Finite Group Databasebeta

← #13130240

Subgroups — #13130240

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#11719285C211yesmaximal, characteristic
2C4×C4⋊#261C211yesmaximal, characteristic, complemented
3#11719054C211yesmaximal, characteristic, complemented
4#11718298C212yesmaximal, complemented
5#11718240C212yesmaximal
6C2×C4⋊#261—21no—
7C2×C4×#261—21no—
8C4×Q8×C13C411yescharacteristic, complemented
9#88201C411yescharacteristic, complemented
10#88200C2211yescharacteristic
11#88152—21no—
12#88149C2211yescharacteristic
13#88148—21no—
14#88144C411yescharacteristic, complemented
15C4×D52—21no—
16C4×D52C411yescharacteristic, complemented
17#88126—21no—
18C42×D13C2211yescharacteristic
19(C2×#261)⋊C4C2212yes—
20#88111C2212yes—
21#88110—21no—
22C4⋊#1057—21no—
23C22×#261—22no—
24C2×Q8×C13C2×C411yescharacteristic
25C2×D52—21no—
26C2×D52C2×C411yescharacteristic
27C2×C4×D13—21no—
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13C2311yescharacteristic
31C2×#1057—22no—
32C4⋊#261—24no—
33C4×#261—42no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4C2×C411yescharacteristic
36C42×C13—21no—
37C42×C13C2×C411yescharacteristic
38#6103—21no—
39#6103—21no—
40#6103—21no—
41#6103—21no—
42#6103—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13C2×C411yescharacteristic
45#6101—21no—
46#6101—21no—
47C4×Dic13C2×C411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13D411yescharacteristic
50#1509—131nomaximal, Sylow
51C22×D13—21no—
52C22×D13C2×D411yescharacteristic
53C2×#261—24no—
54C2×#261—42no—
55C2×#261—42no—
56Q8×C13—41no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C2×Dic13—21no—
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66D52—41no—
67D52—41no—
68D52—41no—
69C4×D13—21no—
70C4×D13—21no—
71C4×D13—22no—
72C4×D13—41no—
73C4×D13—42no—
74#1057—42no—
75#529—131no—
76#432—131no—
77C4×C4⋊C4—131no—
78#328—132no—
79#327—132no—
80C22×C13C2×C22⋊C411yescharacteristic
81C2×D13—21no—
82C2×D13—21no—
83C2×D13—41no—
84C2×D13—41no—
85C2×D13—41no—
86C2×D13AGL(1,ℤ/8)11yescharacteristic
87C2×D13#13711yescharacteristic
88#261—44no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—41no—
92C4×C13—41no—
93C4×C13#10412yes—
94Dic13—21no—
95Dic13—21no—
96Dic13—21no—
97Dic13—41no—
98#126—261no—
99#125—131no—
100#124—131no—
101#123—261no—
102C22⋊Q8—131no—
103#121—131no—
104C4×Q8#26111yescharacteristic, complemented
105C4×D4—131no—
106C4×D4—261no—
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#41011yescharacteristic
116C2×C13#41711yescharacteristic
117C2×C13C2×#10411yescharacteristic
118D13—21no—
119D13—21no—
120D13—81no—
121C2×Q8C2×#26111yescharacteristic
122C2×D4—131no—
123C2×D4—261no—
124C22×C4—131no—
125C22×C4—131no—
126C22×C4—131no—
127C22×C4—262no—
128C22×C4—261no—
129C2×C8—262no—
130C4⋊C4—21no—
131C4⋊C4—131no—
132C4⋊C4—261no—
133C4⋊C4—261no—
134C4⋊C4—261no—
135C4⋊C4—264no—
136C4⋊C4C2×#26111yescharacteristic
137C22⋊C4—261no—
138C22⋊C4—261no—
139C22⋊C4—261no—
140C22⋊C4—261no—
141C22⋊C4—261no—
142C42—21no—
143C42—131no—
144C42—131no—
145C42—131no—
146C42—522no—
147C42C2×#26111yescharacteristic
148C13#150911yescharacteristic, complemented, Sylow
149C23—131no—
150C23—261no—
151Q8—41no—
152D4—521no—
153D4—521no—
154D4—521no—
155C2×C4—21no—
156C2×C4—21no—
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—521no—
166C2×C4—522no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22⋊#26111yescharacteristic
171C2×C4C22×#26111yescharacteristic
172C8—522no—
173C22—131no—
174C22—131no—
175C22—261no—
176C22—261no—
177C22—521no—
178C22—521no—
179C22—521no—
180C22C2×C22⋊#26111yescharacteristic
181C4—21no—
182C4—21no—
183C4—41no—
184C4—41no—
185C4—261no—
186C4—261no—
187C4—261no—
188C4—524no—
189C4—521no—
190C4#8811812yes—
191C2—261no—
192C2—261no—
193C2—1041no—
194C2#1171911611yescharacteristic
195C2C2×#8811811yescharacteristic
196C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radical#88149C22
cosocleC2×C4×D13C23
hypercenterC4×Q8#261
hypocenterC13#1509
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#261C2semidirect
3. #11719054C2semidirect
4. #11718298C2semidirect
8. C4×Q8×C13C4semidirect
9. #88201C4semidirect
14. #88144C4semidirect
16. C4×D52C4semidirect
104. C4×Q8#261semidirect
148. C13#1509semidirect

Maximal subgroups

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

subgroupindex
#117192852
C4×C4⋊#2612
#117190542
#117182982
#117182402
#150913