Finite Group Databasebeta

← C2×#27131376 #37566074

Subgroups — C2×#27131376 #37566074

Order 24256.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 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
1#27131376C2116yesmaximal, direct product factor
2C2×#20258606C212yesmaximal, complemented
3C2×#20258605C214yesmaximal, complemented
4C22×C22⋊D379C214yesmaximal, complemented
5C2×D4×D379C214yesmaximal, complemented
6C22×D4×C379C211yesmaximal, characteristic, complemented
7C23×D379C2214yescomplemented
8#20258606C22116yescomplemented
9#20258605C22132yescomplemented
10C2×Dic758C2212yescomplemented
11C2×D1516C2212yescomplemented
12C2×C22⋊D379C2218yescomplemented
13C2×C22⋊D379C2214yescomplemented
14C2×C22⋊D379C22132yescomplemented
15D4×D379C22132yescomplemented
16C22×Dic379C2214yescomplemented
17C2×C4×D379C2214yescomplemented
18C24×C379C2212yescomplemented
19C2×D4×C379C2214yescomplemented
20C2×D4×C379C2218yescomplemented
21C22×C4×C379C2211yescharacteristic, complemented
22C22×D379—48no—
23C22×D379C2314yes—
24C22×D379C23116yescomplemented
25Dic758C2318yescomplemented
26D1516C2318yescomplemented
27C22⋊D379C23132yescomplemented
28C22⋊D379C23116yescomplemented
29C2×Dic379C2314yes—
30C2×Dic379C23116yescomplemented
31C4×D379C23116yescomplemented
32C23×C379—44no—
33C23×C379C2311yescharacteristic
34C23×C379C2314yes—
35C23×C379C2318yescomplemented
36D4×C379C23116yescomplemented
37C2×C4×C379C2312yes—
38C2×C4×C379C2314yescomplemented
39C22×C379—22no—
40C22×C379—28no—
41C22×C379—48no—
42C22×C379C2412yes—
43C22×C379C2418yes—
44C22×C379C2411yescharacteristic
45C2×D379—28no—
46C2×D379—416no—
47C2×D379C2418yes—
48C4×C379C2414yes—
49Dic379C2418yes—
50C2×C379—28no—
51C2×C379—22no—
52C2×C379H(5,𝔽2)12yescomplemented
53C2×C379C2511yescharacteristic
54D379—28no—
55C379C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—3791nomaximal, Sylow
57H(5,𝔽2)—37916no—
58C2×#41—3794no—
59C2×#41—3792no—
60C22×D4—3794no—
61C22×D4—3794no—
62C22×D4D37911yescharacteristic, complemented
63C24—3794no—
64C24C2×D37912yescomplemented
65#41—37932no—
66#41—37916no—
67C2×Q8—3792no—
68C2×D4—3798no—
69C2×D4—3794no—
70C2×D4—37932no—
71C2×D4—37932no—
72C2×D4—3792no—
73C2×D4C2×D37914yescomplemented
74C2×D4C2×D37918yescomplemented
75C22×C4—3794no—
76C22×C4—3794no—
77C22×C4C2×D37911yescharacteristic, complemented
78C23—44no—
79C23—37916no—
80C23—3794no—
81C23—15168no—
82C23C22×D37914yes—
83C23C22×D37911yescharacteristic
84C23C22×D37918yescomplemented
85Q8—3798no—
86D4—37932no—
87D4—37916no—
88D4—3798no—
89D4C22×D379116yescomplemented
90C2×C4—37916no—
91C2×C4—3794no—
92C2×C4—37916no—
93C2×C4C22×D37912yes—
94C2×C4C22×D37914yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—3798no—
99C22—151616no—
100C22—7588no—
101C22C23×D37918yes—
102C22C23×D37912yes—
103C22C23×D37911yescharacteristic
104C4—3798no—
105C4C23×D37914yes—
106C2—22no—
107C2—28no—
108C2—7588no—
109C2#2713137612yesdirect product factor
110C2C24×D37911yescharacteristic
subgroupG/H
centerC22C23×D379
commutator, cosocleC2×C379C25
FrattiniC2C24×D379
FittingC22×D4×C379C2
socleC22×C379C24
hypercenterC22×D4D379
hypocenterC379C2×H(5,𝔽2)
LCSG ▷ C2×C379 ▷ C379
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #27131376C2direct (N × H)
2. C2×#20258606C2semidirect
3. C2×#20258605C2semidirect
4. C22×C22⋊D379C2semidirect
5. C2×D4×D379C2semidirect
6. C22×D4×C379C2semidirect
7. C23×D379C22semidirect
8. #20258606C22semidirect
9. #20258605C22semidirect
10. C2×Dic758C22semidirect
11. C2×D1516C22semidirect
12. C2×C22⋊D379C22semidirect
13. C2×C22⋊D379C22semidirect
14. C2×C22⋊D379C22semidirect
15. D4×D379C22semidirect
16. C22×Dic379C22semidirect
17. C2×C4×D379C22semidirect
18. C24×C379C22semidirect
19. C2×D4×C379C22semidirect
20. C2×D4×C379C22semidirect
21. C22×C4×C379C22semidirect
24. C22×D379C23semidirect
25. Dic758C23semidirect
26. D1516C23semidirect
27. C22⋊D379C23semidirect
28. C22⋊D379C23semidirect
30. C2×Dic379C23semidirect
31. C4×D379C23semidirect
35. C23×C379C23semidirect
36. D4×C379C23semidirect
38. C2×C4×C379C23semidirect
52. C2×C379H(5,𝔽2)semidirect
55. C379C2×H(5,𝔽2)semidirect
62. C22×D4D379semidirect
64. C24C2×D379semidirect
73. C2×D4C2×D379semidirect
74. C2×D4C2×D379semidirect
77. C22×C4C2×D379semidirect
84. C23C22×D379semidirect
89. D4C22×D379semidirect
94. C2×C4C22×D379semidirect
109. C2#27131376direct (N × H)

Maximal subgroups

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

subgroupindex
#271313762
C2×#202586062
C2×#202586052
C22×C22⋊D3792
C2×D4×D3792
C22×D4×C3792
C2×H(5,𝔽2)379