Finite Group Databasebeta

← #15750624

Subgroups — #15750624

Order 3328.

170 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#11718098C211yesmaximal, characteristic
2#13116620C211yesmaximal, characteristic
3C22×C13×C32C211yesmaximal, characteristic
4C22×C13×C16C2211yescharacteristic
5C2×#88059—21no—
6#11718767—21no—
7C2×C13×C32—21no—
8C2×C13×C32—21no—
9C2×C13×C32C412yescomplemented
10#11718098—21no—
11#11718098C412yescomplemented
12#11718097—21no—
13#11718096C412yes—
14C22×C8×C13D411yescharacteristic
15#88180—41no—
16C2×#6099—41no—
17C2×C13×C16C2×C411yescharacteristic
18C2×C13×C16C2×C411yescharacteristic
19C2×C13×C16C2×C411yescharacteristic
20C2×C13×C16D411yescharacteristic
21C2×C13×C16D411yescharacteristic
22C2×C13×C16Q811yescharacteristic
23#88059—22no—
24#88059—41no—
25#88058—22no—
26#88057—41no—
27C13×C32—22no—
28#7473—131nomaximal, Sylow
29C22×C4×C13D811yescharacteristic
30C2×C8×C13C22⋊C411yescharacteristic
31C2×C8×C13C22⋊C411yescharacteristic
32C2×C8×C13C4⋊C411yescharacteristic
33C2×C8×C13SD1611yescharacteristic
34C2×C8×C13SD1611yescharacteristic
35C2×C8×C13Q1611yescharacteristic
36C22⋊Dic13—81no—
37C4⋊Dic13—42no—
38C4×Dic13—81no—
39#6099—42no—
40#6099—81no—
41C2×#1055—81no—
42C13×C16C4211yescharacteristic
43C13×C16C22⋊C411yescharacteristic
44C13×C16C4⋊C411yescharacteristic
45C13×C16C4⋊C411yescharacteristic
46C22×C32D1311yescharacteristic
47C2×#368—131no—
48#2158—131no—
49C23×C13SD3211yescharacteristic
50C2×C4×C13#10211yescharacteristic
51C2×C4×C13#10211yescharacteristic
52C2×C4×C13#10711yescharacteristic
53C2×C4×C13D1611yescharacteristic
54C2×C4×C13SD3211yescharacteristic
55C2×C4×C13Q3211yescharacteristic
56C2×Dic13—82no—
57C8×C13#9511yescharacteristic
58C8×C13#10311yescharacteristic
59C8×C13#10311yescharacteristic
60C8×C13#10611yescharacteristic
61#1055—82no—
62C22×C16C2×D1311yescharacteristic
63C2×#108—261no—
64#427—261no—
65C2×C32—21no—
66C2×C32—21no—
67C2×C32Dic1312yescomplemented
68#368—132no—
69#368—261no—
70#367—261no—
71#366—132no—
72C22×C13—22no—
73C22×C13#35711yescharacteristic
74C22×C13#35811yescharacteristic
75C22×C13#36711yescharacteristic
76C4×C13#34011yescharacteristic
77C4×C13#35711yescharacteristic
78C4×C13#35811yescharacteristic
79C4×C13#36611yescharacteristic
80Dic13—162no—
81C2×M16—521no—
82C22×C8D5211yescharacteristic
83#117—521no—
84C2×C16Dic2611yescharacteristic
85C2×C16C4×D1311yescharacteristic
86C2×C16C4×D1311yescharacteristic
87C2×C16C2×Dic1311yescharacteristic
88C2×C16C22⋊D1311yescharacteristic
89C2×C16C22⋊D1311yescharacteristic
90#108—262no—
91#108—521no—
92#107—262no—
93#106—521no—
94C32—22no—
95C2×C13—21no—
96C2×C13—21no—
97C2×C13#138011yescharacteristic
98C2×C13#141712yes—
99C22×C4D10411yescharacteristic
100M16—522no—
101M16—1041no—
102C2×C8—1041no—
103C2×C8#609511yescharacteristic
104C2×C8#609511yescharacteristic
105C2×C8Dic5211yescharacteristic
106C2×C8C4⋊Dic1311yescharacteristic
107C2×C8#610311yescharacteristic
108C2×C8#610311yescharacteristic
109C4⋊C4—522no—
110C22⋊C4—1041no—
111C42—1041no—
112C16C4×Dic1311yescharacteristic
113C16#610111yescharacteristic
114C16#610111yescharacteristic
115C16C22⋊Dic1311yescharacteristic
116C13#747311yescharacteristic, complemented, Sylow
117C23#8804011yescharacteristic
118C2×C4—1042no—
119C2×C4D20811yescharacteristic
120C2×C4#8804011yescharacteristic
121C2×C4Dic10411yescharacteristic
122C2×C4#8805811yescharacteristic
123C2×C4#8806111yescharacteristic
124C2×C4#8806111yescharacteristic
125C8—1042no—
126C8#8805611yescharacteristic
127C8#8805611yescharacteristic
128C8#8805711yescharacteristic
129C8#8807111yescharacteristic
130C22—22no—
131C22#1171809511yescharacteristic
132C22#1171809711yescharacteristic
133C22#1171810111yescharacteristic
134C4—2082no—
135C4#1171809511yescharacteristic
136C4#1171809611yescharacteristic
137C4#1171810111yescharacteristic
138C4#1171814311yescharacteristic
139C2—21no—
140C2—21no—
141C2#1311292811yescharacteristic
142C2#1311302112yes—
subgroupG/H
centerC2×C4D208
commutatorC13×C16C42
FrattiniC22×C16C2×D13
FittingC22×C13×C32C2
socleC22×C13#357
prime radicalC23×C13SD32
cosocleC22×C13×C16C22
hypercenterC22×C32D13
hypocenterC13#7473
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
9. C2×C13×C32C4semidirect
11. #11718098C4semidirect
67. C2×C32Dic13semidirect
116. C13#7473semidirect

Maximal subgroups

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

subgroupindex
C2×#117180982
#131166202
C22×C13×C322
#747313