Finite Group Databasebeta

← #15756412

Subgroups — #15756412

Order 3328.

384 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#13113170C212yesmaximal
2#13112692C214yesmaximal, complemented
3C13×#2298C211yesmaximal, characteristic
4C2×C13×#117C2211yescharacteristic
5C13×#388—22no—
6C13×#387—22no—
7C4×C13×C4⋊C4C2212yes—
8C4×C13×C22⋊C4C412yes—
9C13×#376C411yescharacteristic
10C43×C13C411yescharacteristic
11#11718587C2214yes—
12#11718120—22no—
13#11718117—22no—
14C23×C4×C13C2×C411yescharacteristic
15C13×#117—24no—
16C2×C13×C4⋊C4—22no—
17C2×C13×C4⋊C4D412yes—
18C2×C13×C22⋊C4—22no—
19C2×C13×C22⋊C4D412yes—
20C2×C42×C13—22no—
21C2×C42×C13C2×C411yescharacteristic
22C2×C42×C13C2×C412yes—
23C2×C42×C13C2×C412yes—
24C2×C42×C13C2311yescharacteristic
25C13×#95—22no—
26C13×#95—22no—
27C13×#95—22no—
28C22⋊#1055—24no—
29C4⋊#1055—24no—
30#88043—24no—
31#8744—131nomaximal, Sylow
32C24×C13C22⋊C411yescharacteristic
33C22×C4×C13—22no—
34C22×C4×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—42no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×C4×C13C22⋊C412yes—
39C22×C4×C13C22×C411yescharacteristic
40C22×C4×C13C2×D412yes—
41C13×C4⋊C4—24no—
42C13×C4⋊C4—44no—
43C13×C22⋊C4—24no—
44C13×C22⋊C4—44no—
45C42×C13—22no—
46C42×C13—42no—
47C42×C13—42no—
48C42×C13—44no—
49C42×C13#4114yes—
50C2×#1055—44no—
51#2298D1311yescharacteristic
52#1464—132no—
53#1285—134no—
54C23×C13—21no—
55C23×C13—22no—
56C23×C13—42no—
57C23×C13C2×C22⋊C411yescharacteristic
58C2×C4×C13—22no—
59C2×C4×C13—24no—
60C2×C4×C13—22no—
61C2×C4×C13—21no—
62C2×C4×C13—22no—
63C2×C4×C13—42no—
64C2×C4×C13—44no—
65C2×C4×C13—42no—
66C2×C4×C13—42no—
67C2×C4×C13—42no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13#11712yes—
72C2×C4×C13#12314yes—
73#1055—84no—
74C2×#117C2×D1311yescharacteristic
75#432—134no—
76#388—22no—
77#387—22no—
78C4×C4⋊C4C2×D1312yes—
79C4×C22⋊C4Dic1312yes—
80#376Dic1311yescharacteristic
81C43Dic1311yescharacteristic
82#324—262no—
83#323—262no—
84C22×C13—22no—
85C22×C13—41no—
86C22×C13—42no—
87C22×C13—82no—
88C22×C13#38111yescharacteristic
89C22×C13#41312yes—
90C4×C13—22no—
91C4×C13—24no—
92C4×C13—44no—
93C4×C13—41no—
94C4×C13—42no—
95C4×C13—82no—
96C23×C4C2×Dic1311yescharacteristic
97#117—24no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4C22⋊D1312yes—
100C2×C22⋊C4—22no—
101C2×C22⋊C4C22⋊D1312yes—
102C2×C42—22no—
103C2×C42C2×Dic1311yescharacteristic
104C2×C42C2×Dic1312yes—
105C2×C42C2×Dic1312yes—
106C2×C42C22×D1311yescharacteristic
107C4⋊C8—264no—
108C22⋊C8—264no—
109#97—264no—
110#95—22no—
111#95—22no—
112#95—22no—
113C2×C13—22no—
114C2×C13—81no—
115C2×C13#182211yescharacteristic
116C2×C13#182712yes—
117C24C22⋊Dic1311yescharacteristic
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—42no—
122C22×C4C22⋊Dic1311yescharacteristic
123C22×C4C22⋊Dic1312yes—
124C22×C4C22×Dic1311yescharacteristic
125C22×C4C2×C22⋊D1312yes—
126C2×C8—524no—
127C4⋊C4—24no—
128C4⋊C4—44no—
129C22⋊C4—24no—
130C22⋊C4—44no—
131C42—22no—
132C42—42no—
133C42—42no—
134C42—44no—
135C42#612714yes—
136C13#874411yescharacteristic, complemented, Sylow
137C23—21no—
138C23—22no—
139C23—42no—
140C23C2×C22⋊Dic1311yescharacteristic
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—44no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4#8818012yes—
155C2×C4#8818314yes—
156C8—1044no—
157C22—22no—
158C22—41no—
159C22—42no—
160C22—82no—
161C22#1171887211yescharacteristic
162C22#1171889812yes—
163C4—22no—
164C4—24no—
165C4—44no—
166C4—41no—
167C4—42no—
168C4—82no—
169C2—22no—
170C2—81no—
171C2#1311491911yescharacteristic
172C2#1311494012yes—
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2298C2
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2298D13
hypocenterC13#8744
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #13112692C2semidirect
136. C13#8744semidirect

Maximal subgroups

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

subgroupindex
#131131702
#131126922
C13×#22982
#874413