Finite Group Databasebeta

← #13130238

Subgroups — #13130238

Order 1664.

242 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 60 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#11719262C211yesmaximal, characteristic
2C4×C4⋊#261C211yesmaximal, characteristic, complemented
3#11719054C211yesmaximal, characteristic, complemented
4#11718292C212yesmaximal
5#11718241C212yesmaximal, complemented
6C2×C4⋊#261—21no—
7C2×C4×#261—21no—
8C4×D4×C13C411yescharacteristic, complemented
9#88192C2211yescharacteristic
10#88190C411yescharacteristic, complemented
11C4×C22⋊D13—21no—
12#88180—21no—
13#88151C2211yescharacteristic
14#88144C411yescharacteristic, complemented
15#88137—21no—
16#88133—21no—
17C42×D13C2211yescharacteristic
18C4×Dic26C411yescharacteristic, complemented
19(C2×#261)⋊C4C2212yes—
20#88111C2212yes—
21#88110—21no—
22C4⋊#1057—21no—
23C22×#261—22no—
24C2×D4×C13C2×C411yescharacteristic
25C22×C4×C13—21no—
26C2×C22⋊D13—21no—
27C2×C4×D13D411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×C4×D13C2311yescharacteristic
30C2×Dic26C2×C411yescharacteristic
31C2×#1057—22no—
32C4⋊#261—24no—
33C4×#261—42no—
34C13×C4⋊C4C2×C411yescharacteristic
35C13×C22⋊C4—21no—
36C42×C13C2×C411yescharacteristic
37C22⋊Dic13—21no—
38C22⋊Dic13—21no—
39C22⋊Dic13—21no—
40#6103—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13C2×C411yescharacteristic
44#6101—21no—
45#6101—21no—
46C4×Dic13—21no—
47C4×Dic13C2×C411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13D411yescharacteristic
50#1509—131nomaximal, Sylow
51C23×C13—21no—
52C22×D13C2×D411yescharacteristic
53C2×#261—24no—
54C2×#261—42no—
55C2×#261—42no—
56D4×C13—41no—
57C2×C4×C13—21no—
58C2×C4×C13—42no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C22⋊D13—41no—
63C22⋊D13—41no—
64C2×Dic13—21no—
65C2×Dic13—21no—
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C22⋊C411yescharacteristic
68C2×Dic13C2×D411yescharacteristic
69C4×D13—21no—
70C4×D13—21no—
71C4×D13—22no—
72C4×D13—41no—
73Dic26—41no—
74#1057—42no—
75#529—131no—
76#432—131no—
77C4×C4⋊C4—131no—
78#328—132no—
79#327—132no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13—41no—
83C22×C13C2×C22⋊C411yescharacteristic
84C2×D13—21no—
85C2×D13—21no—
86C2×D13AGL(1,ℤ/8)11yescharacteristic
87C2×D13#13711yescharacteristic
88#261—44no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—41no—
92C4×C13#10412yes—
93Dic13—21no—
94Dic13—21no—
95Dic13—21no—
96Dic13—41no—
97Dic13—41no—
98#126—261no—
99#125—131no—
100#124—131no—
101#123—261no—
102C22⋊Q8—131no—
103#121—131no—
104C4×Q8—131no—
105C4×D4—261no—
106C4×D4#26111yescharacteristic, complemented
107#117—261no—
108C2×C4⋊C4—261no—
109C2×C42—131no—
110C2×C42—261no—
111C4⋊C8—261no—
112C22⋊C8—132no—
113#97—261no—
114#95—132no—
115C2×C13—81no—
116C2×C13#41011yescharacteristic
117C2×C13#41711yescharacteristic
118C2×C13C2×#10411yescharacteristic
119D13—21no—
120D13—21no—
121C2×Q8—131no—
122C2×D4—261no—
123C2×D4C2×#26111yescharacteristic
124C22×C4—21no—
125C22×C4—131no—
126C22×C4—131no—
127C22×C4—131no—
128C22×C4—262no—
129C2×C8—262no—
130C4⋊C4—131no—
131C4⋊C4—261no—
132C4⋊C4—261no—
133C4⋊C4—261no—
134C4⋊C4—264no—
135C4⋊C4—261no—
136C4⋊C4C2×#26111yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—261no—
139C22⋊C4—261no—
140C22⋊C4—261no—
141C22⋊C4—261no—
142C42—131no—
143C42—131no—
144C42—131no—
145C42—261no—
146C42—522no—
147C42C2×#26111yescharacteristic
148C13#150911yescharacteristic, complemented, Sylow
149C23—21no—
150C23—131no—
151Q8—521no—
152D4—41no—
153D4—521no—
154D4—521no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—131no—
158C2×C4—131no—
159C2×C4—131no—
160C2×C4—261no—
161C2×C4—261no—
162C2×C4—262no—
163C2×C4—264no—
164C2×C4—261no—
165C2×C4—261no—
166C2×C4—521no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22⋊#26111yescharacteristic
171C2×C4C22×#26111yescharacteristic
172C8—522no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—131no—
177C22—131no—
178C22—261no—
179C22—261no—
180C22C2×C22⋊#26111yescharacteristic
181C4—21no—
182C4—21no—
183C4—41no—
184C4—261no—
185C4—261no—
186C4—261no—
187C4—524no—
188C4—521no—
189C4—521no—
190C4#8811612yes—
191C2—81no—
192C2—261no—
193C2—261no—
194C2#1171911611yescharacteristic
195C2C2×#8811611yescharacteristic
196C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radical#88192C22
cosocleC2×C4×D13C23
hypercenterC4×D4#261
hypocenterC13#1509
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#261C2semidirect
3. #11719054C2semidirect
5. #11718241C2semidirect
8. C4×D4×C13C4semidirect
10. #88190C4semidirect
14. #88144C4semidirect
18. C4×Dic26C4semidirect
106. C4×D4#261semidirect
148. C13#1509semidirect

Maximal subgroups

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

subgroupindex
#117192622
C4×C4⋊#2612
#117190542
#117182922
#117182412
#150913