Finite Group Databasebeta

← #15750456

Subgroups — #15750456

Order 3328.

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

normal subgroups only

This group has 208 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#13112961C211yesmaximal, characteristic
2#13112768C211yesmaximal, characteristic
3C13×#2073C211yesmaximal, characteristic
4C2×C13×#102—21no—
5C13×#390C2211yescharacteristic
6C13×#382C411yescharacteristic, complemented
7C2×#88074—21no—
8C13×#340—21no—
9C13×#336C411yescharacteristic, complemented
10#11718120—21no—
11C22×D4×C13D411yescharacteristic
12C22×C8×C13—21no—
13C2×C13×C4⋊C4—21no—
14C2×C13×C4⋊C4D411yescharacteristic
15C2×C13×C22⋊C4—41no—
16C2×C42×C13C2×C411yescharacteristic
17C2×C22⋊Dic13—41no—
18C13×#102—41no—
19C13×#102—41no—
20C13×#95—41no—
21#88074—22no—
22#88074—41no—
23C22⋊#1055—41no—
24#7412—131nomaximal, Sylow
25C24×C13—21no—
26C2×D4×C13—21no—
27C2×D4×C13—41no—
28C2×D4×C13—41no—
29C2×D4×C13D811yescharacteristic
30C2×D4×C13SD1611yescharacteristic
31C22×C4×C13—21no—
32C22×C4×C13—21no—
33C22×C4×C13—41no—
34C22×C4×C13C22⋊C411yescharacteristic
35C22×Dic13—81no—
36C2×C8×C13—41no—
37C2×C8×C13—41no—
38C2×C8×C13—41no—
39C13×C4⋊C4—41no—
40C13×C4⋊C4—41no—
41C13×C4⋊C4—41no—
42C13×C22⋊C4—82no—
43C42×C13—41no—
44C22⋊Dic13—42no—
45C22⋊Dic13—81no—
46C2×#1055—81no—
47#2073D1311yescharacteristic
48#1393—131no—
49#1318—131no—
50C23×C13—21no—
51C23×C13—21no—
52C23×C13—41no—
53C23×C13—41no—
54C23×C13—81no—
55C23×C13—81no—
56C23×C13#9911yescharacteristic
57D4×C13—41no—
58D4×C13—41no—
59D4×C13—81no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—81no—
67C2×C4×C13—81no—
68C2×C4×C13—81no—
69C2×C4×C13—81no—
70C2×C4×C13#10211yescharacteristic
71C2×C4×C13#10411yescharacteristic
72C2×Dic13—82no—
73C2×Dic13—161no—
74C2×Dic13—161no—
75C8×C13—81no—
76#1055—161no—
77C2×#102—21no—
78C2×#99—261no—
79#390C2×D1311yescharacteristic
80#382Dic1311yescharacteristic, complemented
81#340—21no—
82#336Dic1311yescharacteristic, complemented
83#324—261no—
84C22×C13—21no—
85C22×C13—21no—
86C22×C13—41no—
87C22×C13—41no—
88C22×C13—81no—
89C22×C13—81no—
90C22×C13—81no—
91C22×C13—81no—
92C22×C13—161no—
93C22×C13#32711yescharacteristic
94C22×C13#35211yescharacteristic
95C22×C13#35411yescharacteristic
96C4×C13—21no—
97C4×C13—21no—
98C4×C13—81no—
99C4×C13—81no—
100C4×C13—161no—
101Dic13—162no—
102C22×D4C22⋊D1311yescharacteristic
103C22×C8—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4C22⋊D1311yescharacteristic
106C2×C22⋊C4—41no—
107C2×C22⋊C4—521no—
108C2×C42C2×Dic1311yescharacteristic
109#102—41no—
110#102—41no—
111#99—262no—
112#99—521no—
113C22⋊C8—521no—
114#95—41no—
115C2×C13—21no—
116C2×C13—21no—
117C2×C13—81no—
118C2×C13—81no—
119C2×C13#134411yescharacteristic
120C2×C13#141211yescharacteristic
121C2×C13#141411yescharacteristic
122C24—21no—
123C2×D4—21no—
124C2×D4—41no—
125C2×D4—41no—
126C2×D4#610411yescharacteristic
127C2×D4#610511yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—1041no—
132C22×C4C22⋊Dic1311yescharacteristic
133C2×C8—41no—
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—1041no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C22⋊C4—82no—
141C22⋊C4—522no—
142C22⋊C4—1041no—
143C42—41no—
144C13#741211yescharacteristic, complemented, Sylow
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—81no—
150C23—81no—
151C23#8807411yescharacteristic
152D4—41no—
153D4—41no—
154D4—81no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—1042no—
166C2×C4—2081no—
167C2×C4—2081no—
168C2×C4#8807211yescharacteristic
169C2×C4#8807711yescharacteristic
170C8—81no—
171C8—2081no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1171812911yescharacteristic
182C22#1171813111yescharacteristic
183C22#1171813311yescharacteristic
184C4—21no—
185C4—21no—
186C4—81no—
187C4—81no—
188C4—161no—
189C4—2082no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#1311283611yescharacteristic
195C2#1311300711yescharacteristic
196C2#1311301111yescharacteristic
subgroupG/H
centerC22#11718133
commutatorC2×C42×C13C2×C4
Frattini#390C2×D13
FittingC13×#2073C2
socleC22×C13#354
prime radicalC22×D4×C13D4
cosocleC13×#390C22
hypercenter#2073D13
hypocenterC13#7412
LCSG ▷ C2×C42×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #2073

Complements

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

NH ≅ G/Ntype
6. C13×#382C4semidirect
9. C13×#336C4semidirect
80. #382Dic13semidirect
82. #336Dic13semidirect
144. C13#7412semidirect

Maximal subgroups

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

subgroupindex
#131129612
#131127682
C13×#20732
#741213