Finite Group Databasebeta

← #15750379

Subgroups — #15750379

Order 3328.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×Dic104C211yesmaximal, characteristic
2#13112910C211yesmaximal, characteristic
3C13×#1397C211yesmaximal, characteristic
4C2×Dic104C411yescharacteristic
5C4×Dic52—21no—
6C2×C13×C32—21no—
7C4×C13×C16C2211yescharacteristic
8#11718096C411yescharacteristic
9#11718095—21no—
10#11718050—21no—
11C2×Dic52—21no—
12C4×Dic26—41no—
13C2×C13×C16C2×C411yescharacteristic
14C2×C13×C16D411yescharacteristic
15C4×C8×C13D411yescharacteristic
16#88058—21no—
17#88056—41no—
18C4⋊#1055—41no—
19Dic104—21no—
20Dic104C812yescomplemented
21C13×C32—22no—
22#7386—131nomaximal, Sylow
23C2×Dic26—41no—
24C2×C8×C13C22⋊C411yescharacteristic
25C2×C8×C13SD1611yescharacteristic
26C42×C13D811yescharacteristic
27C4⋊Dic13—41no—
28#6101—81no—
29C4×Dic13—81no—
30C2×#1055—81no—
31Dic52—22no—
32Dic52—41no—
33C13×C16—21no—
34C13×C16C2×C811yescharacteristic
35C13×C16M1611yescharacteristic
36C4×Q32—131no—
37#1397D1311yescharacteristic
38#1372—131no—
39C2×C4×C13#10211yescharacteristic
40C2×C4×C13D1611yescharacteristic
41C2×C4×C13SD3211yescharacteristic
42C2×Dic13—81no—
43C2×Dic13—81no—
44Dic26—42no—
45Dic26—81no—
46C8×C13—21no—
47C8×C13C22⋊C811yescharacteristic
48C8×C13#10411yescharacteristic
49#1055—161no—
50C2×Q32—131no—
51C4×Q16—261no—
52C2×C32—21no—
53#366—131no—
54#358—261no—
55C4×C16C2×D1311yescharacteristic
56#335—261no—
57C22×C13#35711yescharacteristic
58C4×C13—21no—
59C4×C13—21no—
60C4×C13D4⋊C811yescharacteristic
61C4×C13#35911yescharacteristic
62Dic13—82no—
63Dic13—161no—
64C2×Q16—261no—
65C4×Q8—521no—
66Q32—132no—
67Q32—261no—
68C2×C16C4×D1311yescharacteristic
69C2×C16C22⋊D1311yescharacteristic
70#107—261no—
71C4⋊C8—521no—
72#103—521no—
73C4×C8D5211yescharacteristic
74C32—22no—
75C2×C13#133111yescharacteristic
76C2×C13#141811yescharacteristic
77C2×C13#142011yescharacteristic
78C2×Q8—521no—
79Q16—262no—
80Q16—521no—
81C2×C8—1041no—
82C2×C8#609511yescharacteristic
83C2×C8#610311yescharacteristic
84C4⋊C4—521no—
85C4⋊C4—1041no—
86C42—1041no—
87C42D10411yescharacteristic
88C16—21no—
89C16C8×D1311yescharacteristic
90C16#609411yescharacteristic
91C13#738611yescharacteristic, complemented, Sylow
92Q8—522no—
93Q8—1041no—
94C2×C4—1041no—
95C2×C4—1041no—
96C2×C4D20811yescharacteristic
97C2×C4#8804011yescharacteristic
98C2×C4#8806111yescharacteristic
99C8—21no—
100C8—2081no—
101C8#8804511yescharacteristic
102C8#8806011yescharacteristic
103C22#1171810111yescharacteristic
104C4—21no—
105C4—21no—
106C4—1042no—
107C4—2081no—
108C4#1171805111yescharacteristic
109C4#1171810211yescharacteristic
110C2#1311279811yescharacteristic
111C2#1311302411yescharacteristic
112C2#1311303011yescharacteristic
subgroupG/H
centerC22#11718101
commutatorC13×C16C2×C8
FrattiniC4×C16C2×D13
FittingC13×#1397C2
socle, prime radicalC22×C13#357
cosocleC4×C13×C16C22
hypercenter#1397D13
hypocenterC13#7386
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×C16 ◁ #1397

Complements

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

NH ≅ G/Ntype
20. Dic104C8semidirect
91. C13#7386semidirect

Maximal subgroups

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

subgroupindex
C4×Dic1042
#131129102
C13×#13972
#738613