Finite Group Databasebeta

← C2×#41×D353 #36378612

Subgroups — C2×#41×D353 #36378612

Order 22592.

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×#19150738C211yesmaximal, characteristic, complemented
2C2×#19150737C213yesmaximal, complemented
3C2×#19150736C213yesmaximal, complemented
4#41×D353C2116yesmaximal, direct product factor
5C2×Q8×D353C211yesmaximal, characteristic, complemented
6C2×D4×D353C213yesmaximal, complemented
7C22×C4×D353C213yesmaximal, complemented
8C2×#41×C353C211yesmaximal, characteristic, complemented
9C23×D353C2213yes—
10#19150738C2218yescomplemented
11#19150737C22124yescomplemented
12#19150736C22124yescomplemented
13C2×Dic706C2213yescomplemented
14Q8×D353C2218yescomplemented
15C2×D1412C2213yescomplemented
16C2×C22⋊D353C2216yescomplemented
17D4×D353C22124yescomplemented
18C22×Dic353C2213yescomplemented
19C2×C4×D353C2211yescharacteristic
20C2×C4×D353C2213yes—
21C2×C4×D353C2213yescomplemented
22C2×C4×D353C2213yescomplemented
23C2×C4×D353C22124yescomplemented
24#41×C353C2218yescomplemented
25C2×Q8×C353C2211yescharacteristic, complemented
26C2×D4×C353C2213yescomplemented
27C22×C4×C353C2213yescomplemented
28C22×D353—212no—
29C22×D353C23112yes—
30C22×D353C2313yes—
31C22×D353C2311yescharacteristic
32Dic706C23112yescomplemented
33D1412C23112yescomplemented
34C22⋊D353C23124yescomplemented
35C2×Dic353C2311yescharacteristic
36C2×Dic353C2313yes—
37C2×Dic353C23112yescomplemented
38C4×D353C2314yes—
39C4×D353C23112yes—
40C4×D353C23112yescomplemented
41C4×D353C23112yescomplemented
42C23×C353C2313yes—
43Q8×C353C2314yescomplemented
44D4×C353C23112yescomplemented
45C2×C4×C353C2313yes—
46C2×C4×C353C2311yescharacteristic
47C2×C4×C353C23112yescomplemented
48C22×C353—26no—
49C22×C353C2416yes—
50C22×C353C2411yescharacteristic
51C2×D353—26no—
52C2×D353—224no—
53C2×D353#4114yesdirect product factor
54C2×D353C2416yes—
55C2×D353C2412yes—
56C4×C353C2412yes—
57C4×C353C2416yes—
58Dic353C2412yes—
59Dic353C2416yes—
60C2×C353—26no—
61C2×C353C2×#4112yescomplemented
62C2×C353C2511yescharacteristic
63D353—26no—
64D353C2×#4114yesdirect product factor
65C353C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—3531nomaximal, Sylow
67C2×#41—35316no—
68C2×#41—3531no—
69C2×#41—3533no—
70C2×#41—3533no—
71C2×#41D35311yescharacteristic, direct product factor
72C22×Q8—3531no—
73C22×D4—3533no—
74C23×C4—3533no—
75C24—3533no—
76#41—3538no—
77#41—35324no—
78#41—35324no—
79#41C2×D35318yesdirect product factor
80C2×Q8—3538no—
81C2×Q8—3533no—
82C2×Q8C2×D35311yescharacteristic, complemented
83C2×D4—3536no—
84C2×D4—35324no—
85C2×D4—3533no—
86C2×D4C2×D35313yescomplemented
87C22×C4—3533no—
88C22×C4—3533no—
89C22×C4—3533no—
90C22×C4—3531no—
91C22×C4—3533no—
92C22×C4—35324no—
93C22×C4C2×D35313yescomplemented
94C23—3531no—
95C23—35312no—
96C23—3533no—
97C23—70612no—
98C23C22×D35313yes—
99Q8—35312no—
100Q8C22×D35314yescomplemented
101D4—35324no—
102D4—35312no—
103D4C22×D353112yescomplemented
104C2×C4—3531no—
105C2×C4—3533no—
106C2×C4—35312no—
107C2×C4—3534no—
108C2×C4—35312no—
109C2×C4—35312no—
110C2×C4—35312no—
111C2×C4C22×D35313yes—
112C2×C4C22×D35311yescharacteristic
113C2×C4C22×D353112yescomplemented
114C22—26no—
115C22—3534no—
116C22—3532no—
117C22—3536no—
118C22—70624no—
119C22—7066no—
120C22C23×D35316yes—
121C22C23×D35311yescharacteristic
122C4—3532no—
123C4—3536no—
124C4C23×D35312yes—
125C4C23×D35316yes—
126C2—26no—
127C2—3534no—
128C2—7066no—
129C2#41×D35312yesdirect product factor
130C2C24×D35311yescharacteristic
subgroupG/H
centerC2×C4C22×D353
commutator, cosocleC2×C353C25
FrattiniC2C24×D353
FittingC2×#41×C353C2
socleC22×C353C24
hypercenterC2×#41D353
hypocenterC353C22×#41
LCSG ▷ C2×C353 ▷ C353
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#19150738C2semidirect
2. C2×#19150737C2semidirect
3. C2×#19150736C2semidirect
4. #41×D353C2direct (N × H)
5. C2×Q8×D353C2semidirect
6. C2×D4×D353C2semidirect
7. C22×C4×D353C2semidirect
8. C2×#41×C353C2semidirect
10. #19150738C22semidirect
11. #19150737C22semidirect
12. #19150736C22semidirect
13. C2×Dic706C22semidirect
14. Q8×D353C22semidirect
15. C2×D1412C22semidirect
16. C2×C22⋊D353C22semidirect
17. D4×D353C22semidirect
18. C22×Dic353C22semidirect
21. C2×C4×D353C22semidirect
22. C2×C4×D353C22semidirect
23. C2×C4×D353C22semidirect
24. #41×C353C22semidirect
25. C2×Q8×C353C22semidirect
26. C2×D4×C353C22semidirect
27. C22×C4×C353C22semidirect
32. Dic706C23semidirect
33. D1412C23semidirect
34. C22⋊D353C23semidirect
37. C2×Dic353C23semidirect
40. C4×D353C23semidirect
41. C4×D353C23semidirect
43. Q8×C353C23semidirect
44. D4×C353C23semidirect
47. C2×C4×C353C23semidirect
53. C2×D353#41direct (N × H)
61. C2×C353C2×#41semidirect
64. D353C2×#41direct (N × H)
65. C353C22×#41semidirect
71. C2×#41D353direct (N × H)
79. #41C2×D353direct (N × H)
82. C2×Q8C2×D353semidirect
86. C2×D4C2×D353semidirect
93. C22×C4C2×D353semidirect
100. Q8C22×D353semidirect
103. D4C22×D353semidirect
113. C2×C4C22×D353semidirect
129. C2#41×D353direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191507382
C2×#191507372
C2×#191507362
#41×D3532
C2×Q8×D3532
C2×D4×D3532
C22×C4×D3532
C2×#41×C3532
C22×#41353