Finite Group Databasebeta

← #16777900

Subgroups — #16777900

Order 3328.

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

normal subgroups only

This group has 140 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#13129904C211yesmaximal, characteristic
3#13116941C211yesmaximal, characteristic
4#11719092—21no—
5C2×C13×Q32C411yescharacteristic, complemented
6#11718849—21no—
7C2×#88038C2211yescharacteristic
8#11718249—21no—
9#11718156—21no—
10#11718097C411yescharacteristic, complemented
11#88237—41no—
12C2×C13×Q16—21no—
13#88200—41no—
14C2×C8×D13D411yescharacteristic
15#88102—41no—
16#88101—22no—
17C13×Q32—41no—
18C2×C13×C16C2×C411yescharacteristic
19#88075—41no—
20#88058—21no—
21C2×#6090D411yescharacteristic
22#88038—41no—
23#88036—41no—
24#7423—131nomaximal, Sylow
25C2×Q8×C13—41no—
26C2×C4×D13D811yescharacteristic
27C22⋊#261—81no—
28C4⋊#261—42no—
29C4×#261—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#1384—131no—
44C22×D13D1611yescharacteristic
45C2×#261—82no—
46Q8×C13—81no—
47Q8×C13—81no—
48C2×C4×C13—81no—
49C2×C4×C13#10211yescharacteristic
50C2×Dic13—81no—
51C2×Dic13SD3211yescharacteristic
52C4×D13—21no—
53C4×D13—21no—
54C8×C13#9911yescharacteristic
55C8×C13#10411yescharacteristic
56#1055—21no—
57C2×Q32#26111yescharacteristic, complemented
58C2×M32—131no—
59#467—261no—
60#427—261no—
61M64—261no—
62#367—131no—
63#358—261no—
64C22×C13#35711yescharacteristic
65C2×D13—21no—
66C2×D13—41no—
67#261—162no—
68C4×C13—161no—
69C4×C13#32711yescharacteristic
70C4×C13#36011yescharacteristic
71Dic13—21no—
72Dic13—161no—
73C2×Q16—21no—
74C22×C8—131no—
75C22⋊Q8—521no—
76#117—521no—
77Q32—41no—
78M32—521no—
79C2×C16—131no—
80C2×C16C2×#26111yescharacteristic
81#107—261no—
82#107—521no—
83#106—262no—
84#103—521no—
85C32—521no—
86C2×C13—21no—
87C2×C13#134711yescharacteristic
88D13—41no—
89C2×Q8—41no—
90C22×C4—131no—
91Q16—41no—
92Q16—41no—
93C2×C8—131no—
94C2×C8—261no—
95C2×C8—261no—
96C2×C8C22⋊#26111yescharacteristic
97C4⋊C4—522no—
98C4⋊C4—521no—
99C4⋊C4—1041no—
100C22⋊C4—1041no—
101C22⋊C4—1041no—
102C42—1041no—
103C16—21no—
104C16—261no—
105C13#742311yescharacteristic, complemented, Sylow
106C23—131no—
107Q8—81no—
108Q8—81no—
109C2×C4—81no—
110C2×C4—131no—
111C2×C4—261no—
112C2×C4—261no—
113C2×C4—1042no—
114C2×C4—1041no—
115C2×C4#8811511yescharacteristic
116C8—261no—
117C8#8811611yescharacteristic
118C8#8811911yescharacteristic
119C22—261no—
120C22—521no—
121C22#1171827611yescharacteristic
122C4—161no—
123C4—261no—
124C4—2081no—
125C4—2082no—
126C4#1171827511yescharacteristic
127C4#1171829211yescharacteristic
128C2—21no—
129C2—521no—
130C2#1312982211yescharacteristic
subgroupG/H
centerC2#13129822
commutatorC2×C13×C16C2×C4
FrattiniC2×C16C2×#261
FittingC2×C13×Q32C4
socleC2×C13#1347
prime radicalC22×D13D16
cosocleC2×#88038C22
hypercenterC2×Q32#261
hypocenterC13#7423
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
5. C2×C13×Q32C4semidirect
10. #11718097C4semidirect
57. C2×Q32#261semidirect
105. C13#7423semidirect

Maximal subgroups

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

subgroupindex
#131299522
#131299042
#131169412
#742313