Finite Group Databasebeta

← C24×D4×D7 #14267672

Subgroups — C24×D4×D7 #14267672

Order 1792.

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×D7C212yesmaximal, complemented
2C24×C7×D4C211yesmaximal, characteristic, complemented
3C24×C22⋊D7C212yesmaximal, complemented
4C23×D4×D7C21120yesmaximal, direct product factor
5C24×D28C211yesmaximal, characteristic, complemented
6C24×C4×D7C211yesmaximal, characteristic, complemented
7C26×C7C2212yescomplemented
8C25×D7—264no—
9C25×D7C2211yescharacteristic
10C25×D7C221120yescomplemented
11C25×D7C2212yescomplemented
12C23×C7×D4C22160yescomplemented
13C24×C4×C7C2211yescharacteristic, complemented
14C23×C22⋊D7C221120yescomplemented
15C24×Dic7C2211yescharacteristic, complemented
16C22×D4×D7C2212240yesdirect product factor
17C23×D28C22160yescomplemented
18C23×C4×D7C22160yescomplemented
19C25×D4—71nomaximal, Sylow
20C25×C7—232no—
21C25×C7C2311yescharacteristic
22C25×C7C23160yescomplemented
23C24×D7—232no—
24C24×D7—21920no—
25C24×D7D4132yesdirect product factor
26C24×D7C23130yes—
27C24×D7C2311120yescomplemented
28C24×D7C23160yescomplemented
29C22×C7×D4C231560yescomplemented
30C23×C4×C7C23130yescomplemented
31C22×C22⋊D7C2311120yescomplemented
32C23×Dic7C23130yescomplemented
33C2×D4×D7C2317680yesdirect product factor
34C22×D28C231560yescomplemented
35C22×C4×D7C231560yescomplemented
36C27—72no—
37C24×D4—72no—
38C24×D4—7120no—
39C24×D4—71no—
40C24×D4D711yescharacteristic, direct product factor
41C25×C4—71no—
42C24×C7—2480no—
43C24×C7C2×D4116yescomplemented
44C24×C7C24115yes—
45C24×C7C241280yescomplemented
46C23×D7—2480no—
47C23×D7—28960no—
48C23×D7C2×D41480yesdirect product factor
49C23×D7C241140yes—
50C23×D7C2411920yescomplemented
51C23×D7C241280yescomplemented
52C2×C7×D4C241960yescomplemented
53C22×C4×C7C241140yescomplemented
54C2×C22⋊D7C2411920yescomplemented
55C22×Dic7C241140yescomplemented
56D4×D7C2414096yesdirect product factor
57C2×D28C241960yescomplemented
58C2×C4×D7C241960yescomplemented
59C26—71no—
60C26—72no—
61C26—7120no—
62C26—1464no—
63C26C2×D712yescomplemented
64C23×D4—7120no—
65C23×D4—72240no—
66C23×D4—760no—
67C23×D4C2×D7160yesdirect product factor
68C24×C4—71no—
69C24×C4—760no—
70C24×C4C2×D711yescharacteristic, complemented
71C23×C7—21120no—
72C23×C7C22×D41120yescomplemented
73C23×C7C25135yes—
74C23×C7C251240yescomplemented
75C22×D7—21120no—
76C22×D7—27680no—
77C22×D7C22×D411120yesdirect product factor
78C22×D7C251120yes—
79C22×D7C251512yescomplemented
80C22×D7C251240yescomplemented
81C7×D4C251256yescomplemented
82C2×C4×C7C251120yescomplemented
83C22⋊D7C251512yescomplemented
84C2×Dic7C251120yescomplemented
85D28C251256yescomplemented
86C4×D7C251256yescomplemented
87C25—232no—
88C25—732no—
89C25—730no—
90C25—760no—
91C25—71120no—
92C25—141920no—
93C25—1432no—
94C25C22×D711yescharacteristic
95C25C22×D7160yescomplemented
96C22×D4—71120no—
97C22×D4—77680no—
98C22×D4—7560no—
99C22×D4C22×D71560yesdirect product factor
100C23×C4—730no—
101C23×C4—7560no—
102C23×C4C22×D7130yescomplemented
103C22×C7—2480no—
104C22×C7C23×D41140yescomplemented
105C22×C7C26115yes—
106C22×C7C26132yescomplemented
107C2×D7—2480no—
108C2×D7—21024no—
109C2×D7C23×D41480yesdirect product factor
110C2×D7C26116yes—
111C2×D7C26132yescomplemented
112C4×C7C26116yescomplemented
113Dic7C26116yescomplemented
114C24—2480no—
115C24—7480no—
116C24—7140no—
117C24—7280no—
118C24—71920no—
119C24—148960no—
120C24—14480no—
121C24D4×D7116yesdirect product factor
122C24C23×D7115yes—
123C24C23×D71280yescomplemented
124C2×D4—71920no—
125C2×D4—74096no—
126C2×D4—7960no—
127C2×D4C23×D71960yesdirect product factor
128C22×C4—7140no—
129C22×C4—7960no—
130C22×C4C23×D71140yescomplemented
131C2×C7—232no—
132C2×C7C24×D4130yescomplemented
133C2×C7C2711yescharacteristic
134D7—232no—
135D7C24×D4132yesdirect product factor
136C23—21120no—
137C23—7120no—
138C23—71120no—
139C23—7240no—
140C23—7512no—
141C23—147680no—
142C23—141120no—
143C23C2×D4×D71120yesdirect product factor
144C23C24×D7135yes—
145C23C24×D71240yescomplemented
146D4—7512no—
147D4—7256no—
148D4C24×D71256yesdirect product factor
149C2×C4—7120no—
150C2×C4—7256no—
151C2×C4C24×D71120yescomplemented
152C7C25×D411yescharacteristic, complemented, Sylow
153C22—2480no—
154C22—7480no—
155C22—716no—
156C22—732no—
157C22—141024no—
158C22—14480no—
159C22C22×D4×D71140yesdirect product factor
160C22C25×D7115yes—
161C22C25×D7132yescomplemented
162C4—716no—
163C4C25×D7116yescomplemented
164C2—232no—
165C2—732no—
166C2—1432no—
167C2C23×D4×D7130yesdirect product factor
168C2C26×D711yescharacteristic
subgroupG/H
centerC25C22×D7
commutator, cosocleC2×C7C27
FrattiniC2C26×D7
FittingC24×C7×D4C2
socleC25×C7C23
hypercenterC24×D4D7
hypocenterC7C25×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C25 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C26×D7C2semidirect
2. C24×C7×D4C2semidirect
3. C24×C22⋊D7C2semidirect
4. C23×D4×D7C2direct (N × H)
5. C24×D28C2semidirect
6. C24×C4×D7C2semidirect
7. C26×C7C22semidirect
10. C25×D7C22semidirect
11. C25×D7C22semidirect
12. C23×C7×D4C22semidirect
13. C24×C4×C7C22semidirect
14. C23×C22⋊D7C22semidirect
15. C24×Dic7C22semidirect
16. C22×D4×D7C22direct (N × H)
17. C23×D28C22semidirect
18. C23×C4×D7C22semidirect
22. C25×C7C23semidirect
25. C24×D7D4direct (N × H)
27. C24×D7C23semidirect
28. C24×D7C23semidirect
29. C22×C7×D4C23semidirect
30. C23×C4×C7C23semidirect
31. C22×C22⋊D7C23semidirect
32. C23×Dic7C23semidirect
33. C2×D4×D7C23direct (N × H)
34. C22×D28C23semidirect
35. C22×C4×D7C23semidirect
40. C24×D4D7direct (N × H)
43. C24×C7C2×D4semidirect
45. C24×C7C24semidirect
48. C23×D7C2×D4direct (N × H)
50. C23×D7C24semidirect
51. C23×D7C24semidirect
52. C2×C7×D4C24semidirect
53. C22×C4×C7C24semidirect
54. C2×C22⋊D7C24semidirect
55. C22×Dic7C24semidirect
56. D4×D7C24direct (N × H)
57. C2×D28C24semidirect
58. C2×C4×D7C24semidirect
63. C26C2×D7semidirect
67. C23×D4C2×D7direct (N × H)
70. C24×C4C2×D7semidirect
72. C23×C7C22×D4semidirect
74. C23×C7C25semidirect
77. C22×D7C22×D4direct (N × H)
79. C22×D7C25semidirect
80. C22×D7C25semidirect
81. C7×D4C25semidirect
82. C2×C4×C7C25semidirect
83. C22⋊D7C25semidirect
84. C2×Dic7C25semidirect
85. D28C25semidirect
86. C4×D7C25semidirect
95. C25C22×D7semidirect
99. C22×D4C22×D7direct (N × H)
102. C23×C4C22×D7semidirect
104. C22×C7C23×D4semidirect
106. C22×C7C26semidirect
109. C2×D7C23×D4direct (N × H)
111. C2×D7C26semidirect
112. C4×C7C26semidirect
113. Dic7C26semidirect
121. C24D4×D7direct (N × H)
123. C24C23×D7semidirect
127. C2×D4C23×D7direct (N × H)
130. C22×C4C23×D7semidirect
132. C2×C7C24×D4semidirect
135. D7C24×D4direct (N × H)
143. C23C2×D4×D7direct (N × H)
145. C23C24×D7semidirect
148. D4C24×D7direct (N × H)
151. C2×C4C24×D7semidirect
152. C7C25×D4semidirect
159. C22C22×D4×D7direct (N × H)
161. C22C25×D7semidirect
163. C4C25×D7semidirect
167. C2C23×D4×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C26×D72
C24×C7×D42
C24×C22⋊D72
C23×D4×D72
C24×D282
C24×C4×D72
C25×D47