Finite Group Databasebeta

← #13113362

Subgroups — #13113362

Order 1664.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#11719184C211yesmaximal, characteristic
2C13×#432C211yesmaximal, characteristic, complemented
3C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
4#11718062C212yesmaximal
5#11718059C212yesmaximal, complemented
6C2×C42×C13C2211yescharacteristic
7#88184C2211yescharacteristic
8#88183—21no—
9C4×C22⋊D13—21no—
10C2×C4⋊Dic13—21no—
11#88178C2211yescharacteristic
12C2×C4×Dic13—21no—
13#88130—21no—
14#88129C411yescharacteristic, complemented
15C4×D52C411yescharacteristic, complemented
16#88126—21no—
17#88124C411yescharacteristic, complemented
18C4×Dic26C411yescharacteristic, complemented
19C13×C4⋊C8—21no—
20C13×C22⋊C8C2212yes—
21C13×#97—21no—
22#88071C2212yes—
23C22×C4×C13D411yescharacteristic
24C22×C4×C13D411yescharacteristic
25C22×C4×C13C2311yescharacteristic
26C2×C22⋊D13—21no—
27C22×Dic13—22no—
28C2×D52C2×C411yescharacteristic
29C2×C4×D13—21no—
30C2×Dic26C2×C411yescharacteristic
31C2×C8×C13—22no—
32C42×C13C2×C411yescharacteristic
33C42×C13C2×C411yescharacteristic
34C42×C13D411yescharacteristic
35C42×C13D411yescharacteristic
36C22⋊Dic13—21no—
37#6103—21no—
38#6103—21no—
39#6103—21no—
40#6103—21no—
41C4⋊Dic13—24no—
42C4⋊Dic13C2×C411yescharacteristic
43C4⋊Dic13C2×C411yescharacteristic
44#6101—21no—
45#6101—21no—
46#6101—21no—
47#6101—21no—
48C4×Dic13—21no—
49C4×Dic13—42no—
50#1509—131nomaximal, Sylow
51C23×C13C2×D411yescharacteristic
52C22×D13—21no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—22no—
56C2×C4×C13—41no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C2×C4×C13C2×D411yescharacteristic
63C22⋊D13—41no—
64C22⋊D13—41no—
65C2×Dic13—24no—
66C2×Dic13—21no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—42no—
70C2×Dic13—42no—
71D52—41no—
72C4×D13—42no—
73Dic26—41no—
74C8×C13—42no—
75#529—131no—
76#432D1311yescharacteristic, complemented
77C4×C4⋊C4—131no—
78#328—132no—
79#327—132no—
80C22×C13—21no—
81C22×C13—21no—
82C22×C13C2×C22⋊C411yescharacteristic
83C22×C13AGL(1,ℤ/8)11yescharacteristic
84C22×C13#13711yescharacteristic
85C2×D13—41no—
86C2×D13—41no—
87C2×D13—41no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—21no—
93C4×C13#10412yes—
94Dic13—44no—
95Dic13—41no—
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—131no—
106C4×D4—261no—
107#117—261no—
108C2×C4⋊C4—261no—
109C2×C42—261no—
110C2×C42C2×D1311yescharacteristic
111C4⋊C8—21no—
112C22⋊C8C2×D1312yes—
113#97—21no—
114#95—132no—
115C2×C13—21no—
116C2×C13—21no—
117C2×C13#41011yescharacteristic
118C2×C13#41711yescharacteristic
119C2×C13C2×#10411yescharacteristic
120D13—81no—
121C2×Q8—131no—
122C2×D4—131no—
123C2×D4—261no—
124C22×C4—262no—
125C22×C4—261no—
126C22×C4D5211yescharacteristic
127C22×C4D5211yescharacteristic
128C22×C4C22×D1311yescharacteristic
129C2×C8—22no—
130C4⋊C4—131no—
131C4⋊C4—131no—
132C4⋊C4—264no—
133C4⋊C4—261no—
134C4⋊C4—261no—
135C4⋊C4—261no—
136C4⋊C4—261no—
137C22⋊C4—261no—
138C22⋊C4—261no—
139C22⋊C4—261no—
140C22⋊C4—261no—
141C22⋊C4—261no—
142C42—261no—
143C42—522no—
144C42C4×D1311yescharacteristic
145C42C4×D1311yescharacteristic
146C42C22⋊D1311yescharacteristic
147C42C22⋊D1311yescharacteristic
148C13#150911yescharacteristic, complemented, Sylow
149C23—261no—
150C23C2×D5211yescharacteristic
151Q8—521no—
152D4—521no—
153D4—521no—
154D4—521no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—264no—
160C2×C4—261no—
161C2×C4—261no—
162C2×C4—261no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4#610311yescharacteristic
167C2×C4#610311yescharacteristic
168C2×C4#610311yescharacteristic
169C2×C4#610311yescharacteristic
170C2×C4C2×C4×D1311yescharacteristic
171C2×C4C2×C22⋊D1311yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—521no—
176C22—521no—
177C22—521no—
178C22#8816211yescharacteristic
179C22#8816311yescharacteristic
180C22C2×#610311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—524no—
187C4—521no—
188C4—521no—
189C4—521no—
190C4#8806512yes—
191C2—21no—
192C2—21no—
193C2—1041no—
194C2#1171866711yescharacteristic
195C2#1171879411yescharacteristic
196C2C2×#8806511yescharacteristic
subgroupG/H
centerC22C2×#6103
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#432C2
socleC22×C13C2×C22⋊C4
prime radical#88184C22
cosocleC22×C4×C13C23
hypercenter#432D13
hypocenterC13#1509
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C13×#432C2semidirect
3. C4×C4⋊Dic13C2semidirect
5. #11718059C2semidirect
14. #88129C4semidirect
15. C4×D52C4semidirect
17. #88124C4semidirect
18. C4×Dic26C4semidirect
76. #432D13semidirect
148. C13#1509semidirect

Maximal subgroups

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

subgroupindex
#117191842
C13×#4322
C4×C4⋊Dic132
#117180622
#117180592
#150913