Finite Group Databasebeta

← #13124446

Subgroups — #13124446

Order 1664.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88158C211yesmaximal, characteristic, complemented
2C22×#6094C211yesmaximal, characteristic, complemented
3#11719229C212yesmaximal, complemented
4C13×#427C211yesmaximal, characteristic, complemented
5#11718663C212yesmaximal, complemented
6#11718547C214yesmaximal, complemented
7#11718529C212yesmaximal, complemented
8#11718526C212yesmaximal, complemented
9C2×#6127C2212yes—
10C22×C4×D13C2211yescharacteristic
11C22×C8×C13C2211yescharacteristic
12C13×#117C2212yes—
13C22×#1055C2211yescharacteristic
14C2×Dic52C2211yescharacteristic, complemented
15#88158—24no—
16C2×D104C2211yescharacteristic, complemented
17C2×#6095C2212yescomplemented
18C2×#6094—24no—
19C2×#6094C2212yes—
20C2×#6094C2212yes—
21#88151C2214yes—
22#88149C2214yes—
23#88140—22no—
24#88136—22no—
25C4×D52—24no—
26C13×#107C2212yescomplemented
27C13×#106C2212yescomplemented
28#88050C2214yescomplemented
29#88049C2214yescomplemented
30C23×D13D411yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C2×C22⋊D13—22no—
33C22×Dic13D411yescharacteristic
34#6127—24no—
35#6127—24no—
36C2×D52—24no—
37C2×D52C2312yes—
38C2×C4×D13—22no—
39C2×C4×D13—22no—
40C2×C4×D13—22no—
41C2×C4×D13D412yes—
42C2×C4×D13C2312yes—
43C2×Dic26C2312yes—
44C2×C8×C13D414yescomplemented
45C2×C8×C13C2311yescharacteristic
46C2×C8×C13C2311yescharacteristic
47C13×C4⋊C4C2314yes—
48C13×C22⋊C4—22no—
49C42×C13—22no—
50#6103—24no—
51#6103—24no—
52C4⋊Dic13—24no—
53C2×#1055—22no—
54C2×#1055C2312yes—
55Dic52—22no—
56D104—22no—
57#6095—24no—
58#6094—24no—
59#6094—24no—
60#3054—131nomaximal, Sylow
61C23×C13C2×D411yescharacteristic
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—42no—
65C22×D13C2×D412yes—
66C2×C4×C13—24no—
67C2×C4×C13C2×D411yescharacteristic
68C2×C4×C13C2×D412yes—
69C2×C4×C13#4112yes—
70C2×C4×C13C2411yescharacteristic
71C22⋊D13—44no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13C2×D412yes—
75D52—22no—
76D52—22no—
77D52—48no—
78C4×D13—24no—
79C4×D13—22no—
80C4×D13—22no—
81C4×D13—44no—
82Dic26—22no—
83Dic26—22no—
84C8×C13C2×D412yes—
85C8×C13C2×D412yes—
86#1055—22no—
87C2×#135—131no—
88C22×M16—131no—
89#525—132no—
90#470—132no—
91#469—132no—
92#468—134no—
93#427D1311yescharacteristic, complemented
94#416—132no—
95C22×C13—22no—
96C22×C13#12112yes—
97C22×C13C22×D411yescharacteristic
98C2×D13—22no—
99C2×D13—24no—
100C2×D13—44no—
101C2×D13—42no—
102C2×D13—44no—
103C4×C13—44no—
104C4×C13#12112yes—
105C4×C13C22×D411yescharacteristic
106C4×C13C2×#4111yescharacteristic
107Dic13—22no—
108Dic13—42no—
109C2×#41—132no—
110C23×C4—131no—
111#135—264no—
112C2×Q16—131no—
113C2×SD16—132no—
114C2×D8—131no—
115C2×M16—132no—
116C2×M16—132no—
117C2×M16—264no—
118C22×C8—131no—
119C22×C8C2×D1311yescharacteristic
120#123—262no—
121C22⋊Q8—134no—
122#121—134no—
123#120—262no—
124C4×D4—264no—
125#117C2×D1312yes—
126#107C2×D1312yescomplemented
127#106C2×D1312yescomplemented
128#103—134no—
129#102—134no—
130C2×C13—22no—
131C2×C13C2×#12111yescharacteristic
132C2×C13#57512yes—
133D13—42no—
134D13—82no—
135C24—131no—
136#41—264no—
137#41—264no—
138C2×Q8—132no—
139C2×D4—132no—
140C2×D4—264no—
141C2×D4—262no—
142C22×C4—131no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—262no—
146C22×C4—262no—
147C22×C4—262no—
148C22×C4C22×D1311yescharacteristic
149Q16—262no—
150SD16—264no—
151D8—262no—
152M16—264no—
153M16—264no—
154C2×C8—132no—
155C2×C8—262no—
156C2×C8D5214yescomplemented
157C2×C8C22×D1311yescharacteristic
158C2×C8C22×D1311yescharacteristic
159C4⋊C4—264no—
160C4⋊C4C22×D1314yes—
161C22⋊C4—22no—
162C22⋊C4—264no—
163C22⋊C4—264no—
164C42—22no—
165C13#305411yescharacteristic, complemented, Sylow
166C23—132no—
167C23—262no—
168C23—262no—
169C23—522no—
170C23D4×D1311yescharacteristic
171Q8—262no—
172Q8—262no—
173D4—262no—
174D4—262no—
175D4—528no—
176D4—524no—
177C2×C4—24no—
178C2×C4—132no—
179C2×C4—262no—
180C2×C4—264no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—524no—
185C2×C4C2×D5212yes—
186C2×C4D4×D1311yescharacteristic
187C2×C4#613112yes—
188C2×C4C23×D1311yescharacteristic
189C8—262no—
190C8C2×D5212yes—
191C8C2×D5212yes—
192C22—22no—
193C22—262no—
194C22—264no—
195C22—524no—
196C22—522no—
197C22—524no—
198C22#8814912yes—
199C22C2×D4×D1311yescharacteristic
200C4—44no—
201C4—262no—
202C4—522no—
203C4#8814912yes—
204C4C22×D5211yescharacteristic
205C4C2×#613111yescharacteristic
206C2—22no—
207C2—522no—
208C2—1042no—
209C2C2×#8814911yescharacteristic
210C2#1171947312yes—
subgroupG/H
centerC2×C4D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#427C2
socleC22×C13C22×D4
hypercenter#427D13
hypocenterC13#3054
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. C2×#88158C2semidirect
2. C22×#6094C2semidirect
3. #11719229C2semidirect
4. C13×#427C2semidirect
5. #11718663C2semidirect
6. #11718547C2semidirect
7. #11718529C2semidirect
8. #11718526C2semidirect
14. C2×Dic52C22semidirect
16. C2×D104C22semidirect
17. C2×#6095C22semidirect
26. C13×#107C22semidirect
27. C13×#106C22semidirect
28. #88050C22semidirect
29. #88049C22semidirect
44. C2×C8×C13D4semidirect
93. #427D13semidirect
126. #107C2×D13semidirect
127. #106C2×D13semidirect
156. C2×C8D52semidirect
165. C13#3054semidirect

Maximal subgroups

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

subgroupindex
C2×#881582
C22×#60942
#117192292
C13×#4272
#117186632
#117185472
#117185292
#117185262
#305413