Finite Group Databasebeta

← C2×D4×#13181884 #42122875

Subgroups — C2×D4×#13181884 #42122875

Order 27712.

426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C23×#13181884C212yesmaximal, complemented
2D4×#13181884C218yesmaximal, direct product factor
3C2×C4⋊#13181884C211yesmaximal, characteristic, complemented
4C2×C22⋊#13181884C212yesmaximal, complemented
5C2×C4×#13181884C211yesmaximal, characteristic, complemented
6C2×D4×D433C211yesmaximal, characteristic
7C22×#13181884—28no—
8C22×#13181884C2211yescharacteristic
9C22×#13181884C2212yes—
10C22×#13181884C2211yescharacteristic
11C22×#13181884C2218yescomplemented
12C4⋊#13181884C2214yescomplemented
13C22⋊#13181884C2218yescomplemented
14C4×#13181884C2214yescomplemented
15C23×D433C2212yes—
16C2×D1732C411yescharacteristic, complemented
17C2×C22⋊D433C412yescomplemented
18D4×D433C414yescomplemented
19D4×D433C2214yes—
20C2×C4×D433C2211yescharacteristic
21C2×D4×C433C411yescharacteristic, complemented
22C2×#13181884—24no—
23C2×#13181884—22no—
24C2×#13181884—216no—
25C2×#13181884D414yesdirect product factor
26C2×#13181884C2312yes—
27C2×#13181884C2314yes—
28C2×#13181884C2312yes—
29C22×D433—24no—
30C22×D433—24no—
31C22×D433C2×C414yescomplemented
32C22×D433C2×C412yescomplemented
33C22×D433C2314yes—
34C22×D433C2311yescharacteristic
35D1732C2×C414yescomplemented
36C22⋊D433C2×C418yescomplemented
37C2×Dic433C2×C411yescharacteristic, complemented
38C4×D433C2×C412yescomplemented
39C4×D433C2312yes—
40C23×C433C2×C412yescomplemented
41D4×C433C2×C414yescomplemented
42C2×C4×C433C2×C411yescharacteristic, complemented
43C22×C433—24no—
44C22×C433C22×C411yescharacteristic
45C22×C433C22×C414yescomplemented
46C2×D433—24no—
47C2×D433—28no—
48C2×D433—24no—
49C2×D433—24no—
50C2×D433C22×C411yescharacteristic
51C2×D433C22×C414yescomplemented
52C2×D433C2×D412yes—
53C2×D433#4112yes—
54C2×D433C2411yescharacteristic
55#13181884—24no—
56#13181884—22no—
57#13181884C2×D414yesdirect product factor
58C4×C433C22×C412yescomplemented
59Dic433C22×C412yescomplemented
60C2×C433—24no—
61C2×C433C4×D412yescomplemented
62C2×C433C23×C411yescharacteristic
63D433—24no—
64D433C4×D412yescomplemented
65D433C22×D411yescharacteristic
66D433C2×#4111yescharacteristic
67C433C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—4331nomaximal, Sylow
69C22×D4—4331no—
70C23×C4—4332no—
71C4×D4—4338no—
72C2×C4⋊C4—4331no—
73C2×C22⋊C4—4332no—
74C2×C42—4331no—
75C24—4332no—
76C2×D4—4332no—
77C2×D4—4334no—
78C2×D4—4334no—
79C2×D4—4331no—
80C2×D4#1318188411yescharacteristic, direct product factor
81C22×C4—8668no—
82C22×C4—4331no—
83C22×C4—4332no—
84C22×C4—4338no—
85C22×C4—4331no—
86C22×C4—4331no—
87C4⋊C4—4334no—
88C22⋊C4—4338no—
89C42—4334no—
90C23—8664no—
91C23—8664no—
92C23—4332no—
93C23—4334no—
94C23—4334no—
95C23—4331no—
96C23C2×#1318188412yescomplemented
97D4—4338no—
98D4—4334no—
99D4C2×#1318188414yesdirect product factor
100C2×C4—8664no—
101C2×C4—8662no—
102C2×C4—86616no—
103C2×C4—4332no—
104C2×C4—4334no—
105C2×C4—4332no—
106C2×C4—4334no—
107C2×C4—4331no—
108C2×C4—4332no—
109C2×C4—4332no—
110C2×C4C2×#1318188411yescharacteristic, complemented
111C22—24no—
112C22—8664no—
113C22—8664no—
114C22—8668no—
115C22—8664no—
116C22—4334no—
117C22—4332no—
118C22—4332no—
119C22—4331no—
120C22—4331no—
121C22C22×#1318188411yescharacteristic
122C22C22×#1318188414yescomplemented
123C4—8664no—
124C4—8662no—
125C4—4334no—
126C4—4332no—
127C4C22×#1318188412yescomplemented
128C2—24no—
129C2—8664no—
130C2—4331no—
131C2—4331no—
132C2—4332no—
133C2D4×#1318188412yesdirect product factor
134C2C23×#1318188411yescharacteristic
subgroupG/H
centerC22C22×#13181884
commutatorC2×C433C23×C4
FrattiniC2C23×#13181884
FittingC2×D4×C433C4
socleC22×C433C22×C4
prime radicalC2×D4×D433C2
cosocleC2×D433C24
hypercenterC2×D4#13181884
hypocenterC433C2×C4×D4
LCSG ▷ C2×C433 ▷ C433
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#13181884C2semidirect
2. D4×#13181884C2direct (N × H)
3. C2×C4⋊#13181884C2semidirect
4. C2×C22⋊#13181884C2semidirect
5. C2×C4×#13181884C2semidirect
11. C22×#13181884C22semidirect
12. C4⋊#13181884C22semidirect
13. C22⋊#13181884C22semidirect
14. C4×#13181884C22semidirect
16. C2×D1732C4semidirect
17. C2×C22⋊D433C4semidirect
18. D4×D433C4semidirect
21. C2×D4×C433C4semidirect
25. C2×#13181884D4direct (N × H)
31. C22×D433C2×C4semidirect
32. C22×D433C2×C4semidirect
35. D1732C2×C4semidirect
36. C22⋊D433C2×C4semidirect
37. C2×Dic433C2×C4semidirect
38. C4×D433C2×C4semidirect
40. C23×C433C2×C4semidirect
41. D4×C433C2×C4semidirect
42. C2×C4×C433C2×C4semidirect
45. C22×C433C22×C4semidirect
51. C2×D433C22×C4semidirect
57. #13181884C2×D4direct (N × H)
58. C4×C433C22×C4semidirect
59. Dic433C22×C4semidirect
61. C2×C433C4×D4semidirect
64. D433C4×D4semidirect
67. C433C2×C4×D4semidirect
80. C2×D4#13181884direct (N × H)
96. C23C2×#13181884semidirect
99. D4C2×#13181884direct (N × H)
110. C2×C4C2×#13181884semidirect
122. C22C22×#13181884semidirect
127. C4C22×#13181884semidirect
133. C2D4×#13181884direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#131818842
D4×#131818842
C2×C4⋊#131818842
C2×C22⋊#131818842
C2×C4×#131818842
C2×D4×D4332
C2×C4×D4433