Finite Group Databasebeta

← #13129736

Subgroups — #13129736

Order 1664.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#11719136C211yesmaximal, characteristic
2#11719127C211yesmaximal, characteristic
3#11718787C211yesmaximal, characteristic
4C22×C4×D13C2211yescharacteristic
5C2×C22⋊#261C412yes—
6C2×C4⋊#261—21no—
7C2×#6118—21no—
8C2×C13×M16C411yescharacteristic, complemented
9C2×#6099C411yescharacteristic, complemented
10C22⋊#1057C412yescomplemented
11(C2×#261)⋊C4—21no—
12#88111—21no—
13#88060—21no—
14#88060—21no—
15C23×D13C2×C411yescharacteristic
16C22×#261—22no—
17C22×C4×C13C2×C411yescharacteristic
18C22×Dic13C2×C411yescharacteristic
19C2×C4×D13—41no—
20C2×C4×D13—41no—
21C2×C4×D13D411yescharacteristic
22C2×C4×D13D411yescharacteristic
23C2×C4×D13D411yescharacteristic
24C2×C4×D13Q811yescharacteristic
25C22⋊#261—42no—
26C2×#1057—22no—
27C4⋊#261—41no—
28C4⋊#261—41no—
29#6118—41no—
30#6118—41no—
31C13×M16—41no—
32C2×C8×C13—21no—
33#6099—41no—
34C2×#1055—21no—
35#1305—131nomaximal, Sylow
36C23×C13C4211yescharacteristic
37C22×D13—21no—
38C22×D13—21no—
39C22×D13—41no—
40C22×D13—41no—
41C22×D13C22⋊C411yescharacteristic
42C22×D13C4⋊C411yescharacteristic
43C2×#261—42no—
44C2×#261—42no—
45C2×#261—42no—
46C2×C4×C13—21no—
47C2×C4×C13—21no—
48C2×C4×C13C22⋊C411yescharacteristic
49C2×C4×C13C4⋊C411yescharacteristic
50C2×Dic13—41no—
51C2×Dic13C22⋊C411yescharacteristic
52C2×Dic13C4⋊C411yescharacteristic
53C4×D13—21no—
54C4×D13—21no—
55C4×D13—21no—
56C4×D13—21no—
57C4×D13—41no—
58C4×D13—41no—
59#1057—42no—
60C8×C13—41no—
61#1055—41no—
62#407—131no—
63#407—131no—
64#380—131no—
65C22×C13—21no—
66C22×C13—21no—
67C22×C13—21no—
68C22×C13#9511yescharacteristic
69C2×D13—21no—
70C2×D13—21no—
71C2×D13—21no—
72C2×D13—21no—
73C2×D13—21no—
74C2×D13—42no—
75C2×D13—42no—
76C2×D13#10011yescharacteristic
77C2×D13#10111yescharacteristic
78#261—82no—
79C4×C13—21no—
80C4×C13#9911yescharacteristic
81C4×C13#9911yescharacteristic
82Dic13—21no—
83Dic13—21no—
84C23×C4—131no—
85C2×M16—131no—
86C2×M16—261no—
87C2×M16#26111yescharacteristic, complemented
88C2×C4⋊C4—261no—
89C2×C22⋊C4—132no—
90C22⋊C8—132no—
91C22⋊C8—261no—
92C22⋊C8—261no—
93C22⋊C8—261no—
94#95—261no—
95C2×C13—41no—
96C2×C13#34211yescharacteristic
97C2×C13#34311yescharacteristic
98C2×C13#34411yescharacteristic
99D13—21no—
100D13—21no—
101D13—41no—
102C24—131no—
103C22×C4—131no—
104C22×C4—131no—
105C22×C4—131no—
106C22×C4—131no—
107C22×C4—131no—
108C22×C4—262no—
109C22×C4—521no—
110C22×C4—521no—
111C22×C4C2×#26111yescharacteristic
112M16—41no—
113M16—521no—
114M16—521no—
115M16—521no—
116C2×C8—21no—
117C2×C8—262no—
118C2×C8—261no—
119C4⋊C4—521no—
120C4⋊C4—521no—
121C22⋊C4—522no—
122C13#130511yescharacteristic, complemented, Sylow
123C23—131no—
124C23—131no—
125C23—261no—
126C23—261no—
127C23—521no—
128C23—521no—
129C23C4×#26111yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—131no—
133C2×C4—131no—
134C2×C4—261no—
135C2×C4—261no—
136C2×C4—261no—
137C2×C4—261no—
138C2×C4—521no—
139C2×C4—521no—
140C2×C4—521no—
141C2×C4—522no—
142C2×C4—522no—
143C2×C4—522no—
144C2×C4C4⋊#26111yescharacteristic
145C2×C4C22⋊#26111yescharacteristic
146C8—41no—
147C8—522no—
148C8—521no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—131no—
153C22—131no—
154C22—261no—
155C22—261no—
156C22—261no—
157C22—261no—
158C22—261no—
159C22—522no—
160C22—522no—
161C22(C2×#261)⋊C411yescharacteristic
162C4—21no—
163C4—261no—
164C4—261no—
165C4—1042no—
166C4#8810711yescharacteristic
167C4#8811911yescharacteristic
168C2—41no—
169C2—261no—
170C2—261no—
171C2—521no—
172C2#1171827111yescharacteristic
173C2#1171827411yescharacteristic
174C2#1171828911yescharacteristic
subgroupG/H
centerC22(C2×#261)⋊C4
commutatorC23×C13C42
FrattiniC22×C4C2×#261
FittingC2×C13×M16C4
socleC22×C13#95
prime radicalC23×D13C2×C4
cosocleC22×C4×D13C22
hypercenterC2×M16#261
hypocenterC13#1305
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C2×C13×M16C4semidirect
9. C2×#6099C4semidirect
10. C22⋊#1057C4semidirect
87. C2×M16#261semidirect
122. C13#1305semidirect

Maximal subgroups

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

subgroupindex
#117191362
#117191272
#117187872
#130513