Finite Group Databasebeta

← #13129717

Subgroups — #13129717

Order 1664.

246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 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×C22⋊#261C211yesmaximal, characteristic
2#11719127C211yesmaximal, characteristic
3#11718327C211yesmaximal, characteristic
4C22×C4×D13C2211yescharacteristic
5C2×C22⋊#261—21no—
6C2×C4×#261—21no—
7C2×#6118C412yescomplemented
8C2×#6103—21no—
9C2×C4×Dic13—21no—
10C22⋊#1057—21no—
11(C2×#261)⋊C4C412yescomplemented
12#88111—21no—
13C13×#95C411yescharacteristic, complemented
14#88071C411yescharacteristic, complemented
15C23×D13D411yescharacteristic
16C22×#261—22no—
17C22×C4×C13—21no—
18C22×C4×C13C2×C411yescharacteristic
19C22×Dic13—21no—
20C22×Dic13D411yescharacteristic
21C2×C4×D13—42no—
22C2×C4×D13C2×C411yescharacteristic
23C2×C4×D13C2×C411yescharacteristic
24C2×C4×D13D411yescharacteristic
25C2×C4×D13Q811yescharacteristic
26C22⋊#261—22no—
27C22⋊#261—22no—
28C2×#1057—22no—
29C4×#261—42no—
30#6118—42no—
31#6103—24no—
32C4×Dic13—42no—
33#1297—131nomaximal, Sylow
34C23×C13C22⋊C411yescharacteristic
35C22×D13—21no—
36C22×D13—21no—
37C22×D13—22no—
38C22×D13—41no—
39C22×D13C22⋊C411yescharacteristic
40C22×D13C4⋊C411yescharacteristic
41C2×#261—24no—
42C2×#261—42no—
43C2×#261—42no—
44C2×C4×C13—22no—
45C2×C4×C13—41no—
46C2×C4×C13—41no—
47C2×C4×C13—41no—
48C2×C4×C13C4211yescharacteristic
49C2×C4×C13C4⋊C411yescharacteristic
50C2×Dic13—22no—
51C2×Dic13—22no—
52C2×Dic13—41no—
53C2×Dic13—41no—
54C2×Dic13C22⋊C411yescharacteristic
55C2×Dic13C4⋊C411yescharacteristic
56C4×D13—22no—
57C4×D13—22no—
58C4×D13—41no—
59C4×D13—41no—
60#1057—42no—
61#407—131no—
62C4×C22⋊C4—131no—
63C4×C22⋊C4—131no—
64C22×C13—21no—
65C22×C13—21no—
66C22×C13#9511yescharacteristic
67C22×C13#10411yescharacteristic
68C22×C13#10411yescharacteristic
69C2×D13—21no—
70C2×D13—21no—
71C2×D13—21no—
72C2×D13—21no—
73C2×D13—21no—
74C2×D13—42no—
75C2×D13—42no—
76C2×D13#10412yes—
77#261—44no—
78C4×C13—21no—
79C4×C13—21no—
80C4×C13—42no—
81Dic13—21no—
82Dic13—42no—
83Dic13#9912yes—
84C23×C4—131no—
85C2×M16—132no—
86C2×C22⋊C4—261no—
87C2×C22⋊C4—261no—
88C2×C42—261no—
89C2×C42—261no—
90C22⋊C8—261no—
91C22⋊C8—261no—
92#95—132no—
93#95—131no—
94#95#26111yescharacteristic, complemented
95C2×C13—21no—
96C2×C13—21no—
97C2×C13#33911yescharacteristic
98C2×C13#33911yescharacteristic
99C2×C13#34211yescharacteristic
100D13—22no—
101D13—41no—
102C24—131no—
103C22×C4—21no—
104C22×C4—131no—
105C22×C4—131no—
106C22×C4—131no—
107C22×C4—131no—
108C22×C4—131no—
109C22×C4—262no—
110C22×C4—261no—
111C22×C4—522no—
112C22×C4C2×#26111yescharacteristic
113M16—522no—
114C2×C8—262no—
115C22⋊C4—264no—
116C22⋊C4—262no—
117C22⋊C4—262no—
118C42—522no—
119C42—522no—
120C13#129711yescharacteristic, complemented, Sylow
121C23—131no—
122C23—131no—
123C23—262no—
124C23—261no—
125C23—261no—
126C23—521no—
127C23C22⋊#26111yescharacteristic
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—131no—
133C2×C4—131no—
134C2×C4—262no—
135C2×C4—262no—
136C2×C4—262no—
137C2×C4—262no—
138C2×C4—264no—
139C2×C4—521no—
140C2×C4—521no—
141C2×C4—521no—
142C2×C4—522no—
143C2×C4—522no—
144C2×C4—521no—
145C2×C4C4×#26111yescharacteristic
146C2×C4C4⋊#26111yescharacteristic
147C8—522no—
148C22—21no—
149C22—21no—
150C22—132no—
151C22—261no—
152C22—261no—
153C22—261no—
154C22—261no—
155C22—261no—
156C22—522no—
157C22—522no—
158C22(C2×#261)⋊C411yescharacteristic
159C22#8811611yescharacteristic
160C22#8811811yescharacteristic
161C4—21no—
162C4—21no—
163C4—42no—
164C4—132no—
165C4—261no—
166C4—522no—
167C4—524no—
168C2—21no—
169C2—21no—
170C2—262no—
171C2—521no—
172C2#1171823411yescharacteristic
173C2#1171823811yescharacteristic
174C2#1171824711yescharacteristic
subgroupG/H
centerC22(C2×#261)⋊C4
commutatorC2×C4×C13C42
FrattiniC22×C4C2×#261
FittingC13×#95C4
socleC22×C13#95
prime radicalC23×D13D4
cosocleC22×C4×D13C22
hypercenter#95#261
hypocenterC13#1297
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
7. C2×#6118C4semidirect
11. (C2×#261)⋊C4C4semidirect
13. C13×#95C4semidirect
14. #88071C4semidirect
94. #95#261semidirect
120. C13#1297semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#2612
#117191272
#117183272
#129713