Finite Group Databasebeta

← #16778542

Subgroups — #16778542

Order 3328.

490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 96 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#13130727C212yesmaximal
2#13129655C214yesmaximal, complemented
3#13117318C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8#11718634C412yes—
9#11718634C2212yes—
10#11718607—22no—
11C4×#6101—22no—
12#11718290—22no—
13#11718290C2214yes—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13D412yes—
16C22×#1057—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4C2×C412yes—
19C2×C13×C22⋊C4—21no—
20C2×C42×C13—21no—
21C2×C22⋊Dic13—21no—
22#88180—24no—
23C2×C4⋊Dic13C2×C412yes—
24C2×#6101—22no—
25C2×#6101—22no—
26C2×C4×Dic13—21no—
27C2×C4×Dic13—42no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13D412yes—
30C2×C4×Dic13C2311yescharacteristic
31C22⋊#1057—44no—
32#88071—22no—
33#88071—22no—
34#7646—131nomaximal, Sylow
35C24×C13C22⋊C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13C22⋊C411yescharacteristic
41C22×C4×C13C22×C411yescharacteristic
42C22×Dic13—24no—
43C22×Dic13—22no—
44C22×Dic13—24no—
45C22×Dic13—42no—
46C22×Dic13C22⋊C412yes—
47C22×Dic13C2×D412yes—
48C2×#1057—44no—
49C2×#1057—44no—
50C2×#1057—44no—
51C13×C4⋊C4—42no—
52C13×C22⋊C4—42no—
53C42×C13—42no—
54C22⋊Dic13—24no—
55C4⋊Dic13—22no—
56C4⋊Dic13M1614yes—
57#6101—44no—
58#6101—44no—
59C4×Dic13—24no—
60C4×Dic13—41no—
61C4×Dic13—42no—
62C4×Dic13—41no—
63#2296—131no—
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—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13#10112yes—
81C2×C4×C13C2×M1612yes—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—24no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—48no—
89C2×Dic13—42no—
90C2×Dic13—42no—
91C2×Dic13#13514yes—
92#1057—84no—
93C2×#117—131no—
94C2×#117#26111yescharacteristic
95C22×C42—131no—
96C2×C22⋊C8—262no—
97#389—132no—
98#389—132no—
99#385—262no—
100C4×C4⋊C4—262no—
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—82no—
116Dic13—24no—
117Dic13—44no—
118Dic13—42no—
119C23×C4—132no—
120C23×C4C2×#26111yescharacteristic
121C22×C8—264no—
122#117—42no—
123#117—264no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—262no—
126C2×C4⋊C4—262no—
127C2×C4⋊C4C2×#26112yes—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—261no—
130C2×C42—21no—
131C2×C42—132no—
132C2×C42—131no—
133C2×C42—131no—
134C2×C42—261no—
135C2×C42—522no—
136C22⋊C8—524no—
137#95—262no—
138#95—262no—
139C2×C13—42no—
140C2×C13#146311yescharacteristic
141C2×C13#148812yes—
142C2×C13#151612yes—
143C2×C13#153711yescharacteristic
144C2×C13#154411yescharacteristic
145C24C22⋊#26111yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4—264no—
153C22×C4—264no—
154C22×C4—262no—
155C22×C4—522no—
156C22×C4C22⋊#26111yescharacteristic
157C22×C4C22×#26111yescharacteristic
158C2×C8—524no—
159C2×C8—524no—
160C2×C8—524no—
161C4⋊C4—42no—
162C4⋊C4—134no—
163C4⋊C4—262no—
164C4⋊C4—524no—
165C4⋊C4—524no—
166C22⋊C4—42no—
167C22⋊C4—264no—
168C42—42no—
169C42—264no—
170C42—522no—
171C42—521no—
172C42—521no—
173C13#764611yescharacteristic, complemented, Sylow
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23#8811912yes—
179C23C2×C22⋊#26111yescharacteristic
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—134no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—264no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—528no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4#8811312yes—
199C2×C4D13⋊M1612yes—
200C8—1044no—
201C22—24no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—42no—
206C22#1171912611yescharacteristic
207C22C2×#8811311yescharacteristic
208C22#1171916512yes—
209C22#1171916612yes—
210C22C2×#8811911yescharacteristic
211C4—22no—
212C4—22no—
213C4—82no—
214C4—264no—
215C4—522no—
216C4—524no—
217C2—42no—
218C2#1313008611yescharacteristic
219C2#1313016912yes—
220C2#1313026212yes—
221C2#1313032711yescharacteristic
222C2#1313034111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#7646
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129655C2semidirect
173. C13#7646semidirect

Maximal subgroups

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

subgroupindex
#131307272
#131296552
#131173182
#764613