Finite Group Databasebeta

← #15777325

Subgroups — #15777325

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#13117079C211yesmaximal, characteristic, complemented
2#13117009C211yesmaximal, characteristic, complemented
3#13116913C211yesmaximal, characteristic
4#13116677C211yesmaximal, characteristic, complemented
5#13112903C211yesmaximal, characteristic, complemented
6#13112872C211yesmaximal, characteristic, complemented
7C13×#1366C211yesmaximal, characteristic, complemented
8C13×#499C2211yescharacteristic
9#11718569—21no—
10#11718568—21no—
11#11718361C2211yescharacteristic
12#11718356C2211yescharacteristic
13C13×#364C2211yescharacteristic
14C13×#364C2211yescharacteristic
15#11718108—21no—
16#11718107—21no—
17#11718083—21no—
18#11718083—21no—
19#11718080—21no—
20#11718079—21no—
21#11718055C2211yescharacteristic
22#11718053C2211yescharacteristic
23C13×#125—21no—
24#88158D411yescharacteristic
25C2×D104—21no—
26C2×D104—21no—
27#88155—21no—
28#88128—21no—
29C13×M32—21no—
30C13×M32—21no—
31C13×#107—21no—
32C13×#106—21no—
33C4×C8×C13C2311yescharacteristic
34#88059D411yescharacteristic
35#88052—21no—
36C2×#6090D411yescharacteristic
37C2×#6090D411yescharacteristic
38#88045—21no—
39#88040—41no—
40D208—41no—
41#88038—41no—
42C16×D13—41no—
43#12465—131nomaximal, Sylow
44#6127—21no—
45C2×D52—41no—
46C2×D52—81no—
47C2×C8×C13C2×D411yescharacteristic
48C2×C8×C13C2×D411yescharacteristic
49C13×C4⋊C4—41no—
50C13×C4⋊C4—81no—
51C42×C13#4111yescharacteristic
52#6099—21no—
53Dic52SD1611yescharacteristic
54D104—41no—
55D104—41no—
56D104—41no—
57D104—41no—
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#1366D1311yescharacteristic, complemented
73#1357—131no—
74C22×D13—81no—
75C2×C4×C13—21no—
76C2×C4×C13—81no—
77C2×C4×C13#12111yescharacteristic
78C22⋊D13—41no—
79D52—21no—
80D52—81no—
81D52—81no—
82D52—162no—
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#499C2×D1311yescharacteristic
93#493—131no—
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#47211yescharacteristic
106C2×D13—41no—
107C2×D13—162no—
108C2×D13—161no—
109C4×C13—41no—
110C4×C13—161no—
111C4×C13#46311yescharacteristic
112C4×C13#46511yescharacteristic
113Dic13—41no—
114#135—131no—
115C2×D8—261no—
116C2×D8—261no—
117#131—261no—
118#127—261no—
119#125—21no—
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—21no—
131#106—21no—
132#104—261no—
133C4×C8C22×D1311yescharacteristic
134C2×C13—21no—
135C2×C13#167711yescharacteristic
136D13—81no—
137D13—321no—
138#41—261no—
139C2×D4—521no—
140C2×D4—1041no—
141Q16—131no—
142SD16—261no—
143D8—131no—
144D8—521no—
145D8—521no—
146D8—521no—
147D8—521no—
148M16—261no—
149M16—521no—
150C2×C8—521no—
151C2×C8D4×D1311yescharacteristic
152C2×C8D4×D1311yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—81no—
155C42#612711yescharacteristic
156C16—41no—
157C16—41no—
158C16—261no—
159C16—261no—
160C16—521no—
161C13#1246511yescharacteristic, complemented, Sylow
162C23—1041no—
163Q8—261no—
164D4—261no—
165D4—521no—
166D4—1041no—
167D4—1041no—
168D4—2082no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—521no—
172C2×C4#8813811yescharacteristic
173C8—521no—
174C8SD16×D1311yescharacteristic
175C8#8816811yescharacteristic
176C8#8817311yescharacteristic
177C8#8817311yescharacteristic
178C22—521no—
179C22—2082no—
180C22—2081no—
181C22#1171841011yescharacteristic
182C4—41no—
183C4—161no—
184C4—521no—
185C4#1171846811yescharacteristic
186C4#1171848011yescharacteristic
187C2—21no—
188C2—1041no—
189C2—4161no—
190C2#1311424811yescharacteristic
subgroupG/H
centerC2#13114248
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1366C2
socleC2×C13#1677
prime radical#13116913C2
hypercenter#1366D13
hypocenterC13#12465
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
1. #13117079C2semidirect
2. #13117009C2semidirect
4. #13116677C2semidirect
5. #13112903C2semidirect
6. #13112872C2semidirect
7. C13×#1366C2semidirect
72. #1366D13semidirect
161. C13#12465semidirect

Maximal subgroups

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

subgroupindex
#131170792
#131170092
#131169132
#131166772
#131129032
#131128722
C13×#13662
#1246513