Finite Group Databasebeta

← #15772348

Subgroups — #15772348

Order 3328.

330 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 69 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#13123465C211yesmaximal, characteristic
2#13116645C212yesmaximal, complemented
3#13112786C212yesmaximal, complemented
4#13112772C211yesmaximal, characteristic
5C13×#1320C211yesmaximal, characteristic
6C22×C4×Dic13C411yescharacteristic
7C13×#407C2211yescharacteristic
8#11718868C411yescharacteristic
9#11718779C411yescharacteristic
10#11718779C2211yescharacteristic
11M16×Dic13C411yescharacteristic
12M16×Dic13C2211yescharacteristic
13#11718380—22no—
14#11718379—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C23×C4×C13C2×C411yescharacteristic
20C23×Dic13—21no—
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23C2×C4×Dic13—21no—
24C2×C4×Dic13—21no—
25C2×C4×Dic13—21no—
26C2×C4×Dic13—21no—
27C2×C4×Dic13—21no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13C2×C411yescharacteristic
30C2×#6099C2×C411yescharacteristic
31C2×#6099C2×C411yescharacteristic
32C13×M32—22no—
33C13×C22⋊C8—22no—
34C22⋊#1055—22no—
35#88055—21no—
36#88055D412yes—
37#88054—22no—
38#88054—22no—
39C8×Dic13—21no—
40C8×Dic13D412yes—
41#88052—22no—
42#11521—131nomaximal, Sylow
43C24×C13M1611yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—41no—
47C22×C4×C13—41no—
48C22×C4×C13M1611yescharacteristic
49C22×C4×C13C22×C411yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13—21no—
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13—21no—
56C22×Dic13—44no—
57C13×M16—41no—
58C13×M16—41no—
59C2×C8×C13—21no—
60C2×C8×C13C2×D412yes—
61C4×Dic13—21no—
62C4×Dic13—21no—
63C4×Dic13—21no—
64C4×Dic13—21no—
65C4×Dic13—21no—
66C4×Dic13—21no—
67C4×Dic13C22⋊C411yescharacteristic
68C4×Dic13C22⋊C411yescharacteristic
69C4×Dic13M1611yescharacteristic
70C4×Dic13M1611yescharacteristic
71#6099—41no—
72#6099—41no—
73C2×#1055—21no—
74C2×#1055C22⋊C412yes—
75C13×C16—42no—
76#6090—42no—
77#2920—131no—
78#2165—132no—
79#1327—132no—
80#1320—131no—
81#1320D1311yescharacteristic
82C23×C13—21no—
83C23×C13—42no—
84C23×C13—41no—
85C23×C13C2×M1611yescharacteristic
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13C2×M1611yescharacteristic
95C2×Dic13—24no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C8×C13—22no—
106C8×C13—41no—
107#1055—22no—
108#1055—41no—
109C22×C42—131no—
110#432—262no—
111#431—262no—
112#423—131no—
113#423—131no—
114#407—131no—
115#407C2×D1311yescharacteristic
116C4×M16—131no—
117C4×M16—131no—
118#364—262no—
119#349—132no—
120#349C2×D1312yes—
121#347—262no—
122C22×C13—22no—
123C22×C13—21no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—41no—
129C22×C13#40711yescharacteristic
130C4×C13—21no—
131C4×C13—41no—
132C4×C13#41011yescharacteristic
133C4×C13#41311yescharacteristic
134Dic13—22no—
135Dic13—22no—
136Dic13—41no—
137Dic13—41no—
138C23×C4—261no—
139C23×C4C4×D1311yescharacteristic
140C2×M16—131no—
141C2×M16—131no—
142C2×M16C4×D1311yescharacteristic
143C2×M16C22×D1311yescharacteristic
144C2×C42—131no—
145C2×C42—131no—
146C2×C42—261no—
147C2×C42—261no—
148C2×C42—261no—
149C2×C42—261no—
150C2×C42—261no—
151M32—22no—
152M32—262no—
153C4⋊C8—262no—
154C4⋊C8—262no—
155C22⋊C8—22no—
156C22⋊C8—262no—
157#97—132no—
158#97—261no—
159C4×C8—132no—
160C4×C8—261no—
161C2×C13—21no—
162C2×C13—42no—
163C2×C13—41no—
164C2×C13#146411yescharacteristic
165C24#609411yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—261no—
171C22×C4—261no—
172C22×C4—261no—
173C22×C4—261no—
174C22×C4—261no—
175C22×C4—261no—
176C22×C4—524no—
177C22×C4#609411yescharacteristic
178C22×C4C2×C4×D1311yescharacteristic
179M16—41no—
180M16—41no—
181M16—521no—
182M16—521no—
183C2×C8—21no—
184C2×C8—132no—
185C2×C8—261no—
186C2×C8D4×D1312yes—
187C42—131no—
188C42—131no—
189C42—131no—
190C42—131no—
191C42—261no—
192C42—261no—
193C42—261no—
194C42—261no—
195C42—261no—
196C42—261no—
197C16—42no—
198C16—522no—
199C13#1152111yescharacteristic, complemented, Sylow
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#609411yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—264no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—522no—
217C2×C4—522no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4—522no—
221C2×C4C22⋊C4×D1311yescharacteristic
222C2×C4M16×D1311yescharacteristic
223C8—22no—
224C8—41no—
225C8—262no—
226C8—521no—
227C22—22no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22#1171838711yescharacteristic
235C4—21no—
236C4—41no—
237C4—262no—
238C4—262no—
239C4—521no—
240C4—521no—
241C4#1171840111yescharacteristic
242C4#1171840611yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2#1311316711yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1320C2
socleC2×C13#1464
prime radicalC24×C13M16
cosocleC2×C13×M16C23
hypercenter#1320D13
hypocenterC13#11521
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. #13116645C2semidirect
3. #13112786C2semidirect
199. C13#11521semidirect

Maximal subgroups

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

subgroupindex
#131234652
#131166452
#131127862
#131127722
C13×#13202
#1152113