4—262no—
186C4—521no—
187C4#8810712yes—
188C2—21no—
189C2—21no—
190C2—522no—
191C2—522no—
192C2C2×#8810711yescharacteristic
193C2#1171912711yescharacteristic
194C2#1171913211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C42×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D52C4
cosocleC22×Dic13C23
hypercenterC2×C42#261
hypocenterC13#1465
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11719127C2semidirect
3. #11718287C2semidirect
4. #11718285C2semidirect
51. C22×D13M16semidirect
59. C2×C4×C13M16semidirect
137. C13#1465semidirect
163. C2×C4#6118semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D522
#117191272
#117182872
#117182852
#146513