Finite Group Databasebeta

← #13130117

Subgroups — #13130117

Order 1664.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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×#88133C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic, complemented
3#11719125C211yesmaximal, characteristic, complemented
4#11718305C212yesmaximal
5#11718285C212yesmaximal, complemented
6C2×C13×C22⋊C4C411yescharacteristic
7C2×C22⋊Dic13C411yescharacteristic
8C2×C22⋊Dic13C2211yescharacteristic
9C2×C4⋊Dic13C2211yescharacteristic
10C2×#6101C411yescharacteristic
11C2×#6101C411yescharacteristic
12C2×C4×Dic13C2211yescharacteristic
13#88133—21no—
14#88133—21no—
15#88133—21no—
16#88133—21no—
17C22⋊#1057C2212yes—
18C22⋊#1057C2212yes—
19#88112—21no—
20#88110—21no—
21C4⋊#1057—21no—
22C4×#1057—21no—
23C24×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C22×C4×C13C2×C411yescharacteristic
26C22×Dic13C2×C411yescharacteristic
27C22×Dic13C2×C411yescharacteristic
28C22×Dic13C2×C411yescharacteristic
29C22×Dic13C2311yescharacteristic
30C2×#1057—22no—
31C2×#1057—22no—
32C13×C22⋊C4—21no—
33C13×C22⋊C4—21no—
34C22⋊Dic13—21no—
35C22⋊Dic13—21no—
36C22⋊Dic13—21no—
37C22⋊Dic13—21no—
38C4⋊Dic13—21no—
39C4⋊Dic13—21no—
40#6101—21no—
41#6101—21no—
42#6101—21no—
43#6101—21no—
44C4×Dic13D411yescharacteristic
45C4×Dic13D411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48#1473—131nomaximal, Sylow
49C23×C13—21no—
50C23×C13—22no—
51C23×C13—41no—
52C23×C13—41no—
53C23×C13C22×C411yescharacteristic
54C2×C4×C13—21no—
55C2×C4×C13—22no—
56C2×C4×C13—41no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22⋊C411yescharacteristic
59C2×Dic13—22no—
60C2×Dic13—21no—
61C2×Dic13—21no—
62C2×Dic13—41no—
63C2×Dic13—41no—
64C2×Dic13—41no—
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C2×D411yescharacteristic
68C2×Dic13C2×D411yescharacteristic
69#1057—42no—
70#1057—42no—
71C2×#126—131no—
72#432—131no—
73#431—131no—
74#324—132no—
75#323—132no—
76C22×C13—21no—
77C22×C13—21no—
78C22×C13—41no—
79C22×C13—41no—
80C22×C13—41no—
81C22×C13—82no—
82C22×C13C2×C22⋊C411yescharacteristic
83C22×C13#13112yes—
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—41no—
87Dic13—21no—
88Dic13—21no—
89Dic13—21no—
90Dic13—21no—
91Dic13—41no—
92Dic13—41no—
93#126—261no—
94#126—261no—
95#126—261no—
96#126—261no—
97C2×C4⋊C4—131no—
98C2×C4⋊C4—131no—
99C2×C4⋊C4—131no—
100C2×C22⋊C4—131no—
101C2×C22⋊C4—131no—
102C2×C22⋊C4#26111yescharacteristic
103C2×C42—131no—
104C4⋊C8—261no—
105C4⋊C8—261no—
106C22⋊C8—132no—
107C22⋊C8—132no—
108#97—261no—
109C4×C8—261no—
110C2×C13—22no—
111C2×C13—81no—
112C2×C13#40811yescharacteristic
113C2×C13#41011yescharacteristic
114C2×C13#41311yescharacteristic
115C24C2×#26111yescharacteristic
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—131no—
119C22×C4—131no—
120C22×C4C2×#26111yescharacteristic
121C22×C4C2×#26111yescharacteristic
122C2×C8—262no—
123C2×C8—262no—
124C4⋊C4—261no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C4⋊C4—261no—
128C4⋊C4—261no—
129C4⋊C4—261no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—261no—
133C22⋊C4—261no—
134C22⋊C4—261no—
135C22⋊C4—261no—
136C42—131no—
137C42—131no—
138C42—131no—
139C42—131no—
140C13#147311yescharacteristic, complemented, Sylow
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×#26111yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—131no—
150C2×C4—131no—
151C2×C4—131no—
152C2×C4—131no—
153C2×C4—262no—
154C2×C4—261no—
155C2×C4—261no—
156C2×C4—521no—
157C2×C4—521no—
158C2×C4—521no—
159C2×C4C22⋊#26111yescharacteristic
160C2×C4C22⋊#26111yescharacteristic
161C8—522no—
162C8—522no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22#8823812yes—
170C22C2×C22⋊#26111yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—261no—
175C4—261no—
176C4—261no—
177C4—261no—
178C4—521no—
179C4—521no—
180C2—22no—
181C2—81no—
182C2#1171911611yescharacteristic
183C2#1171914711yescharacteristic
184C2#1171914811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC24×C13C2×C4
cosocleC22×Dic13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1473
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11719130C2semidirect
3. #11719125C2semidirect
5. #11718285C2semidirect
140. C13#1473semidirect

Maximal subgroups

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

subgroupindex
C2×#881332
#117191302
#117191252
#117183052
#117182852
#147313