Finite Group Databasebeta

← #16777904

Subgroups — #16777904

Order 3328.

136 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 34 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#13129952C211yesmaximal, characteristic
2#13129906C211yesmaximal, characteristic
3#13116941C211yesmaximal, characteristic
4D13⋊#108—21no—
5C2×C13×Q32C411yescharacteristic
6#11718849—21no—
7C2×#88038C2211yescharacteristic
8#11718249—21no—
9#11718156—21no—
10#11718097C411yescharacteristic
11D13⋊M16—41no—
12C2×C13×Q16—21no—
13#88200—41no—
14C2×C8×D13D411yescharacteristic
15#88104—41no—
16#88103—22no—
17C13×Q32—41no—
18C2×C13×C16C2×C411yescharacteristic
19#88075—41no—
20#88058—21no—
21C2×#6090D411yescharacteristic
22#88038—41no—
23#88036—41no—
24#7425—131nomaximal, Sylow
25C2×Q8×C13—41no—
26C2×C4×D13D811yescharacteristic
27#6122—81no—
28#6118—42no—
29D13⋊C8—81no—
30C13×Q16—41no—
31C13×Q16—41no—
32C2×C8×C13C22⋊C411yescharacteristic
33#6103—81no—
34C4⋊Dic13—41no—
35#6101—81no—
36C2×#1055SD1611yescharacteristic
37C8×D13—21no—
38C8×D13—21no—
39C13×C16—21no—
40#6090—21no—
41#2219—131no—
42#1400—131no—
43#1385—131no—
44C22×D13SD3211yescharacteristic
45Q8×C13—81no—
46Q8×C13—81no—
47C2×C4×C13—81no—
48C2×C4×C13#10211yescharacteristic
49C2×Dic13—81no—
50C2×Dic13D1611yescharacteristic
51C4×D13—21no—
52C4×D13—21no—
53#1057—82no—
54C8×C13#9911yescharacteristic
55C8×C13#10411yescharacteristic
56#1055—21no—
57C2×Q32#26111yescharacteristic
58C2×M32—131no—
59#467—261no—
60C2×#108—261no—
61M64—261no—
62#367—131no—
63#358—261no—
64C22×C13#35711yescharacteristic
65C2×D13—21no—
66C2×D13—41no—
67C4×C13—161no—
68C4×C13#32711yescharacteristic
69C4×C13#36011yescharacteristic
70Dic13—21no—
71Dic13—161no—
72C2×Q16—21no—
73C2×M16—521no—
74C22×C8—131no—
75C22⋊Q8—521no—
76Q32—41no—
77M32—521no—
78C2×C16—131no—
79C2×C16C2×#26111yescharacteristic
80#108—262no—
81#108—521no—
82#107—261no—
83#103—521no—
84C32—521no—
85C2×C13—21no—
86C2×C13#134711yescharacteristic
87D13—41no—
88C2×Q8—41no—
89C22×C4—131no—
90Q16—41no—
91Q16—41no—
92M16—522no—
93M16—1041no—
94C2×C8—131no—
95C2×C8—261no—
96C2×C8—261no—
97C2×C8—1041no—
98C2×C8C22⋊#26111yescharacteristic
99C4⋊C4—521no—
100C4⋊C4—1041no—
101C22⋊C4—1041no—
102C16—21no—
103C16—261no—
104C13#742511yescharacteristic, complemented, Sylow
105C23—131no—
106Q8—81no—
107Q8—81no—
108C2×C4—81no—
109C2×C4—131no—
110C2×C4—261no—
111C2×C4—261no—
112C2×C4—1041no—
113C2×C4#8811511yescharacteristic
114C8—261no—
115C8—1042no—
116C8#8811611yescharacteristic
117C8#8811911yescharacteristic
118C22—261no—
119C22—521no—
120C22#1171827611yescharacteristic
121C4—161no—
122C4—261no—
123C4—2081no—
124C4#1171827511yescharacteristic
125C4#1171829211yescharacteristic
126C2—21no—
127C2—521no—
128C2#1312982211yescharacteristic
subgroupG/H
centerC2#13129822
commutatorC2×C13×C16C2×C4
FrattiniC2×C16C2×#261
FittingC2×C13×Q32C4
socleC2×C13#1347
prime radicalC22×D13SD32
cosocleC2×#88038C22
hypercenterC2×Q32#261
hypocenterC13#7425
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
104. C13#7425semidirect

Maximal subgroups

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

subgroupindex
#131299522
#131299062
#131169412
#742513