Finite Group Databasebeta

← #15772416

Subgroups — #15772416

Order 3328.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#13123526C211yesmaximal, characteristic
2#13116649C212yesmaximal, complemented
3#13112773C212yesmaximal, complemented
4#13112772C211yesmaximal, characteristic, complemented
5C13×#1320C211yesmaximal, characteristic, complemented
6#11719496C411yescharacteristic
7C23×#1055C411yescharacteristic
8C2×#88161C411yescharacteristic
9C13×#407C2211yescharacteristic
10#11718790C2211yescharacteristic
11#11718783C2211yescharacteristic
12#11718780C411yescharacteristic
13#11718391—22no—
14#11718386—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C23×C4×C13C2×C411yescharacteristic
20C2×#6127C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23#88207—21no—
24#88184—21no—
25#88183—21no—
26C4×C22⋊D13—22no—
27#88180C2×C411yescharacteristic
28#88178—21no—
29C22×#1055—21no—
30C22×#1055—21no—
31C22×#1055—42no—
32C22×#1055C2×C411yescharacteristic
33C22×#1055C2×C411yescharacteristic
34#88161—42no—
35C2×#6094—21no—
36C2×C8×D13—21no—
37C13×M32—22no—
38C13×C22⋊C8—22no—
39#88060—22no—
40#88055D412yes—
41#88054—22no—
42C8×Dic13D412yes—
43#88052—22no—
44#11537—131nomaximal, Sylow
45C24×C13M1611yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13M1611yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C2×C22⋊D13—22no—
53C2×C22⋊D13—21no—
54#6127—41no—
55#6127—41no—
56C2×D52M1611yescharacteristic
57C2×C4×D13—21no—
58C2×Dic26M1611yescharacteristic
59C13×M16—41no—
60C13×M16—41no—
61C2×C8×C13—21no—
62C2×C8×C13C2×D412yes—
63C22⋊Dic13—22no—
64C22⋊Dic13—21no—
65#6103—22no—
66C4⋊Dic13—21no—
67#6101—22no—
68C4×Dic13C22⋊C412yes—
69C2×#1055—22no—
70C2×#1055—21no—
71C2×#1055—42no—
72C2×#1055—42no—
73C2×#1055—41no—
74C2×#1055C22⋊C411yescharacteristic
75C2×#1055C22⋊C411yescharacteristic
76#6094—42no—
77C8×D13—42no—
78C13×C16—42no—
79#6090—42no—
80#2929—131no—
81#2166—132no—
82#1321—132no—
83#1320—131no—
84#1320D1311yescharacteristic, complemented
85C23×C13—21no—
86C23×C13—41no—
87C23×C13—42no—
88C23×C13C2×M1611yescharacteristic
89C22×D13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—42no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13C2×C22⋊C411yescharacteristic
98C2×C4×C13C2×M1611yescharacteristic
99C22⋊D13—42no—
100C22⋊D13—44no—
101C2×Dic13—22no—
102C2×Dic13—21no—
103D52—41no—
104C4×D13—41no—
105C4×D13—41no—
106Dic26—41no—
107C8×C13—22no—
108C8×C13—41no—
109#1055—21no—
110#1055—41no—
111#1055#10012yes—
112C2×#131—131no—
113C23×C8—131no—
114#525—131no—
115#435—262no—
116C8×D4—262no—
117#424—131no—
118#408—131no—
119#407C2×D1311yescharacteristic
120#405—131no—
121#364—262no—
122#349—132no—
123#349C2×D1312yes—
124#347—262no—
125C22×C13—22no—
126C22×C13—21no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—41no—
132C22×C13#40711yescharacteristic
133C2×D13—42no—
134C2×D13—41no—
135C4×C13—21no—
136C4×C13—41no—
137C4×C13#41011yescharacteristic
138C4×C13C2×#10011yescharacteristic
139Dic13—42no—
140Dic13—41no—
141C2×#41—131no—
142C23×C4C4×D1311yescharacteristic
143#131—522no—
144C2×M16—261no—
145C2×M16C4×D1311yescharacteristic
146C2×M16C22×D1311yescharacteristic
147C22×C8—131no—
148C22×C8—131no—
149C22×C8—261no—
150C22×C8—261no—
151C22×C8—261no—
152C22×C8—522no—
153#123—261no—
154C22⋊Q8—261no—
155#121—261no—
156#120—261no—
157C4×D4—262no—
158#117—131no—
159M32—22no—
160M32—262no—
161C4⋊C8—262no—
162C22⋊C8—22no—
163C22⋊C8—262no—
164#97—132no—
165C4×C8—132no—
166C2×C13—21no—
167C2×C13—42no—
168C2×C13—41no—
169C2×C13#146611yescharacteristic
170D13—81no—
171C24#609411yescharacteristic
172#41—521no—
173#41—521no—
174C2×Q8—131no—
175C2×D4—131no—
176C2×D4—262no—
177C2×D4—261no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—261no—
183C22×C4#609411yescharacteristic
184C22×C4C2×C4×D1311yescharacteristic
185M16—41no—
186M16—41no—
187M16—522no—
188C2×C8—21no—
189C2×C8—131no—
190C2×C8—131no—
191C2×C8—262no—
192C2×C8—261no—
193C2×C8—522no—
194C2×C8—522no—
195C2×C8—522no—
196C2×C8—521no—
197C2×C8D4×D1312yes—
198C4⋊C4—262no—
199C4⋊C4—261no—
200C22⋊C4—262no—
201C22⋊C4—262no—
202C22⋊C4—261no—
203C42—132no—
204C16—42no—
205C16—522no—
206C13#1153711yescharacteristic, complemented, Sylow
207C23—21no—
208C23—41no—
209C23—42no—
210C23—261no—
211C23C2×#609411yescharacteristic
212Q8—521no—
213D4—521no—
214D4—524no—
215D4—522no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—262no—
224C2×C4—261no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4C22⋊C4×D1311yescharacteristic
228C2×C4M16×D1311yescharacteristic
229C8—22no—
230C8—41no—
231C8—132no—
232C8—261no—
233C8—521no—
234C22—22no—
235C22—21no—
236C22—41no—
237C22—41no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—522no—
242C22—521no—
243C22#1171838711yescharacteristic
244C4—21no—
245C4—41no—
246C4—522no—
247C4—521no—
248C4#1171840111yescharacteristic
249C4D13×#10011yescharacteristic
250C2—21no—
251C2—42no—
252C2—41no—
253C2—1041no—
254C2#1311317511yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1320C2
socleC2×C13#1466
prime radical#11719496C4
cosocleC2×C13×M16C23
hypercenter#1320D13
hypocenterC13#11537
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #13116649C2semidirect
3. #13112773C2semidirect
4. #13112772C2semidirect
5. C13×#1320C2semidirect
84. #1320D13semidirect
206. C13#11537semidirect

Maximal subgroups

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

subgroupindex
#131235262
#131166492
#131127732
#131127722
C13×#13202
#1153713