Finite Group Databasebeta

← C2×#41×D373 #37560247

Subgroups — C2×#41×D373 #37560247

Order 23872.

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×#20238611C211yesmaximal, characteristic, complemented
2C2×#20238610C213yesmaximal, complemented
3C2×#20238609C213yesmaximal, complemented
4#41×D373C2116yesmaximal, direct product factor
5C2×Q8×D373C211yesmaximal, characteristic, complemented
6C2×D4×D373C213yesmaximal, complemented
7C22×C4×D373C213yesmaximal, complemented
8C2×#41×C373C211yesmaximal, characteristic, complemented
9C23×D373C2213yes—
10#20238611C2218yescomplemented
11#20238610C22124yescomplemented
12#20238609C22124yescomplemented
13C2×Dic746C2213yescomplemented
14Q8×D373C2218yescomplemented
15C2×D1492C2213yescomplemented
16C2×C22⋊D373C2216yescomplemented
17D4×D373C22124yescomplemented
18C22×Dic373C2213yescomplemented
19C2×C4×D373C2211yescharacteristic
20C2×C4×D373C2213yes—
21C2×C4×D373C2213yescomplemented
22C2×C4×D373C2213yescomplemented
23C2×C4×D373C22124yescomplemented
24#41×C373C2218yescomplemented
25C2×Q8×C373C2211yescharacteristic, complemented
26C2×D4×C373C2213yescomplemented
27C22×C4×C373C2213yescomplemented
28C22×D373—212no—
29C22×D373C23112yes—
30C22×D373C2313yes—
31C22×D373C2311yescharacteristic
32Dic746C23112yescomplemented
33D1492C23112yescomplemented
34C22⋊D373C23124yescomplemented
35C2×Dic373C2311yescharacteristic
36C2×Dic373C2313yes—
37C2×Dic373C23112yescomplemented
38C4×D373C2314yes—
39C4×D373C23112yes—
40C4×D373C23112yescomplemented
41C4×D373C23112yescomplemented
42C23×C373C2313yes—
43Q8×C373C2314yescomplemented
44D4×C373C23112yescomplemented
45C2×C4×C373C2313yes—
46C2×C4×C373C2311yescharacteristic
47C2×C4×C373C23112yescomplemented
48C22×C373—26no—
49C22×C373C2416yes—
50C22×C373C2411yescharacteristic
51C2×D373—26no—
52C2×D373—224no—
53C2×D373#4114yesdirect product factor
54C2×D373C2416yes—
55C2×D373C2412yes—
56C4×C373C2412yes—
57C4×C373C2416yes—
58Dic373C2412yes—
59Dic373C2416yes—
60C2×C373—26no—
61C2×C373C2×#4112yescomplemented
62C2×C373C2511yescharacteristic
63D373—26no—
64D373C2×#4114yesdirect product factor
65C373C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—3731nomaximal, Sylow
67C2×#41—37316no—
68C2×#41—3731no—
69C2×#41—3733no—
70C2×#41—3733no—
71C2×#41D37311yescharacteristic, direct product factor
72C22×Q8—3731no—
73C22×D4—3733no—
74C23×C4—3733no—
75C24—3733no—
76#41—3738no—
77#41—37324no—
78#41—37324no—
79#41C2×D37318yesdirect product factor
80C2×Q8—3738no—
81C2×Q8—3733no—
82C2×Q8C2×D37311yescharacteristic, complemented
83C2×D4—3736no—
84C2×D4—37324no—
85C2×D4—3733no—
86C2×D4C2×D37313yescomplemented
87C22×C4—3733no—
88C22×C4—3733no—
89C22×C4—3733no—
90C22×C4—3731no—
91C22×C4—3733no—
92C22×C4—37324no—
93C22×C4C2×D37313yescomplemented
94C23—3731no—
95C23—37312no—
96C23—3733no—
97C23—74612no—
98C23C22×D37313yes—
99Q8—37312no—
100Q8C22×D37314yescomplemented
101D4—37324no—
102D4—37312no—
103D4C22×D373112yescomplemented
104C2×C4—3731no—
105C2×C4—3733no—
106C2×C4—37312no—
107C2×C4—3734no—
108C2×C4—37312no—
109C2×C4—37312no—
110C2×C4—37312no—
111C2×C4C22×D37313yes—
112C2×C4C22×D37311yescharacteristic
113C2×C4C22×D373112yescomplemented
114C22—26no—
115C22—3734no—
116C22—3732no—
117C22—3736no—
118C22—74624no—
119C22—7466no—
120C22C23×D37316yes—
121C22C23×D37311yescharacteristic
122C4—3732no—
123C4—3736no—
124C4C23×D37312yes—
125C4C23×D37316yes—
126C2—26no—
127C2—3734no—
128C2—7466no—
129C2#41×D37312yesdirect product factor
130C2C24×D37311yescharacteristic
subgroupG/H
centerC2×C4C22×D373
commutator, cosocleC2×C373C25
FrattiniC2C24×D373
FittingC2×#41×C373C2
socleC22×C373C24
hypercenterC2×#41D373
hypocenterC373C22×#41
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20238611C2semidirect
2. C2×#20238610C2semidirect
3. C2×#20238609C2semidirect
4. #41×D373C2direct (N × H)
5. C2×Q8×D373C2semidirect
6. C2×D4×D373C2semidirect
7. C22×C4×D373C2semidirect
8. C2×#41×C373C2semidirect
10. #20238611C22semidirect
11. #20238610C22semidirect
12. #20238609C22semidirect
13. C2×Dic746C22semidirect
14. Q8×D373C22semidirect
15. C2×D1492C22semidirect
16. C2×C22⋊D373C22semidirect
17. D4×D373C22semidirect
18. C22×Dic373C22semidirect
21. C2×C4×D373C22semidirect
22. C2×C4×D373C22semidirect
23. C2×C4×D373C22semidirect
24. #41×C373C22semidirect
25. C2×Q8×C373C22semidirect
26. C2×D4×C373C22semidirect
27. C22×C4×C373C22semidirect
32. Dic746C23semidirect
33. D1492C23semidirect
34. C22⋊D373C23semidirect
37. C2×Dic373C23semidirect
40. C4×D373C23semidirect
41. C4×D373C23semidirect
43. Q8×C373C23semidirect
44. D4×C373C23semidirect
47. C2×C4×C373C23semidirect
53. C2×D373#41direct (N × H)
61. C2×C373C2×#41semidirect
64. D373C2×#41direct (N × H)
65. C373C22×#41semidirect
71. C2×#41D373direct (N × H)
79. #41C2×D373direct (N × H)
82. C2×Q8C2×D373semidirect
86. C2×D4C2×D373semidirect
93. C22×C4C2×D373semidirect
100. Q8C22×D373semidirect
103. D4C22×D373semidirect
113. C2×C4C22×D373semidirect
129. C2#41×D373direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202386112
C2×#202386102
C2×#202386092
#41×D3732
C2×Q8×D3732
C2×D4×D3732
C22×C4×D3732
C2×#41×C3732
C22×#41373