Finite Group Databasebeta

← #15750549

Subgroups — #15750549

Order 3328.

198 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 43 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#13112782C211yesmaximal, characteristic
2#13112719C211yesmaximal, characteristic
3C13×#2060C211yesmaximal, characteristic
4C13×#544C411yescharacteristic
5C13×#428—21no—
6C13×#384C2211yescharacteristic
7C2×C4⋊#1055—21no—
8C13×#343C411yescharacteristic
9C13×#339—21no—
10#11718120—21no—
11C2×C13×M16—21no—
12C13×C4⋊Q8—41no—
13C13×#125—41no—
14C13×C22⋊Q8—41no—
15C13×#117—21no—
16C2×C13×C4⋊C4—41no—
17C2×C13×C4⋊C4C2×C411yescharacteristic
18C2×C13×C4⋊C4D411yescharacteristic
19C2×C42×C13D411yescharacteristic
20C22×#1055—41no—
21C13×#107—41no—
22C13×#106—41no—
23C22⋊#1055—41no—
24C4⋊#1055—22no—
25C4⋊#1055—41no—
26#7443—131nomaximal, Sylow
27C2×Q8×C13—41no—
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13—21no—
31C22×C4×C13C22⋊C411yescharacteristic
32C13×M16—22no—
33C13×M16—41no—
34C2×C8×C13—41no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4—41no—
38C13×C4⋊C4—41no—
39C13×C4⋊C4—41no—
40C13×C4⋊C4—42no—
41C13×C4⋊C4—81no—
42C13×C4⋊C4—81no—
43C13×C22⋊C4—41no—
44C42×C13—21no—
45C42×C13—41no—
46C42×C13SD1611yescharacteristic
47C42×C13Q1611yescharacteristic
48C2×#1055—42no—
49C2×#1055—81no—
50C2×#1055—81no—
51C2×#1055—81no—
52#2060D1311yescharacteristic
53#1325—131no—
54#1296—131no—
55C23×C13#9911yescharacteristic
56Q8×C13—161no—
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—21no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—81no—
70C2×C4×C13—81no—
71C2×C4×C13#10311yescharacteristic
72C2×C4×C13#10411yescharacteristic
73C8×C13—42no—
74#1055—82no—
75#1055—161no—
76#544Dic1311yescharacteristic
77#428—21no—
78C2×C4⋊C8—261no—
79#384C2×D1311yescharacteristic
80#343Dic1311yescharacteristic
81#339—21no—
82#324—261no—
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—
96C4×C13—81no—
97C4×C13—81no—
98C2×M16—21no—
99C22×C8—521no—
100C4⋊Q8—41no—
101#125—41no—
102C22⋊Q8—41no—
103#117—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4C2×Dic1311yescharacteristic
106C2×C4⋊C4C22⋊D1311yescharacteristic
107C2×C42C22⋊D1311yescharacteristic
108#107—41no—
109#106—41no—
110C4⋊C8—262no—
111C4⋊C8—521no—
112C22⋊C8—521no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13#135411yescharacteristic
116C2×C13#140211yescharacteristic
117C2×C13#140511yescharacteristic
118C2×Q8—41no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4C22⋊Dic1311yescharacteristic
123M16—22no—
124M16—41no—
125C2×C8—41no—
126C2×C8—522no—
127C2×C8—1041no—
128C2×C8—1041no—
129C2×C8—1041no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—41no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—42no—
136C4⋊C4—81no—
137C4⋊C4—81no—
138C22⋊C4—41no—
139C42—21no—
140C42—41no—
141C42#610611yescharacteristic
142C42#610711yescharacteristic
143C13#744311yescharacteristic, complemented, Sylow
144C23#8807411yescharacteristic
145Q8—161no—
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—41no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4#8807511yescharacteristic
161C2×C4#8807711yescharacteristic
162C8—42no—
163C8—1042no—
164C8—2081no—
165C22—21no—
166C22—21no—
167C22#1171812811yescharacteristic
168C22#1171813011yescharacteristic
169C22#1171814011yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—81no—
179C4—81no—
180C2—21no—
181C2—21no—
182C2#1311286611yescharacteristic
183C2#1311298111yescharacteristic
184C2#1311299011yescharacteristic
subgroupG/H
centerC22#11718128
commutatorC2×C13×C4⋊C4C2×C4
Frattini#384C2×D13
FittingC13×#2060C2
socleC22×C13AΣL(1,𝔽16)
prime radicalC23×C13#99
cosocleC13×#384C22
hypercenter#2060D13
hypocenterC13#7443
LCSG ▷ C2×C13×C4⋊C4 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #2060

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
#131127822
#131127192
C13×#20602
#744313