Finite Group Databasebeta

← C2×#41×D491 #44537550

Subgroups — C2×#41×D491 #44537550

Order 31424.

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×#21463329C211yesmaximal, characteristic, complemented
2C2×#21463328C213yesmaximal, complemented
3C2×#21463327C213yesmaximal, complemented
4#41×D491C2116yesmaximal, direct product factor
5C2×Q8×D491C211yesmaximal, characteristic, complemented
6C2×D4×D491C213yesmaximal, complemented
7C22×C4×D491C213yesmaximal, complemented
8C2×#41×C491C211yesmaximal, characteristic, complemented
9C23×D491C2213yes—
10#21463329C2218yescomplemented
11#21463328C22124yescomplemented
12#21463327C22124yescomplemented
13C2×Dic982C2213yescomplemented
14Q8×D491C2218yescomplemented
15C2×D1964C2213yescomplemented
16C2×C22⋊D491C2216yescomplemented
17D4×D491C22124yescomplemented
18C22×Dic491C2213yescomplemented
19C2×C4×D491C2211yescharacteristic
20C2×C4×D491C2213yes—
21C2×C4×D491C2213yescomplemented
22C2×C4×D491C2213yescomplemented
23C2×C4×D491C22124yescomplemented
24#41×C491C2218yescomplemented
25C2×Q8×C491C2211yescharacteristic, complemented
26C2×D4×C491C2213yescomplemented
27C22×C4×C491C2213yescomplemented
28C22×D491—212no—
29C22×D491C23112yes—
30C22×D491C2313yes—
31C22×D491C2311yescharacteristic
32Dic982C23112yescomplemented
33D1964C23112yescomplemented
34C22⋊D491C23124yescomplemented
35C2×Dic491C2311yescharacteristic
36C2×Dic491C2313yes—
37C2×Dic491C23112yescomplemented
38C4×D491C2314yes—
39C4×D491C23112yes—
40C4×D491C23112yescomplemented
41C4×D491C23112yescomplemented
42C23×C491C2313yes—
43Q8×C491C2314yescomplemented
44D4×C491C23112yescomplemented
45C2×C4×C491C2313yes—
46C2×C4×C491C2311yescharacteristic
47C2×C4×C491C23112yescomplemented
48C22×C491—26no—
49C22×C491C2416yes—
50C22×C491C2411yescharacteristic
51C2×D491—26no—
52C2×D491—224no—
53C2×D491#4114yesdirect product factor
54C2×D491C2416yes—
55C2×D491C2412yes—
56C4×C491C2412yes—
57C4×C491C2416yes—
58Dic491C2412yes—
59Dic491C2416yes—
60C2×C491—26no—
61C2×C491C2×#4112yescomplemented
62C2×C491C2511yescharacteristic
63D491—26no—
64D491C2×#4114yesdirect product factor
65C491C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—4911nomaximal, Sylow
67C2×#41—49116no—
68C2×#41—4911no—
69C2×#41—4913no—
70C2×#41—4913no—
71C2×#41D49111yescharacteristic, direct product factor
72C22×Q8—4911no—
73C22×D4—4913no—
74C23×C4—4913no—
75C24—4913no—
76#41—4918no—
77#41—49124no—
78#41—49124no—
79#41C2×D49118yesdirect product factor
80C2×Q8—4918no—
81C2×Q8—4913no—
82C2×Q8C2×D49111yescharacteristic, complemented
83C2×D4—4916no—
84C2×D4—49124no—
85C2×D4—4913no—
86C2×D4C2×D49113yescomplemented
87C22×C4—4913no—
88C22×C4—4913no—
89C22×C4—4913no—
90C22×C4—4911no—
91C22×C4—4913no—
92C22×C4—49124no—
93C22×C4C2×D49113yescomplemented
94C23—98212no—
95C23—49112no—
96C23—4913no—
97C23—4911no—
98C23C22×D49113yes—
99Q8—49112no—
100Q8C22×D49114yescomplemented
101D4—49124no—
102D4—49112no—
103D4C22×D491112yescomplemented
104C2×C4—4911no—
105C2×C4—4913no—
106C2×C4—49112no—
107C2×C4—4914no—
108C2×C4—49112no—
109C2×C4—49112no—
110C2×C4—49112no—
111C2×C4C22×D49113yes—
112C2×C4C22×D49111yescharacteristic
113C2×C4C22×D491112yescomplemented
114C22—26no—
115C22—98224no—
116C22—9826no—
117C22—4916no—
118C22—4914no—
119C22—4912no—
120C22C23×D49116yes—
121C22C23×D49111yescharacteristic
122C4—4912no—
123C4—4916no—
124C4C23×D49112yes—
125C4C23×D49116yes—
126C2—26no—
127C2—9826no—
128C2—4914no—
129C2#41×D49112yesdirect product factor
130C2C24×D49111yescharacteristic
subgroupG/H
centerC2×C4C22×D491
commutator, cosocleC2×C491C25
FrattiniC2C24×D491
FittingC2×#41×C491C2
socleC22×C491C24
hypercenterC2×#41D491
hypocenterC491C22×#41
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#21463329C2semidirect
2. C2×#21463328C2semidirect
3. C2×#21463327C2semidirect
4. #41×D491C2direct (N × H)
5. C2×Q8×D491C2semidirect
6. C2×D4×D491C2semidirect
7. C22×C4×D491C2semidirect
8. C2×#41×C491C2semidirect
10. #21463329C22semidirect
11. #21463328C22semidirect
12. #21463327C22semidirect
13. C2×Dic982C22semidirect
14. Q8×D491C22semidirect
15. C2×D1964C22semidirect
16. C2×C22⋊D491C22semidirect
17. D4×D491C22semidirect
18. C22×Dic491C22semidirect
21. C2×C4×D491C22semidirect
22. C2×C4×D491C22semidirect
23. C2×C4×D491C22semidirect
24. #41×C491C22semidirect
25. C2×Q8×C491C22semidirect
26. C2×D4×C491C22semidirect
27. C22×C4×C491C22semidirect
32. Dic982C23semidirect
33. D1964C23semidirect
34. C22⋊D491C23semidirect
37. C2×Dic491C23semidirect
40. C4×D491C23semidirect
41. C4×D491C23semidirect
43. Q8×C491C23semidirect
44. D4×C491C23semidirect
47. C2×C4×C491C23semidirect
53. C2×D491#41direct (N × H)
61. C2×C491C2×#41semidirect
64. D491C2×#41direct (N × H)
65. C491C22×#41semidirect
71. C2×#41D491direct (N × H)
79. #41C2×D491direct (N × H)
82. C2×Q8C2×D491semidirect
86. C2×D4C2×D491semidirect
93. C22×C4C2×D491semidirect
100. Q8C22×D491semidirect
103. D4C22×D491semidirect
113. C2×C4C22×D491semidirect
129. C2#41×D491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#214633292
C2×#214633282
C2×#214633272
#41×D4912
C2×Q8×D4912
C2×D4×D4912
C22×C4×D4912
C2×#41×C4912
C22×#41491