Finite Group Databasebeta

← #13114166

Subgroups — #13114166

Order 1664.

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

normal subgroups only

This group has 172 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⋊#564C211yesmaximal, characteristic
2#11718726C211yesmaximal, characteristic
3#11718364C211yesmaximal, characteristic
4#11718363C211yesmaximal, characteristic
5C13×#330C211yesmaximal, characteristic
6#11718057C211yesmaximal, characteristic
7#11718057C211yesmaximal, characteristic
8C13×#125C2211yescharacteristic
9#88144—21no—
10#88144—21no—
11#88143—21no—
12#88143—21no—
13#88143—21no—
14#88143—21no—
15#88124C2211yescharacteristic
16#88124C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×#97C2211yescharacteristic
19C13×#97C2211yescharacteristic
20#88058—21no—
21#88057—21no—
22#88056—21no—
23#88056—21no—
24#88048—21no—
25#88047—21no—
26#88043C2211yescharacteristic
27C2×Dic26—21no—
28C2×C8×C13—21no—
29C2×C8×C13—21no—
30C13×C4⋊C4—21no—
31C13×C4⋊C4—21no—
32C13×C4⋊C4D411yescharacteristic
33C13×C4⋊C4D411yescharacteristic
34C42×C13C2311yescharacteristic
35C4⋊Dic13—21no—
36C4⋊Dic13—21no—
37C4⋊Dic13—21no—
38C4⋊Dic13—21no—
39C4⋊Dic13D411yescharacteristic
40C4⋊Dic13D411yescharacteristic
41C4⋊Dic13D411yescharacteristic
42C4⋊Dic13D411yescharacteristic
43#6101—21no—
44#6101—21no—
45#6101—21no—
46#6101—21no—
47#6101—21no—
48#6101—21no—
49#6101—21no—
50#6101—21no—
51C4×Dic13—21no—
52C4×Dic13—21no—
53C2×#1055—21no—
54#1663—131nomaximal, Sylow
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13C2×D411yescharacteristic
58C2×C4×C13C2×D411yescharacteristic
59C2×C4×C13C2×D411yescharacteristic
60C2×Dic13—21no—
61C2×Dic13—21no—
62C2×Dic13—21no—
63C2×Dic13—21no—
64C2×Dic13—41no—
65Dic26—42no—
66C8×C13—22no—
67C8×C13—41no—
68#1055—22no—
69#564—131no—
70#501—131no—
71#501—131no—
72#491—131no—
73#330—131no—
74#330—131no—
75#330D1311yescharacteristic
76C22×C13#12011yescharacteristic
77C4×C13—21no—
78C4×C13—21no—
79C4×C13—21no—
80C4×C13—41no—
81C4×C13—41no—
82Dic13—41no—
83Dic13—41no—
84Dic13—41no—
85Dic13—41no—
86Dic13—81no—
87C4⋊Q8—131no—
88#125—131no—
89#125—131no—
90#125—261no—
91#125—261no—
92#125—261no—
93#125—261no—
94#125—261no—
95#125—261no—
96#125C2×D1311yescharacteristic
97#107—261no—
98#107—261no—
99#106—261no—
100#106—261no—
101#103—261no—
102#103—261no—
103#97—131no—
104#97C2×D1311yescharacteristic
105#97C2×D1311yescharacteristic
106C2×C13#45411yescharacteristic
107C2×C13#45611yescharacteristic
108C2×C13#45611yescharacteristic
109C2×Q8—261no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—261no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—131no—
116C4⋊C4—131no—
117C4⋊C4—131no—
118C4⋊C4—131no—
119C4⋊C4—261no—
120C4⋊C4—261no—
121C4⋊C4—261no—
122C4⋊C4—261no—
123C4⋊C4—261no—
124C4⋊C4—261no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C4⋊C4—261no—
128C4⋊C4—261no—
129C4⋊C4—261no—
130C4⋊C4—261no—
131C4⋊C4D5211yescharacteristic
132C4⋊C4D5211yescharacteristic
133C42—261no—
134C42—261no—
135C42C22×D1311yescharacteristic
136C13#166311yescharacteristic, complemented, Sylow
137Q8—522no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—261no—
141C2×C4—261no—
142C2×C4—261no—
143C2×C4—261no—
144C2×C4—521no—
145C2×C4C2×D5211yescharacteristic
146C2×C4D4×D1311yescharacteristic
147C2×C4D4×D1311yescharacteristic
148C8—22no—
149C8—41no—
150C8—262no—
151C22#8813611yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—521no—
158C4—521no—
159C4—521no—
160C4—521no—
161C4—1041no—
162C2#1171841311yescharacteristic
163C2#1171848711yescharacteristic
164C2#1171848811yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#330C2
socle, prime radicalC22×C13#120
hypercenter#330D13
hypocenterC13#1663
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
136. C13#1663semidirect

Maximal subgroups

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

subgroupindex
C13⋊#5642
#117187262
#117183642
#117183632
C13×#3302
#117180572
#166313