Finite Group Databasebeta

← C2×#41×D419 #41001186

Subgroups — C2×#41×D419 #41001186

Order 26816.

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×#20269412C211yesmaximal, characteristic, complemented
2C2×#20269411C213yesmaximal, complemented
3C2×#20269410C213yesmaximal, complemented
4#41×D419C2116yesmaximal, direct product factor
5C2×Q8×D419C211yesmaximal, characteristic, complemented
6C2×D4×D419C213yesmaximal, complemented
7C22×C4×D419C213yesmaximal, complemented
8C2×#41×C419C211yesmaximal, characteristic, complemented
9C23×D419C2213yes—
10#20269412C2218yescomplemented
11#20269411C22124yescomplemented
12#20269410C22124yescomplemented
13C2×Dic838C2213yescomplemented
14Q8×D419C2218yescomplemented
15C2×D1676C2213yescomplemented
16C2×C22⋊D419C2216yescomplemented
17D4×D419C22124yescomplemented
18C22×Dic419C2213yescomplemented
19C2×C4×D419C2211yescharacteristic
20C2×C4×D419C2213yes—
21C2×C4×D419C2213yescomplemented
22C2×C4×D419C2213yescomplemented
23C2×C4×D419C22124yescomplemented
24#41×C419C2218yescomplemented
25C2×Q8×C419C2211yescharacteristic, complemented
26C2×D4×C419C2213yescomplemented
27C22×C4×C419C2213yescomplemented
28C22×D419—212no—
29C22×D419C23112yes—
30C22×D419C2313yes—
31C22×D419C2311yescharacteristic
32Dic838C23112yescomplemented
33D1676C23112yescomplemented
34C22⋊D419C23124yescomplemented
35C2×Dic419C2311yescharacteristic
36C2×Dic419C2313yes—
37C2×Dic419C23112yescomplemented
38C4×D419C2314yes—
39C4×D419C23112yes—
40C4×D419C23112yescomplemented
41C4×D419C23112yescomplemented
42C23×C419C2313yes—
43Q8×C419C2314yescomplemented
44D4×C419C23112yescomplemented
45C2×C4×C419C2313yes—
46C2×C4×C419C2311yescharacteristic
47C2×C4×C419C23112yescomplemented
48C22×C419—26no—
49C22×C419C2416yes—
50C22×C419C2411yescharacteristic
51C2×D419—26no—
52C2×D419—224no—
53C2×D419#4114yesdirect product factor
54C2×D419C2416yes—
55C2×D419C2412yes—
56C4×C419C2412yes—
57C4×C419C2416yes—
58Dic419C2412yes—
59Dic419C2416yes—
60C2×C419—26no—
61C2×C419C2×#4112yescomplemented
62C2×C419C2511yescharacteristic
63D419—26no—
64D419C2×#4114yesdirect product factor
65C419C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—4191nomaximal, Sylow
67C2×#41—41916no—
68C2×#41—4191no—
69C2×#41—4193no—
70C2×#41—4193no—
71C2×#41D41911yescharacteristic, direct product factor
72C22×Q8—4191no—
73C22×D4—4193no—
74C23×C4—4193no—
75C24—4193no—
76#41—4198no—
77#41—41924no—
78#41—41924no—
79#41C2×D41918yesdirect product factor
80C2×Q8—4198no—
81C2×Q8—4193no—
82C2×Q8C2×D41911yescharacteristic, complemented
83C2×D4—4196no—
84C2×D4—41924no—
85C2×D4—4193no—
86C2×D4C2×D41913yescomplemented
87C22×C4—4193no—
88C22×C4—4193no—
89C22×C4—4193no—
90C22×C4—4191no—
91C22×C4—4193no—
92C22×C4—41924no—
93C22×C4C2×D41913yescomplemented
94C23—83812no—
95C23—41912no—
96C23—4193no—
97C23—4191no—
98C23C22×D41913yes—
99Q8—41912no—
100Q8C22×D41914yescomplemented
101D4—41924no—
102D4—41912no—
103D4C22×D419112yescomplemented
104C2×C4—4191no—
105C2×C4—4193no—
106C2×C4—41912no—
107C2×C4—4194no—
108C2×C4—41912no—
109C2×C4—41912no—
110C2×C4—41912no—
111C2×C4C22×D41913yes—
112C2×C4C22×D41911yescharacteristic
113C2×C4C22×D419112yescomplemented
114C22—26no—
115C22—83824no—
116C22—8386no—
117C22—4196no—
118C22—4194no—
119C22—4192no—
120C22C23×D41916yes—
121C22C23×D41911yescharacteristic
122C4—4192no—
123C4—4196no—
124C4C23×D41912yes—
125C4C23×D41916yes—
126C2—26no—
127C2—8386no—
128C2—4194no—
129C2#41×D41912yesdirect product factor
130C2C24×D41911yescharacteristic
subgroupG/H
centerC2×C4C22×D419
commutator, cosocleC2×C419C25
FrattiniC2C24×D419
FittingC2×#41×C419C2
socleC22×C419C24
hypercenterC2×#41D419
hypocenterC419C22×#41
LCSG ▷ C2×C419 ▷ C419
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20269412C2semidirect
2. C2×#20269411C2semidirect
3. C2×#20269410C2semidirect
4. #41×D419C2direct (N × H)
5. C2×Q8×D419C2semidirect
6. C2×D4×D419C2semidirect
7. C22×C4×D419C2semidirect
8. C2×#41×C419C2semidirect
10. #20269412C22semidirect
11. #20269411C22semidirect
12. #20269410C22semidirect
13. C2×Dic838C22semidirect
14. Q8×D419C22semidirect
15. C2×D1676C22semidirect
16. C2×C22⋊D419C22semidirect
17. D4×D419C22semidirect
18. C22×Dic419C22semidirect
21. C2×C4×D419C22semidirect
22. C2×C4×D419C22semidirect
23. C2×C4×D419C22semidirect
24. #41×C419C22semidirect
25. C2×Q8×C419C22semidirect
26. C2×D4×C419C22semidirect
27. C22×C4×C419C22semidirect
32. Dic838C23semidirect
33. D1676C23semidirect
34. C22⋊D419C23semidirect
37. C2×Dic419C23semidirect
40. C4×D419C23semidirect
41. C4×D419C23semidirect
43. Q8×C419C23semidirect
44. D4×C419C23semidirect
47. C2×C4×C419C23semidirect
53. C2×D419#41direct (N × H)
61. C2×C419C2×#41semidirect
64. D419C2×#41direct (N × H)
65. C419C22×#41semidirect
71. C2×#41D419direct (N × H)
79. #41C2×D419direct (N × H)
82. C2×Q8C2×D419semidirect
86. C2×D4C2×D419semidirect
93. C22×C4C2×D419semidirect
100. Q8C22×D419semidirect
103. D4C22×D419semidirect
113. C2×C4C22×D419semidirect
129. C2#41×D419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202694122
C2×#202694112
C2×#202694102
#41×D4192
C2×Q8×D4192
C2×D4×D4192
C22×C4×D4192
C2×#41×C4192
C22×#41419