Finite Group Databasebeta

← #15751020

Subgroups — #15751020

Order 3328.

514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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#13114816C212yesmaximal
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—
12C2×C4⋊#1055—22no—
13#11718116C2214yes—
14C23×C4×C13C2×C411yescharacteristic
15C23×C4×C13D412yes—
16C13×#117—22no—
17C13×#117—42no—
18C13×#117C814yescomplemented
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C13×C4⋊C4C2×C412yes—
23C2×C13×C22⋊C4—21no—
24C2×C13×C22⋊C4—21no—
25C2×C42×C13—21no—
26C2×C42×C13—21no—
27C2×C42×C13—42no—
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13D412yes—
30C2×C42×C13C2311yescharacteristic
31C22×#1055—24no—
32C13×#95—22no—
33C13×#95—22no—
34C22⋊#1055—44no—
35C4⋊#1055—44no—
36#7598—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—42no—
45C22×C4×C13—42no—
46C22×C4×C13C22⋊C412yes—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C2×C812yes—
49C22×C4×C13M1612yes—
50C22×C4×C13C22×C411yescharacteristic
51C22×C4×C13C2×D412yes—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—44no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4C2×C814yes—
58C13×C22⋊C4—24no—
59C13×C22⋊C4—42no—
60C42×C13—24no—
61C42×C13—24no—
62C42×C13—41no—
63C42×C13—41no—
64C42×C13—42no—
65C2×#1055—44no—
66C2×#1055—44no—
67C2×#1055—44no—
68#2296D1311yescharacteristic
69#1797—132no—
70#1271—134no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13C22⋊C812yes—
76C23×C13C2×C22⋊C411yescharacteristic
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—24no—
82C2×C4×C13—24no—
83C2×C4×C13—24no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—44no—
88C2×C4×C13—44no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13C22⋊C812yes—
95C2×C4×C13#9912yes—
96C2×C4×C13#10112yes—
97C2×C4×C13C22×C811yescharacteristic
98C2×C4×C13C2×M1611yescharacteristic
99C2×C4×C13AGL(1,ℤ/8)12yes—
100C2×C4×C13#13712yes—
101#1055—84no—
102C2×#117Dic1311yescharacteristic
103C2×#117Dic1311yescharacteristic
104C22×C42C2×D1311yescharacteristic
105C2×C4⋊C8—262no—
106C2×C22⋊C8—262no—
107#389Dic1312yes—
108#389C2×D1312yes—
109#385—22no—
110C4×C4⋊C4—22no—
111#336—134no—
112C22×C13—22no—
113C22×C13—24no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—42no—
117C22×C13C2×C22⋊C811yescharacteristic
118C22×C13C2×#9911yescharacteristic
119C22×C13C2×#10111yescharacteristic
120C22×C13#41712yes—
121C22×C13#42112yes—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—44no—
127C4×C13—42no—
128C4×C13—82no—
129C4×C13#32414yes—
130C23×C4C2×Dic1311yescharacteristic
131C23×C4C22⋊D1312yes—
132C22×C8—264no—
133#117—22no—
134#117—42no—
135#117#105514yescomplemented
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4C2×Dic1312yes—
139C2×C4⋊C4C2×Dic1312yes—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—21no—
142C2×C42—21no—
143C2×C42—21no—
144C2×C42—42no—
145C2×C42C2×Dic1311yescharacteristic
146C2×C42C22⋊D1312yes—
147C2×C42C22×D1311yescharacteristic
148C4⋊C8—524no—
149C22⋊C8—524no—
150#95—22no—
151#95—22no—
152C2×C13—42no—
153C2×C13C2×#32411yescharacteristic
154C2×C13#147712yes—
155C2×C13#151312yes—
156C2×C13#153711yescharacteristic
157C2×C13#156111yescharacteristic
158C24C22⋊Dic1311yescharacteristic
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4C2×#105512yes—
168C22×C4#609912yes—
169C22×C4C22⋊Dic1312yes—
170C22×C4C22⋊Dic1311yescharacteristic
171C22×C4C22×Dic1311yescharacteristic
172C22×C4C2×C22⋊D1312yes—
173C2×C8—524no—
174C2×C8—524no—
175C2×C8—524no—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—44no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4C2×#105514yes—
182C22⋊C4—24no—
183C22⋊C4—42no—
184C42—24no—
185C42—24no—
186C42—41no—
187C42—41no—
188C42—42no—
189C13#759811yescharacteristic, complemented, Sylow
190C23—21no—
191C23—21no—
192C23—22no—
193C23—22no—
194C23C22⋊#105512yes—
195C23C2×C22⋊Dic1311yescharacteristic
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—44no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4C22⋊#105512yes—
214C2×C4#8807412yes—
215C2×C4#8807612yes—
216C2×C4C22×#105511yescharacteristic
217C2×C4C2×#609911yescharacteristic
218C2×C4#8820312yes—
219C2×C4#8820512yes—
220C8—1044no—
221C22—22no—
222C22—24no—
223C22—42no—
224C22—41no—
225C22—41no—
226C22C2×C22⋊#105511yescharacteristic
227C22C2×#8807411yescharacteristic
228C22C2×#8807611yescharacteristic
229C22#1171889312yes—
230C22#1171889712yes—
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—44no—
237C4—82no—
238C4#1171812014yes—
239C2—42no—
240C2C2×#1171812011yescharacteristic
241C2#1311322312yes—
242C2#1311337912yes—
243C2#1311347411yescharacteristic
244C2#1311357411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#2296C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2296D13
hypocenterC13#7598
LCSG ▷ C2×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
18. C13×#117C8semidirect
135. #117#1055semidirect
189. C13#7598semidirect

Maximal subgroups

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

subgroupindex
#131148162
#131126592
C13×#22962
#759813