Finite Group Databasebeta

← #16777703

Subgroups — #16777703

Order 3328.

182 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C22⋊#88036C212yesmaximal, complemented
2C2×#11718099C211yesmaximal, characteristic
3C22×C8×D13C411yescharacteristic
4C22×C13×C16C411yescharacteristic
5C22×#6090C2211yescharacteristic
6C2×#88036—22no—
7#11718099—22no—
8C22×C4×D13C811yescharacteristic
9C22×C8×C13C2×C411yescharacteristic
10C22×#1055C811yescharacteristic
11C2×C8×D13—21no—
12C2×C8×D13—21no—
13C2×C8×D13—41no—
14C2×C8×D13—41no—
15C2×C13×C16—21no—
16C2×C13×C16—41no—
17C2×#6090—41no—
18C2×#6090D412yes—
19#88036—42no—
20#7334—131nomaximal, Sylow
21C23×D13C1611yescharacteristic
22C22×C4×C13C2×C811yescharacteristic
23C22×Dic13C1611yescharacteristic
24C2×C4×D13—21no—
25C2×C4×D13—21no—
26C2×C4×D13—41no—
27C2×C4×D13—41no—
28C2×C8×C13—21no—
29C2×C8×C13—21no—
30C2×C8×C13C22⋊C411yescharacteristic
31C2×C8×C13M1611yescharacteristic
32C2×#1055—21no—
33C2×#1055—41no—
34C8×D13—42no—
35C8×D13—41no—
36C8×D13—41no—
37C13×C16—41no—
38#6090—22no—
39C2×C22⋊C16—131no—
40C22⋊C32—132no—
41C23×C13C2×C1611yescharacteristic
42C22×D13—21no—
43C22×D13—21no—
44C22×D13—41no—
45C22×D13—41no—
46C22×D13C3212yescomplemented
47C2×C4×C13—21no—
48C2×C4×C13—21no—
49C2×C4×C13C22⋊C811yescharacteristic
50C2×C4×C13M3211yescharacteristic
51C2×Dic13—21no—
52C2×Dic13—41no—
53C4×D13—42no—
54C4×D13—41no—
55C4×D13—41no—
56C8×C13—21no—
57C8×C13#9911yescharacteristic
58C8×C13#10011yescharacteristic
59#1055—41no—
60C23×C8—131no—
61C22×C16—131no—
62C22×C16#26111yescharacteristic
63C2×C32—262no—
64C22⋊C16—262no—
65C22×C13—21no—
66C22×C13—21no—
67C22×C13C22⋊C1611yescharacteristic
68C22×C13C2×C3211yescharacteristic
69C22×C13M6411yescharacteristic
70C2×D13—22no—
71C2×D13—42no—
72C2×D13—41no—
73C2×D13—41no—
74C2×D13—42no—
75C4×C13—21no—
76C4×C13#32311yescharacteristic
77C4×C13#34911yescharacteristic
78Dic13—41no—
79C23×C4—131no—
80C22×C8—131no—
81C22×C8—261no—
82C22×C8—261no—
83C22×C8—521no—
84C22×C8—521no—
85C22×C8C2×#26111yescharacteristic
86C2×C16—21no—
87C2×C16—41no—
88C2×C16—132no—
89C2×C16—521no—
90C32—522no—
91C2×C13—21no—
92C2×C13—21no—
93C2×C13#131411yescharacteristic
94C2×C13C22⋊C3211yescharacteristic
95C2×C13#140011yescharacteristic
96D13—42no—
97C24—131no—
98C22×C4—131no—
99C22×C4—261no—
100C22×C4—261no—
101C22×C4—521no—
102C22×C4—521no—
103C22×C4D13⋊C811yescharacteristic
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—261no—
107C2×C8—522no—
108C2×C8—521no—
109C2×C8—521no—
110C2×C8—521no—
111C2×C8#611811yescharacteristic
112C2×C8C22⋊#26111yescharacteristic
113C16—41no—
114C16—262no—
115C13#733411yescharacteristic, complemented, Sylow
116C23—132no—
117C23—261no—
118C23—261no—
119C23—521no—
120C23—521no—
121C23D13⋊C1611yescharacteristic
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—261no—
125C2×C4—522no—
126C2×C4—521no—
127C2×C4—521no—
128C2×C4—521no—
129C2×C4#8809811yescharacteristic
130C2×C4#8811111yescharacteristic
131C8—21no—
132C8—521no—
133C8#8810711yescharacteristic
134C8#8812111yescharacteristic
135C22—21no—
136C22—21no—
137C22—262no—
138C22—522no—
139C22—522no—
140C22—521no—
141C22—521no—
142C22D13⋊C3211yescharacteristic
143C22#1171821411yescharacteristic
144C22#1171825911yescharacteristic
145C4—21no—
146C4—521no—
147C4#1171826311yescharacteristic
148C4#1171828711yescharacteristic
149C2—21no—
150C2—21no—
151C2—522no—
152C2#1312975711yescharacteristic
153C2#1312995011yescharacteristic
154C2#1312995211yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC22×C13C2×C32
FrattiniC22×C8C2×#261
FittingC22×C13×C16C4
socleC22×C13C22⋊C16
prime radicalC23×D13C16
cosocleC22×#6090C22
hypercenterC22×C16#261
hypocenterC13#7334
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
1. C22⋊#88036C2semidirect
46. C22×D13C32semidirect
115. C13#7334semidirect

Maximal subgroups

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

subgroupindex
C22⋊#880362
C2×#117180992
#733413