Finite Group Databasebeta

← #13130085

Subgroups — #13130085

Order 1664.

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

normal subgroups only

This group has 312 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⋊C4×D13C211yesmaximal, characteristic
2#11719127C212yesmaximal
3#11718286C212yesmaximal, complemented
4#11718285C212yesmaximal, complemented
5C22×C4×D13C411yescharacteristic
6C22×C4×D13C411yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×#6118—22no—
9C2×C13×C4⋊C4C411yescharacteristic
10C2×C4⋊Dic13C2211yescharacteristic
11C2×#6101C411yescharacteristic
12C2×#6101C2211yescharacteristic
13C4⋊C4×D13—22no—
14C4⋊C4×D13—22no—
15C22⋊#1057C2214yes—
16#88111—22no—
17C23×D13C2×C411yescharacteristic
18C22×C4×C13C2×C411yescharacteristic
19C22×C4×C13C2×C411yescharacteristic
20C22×C4×C13C2×C411yescharacteristic
21C22×Dic13C2×C411yescharacteristic
22C22×Dic13C2×C411yescharacteristic
23C22×Dic13C2311yescharacteristic
24C2×C4×D13—21no—
25C2×C4×D13—21no—
26C2×C4×D13—22no—
27C2×C4×D13—22no—
28C2×C4×D13—21no—
29C2×C4×D13—21no—
30C2×C4×D13—42no—
31C2×C4×D13—42no—
32C2×C4×D13D412yes—
33C2×C4×D13D412yes—
34C2×#1057—24no—
35#6118—44no—
36C13×C4⋊C4—22no—
37C4⋊Dic13—22no—
38#6101—22no—
39#6101—22no—
40#1463—131nomaximal, Sylow
41C23×C13C22×C411yescharacteristic
42C22×D13—21no—
43C22×D13—21no—
44C22×D13—22no—
45C22×D13—22no—
46C22×D13C22⋊C411yescharacteristic
47C22×D13C22⋊C411yescharacteristic
48C2×C4×C13—21no—
49C2×C4×C13—21no—
50C2×C4×C13—21no—
51C2×C4×C13—41no—
52C2×C4×C13—41no—
53C2×C4×C13C22⋊C412yes—
54C2×C4×C13M1612yescomplemented
55C2×Dic13—21no—
56C2×Dic13—21no—
57C2×Dic13—21no—
58C2×Dic13—41no—
59C2×Dic13—41no—
60C2×Dic13M1612yescomplemented
61C2×Dic13C2×D412yes—
62C4×D13—24no—
63C4×D13—24no—
64C4×D13—24no—
65C4×D13—42no—
66C4×D13—42no—
67C4×D13—42no—
68#1057—44no—
69C22×C4⋊C4—131no—
70#407—132no—
71#324—132no—
72#324—132no—
73C22×C13—21no—
74C22×C13—21no—
75C22×C13C2×C22⋊C411yescharacteristic
76C22×C13C2×M1611yescharacteristic
77C22×C13C2×M1611yescharacteristic
78C2×D13—24no—
79C2×D13—24no—
80C2×D13—21no—
81C2×D13—21no—
82C2×D13—21no—
83C2×D13—21no—
84C2×D13#9912yes—
85C2×D13#10112yes—
86C4×C13—22no—
87C4×C13—22no—
88C4×C13—41no—
89Dic13—22no—
90Dic13—22no—
91Dic13—41no—
92C23×C4—131no—
93C23×C4—131no—
94C23×C4—131no—
95C2×M16—262no—
96C2×C4⋊C4—131no—
97C2×C4⋊C4—131no—
98C2×C4⋊C4—131no—
99C2×C4⋊C4—262no—
100C2×C4⋊C4—262no—
101C2×C4⋊C4#26111yescharacteristic
102C22⋊C8—134no—
103C22⋊C8—262no—
104C2×C13—21no—
105C2×C13—21no—
106C2×C13#40711yescharacteristic
107C2×C13C2×#9911yescharacteristic
108C2×C13C2×#10111yescharacteristic
109D13—22no—
110D13—22no—
111C24—131no—
112C22×C4—131no—
113C22×C4—131no—
114C22×C4—132no—
115C22×C4—132no—
116C22×C4—131no—
117C22×C4—262no—
118C22×C4—261no—
119C22×C4—261no—
120C22×C4—261no—
121C22×C4—261no—
122C22×C4—262no—
123C22×C4—522no—
124C22×C4—522no—
125C22×C4C2×#26111yescharacteristic
126C22×C4C2×#26111yescharacteristic
127C22×C4C2×#26111yescharacteristic
128M16—524no—
129C2×C8—264no—
130C4⋊C4—22no—
131C4⋊C4—262no—
132C4⋊C4—262no—
133C4⋊C4—262no—
134C13#146311yescharacteristic, complemented, Sylow
135C23—131no—
136C23—131no—
137C23—262no—
138C23—262no—
139C23—261no—
140C23—261no—
141C23C22×#26111yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—132no—
148C2×C4—132no—
149C2×C4—264no—
150C2×C4—264no—
151C2×C4—264no—
152C2×C4—261no—
153C2×C4—261no—
154C2×C4—261no—
155C2×C4—522no—
156C2×C4—522no—
157C2×C4—522no—
158C2×C4—521no—
159C2×C4—521no—
160C2×C4#611812yescomplemented
161C2×C4C22⋊#26112yes—
162C8—524no—
163C22—21no—
164C22—21no—
165C22—132no—
166C22—132no—
167C22—264no—
168C22—264no—
169C22—261no—
170C22—261no—
171C22—261no—
172C22—261no—
173C22C2×#611811yescharacteristic
174C22D13⋊M1611yescharacteristic
175C22C2×C22⋊#26111yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—262no—
180C4—262no—
181C4—521no—
182C2—21no—
183C2—21no—
184C2—262no—
185C2—262no—
186C2#1171912711yescharacteristic
187C2D13⋊#9911yescharacteristic
188C2D13⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13C2×C4
cosocleC22×Dic13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1463
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
3. #11718286C2semidirect
4. #11718285C2semidirect
54. C2×C4×C13M16semidirect
60. C2×Dic13M16semidirect
134. C13#1463semidirect
160. 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⋊C4×D132
#117191272
#117182862
#117182852
#146313