Finite Group Databasebeta

← #16788643

Subgroups — #16788643

Order 3328.

258 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 64 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#13131205C212yesmaximal
2#13129856C214yesmaximal, complemented
3#13125385C211yesmaximal, characteristic
4C2×C13×#125C411yescharacteristic
5#11719175C411yescharacteristic
6#11718726—22no—
7#11718725C412yes—
8#11718725C2212yes—
9#11718625—22no—
10C4×#6099C2211yescharacteristic
11#11718284—22no—
12#11718233C2214yes—
13#11718232—22no—
14C13×#125—21no—
15C13×#125—41no—
16C13×#125C2×C412yes—
17C2×C13×C4⋊C4—21no—
18C2×C13×C4⋊C4—41no—
19C2×C42×C13C2×C411yescharacteristic
20#88180—21no—
21#88178—41no—
22C2×#6099D412yes—
23#88124C2×C412yes—
24#88123—21no—
25C4×Dic26—41no—
26#88106—24no—
27#88048—22no—
28#88048—22no—
29#88047—22no—
30#88047—22no—
31#88043D412yes—
32C4×#1055C2×C411yescharacteristic
33C4×#1055C2311yescharacteristic
34#11994—131nomaximal, Sylow
35C22×C4×C13—21no—
36C22×C4×C13—41no—
37C22×C4×C13C22⋊C411yescharacteristic
38C2×Dic26—41no—
39C13×C4⋊C4—22no—
40C13×C4⋊C4—42no—
41C13×C4⋊C4—42no—
42C13×C4⋊C4—41no—
43C42×C13—21no—
44C42×C13C22⋊C411yescharacteristic
45C42×C13C22×C411yescharacteristic
46C22⋊Dic13—41no—
47C4⋊Dic13—22no—
48C4⋊Dic13—41no—
49#6101—42no—
50C4×Dic13—41no—
51#6099—24no—
52C2×#1055C22⋊C412yes—
53C2×#1055C2×D412yes—
54#6092—44no—
55#3166—131no—
56#2165—132no—
57#1366—134no—
58C23×C13#10011yescharacteristic
59C2×C4×C13—22no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—42no—
63C2×C4×C13—81no—
64C2×C4×C13—82no—
65C2×C4×C13#10011yescharacteristic
66C2×C4×C13C2×C22⋊C411yescharacteristic
67C2×Dic13—42no—
68Dic26—82no—
69#1055—22no—
70#1055#13714yes—
71#533—131no—
72C2×#125#26111yescharacteristic
73#501—262no—
74#499—132no—
75#499—132no—
76#428—262no—
77C4×M16—131no—
78#364—134no—
79#349—262no—
80#347—262no—
81C22×C13—21no—
82C22×C13—41no—
83C22×C13C2×#10011yescharacteristic
84C4×C13—21no—
85C4×C13—41no—
86C4×C13—41no—
87C4×C13—82no—
88C4×C13#41912yes—
89Dic13—82no—
90C2×M16—132no—
91C4⋊Q8—261no—
92#125—21no—
93#125—41no—
94#125—132no—
95#125C2×#26112yes—
96C22⋊Q8—521no—
97C4×Q8—521no—
98#117—261no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C42C2×#26111yescharacteristic
102M32—264no—
103#107—262no—
104#107—262no—
105#106—262no—
106#106—262no—
107#97—132no—
108C4×C8—131no—
109C4×C8—131no—
110C2×C13—21no—
111C2×C13—41no—
112C2×C13#155811yescharacteristic
113C2×Q8—521no—
114C22×C4—21no—
115C22×C4—41no—
116C22×C4C22⋊#26111yescharacteristic
117M16—264no—
118C2×C8—132no—
119C2×C8—132no—
120C4⋊C4—22no—
121C4⋊C4—42no—
122C4⋊C4—42no—
123C4⋊C4—41no—
124C4⋊C4—262no—
125C4⋊C4—522no—
126C4⋊C4—521no—
127C22⋊C4—521no—
128C42—21no—
129C42—521no—
130C42C22⋊#26111yescharacteristic
131C42C22×#26111yescharacteristic
132C16—524no—
133C13#1199411yescharacteristic, complemented, Sylow
134C23#8812111yescharacteristic
135Q8—1042no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—42no—
140C2×C4—81no—
141C2×C4—82no—
142C2×C4—522no—
143C2×C4#8812111yescharacteristic
144C2×C4C2×C22⋊#26111yescharacteristic
145C8—134no—
146C8—262no—
147C22—21no—
148C22—41no—
149C22C2×#8812111yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—1042no—
155C4#1171915312yes—
156C2—21no—
157C2—41no—
158C2#1313036911yescharacteristic
subgroupG/H
centerC2#13130369
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×#125C4
socleC2×C13#1558
prime radicalC23×C13#100
cosocleC4×#1055C23
hypercenterC2×#125#261
hypocenterC13#11994
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #13129856C2semidirect
133. C13#11994semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131298562
#131253852
#1199413