Finite Group Databasebeta

← #13116832

Subgroups — #13116832

Order 1664.

246 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C13×#559C211yesmaximal, characteristic, complemented
2#11718738C211yesmaximal, characteristic
3#11718714C212yesmaximal, complemented
4#11718137C211yesmaximal, characteristic, complemented
5#11718131C212yesmaximal, complemented
6#88251C2211yescharacteristic
7C13×#127C2211yescharacteristic
8C13×#124—22no—
9C13×#123—21no—
10C13×#123C2212yes—
11C4×Q8×C13—21no—
12C4×D4×C13—22no—
13#88186—21no—
14#88183—22no—
15#88074C2212yes—
16#88073C2211yescharacteristic
17#88046—22no—
18#88045—21no—
19C2×Q8×C13—21no—
20C2×D4×C13—22no—
21C2×D4×C13D411yescharacteristic
22C2×D4×C13C2311yescharacteristic
23C22×C4×C13—21no—
24C22×C4×C13D412yes—
25C2×C22⋊D13—22no—
26#6129—41no—
27D4×D13—41no—
28#6127—21no—
29C13×C4⋊C4—21no—
30C13×C4⋊C4—22no—
31C13×C22⋊C4—22no—
32C13×C22⋊C4—21no—
33C13×C22⋊C4—22no—
34C13×C22⋊C4D412yes—
35C42×C13—22no—
36C42×C13D411yescharacteristic
37C22⋊Dic13—22no—
38#6105—41no—
39#6104—41no—
40#6103—42no—
41#6101—42no—
42#6099—21no—
43#2198—131nomaximal, Sylow
44C23×C13—21no—
45C23×C13C2×D412yes—
46C22×D13—22no—
47Q8×C13—42no—
48D4×C13—41no—
49D4×C13—44no—
50D4×C13—41no—
51C2×C4×C13—21no—
52C2×C4×C13—22no—
53C2×C4×C13—22no—
54C2×C4×C13—42no—
55C2×C4×C13—81no—
56C2×C4×C13C2×D411yescharacteristic
57C22⋊D13—42no—
58C22⋊D13—41no—
59C2×Dic13—22no—
60C2×Dic13—42no—
61D52—21no—
62C4×D13—41no—
63Dic26—21no—
64#1055—41no—
65#559D1311yescharacteristic, complemented
66#458—132no—
67#453—131no—
68#353—131no—
69#352—132no—
70C22×C13—22no—
71C22×C13—42no—
72C22×C13—42no—
73C22×C13—41no—
74C22×C13#12011yescharacteristic
75C2×D13—41no—
76C2×D13—82no—
77C4×C13—22no—
78C4×C13—21no—
79C4×C13—42no—
80C4×C13—42no—
81Dic13—41no—
82Dic13—82no—
83H(5,𝔽2)—131no—
84AGL(1,ℤ/8)—261no—
85#127C2×D1311yescharacteristic
86#124—22no—
87#123—21no—
88#123—262no—
89#123C2×D1312yes—
90C4×Q8—21no—
91C4×D4—22no—
92#104—261no—
93#100—131no—
94#99—132no—
95#99—262no—
96C2×C13—21no—
97C2×C13—42no—
98C2×C13—81no—
99C2×C13B(4,𝔽2)11yescharacteristic
100D13—81no—
101#41—261no—
102#41—521no—
103C2×Q8—21no—
104C2×D4—22no—
105C2×D4—262no—
106C2×D4—521no—
107C2×D4C22⋊D1311yescharacteristic
108C2×D4C22×D1311yescharacteristic
109C22×C4—21no—
110C22×C4C22⋊D1312yes—
111SD16—521no—
112D8—521no—
113M16—261no—
114C4⋊C4—21no—
115C4⋊C4—22no—
116C4⋊C4—522no—
117C22⋊C4—22no—
118C22⋊C4—21no—
119C22⋊C4—22no—
120C22⋊C4—262no—
121C22⋊C4—522no—
122C22⋊C4C22⋊D1312yes—
123C42—22no—
124C42C22⋊D1311yescharacteristic
125C13#219811yescharacteristic, complemented, Sylow
126C23—21no—
127C23—262no—
128C23C2×C22⋊D1312yes—
129Q8—42no—
130Q8—261no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—261no—
135D4—522no—
136D4—521no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—262no—
143C2×C4—521no—
144C2×C4—522no—
145C2×C4C2×C22⋊D1311yescharacteristic
146C8—521no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—521no—
152C22—1042no—
153C22#8820711yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—521no—
159C4—1042no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—1041no—
164C2#1171890511yescharacteristic
subgroupG/H
centerC2#11718905
commutator, cosocleC2×D4×C13C23
FrattiniC2×D4C22×D13
FittingC13×#559C2
socleC2×C13B(4,𝔽2)
prime radical#11718738C2
hypercenter#559D13
hypocenterC13#2198
LCSG ▷ C2×D4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. C13×#559C2semidirect
3. #11718714C2semidirect
4. #11718137C2semidirect
5. #11718131C2semidirect
65. #559D13semidirect
125. C13#2198semidirect

Maximal subgroups

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

subgroupindex
C13×#5592
#117187382
#117187142
#117181372
#117181312
#219813