Finite Group Databasebeta

← #16777936

Subgroups — #16777936

Order 3328.

170 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 32 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#13129928C211yesmaximal, characteristic
2#13129759C211yesmaximal, characteristic
3#13116390C211yesmaximal, characteristic
4#11719132—21no—
5#11718790C2211yescharacteristic
6#11718786C411yescharacteristic
7#11718666—21no—
8#11718660—21no—
9C22⋊#6092—21no—
10C13×H(3,ℤ/4)C411yescharacteristic
11C2×#6127D411yescharacteristic
12D13⋊M16—41no—
13C2×C13×M16C2×C411yescharacteristic
14C13×#117—21no—
15C2×#6099—21no—
16C22×#1055D411yescharacteristic
17#88121—22no—
18#88113—41no—
19C2×#6092—41no—
20#88060—41no—
21#88059—41no—
22#88045—42no—
23C4⋊#1055—42no—
24#7439—131nomaximal, Sylow
25C22×C4×C13C22⋊C411yescharacteristic
26C2×C22⋊D13—21no—
27#6127—41no—
28#6127—41no—
29C2×D52Q1611yescharacteristic
30C2×C4×D13—21no—
31C2×Dic26SD1611yescharacteristic
32#6122—42no—
33#6118—81no—
34D13⋊C8—81no—
35C13×M16—41no—
36C2×C8×C13—21no—
37C13×C4⋊C4—41no—
38C13×C22⋊C4—41no—
39C42×C13—22no—
40#6099—41no—
41#6099—41no—
42C2×#1055—21no—
43C2×#1055—41no—
44C2×#1055—41no—
45#6092—81no—
46#2098—131no—
47#1392—131no—
48#1315—131no—
49C23×C13#10411yescharacteristic
50C22×D13—21no—
51C2×C4×C13—21no—
52C2×C4×C13—21no—
53C2×C4×C13—42no—
54C2×C4×C13#9911yescharacteristic
55C2×C4×C13#10311yescharacteristic
56C22⋊D13—81no—
57C2×Dic13—21no—
58D52—41no—
59C4×D13—41no—
60C4×D13—41no—
61Dic26—41no—
62#1057—82no—
63C8×C13—41no—
64#1055—41no—
65#1055—81no—
66#430—131no—
67#424—261no—
68#421—261no—
69#413—261no—
70#408—131no—
71C22⋊C16—261no—
72H(3,ℤ/4)#26111yescharacteristic
73C22×C13—21no—
74C22×C13—41no—
75C22×C13#32811yescharacteristic
76C2×D13—41no—
77C2×D13—81no—
78C4×C13—21no—
79C4×C13—82no—
80C4×C13#35211yescharacteristic
81C4×C13#35311yescharacteristic
82Dic13—41no—
83C2×#41—131no—
84C2×M16—261no—
85C2×M16—521no—
86C2×M16C2×#26111yescharacteristic
87C22×C8—131no—
88#117—21no—
89C2×C16—521no—
90#108—521no—
91C4⋊C8—522no—
92#104—522no—
93#101—521no—
94#100—262no—
95C22⋊C8—521no—
96C2×C13—21no—
97C2×C13—41no—
98C2×C13#135211yescharacteristic
99D13—81no—
100#41—521no—
101#41—521no—
102C2×Q8—131no—
103C2×D4—131no—
104C2×D4—261no—
105C22×C4—261no—
106C22×C4C22⋊#26111yescharacteristic
107M16—41no—
108M16—521no—
109M16—522no—
110M16—521no—
111M16—1041no—
112C2×C8—21no—
113C2×C8—261no—
114C2×C8—521no—
115C2×C8—521no—
116C2×C8—1041no—
117C4⋊C4—41no—
118C22⋊C4—41no—
119C42—22no—
120C16—1041no—
121C13#743911yescharacteristic, complemented, Sylow
122C23—261no—
123C23#8811611yescharacteristic
124Q8—521no—
125D4—521no—
126D4—1041no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—42no—
130C2×C4—261no—
131C2×C4—521no—
132C2×C4—521no—
133C2×C4#8810711yescharacteristic
134C2×C4#8811711yescharacteristic
135C8—41no—
136C8—521no—
137C8—1042no—
138C8—1041no—
139C22—21no—
140C22—41no—
141C22—521no—
142C22—1041no—
143C22#1171824111yescharacteristic
144C4—21no—
145C4—82no—
146C4—521no—
147C4#1171822511yescharacteristic
148C4#1171823711yescharacteristic
149C2—21no—
150C2—41no—
151C2—1041no—
152C2#1312983211yescharacteristic
subgroupG/H
centerC4#11718225
commutatorC2×C13×M16C2×C4
FrattiniC2×M16C2×#261
FittingC13×H(3,ℤ/4)C4
socleC2×C13#1352
prime radicalC2×#6127D4
cosocle#11718790C22
hypercenterH(3,ℤ/4)#261
hypocenterC13#7439
LCSG ▷ C2×C13×M16 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
121. C13#7439semidirect

Maximal subgroups

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

subgroupindex
#131299282
#131297592
#131163902
#743913