Finite Group Databasebeta

← #13130744

Subgroups — #13130744

Order 1664.

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

normal subgroups only

This group has 306 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
1D13×#117C211yesmaximal, characteristic
2C4×C22⋊#261C211yesmaximal, characteristic
3#11719127C211yesmaximal, characteristic
4#11718247C212yesmaximal, complemented
5#11718247C212yesmaximal, complemented
6C22×C4×D13C2211yescharacteristic
7C2×C22⋊#261—21no—
8C2×C4×#261C2212yes—
9C2×#6118C2212yes—
10C13×#117C411yescharacteristic, complemented
11#88180C411yescharacteristic, complemented
12#88146C2211yescharacteristic
13#88146C2211yescharacteristic
14C4⋊C4×D13C411yescharacteristic, complemented
15C4⋊C4×D13C411yescharacteristic, complemented
16C22⋊C4×D13—21no—
17#88131—21no—
18#88126—21no—
19C42×D13—21no—
20C22⋊#1057—21no—
21(C2×#261)⋊C4—21no—
22#88111—21no—
23C23×D13D411yescharacteristic
24C22×#261—22no—
25C22×C4×C13C2×C411yescharacteristic
26C22×Dic13D411yescharacteristic
27C2×C4×D13—24no—
28C2×C4×D13—21no—
29C2×C4×D13—21no—
30C2×C4×D13C2×C411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13C2311yescharacteristic
34C22⋊#261—24no—
35C2×#1057—22no—
36C4×#261—24no—
37#6118—24no—
38C13×C4⋊C4C2×C411yescharacteristic
39C13×C4⋊C4C2×C411yescharacteristic
40C13×C22⋊C4—21no—
41C42×C13—21no—
42C22⋊Dic13—21no—
43#6103—21no—
44#6103—21no—
45C4⋊Dic13C2×C411yescharacteristic
46C4⋊Dic13C2×C411yescharacteristic
47#6101—21no—
48#6101—21no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51C4×Dic13—21no—
52#1826—131nomaximal, Sylow
53C23×C13C22⋊C411yescharacteristic
54C22×D13—22no—
55C22×D13—22no—
56C22×D13—41no—
57C22×D13C22⋊C411yescharacteristic
58C22×D13C2×D411yescharacteristic
59C2×#261—24no—
60C2×#261—42no—
61C2×#261—42no—
62C2×C4×C13—22no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13C22⋊C411yescharacteristic
66C2×C4×C13C22×C411yescharacteristic
67C2×Dic13—22no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13C22⋊C411yescharacteristic
71C2×Dic13C2×D411yescharacteristic
72C4×D13—22no—
73C4×D13—22no—
74C4×D13—22no—
75C4×D13—42no—
76C4×D13—42no—
77C4×D13#4114yes—
78#1057—42no—
79C2×#117—131no—
80#407—131no—
81C4×C22⋊C4—131no—
82#339—132no—
83#339—132no—
84C22×C13—21no—
85C22×C13—21no—
86C22×C13—21no—
87C22×C13C2×C22⋊C411yescharacteristic
88C2×D13—21no—
89C2×D13—21no—
90C2×D13—21no—
91C2×D13—21no—
92C2×D13—44no—
93C2×D13#10412yes—
94C2×D13#12312yes—
95#261—44no—
96C4×C13—21no—
97C4×C13—41no—
98C4×C13—41no—
99C4×C13#11712yes—
100Dic13—21no—
101Dic13—41no—
102Dic13—41no—
103Dic13#12312yes—
104C23×C4—131no—
105C2×M16—132no—
106#117—131no—
107#117—131no—
108#117—131no—
109#117—261no—
110#117—261no—
111#117#26111yescharacteristic, complemented
112C2×C4⋊C4—131no—
113C2×C4⋊C4—131no—
114C2×C22⋊C4—261no—
115C2×C22⋊C4—261no—
116C2×C42—132no—
117C2×C42—261no—
118C22⋊C8—261no—
119C22⋊C8—261no—
120#95—261no—
121C2×C13—41no—
122C2×C13#38111yescharacteristic
123C2×C13C2×#10411yescharacteristic
124C2×C13#42111yescharacteristic
125D13—22no—
126D13—22no—
127C24—131no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—131no—
131C22×C4—131no—
132C22×C4—131no—
133C22×C4—264no—
134C22×C4—261no—
135C22×C4—261no—
136C22×C4—262no—
137C22×C4C2×#26111yescharacteristic
138M16—264no—
139C2×C8—262no—
140C4⋊C4—131no—
141C4⋊C4—131no—
142C4⋊C4—261no—
143C4⋊C4—261no—
144C4⋊C4C2×#26111yescharacteristic
145C4⋊C4C2×#26111yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—261no—
148C22⋊C4—261no—
149C22⋊C4—264no—
150C22⋊C4—261no—
151C42—21no—
152C42—261no—
153C42—261no—
154C42—264no—
155C42—261no—
156C13#182611yescharacteristic, complemented, Sylow
157C23—131no—
158C23—131no—
159C23—262no—
160C23—262no—
161C23—521no—
162C23C22⋊#26111yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—131no—
167C2×C4—134no—
168C2×C4—131no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—264no—
174C2×C4—261no—
175C2×C4—261no—
176C2×C4—522no—
177C2×C4—522no—
178C2×C4—522no—
179C2×C4—522no—
180C2×C4C22⋊#26111yescharacteristic
181C2×C4C22×#26111yescharacteristic
182C8—522no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—132no—
187C22—132no—
188C22—261no—
189C22—261no—
190C22—261no—
191C22—261no—
192C22—524no—
193C22C2×C22⋊#26111yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—132no—
198C4—261no—
199C4—524no—
200C4—521no—
201C4—521no—
202C4#8823712yes—
203C2—41no—
204C2—262no—
205C2—262no—
206C2#1171913511yescharacteristic
207C2D13⋊#10411yescharacteristic
208C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#117C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenter#117#261
hypocenterC13#1826
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11718247C2semidirect
5. #11718247C2semidirect
10. C13×#117C4semidirect
11. #88180C4semidirect
14. C4⋊C4×D13C4semidirect
15. C4⋊C4×D13C4semidirect
111. #117#261semidirect
156. C13#1826semidirect

Maximal subgroups

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

subgroupindex
D13×#1172
C4×C22⋊#2612
#117191272
#117182472
#182613