Finite Group Databasebeta

← C2×#121×C359 #37526097

Subgroups — C2×#121×C359 #37526097

Order 22976.

426 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 194 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×D4×C359C212yesmaximal, complemented
2C22×D4×C359C211yesmaximal, characteristic, complemented
3C23×C4×C359C211yesmaximal, characteristic, complemented
4#121×C359C218yesmaximal, direct product factor
5C2×C4⋊C4×C359C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×C359C212yesmaximal, complemented
7C24×C359C2212yes—
8C24×C359C2211yescharacteristic
9C2×D4×C359—28no—
10C2×D4×C359—24no—
11C2×D4×C359C2218yescomplemented
12C2×D4×C359C2214yescomplemented
13C22×C4×C359—24no—
14C22×C4×C359C2211yescharacteristic
15C22×C4×C359C2212yes—
16C22×C4×C359C2211yescharacteristic
17C22×C4×C359C2214yescomplemented
18C4⋊C4×C359C2214yescomplemented
19C22⋊C4×C359C2218yescomplemented
20C23×C359—22no—
21C23×C359—22no—
22C23×C359—24no—
23C23×C359—24no—
24C23×C359—24no—
25C23×C359D414yescomplemented
26C23×C359C2314yes—
27C23×C359C2312yes—
28C23×C359C2311yescharacteristic
29D4×C359—216no—
30D4×C359—28no—
31C2×C4×C359—22no—
32C2×C4×C359—24no—
33C2×C4×C359—28no—
34C2×C4×C359D414yescomplemented
35C2×C4×C359C2312yes—
36C2×C4×C359C2314yes—
37C2×C4×C359C2312yes—
38C22×C359—28no—
39C22×C359—22no—
40C22×C359—22no—
41C22×C359—24no—
42C22×C359—24no—
43C22×C359—24no—
44C22×C359—48no—
45C22×C359C2×D412yes—
46C22×C359C2×D412yes—
47C22×C359C2×D414yescomplemented
48C22×C359#4112yes—
49C22×C359C2411yescharacteristic
50C4×C359—22no—
51C4×C359—24no—
52C4×C359C2×D414yescomplemented
53C2×C359—24no—
54C2×C359—44no—
55C2×C359#12114yesdirect product factor
56C2×C359C22×D411yescharacteristic
57C2×C359C22×D411yescharacteristic
58C2×C359C2×#4111yescharacteristic
59C359C2×#12111yescharacteristic, direct product factor, Sylow
60C2×#121C35911yesmaximal, characteristic, direct product factor, Sylow
61C22×D4C2×C35912yescomplemented
62C22×D4C2×C35911yescharacteristic, complemented
63C23×C4C2×C35911yescharacteristic, complemented
64#121C2×C35918yesdirect product factor
65C2×C4⋊C4C2×C35911yescharacteristic, complemented
66C2×C22⋊C4C2×C35912yescomplemented
67C24C22×C35912yes—
68C24C22×C35911yescharacteristic
69C2×D4—28no—
70C2×D4—24no—
71C2×D4C22×C35918yescomplemented
72C2×D4C22×C35914yescomplemented
73C22×C4—24no—
74C22×C4C22×C35911yescharacteristic
75C22×C4C22×C35912yes—
76C22×C4C22×C35911yescharacteristic
77C22×C4C22×C35914yescomplemented
78C4⋊C4C22×C35914yescomplemented
79C22⋊C4C22×C35918yescomplemented
80C23—22no—
81C23—22no—
82C23—24no—
83C23—24no—
84C23—24no—
85C23D4×C35914yescomplemented
86C23C23×C35914yes—
87C23C23×C35912yes—
88C23C23×C35911yescharacteristic
89D4—216no—
90D4—28no—
91C2×C4—22no—
92C2×C4—24no—
93C2×C4—28no—
94C2×C4D4×C35914yescomplemented
95C2×C4C23×C35912yes—
96C2×C4C23×C35914yes—
97C2×C4C23×C35912yes—
98C22—28no—
99C22—22no—
100C22—22no—
101C22—24no—
102C22—24no—
103C22—24no—
104C22—48no—
105C22C2×D4×C35912yes—
106C22C2×D4×C35912yes—
107C22C2×D4×C35914yescomplemented
108C22#41×C35912yes—
109C22C24×C35911yescharacteristic
110C4—22no—
111C4—24no—
112C4C2×D4×C35914yescomplemented
113C2—24no—
114C2—44no—
115C2#121×C35914yesdirect product factor
116C2C22×D4×C35911yescharacteristic
117C2C22×D4×C35911yescharacteristic
118C2C2×#41×C35911yescharacteristic
subgroupG/H
center, socleC23×C359C23
commutator, Frattini, cosocleC22C24×C359
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C359 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×D4×C359C2semidirect
2. C22×D4×C359C2semidirect
3. C23×C4×C359C2semidirect
4. #121×C359C2direct (N × H)
5. C2×C4⋊C4×C359C2semidirect
6. C2×C22⋊C4×C359C2semidirect
11. C2×D4×C359C22semidirect
12. C2×D4×C359C22semidirect
17. C22×C4×C359C22semidirect
18. C4⋊C4×C359C22semidirect
19. C22⋊C4×C359C22semidirect
25. C23×C359D4semidirect
34. C2×C4×C359D4semidirect
47. C22×C359C2×D4semidirect
52. C4×C359C2×D4semidirect
55. C2×C359#121direct (N × H)
59. C359C2×#121direct (N × H)
60. C2×#121C359direct (N × H)
61. C22×D4C2×C359semidirect
62. C22×D4C2×C359semidirect
63. C23×C4C2×C359semidirect
64. #121C2×C359direct (N × H)
65. C2×C4⋊C4C2×C359semidirect
66. C2×C22⋊C4C2×C359semidirect
71. C2×D4C22×C359semidirect
72. C2×D4C22×C359semidirect
77. C22×C4C22×C359semidirect
78. C4⋊C4C22×C359semidirect
79. C22⋊C4C22×C359semidirect
85. C23D4×C359semidirect
94. C2×C4D4×C359semidirect
107. C22C2×D4×C359semidirect
112. C4C2×D4×C359semidirect
115. C2#121×C359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C3592
C23×C4×C3592
#121×C3592
C2×C4⋊C4×C3592
C2×C22⋊C4×C3592
C2×#121359