Finite Group Databasebeta

← #13113533

Subgroups — #13113533

Order 1664.

208 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 67 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#11719433C211yesmaximal, characteristic
2#11718496C211yesmaximal, characteristic
3D13×C4⋊C8C211yesmaximal, characteristic
4C13×#332C211yesmaximal, characteristic, complemented
5#11718139C211yesmaximal, characteristic, complemented
6#11718078C211yesmaximal, characteristic, complemented
7#11718074C211yesmaximal, characteristic, complemented
8C13×C4⋊Q8C2211yescharacteristic
9#88200—21no—
10Q8×Dic13—21no—
11C2×C8×D13—21no—
12#88151—21no—
13#88146C412yes—
14#88144C412yes—
15#88141—21no—
16C42×D13C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20#88060—21no—
21#88055—21no—
22#88054—21no—
23C4⋊#1055C2211yescharacteristic
24C4⋊#1055C2211yescharacteristic
25C2×Q8×C13—21no—
26C2×C4×D13C2×C411yescharacteristic
27C2×C4×D13D411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×Dic26—21no—
30C2×C8×C13—21no—
31C2×C8×C13—21no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4C2×C412yes—
34C42×C13C2311yescharacteristic
35#6103—22no—
36C4⋊Dic13—21no—
37C4⋊Dic13—22no—
38C4⋊Dic13C2×C412yes—
39#6101—22no—
40C4×Dic13—22no—
41C4×Dic13C2×C411yescharacteristic
42C4×Dic13D411yescharacteristic
43C4×Dic13D411yescharacteristic
44C2×#1055—21no—
45C2×#1055—21no—
46C8×D13—42no—
47#1552—131nomaximal, Sylow
48C22×D13C22⋊C411yescharacteristic
49Q8×C13—41no—
50Q8×C13—41no—
51C2×C4×C13—22no—
52C2×C4×C13C22×C411yescharacteristic
53C2×C4×C13C2×D411yescharacteristic
54C2×C4×C13C2×D411yescharacteristic
55C2×Dic13—22no—
56C2×Dic13C22⋊C411yescharacteristic
57C2×Dic13C22⋊C411yescharacteristic
58C2×Dic13C22⋊C411yescharacteristic
59C4×D13—22no—
60C4×D13—21no—
61C4×D13—21no—
62C4×D13—21no—
63C4×D13—21no—
64Dic26—41no—
65Dic26—41no—
66C8×C13—41no—
67C8×C13—41no—
68#1055—41no—
69#1055—41no—
70#533—131no—
71#432—131no—
72C2×C4⋊C8—131no—
73#332—131no—
74#332—131no—
75#332—131no—
76#332D1311yescharacteristic, complemented
77C22×C13C2×C22⋊C411yescharacteristic
78C2×D13—21no—
79C2×D13—21no—
80C2×D13#10112yes—
81C4×C13—21no—
82C4×C13—42no—
83C4×C13#13511yescharacteristic
84C4×C13#13511yescharacteristic
85C4×C13AGL(1,ℤ/8)11yescharacteristic
86C4×C13#13711yescharacteristic
87Dic13—21no—
88Dic13—21no—
89Dic13—21no—
90Dic13—42no—
91C22×C8—261no—
92C4⋊Q8—131no—
93C4⋊Q8C2×D1311yescharacteristic
94#125—132no—
95C22⋊Q8—261no—
96C22⋊Q8—261no—
97C4×Q8—261no—
98C4×Q8—261no—
99#117—132no—
100C2×C42—131no—
101C4⋊C8—131no—
102C4⋊C8—131no—
103C4⋊C8—261no—
104C4⋊C8C2×D1311yescharacteristic
105C4⋊C8C2×D1311yescharacteristic
106C22⋊C8—261no—
107#97—261no—
108C2×C13C2×#10111yescharacteristic
109C2×C13#41611yescharacteristic
110C2×C13#41711yescharacteristic
111D13—22no—
112C2×Q8—21no—
113C2×Q8—261no—
114C22×C4—131no—
115C22×C4—131no—
116C22×C4—131no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—261no—
120C2×C8—261no—
121C2×C8—522no—
122C4⋊C4—21no—
123C4⋊C4—132no—
124C4⋊C4—262no—
125C4⋊C4—262no—
126C4⋊C4—261no—
127C4⋊C4C4×D1312yes—
128C22⋊C4—262no—
129C42—131no—
130C42—131no—
131C42—131no—
132C42—262no—
133C42C22×D1311yescharacteristic
134C13#155211yescharacteristic, complemented, Sylow
135C23—131no—
136Q8—41no—
137Q8—41no—
138Q8—521no—
139Q8—521no—
140C2×C4—22no—
141C2×C4—131no—
142C2×C4—131no—
143C2×C4—131no—
144C2×C4—262no—
145C2×C4—261no—
146C2×C4—261no—
147C2×C4—261no—
148C2×C4—261no—
149C2×C4—262no—
150C2×C4C2×C4×D1311yescharacteristic
151C2×C4D4×D1311yescharacteristic
152C2×C4D4×D1311yescharacteristic
153C8—41no—
154C8—41no—
155C8—521no—
156C8—521no—
157C22—132no—
158C22—261no—
159C22—261no—
160C22C22⋊C4×D1311yescharacteristic
161C4—21no—
162C4—42no—
163C4—261no—
164C4—261no—
165C4—261no—
166C4—522no—
167C4#8816611yescharacteristic
168C4#8816811yescharacteristic
169C4#8817011yescharacteristic
170C4#8817211yescharacteristic
171C2—262no—
172C2D13×#10111yescharacteristic
173C2#1171843311yescharacteristic
174C2#1171846411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#332C2
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC42×C13C23
hypercenter#332D13
hypocenterC13#1552
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. C13×#332C2semidirect
5. #11718139C2semidirect
6. #11718078C2semidirect
7. #11718074C2semidirect
76. #332D13semidirect
134. C13#1552semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117184962
D13×C4⋊C82
C13×#3322
#117181392
#117180782
#117180742
#155213