Finite Group Databasebeta

← C2×#27131377 #37566075

Subgroups — C2×#27131377 #37566075

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#27131377C2116yesmaximal, direct product factor
2C2×#20258607C212yesmaximal, complemented
3C2×#20258606C213yesmaximal, complemented
4C22×D1516C213yesmaximal, complemented
5C2×D4×D379C216yesmaximal, complemented
6C2×#41×C379C211yesmaximal, characteristic, complemented
7C23×D379C2216yescomplemented
8#20258607C22116yescomplemented
9#20258606C22124yescomplemented
10C2×Dic758C2211yescharacteristic, complemented
11C2×D1516C2216yescomplemented
12C2×D1516C2213yescomplemented
13C2×D1516C22124yescomplemented
14C2×C22⋊D379C2216yescomplemented
15D4×D379C22148yescomplemented
16C2×C4×D379C2216yescomplemented
17#41×C379C2218yescomplemented
18C2×Q8×C379C2211yescharacteristic, complemented
19C2×D4×C379C2213yescomplemented
20C22×C4×C379C2213yescomplemented
21C22×D379—412no—
22C22×D379C2316yes—
23C22×D379C23124yescomplemented
24Dic758C2314yescomplemented
25D1516C23124yescomplemented
26D1516C23112yescomplemented
27C22⋊D379C23124yescomplemented
28C2×Dic379C2312yes—
29C4×D379C23124yescomplemented
30C23×C379C2313yes—
31Q8×C379C2314yescomplemented
32D4×C379C23112yescomplemented
33C2×C4×C379C2311yescharacteristic
34C2×C4×C379C2313yes—
35C2×C4×C379C23112yescomplemented
36C22×C379—26no—
37C22×C379C2416yes—
38C22×C379C2411yescharacteristic
39C2×D379—212no—
40C2×D379—424no—
41C2×D379C24112yes—
42C4×C379C2412yes—
43C4×C379C2416yes—
44Dic379C2414yes—
45C2×C379—26no—
46C2×C379H(5,𝔽2)12yescomplemented
47C2×C379C2511yescharacteristic
48D379—212no—
49C379C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—3791nomaximal, Sylow
51H(5,𝔽2)—37916no—
52C2×#41—3792no—
53C2×#41—3793no—
54C2×#41D37911yescharacteristic, complemented
55C22×D4—3796no—
56C22×D4—3793no—
57C24—3796no—
58#41—37916no—
59#41—37924no—
60#41C2×D37918yescomplemented
61C2×Q8—3791no—
62C2×Q8C2×D37911yescharacteristic, complemented
63C2×D4—3796no—
64C2×D4—37948no—
65C2×D4—3796no—
66C2×D4—3793no—
67C2×D4—37924no—
68C2×D4C2×D37913yescomplemented
69C22×C4—3796no—
70C22×C4C2×D37913yescomplemented
71C23—37924no—
72C23—3796no—
73C23—151612no—
74C23C22×D37913yes—
75Q8—3794no—
76Q8C22×D37914yescomplemented
77D4—37924no—
78D4—37924no—
79D4—37912no—
80D4C22×D379112yescomplemented
81C2×C4—3792no—
82C2×C4—37924no—
83C2×C4C22×D37913yes—
84C2×C4C22×D37911yescharacteristic
85C2×C4C22×D379112yescomplemented
86C22—26no—
87C22—37912no—
88C22—151624no—
89C22—75812no—
90C22C23×D37916yes—
91C22C23×D37911yescharacteristic
92C4—3794no—
93C4C23×D37916yes—
94C4C23×D37912yes—
95C2—26no—
96C2—75812no—
97C2#2713137712yesdirect product factor
98C2C24×D37911yescharacteristic
subgroupG/H
centerC22C23×D379
commutator, cosocleC2×C379C25
FrattiniC2C24×D379
FittingC2×#41×C379C2
socleC22×C379C24
hypercenterC2×#41D379
hypocenterC379C2×H(5,𝔽2)
LCSG ▷ C2×C379 ▷ C379
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #27131377C2direct (N × H)
2. C2×#20258607C2semidirect
3. C2×#20258606C2semidirect
4. C22×D1516C2semidirect
5. C2×D4×D379C2semidirect
6. C2×#41×C379C2semidirect
7. C23×D379C22semidirect
8. #20258607C22semidirect
9. #20258606C22semidirect
10. C2×Dic758C22semidirect
11. C2×D1516C22semidirect
12. C2×D1516C22semidirect
13. C2×D1516C22semidirect
14. C2×C22⋊D379C22semidirect
15. D4×D379C22semidirect
16. C2×C4×D379C22semidirect
17. #41×C379C22semidirect
18. C2×Q8×C379C22semidirect
19. C2×D4×C379C22semidirect
20. C22×C4×C379C22semidirect
23. C22×D379C23semidirect
24. Dic758C23semidirect
25. D1516C23semidirect
26. D1516C23semidirect
27. C22⋊D379C23semidirect
29. C4×D379C23semidirect
31. Q8×C379C23semidirect
32. D4×C379C23semidirect
35. C2×C4×C379C23semidirect
46. C2×C379H(5,𝔽2)semidirect
49. C379C2×H(5,𝔽2)semidirect
54. C2×#41D379semidirect
60. #41C2×D379semidirect
62. C2×Q8C2×D379semidirect
68. C2×D4C2×D379semidirect
70. C22×C4C2×D379semidirect
76. Q8C22×D379semidirect
80. D4C22×D379semidirect
85. C2×C4C22×D379semidirect
97. C2#27131377direct (N × H)

Maximal subgroups

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

subgroupindex
#271313772
C2×#202586072
C2×#202586062
C22×D15162
C2×D4×D3792
C2×#41×C3792
C2×H(5,𝔽2)379