Finite Group Databasebeta

← C2×#41×D383 #37589176

Subgroups — C2×#41×D383 #37589176

Order 24512.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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
1C2×#20259458C211yesmaximal, characteristic, complemented
2C2×#20259457C213yesmaximal, complemented
3C2×#20259456C213yesmaximal, complemented
4#41×D383C2116yesmaximal, direct product factor
5C2×Q8×D383C211yesmaximal, characteristic, complemented
6C2×D4×D383C213yesmaximal, complemented
7C22×C4×D383C213yesmaximal, complemented
8C2×#41×C383C211yesmaximal, characteristic, complemented
9C23×D383C2213yes—
10#20259458C2218yescomplemented
11#20259457C22124yescomplemented
12#20259456C22124yescomplemented
13C2×Dic766C2213yescomplemented
14Q8×D383C2218yescomplemented
15C2×D1532C2213yescomplemented
16C2×C22⋊D383C2216yescomplemented
17D4×D383C22124yescomplemented
18C22×Dic383C2213yescomplemented
19C2×C4×D383C2211yescharacteristic
20C2×C4×D383C2213yes—
21C2×C4×D383C2213yescomplemented
22C2×C4×D383C2213yescomplemented
23C2×C4×D383C22124yescomplemented
24#41×C383C2218yescomplemented
25C2×Q8×C383C2211yescharacteristic, complemented
26C2×D4×C383C2213yescomplemented
27C22×C4×C383C2213yescomplemented
28C22×D383—212no—
29C22×D383C23112yes—
30C22×D383C2313yes—
31C22×D383C2311yescharacteristic
32Dic766C23112yescomplemented
33D1532C23112yescomplemented
34C22⋊D383C23124yescomplemented
35C2×Dic383C2311yescharacteristic
36C2×Dic383C2313yes—
37C2×Dic383C23112yescomplemented
38C4×D383C2314yes—
39C4×D383C23112yes—
40C4×D383C23112yescomplemented
41C4×D383C23112yescomplemented
42C23×C383C2313yes—
43Q8×C383C2314yescomplemented
44D4×C383C23112yescomplemented
45C2×C4×C383C2313yes—
46C2×C4×C383C2311yescharacteristic
47C2×C4×C383C23112yescomplemented
48C22×C383—26no—
49C22×C383C2416yes—
50C22×C383C2411yescharacteristic
51C2×D383—26no—
52C2×D383—224no—
53C2×D383#4114yesdirect product factor
54C2×D383C2416yes—
55C2×D383C2412yes—
56C4×C383C2412yes—
57C4×C383C2416yes—
58Dic383C2412yes—
59Dic383C2416yes—
60C2×C383—26no—
61C2×C383C2×#4112yescomplemented
62C2×C383C2511yescharacteristic
63D383—26no—
64D383C2×#4114yesdirect product factor
65C383C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—3831nomaximal, Sylow
67C2×#41—38316no—
68C2×#41—3831no—
69C2×#41—3833no—
70C2×#41—3833no—
71C2×#41D38311yescharacteristic, direct product factor
72C22×Q8—3831no—
73C22×D4—3833no—
74C23×C4—3833no—
75C24—3833no—
76#41—3838no—
77#41—38324no—
78#41—38324no—
79#41C2×D38318yesdirect product factor
80C2×Q8—3838no—
81C2×Q8—3833no—
82C2×Q8C2×D38311yescharacteristic, complemented
83C2×D4—3836no—
84C2×D4—38324no—
85C2×D4—3833no—
86C2×D4C2×D38313yescomplemented
87C22×C4—3833no—
88C22×C4—3833no—
89C22×C4—3833no—
90C22×C4—3831no—
91C22×C4—3833no—
92C22×C4—38324no—
93C22×C4C2×D38313yescomplemented
94C23—3831no—
95C23—38312no—
96C23—3833no—
97C23—76612no—
98C23C22×D38313yes—
99Q8—38312no—
100Q8C22×D38314yescomplemented
101D4—38324no—
102D4—38312no—
103D4C22×D383112yescomplemented
104C2×C4—3831no—
105C2×C4—3833no—
106C2×C4—38312no—
107C2×C4—3834no—
108C2×C4—38312no—
109C2×C4—38312no—
110C2×C4—38312no—
111C2×C4C22×D38313yes—
112C2×C4C22×D38311yescharacteristic
113C2×C4C22×D383112yescomplemented
114C22—26no—
115C22—3834no—
116C22—3832no—
117C22—3836no—
118C22—76624no—
119C22—7666no—
120C22C23×D38316yes—
121C22C23×D38311yescharacteristic
122C4—3832no—
123C4—3836no—
124C4C23×D38312yes—
125C4C23×D38316yes—
126C2—26no—
127C2—3834no—
128C2—7666no—
129C2#41×D38312yesdirect product factor
130C2C24×D38311yescharacteristic
subgroupG/H
centerC2×C4C22×D383
commutator, cosocleC2×C383C25
FrattiniC2C24×D383
FittingC2×#41×C383C2
socleC22×C383C24
hypercenterC2×#41D383
hypocenterC383C22×#41
LCSG ▷ C2×C383 ▷ C383
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20259458C2semidirect
2. C2×#20259457C2semidirect
3. C2×#20259456C2semidirect
4. #41×D383C2direct (N × H)
5. C2×Q8×D383C2semidirect
6. C2×D4×D383C2semidirect
7. C22×C4×D383C2semidirect
8. C2×#41×C383C2semidirect
10. #20259458C22semidirect
11. #20259457C22semidirect
12. #20259456C22semidirect
13. C2×Dic766C22semidirect
14. Q8×D383C22semidirect
15. C2×D1532C22semidirect
16. C2×C22⋊D383C22semidirect
17. D4×D383C22semidirect
18. C22×Dic383C22semidirect
21. C2×C4×D383C22semidirect
22. C2×C4×D383C22semidirect
23. C2×C4×D383C22semidirect
24. #41×C383C22semidirect
25. C2×Q8×C383C22semidirect
26. C2×D4×C383C22semidirect
27. C22×C4×C383C22semidirect
32. Dic766C23semidirect
33. D1532C23semidirect
34. C22⋊D383C23semidirect
37. C2×Dic383C23semidirect
40. C4×D383C23semidirect
41. C4×D383C23semidirect
43. Q8×C383C23semidirect
44. D4×C383C23semidirect
47. C2×C4×C383C23semidirect
53. C2×D383#41direct (N × H)
61. C2×C383C2×#41semidirect
64. D383C2×#41direct (N × H)
65. C383C22×#41semidirect
71. C2×#41D383direct (N × H)
79. #41C2×D383direct (N × H)
82. C2×Q8C2×D383semidirect
86. C2×D4C2×D383semidirect
93. C22×C4C2×D383semidirect
100. Q8C22×D383semidirect
103. D4C22×D383semidirect
113. C2×C4C22×D383semidirect
129. C2#41×D383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202594582
C2×#202594572
C2×#202594562
#41×D3832
C2×Q8×D3832
C2×D4×D3832
C22×C4×D3832
C2×#41×C3832
C22×#41383