Finite Group Databasebeta

← #15774455

Subgroups — #15774455

Order 3328.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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#13116648C212yesmaximal, complemented
2#13112877C212yesmaximal, complemented
3#13112875C212yesmaximal, complemented
4C13×#3152C211yesmaximal, characteristic
5C2×C13×#137—22no—
6C13×#532C411yescharacteristic
7C2×C13×C4⋊Q8C411yescharacteristic
8C13×#497—22no—
9C13×#494C411yescharacteristic
10C13×#494C2211yescharacteristic
11C13×#492C411yescharacteristic
12C13×#492C2211yescharacteristic
13C4×C13×M16C2211yescharacteristic
14#11718145—22no—
15#11718058—22no—
16#11718055C2214yes—
17C2×C13×#41—21no—
18C22×Q8×C13—21no—
19C13×#137—48no—
20C2×C13×Q16—22no—
21C2×C13×Q16—22no—
22C2×C13×SD16—22no—
23C2×C13×SD16—22no—
24C2×C13×M16D412yes—
25C13×C4⋊Q8—21no—
26C13×C4⋊Q8—41no—
27C13×C4⋊Q8C2×C411yescharacteristic
28C13×C4⋊Q8C2×C411yescharacteristic
29C13×C4⋊Q8C2×C411yescharacteristic
30C13×#127C2×C411yescharacteristic
31C13×#124—21no—
32C13×#121—41no—
33C4×D4×C13—41no—
34C2×C13×C4⋊C4—41no—
35C2×C42×C13C2×C411yescharacteristic
36C13×#97D412yes—
37C4×C8×C13C2×C411yescharacteristic
38C4×C8×C13C2311yescharacteristic
39#88052—24no—
40#11993—131nomaximal, Sylow
41C13×#41—44no—
42C2×Q8×C13—21no—
43C2×Q8×C13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13—44no—
46C2×Q8×C13—41no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13—41no—
53C22×C4×C13C22⋊C411yescharacteristic
54C13×Q16—44no—
55C13×Q16—44no—
56C13×SD16—44no—
57C13×SD16—44no—
58C13×M16—24no—
59C2×C8×C13C22⋊C412yes—
60C2×C8×C13C2×D412yes—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—42no—
65C13×C22⋊C4—42no—
66C42×C13—21no—
67C42×C13C22⋊C411yescharacteristic
68C42×C13C22×C411yescharacteristic
69#6090—44no—
70#3152D1311yescharacteristic
71#2165—132no—
72#1359—132no—
73#1358—132no—
74C23×C13—41no—
75C23×C13#10011yescharacteristic
76Q8×C13—42no—
77Q8×C13—42no—
78Q8×C13—42no—
79Q8×C13—82no—
80D4×C13—42no—
81D4×C13—82no—
82D4×C13—82no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—42no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—82no—
91C2×C4×C13—82no—
92C2×C4×C13#10011yescharacteristic
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C8×C13—22no—
95C8×C13AGL(1,ℤ/8)14yes—
96C2×#137—22no—
97#532Dic1311yescharacteristic
98C2×C4⋊Q8Dic1311yescharacteristic
99#497—22no—
100#494Dic1311yescharacteristic
101#494C2×D1311yescharacteristic
102#492Dic1311yescharacteristic
103#492C2×D1311yescharacteristic
104C4×M16C2×D1311yescharacteristic
105#364—134no—
106#349—262no—
107#347—262no—
108C22×C13—21no—
109C22×C13—41no—
110C22×C13—82no—
111C22×C13—81no—
112C22×C13C2×#10011yescharacteristic
113C4×C13—22no—
114C4×C13—21no—
115C4×C13—41no—
116C4×C13—81no—
117C4×C13—81no—
118C4×C13—81no—
119C4×C13#41812yes—
120C2×#41—21no—
121C22×Q8—21no—
122#137—48no—
123C2×Q16—22no—
124C2×Q16—22no—
125C2×SD16—22no—
126C2×SD16—22no—
127C2×M16C22⋊D1312yes—
128C4⋊Q8—21no—
129C4⋊Q8—41no—
130C4⋊Q8C2×Dic1311yescharacteristic
131C4⋊Q8C2×Dic1311yescharacteristic
132C4⋊Q8C2×Dic1311yescharacteristic
133#127C2×Dic1311yescharacteristic
134#124—21no—
135#121—41no—
136C4×D4—41no—
137C2×C4⋊C4—41no—
138C2×C42C2×Dic1311yescharacteristic
139M32—264no—
140#97C22⋊D1312yes—
141C4×C8C2×Dic1311yescharacteristic
142C4×C8C22×D1311yescharacteristic
143C2×C13—21no—
144C2×C13—41no—
145C2×C13—161no—
146C2×C13#155511yescharacteristic
147#41—44no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—44no—
152C2×Q8—41no—
153C2×D4—21no—
154C2×D4—41no—
155C2×D4—41no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4C22⋊Dic1311yescharacteristic
160Q16—44no—
161Q16—44no—
162SD16—44no—
163SD16—44no—
164M16—24no—
165C2×C8C22⋊Dic1312yes—
166C2×C8C2×C22⋊D1312yes—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C22⋊C4—42no—
172C42—21no—
173C42C22⋊Dic1311yescharacteristic
174C42C22×Dic1311yescharacteristic
175C16—524no—
176C13#1199311yescharacteristic, complemented, Sylow
177C23—41no—
178C23#8807311yescharacteristic
179Q8—42no—
180Q8—42no—
181Q8—42no—
182Q8—82no—
183D4—42no—
184D4—82no—
185D4—82no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4#8807311yescharacteristic
196C2×C4C2×C22⋊Dic1311yescharacteristic
197C8—22no—
198C8#8818614yes—
199C22—21no—
200C22—41no—
201C22—82no—
202C22—81no—
203C22C2×#8807311yescharacteristic
204C4—22no—
205C4—21no—
206C4—41no—
207C4—81no—
208C4—81no—
209C4—81no—
210C4#1171887612yes—
211C2—21no—
212C2—41no—
213C2—161no—
214C2#1311355011yescharacteristic
subgroupG/H
centerC2#13113550
commutatorC42×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#3152C2
socleC2×C13#1555
prime radicalC13×#532C4
cosocleC4×C8×C13C23
hypercenter#3152D13
hypocenterC13#11993
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3152

Complements

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

NH ≅ G/Ntype
1. #13116648C2semidirect
2. #13112877C2semidirect
3. #13112875C2semidirect
176. C13#11993semidirect

Maximal subgroups

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

subgroupindex
#131166482
#131128772
#131128752
C13×#31522
#1199313