Finite Group Databasebeta

← #15777038

Subgroups — #15777038

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#13116970C211yesmaximal, characteristic, complemented
2#13116872C211yesmaximal, characteristic
3#13114429C211yesmaximal, characteristic, complemented
4#13113630C211yesmaximal, characteristic, complemented
5#13112899C211yesmaximal, characteristic, complemented
6#13112881C211yesmaximal, characteristic, complemented
7C13×#1364C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9#11718749—21no—
10#11718746—21no—
11C2×D208—21no—
12#11718495—21no—
13#11718356C2211yescharacteristic
14C4×D104C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718101—21no—
18#11718083—21no—
19#11718081—21no—
20#11718075—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C13×C4⋊Q8—21no—
24C2×#6106—41no—
25C2×#6106—41no—
26C2×D104—21no—
27C2×D104—21no—
28C2×D104D411yescharacteristic
29C2×C8×D13—41no—
30#88128—21no—
31C4×D52—21no—
32C2×C13×C16—21no—
33C13×#107—21no—
34C13×#107—21no—
35C13×C4⋊C8—21no—
36C4×C8×C13C2311yescharacteristic
37#88061—21no—
38#88060—41no—
39#88058D411yescharacteristic
40C2×#6090—21no—
41#88049—42no—
42C4×#1055D411yescharacteristic
43C4×#1055D411yescharacteristic
44D208—42no—
45#12416—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D52—21no—
48C2×D52—41no—
49C2×D52—41no—
50C2×D52—41no—
51C2×C4×D13—41no—
52C2×C8×C13—41no—
53C2×C8×C13C2×D411yescharacteristic
54C2×C8×C13#4111yescharacteristic
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C42×C13C2×D411yescharacteristic
58#6106—82no—
59#6106—82no—
60#6103—41no—
61C4⋊Dic13—21no—
62C2×#1055—21no—
63C2×#1055D811yescharacteristic
64C2×#1055D811yescharacteristic
65D104—21no—
66D104—41no—
67D104—41no—
68D104—81no—
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#1364D1311yescharacteristic, complemented
79#1361—131no—
80C22×D13—41no—
81C22×D13—81no—
82Q8×C13—81no—
83Q8×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13#12111yescharacteristic
86C2×C4×C13C2×D811yescharacteristic
87C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
88C2×Dic13—41no—
89D52—22no—
90D52—41no—
91D52—82no—
92D52—81no—
93D52—81no—
94D52—81no—
95D52—81no—
96C4×D13—81no—
97C4×D13—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#500C2×D1311yescharacteristic
107#493—131no—
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#45911yescharacteristic
121C2×D13—42no—
122C2×D13—81no—
123C2×D13—81no—
124C2×D13—161no—
125C2×D13—161no—
126C2×D13—161no—
127C4×C13—21no—
128C4×C13—161no—
129C4×C13#46511yescharacteristic
130C4×C13#47111yescharacteristic
131C4×C13C2×D1611yescharacteristic
132C4×C13#50911yescharacteristic
133Dic13—81no—
134C2×SD16—521no—
135C2×SD16—521no—
136C2×D8—131no—
137C2×D8—261no—
138C2×D8—261no—
139C22×C8—521no—
140C4⋊Q8—21no—
141#127—261no—
142C4×D4—261no—
143D16—522no—
144C2×C16—21no—
145C2×C16—261no—
146#107—21no—
147#107—21no—
148#107—131no—
149C4⋊C8—21no—
150#102—261no—
151#102—522no—
152C22⋊C8—521no—
153C4×C8—131no—
154C4×C8—131no—
155C4×C8C22×D1311yescharacteristic
156C2×C13#166511yescharacteristic
157C2×C13#220611yescharacteristic
158C2×C13#221211yescharacteristic
159D13—82no—
160D13—321no—
161C2×Q8—41no—
162C2×D4—261no—
163C2×D4—521no—
164C2×D4—521no—
165C2×D4—521no—
166C22×C4—521no—
167SD16—1042no—
168SD16—1042no—
169D8—132no—
170D8—261no—
171D8—521no—
172D8—521no—
173D8—1041no—
174C2×C8—41no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8—261no—
178C2×C8—1042no—
179C2×C8#612711yescharacteristic
180C2×C8D4×D1311yescharacteristic
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—261no—
184C22⋊C4—521no—
185C42D4×D1311yescharacteristic
186C16—41no—
187C16—521no—
188C13#1241611yescharacteristic, complemented, Sylow
189C23—521no—
190C23—1041no—
191Q8—81no—
192Q8—81no—
193D4—262no—
194D4—521no—
195D4—1042no—
196D4—1041no—
197D4—1041no—
198D4—1041no—
199D4—1041no—
200C2×C4—81no—
201C2×C4—521no—
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—
212C8SD16×D1311yescharacteristic
213C8#8817311yescharacteristic
214C22—522no—
215C22—1041no—
216C22—1041no—
217C22—2081no—
218C22—2081no—
219C22—2081no—
220C22#1171844711yescharacteristic
221C4—21no—
222C4—161no—
223C4—1041no—
224C4#1171841511yescharacteristic
225C4#1171846811yescharacteristic
226C4D13×D1611yescharacteristic
227C4#1171857511yescharacteristic
228C2—1042no—
229C2—4161no—
230C2#1311418011yescharacteristic
231C2#1311687011yescharacteristic
232C2#1311690811yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1364C2
socleC22×C13#459
prime radical#13116872C2
hypercenter#1364D13
hypocenterC13#12416
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #13116970C2semidirect
3. #13114429C2semidirect
4. #13113630C2semidirect
5. #13112899C2semidirect
6. #13112881C2semidirect
7. C13×#1364C2semidirect
69. D104SD16semidirect
78. #1364D13semidirect
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
#131169702
#131168722
#131144292
#131136302
#131128992
#131128812
C13×#13642
#1241613