Finite Group Databasebeta

← #15750493

Subgroups — #15750493

Order 3328.

146 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 41 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#13116939C211yesmaximal, characteristic
2#13112940C211yesmaximal, characteristic, complemented
3C13×#1400C211yesmaximal, characteristic, complemented
4C2×C13×M32C2211yescharacteristic
5#11718776—21no—
6C2×#88059—21no—
7C2×D208C411yescharacteristic
8C13×M64—21no—
9#11718101—21no—
10#11718097C411yescharacteristic
11C22×C8×C13D411yescharacteristic
12#88184—41no—
13C2×#6099—41no—
14C2×D104—21no—
15C13×M32—41no—
16C2×C13×C16C2×C411yescharacteristic
17C2×C13×C16D411yescharacteristic
18#88061—41no—
19#88059—22no—
20#88059—41no—
21#88058—21no—
22D208—41no—
23C13×C32—41no—
24#7424—131nomaximal, Sylow
25C22×C4×C13D811yescharacteristic
26C2×C22⋊D13—81no—
27C2×D52—41no—
28C2×C8×C13—21no—
29C2×C8×C13—21no—
30C2×C8×C13C22⋊C411yescharacteristic
31C2×C8×C13SD1611yescharacteristic
32#6103—81no—
33C4⋊Dic13—41no—
34#6099—42no—
35#6099—81no—
36C2×#1055—81no—
37D104—41no—
38D104—41no—
39C13×C16—21no—
40C13×C16—21no—
41#2218—131no—
42#1400D1311yescharacteristic, complemented
43#1385—131no—
44C23×C13SD3211yescharacteristic
45C22×D13—81no—
46C2×C4×C13—21no—
47C2×C4×C13—21no—
48C2×C4×C13#10211yescharacteristic
49C2×C4×C13D1611yescharacteristic
50C22⋊D13—162no—
51C2×Dic13—81no—
52D52—81no—
53D52—81no—
54C8×C13—21no—
55C8×C13#9911yescharacteristic
56C8×C13#10411yescharacteristic
57#1055—82no—
58C2×D16—131no—
59C2×M32C2×D1311yescharacteristic
60#466—261no—
61C2×#108—261no—
62M64—21no—
63#367—131no—
64#357—261no—
65C22×C13—21no—
66C22×C13—41no—
67C22×C13#35711yescharacteristic
68C2×D13—161no—
69C2×D13—161no—
70C2×D13—161no—
71C4×C13—21no—
72C4×C13#32711yescharacteristic
73C4×C13#36011yescharacteristic
74Dic13—161no—
75C2×D8—261no—
76C2×M16—521no—
77C22×C8D5211yescharacteristic
78#121—521no—
79D16—521no—
80M32—41no—
81C2×C16C4×D1311yescharacteristic
82C2×C16C22⋊D1311yescharacteristic
83#108—262no—
84#108—521no—
85#107—261no—
86#102—521no—
87C32—41no—
88C2×C13—21no—
89C2×C13—41no—
90C2×C13#134711yescharacteristic
91D13—321no—
92C2×D4—521no—
93C2×D4—1041no—
94C22×C4D10411yescharacteristic
95D8—521no—
96D8—521no—
97M16—522no—
98M16—1041no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8—1041no—
102C2×C8#609511yescharacteristic
103C2×C8#610311yescharacteristic
104C4⋊C4—521no—
105C22⋊C4—1041no—
106C16—21no—
107C16—21no—
108C13#742411yescharacteristic, complemented, Sylow
109C23—1041no—
110C23#8804011yescharacteristic
111D4—1041no—
112D4—1041no—
113D4—2082no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—1041no—
117C2×C4D20811yescharacteristic
118C2×C4#8806111yescharacteristic
119C8—21no—
120C8—1042no—
121C8#8804611yescharacteristic
122C8#8806511yescharacteristic
123C22—21no—
124C22—41no—
125C22—2081no—
126C22—2081no—
127C22—2081no—
128C22#1171810111yescharacteristic
129C4—21no—
130C4—2081no—
131C4#1171806211yescharacteristic
132C4#1171811011yescharacteristic
133C2—21no—
134C2—41no—
135C2—4161no—
136C2#1311284611yescharacteristic
subgroupG/H
centerC2#13112846
commutatorC2×C13×C16C2×C4
FrattiniC2×M32C2×D13
FittingC13×#1400C2
socleC2×C13#1347
prime radical#13116939C2
cosocleC2×C13×M32C22
hypercenter#1400D13
hypocenterC13#7424
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #1400

Complements

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

NH ≅ G/Ntype
2. #13112940C2semidirect
3. C13×#1400C2semidirect
42. #1400D13semidirect
108. C13#7424semidirect

Maximal subgroups

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

subgroupindex
#131169392
#131129402
C13×#14002
#742413