Finite Group Databasebeta

← #15773765

Subgroups — #15773765

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#13116648C211yesmaximal, characteristic, complemented
3#13112826C212yesmaximal, complemented
4#13112820C212yesmaximal, complemented
5C13×#1841C211yesmaximal, 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×#344—21no—
16C13×#339—21no—
17C13×#338C2211yescharacteristic
18C13×H(3,ℤ/4)C2211yescharacteristic
19#11718145C2212yes—
20#11718058—21no—
21#11718055—21no—
22C2×#6127—41no—
23C2×C13×M16—21no—
24C2×C13×M16D411yescharacteristic
25C2×C13×M16C2311yescharacteristic
26C13×#117—21no—
27C2×C42×C13D411yescharacteristic
28#88184—22no—
29#88184—41no—
30C2×D104—21no—
31C2×D104C2×C412yes—
32#88129—41no—
33#88128—21no—
34C4×D52—22no—
35C4×D52—41no—
36#88123—21no—
37C13×#97C2×C411yescharacteristic
38C13×#97D411yescharacteristic
39C4×C8×C13C2×C411yescharacteristic
40C4×C8×C13D411yescharacteristic
41#88061—22no—
42#88061—22no—
43#88057—21no—
44#88057C2×C412yes—
45#88052—22no—
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—
58C13×M16—41no—
59C13×M16—41no—
60C2×C8×C13—41no—
61C2×C8×C13C22⋊C411yescharacteristic
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22×C411yescharacteristic
64C2×C8×C13C2×D411yescharacteristic
65C13×C4⋊C4—41no—
66C13×C22⋊C4—41no—
67C42×C13—21no—
68C42×C13—41no—
69C42×C13C22⋊C411yescharacteristic
70C42×C13C22⋊C411yescharacteristic
71#6103—42no—
72#6103—42no—
73C4⋊Dic13—22no—
74C4⋊Dic13—41no—
75D104—42no—
76D104—42no—
77#6090—42no—
78#3184—131no—
79#2165—131no—
80#1841D1311yescharacteristic, complemented
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×C13—81no—
91C2×C4×C13C2×C22⋊C411yescharacteristic
92C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
93C22⋊D13—84no—
94C2×Dic13—42no—
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—
105C8×C13—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—261no—
116#349—132no—
117#347—261no—
118#344—21no—
119#339—21no—
120#338C2×D1311yescharacteristic
121H(3,ℤ/4)C2×D1311yescharacteristic
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—161no—
132C4×C13#41011yescharacteristic
133C4×C13#42111yescharacteristic
134Dic13—82no—
135C2×#41—521no—
136C2×D8—132no—
137C2×D8—261no—
138C2×M16—21no—
139C2×M16C22⋊D1311yescharacteristic
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—21no—
149C2×C42C22⋊D1311yescharacteristic
150M32—262no—
151#106—132no—
152#106—261no—
153#102—262no—
154#102—262no—
155#97C4×D1311yescharacteristic
156#97D5211yescharacteristic
157C4×C8C4×D1311yescharacteristic
158C4×C8D5211yescharacteristic
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×C22⋊D1311yescharacteristic
172D8—522no—
173D8—522no—
174M16—41no—
175M16—41no—
176M16—41no—
177M16—41no—
178C2×C8—41no—
179C2×C8#610311yescharacteristic
180C2×C8#610311yescharacteristic
181C2×C8C2×C4×D1311yescharacteristic
182C2×C8C2×D5211yescharacteristic
183C4⋊C4—41no—
184C4⋊C4—262no—
185C4⋊C4—521no—
186C22⋊C4—41no—
187C22⋊C4—522no—
188C22⋊C4—522no—
189C42—21no—
190C42—41no—
191C42#610311yescharacteristic
192C42#610311yescharacteristic
193C16—522no—
194C13#1183711yescharacteristic, complemented, Sylow
195C23—522no—
196C23#8820311yescharacteristic
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—81no—
209C2×C4—522no—
210C2×C4—1044no—
211C2×C4C2×#610311yescharacteristic
212C2×C4#8820311yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—21no—
217C8—81no—
218C22—21no—
219C22—41no—
220C22—1042no—
221C22—1042no—
222C22—1042no—
223C22#1171866211yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—161no—
228C4—1042no—
229C4#1171866611yescharacteristic
230C4#1171866711yescharacteristic
231C2—21no—
232C2—41no—
233C2—2082no—
234C2#1311338211yescharacteristic
subgroupG/H
centerC2#13113382
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1841C2
socleC2×C13#1514
prime radical#13125574C2
cosocleC2×C13×M16C23
hypercenter#1841D13
hypocenterC13#11837
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #1841

Complements

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

NH ≅ G/Ntype
2. #13116648C2semidirect
3. #13112826C2semidirect
4. #13112820C2semidirect
5. C13×#1841C2semidirect
11. #11718372C4semidirect
12. #11718356C4semidirect
14. #11718341C4semidirect
80. #1841D13semidirect
194. C13#11837semidirect

Maximal subgroups

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

subgroupindex
#131255742
#131166482
#131128262
#131128202
C13×#18412
#1183713