Finite Group Databasebeta

← #16790205

Subgroups — #16790205

Order 3328.

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

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 140 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
1C2×C4⋊#6092C212yesmaximal
2#13129874C214yesmaximal
3#13114523C211yesmaximal, characteristic
4C22×#6092C2214yes—
5C13×#376C411yescharacteristic
6C2×#88043C412yes—
7C2×#88043C411yescharacteristic
8C2×C4×#1055C2212yes—
9C2×C4×#1055C2211yescharacteristic
10C4⋊#6092—24no—
11C2×C42×C13C2×C412yes—
12C2×C42×C13C2×C411yescharacteristic
13C22×#1055C2×C411yescharacteristic
14C22×#1055C2×C412yes—
15C22×#1055C2311yescharacteristic
16C2×#6092—24no—
17C2×#6092—28no—
18C13×#95C814yes—
19#88043—22no—
20#88043—24no—
21C4×#1055—24no—
22C4×#1055D412yes—
23C4×#1055Q812yes—
24#12880—131nomaximal, Sylow
25C22×C4×C13C2×C814yes—
26C22×C4×C13C2×C812yes—
27C22×C4×C13C22×C411yescharacteristic
28C42×C13—22no—
29C42×C13—22no—
30C42×C13C4⋊C412yes—
31C42×C13M1612yes—
32C2×#1055—22no—
33C2×#1055—22no—
34C2×#1055—22no—
35C2×#1055C4⋊C412yes—
36C2×#1055M1614yes—
37C2×#1055C2×D411yescharacteristic
38C2×#1055C2×Q811yescharacteristic
39C2×#1055#4114yes—
40#6092—44no—
41C2×C4⋊C16—132no—
42#1726—131no—
43#1374—134no—
44C23×C13C22×C811yescharacteristic
45C2×C4×C13—24no—
46C2×C4×C13—24no—
47C2×C4×C13—28no—
48C2×C4×C13C4⋊C814yes—
49C2×C4×C13C2×C4⋊C411yescharacteristic
50C2×C4×C13#11712yes—
51C2×C4×C13C2×M1612yes—
52C2×C4×C13C2×M1611yescharacteristic
53#1055—22no—
54#1055—24no—
55#1055#12412yes—
56#1055#12512yes—
57C22×C16—134no—
58C2×#97—132no—
59C2×#97—131no—
60C2×C4×C8—131no—
61C2×C4×C8—132no—
62#376#26111yescharacteristic
63C4⋊C16—264no—
64C22×C13C2×C4⋊C811yescharacteristic
65C22×C13#43112yes—
66C22×C13#50414yes—
67C4×C13—24no—
68C4×C13—44no—
69C4×C13#38211yescharacteristic
70C4×C13#42311yescharacteristic
71C4×C13#43212yes—
72C22×C8—131no—
73C22×C8—132no—
74C22×C8—131no—
75C2×C42C2×#26112yes—
76C2×C42C2×#26111yescharacteristic
77C2×C16—264no—
78C2×C16—268no—
79#97—264no—
80#97—262no—
81C4×C8—132no—
82C4×C8—132no—
83C4×C8—264no—
84#95#105714yes—
85C2×C13#183111yescharacteristic
86C2×C13#215112yes—
87C2×C13#216414yes—
88C22×C4C2×#105714yes—
89C22×C4C2×#105712yes—
90C22×C4C22×#26111yescharacteristic
91C2×C8—131no—
92C2×C8—131no—
93C2×C8—134no—
94C2×C8—134no—
95C2×C8—132no—
96C2×C8—262no—
97C2×C8—262no—
98C2×C8—262no—
99C42—22no—
100C42—22no—
101C42#611812yes—
102C42C4⋊#26112yes—
103C16—524no—
104C13#1288011yescharacteristic, complemented, Sylow
105C23C22×#105711yescharacteristic
106C2×C4—24no—
107C2×C4—24no—
108C2×C4—28no—
109C2×C4C4⋊#105714yes—
110C2×C4C2×#611811yescharacteristic
111C2×C4D13⋊M1612yes—
112C2×C4C2×C4⋊#26111yescharacteristic
113C2×C4#8823712yes—
114C8—132no—
115C8—132no—
116C8—262no—
117C8—264no—
118C22C2×C4⋊#105711yescharacteristic
119C22#1171911912yes—
120C22#1171916214yes—
121C4—24no—
122C4—44no—
123C4#1171905311yescharacteristic
124C4#1171905412yes—
125C4#1171906011yescharacteristic
126C2#1313075111yescharacteristic
127C2#1313117112yes—
128C2#1313120114yes—
subgroupG/H
center, FrattiniC22×C4C22×#261
commutator, socle, prime radicalC23×C13C22×C8
FittingC13×#376C4
cosocleC22×#1055C23
hypercenter#376#261
hypocenterC13#12880
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
104. C13#12880semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#60922
#131298742
#131145232
#1288013