Finite Group Databasebeta

← C22×C3×#3958 #14478198

Subgroups — C22×C3×#3958 #14478198

Order 1920.

880 conjugacy classes of subgroups; only the 298 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 298 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
1C22×C3×C5×D8C211yesmaximal, characteristic, complemented
2C22×C3×D40C211yesmaximal, characteristic, complemented
3C2×C3×#3958C2112yesmaximal, direct product factor
4C22×C3×#672C211yesmaximal, characteristic, complemented
5C22×#3958C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×D4—21no—
7C22×C3×D20—21no—
8C2×C3×C5×D8—23no—
9C2×C3×C5×D8C2216yescomplemented
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×D40—23no—
12C2×C3×D40C2216yescomplemented
13C3×#3958C22116yesdirect product factor
14C2×C3×#672C2216yescomplemented
15C22×C3×D16—51nomaximal, Hall
16C22×C5×D8C2×C311yescharacteristic, complemented
17C22×D40C2×C311yescharacteristic, complemented
18C2×#3958C2×C3112yesdirect product factor
19C22×#672C2×C311yescharacteristic, complemented
20C24×C3×C5—41no—
21C23×C3×D5—41no—
22C2×C3×C5×D4—26no—
23C2×C3×C5×D4—43no—
24C22×C3×C4×C5D411yescharacteristic
25C2×C3×D20—26no—
26C2×C3×D20—43no—
27C3×C5×D8—26no—
28C3×C5×D8C2314yescomplemented
29C2×C3×C5×C8D413yes—
30C2×C3×C5×C8C2313yes—
31C3×D40—26no—
32C3×D40C2314yescomplemented
33C3×#672C2314yescomplemented
34C22×C3×D8—51no—
35C22×C3×D8D511yescharacteristic, complemented
36C2×C3×D16—512no—
37C22×C3×C16—51no—
38C22×C5×D4—21no—
39C22×D20—21no—
40C2×C5×D8—23no—
41C2×C5×D8C22×C316yescomplemented
42C22×C5×C8C22×C311yescharacteristic
43C2×D40—23no—
44C2×D40C22×C316yescomplemented
45#3958C22×C3116yesdirect product factor
46C2×#672C22×C316yescomplemented
47C22×D16—51noSylow
48C23×C3×C5—46no—
49C23×C3×C5—84no—
50C23×C3×C5D811yescharacteristic
51C22×C3×D5—46no—
52C22×C3×D5—84no—
53C3×C5×D4—24no—
54C3×C5×D4—46no—
55C2×C3×C4×C5D813yes—
56C2×C3×C4×C5C2×D413yes—
57C3×D20—24no—
58C3×D20—46no—
59C3×C5×C8C2×D413yes—
60C3×C5×C8C2411yescharacteristic
61C22×C3×D4—21no—
62C22×C3×D4—101no—
63C2×C3×D8—23no—
64C2×C3×D8—56no—
65C2×C3×D8—103no—
66C2×C3×D8C2×D516yescomplemented
67C22×C3×C8C2×D511yescharacteristic
68C3×D16—516no—
69C2×C3×C16—56no—
70C24×C5—41no—
71C23×D5—41no—
72C2×C5×D4—26no—
73C2×C5×D4—43no—
74C22×C4×C5C3×D411yescharacteristic
75C2×D20—26no—
76C2×D20—43no—
77C5×D8—26no—
78C5×D8C23×C314yescomplemented
79C2×C5×C8C3×D413yes—
80C2×C5×C8C23×C313yes—
81D40—26no—
82D40C23×C314yescomplemented
83#672C23×C314yescomplemented
84C22×D8—51no—
85C22×D8C3×D511yescharacteristic, complemented
86C2×D16—512no—
87C22×C16—51no—
88C22×C3×C5—44no—
89C22×C3×C5—812no—
90C22×C3×C5D1614yescomplemented
91C22×C3×C5C2×D813yes—
92C2×C3×D5—44no—
93C2×C3×D5—812no—
94C3×C4×C5C2×D813yes—
95C3×C4×C5C22×D411yescharacteristic
96C24×C3—41no—
97C24×C3—201no—
98C2×C3×D4—26no—
99C2×C3×D4—43no—
100C2×C3×D4—106no—
101C2×C3×D4—203no—
102C22×C3×C4C22⋊D511yescharacteristic
103C3×D8—26no—
104C3×D8—54no—
105C3×D8—106no—
106C3×D8C22×D514yescomplemented
107C2×C3×C8C22⋊D513yes—
108C2×C3×C8C22×D513yes—
109C3×C16—54no—
110C23×C5—46no—
111C23×C5—84no—
112C23×C5C3×D811yescharacteristic
113C22×D5—46no—
114C22×D5—84no—
115C5×D4—24no—
116C5×D4—46no—
117C2×C4×C5C3×D813yes—
118C2×C4×C5C2×C3×D413yes—
119D20—24no—
120D20—46no—
121C5×C8C2×C3×D413yes—
122C5×C8C24×C311yescharacteristic
123C22×D4—21no—
124C22×D4—101no—
125C2×D8—23no—
126C2×D8—56no—
127C2×D8—103no—
128C2×D8C2×C3×D516yescomplemented
129C22×C8C2×C3×D511yescharacteristic
130D16—516no—
131C2×C16—56no—
132C2×C3×C5—84no—
133C2×C3×C5C2×D1616yescomplemented
134C2×C3×C5C22×D811yescharacteristic
135C3×D5—84no—
136C23×C3—46no—
137C23×C3—84no—
138C23×C3—206no—
139C23×C3—404no—
140C23×C3#68611yescharacteristic
141C3×D4—24no—
142C3×D4—46no—
143C3×D4—104no—
144C3×D4—206no—
145C2×C3×C4#68613yes—
146C2×C3×C4C2×C22⋊D513yes—
147C3×C8C2×C22⋊D513yes—
148C3×C8C23×D511yescharacteristic
149C22×C5—44no—
150C22×C5—812no—
151C22×C5C3×D1614yescomplemented
152C22×C5C2×C3×D813yes—
153C2×D5—44no—
154C2×D5—812no—
155C4×C5C2×C3×D813yes—
156C4×C5C22×C3×D411yescharacteristic
157C24—41no—
158C24—201no—
159C2×D4—26no—
160C2×D4—43no—
161C2×D4—106no—
162C2×D4—203no—
163C22×C4C3×C22⋊D511yescharacteristic
164D8—26no—
165D8—54no—
166D8—106no—
167D8C22×C3×D514yescomplemented
168C2×C8C3×C22⋊D513yes—
169C2×C8C22×C3×D513yes—
170C16—54no—
171C3×C5C22×D1611yescharacteristic, complemented, Hall
172C22×C3—44no—
173C22×C3—812no—
174C22×C3—204no—
175C22×C3—4012no—
176C22×C3#395814yesdirect product factor
177C22×C3C2×#68613yes—
178C3×C4C2×#68613yes—
179C3×C4C22×C22⋊D511yescharacteristic
180C2×C5—84no—
181C2×C5C2×C3×D1616yescomplemented
182C2×C5C22×C3×D811yescharacteristic
183D5—84no—
184C23—46no—
185C23—84no—
186C23—206no—
187C23—404no—
188C23C3×#68611yescharacteristic
189D4—24no—
190D4—46no—
191D4—104no—
192D4—206no—
193C2×C4C3×#68613yes—
194C2×C4C2×C3×C22⋊D513yes—
195C8C2×C3×C22⋊D513yes—
196C8C23×C3×D511yescharacteristic
197C2×C3—84no—
198C2×C3—404no—
199C2×C3C2×#395816yesdirect product factor
200C2×C3C22×#68611yescharacteristic
201C5C22×C3×D1611yescharacteristic, complemented, Sylow
202C22—44no—
203C22—812no—
204C22—204no—
205C22—4012no—
206C22C3×#395814yesdirect product factor
207C22C2×C3×#68613yes—
208C4C2×C3×#68613yes—
209C4C22×C3×C22⋊D511yescharacteristic
210C3C22×#395811yescharacteristic, direct product factor, Sylow
211C2—84no—
212C2—404no—
213C2C2×C3×#395816yesdirect product factor
214C2C22×C3×#68611yescharacteristic
subgroupG/H
centerC23×C3#686
commutator, cosocleC5×C8C24×C3
FrattiniC8C23×C3×D5
FittingC22×C3×C5×D8C2
socleC23×C3×C5D8
hypercenterC22×C3×D8D5
hypocenterC5C22×C3×D16
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C22×C3×D8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×D8C2semidirect
2. C22×C3×D40C2semidirect
3. C2×C3×#3958C2direct (N × H)
4. C22×C3×#672C2semidirect
5. C22×#3958C3direct (N × H)
9. C2×C3×C5×D8C22semidirect
12. C2×C3×D40C22semidirect
13. C3×#3958C22direct (N × H)
14. C2×C3×#672C22semidirect
16. C22×C5×D8C2×C3semidirect
17. C22×D40C2×C3semidirect
18. C2×#3958C2×C3direct (N × H)
19. C22×#672C2×C3semidirect
28. C3×C5×D8C23semidirect
32. C3×D40C23semidirect
33. C3×#672C23semidirect
35. C22×C3×D8D5semidirect
41. C2×C5×D8C22×C3semidirect
44. C2×D40C22×C3semidirect
45. #3958C22×C3direct (N × H)
46. C2×#672C22×C3semidirect
66. C2×C3×D8C2×D5semidirect
78. C5×D8C23×C3semidirect
82. D40C23×C3semidirect
83. #672C23×C3semidirect
85. C22×D8C3×D5semidirect
90. C22×C3×C5D16semidirect
106. C3×D8C22×D5semidirect
128. C2×D8C2×C3×D5semidirect
133. C2×C3×C5C2×D16semidirect
151. C22×C5C3×D16semidirect
167. D8C22×C3×D5semidirect
171. C3×C5C22×D16semidirect
176. C22×C3#3958direct (N × H)
181. C2×C5C2×C3×D16semidirect
199. C2×C3C2×#3958direct (N × H)
201. C5C22×C3×D16semidirect
206. C22C3×#3958direct (N × H)
210. C3C22×#3958direct (N × H)
213. C2C2×C3×#3958direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×D82
C22×C3×D402
C2×C3×#39582
C22×C3×#6722
C22×#39583
C22×C3×D165