Finite Group Databasebeta

← C2×#41×D241 #29508542

Subgroups — C2×#41×D241 #29508542

Order 15424.

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×#16838771C211yesmaximal, characteristic, complemented
2C2×#16838770C213yesmaximal, complemented
3C2×#16838769C213yesmaximal, complemented
4#41×D241C2116yesmaximal, direct product factor
5C2×Q8×D241C211yesmaximal, characteristic, complemented
6C2×D4×D241C213yesmaximal, complemented
7C22×C4×D241C213yesmaximal, complemented
8C2×#41×C241C211yesmaximal, characteristic, complemented
9C23×D241C2213yes—
10#16838771C2218yescomplemented
11#16838770C22124yescomplemented
12#16838769C22124yescomplemented
13C2×Dic482C2213yescomplemented
14Q8×D241C2218yescomplemented
15C2×D964C2213yescomplemented
16C2×C22⋊D241C2216yescomplemented
17D4×D241C22124yescomplemented
18C22×Dic241C2213yescomplemented
19C2×C4×D241C2211yescharacteristic
20C2×C4×D241C2213yes—
21C2×C4×D241C2213yescomplemented
22C2×C4×D241C2213yescomplemented
23C2×C4×D241C22124yescomplemented
24#41×C241C2218yescomplemented
25C2×Q8×C241C2211yescharacteristic, complemented
26C2×D4×C241C2213yescomplemented
27C22×C4×C241C2213yescomplemented
28C22×D241—212no—
29C22×D241C23112yes—
30C22×D241C2313yes—
31C22×D241C2311yescharacteristic
32Dic482C23112yescomplemented
33D964C23112yescomplemented
34C22⋊D241C23124yescomplemented
35C2×Dic241C2311yescharacteristic
36C2×Dic241C2313yes—
37C2×Dic241C23112yescomplemented
38C4×D241C2314yes—
39C4×D241C23112yes—
40C4×D241C23112yescomplemented
41C4×D241C23112yescomplemented
42C23×C241C2313yes—
43Q8×C241C2314yescomplemented
44D4×C241C23112yescomplemented
45C2×C4×C241C2313yes—
46C2×C4×C241C2311yescharacteristic
47C2×C4×C241C23112yescomplemented
48C22×C241—26no—
49C22×C241C2416yes—
50C22×C241C2411yescharacteristic
51C2×D241—26no—
52C2×D241—224no—
53C2×D241#4114yesdirect product factor
54C2×D241C2416yes—
55C2×D241C2412yes—
56C4×C241C2412yes—
57C4×C241C2416yes—
58Dic241C2412yes—
59Dic241C2416yes—
60C2×C241—26no—
61C2×C241C2×#4112yescomplemented
62C2×C241C2511yescharacteristic
63D241—26no—
64D241C2×#4114yesdirect product factor
65C241C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—2411nomaximal, Sylow
67C2×#41—24116no—
68C2×#41—2411no—
69C2×#41—2413no—
70C2×#41—2413no—
71C2×#41D24111yescharacteristic, direct product factor
72C22×Q8—2411no—
73C22×D4—2413no—
74C23×C4—2413no—
75C24—2413no—
76#41—2418no—
77#41—24124no—
78#41—24124no—
79#41C2×D24118yesdirect product factor
80C2×Q8—2418no—
81C2×Q8—2413no—
82C2×Q8C2×D24111yescharacteristic, complemented
83C2×D4—2416no—
84C2×D4—24124no—
85C2×D4—2413no—
86C2×D4C2×D24113yescomplemented
87C22×C4—2413no—
88C22×C4—2413no—
89C22×C4—2413no—
90C22×C4—2411no—
91C22×C4—2413no—
92C22×C4—24124no—
93C22×C4C2×D24113yescomplemented
94C23—48212no—
95C23—24112no—
96C23—2413no—
97C23—2411no—
98C23C22×D24113yes—
99Q8—24112no—
100Q8C22×D24114yescomplemented
101D4—24124no—
102D4—24112no—
103D4C22×D241112yescomplemented
104C2×C4—2411no—
105C2×C4—2413no—
106C2×C4—24112no—
107C2×C4—2414no—
108C2×C4—24112no—
109C2×C4—24112no—
110C2×C4—24112no—
111C2×C4C22×D24113yes—
112C2×C4C22×D24111yescharacteristic
113C2×C4C22×D241112yescomplemented
114C22—26no—
115C22—48224no—
116C22—4826no—
117C22—2416no—
118C22—2414no—
119C22—2412no—
120C22C23×D24116yes—
121C22C23×D24111yescharacteristic
122C4—2412no—
123C4—2416no—
124C4C23×D24112yes—
125C4C23×D24116yes—
126C2—26no—
127C2—4826no—
128C2—2414no—
129C2#41×D24112yesdirect product factor
130C2C24×D24111yescharacteristic
subgroupG/H
centerC2×C4C22×D241
commutator, cosocleC2×C241C25
FrattiniC2C24×D241
FittingC2×#41×C241C2
socleC22×C241C24
hypercenterC2×#41D241
hypocenterC241C22×#41
LCSG ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16838771C2semidirect
2. C2×#16838770C2semidirect
3. C2×#16838769C2semidirect
4. #41×D241C2direct (N × H)
5. C2×Q8×D241C2semidirect
6. C2×D4×D241C2semidirect
7. C22×C4×D241C2semidirect
8. C2×#41×C241C2semidirect
10. #16838771C22semidirect
11. #16838770C22semidirect
12. #16838769C22semidirect
13. C2×Dic482C22semidirect
14. Q8×D241C22semidirect
15. C2×D964C22semidirect
16. C2×C22⋊D241C22semidirect
17. D4×D241C22semidirect
18. C22×Dic241C22semidirect
21. C2×C4×D241C22semidirect
22. C2×C4×D241C22semidirect
23. C2×C4×D241C22semidirect
24. #41×C241C22semidirect
25. C2×Q8×C241C22semidirect
26. C2×D4×C241C22semidirect
27. C22×C4×C241C22semidirect
32. Dic482C23semidirect
33. D964C23semidirect
34. C22⋊D241C23semidirect
37. C2×Dic241C23semidirect
40. C4×D241C23semidirect
41. C4×D241C23semidirect
43. Q8×C241C23semidirect
44. D4×C241C23semidirect
47. C2×C4×C241C23semidirect
53. C2×D241#41direct (N × H)
61. C2×C241C2×#41semidirect
64. D241C2×#41direct (N × H)
65. C241C22×#41semidirect
71. C2×#41D241direct (N × H)
79. #41C2×D241direct (N × H)
82. C2×Q8C2×D241semidirect
86. C2×D4C2×D241semidirect
93. C22×C4C2×D241semidirect
100. Q8C22×D241semidirect
103. D4C22×D241semidirect
113. C2×C4C22×D241semidirect
129. C2#41×D241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168387712
C2×#168387702
C2×#168387692
#41×D2412
C2×Q8×D2412
C2×D4×D2412
C22×C4×D2412
C2×#41×C2412
C22×#41241