Finite Group Databasebeta

← C2×#41×D193 #27136084

Subgroups — C2×#41×D193 #27136084

Order 12352.

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×#15690556C211yesmaximal, characteristic, complemented
2C2×#15690555C213yesmaximal, complemented
3C2×#15690554C213yesmaximal, complemented
4#41×D193C2116yesmaximal, direct product factor
5C2×Q8×D193C211yesmaximal, characteristic, complemented
6C2×D4×D193C213yesmaximal, complemented
7C22×C4×D193C213yesmaximal, complemented
8C2×#41×C193C211yesmaximal, characteristic, complemented
9C23×D193C2213yes—
10#15690556C2218yescomplemented
11#15690555C22124yescomplemented
12#15690554C22124yescomplemented
13C2×Dic386C2213yescomplemented
14Q8×D193C2218yescomplemented
15C2×D772C2213yescomplemented
16C2×C22⋊D193C2216yescomplemented
17D4×D193C22124yescomplemented
18C22×Dic193C2213yescomplemented
19C2×C4×D193C2211yescharacteristic
20C2×C4×D193C2213yes—
21C2×C4×D193C2213yescomplemented
22C2×C4×D193C2213yescomplemented
23C2×C4×D193C22124yescomplemented
24#41×C193C2218yescomplemented
25C2×Q8×C193C2211yescharacteristic, complemented
26C2×D4×C193C2213yescomplemented
27C22×C4×C193C2213yescomplemented
28C22×D193—212no—
29C22×D193C23112yes—
30C22×D193C2313yes—
31C22×D193C2311yescharacteristic
32Dic386C23112yescomplemented
33D772C23112yescomplemented
34C22⋊D193C23124yescomplemented
35C2×Dic193C2311yescharacteristic
36C2×Dic193C2313yes—
37C2×Dic193C23112yescomplemented
38C4×D193C2314yes—
39C4×D193C23112yes—
40C4×D193C23112yescomplemented
41C4×D193C23112yescomplemented
42C23×C193C2313yes—
43Q8×C193C2314yescomplemented
44D4×C193C23112yescomplemented
45C2×C4×C193C2313yes—
46C2×C4×C193C2311yescharacteristic
47C2×C4×C193C23112yescomplemented
48C22×C193—26no—
49C22×C193C2416yes—
50C22×C193C2411yescharacteristic
51C2×D193—26no—
52C2×D193—224no—
53C2×D193#4114yesdirect product factor
54C2×D193C2416yes—
55C2×D193C2412yes—
56C4×C193C2412yes—
57C4×C193C2416yes—
58Dic193C2412yes—
59Dic193C2416yes—
60C2×C193—26no—
61C2×C193C2×#4112yescomplemented
62C2×C193C2511yescharacteristic
63D193—26no—
64D193C2×#4114yesdirect product factor
65C193C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—1931nomaximal, Sylow
67C2×#41—19316no—
68C2×#41—1931no—
69C2×#41—1933no—
70C2×#41—1933no—
71C2×#41D19311yescharacteristic, direct product factor
72C22×Q8—1931no—
73C22×D4—1933no—
74C23×C4—1933no—
75C24—1933no—
76#41—1938no—
77#41—19324no—
78#41—19324no—
79#41C2×D19318yesdirect product factor
80C2×Q8—1938no—
81C2×Q8—1933no—
82C2×Q8C2×D19311yescharacteristic, complemented
83C2×D4—1936no—
84C2×D4—19324no—
85C2×D4—1933no—
86C2×D4C2×D19313yescomplemented
87C22×C4—1933no—
88C22×C4—1933no—
89C22×C4—1933no—
90C22×C4—1931no—
91C22×C4—1933no—
92C22×C4—19324no—
93C22×C4C2×D19313yescomplemented
94C23—38612no—
95C23—19312no—
96C23—1933no—
97C23—1931no—
98C23C22×D19313yes—
99Q8—19312no—
100Q8C22×D19314yescomplemented
101D4—19324no—
102D4—19312no—
103D4C22×D193112yescomplemented
104C2×C4—1931no—
105C2×C4—1933no—
106C2×C4—19312no—
107C2×C4—1934no—
108C2×C4—19312no—
109C2×C4—19312no—
110C2×C4—19312no—
111C2×C4C22×D19313yes—
112C2×C4C22×D19311yescharacteristic
113C2×C4C22×D193112yescomplemented
114C22—26no—
115C22—38624no—
116C22—3866no—
117C22—1936no—
118C22—1934no—
119C22—1932no—
120C22C23×D19316yes—
121C22C23×D19311yescharacteristic
122C4—1932no—
123C4—1936no—
124C4C23×D19312yes—
125C4C23×D19316yes—
126C2—26no—
127C2—3866no—
128C2—1934no—
129C2#41×D19312yesdirect product factor
130C2C24×D19311yescharacteristic
subgroupG/H
centerC2×C4C22×D193
commutator, cosocleC2×C193C25
FrattiniC2C24×D193
FittingC2×#41×C193C2
socleC22×C193C24
hypercenterC2×#41D193
hypocenterC193C22×#41
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#15690556C2semidirect
2. C2×#15690555C2semidirect
3. C2×#15690554C2semidirect
4. #41×D193C2direct (N × H)
5. C2×Q8×D193C2semidirect
6. C2×D4×D193C2semidirect
7. C22×C4×D193C2semidirect
8. C2×#41×C193C2semidirect
10. #15690556C22semidirect
11. #15690555C22semidirect
12. #15690554C22semidirect
13. C2×Dic386C22semidirect
14. Q8×D193C22semidirect
15. C2×D772C22semidirect
16. C2×C22⋊D193C22semidirect
17. D4×D193C22semidirect
18. C22×Dic193C22semidirect
21. C2×C4×D193C22semidirect
22. C2×C4×D193C22semidirect
23. C2×C4×D193C22semidirect
24. #41×C193C22semidirect
25. C2×Q8×C193C22semidirect
26. C2×D4×C193C22semidirect
27. C22×C4×C193C22semidirect
32. Dic386C23semidirect
33. D772C23semidirect
34. C22⋊D193C23semidirect
37. C2×Dic193C23semidirect
40. C4×D193C23semidirect
41. C4×D193C23semidirect
43. Q8×C193C23semidirect
44. D4×C193C23semidirect
47. C2×C4×C193C23semidirect
53. C2×D193#41direct (N × H)
61. C2×C193C2×#41semidirect
64. D193C2×#41direct (N × H)
65. C193C22×#41semidirect
71. C2×#41D193direct (N × H)
79. #41C2×D193direct (N × H)
82. C2×Q8C2×D193semidirect
86. C2×D4C2×D193semidirect
93. C22×C4C2×D193semidirect
100. Q8C22×D193semidirect
103. D4C22×D193semidirect
113. C2×C4C22×D193semidirect
129. C2#41×D193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156905562
C2×#156905552
C2×#156905542
#41×D1932
C2×Q8×D1932
C2×D4×D1932
C22×C4×D1932
C2×#41×C1932
C22×#41193