Finite Group Databasebeta

← #15750550

Subgroups — #15750550

Order 3328.

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

normal subgroups only

This group has 198 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#13116181C211yesmaximal, characteristic
2#13112719C211yesmaximal, characteristic
3C13×#1325C211yesmaximal, characteristic
4#11719205C411yescharacteristic
5C13×#384C2211yescharacteristic
6#11718625—21no—
7C2×C4⋊#1055—21no—
8C13×#324—21no—
9#11718122C411yescharacteristic
10#11718115—21no—
11C2×C13×C4⋊C4—41no—
12C2×C13×C4⋊C4C2×C411yescharacteristic
13C2×C13×C4⋊C4D411yescharacteristic
14C2×C42×C13D411yescharacteristic
15#88180—21no—
16#88178—41no—
17C2×#6099—21no—
18C22×#1055—41no—
19#88144—41no—
20#88142—41no—
21C13×C22⋊C8—41no—
22#88048—41no—
23#88047—41no—
24C4⋊#1055—22no—
25C4⋊#1055—41no—
26#7443—131nomaximal, Sylow
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13C22⋊C411yescharacteristic
31C2×Dic26—41no—
32C2×C8×C13—81no—
33C13×C4⋊C4—41no—
34C13×C4⋊C4—41no—
35C13×C4⋊C4—81no—
36C13×C4⋊C4—81no—
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—42no—
50C2×#1055—81no—
51C2×#1055—81no—
52#2060—131no—
53#1325D1311yescharacteristic
54#1296—131no—
55C23×C13#9911yescharacteristic
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—81no—
67C2×C4×C13—81no—
68C2×C4×C13#10311yescharacteristic
69C2×C4×C13#10411yescharacteristic
70C2×Dic13—41no—
71C2×Dic13—41no—
72Dic26—161no—
73C8×C13—161no—
74#1055—42no—
75#1055—82no—
76#544—131no—
77#428—261no—
78C2×C4⋊C8—261no—
79#384C2×D1311yescharacteristic
80#343—131no—
81#339—261no—
82#324—21no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13#32811yescharacteristic
86C22×C13AΣL(1,𝔽16)11yescharacteristic
87C22×C13#35611yescharacteristic
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—21no—
93C4×C13—21no—
94C4×C13—81no—
95C4×C13—81no—
96Dic13—81no—
97Dic13—81no—
98C2×M16—261no—
99C22×C8—521no—
100C4⋊Q8—521no—
101#125—521no—
102C22⋊Q8—521no—
103#117—261no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4C4×D1311yescharacteristic
106C2×C4⋊C4C22⋊D1311yescharacteristic
107C2×C42D5211yescharacteristic
108#107—521no—
109#106—521no—
110C4⋊C8—262no—
111C4⋊C8—521no—
112C22⋊C8—41no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13#135411yescharacteristic
116C2×C13#140211yescharacteristic
117C2×C13#140511yescharacteristic
118C2×Q8—521no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4#610311yescharacteristic
123M16—262no—
124M16—521no—
125C2×C8—81no—
126C2×C8—521no—
127C2×C8—522no—
128C2×C8—1041no—
129C2×C8—1041no—
130C4⋊C4—41no—
131C4⋊C4—41no—
132C4⋊C4—81no—
133C4⋊C4—81no—
134C4⋊C4—261no—
135C4⋊C4—261no—
136C4⋊C4—521no—
137C4⋊C4—522no—
138C22⋊C4—521no—
139C42—21no—
140C42—521no—
141C42#609511yescharacteristic
142C42Dic5211yescharacteristic
143C13#744311yescharacteristic, complemented, Sylow
144C23#8804611yescharacteristic
145Q8—2081no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—521no—
159C2×C4—521no—
160C2×C4#8805611yescharacteristic
161C2×C4#8806511yescharacteristic
162C8—161no—
163C8—522no—
164C8—1042no—
165C22—21no—
166C22—21no—
167C22#1171805911yescharacteristic
168C22#1171806311yescharacteristic
169C22#1171807011yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—1041no—
179C4—1041no—
180C2—21no—
181C2—21no—
182C2#1311286711yescharacteristic
183C2#1311298011yescharacteristic
184C2#1311298911yescharacteristic
subgroupG/H
centerC22#11718063
commutatorC2×C13×C4⋊C4C2×C4
Frattini#384C2×D13
FittingC13×#1325C2
socleC22×C13AΣL(1,𝔽16)
prime radicalC23×C13#99
cosocleC13×#384C22
hypercenter#1325D13
hypocenterC13#7443
LCSG ▷ C2×C13×C4⋊C4 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
143. C13#7443semidirect

Maximal subgroups

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

subgroupindex
#131161812
#131127192
C13×#13252
#744313