Finite Group Databasebeta

← C22×D4×D223 #28384400

Subgroups — C22×D4×D223 #28384400

Order 14272.

1362 conjugacy classes of subgroups; only the 503 normal subgroups are shown.

normal subgroups only

This group has 1362 conjugacy classes of subgroups — too many to draw. Only its 503 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
1C24×D223C212yesmaximal, complemented
2C22×D892C211yesmaximal, characteristic, complemented
3C22×C22⋊D223C212yesmaximal, complemented
4C2×D4×D223C2124yesmaximal, direct product factor
5C22×C4×D223C211yesmaximal, characteristic, complemented
6C22×D4×C223C211yesmaximal, characteristic, complemented
7C23×D223—216no—
8C23×D223C2211yescharacteristic
9C23×D223C2212yescomplemented
10C23×D223C22124yescomplemented
11C2×D892C22112yescomplemented
12C2×C22⋊D223C22124yescomplemented
13D4×D223C22164yesdirect product factor
14C22×Dic223C2211yescharacteristic, complemented
15C2×C4×D223C22112yescomplemented
16C24×C223C2212yescomplemented
17C2×D4×C223C22112yescomplemented
18C22×C4×C223C2211yescharacteristic, complemented
19C22×D223—28no—
20C22×D223—296no—
21C22×D223D418yesdirect product factor
22C22×D223C2316yes—
23C22×D223C23132yescomplemented
24C22×D223C23112yescomplemented
25D892C23116yescomplemented
26C22⋊D223C23132yescomplemented
27C2×Dic223C2316yescomplemented
28C4×D223C23116yescomplemented
29C23×C223—28no—
30C23×C223C2311yescharacteristic
31C23×C223C23112yescomplemented
32D4×C223C23116yescomplemented
33C2×C4×C223C2316yescomplemented
34C22×C223—224no—
35C22×C223C2×D414yescomplemented
36C22×C223C2413yes—
37C22×C223C2418yescomplemented
38C2×D223—224no—
39C2×D223—264no—
40C2×D223C2×D4124yesdirect product factor
41C2×D223C2414yes—
42C2×D223C2418yescomplemented
43C4×C223C2414yescomplemented
44Dic223C2414yescomplemented
45C2×C223—28no—
46C2×C223C22×D416yescomplemented
47C2×C223C2511yescharacteristic
48D223—28no—
49D223C22×D418yesdirect product factor
50C223C23×D411yescharacteristic, complemented, Sylow
51C23×D4—2231nomaximal, Sylow
52C25—2232no—
53C22×D4—2232no—
54C22×D4—22324no—
55C22×D4—2231no—
56C22×D4D22311yescharacteristic, direct product factor
57C23×C4—2231no—
58C24—44616no—
59C24—2232no—
60C24—22324no—
61C24—2231no—
62C24C2×D22312yescomplemented
63C2×D4—22324no—
64C2×D4—22364no—
65C2×D4—22312no—
66C2×D4C2×D223112yesdirect product factor
67C22×C4—2231no—
68C22×C4—22312no—
69C22×C4C2×D22311yescharacteristic, complemented
70C23—28no—
71C23—44696no—
72C23—4468no—
73C23—22312no—
74C23—22332no—
75C23—2238no—
76C23—2236no—
77C23C22×D22311yescharacteristic
78C23C22×D223112yescomplemented
79D4—22332no—
80D4—22316no—
81D4C22×D223116yesdirect product factor
82C2×C4—2236no—
83C2×C4—22316no—
84C2×C4C22×D22316yescomplemented
85C22—224no—
86C22—44664no—
87C22—44624no—
88C22—2238no—
89C22—22324no—
90C22—2234no—
91C22D4×D22314yesdirect product factor
92C22C23×D22313yes—
93C22C23×D22318yescomplemented
94C4—2234no—
95C4C23×D22314yescomplemented
96C2—28no—
97C2—4468no—
98C2—2238no—
99C2C2×D4×D22316yesdirect product factor
100C2C24×D22311yescharacteristic
subgroupG/H
centerC23C22×D223
commutator, cosocleC2×C223C25
FrattiniC2C24×D223
FittingC22×D4×C223C2
socleC23×C223C23
hypercenterC22×D4D223
hypocenterC223C23×D4
LCSG ▷ C2×C223 ▷ C223
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D223C2semidirect
2. C22×D892C2semidirect
3. C22×C22⋊D223C2semidirect
4. C2×D4×D223C2direct (N × H)
5. C22×C4×D223C2semidirect
6. C22×D4×C223C2semidirect
9. C23×D223C22semidirect
10. C23×D223C22semidirect
11. C2×D892C22semidirect
12. C2×C22⋊D223C22semidirect
13. D4×D223C22direct (N × H)
14. C22×Dic223C22semidirect
15. C2×C4×D223C22semidirect
16. C24×C223C22semidirect
17. C2×D4×C223C22semidirect
18. C22×C4×C223C22semidirect
21. C22×D223D4direct (N × H)
23. C22×D223C23semidirect
24. C22×D223C23semidirect
25. D892C23semidirect
26. C22⋊D223C23semidirect
27. C2×Dic223C23semidirect
28. C4×D223C23semidirect
31. C23×C223C23semidirect
32. D4×C223C23semidirect
33. C2×C4×C223C23semidirect
35. C22×C223C2×D4semidirect
37. C22×C223C24semidirect
40. C2×D223C2×D4direct (N × H)
42. C2×D223C24semidirect
43. C4×C223C24semidirect
44. Dic223C24semidirect
46. C2×C223C22×D4semidirect
49. D223C22×D4direct (N × H)
50. C223C23×D4semidirect
56. C22×D4D223direct (N × H)
62. C24C2×D223semidirect
66. C2×D4C2×D223direct (N × H)
69. C22×C4C2×D223semidirect
78. C23C22×D223semidirect
81. D4C22×D223direct (N × H)
84. C2×C4C22×D223semidirect
91. C22D4×D223direct (N × H)
93. C22C23×D223semidirect
95. C4C23×D223semidirect
99. C2C2×D4×D223direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D2232
C22×D8922
C22×C22⋊D2232
C2×D4×D2232
C22×C4×D2232
C22×D4×C2232
C23×D4223