Finite Group Databasebeta

← #13115903

Subgroups — #13115903

Order 1664.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#11719496C212yesmaximal, complemented
2#11719453C211yesmaximal, characteristic, complemented
3C13×#407C211yesmaximal, characteristic, complemented
4#11718800C212yesmaximal, complemented
5#11718149C211yesmaximal, characteristic, complemented
6C23×C4×C13C2211yescharacteristic
7C2×#6127C2212yes—
8C2×C13×M16C2211yescharacteristic
9C2×C13×M16C2211yescharacteristic
10#88207—22no—
11#88184—22no—
12#88183—22no—
13C4×C22⋊D13—24no—
14#88180C2212yes—
15#88178—22no—
16#88163—22no—
17#88162—22no—
18#88158—22no—
19C13×C22⋊C8—22no—
20#88065—24no—
21C24×C13D411yescharacteristic
22C22×C4×C13—21no—
23C22×C4×C13—22no—
24C22×C4×C13—22no—
25C22×C4×C13—21no—
26C22×C4×C13D411yescharacteristic
27C22×C4×C13C2311yescharacteristic
28C2×C22⋊D13—24no—
29C2×C22⋊D13—22no—
30#6127—22no—
31#6127—22no—
32#6127—22no—
33#6127—22no—
34C2×D52D412yescomplemented
35C2×C4×D13—22no—
36C2×Dic26D412yescomplemented
37C13×M16—22no—
38C13×M16—22no—
39C2×C8×C13—21no—
40C2×C8×C13D412yescomplemented
41C22⋊Dic13—24no—
42C22⋊Dic13—22no—
43#6103—24no—
44C4⋊Dic13—22no—
45#6101—24no—
46C4×Dic13D414yescomplemented
47Dic52—22no—
48D104—22no—
49#6095—24no—
50#2010—131nomaximal, Sylow
51C23×C13—22no—
52C23×C13—21no—
53C23×C13—42no—
54C23×C13C2×D411yescharacteristic
55C22×D13—22no—
56C2×C4×C13—22no—
57C2×C4×C13—21no—
58C2×C4×C13—41no—
59C2×C4×C13—42no—
60C2×C4×C13—41no—
61C2×C4×C13C2×D412yes—
62C2×C4×C13C2×D411yescharacteristic
63C2×C4×C13C2×D412yes—
64C2×C4×C13#4111yescharacteristic
65C22⋊D13—48no—
66C22⋊D13—42no—
67C22⋊D13—42no—
68C2×Dic13—24no—
69C2×Dic13—22no—
70D52—22no—
71D52—22no—
72C4×D13—42no—
73C4×D13—42no—
74Dic26—22no—
75Dic26—22no—
76C8×C13—22no—
77C8×C13—41no—
78#575—131no—
79#525—132no—
80#421—132no—
81#407D1311yescharacteristic, complemented
82H(3,ℤ/4)—131no—
83C22×C13—24no—
84C22×C13—22no—
85C22×C13—41no—
86C22×C13—42no—
87C22×C13—41no—
88C22×C13—41no—
89C22×C13#12012yes—
90C22×C13#12111yescharacteristic
91C2×D13—44no—
92C2×D13—42no—
93C4×C13—41no—
94C4×C13#12011yescharacteristic
95C4×C13#12112yes—
96C4×C13#12711yescharacteristic
97Dic13—44no—
98Dic13—42no—
99C2×#41—132no—
100C23×C4C2×D1311yescharacteristic
101#137—262no—
102AGL(1,ℤ/8)—262no—
103#135—262no—
104C2×M16C2×D1311yescharacteristic
105C2×M16C2×D1311yescharacteristic
106#123—262no—
107C22⋊Q8—262no—
108#121—262no—
109#120—262no—
110C4×D4—264no—
111#117—132no—
112#104—264no—
113C22⋊C8—22no—
114C2×C13—22no—
115C2×C13—21no—
116C2×C13—42no—
117C2×C13#39211yescharacteristic
118D13—82no—
119C24D5211yescharacteristic
120#41—262no—
121#41—262no—
122#41—262no—
123#41—262no—
124C2×Q8—132no—
125C2×D4—132no—
126C2×D4—264no—
127C2×D4—262no—
128C22×C4—21no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—262no—
133C22×C4D5211yescharacteristic
134C22×C4C22×D1311yescharacteristic
135Q16—262no—
136SD16—264no—
137D8—262no—
138M16—22no—
139M16—22no—
140C2×C8—21no—
141C2×C8C22⋊D1312yescomplemented
142C4⋊C4—264no—
143C4⋊C4—262no—
144C22⋊C4—264no—
145C22⋊C4—264no—
146C22⋊C4—262no—
147C42—134no—
148C13#201011yescharacteristic, complemented, Sylow
149C23—22no—
150C23—21no—
151C23—42no—
152C23—262no—
153C23C2×D5211yescharacteristic
154Q8—262no—
155Q8—262no—
156D4—262no—
157D4—262no—
158D4—528no—
159D4—522no—
160D4—522no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—264no—
167C2×C4—262no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4#612711yescharacteristic
171C2×C4D4×D1312yes—
172C2×C4D4×D1312yes—
173C2×C4C2×C22⋊D1311yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—524no—
183C22—522no—
184C22#8813612yes—
185C22#8818411yescharacteristic
186C4—41no—
187C4—524no—
188C4—522no—
189C4#8813812yes—
190C4#8819111yescharacteristic
191C4#8819411yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—1042no—
196C2#1171862111yescharacteristic
subgroupG/H
centerC4#88194
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#407C2
socleC2×C13#392
hypercenter#407D13
hypocenterC13#2010
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #11719496C2semidirect
2. #11719453C2semidirect
3. C13×#407C2semidirect
4. #11718800C2semidirect
5. #11718149C2semidirect
34. C2×D52D4semidirect
36. C2×Dic26D4semidirect
40. C2×C8×C13D4semidirect
46. C4×Dic13D4semidirect
81. #407D13semidirect
141. C2×C8C22⋊D13semidirect
148. C13#2010semidirect

Maximal subgroups

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

subgroupindex
#117194962
#117194532
C13×#4072
#117188002
#117181492
#201013