Finite Group Databasebeta

← C24×D4×D79 #35202145

Subgroups — C24×D4×D79 #35202145

Order 20224.

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×D79C212yesmaximal, complemented
2C24×D316C211yesmaximal, characteristic, complemented
3C24×C22⋊D79C212yesmaximal, complemented
4C23×D4×D79C21120yesmaximal, direct product factor
5C24×C4×D79C211yesmaximal, characteristic, complemented
6C24×D4×C79C211yesmaximal, characteristic, complemented
7C25×D79—264no—
8C25×D79C2211yescharacteristic
9C25×D79C221120yescomplemented
10C25×D79C2212yescomplemented
11C23×D316C22160yescomplemented
12C23×C22⋊D79C221120yescomplemented
13C22×D4×D79C2212240yesdirect product factor
14C24×Dic79C2211yescharacteristic, complemented
15C23×C4×D79C22160yescomplemented
16C26×C79C2212yescomplemented
17C23×D4×C79C22160yescomplemented
18C24×C4×C79C2211yescharacteristic, complemented
19C24×D79—232no—
20C24×D79—21920no—
21C24×D79D4132yesdirect product factor
22C24×D79C23130yes—
23C24×D79C2311120yescomplemented
24C24×D79C23160yescomplemented
25C22×D316C231560yescomplemented
26C22×C22⋊D79C2311120yescomplemented
27C2×D4×D79C2317680yesdirect product factor
28C23×Dic79C23130yescomplemented
29C22×C4×D79C231560yescomplemented
30C25×C79—232no—
31C25×C79C2311yescharacteristic
32C25×C79C23160yescomplemented
33C22×D4×C79C231560yescomplemented
34C23×C4×C79C23130yescomplemented
35C23×D79—2480no—
36C23×D79—28960no—
37C23×D79C2×D41480yesdirect product factor
38C23×D79C241140yes—
39C23×D79C2411920yescomplemented
40C23×D79C241280yescomplemented
41C2×D316C241960yescomplemented
42C2×C22⋊D79C2411920yescomplemented
43D4×D79C2414096yesdirect product factor
44C22×Dic79C241140yescomplemented
45C2×C4×D79C241960yescomplemented
46C24×C79—2480no—
47C24×C79C2×D4116yescomplemented
48C24×C79C24115yes—
49C24×C79C241280yescomplemented
50C2×D4×C79C241960yescomplemented
51C22×C4×C79C241140yescomplemented
52C23×C79—21120no—
53C23×C79C22×D41120yescomplemented
54C23×C79C25135yes—
55C23×C79C251240yescomplemented
56C22×D79—21120no—
57C22×D79—27680no—
58C22×D79C22×D411120yesdirect product factor
59C22×D79C251120yes—
60C22×D79C251512yescomplemented
61C22×D79C251240yescomplemented
62D4×C79C251256yescomplemented
63C2×C4×C79C251120yescomplemented
64C22⋊D79C251512yescomplemented
65C2×Dic79C251120yescomplemented
66D316C251256yescomplemented
67C4×D79C251256yescomplemented
68C22×C79—2480no—
69C22×C79C23×D41140yescomplemented
70C22×C79C26115yes—
71C22×C79C26132yescomplemented
72C2×D79—2480no—
73C2×D79—21024no—
74C2×D79C23×D41480yesdirect product factor
75C2×D79C26116yes—
76C2×D79C26132yescomplemented
77C4×C79C26116yescomplemented
78Dic79C26116yescomplemented
79C25×D4—791nomaximal, Sylow
80C2×C79—232no—
81C2×C79C24×D4130yescomplemented
82C2×C79C2711yescharacteristic
83D79—232no—
84D79C24×D4132yesdirect product factor
85C27—792no—
86C24×D4—792no—
87C24×D4—79120no—
88C24×D4—791no—
89C24×D4D7911yescharacteristic, direct product factor
90C25×C4—791no—
91C79C25×D411yescharacteristic, complemented, Sylow
92C26—791no—
93C26—792no—
94C26—79120no—
95C26—15864no—
96C26C2×D7912yescomplemented
97C23×D4—79120no—
98C23×D4—792240no—
99C23×D4—7960no—
100C23×D4C2×D79160yesdirect product factor
101C24×C4—791no—
102C24×C4—7960no—
103C24×C4C2×D7911yescharacteristic, complemented
104C25—232no—
105C25—7932no—
106C25—7930no—
107C25—7960no—
108C25—791120no—
109C25—1581920no—
110C25—15832no—
111C25C22×D7911yescharacteristic
112C25C22×D79160yescomplemented
113C22×D4—791120no—
114C22×D4—797680no—
115C22×D4—79560no—
116C22×D4C22×D791560yesdirect product factor
117C23×C4—7930no—
118C23×C4—79560no—
119C23×C4C22×D79130yescomplemented
120C24—2480no—
121C24—79140no—
122C24—79480no—
123C24—79280no—
124C24—791920no—
125C24—1588960no—
126C24—158480no—
127C24D4×D79116yesdirect product factor
128C24C23×D79115yes—
129C24C23×D791280yescomplemented
130C2×D4—791920no—
131C2×D4—794096no—
132C2×D4—79960no—
133C2×D4C23×D791960yesdirect product factor
134C22×C4—79140no—
135C22×C4—79960no—
136C22×C4C23×D791140yescomplemented
137C23—21120no—
138C23—79120no—
139C23—791120no—
140C23—79240no—
141C23—79512no—
142C23—1587680no—
143C23—1581120no—
144C23C2×D4×D791120yesdirect product factor
145C23C24×D79135yes—
146C23C24×D791240yescomplemented
147D4—79512no—
148D4—79256no—
149D4C24×D791256yesdirect product factor
150C2×C4—79120no—
151C2×C4—79256no—
152C2×C4C24×D791120yescomplemented
153C22—2480no—
154C22—79480no—
155C22—7916no—
156C22—7932no—
157C22—1581024no—
158C22—158480no—
159C22C22×D4×D791140yesdirect product factor
160C22C25×D79115yes—
161C22C25×D79132yescomplemented
162C4—7916no—
163C4C25×D79116yescomplemented
164C2—232no—
165C2—7932no—
166C2—15832no—
167C2C23×D4×D79130yesdirect product factor
168C2C26×D7911yescharacteristic
subgroupG/H
centerC25C22×D79
commutator, cosocleC2×C79C27
FrattiniC2C26×D79
FittingC24×D4×C79C2
socleC25×C79C23
hypercenterC24×D4D79
hypocenterC79C25×D4
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C25 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C26×D79C2semidirect
2. C24×D316C2semidirect
3. C24×C22⋊D79C2semidirect
4. C23×D4×D79C2direct (N × H)
5. C24×C4×D79C2semidirect
6. C24×D4×C79C2semidirect
9. C25×D79C22semidirect
10. C25×D79C22semidirect
11. C23×D316C22semidirect
12. C23×C22⋊D79C22semidirect
13. C22×D4×D79C22direct (N × H)
14. C24×Dic79C22semidirect
15. C23×C4×D79C22semidirect
16. C26×C79C22semidirect
17. C23×D4×C79C22semidirect
18. C24×C4×C79C22semidirect
21. C24×D79D4direct (N × H)
23. C24×D79C23semidirect
24. C24×D79C23semidirect
25. C22×D316C23semidirect
26. C22×C22⋊D79C23semidirect
27. C2×D4×D79C23direct (N × H)
28. C23×Dic79C23semidirect
29. C22×C4×D79C23semidirect
32. C25×C79C23semidirect
33. C22×D4×C79C23semidirect
34. C23×C4×C79C23semidirect
37. C23×D79C2×D4direct (N × H)
39. C23×D79C24semidirect
40. C23×D79C24semidirect
41. C2×D316C24semidirect
42. C2×C22⋊D79C24semidirect
43. D4×D79C24direct (N × H)
44. C22×Dic79C24semidirect
45. C2×C4×D79C24semidirect
47. C24×C79C2×D4semidirect
49. C24×C79C24semidirect
50. C2×D4×C79C24semidirect
51. C22×C4×C79C24semidirect
53. C23×C79C22×D4semidirect
55. C23×C79C25semidirect
58. C22×D79C22×D4direct (N × H)
60. C22×D79C25semidirect
61. C22×D79C25semidirect
62. D4×C79C25semidirect
63. C2×C4×C79C25semidirect
64. C22⋊D79C25semidirect
65. C2×Dic79C25semidirect
66. D316C25semidirect
67. C4×D79C25semidirect
69. C22×C79C23×D4semidirect
71. C22×C79C26semidirect
74. C2×D79C23×D4direct (N × H)
76. C2×D79C26semidirect
77. C4×C79C26semidirect
78. Dic79C26semidirect
81. C2×C79C24×D4semidirect
84. D79C24×D4direct (N × H)
89. C24×D4D79direct (N × H)
91. C79C25×D4semidirect
96. C26C2×D79semidirect
100. C23×D4C2×D79direct (N × H)
103. C24×C4C2×D79semidirect
112. C25C22×D79semidirect
116. C22×D4C22×D79direct (N × H)
119. C23×C4C22×D79semidirect
127. C24D4×D79direct (N × H)
129. C24C23×D79semidirect
133. C2×D4C23×D79direct (N × H)
136. C22×C4C23×D79semidirect
144. C23C2×D4×D79direct (N × H)
146. C23C24×D79semidirect
149. D4C24×D79direct (N × H)
152. C2×C4C24×D79semidirect
159. C22C22×D4×D79direct (N × H)
161. C22C25×D79semidirect
163. C4C25×D79semidirect
167. C2C23×D4×D79direct (N × H)

Maximal subgroups

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

subgroupindex
C26×D792
C24×D3162
C24×C22⋊D792
C23×D4×D792
C24×C4×D792
C24×D4×C792
C25×D479