Finite Group Databasebeta

← #13113540

Subgroups — #13113540

Order 1664.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#11719430C211yesmaximal, characteristic
2#11718496C211yesmaximal, characteristic, complemented
3#11718494C211yesmaximal, characteristic, complemented
4C13×#332C211yesmaximal, characteristic, complemented
5#11718139C211yesmaximal, characteristic, complemented
6#11718077C211yesmaximal, characteristic, complemented
7#11718077C211yesmaximal, characteristic, complemented
8C2×#6131—21no—
9C13×C4⋊Q8C2211yescharacteristic
10#88201—21no—
11#88149—21no—
12#88149C412yes—
13#88147—21no—
14#88147C412yes—
15#88128C2211yescharacteristic
16C42×D13C2211yescharacteristic
17C13×C4⋊C8C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19#88060—21no—
20#88060—21no—
21#88055—21no—
22C8×Dic13—21no—
23C4⋊#1055C2211yescharacteristic
24C4⋊#1055C2211yescharacteristic
25C2×Q8×C13—21no—
26#6131—42no—
27#6131—42no—
28C2×D52—22no—
29C2×D52—21no—
30C2×D52—21no—
31C2×D52C2×C412yes—
32C2×C4×D13—22no—
33C2×C4×D13C2×C411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C8×C13—21no—
37C2×C8×C13—21no—
38C13×C4⋊C4—21no—
39C13×C4⋊C4C2×C412yes—
40C42×C13C2311yescharacteristic
41#6103—22no—
42#6103—22no—
43C4×Dic13C2×C411yescharacteristic
44C4×Dic13D411yescharacteristic
45C4×Dic13D411yescharacteristic
46C2×#1055—21no—
47C2×#1055—21no—
48#1553—131nomaximal, Sylow
49C22×D13—22no—
50C22×D13C22⋊C411yescharacteristic
51Q8×C13—41no—
52Q8×C13—41no—
53C2×C4×C13—22no—
54C2×C4×C13C22×C411yescharacteristic
55C2×C4×C13C2×D411yescharacteristic
56C2×C4×C13C2×D411yescharacteristic
57C2×Dic13C22⋊C411yescharacteristic
58C2×Dic13C22⋊C411yescharacteristic
59C2×Dic13C22⋊C411yescharacteristic
60D52—42no—
61D52—44no—
62D52—41no—
63D52—41no—
64D52—41no—
65D52—41no—
66C4×D13—21no—
67C4×D13—21no—
68C4×D13—21no—
69C4×D13—21no—
70C4×D13—41no—
71C4×D13—44no—
72C8×C13—41no—
73C8×C13—41no—
74#1055—41no—
75#1055—41no—
76#532—131no—
77#432—131no—
78#431—131no—
79#332—131no—
80#332D1311yescharacteristic, complemented
81#331—131no—
82#331—131no—
83C22×C13C2×C22⋊C411yescharacteristic
84C2×D13—21no—
85C2×D13—21no—
86C2×D13—21no—
87C2×D13—42no—
88C2×D13—42no—
89C2×D13—42no—
90C4×C13—21no—
91C4×C13—42no—
92C4×C13#13511yescharacteristic
93C4×C13#13511yescharacteristic
94C4×C13AGL(1,ℤ/8)11yescharacteristic
95C4×C13AGL(1,ℤ/8)11yescharacteristic
96Dic13—21no—
97Dic13—21no—
98Dic13—21no—
99C2×#41—261no—
100C4⋊Q8C2×D1311yescharacteristic
101#127—131no—
102#124—261no—
103#121—132no—
104#121—261no—
105C4×D4—132no—
106C4×D4—261no—
107C2×C42—131no—
108C4⋊C8—131no—
109C4⋊C8—131no—
110C4⋊C8C2×D1311yescharacteristic
111C4⋊C8C2×D1311yescharacteristic
112C22⋊C8—261no—
113C22⋊C8—261no—
114#97—261no—
115C4×C8—261no—
116C2×C13#41311yescharacteristic
117C2×C13#41611yescharacteristic
118C2×C13#41811yescharacteristic
119D13—41no—
120D13—82no—
121#41—522no—
122#41—522no—
123C2×Q8—21no—
124C2×D4—132no—
125C2×D4—262no—
126C2×D4—261no—
127C2×D4—261no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—131no—
131C22×C4—262no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—261no—
135C2×C8—261no—
136C4⋊C4—21no—
137C4⋊C4C4×D1312yes—
138C22⋊C4—262no—
139C22⋊C4—262no—
140C42—131no—
141C42—131no—
142C42—131no—
143C42C22×D1311yescharacteristic
144C13#155311yescharacteristic, complemented, Sylow
145C23—131no—
146C23—262no—
147Q8—41no—
148Q8—41no—
149D4—522no—
150D4—524no—
151D4—521no—
152D4—521no—
153D4—521no—
154D4—521no—
155C2×C4—22no—
156C2×C4—131no—
157C2×C4—131no—
158C2×C4—131no—
159C2×C4—261no—
160C2×C4—261no—
161C2×C4—261no—
162C2×C4—261no—
163C2×C4—521no—
164C2×C4—524no—
165C2×C4C2×C4×D1311yescharacteristic
166C2×C4D4×D1311yescharacteristic
167C2×C4D4×D1311yescharacteristic
168C8—41no—
169C8—41no—
170C8—521no—
171C8—521no—
172C22—261no—
173C22—261no—
174C22—261no—
175C22—522no—
176C22—522no—
177C22—522no—
178C22C22⋊C4×D1311yescharacteristic
179C4—21no—
180C4—42no—
181C4—261no—
182C4—261no—
183C4—261no—
184C4#8816511yescharacteristic
185C4#8816811yescharacteristic
186C4#8817011yescharacteristic
187C4#8817311yescharacteristic
188C2—521no—
189C2—1042no—
190C2#1171841211yescharacteristic
191C2#1171843111yescharacteristic
192C2#1171846511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#332C2
socleC22×C13C2×C22⋊C4
prime radical#11719430C2
cosocleC42×C13C23
hypercenter#332D13
hypocenterC13#1553
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #11718496C2semidirect
3. #11718494C2semidirect
4. C13×#332C2semidirect
5. #11718139C2semidirect
6. #11718077C2semidirect
7. #11718077C2semidirect
80. #332D13semidirect
144. C13#1553semidirect

Maximal subgroups

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

subgroupindex
#117194302
#117184962
#117184942
C13×#3322
#117181392
#117180772
#155313