Finite Group Databasebeta

← #15751220

Subgroups — #15751220

Order 3328.

490 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 123 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#13114904C212yesmaximal
2#13112659C214yesmaximal, complemented
3C13×#2296C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×C13×#117C411yescharacteristic
6C22×C42×C13C2211yescharacteristic
7C13×#389C412yes—
8C13×#389C2212yes—
9C13×#385—22no—
10C4×C13×C4⋊C4—22no—
11C2×C22⋊#1055—22no—
12#11718116—22no—
13#11718116C2214yes—
14C23×C4×C13C2×C411yescharacteristic
15C23×C4×C13D412yes—
16C13×#117—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4C2×C412yes—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C13×C22⋊C4—21no—
23C2×C13×C22⋊C4—21no—
24C2×C42×C13—21no—
25C2×C42×C13—21no—
26C2×C42×C13—42no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30C22×#1055—24no—
31C13×#95—22no—
32C13×#95—22no—
33C22⋊#1055—44no—
34#7646—131nomaximal, Sylow
35C24×C13C22⋊C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—24no—
40C22×C4×C13—22no—
41C22×C4×C13—24no—
42C22×C4×C13—22no—
43C22×C4×C13—42no—
44C22×C4×C13C22⋊C412yes—
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C22×C411yescharacteristic
47C22×C4×C13C2×D412yes—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—42no—
50C13×C4⋊C4—44no—
51C13×C4⋊C4—44no—
52C13×C4⋊C4M1614yes—
53C13×C22⋊C4—24no—
54C13×C22⋊C4—42no—
55C42×C13—24no—
56C42×C13—41no—
57C42×C13—42no—
58C42×C13—41no—
59C42×C13—42no—
60C2×#1055—44no—
61C2×#1055—44no—
62C2×#1055—44no—
63#2296D1311yescharacteristic
64#1817—132no—
65#1271—134no—
66C23×C13—21no—
67C23×C13—21no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13#9912yes—
71C23×C13C2×C22⋊C411yescharacteristic
72C2×C4×C13—28no—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—24no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—48no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13#10112yes—
90C2×C4×C13C2×M1612yes—
91C2×C4×C13#13514yes—
92#1055—84no—
93C2×#117Dic1311yescharacteristic
94C2×#117Dic1311yescharacteristic
95C22×C42C2×D1311yescharacteristic
96C2×C22⋊C8—262no—
97#389Dic1312yes—
98#389C2×D1312yes—
99#385—22no—
100C4×C4⋊C4—22no—
101#336—134no—
102#336—262no—
103C22×C13—22no—
104C22×C13—24no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13—42no—
108C22×C13#40711yescharacteristic
109C22×C13C2×#9911yescharacteristic
110C22×C13C2×#10111yescharacteristic
111C22×C13#41612yes—
112C22×C13#42112yes—
113C4×C13—22no—
114C4×C13—22no—
115C4×C13—24no—
116C4×C13—44no—
117C4×C13—42no—
118C4×C13—82no—
119C23×C4C2×Dic1311yescharacteristic
120C23×C4C22⋊D1312yes—
121C22×C8—264no—
122#117—24no—
123#117—42no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4C2×Dic1312yes—
127C2×C4⋊C4C2×Dic1312yes—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—21no—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—42no—
133C2×C42C2×Dic1311yescharacteristic
134C2×C42C22⋊D1312yes—
135C2×C42C22×D1311yescharacteristic
136C22⋊C8—524no—
137#95—22no—
138#95—22no—
139C2×C13—42no—
140C2×C13#146311yescharacteristic
141C2×C13#148812yes—
142C2×C13#151612yes—
143C2×C13#153711yescharacteristic
144C2×C13#154411yescharacteristic
145C24C22⋊Dic1311yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—24no—
150C22×C4—22no—
151C22×C4—24no—
152C22×C4—22no—
153C22×C4—42no—
154C22×C4C22⋊Dic1312yes—
155C22×C4C22⋊Dic1311yescharacteristic
156C22×C4C22×Dic1311yescharacteristic
157C22×C4C2×C22⋊D1312yes—
158C2×C8—524no—
159C2×C8—524no—
160C2×C8—524no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—44no—
164C4⋊C4—44no—
165C4⋊C4#609914yes—
166C22⋊C4—24no—
167C22⋊C4—42no—
168C42—24no—
169C42—41no—
170C42—42no—
171C42—41no—
172C42—42no—
173C13#764611yescharacteristic, complemented, Sylow
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23#8807412yes—
179C23C2×C22⋊Dic1311yescharacteristic
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—48no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4#8807612yes—
198C2×C4C2×#609912yes—
199C2×C4#8820414yes—
200C8—1044no—
201C22—24no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—42no—
206C22#1171886811yescharacteristic
207C22C2×#8807411yescharacteristic
208C22C2×#8807611yescharacteristic
209C22#1171889412yes—
210C22#1171889712yes—
211C4—24no—
212C4—22no—
213C4—22no—
214C4—42no—
215C4—44no—
216C4—82no—
217C2—42no—
218C2#1311316611yescharacteristic
219C2#1311327012yes—
220C2#1311339212yes—
221C2#1311347411yescharacteristic
222C2#1311350111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2296C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2296D13
hypocenterC13#7646
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #13112659C2semidirect
173. C13#7646semidirect

Maximal subgroups

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

subgroupindex
#131149042
#131126592
C13×#22962
#764613