Finite Group Databasebeta

← #13115376

Subgroups — #13115376

Order 1664.

380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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#11719509C211yesmaximal, characteristic
2#11719503C211yesmaximal, characteristic, complemented
3C2×C13×#99C211yesmaximal, characteristic, complemented
4C2×#88046C212yesmaximal, complemented
5#11718118C212yesmaximal, complemented
6C22×D4×C13C2211yescharacteristic
7C22×C22⋊D13C2211yescharacteristic
8C2×C13×C22⋊C4C2212yes—
9#88207—21no—
10C2×C22⋊Dic13—21no—
11C2×C22⋊Dic13C2211yescharacteristic
12C2×C22⋊Dic13C2212yes—
13#88193—22no—
14#88191C412yescomplemented
15#88189C412yescomplemented
16D4×Dic13—24no—
17#88183—21no—
18#88180—21no—
19C13×#99—22no—
20#88046—24no—
21C24×C13D411yescharacteristic
22C24×C13C2311yescharacteristic
23C23×D13C2×C411yescharacteristic, complemented
24C2×D4×C13—22no—
25C2×D4×C13—22no—
26C2×D4×C13C2×C412yes—
27C2×D4×C13D412yes—
28C22×C4×C13—22no—
29C22×C4×C13D411yescharacteristic
30C2×C22⋊D13—21no—
31C2×C22⋊D13—21no—
32C2×C22⋊D13—22no—
33C2×C22⋊D13—22no—
34C2×C22⋊D13—22no—
35C22×Dic13—22no—
36C22×Dic13—22no—
37C22×Dic13—21no—
38C22×Dic13C2×C411yescharacteristic, complemented
39C13×C22⋊C4—22no—
40C13×C22⋊C4—22no—
41C22⋊Dic13—22no—
42C22⋊Dic13—22no—
43C22⋊Dic13—22no—
44C22⋊Dic13—21no—
45C22⋊Dic13C2×C412yescomplemented
46C22⋊Dic13D414yescomplemented
47#6103—22no—
48C4⋊Dic13—22no—
49#6101—22no—
50C4×Dic13—22no—
51#1913—131nomaximal, Sylow
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—81no—
55C23×C13—81no—
56C23×C13C22⋊C412yes—
57C23×C13C22×C411yescharacteristic
58C23×C13C2×D411yescharacteristic
59C23×C13C2×D411yescharacteristic
60C23×C13C2×D412yes—
61C23×C13#4112yes—
62C22×D13—21no—
63C22×D13—22no—
64C22×D13—81no—
65D4×C13—24no—
66D4×C13—24no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—42no—
70C2×C4×C13—82no—
71C2×C4×C13C22⋊C412yes—
72C22⋊D13—41no—
73C22⋊D13—42no—
74C22⋊D13—41no—
75C22⋊D13—82no—
76C2×Dic13—21no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—24no—
80C2×Dic13—82no—
81C2×Dic13—82no—
82C2×Dic13—81no—
83#534—131no—
84#518—131no—
85C2×#99—132no—
86C2×#99D1311yescharacteristic, complemented
87#342—132no—
88C22×C13—22no—
89C22×C13—42no—
90C22×C13—41no—
91C22×C13—42no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13—42no—
95C22×C13—42no—
96C22×C13—81no—
97C22×C13C2×C22⋊C411yescharacteristic
98C22×C13C4×D412yes—
99C22×C13#12011yescharacteristic
100C22×C13#12112yes—
101C22×C13#12311yescharacteristic
102C2×D13—42no—
103C2×D13—41no—
104C2×D13—82no—
105C4×C13—22no—
106C4×C13—82no—
107Dic13—44no—
108Dic13—42no—
109Dic13—41no—
110C22×D4—131no—
111C22×D4C2×D1311yescharacteristic
112#123—132no—
113#123—261no—
114#121—262no—
115#120—132no—
116#120—261no—
117C4×D4—264no—
118#117—261no—
119C2×C22⋊C4—132no—
120C2×C22⋊C4—131no—
121C2×C22⋊C4—261no—
122C2×C22⋊C4C2×D1312yes—
123#99—22no—
124#99—264no—
125C2×C13—21no—
126C2×C13—21no—
127C2×C13—22no—
128C2×C13—22no—
129C2×C13—21no—
130C2×C13—42no—
131C2×C13#38611yescharacteristic
132D13—81no—
133C24—131no—
134C24D5211yescharacteristic
135C24C22×D1311yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—261no—
139C2×D4—262no—
140C2×D4—262no—
141C2×D4—261no—
142C2×D4—262no—
143C2×D4C4×D1312yes—
144C2×D4C22⋊D1312yes—
145C22×C4—22no—
146C22×C4—131no—
147C22×C4—262no—
148C22×C4—262no—
149C22×C4—261no—
150C22×C4D5211yescharacteristic
151C4⋊C4—262no—
152C4⋊C4—262no—
153C22⋊C4—22no—
154C22⋊C4—22no—
155C22⋊C4—132no—
156C22⋊C4—134no—
157C22⋊C4—262no—
158C22⋊C4—262no—
159C22⋊C4—262no—
160C22⋊C4—261no—
161C22⋊C4—262no—
162C42—262no—
163C13#191311yescharacteristic, complemented, Sylow
164C23—21no—
165C23—21no—
166C23—81no—
167C23—81no—
168C23—261no—
169C23—262no—
170C23—1041no—
171C23#610312yes—
172C23C2×C4×D1311yescharacteristic
173C23C2×D5211yescharacteristic
174C23D4×D1312yes—
175C23#612912yes—
176C23C2×C22⋊D1311yescharacteristic
177D4—24no—
178D4—24no—
179D4—521no—
180D4—521no—
181D4—522no—
182D4—1042no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—82no—
187C2×C4—262no—
188C2×C4—264no—
189C2×C4—262no—
190C2×C4—261no—
191C2×C4—1042no—
192C2×C4—1042no—
193C2×C4—1041no—
194C2×C4#610312yes—
195C22—22no—
196C22—42no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—522no—
205C22—521no—
206C22—1042no—
207C22#8813512yes—
208C22#8813611yescharacteristic
209C22#8814011yescharacteristic
210C22C2×#610311yescharacteristic
211C22#8819312yes—
212C4—22no—
213C4—82no—
214C4—524no—
215C4—522no—
216C4—521no—
217C2—22no—
218C2—21no—
219C2—21no—
220C2—21no—
221C2—22no—
222C2—42no—
223C2—1041no—
224C2#1171861911yescharacteristic
subgroupG/H
centerC2#11718619
commutatorC23×C13C22×C4
FrattiniC24C22×D13
FittingC2×C13×#99C2
socleC2×C13#386
prime radical#11719509C2
cosocleC24×C13C23
hypercenterC2×#99D13
hypocenterC13#1913
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #11719503C2semidirect
3. C2×C13×#99C2semidirect
4. C2×#88046C2semidirect
5. #11718118C2semidirect
14. #88191C4semidirect
15. #88189C4semidirect
23. C23×D13C2×C4semidirect
38. C22×Dic13C2×C4semidirect
45. C22⋊Dic13C2×C4semidirect
46. C22⋊Dic13D4semidirect
86. C2×#99D13semidirect
163. C13#1913semidirect

Maximal subgroups

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

subgroupindex
#117195092
#117195032
C2×C13×#992
C2×#880462
#117181182
#191313