Finite Group Databasebeta

← #15777321

Subgroups — #15777321

Order 3328.

196 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 53 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#13117077C211yesmaximal, characteristic, complemented
2#13117013C211yesmaximal, characteristic, complemented
3#13116909C211yesmaximal, characteristic
4#13116677C211yesmaximal, characteristic, complemented
5#13112903C211yesmaximal, characteristic, complemented
6#13112898C211yesmaximal, characteristic, complemented
7C13×#1357C211yesmaximal, characteristic, complemented
8C13×#493C2211yescharacteristic
9#11718808—21no—
10#11718568—21no—
11#11718361C2211yescharacteristic
12#11718344C2211yescharacteristic
13C13×#364C2211yescharacteristic
14C13×#364C2211yescharacteristic
15#11718155—21no—
16#11718154—21no—
17#11718154—21no—
18#11718110—21no—
19#11718107—21no—
20#11718105—21no—
21#11718055C2211yescharacteristic
22#11718053C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×#127—21no—
26#88158D411yescharacteristic
27#88155—21no—
28#88124—21no—
29C13×M32—21no—
30C13×M32—21no—
31C4×C8×C13C2311yescharacteristic
32#88067—41no—
33#88066—41no—
34#88059D411yescharacteristic
35#88058—21no—
36#88057—21no—
37#88052—21no—
38C2×#6090D411yescharacteristic
39C2×#6090D411yescharacteristic
40#88045—21no—
41#88038—41no—
42C16×D13—41no—
43#12465—131nomaximal, Sylow
44C2×D4×C13—41no—
45C2×D4×C13—81no—
46#6127—21no—
47C13×D8—41no—
48C13×D8—41no—
49C13×D8—41no—
50C13×D8—41no—
51C2×C8×C13C2×D411yescharacteristic
52C2×C8×C13C2×D411yescharacteristic
53C42×C13#4111yescharacteristic
54C4⋊Dic13—41no—
55#6101—81no—
56#6099—21no—
57Dic52SD1611yescharacteristic
58D104SD1611yescharacteristic
59#6095—21no—
60#6094—41no—
61C8×D13—41no—
62C13×C16—41no—
63C13×C16—41no—
64#6090—21no—
65#6090—21no—
66#6090—41no—
67#2244—131no—
68#2231—131no—
69#2213—131no—
70#2171—131no—
71#1369—131no—
72#1366—131no—
73#1357D1311yescharacteristic, complemented
74C23×C13—81no—
75D4×C13—81no—
76D4×C13—81no—
77D4×C13—162no—
78C2×C4×C13—21no—
79C2×C4×C13#12111yescharacteristic
80C22⋊D13—41no—
81C2×Dic13—81no—
82D52—21no—
83C4×D13—41no—
84Dic26—21no—
85C8×C13C2×SD1611yescharacteristic
86C8×C13#13511yescharacteristic
87C8×C13#13511yescharacteristic
88C8×C13AGL(1,ℤ/8)11yescharacteristic
89#1055—41no—
90#509—261no—
91#504—261no—
92#499—131no—
93#493C2×D1311yescharacteristic
94#443—131no—
95#365—261no—
96#364—131no—
97#364C2×D1311yescharacteristic
98#364C2×D1311yescharacteristic
99#361—261no—
100#360—261no—
101#357—261no—
102#357—261no—
103#350—261no—
104#346—131no—
105C22×C13—162no—
106C22×C13—161no—
107C22×C13#47211yescharacteristic
108C2×D13—41no—
109C4×C13—41no—
110C4×C13#46311yescharacteristic
111C4×C13#46511yescharacteristic
112Dic13—41no—
113Dic13—161no—
114#135—131no—
115C2×D8—21no—
116C2×D8—21no—
117#131—261no—
118#127—21no—
119#125—261no—
120SD32—521no—
121D16—521no—
122M32—21no—
123M32—21no—
124M32—261no—
125M32—521no—
126C2×C16—131no—
127C2×C16—131no—
128C2×C16—521no—
129#108—131no—
130#107—261no—
131#106—261no—
132#104—261no—
133C4×C8C22×D1311yescharacteristic
134C2×C13—21no—
135C2×C13—321no—
136C2×C13#167711yescharacteristic
137D13—81no—
138#41—261no—
139C2×D4—41no—
140C2×D4—81no—
141Q16—131no—
142SD16—261no—
143D8—41no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—131no—
148M16—261no—
149M16—521no—
150C2×C8—521no—
151C2×C8D4×D1311yescharacteristic
152C2×C8D4×D1311yescharacteristic
153C4⋊C4—521no—
154C4⋊C4—1041no—
155C42#612711yescharacteristic
156C16—41no—
157C16—41no—
158C16—261no—
159C16—261no—
160C16—521no—
161C13#1246511yescharacteristic, complemented, Sylow
162C23—81no—
163Q8—261no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—261no—
168D4—521no—
169C2×C4—21no—
170C2×C4—521no—
171C2×C4—1041no—
172C2×C4#8813811yescharacteristic
173C8—521no—
174C8#8816511yescharacteristic
175C8#8816611yescharacteristic
176C8SD16×D1311yescharacteristic
177C8#8817011yescharacteristic
178C22—162no—
179C22—161no—
180C22—521no—
181C22#1171841011yescharacteristic
182C4—41no—
183C4—521no—
184C4—2081no—
185C4#1171843911yescharacteristic
186C4#1171844811yescharacteristic
187C2—21no—
188C2—321no—
189C2—1041no—
190C2#1311424411yescharacteristic
subgroupG/H
centerC2#13114244
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1357C2
socleC2×C13#1677
prime radical#13116909C2
hypercenter#1357D13
hypocenterC13#12465
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
1. #13117077C2semidirect
2. #13117013C2semidirect
4. #13116677C2semidirect
5. #13112903C2semidirect
6. #13112898C2semidirect
7. C13×#1357C2semidirect
73. #1357D13semidirect
161. C13#12465semidirect

Maximal subgroups

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

subgroupindex
#131170772
#131170132
#131169092
#131166772
#131129032
#131128982
C13×#13572
#1246513