Finite Group Databasebeta

← C24×D4×D61 #30593889

Subgroups — C24×D4×D61 #30593889

Order 15616.

111198 conjugacy classes of subgroups; only the 34795 normal subgroups are shown.

normal subgroups only

This group has 111198 conjugacy classes of subgroups — too many to draw. Only its 34795 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
1C26×D61C212yesmaximal, complemented
2C24×D244C211yesmaximal, characteristic, complemented
3C24×C22⋊D61C212yesmaximal, complemented
4C23×D4×D61C21120yesmaximal, direct product factor
5C24×C4×D61C211yesmaximal, characteristic, complemented
6C24×D4×C61C211yesmaximal, characteristic, complemented
7C25×D61—264no—
8C25×D61C2211yescharacteristic
9C25×D61C221120yescomplemented
10C25×D61C2212yescomplemented
11C23×D244C22160yescomplemented
12C23×C22⋊D61C221120yescomplemented
13C22×D4×D61C2212240yesdirect product factor
14C24×Dic61C2211yescharacteristic, complemented
15C23×C4×D61C22160yescomplemented
16C26×C61C2212yescomplemented
17C23×D4×C61C22160yescomplemented
18C24×C4×C61C2211yescharacteristic, complemented
19C24×D61—232no—
20C24×D61—21920no—
21C24×D61D4132yesdirect product factor
22C24×D61C23130yes—
23C24×D61C2311120yescomplemented
24C24×D61C23160yescomplemented
25C22×D244C231560yescomplemented
26C22×C22⋊D61C2311120yescomplemented
27C2×D4×D61C2317680yesdirect product factor
28C23×Dic61C23130yescomplemented
29C22×C4×D61C231560yescomplemented
30C25×C61—232no—
31C25×C61C2311yescharacteristic
32C25×C61C23160yescomplemented
33C22×D4×C61C231560yescomplemented
34C23×C4×C61C23130yescomplemented
35C24×C61—2480no—
36C24×C61C2×D4116yescomplemented
37C24×C61C24115yes—
38C24×C61C241280yescomplemented
39C23×D61—2480no—
40C23×D61—28960no—
41C23×D61C2×D41480yesdirect product factor
42C23×D61C241140yes—
43C23×D61C2411920yescomplemented
44C23×D61C241280yescomplemented
45C2×D4×C61C241960yescomplemented
46C22×C4×C61C241140yescomplemented
47C2×C22⋊D61C2411920yescomplemented
48C22×Dic61C241140yescomplemented
49D4×D61C2414096yesdirect product factor
50C2×D244C241960yescomplemented
51C2×C4×D61C241960yescomplemented
52C23×C61—21120no—
53C23×C61C22×D41120yescomplemented
54C23×C61C25135yes—
55C23×C61C251240yescomplemented
56C22×D61—21120no—
57C22×D61—27680no—
58C22×D61C22×D411120yesdirect product factor
59C22×D61C251120yes—
60C22×D61C251512yescomplemented
61C22×D61C251240yescomplemented
62D4×C61C251256yescomplemented
63C2×C4×C61C251120yescomplemented
64C22⋊D61C251512yescomplemented
65C2×Dic61C251120yescomplemented
66D244C251256yescomplemented
67C4×D61C251256yescomplemented
68C25×D4—611nomaximal, Sylow
69C22×C61—2480no—
70C22×C61C23×D41140yescomplemented
71C22×C61C26115yes—
72C22×C61C26132yescomplemented
73C2×D61—2480no—
74C2×D61—21024no—
75C2×D61C23×D41480yesdirect product factor
76C2×D61C26116yes—
77C2×D61C26132yescomplemented
78C4×C61C26116yescomplemented
79Dic61C26116yescomplemented
80C27—612no—
81C24×D4—612no—
82C24×D4—61120no—
83C24×D4—611no—
84C24×D4D6111yescharacteristic, direct product factor
85C25×C4—611no—
86C2×C61—232no—
87C2×C61C24×D4130yescomplemented
88C2×C61C2711yescharacteristic
89D61—232no—
90D61C24×D4132yesdirect product factor
91C26—611no—
92C26—612no—
93C26—61120no—
94C26—12264no—
95C26C2×D6112yescomplemented
96C23×D4—61120no—
97C23×D4—612240no—
98C23×D4—6160no—
99C23×D4C2×D61160yesdirect product factor
100C24×C4—611no—
101C24×C4—6160no—
102C24×C4C2×D6111yescharacteristic, complemented
103C61C25×D411yescharacteristic, complemented, Sylow
104C25—232no—
105C25—6132no—
106C25—6130no—
107C25—6160no—
108C25—611120no—
109C25—1221920no—
110C25—12232no—
111C25C22×D6111yescharacteristic
112C25C22×D61160yescomplemented
113C22×D4—611120no—
114C22×D4—617680no—
115C22×D4—61560no—
116C22×D4C22×D611560yesdirect product factor
117C23×C4—6130no—
118C23×C4—61560no—
119C23×C4C22×D61130yescomplemented
120C24—2480no—
121C24—61480no—
122C24—61140no—
123C24—61280no—
124C24—611920no—
125C24—1228960no—
126C24—122480no—
127C24D4×D61116yesdirect product factor
128C24C23×D61115yes—
129C24C23×D611280yescomplemented
130C2×D4—611920no—
131C2×D4—614096no—
132C2×D4—61960no—
133C2×D4C23×D611960yesdirect product factor
134C22×C4—61140no—
135C22×C4—61960no—
136C22×C4C23×D611140yescomplemented
137C23—21120no—
138C23—611120no—
139C23—61120no—
140C23—61240no—
141C23—61512no—
142C23—1227680no—
143C23—1221120no—
144C23C2×D4×D611120yesdirect product factor
145C23C24×D61135yes—
146C23C24×D611240yescomplemented
147D4—61512no—
148D4—61256no—
149D4C24×D611256yesdirect product factor
150C2×C4—61120no—
151C2×C4—61256no—
152C2×C4C24×D611120yescomplemented
153C22—2480no—
154C22—61480no—
155C22—6116no—
156C22—6132no—
157C22—1221024no—
158C22—122480no—
159C22C22×D4×D611140yesdirect product factor
160C22C25×D61115yes—
161C22C25×D61132yescomplemented
162C4—6116no—
163C4C25×D61116yescomplemented
164C2—232no—
165C2—6132no—
166C2—12232no—
167C2C23×D4×D61130yesdirect product factor
168C2C26×D6111yescharacteristic
subgroupG/H
centerC25C22×D61
commutator, cosocleC2×C61C27
FrattiniC2C26×D61
FittingC24×D4×C61C2
socleC25×C61C23
hypercenterC24×D4D61
hypocenterC61C25×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C25 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C26×D61C2semidirect
2. C24×D244C2semidirect
3. C24×C22⋊D61C2semidirect
4. C23×D4×D61C2direct (N × H)
5. C24×C4×D61C2semidirect
6. C24×D4×C61C2semidirect
9. C25×D61C22semidirect
10. C25×D61C22semidirect
11. C23×D244C22semidirect
12. C23×C22⋊D61C22semidirect
13. C22×D4×D61C22direct (N × H)
14. C24×Dic61C22semidirect
15. C23×C4×D61C22semidirect
16. C26×C61C22semidirect
17. C23×D4×C61C22semidirect
18. C24×C4×C61C22semidirect
21. C24×D61D4direct (N × H)
23. C24×D61C23semidirect
24. C24×D61C23semidirect
25. C22×D244C23semidirect
26. C22×C22⋊D61C23semidirect
27. C2×D4×D61C23direct (N × H)
28. C23×Dic61C23semidirect
29. C22×C4×D61C23semidirect
32. C25×C61C23semidirect
33. C22×D4×C61C23semidirect
34. C23×C4×C61C23semidirect
36. C24×C61C2×D4semidirect
38. C24×C61C24semidirect
41. C23×D61C2×D4direct (N × H)
43. C23×D61C24semidirect
44. C23×D61C24semidirect
45. C2×D4×C61C24semidirect
46. C22×C4×C61C24semidirect
47. C2×C22⋊D61C24semidirect
48. C22×Dic61C24semidirect
49. D4×D61C24direct (N × H)
50. C2×D244C24semidirect
51. C2×C4×D61C24semidirect
53. C23×C61C22×D4semidirect
55. C23×C61C25semidirect
58. C22×D61C22×D4direct (N × H)
60. C22×D61C25semidirect
61. C22×D61C25semidirect
62. D4×C61C25semidirect
63. C2×C4×C61C25semidirect
64. C22⋊D61C25semidirect
65. C2×Dic61C25semidirect
66. D244C25semidirect
67. C4×D61C25semidirect
70. C22×C61C23×D4semidirect
72. C22×C61C26semidirect
75. C2×D61C23×D4direct (N × H)
77. C2×D61C26semidirect
78. C4×C61C26semidirect
79. Dic61C26semidirect
84. C24×D4D61direct (N × H)
87. C2×C61C24×D4semidirect
90. D61C24×D4direct (N × H)
95. C26C2×D61semidirect
99. C23×D4C2×D61direct (N × H)
102. C24×C4C2×D61semidirect
103. C61C25×D4semidirect
112. C25C22×D61semidirect
116. C22×D4C22×D61direct (N × H)
119. C23×C4C22×D61semidirect
127. C24D4×D61direct (N × H)
129. C24C23×D61semidirect
133. C2×D4C23×D61direct (N × H)
136. C22×C4C23×D61semidirect
144. C23C2×D4×D61direct (N × H)
146. C23C24×D61semidirect
149. D4C24×D61direct (N × H)
152. C2×C4C24×D61semidirect
159. C22C22×D4×D61direct (N × H)
161. C22C25×D61semidirect
163. C4C25×D61semidirect
167. C2C23×D4×D61direct (N × H)

Maximal subgroups

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

subgroupindex
C26×D612
C24×D2442
C24×C22⋊D612
C23×D4×D612
C24×C4×D612
C24×D4×C612
C25×D461