Finite Group Databasebeta

← #15756455

Subgroups — #15756455

Order 3328.

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

normal subgroups only

This group has 438 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#13113166C212yesmaximal
2#13112742C214yesmaximal
3C13×#2316C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×C13×#117C411yescharacteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C13×#389—22no—
8C13×#389—22no—
9C13×#380C412yes—
10C13×#380C2212yes—
11#11718868C2214yes—
12#11718120—22no—
13#11718120—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×C4×C13C2×C411yescharacteristic
16C23×C4×C13C2311yescharacteristic
17C13×#117—42no—
18C13×#117—42no—
19C2×C13×C4⋊C4—24no—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4D412yes—
26C2×C13×C22⋊C4C2×C412yes—
27C2×C13×C22⋊C4C2×C412yes—
28C2×C42×C13—21no—
29C2×C42×C13—21no—
30C2×#6099—24no—
31C13×#95—22no—
32C13×#95—22no—
33C22⋊#1055—24no—
34C22⋊#1055—24no—
35#8757—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—22no—
43C22×C4×C13—81no—
44C22×C4×C13—81no—
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22⋊C412yes—
48C22×C4×C13C2×D412yes—
49C22×C4×C13#4114yes—
50C13×C4⋊C4—24no—
51C13×C4⋊C4—24no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—82no—
55C13×C4⋊C4—82no—
56C13×C22⋊C4—42no—
57C13×C22⋊C4—42no—
58C42×C13—42no—
59C42×C13—42no—
60#6099—84no—
61C2×#1055—44no—
62#2316D1311yescharacteristic
63#1463—132no—
64#1305—134no—
65C23×C13—21no—
66C23×C13—21no—
67C23×C13—41no—
68C23×C13—41no—
69C23×C13C2×C22⋊C411yescharacteristic
70C23×C13#11712yes—
71C2×C4×C13—28no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—44no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—82no—
87C2×C4×C13#10012yes—
88C2×C4×C13#10112yes—
89C2×C4×C13#12314yes—
90#1055—84no—
91C2×#117Dic1311yescharacteristic
92C2×#117Dic1311yescharacteristic
93C22×C4⋊C4C2×D1311yescharacteristic
94#407—134no—
95#389—22no—
96#389—22no—
97#380Dic1312yes—
98#380C2×D1312yes—
99#324—262no—
100#324—262no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—22no—
104C22×C13—22no—
105C22×C13—22no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13#38111yescharacteristic
109C22×C13C2×#10011yescharacteristic
110C22×C13C2×#10111yescharacteristic
111C4×C13—22no—
112C4×C13—22no—
113C4×C13—24no—
114C4×C13—42no—
115C4×C13—82no—
116C4×C13—82no—
117C23×C4C2×Dic1311yescharacteristic
118C23×C4C2×Dic1311yescharacteristic
119C23×C4C22×D1311yescharacteristic
120C2×M16—264no—
121#117—42no—
122#117—42no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4C22⋊D1312yes—
129C2×C4⋊C4C22⋊D1312yes—
130C2×C22⋊C4C2×Dic1312yes—
131C2×C22⋊C4C2×Dic1312yes—
132C2×C42—21no—
133C2×C42—21no—
134C22⋊C8—264no—
135C22⋊C8—264no—
136#95—22no—
137#95—22no—
138C2×C13—21no—
139C2×C13—21no—
140C2×C13—42no—
141C2×C13#182111yescharacteristic
142C2×C13#182811yescharacteristic
143C2×C13#183011yescharacteristic
144C24C22×Dic1311yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—81no—
152C22×C4—81no—
153C22×C4C22⋊Dic1311yescharacteristic
154C22×C4C22⋊Dic1311yescharacteristic
155C22×C4C22⋊Dic1312yes—
156C22×C4#612714yes—
157C22×C4C2×C22⋊D1312yes—
158M16—1044no—
159C2×C8—524no—
160C4⋊C4—24no—
161C4⋊C4—24no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—82no—
165C4⋊C4—82no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C42—42no—
169C42—42no—
170C13#875711yescharacteristic, complemented, Sylow
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23#8818012yes—
176C23C2×C22⋊Dic1311yescharacteristic
177C2×C4—28no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—82no—
193C2×C4#8807312yes—
194C2×C4#8807612yes—
195C2×C4#8818314yes—
196C8—1044no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22#1171887211yescharacteristic
205C22C2×#8807311yescharacteristic
206C22C2×#8807611yescharacteristic
207C4—22no—
208C4—22no—
209C4—24no—
210C4—42no—
211C4—82no—
212C4—82no—
213C2—21no—
214C2—21no—
215C2—42no—
216C2#1311491611yescharacteristic
217C2#1311494411yescharacteristic
218C2#1311495011yescharacteristic
subgroupG/H
centerC22#11718872
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2316C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenter#2316D13
hypocenterC13#8757
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
170. C13#8757semidirect

Maximal subgroups

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

subgroupindex
#131131662
#131127422
C13×#23162
#875713