Finite Group Databasebeta

← C2×#41×D179 #26039264

Subgroups — C2×#41×D179 #26039264

Order 11456.

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×#15668260C211yesmaximal, characteristic, complemented
2C2×#15668259C213yesmaximal, complemented
3C2×#15668258C213yesmaximal, complemented
4#41×D179C2116yesmaximal, direct product factor
5C2×Q8×D179C211yesmaximal, characteristic, complemented
6C2×D4×D179C213yesmaximal, complemented
7C22×C4×D179C213yesmaximal, complemented
8C2×#41×C179C211yesmaximal, characteristic, complemented
9C23×D179C2213yes—
10#15668260C2218yescomplemented
11#15668259C22124yescomplemented
12#15668258C22124yescomplemented
13C2×Dic358C2213yescomplemented
14Q8×D179C2218yescomplemented
15C2×D716C2213yescomplemented
16C2×C22⋊D179C2216yescomplemented
17D4×D179C22124yescomplemented
18C22×Dic179C2213yescomplemented
19C2×C4×D179C2213yes—
20C2×C4×D179C2211yescharacteristic
21C2×C4×D179C2213yescomplemented
22C2×C4×D179C2213yescomplemented
23C2×C4×D179C22124yescomplemented
24#41×C179C2218yescomplemented
25C2×Q8×C179C2211yescharacteristic, complemented
26C2×D4×C179C2213yescomplemented
27C22×C4×C179C2213yescomplemented
28C22×D179—212no—
29C22×D179C23112yes—
30C22×D179C2313yes—
31C22×D179C2311yescharacteristic
32Dic358C23112yescomplemented
33D716C23112yescomplemented
34C22⋊D179C23124yescomplemented
35C2×Dic179C2311yescharacteristic
36C2×Dic179C2313yes—
37C2×Dic179C23112yescomplemented
38C4×D179C2314yes—
39C4×D179C23112yes—
40C4×D179C23112yescomplemented
41C4×D179C23112yescomplemented
42C23×C179C2313yes—
43Q8×C179C2314yescomplemented
44D4×C179C23112yescomplemented
45C2×C4×C179C2313yes—
46C2×C4×C179C2311yescharacteristic
47C2×C4×C179C23112yescomplemented
48C22×C179—26no—
49C22×C179C2416yes—
50C22×C179C2411yescharacteristic
51C2×D179—26no—
52C2×D179—224no—
53C2×D179#4114yesdirect product factor
54C2×D179C2416yes—
55C2×D179C2412yes—
56C4×C179C2412yes—
57C4×C179C2416yes—
58Dic179C2412yes—
59Dic179C2416yes—
60C2×C179—26no—
61C2×C179C2×#4112yescomplemented
62C2×C179C2511yescharacteristic
63D179—26no—
64D179C2×#4114yesdirect product factor
65C179C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—1791nomaximal, Sylow
67C2×#41—17916no—
68C2×#41—1791no—
69C2×#41—1793no—
70C2×#41—1793no—
71C2×#41D17911yescharacteristic, direct product factor
72C22×Q8—1791no—
73C22×D4—1793no—
74C23×C4—1793no—
75C24—1793no—
76#41—1798no—
77#41—17924no—
78#41—17924no—
79#41C2×D17918yesdirect product factor
80C2×Q8—1798no—
81C2×Q8—1793no—
82C2×Q8C2×D17911yescharacteristic, complemented
83C2×D4—1796no—
84C2×D4—17924no—
85C2×D4—1793no—
86C2×D4C2×D17913yescomplemented
87C22×C4—1793no—
88C22×C4—1793no—
89C22×C4—1793no—
90C22×C4—1791no—
91C22×C4—1793no—
92C22×C4—17924no—
93C22×C4C2×D17913yescomplemented
94C23—35812no—
95C23—17912no—
96C23—1793no—
97C23—1791no—
98C23C22×D17913yes—
99Q8—17912no—
100Q8C22×D17914yescomplemented
101D4—17924no—
102D4—17912no—
103D4C22×D179112yescomplemented
104C2×C4—1791no—
105C2×C4—1793no—
106C2×C4—17912no—
107C2×C4—1794no—
108C2×C4—17912no—
109C2×C4—17912no—
110C2×C4—17912no—
111C2×C4C22×D17913yes—
112C2×C4C22×D17911yescharacteristic
113C2×C4C22×D179112yescomplemented
114C22—26no—
115C22—35824no—
116C22—3586no—
117C22—1796no—
118C22—1794no—
119C22—1792no—
120C22C23×D17916yes—
121C22C23×D17911yescharacteristic
122C4—1792no—
123C4—1796no—
124C4C23×D17912yes—
125C4C23×D17916yes—
126C2—26no—
127C2—3586no—
128C2—1794no—
129C2#41×D17912yesdirect product factor
130C2C24×D17911yescharacteristic
subgroupG/H
centerC2×C4C22×D179
commutator, cosocleC2×C179C25
FrattiniC2C24×D179
FittingC2×#41×C179C2
socleC22×C179C24
hypercenterC2×#41D179
hypocenterC179C22×#41
LCSG ▷ C2×C179 ▷ C179
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#15668260C2semidirect
2. C2×#15668259C2semidirect
3. C2×#15668258C2semidirect
4. #41×D179C2direct (N × H)
5. C2×Q8×D179C2semidirect
6. C2×D4×D179C2semidirect
7. C22×C4×D179C2semidirect
8. C2×#41×C179C2semidirect
10. #15668260C22semidirect
11. #15668259C22semidirect
12. #15668258C22semidirect
13. C2×Dic358C22semidirect
14. Q8×D179C22semidirect
15. C2×D716C22semidirect
16. C2×C22⋊D179C22semidirect
17. D4×D179C22semidirect
18. C22×Dic179C22semidirect
21. C2×C4×D179C22semidirect
22. C2×C4×D179C22semidirect
23. C2×C4×D179C22semidirect
24. #41×C179C22semidirect
25. C2×Q8×C179C22semidirect
26. C2×D4×C179C22semidirect
27. C22×C4×C179C22semidirect
32. Dic358C23semidirect
33. D716C23semidirect
34. C22⋊D179C23semidirect
37. C2×Dic179C23semidirect
40. C4×D179C23semidirect
41. C4×D179C23semidirect
43. Q8×C179C23semidirect
44. D4×C179C23semidirect
47. C2×C4×C179C23semidirect
53. C2×D179#41direct (N × H)
61. C2×C179C2×#41semidirect
64. D179C2×#41direct (N × H)
65. C179C22×#41semidirect
71. C2×#41D179direct (N × H)
79. #41C2×D179direct (N × H)
82. C2×Q8C2×D179semidirect
86. C2×D4C2×D179semidirect
93. C22×C4C2×D179semidirect
100. Q8C22×D179semidirect
103. D4C22×D179semidirect
113. C2×C4C22×D179semidirect
129. C2#41×D179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156682602
C2×#156682592
C2×#156682582
#41×D1792
C2×Q8×D1792
C2×D4×D1792
C22×C4×D1792
C2×#41×C1792
C22×#41179