Finite Group Databasebeta

← #15777034

Subgroups — #15777034

Order 3328.

256 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 65 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#13116974C211yesmaximal, characteristic, complemented
2#13116868C211yesmaximal, characteristic
3#13114425C211yesmaximal, characteristic, complemented
4#13113630C211yesmaximal, characteristic, complemented
5#13112899C211yesmaximal, characteristic, complemented
6#13112892C211yesmaximal, characteristic, complemented
7C13×#1361C211yesmaximal, characteristic, complemented
8C13×#493C2211yescharacteristic
9C2×#88066—21no—
10#11718737—21no—
11#11718731—21no—
12#11718495—21no—
13C4×D104C2211yescharacteristic
14#11718343C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718154—21no—
18#11718101—21no—
19#11718096—21no—
20#11718075—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×#127—21no—
26C2×#6105—41no—
27C2×#6105—41no—
28C2×D104D411yescharacteristic
29C2×C8×D13—41no—
30C4×D52—21no—
31#88123—21no—
32C2×C13×C16—21no—
33C13×C4⋊C8—21no—
34C4×C8×C13C2311yescharacteristic
35#88072—42no—
36#88066—42no—
37#88061—21no—
38#88060—41no—
39#88058—21no—
40#88058—21no—
41#88058D411yescharacteristic
42C2×#6090—21no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45#12416—131nomaximal, Sylow
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D52—21no—
50C2×C4×D13—41no—
51C2×Dic26—41no—
52C13×D8—41no—
53C13×D8—41no—
54C13×D8—81no—
55C2×C8×C13—41no—
56C2×C8×C13C2×D411yescharacteristic
57C2×C8×C13#4111yescharacteristic
58C42×C13C2×D411yescharacteristic
59#6105—82no—
60#6105—82no—
61#6103—41no—
62C4⋊Dic13—21no—
63C4⋊Dic13—41no—
64C4⋊Dic13—41no—
65C2×#1055—21no—
66C2×#1055D811yescharacteristic
67C2×#1055D811yescharacteristic
68D104—21no—
69D104SD1612yescomplemented
70C8×D13—82no—
71C13×C16—41no—
72#6090—41no—
73#2224—131no—
74#2206—131no—
75#1706—131no—
76C8×D8—131no—
77#1367—131no—
78#1364—131no—
79#1361D1311yescharacteristic, complemented
80C23×C13—81no—
81C22×D13—41no—
82D4×C13—82no—
83D4×C13—81no—
84D4×C13—81no—
85D4×C13—81no—
86D4×C13—81no—
87C2×C4×C13#12111yescharacteristic
88C2×C4×C13C2×D811yescharacteristic
89C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
90C2×Dic13—41no—
91C2×Dic13—81no—
92D52—22no—
93D52—41no—
94C4×D13—81no—
95C4×D13—81no—
96Dic26—81no—
97Dic26—81no—
98C8×C13—21no—
99C8×C13—81no—
100C8×C13C2×SD1611yescharacteristic
101C8×C13#13511yescharacteristic
102#1055—21no—
103#1055—41no—
104#1055D1612yescomplemented
105C2×D16—261no—
106#500—131no—
107#493C2×D1311yescharacteristic
108#492—261no—
109#486—261no—
110C4×D8—131no—
111C8×D4—261no—
112#366—261no—
113C4⋊C16—131no—
114C4⋊C16C2×D1311yescharacteristic
115#357—261no—
116#357—261no—
117#335C2×D1311yescharacteristic
118D4⋊C8—261no—
119C82—131no—
120C22×C13—161no—
121C22×C13—161no—
122C22×C13—161no—
123C22×C13#45911yescharacteristic
124C2×D13—42no—
125C2×D13—81no—
126C2×D13—81no—
127C4×C13—21no—
128C4×C13#46511yescharacteristic
129C4×C13#47111yescharacteristic
130C4×C13C2×D1611yescharacteristic
131C4×C13#50911yescharacteristic
132Dic13—81no—
133Dic13—161no—
134C2×SD16—521no—
135C2×SD16—521no—
136C2×D8—21no—
137C2×D8—21no—
138C2×D8—131no—
139C22×C8—521no—
140C4⋊Q8—261no—
141#127—21no—
142C4×D4—261no—
143D16—522no—
144C2×C16—21no—
145C2×C16—261no—
146#107—131no—
147#107—261no—
148#107—261no—
149C4⋊C8—21no—
150#102—261no—
151#102—522no—
152C22⋊C8—521no—
153C4×C8—131no—
154C4×C8—131no—
155C4×C8C22×D1311yescharacteristic
156C2×C13—321no—
157C2×C13#166511yescharacteristic
158C2×C13#220611yescharacteristic
159C2×C13#221211yescharacteristic
160D13—82no—
161C2×Q8—521no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—41no—
165C2×D4—261no—
166C22×C4—521no—
167SD16—1042no—
168SD16—1042no—
169D8—41no—
170D8—41no—
171D8—81no—
172D8—132no—
173D8—261no—
174C2×C8—41no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8—261no—
178C2×C8—1042no—
179C2×C8#612711yescharacteristic
180C2×C8D4×D1311yescharacteristic
181C4⋊C4—261no—
182C4⋊C4—521no—
183C4⋊C4—521no—
184C22⋊C4—521no—
185C42D4×D1311yescharacteristic
186C16—41no—
187C16—521no—
188C13#1241611yescharacteristic, complemented, Sylow
189C23—81no—
190C23—521no—
191Q8—1041no—
192Q8—1041no—
193D4—82no—
194D4—81no—
195D4—81no—
196D4—81no—
197D4—81no—
198D4—262no—
199D4—521no—
200C2×C4—521no—
201C2×C4—1041no—
202C2×C4—1041no—
203C2×C4—1041no—
204C2×C4#8813811yescharacteristic
205C2×C4D8×D1311yescharacteristic
206C2×C4#8816811yescharacteristic
207C8—21no—
208C8—81no—
209C8—132no—
210C8—261no—
211C8—521no—
212C8#8816611yescharacteristic
213C8SD16×D1311yescharacteristic
214C22—161no—
215C22—161no—
216C22—161no—
217C22—522no—
218C22—1041no—
219C22—1041no—
220C22#1171844711yescharacteristic
221C4—21no—
222C4—1041no—
223C4—2081no—
224C4#1171840911yescharacteristic
225C4#1171843911yescharacteristic
226C4D13×D1611yescharacteristic
227C4#1171857511yescharacteristic
228C2—321no—
229C2—1042no—
230C2#1311417611yescharacteristic
231C2#1311687011yescharacteristic
232C2#1311690411yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1361C2
socleC22×C13#459
prime radical#13116868C2
hypercenter#1361D13
hypocenterC13#12416
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #13116974C2semidirect
3. #13114425C2semidirect
4. #13113630C2semidirect
5. #13112899C2semidirect
6. #13112892C2semidirect
7. C13×#1361C2semidirect
69. D104SD16semidirect
79. #1361D13semidirect
104. #1055D16semidirect
188. C13#12416semidirect

Maximal subgroups

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

subgroupindex
#131169742
#131168682
#131144252
#131136302
#131128992
#131128922
C13×#13612
#1241613