Finite Group Databasebeta

← #13113173

Subgroups — #13113173

Order 1664.

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

normal subgroups only

This group has 316 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
1C2×#88147C211yesmaximal, characteristic
2#11718387C212yesmaximal, complemented
3C13×#324C211yesmaximal, characteristic, complemented
4#11718120C211yesmaximal, characteristic, complemented
5#11718060C212yesmaximal, complemented
6C22×D52C411yescharacteristic
7C22×C4×D13C411yescharacteristic
8C22×C4×D13C2211yescharacteristic
9C2×C13×C4⋊C4C2211yescharacteristic
10C2×#6103C411yescharacteristic
11C2×#6103C2211yescharacteristic
12C2×C4×Dic13C411yescharacteristic
13C2×#6094—22no—
14#88147—22no—
15#88147—22no—
16C13×C22⋊C8C2212yes—
17C22⋊#1055C2212yes—
18#88060—22no—
19C23×D13C2×C411yescharacteristic
20C23×D13C2×C411yescharacteristic
21C22×C4×C13C2×C411yescharacteristic
22C22×C4×C13C2×C411yescharacteristic
23C22×C4×C13C2311yescharacteristic
24C22×Dic13C2×C411yescharacteristic
25C22×Dic13C2×C411yescharacteristic
26C2×D52—22no—
27C2×D52—22no—
28C2×D52—22no—
29C2×C4×D13—21no—
30C2×C4×D13—21no—
31C2×C4×D13—42no—
32C2×C4×D13—42no—
33C2×C4×D13D412yes—
34C2×C4×D13D412yes—
35C2×C8×C13—22no—
36C13×C4⋊C4—22no—
37#6103—22no—
38#6103—22no—
39C4×Dic13—21no—
40C4×Dic13—21no—
41C2×#1055—22no—
42#6094—44no—
43#1465—131nomaximal, Sylow
44C23×C13C22×C411yescharacteristic
45C22×D13—21no—
46C22×D13—21no—
47C22×D13—21no—
48C22×D13—21no—
49C22×D13—41no—
50C22×D13—41no—
51C22×D13—41no—
52C22×D13—41no—
53C22×D13C22⋊C412yes—
54C22×D13M1612yescomplemented
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13M1612yescomplemented
61C2×C4×C13C2×D412yes—
62C2×Dic13—22no—
63C2×Dic13—21no—
64C2×Dic13—41no—
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C22⋊C411yescharacteristic
67D52—28no—
68C4×D13—24no—
69C4×D13—42no—
70C4×D13—42no—
71C4×D13—42no—
72C8×C13—42no—
73#1055—42no—
74C2×C4×D4—131no—
75#407—132no—
76#324—131no—
77#324D1311yescharacteristic, complemented
78#323—132no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13C2×C22⋊C411yescharacteristic
82C22×C13C2×M1611yescharacteristic
83C22×C13C2×M1611yescharacteristic
84C2×D13—22no—
85C2×D13—22no—
86C2×D13—22no—
87C2×D13—22no—
88C2×D13—42no—
89C2×D13—42no—
90C2×D13—42no—
91C2×D13—41no—
92C2×D13—41no—
93C2×D13—42no—
94C4×C13—22no—
95C4×C13—22no—
96C4×C13—41no—
97Dic13—21no—
98Dic13—41no—
99Dic13#9912yes—
100C22×D4—131no—
101C23×C4—131no—
102C23×C4—131no—
103C2×M16—262no—
104C4×D4—262no—
105C4×D4—262no—
106C2×C4⋊C4C2×D1311yescharacteristic
107C2×C22⋊C4—131no—
108C2×C22⋊C4—131no—
109C2×C42—131no—
110C22⋊C8—132no—
111C22⋊C8—262no—
112C22⋊C8C2×D1312yes—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13#40711yescharacteristic
116C2×C13C2×#9911yescharacteristic
117C2×C13#41311yescharacteristic
118D13—42no—
119D13—42no—
120C24—131no—
121C24—131no—
122C2×D4—262no—
123C2×D4—262no—
124C2×D4—262no—
125C22×C4—131no—
126C22×C4—132no—
127C22×C4—132no—
128C22×C4—131no—
129C22×C4—261no—
130C22×C4—261no—
131C22×C4—522no—
132C22×C4—522no—
133C22×C4C4×D1311yescharacteristic
134C22×C4C4×D1311yescharacteristic
135C22×C4C22×D1311yescharacteristic
136M16—524no—
137C2×C8—22no—
138C2×C8—262no—
139C4⋊C4—22no—
140C22⋊C4—262no—
141C22⋊C4—262no—
142C42—261no—
143C42—261no—
144C13#146511yescharacteristic, complemented, Sylow
145C23—132no—
146C23—132no—
147C23—261no—
148C23—261no—
149C23—261no—
150C23—261no—
151C23—521no—
152C23—521no—
153C23—521no—
154C23—521no—
155C23C2×C4×D1311yescharacteristic
156D4—268no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—264no—
165C2×C4—262no—
166C2×C4—261no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4—521no—
171C2×C4#609412yescomplemented
172C2×C4D4×D1312yes—
173C8—42no—
174C8—522no—
175C22—21no—
176C22—21no—
177C22—262no—
178C22—262no—
179C22—262no—
180C22—262no—
181C22—522no—
182C22—522no—
183C22—522no—
184C22—522no—
185C22—521no—
186C22—521no—
187C22C22⋊C4×D1311yescharacteristic
188C22C2×#609411yescharacteristic
189C22M16×D1311yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—132no—
194C4—261no—
195C4—521no—
196C2—21no—
197C2—21no—
198C2—522no—
199C2—522no—
200C2#1171838711yescharacteristic
201C2D13×#9911yescharacteristic
202C2#1171841211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC23×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#324C2
socleC22×C13C2×C22⋊C4
prime radicalC22×D52C4
cosocleC22×C4×C13C23
hypercenter#324D13
hypocenterC13#1465
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #11718387C2semidirect
3. C13×#324C2semidirect
4. #11718120C2semidirect
5. #11718060C2semidirect
54. C22×D13M16semidirect
60. C2×C4×C13M16semidirect
77. #324D13semidirect
144. C13#1465semidirect
171. C2×C4#6094semidirect

Maximal subgroups

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

subgroupindex
C2×#881472
#117183872
C13×#3242
#117181202
#117180602
#146513