Finite Group Databasebeta

← C22×D4×D13⋊C3 #72276173

Subgroups — C22×D4×D13⋊C3 #72276173

Order 2496.

2724 conjugacy classes of subgroups; only the 928 normal subgroups are shown.

normal subgroups only

This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 928 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
1C24×D13⋊C3C212yesmaximal, complemented
2C22×D4×C13⋊C3C211yesmaximal, characteristic, complemented
3C22×(C22⋊D13)⋊C3C212yesmaximal, complemented
4C2×D4×D13⋊C3C2124yesmaximal, direct product factor
5C22×C4⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
6C22×C4×D13⋊C3C211yesmaximal, characteristic, complemented
7C22×D4×D13C311yesmaximal, characteristic, complemented, Hall
8C24×C13⋊C3C2212yescomplemented
9C23×D13⋊C3—216no—
10C23×D13⋊C3C2211yescharacteristic
11C23×D13⋊C3C22124yescomplemented
12C23×D13⋊C3C2212yescomplemented
13C2×D4×C13⋊C3C22112yescomplemented
14C22×C4×C13⋊C3C2211yescharacteristic, complemented
15C2×(C22⋊D13)⋊C3C22124yescomplemented
16C22×Dic13⋊C3C2211yescharacteristic, complemented
17D4×D13⋊C3C22164yesdirect product factor
18C2×C4⋊(D13⋊C3)C22112yescomplemented
19C2×C4×D13⋊C3C22112yescomplemented
20C24×D13C2×C312yescomplemented
21C22×D4×C13C2×C311yescharacteristic, complemented
22C22×C22⋊D13C2×C312yescomplemented
23C2×D4×D13C2×C3124yescomplemented
24C22×D52C2×C311yescharacteristic, complemented
25C22×C4×D13C2×C311yescharacteristic, complemented
26C23×C13⋊C3—28no—
27C23×C13⋊C3C2311yescharacteristic
28C23×C13⋊C3C23112yescomplemented
29C22×D13⋊C3—28no—
30C22×D13⋊C3—296no—
31C22×D13⋊C3D418yesdirect product factor
32C22×D13⋊C3C2316yes—
33C22×D13⋊C3C23132yescomplemented
34C22×D13⋊C3C23112yescomplemented
35D4×C13⋊C3C23116yescomplemented
36C2×C4×C13⋊C3C2316yescomplemented
37(C22⋊D13)⋊C3C23132yescomplemented
38C2×Dic13⋊C3C2316yescomplemented
39C4⋊(D13⋊C3)C23116yescomplemented
40C4×D13⋊C3C23116yescomplemented
41C24×C13C22×C312yescomplemented
42C23×D13—216no—
43C23×D13C22×C311yescharacteristic
44C23×D13C22×C3124yescomplemented
45C23×D13C22×C312yescomplemented
46C2×D4×C13C22×C3112yescomplemented
47C22×C4×C13C22×C311yescharacteristic, complemented
48C2×C22⋊D13C22×C3124yescomplemented
49C22×Dic13C22×C311yescharacteristic, complemented
50D4×D13C22×C3164yescomplemented
51C2×D52C22×C3112yescomplemented
52C2×C4×D13C22×C3112yescomplemented
53C23×C3×D4—131nomaximal, Hall
54C22×C13⋊C3—224no—
55C22×C13⋊C3C2×D414yescomplemented
56C22×C13⋊C3C2413yes—
57C22×C13⋊C3C2418yescomplemented
58C2×D13⋊C3—224no—
59C2×D13⋊C3—264no—
60C2×D13⋊C3C2×D4124yesdirect product factor
61C2×D13⋊C3C2414yes—
62C2×D13⋊C3C2418yescomplemented
63C4×C13⋊C3C2414yescomplemented
64Dic13⋊C3C2414yescomplemented
65C23×C13—28no—
66C23×C13C23×C311yescharacteristic
67C23×C13C23×C3112yescomplemented
68C22×D13—28no—
69C22×D13—296no—
70C22×D13C3×D418yescomplemented
71C22×D13C23×C316yes—
72C22×D13C23×C3132yescomplemented
73C22×D13C23×C3112yescomplemented
74D4×C13C23×C3116yescomplemented
75C2×C4×C13C23×C316yescomplemented
76C22⋊D13C23×C3132yescomplemented
77C2×Dic13C23×C316yescomplemented
78D52C23×C3116yescomplemented
79C4×D13C23×C3116yescomplemented
80C25×C3—132no—
81C22×C3×D4—131no—
82C22×C3×D4—1324no—
83C22×C3×D4—132no—
84C22×C3×D4—131no—
85C23×C3×C4—131no—
86C2×C13⋊C3—28no—
87C2×C13⋊C3C22×D416yescomplemented
88C2×C13⋊C3C2511yescharacteristic
89D13⋊C3—28no—
90D13⋊C3C22×D418yesdirect product factor
91C23×D4—131noSylow
92C22×C13—224no—
93C22×C13C2×C3×D414yescomplemented
94C22×C13C24×C313yes—
95C22×C13C24×C318yescomplemented
96C2×D13—224no—
97C2×D13—264no—
98C2×D13C2×C3×D4124yescomplemented
99C2×D13C24×C314yes—
100C2×D13C24×C318yescomplemented
101C4×C13C24×C314yescomplemented
102Dic13C24×C314yescomplemented
103C24×C3—131no—
104C24×C3—132no—
105C24×C3—1324no—
106C24×C3—132no—
107C24×C3—2616no—
108C2×C3×D4—1312no—
109C2×C3×D4—1364no—
110C2×C3×D4—1324no—
111C2×C3×D4—1312no—
112C22×C3×C4—1312no—
113C22×C3×C4—131no—
114C22×C3×C4—131no—
115C13⋊C3C23×D411yescharacteristic, complemented, Hall
116C25—132no—
117C22×D4—132no—
118C22×D4—1324no—
119C22×D4—131no—
120C22×D4D13⋊C311yescharacteristic, direct product factor
121C23×C4—131no—
122C2×C13—28no—
123C2×C13C22×C3×D416yescomplemented
124C2×C13C25×C311yescharacteristic
125D13—28no—
126D13C22×C3×D418yescomplemented
127C23×C3—138no—
128C23×C3—136no—
129C23×C3—1312no—
130C23×C3—1332no—
131C23×C3—131no—
132C23×C3—1312no—
133C23×C3—268no—
134C23×C3—2696no—
135C23×C3—268no—
136C3×D4—1316no—
137C3×D4—1332no—
138C3×D4—1316no—
139C2×C3×C4—1316no—
140C2×C3×C4—136no—
141C2×C3×C4—136no—
142C24—131no—
143C24—132no—
144C24—1324no—
145C24—2616no—
146C24C2×D13⋊C312yescomplemented
147C2×D4—1324no—
148C2×D4—1364no—
149C2×D4—1312no—
150C2×D4C2×D13⋊C3112yesdirect product factor
151C22×C4—131no—
152C22×C4—1312no—
153C22×C4C2×D13⋊C311yescharacteristic, complemented
154C13C23×C3×D411yescharacteristic, complemented, Sylow
155C22×C3—134no—
156C22×C3—1324no—
157C22×C3—138no—
158C22×C3—134no—
159C22×C3—133no—
160C22×C3—138no—
161C22×C3—2624no—
162C22×C3—2664no—
163C22×C3—2624no—
164C3×C4—134no—
165C3×C4—134no—
166C23—28no—
167C23—138no—
168C23—136no—
169C23—1312no—
170C23—1332no—
171C23—2696no—
172C23—268no—
173C23C22×D13⋊C311yescharacteristic
174C23C22×D13⋊C3112yescomplemented
175D4—1332no—
176D4—1316no—
177D4C22×D13⋊C3116yesdirect product factor
178C2×C4—136no—
179C2×C4—1316no—
180C2×C4C22×D13⋊C316yescomplemented
181C2×C3—138no—
182C2×C3—136no—
183C2×C3—131no—
184C2×C3—268no—
185C2×C3—268no—
186C22—224no—
187C22—1324no—
188C22—134no—
189C22—138no—
190C22—2664no—
191C22—2624no—
192C22D4×D13⋊C314yesdirect product factor
193C22C23×D13⋊C313yes—
194C22C23×D13⋊C318yescomplemented
195C4—134no—
196C4C23×D13⋊C314yescomplemented
197C3—131noSylow
198C2—28no—
199C2—138no—
200C2—268no—
201C2C2×D4×D13⋊C316yesdirect product factor
202C2C24×D13⋊C311yescharacteristic
subgroupG/H
centerC23C22×D13⋊C3
commutator, cosocleC2×C13C25×C3
FrattiniC2C24×D13⋊C3
FittingC22×D4×C13C2×C3
socleC23×C13C23×C3
hypercenterC22×D4D13⋊C3
hypocenterC13C23×C3×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D13⋊C3C2semidirect
2. C22×D4×C13⋊C3C2semidirect
3. C22×(C22⋊D13)⋊C3C2semidirect
4. C2×D4×D13⋊C3C2direct (N × H)
5. C22×C4⋊(D13⋊C3)C2semidirect
6. C22×C4×D13⋊C3C2semidirect
7. C22×D4×D13C3semidirect
8. C24×C13⋊C3C22semidirect
11. C23×D13⋊C3C22semidirect
12. C23×D13⋊C3C22semidirect
13. C2×D4×C13⋊C3C22semidirect
14. C22×C4×C13⋊C3C22semidirect
15. C2×(C22⋊D13)⋊C3C22semidirect
16. C22×Dic13⋊C3C22semidirect
17. D4×D13⋊C3C22direct (N × H)
18. C2×C4⋊(D13⋊C3)C22semidirect
19. C2×C4×D13⋊C3C22semidirect
20. C24×D13C2×C3semidirect
21. C22×D4×C13C2×C3semidirect
22. C22×C22⋊D13C2×C3semidirect
23. C2×D4×D13C2×C3semidirect
24. C22×D52C2×C3semidirect
25. C22×C4×D13C2×C3semidirect
28. C23×C13⋊C3C23semidirect
31. C22×D13⋊C3D4direct (N × H)
33. C22×D13⋊C3C23semidirect
34. C22×D13⋊C3C23semidirect
35. D4×C13⋊C3C23semidirect
36. C2×C4×C13⋊C3C23semidirect
37. (C22⋊D13)⋊C3C23semidirect
38. C2×Dic13⋊C3C23semidirect
39. C4⋊(D13⋊C3)C23semidirect
40. C4×D13⋊C3C23semidirect
41. C24×C13C22×C3semidirect
44. C23×D13C22×C3semidirect
45. C23×D13C22×C3semidirect
46. C2×D4×C13C22×C3semidirect
47. C22×C4×C13C22×C3semidirect
48. C2×C22⋊D13C22×C3semidirect
49. C22×Dic13C22×C3semidirect
50. D4×D13C22×C3semidirect
51. C2×D52C22×C3semidirect
52. C2×C4×D13C22×C3semidirect
55. C22×C13⋊C3C2×D4semidirect
57. C22×C13⋊C3C24semidirect
60. C2×D13⋊C3C2×D4direct (N × H)
62. C2×D13⋊C3C24semidirect
63. C4×C13⋊C3C24semidirect
64. Dic13⋊C3C24semidirect
67. C23×C13C23×C3semidirect
70. C22×D13C3×D4semidirect
72. C22×D13C23×C3semidirect
73. C22×D13C23×C3semidirect
74. D4×C13C23×C3semidirect
75. C2×C4×C13C23×C3semidirect
76. C22⋊D13C23×C3semidirect
77. C2×Dic13C23×C3semidirect
78. D52C23×C3semidirect
79. C4×D13C23×C3semidirect
87. C2×C13⋊C3C22×D4semidirect
90. D13⋊C3C22×D4direct (N × H)
93. C22×C13C2×C3×D4semidirect
95. C22×C13C24×C3semidirect
98. C2×D13C2×C3×D4semidirect
100. C2×D13C24×C3semidirect
101. C4×C13C24×C3semidirect
102. Dic13C24×C3semidirect
115. C13⋊C3C23×D4semidirect
120. C22×D4D13⋊C3direct (N × H)
123. C2×C13C22×C3×D4semidirect
126. D13C22×C3×D4semidirect
146. C24C2×D13⋊C3semidirect
150. C2×D4C2×D13⋊C3direct (N × H)
153. C22×C4C2×D13⋊C3semidirect
154. C13C23×C3×D4semidirect
174. C23C22×D13⋊C3semidirect
177. D4C22×D13⋊C3direct (N × H)
180. C2×C4C22×D13⋊C3semidirect
192. C22D4×D13⋊C3direct (N × H)
194. C22C23×D13⋊C3semidirect
196. C4C23×D13⋊C3semidirect
201. C2C2×D4×D13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D13⋊C32
C22×D4×C13⋊C32
C22×(C22⋊D13)⋊C32
C2×D4×D13⋊C32
C22×C4⋊(D13⋊C3)2
C22×C4×D13⋊C32
C22×D4×D133
C23×C3×D413