Finite Group Databasebeta

← #15750545

Subgroups — #15750545

Order 3328.

194 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 41 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#13116186C211yesmaximal, characteristic
2#13112780C211yesmaximal, characteristic
3C13×#1295C211yesmaximal, characteristic
4#11719205C411yescharacteristic
5C2×C13×#97—21no—
6C13×#382C2211yescharacteristic
7#11718625—21no—
8#11718122C411yescharacteristic
9#11718120—21no—
10#11718115—21no—
11C22×C8×C13—41no—
12C2×C13×C4⋊C4C2×C411yescharacteristic
13C2×C13×C4⋊C4D411yescharacteristic
14C2×C42×C13D411yescharacteristic
15#88180—21no—
16#88178—41no—
17C2×#6099—21no—
18#88144—41no—
19#88142—41no—
20C13×#97—22no—
21C13×#97—41no—
22C13×#95—41no—
23C22⋊#1055—41no—
24#88048—41no—
25#88047—41no—
26#7442—131nomaximal, Sylow
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13C22⋊C411yescharacteristic
31C2×Dic26—41no—
32C2×C8×C13—42no—
33C2×C8×C13—42no—
34C2×C8×C13—42no—
35C13×C4⋊C4—41no—
36C13×C4⋊C4—41no—
37C42×C13—21no—
38C42×C13SD1611yescharacteristic
39C42×C13Q1611yescharacteristic
40C22⋊Dic13—41no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13—41no—
44#6101—42no—
45C4×Dic13—41no—
46#6099—22no—
47#6099—41no—
48C2×#1055—41no—
49C2×#1055—81no—
50#2061—131no—
51#1324—131no—
52#1295D1311yescharacteristic
53C23×C13#9911yescharacteristic
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—81no—
63C2×C4×C13—81no—
64C2×C4×C13#10311yescharacteristic
65C2×C4×C13#10411yescharacteristic
66C2×Dic13—41no—
67C2×Dic13—41no—
68Dic26—161no—
69C8×C13—44no—
70#1055—42no—
71#1055—161no—
72#544—131no—
73#428—261no—
74C2×#97—21no—
75#382C2×D1311yescharacteristic
76#343—131no—
77#339—261no—
78#324—261no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13#32811yescharacteristic
82C22×C13AΣL(1,𝔽16)11yescharacteristic
83C22×C13#35611yescharacteristic
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—41no—
87C4×C13—41no—
88C4×C13—81no—
89C4×C13—81no—
90Dic13—81no—
91Dic13—81no—
92C2×M16—261no—
93C22×C8—41no—
94C4⋊Q8—521no—
95#125—521no—
96C22⋊Q8—521no—
97#117—261no—
98C2×C4⋊C4C4×D1311yescharacteristic
99C2×C4⋊C4D5211yescharacteristic
100C2×C42C22⋊D1311yescharacteristic
101#107—521no—
102#106—521no—
103C22⋊C8—521no—
104#97—22no—
105#97—41no—
106#95—41no—
107C2×C13—21no—
108C2×C13—21no—
109C2×C13#135411yescharacteristic
110C2×C13#140311yescharacteristic
111C2×C13#140411yescharacteristic
112C2×Q8—521no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4#610311yescharacteristic
117M16—262no—
118M16—521no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—42no—
122C2×C8—521no—
123C2×C8—1041no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—261no—
127C4⋊C4—261no—
128C4⋊C4—521no—
129C4⋊C4—522no—
130C22⋊C4—521no—
131C42—21no—
132C42—521no—
133C42#610511yescharacteristic
134C42#610711yescharacteristic
135C13#744211yescharacteristic, complemented, Sylow
136C23#8804611yescharacteristic
137Q8—2081no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—521no—
149C2×C4—521no—
150C2×C4#8804511yescharacteristic
151C2×C4#8805011yescharacteristic
152C8—44no—
153C8—522no—
154C8—2081no—
155C22—21no—
156C22—21no—
157C22#1171804411yescharacteristic
158C22#1171806711yescharacteristic
159C22#1171807011yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—1041no—
167C4—1041no—
168C2—21no—
169C2—21no—
170C2#1311286511yescharacteristic
171C2#1311298511yescharacteristic
172C2#1311298811yescharacteristic
subgroupG/H
centerC22#11718067
commutatorC2×C13×C4⋊C4C2×C4
Frattini#382C2×D13
FittingC13×#1295C2
socleC22×C13AΣL(1,𝔽16)
prime radicalC23×C13#99
cosocleC13×#382C22
hypercenter#1295D13
hypocenterC13#7442
LCSG ▷ C2×C13×C4⋊C4 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1295

Complements

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

NH ≅ G/Ntype
135. C13#7442semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131127802
C13×#12952
#744213