Finite Group Databasebeta

← #15756409

Subgroups — #15756409

Order 3328.

450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2296C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×C13×#117C2211yescharacteristic
6C22×C42×C13C411yescharacteristic
7C13×#389—22no—
8C13×#385—22no—
9C4×C13×C4⋊C4C412yes—
10C4×C13×C4⋊C4C2212yes—
11#11718587C2214yes—
12#11718120—22no—
13#11718117—22no—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C13×#117—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4D412yes—
22C2×C13×C22⋊C4—21no—
23C2×C13×C22⋊C4D412yes—
24C2×C42×C13—21no—
25C2×C42×C13—42no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13C2×C412yes—
28C2×C42×C13C2×C412yes—
29C2×C42×C13C2311yescharacteristic
30C13×#95—22no—
31C13×#95—22no—
32C22⋊#1055—24no—
33C4⋊#1055—24no—
34#88043—24no—
35#8743—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—44no—
43C22×C4×C13—42no—
44C22×C4×C13C22⋊C411yescharacteristic
45C22×C4×C13C22⋊C412yes—
46C22×C4×C13C22×C411yescharacteristic
47C22×C4×C13C2×D412yes—
48C13×C4⋊C4—24no—
49C13×C4⋊C4—44no—
50C13×C4⋊C4—44no—
51C13×C4⋊C4—42no—
52C13×C22⋊C4—24no—
53C13×C22⋊C4—42no—
54C42×C13—22no—
55C42×C13—42no—
56C42×C13—42no—
57C42×C13—42no—
58C42×C13#4114yes—
59C2×#1055—44no—
60#2296D1311yescharacteristic
61#1464—132no—
62#1285—134no—
63C23×C13—21no—
64C23×C13—21no—
65C23×C13—42no—
66C23×C13#10112yes—
67C23×C13C2×C22⋊C411yescharacteristic
68C2×C4×C13—28no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—24no—
74C2×C4×C13—22no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13—48no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13#10012yes—
84C2×C4×C13#11712yes—
85C2×C4×C13#12314yes—
86#1055—84no—
87C2×#117Dic1311yescharacteristic
88C2×#117C2×D1311yescharacteristic
89C22×C42Dic1311yescharacteristic
90#432—134no—
91#389—22no—
92#385—22no—
93C4×C4⋊C4Dic1312yes—
94C4×C4⋊C4C2×D1312yes—
95#324—262no—
96#323—262no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13#38111yescharacteristic
103C22×C13C2×#10011yescharacteristic
104C22×C13C2×#10111yescharacteristic
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—24no—
108C4×C13—44no—
109C4×C13—42no—
110C4×C13—82no—
111C23×C4—21no—
112C23×C4C2×Dic1311yescharacteristic
113#117—24no—
114#117—42no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4C22⋊D1312yes—
119C2×C22⋊C4—21no—
120C2×C22⋊C4C22⋊D1312yes—
121C2×C42—21no—
122C2×C42—42no—
123C2×C42C2×Dic1311yescharacteristic
124C2×C42C2×Dic1312yes—
125C2×C42C2×Dic1312yes—
126C2×C42C22×D1311yescharacteristic
127C4⋊C8—264no—
128C22⋊C8—264no—
129#97—264no—
130#95—22no—
131#95—22no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13—42no—
135C2×C13#182111yescharacteristic
136C2×C13#182712yes—
137C24C22⋊Dic1311yescharacteristic
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—44no—
144C22×C4—42no—
145C22×C4C22⋊Dic1311yescharacteristic
146C22×C4C22⋊Dic1312yes—
147C22×C4C22×Dic1311yescharacteristic
148C22×C4C2×C22⋊D1312yes—
149C2×C8—524no—
150C4⋊C4—24no—
151C4⋊C4—44no—
152C4⋊C4—44no—
153C4⋊C4—42no—
154C22⋊C4—24no—
155C22⋊C4—42no—
156C42—22no—
157C42—42no—
158C42—42no—
159C42—42no—
160C42#612714yes—
161C13#874311yescharacteristic, complemented, Sylow
162C23—21no—
163C23—21no—
164C23—42no—
165C23#8807612yes—
166C23C2×C22⋊Dic1311yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4#8807312yes—
183C2×C4#8818012yes—
184C2×C4#8818314yes—
185C8—1044no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22#1171887211yescharacteristic
192C22C2×#8807311yescharacteristic
193C22C2×#8807611yescharacteristic
194C4—22no—
195C4—22no—
196C4—24no—
197C4—44no—
198C4—42no—
199C4—82no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2#1311491611yescharacteristic
204C2#1311494012yes—
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2296C2
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2296D13
hypocenterC13#8743
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #13112692C2semidirect
161. C13#8743semidirect

Maximal subgroups

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

subgroupindex
#131131702
#131126922
C13×#22962
#874313