Finite Group Databasebeta

← C2×#41×D239 #29505597

Subgroups — C2×#41×D239 #29505597

Order 15296.

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×#16838549C211yesmaximal, characteristic, complemented
2C2×#16838548C213yesmaximal, complemented
3C2×#16838547C213yesmaximal, complemented
4#41×D239C2116yesmaximal, direct product factor
5C2×Q8×D239C211yesmaximal, characteristic, complemented
6C2×D4×D239C213yesmaximal, complemented
7C22×C4×D239C213yesmaximal, complemented
8C2×#41×C239C211yesmaximal, characteristic, complemented
9C23×D239C2213yes—
10#16838549C2218yescomplemented
11#16838548C22124yescomplemented
12#16838547C22124yescomplemented
13C2×Dic478C2213yescomplemented
14Q8×D239C2218yescomplemented
15C2×D956C2213yescomplemented
16C2×C22⋊D239C2216yescomplemented
17D4×D239C22124yescomplemented
18C22×Dic239C2213yescomplemented
19C2×C4×D239C2211yescharacteristic
20C2×C4×D239C2213yes—
21C2×C4×D239C2213yescomplemented
22C2×C4×D239C2213yescomplemented
23C2×C4×D239C22124yescomplemented
24#41×C239C2218yescomplemented
25C2×Q8×C239C2211yescharacteristic, complemented
26C2×D4×C239C2213yescomplemented
27C22×C4×C239C2213yescomplemented
28C22×D239—212no—
29C22×D239C23112yes—
30C22×D239C2313yes—
31C22×D239C2311yescharacteristic
32Dic478C23112yescomplemented
33D956C23112yescomplemented
34C22⋊D239C23124yescomplemented
35C2×Dic239C2311yescharacteristic
36C2×Dic239C2313yes—
37C2×Dic239C23112yescomplemented
38C4×D239C2314yes—
39C4×D239C23112yes—
40C4×D239C23112yescomplemented
41C4×D239C23112yescomplemented
42C23×C239C2313yes—
43Q8×C239C2314yescomplemented
44D4×C239C23112yescomplemented
45C2×C4×C239C2313yes—
46C2×C4×C239C2311yescharacteristic
47C2×C4×C239C23112yescomplemented
48C22×C239—26no—
49C22×C239C2416yes—
50C22×C239C2411yescharacteristic
51C2×D239—26no—
52C2×D239—224no—
53C2×D239#4114yesdirect product factor
54C2×D239C2416yes—
55C2×D239C2412yes—
56C4×C239C2412yes—
57C4×C239C2416yes—
58Dic239C2412yes—
59Dic239C2416yes—
60C2×C239—26no—
61C2×C239C2×#4112yescomplemented
62C2×C239C2511yescharacteristic
63D239—26no—
64D239C2×#4114yesdirect product factor
65C239C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—2391nomaximal, Sylow
67C2×#41—23916no—
68C2×#41—2391no—
69C2×#41—2393no—
70C2×#41—2393no—
71C2×#41D23911yescharacteristic, direct product factor
72C22×Q8—2391no—
73C22×D4—2393no—
74C23×C4—2393no—
75C24—2393no—
76#41—2398no—
77#41—23924no—
78#41—23924no—
79#41C2×D23918yesdirect product factor
80C2×Q8—2398no—
81C2×Q8—2393no—
82C2×Q8C2×D23911yescharacteristic, complemented
83C2×D4—2396no—
84C2×D4—23924no—
85C2×D4—2393no—
86C2×D4C2×D23913yescomplemented
87C22×C4—2393no—
88C22×C4—2393no—
89C22×C4—2393no—
90C22×C4—2391no—
91C22×C4—2393no—
92C22×C4—23924no—
93C22×C4C2×D23913yescomplemented
94C23—47812no—
95C23—23912no—
96C23—2393no—
97C23—2391no—
98C23C22×D23913yes—
99Q8—23912no—
100Q8C22×D23914yescomplemented
101D4—23924no—
102D4—23912no—
103D4C22×D239112yescomplemented
104C2×C4—2391no—
105C2×C4—2393no—
106C2×C4—23912no—
107C2×C4—2394no—
108C2×C4—23912no—
109C2×C4—23912no—
110C2×C4—23912no—
111C2×C4C22×D23913yes—
112C2×C4C22×D23911yescharacteristic
113C2×C4C22×D239112yescomplemented
114C22—26no—
115C22—47824no—
116C22—4786no—
117C22—2396no—
118C22—2394no—
119C22—2392no—
120C22C23×D23916yes—
121C22C23×D23911yescharacteristic
122C4—2392no—
123C4—2396no—
124C4C23×D23912yes—
125C4C23×D23916yes—
126C2—26no—
127C2—4786no—
128C2—2394no—
129C2#41×D23912yesdirect product factor
130C2C24×D23911yescharacteristic
subgroupG/H
centerC2×C4C22×D239
commutator, cosocleC2×C239C25
FrattiniC2C24×D239
FittingC2×#41×C239C2
socleC22×C239C24
hypercenterC2×#41D239
hypocenterC239C22×#41
LCSG ▷ C2×C239 ▷ C239
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16838549C2semidirect
2. C2×#16838548C2semidirect
3. C2×#16838547C2semidirect
4. #41×D239C2direct (N × H)
5. C2×Q8×D239C2semidirect
6. C2×D4×D239C2semidirect
7. C22×C4×D239C2semidirect
8. C2×#41×C239C2semidirect
10. #16838549C22semidirect
11. #16838548C22semidirect
12. #16838547C22semidirect
13. C2×Dic478C22semidirect
14. Q8×D239C22semidirect
15. C2×D956C22semidirect
16. C2×C22⋊D239C22semidirect
17. D4×D239C22semidirect
18. C22×Dic239C22semidirect
21. C2×C4×D239C22semidirect
22. C2×C4×D239C22semidirect
23. C2×C4×D239C22semidirect
24. #41×C239C22semidirect
25. C2×Q8×C239C22semidirect
26. C2×D4×C239C22semidirect
27. C22×C4×C239C22semidirect
32. Dic478C23semidirect
33. D956C23semidirect
34. C22⋊D239C23semidirect
37. C2×Dic239C23semidirect
40. C4×D239C23semidirect
41. C4×D239C23semidirect
43. Q8×C239C23semidirect
44. D4×C239C23semidirect
47. C2×C4×C239C23semidirect
53. C2×D239#41direct (N × H)
61. C2×C239C2×#41semidirect
64. D239C2×#41direct (N × H)
65. C239C22×#41semidirect
71. C2×#41D239direct (N × H)
79. #41C2×D239direct (N × H)
82. C2×Q8C2×D239semidirect
86. C2×D4C2×D239semidirect
93. C22×C4C2×D239semidirect
100. Q8C22×D239semidirect
103. D4C22×D239semidirect
113. C2×C4C22×D239semidirect
129. C2#41×D239direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168385492
C2×#168385482
C2×#168385472
#41×D2392
C2×Q8×D2392
C2×D4×D2392
C22×C4×D2392
C2×#41×C2392
C22×#41239