Finite Group Databasebeta

← #15773768

Subgroups — #15773768

Order 3328.

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

normal subgroups only

This group has 324 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#13125574C211yesmaximal, characteristic
2#13114985C211yesmaximal, characteristic, complemented
3#13112828C212yesmaximal, complemented
4#13112822C212yesmaximal, complemented
5C13×#2165C211yesmaximal, characteristic, complemented
6#11719182—21no—
7C4×C13×M16C2211yescharacteristic
8#11718796—21no—
9#11718796C2212yes—
10#11718372—21no—
11#11718372C412yescomplemented
12#11718356C411yescharacteristic, complemented
13#11718355—21no—
14#11718341C411yescharacteristic, complemented
15C13×#364—21no—
16C13×#349C2212yes—
17C13×#347—21no—
18#11718152C2211yescharacteristic
19#11718149C2211yescharacteristic
20#11718148—21no—
21#11718115—21no—
22C2×#6127—41no—
23C2×C13×M16D411yescharacteristic
24C2×C13×M16C2311yescharacteristic
25C2×C42×C13D411yescharacteristic
26#88184—22no—
27#88184—41no—
28#88180—21no—
29C2×#6099—21no—
30C2×D104—21no—
31C2×D104C2×C412yes—
32#88129—41no—
33#88128—21no—
34C4×D52—22no—
35C4×D52—41no—
36#88123—21no—
37C13×M32—22no—
38C13×#97C2×C411yescharacteristic
39C13×#97D411yescharacteristic
40C4×C8×C13C2×C411yescharacteristic
41C4×C8×C13D411yescharacteristic
42#88061—22no—
43#88061—22no—
44#88057—21no—
45#88057C2×C412yes—
46#11837—131nomaximal, Sylow
47C22×C4×C13—21no—
48C22×C4×C13C2×D411yescharacteristic
49C2×C22⋊D13—42no—
50#6127—84no—
51C2×D52—22no—
52C2×D52—41no—
53C2×D52—41no—
54C2×C4×D13—42no—
55C2×Dic26—41no—
56C13×M16—41no—
57C13×M16—41no—
58C2×C8×C13C22⋊C411yescharacteristic
59C2×C8×C13C22⋊C411yescharacteristic
60C2×C8×C13C22×C411yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C42×C13—21no—
63C42×C13C22⋊C411yescharacteristic
64C42×C13C22⋊C411yescharacteristic
65C22⋊Dic13—41no—
66#6103—42no—
67#6103—42no—
68C4⋊Dic13—22no—
69C4⋊Dic13—41no—
70C4⋊Dic13—41no—
71C4×Dic13—41no—
72#6099—41no—
73#6099—41no—
74C2×#1055—41no—
75D104—42no—
76D104—42no—
77C13×C16—42no—
78#3184—131no—
79#2165D1311yescharacteristic, complemented
80#1841—131no—
81#1341—132no—
82#1339—132no—
83C23×C13AGL(1,ℤ/8)11yescharacteristic
84C22×D13—42no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13C2×C22⋊C411yescharacteristic
91C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
92C22⋊D13—84no—
93C2×Dic13—42no—
94C2×Dic13—81no—
95D52—42no—
96D52—42no—
97D52—82no—
98D52—82no—
99C4×D13—84no—
100Dic26—82no—
101C8×C13—21no—
102C8×C13—21no—
103C8×C13—21no—
104C8×C13—21no—
105#1055—81no—
106#532—261no—
107#498—131no—
108#493—131no—
109#486—261no—
110#469—132no—
111#469—261no—
112#442—132no—
113#442—261no—
114C4×M16C2×D1311yescharacteristic
115#364—21no—
116#349C2×D1312yes—
117#347—21no—
118#344—261no—
119#339—261no—
120#338—131no—
121H(3,ℤ/4)—131no—
122C22×C13—21no—
123C22×C13—41no—
124C22×C13#41811yescharacteristic
125C2×D13—82no—
126C2×D13—82no—
127C2×D13—82no—
128C4×C13—22no—
129C4×C13—21no—
130C4×C13—41no—
131C4×C13#41011yescharacteristic
132C4×C13#42111yescharacteristic
133Dic13—82no—
134Dic13—161no—
135C2×#41—521no—
136C2×D8—132no—
137C2×D8—261no—
138C2×M16—261no—
139C2×M16D5211yescharacteristic
140C2×M16C22×D1311yescharacteristic
141C4⋊Q8—261no—
142#127—261no—
143#124—521no—
144#121—262no—
145#121—521no—
146C4×D4—262no—
147C4×D4—521no—
148#117—261no—
149C2×C42D5211yescharacteristic
150M32—22no—
151#106—132no—
152#106—261no—
153#102—262no—
154#102—262no—
155#97C4×D1311yescharacteristic
156#97C22⋊D1311yescharacteristic
157C4×C8C4×D1311yescharacteristic
158C4×C8C22⋊D1311yescharacteristic
159C2×C13—21no—
160C2×C13—41no—
161C2×C13#151411yescharacteristic
162D13—162no—
163#41—1044no—
164C2×Q8—521no—
165C2×D4—262no—
166C2×D4—521no—
167C2×D4—521no—
168C2×D4—522no—
169C22×C4—21no—
170C22×C4—522no—
171C22×C4C2×D5211yescharacteristic
172D8—522no—
173D8—522no—
174M16—41no—
175M16—41no—
176M16—521no—
177M16—521no—
178C2×C8—521no—
179C2×C8#610311yescharacteristic
180C2×C8#610311yescharacteristic
181C2×C8C2×C4×D1311yescharacteristic
182C2×C8C2×C22⋊D1311yescharacteristic
183C4⋊C4—262no—
184C4⋊C4—521no—
185C4⋊C4—521no—
186C22⋊C4—522no—
187C22⋊C4—522no—
188C22⋊C4—521no—
189C42—21no—
190C42—521no—
191C42#610311yescharacteristic
192C42#610311yescharacteristic
193C16—42no—
194C13#1183711yescharacteristic, complemented, Sylow
195C23—522no—
196C23#8816211yescharacteristic
197Q8—1042no—
198D4—522no—
199D4—522no—
200D4—1042no—
201D4—1042no—
202D4—1044no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—522no—
209C2×C4—1044no—
210C2×C4—1041no—
211C2×C4#8816211yescharacteristic
212C2×C4C2×#610311yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—21no—
217C8—1041no—
218C22—21no—
219C22—41no—
220C22—1042no—
221C22—1042no—
222C22—1042no—
223C22#1171879211yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—1042no—
228C4—2081no—
229C4#1171866711yescharacteristic
230C4#1171880011yescharacteristic
231C2—21no—
232C2—41no—
233C2—2082no—
234C2#1311338411yescharacteristic
subgroupG/H
centerC2#13113384
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2165C2
socleC2×C13#1514
prime radical#13125574C2
cosocleC2×C13×M16C23
hypercenter#2165D13
hypocenterC13#11837
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #13114985C2semidirect
3. #13112828C2semidirect
4. #13112822C2semidirect
5. C13×#2165C2semidirect
11. #11718372C4semidirect
12. #11718356C4semidirect
14. #11718341C4semidirect
79. #2165D13semidirect
194. C13#11837semidirect

Maximal subgroups

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

subgroupindex
#131255742
#131149852
#131128282
#131128222
C13×#21652
#1183713