Finite Group Databasebeta

← C2×#41×D349 #36374969

Subgroups — C2×#41×D349 #36374969

Order 22336.

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×#19150234C211yesmaximal, characteristic, complemented
2C2×#19150233C213yesmaximal, complemented
3C2×#19150232C213yesmaximal, complemented
4#41×D349C2116yesmaximal, direct product factor
5C2×Q8×D349C211yesmaximal, characteristic, complemented
6C2×D4×D349C213yesmaximal, complemented
7C22×C4×D349C213yesmaximal, complemented
8C2×#41×C349C211yesmaximal, characteristic, complemented
9C23×D349C2213yes—
10#19150234C2218yescomplemented
11#19150233C22124yescomplemented
12#19150232C22124yescomplemented
13C2×Dic698C2213yescomplemented
14Q8×D349C2218yescomplemented
15C2×D1396C2213yescomplemented
16C2×C22⋊D349C2216yescomplemented
17D4×D349C22124yescomplemented
18C22×Dic349C2213yescomplemented
19C2×C4×D349C2211yescharacteristic
20C2×C4×D349C2213yes—
21C2×C4×D349C2213yescomplemented
22C2×C4×D349C2213yescomplemented
23C2×C4×D349C22124yescomplemented
24#41×C349C2218yescomplemented
25C2×Q8×C349C2211yescharacteristic, complemented
26C2×D4×C349C2213yescomplemented
27C22×C4×C349C2213yescomplemented
28C22×D349—212no—
29C22×D349C23112yes—
30C22×D349C2313yes—
31C22×D349C2311yescharacteristic
32Dic698C23112yescomplemented
33D1396C23112yescomplemented
34C22⋊D349C23124yescomplemented
35C2×Dic349C2311yescharacteristic
36C2×Dic349C2313yes—
37C2×Dic349C23112yescomplemented
38C4×D349C2314yes—
39C4×D349C23112yes—
40C4×D349C23112yescomplemented
41C4×D349C23112yescomplemented
42C23×C349C2313yes—
43Q8×C349C2314yescomplemented
44D4×C349C23112yescomplemented
45C2×C4×C349C2313yes—
46C2×C4×C349C2311yescharacteristic
47C2×C4×C349C23112yescomplemented
48C22×C349—26no—
49C22×C349C2416yes—
50C22×C349C2411yescharacteristic
51C2×D349—26no—
52C2×D349—224no—
53C2×D349#4114yesdirect product factor
54C2×D349C2416yes—
55C2×D349C2412yes—
56C4×C349C2412yes—
57C4×C349C2416yes—
58Dic349C2412yes—
59Dic349C2416yes—
60C2×C349—26no—
61C2×C349C2×#4112yescomplemented
62C2×C349C2511yescharacteristic
63D349—26no—
64D349C2×#4114yesdirect product factor
65C349C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—3491nomaximal, Sylow
67C2×#41—34916no—
68C2×#41—3491no—
69C2×#41—3493no—
70C2×#41—3493no—
71C2×#41D34911yescharacteristic, direct product factor
72C22×Q8—3491no—
73C22×D4—3493no—
74C23×C4—3493no—
75C24—3493no—
76#41—3498no—
77#41—34924no—
78#41—34924no—
79#41C2×D34918yesdirect product factor
80C2×Q8—3498no—
81C2×Q8—3493no—
82C2×Q8C2×D34911yescharacteristic, complemented
83C2×D4—3496no—
84C2×D4—34924no—
85C2×D4—3493no—
86C2×D4C2×D34913yescomplemented
87C22×C4—3493no—
88C22×C4—3493no—
89C22×C4—3493no—
90C22×C4—3491no—
91C22×C4—3493no—
92C22×C4—34924no—
93C22×C4C2×D34913yescomplemented
94C23—3491no—
95C23—34912no—
96C23—3493no—
97C23—69812no—
98C23C22×D34913yes—
99Q8—34912no—
100Q8C22×D34914yescomplemented
101D4—34924no—
102D4—34912no—
103D4C22×D349112yescomplemented
104C2×C4—3491no—
105C2×C4—3493no—
106C2×C4—34912no—
107C2×C4—3494no—
108C2×C4—34912no—
109C2×C4—34912no—
110C2×C4—34912no—
111C2×C4C22×D34913yes—
112C2×C4C22×D34911yescharacteristic
113C2×C4C22×D349112yescomplemented
114C22—26no—
115C22—3494no—
116C22—3492no—
117C22—3496no—
118C22—69824no—
119C22—6986no—
120C22C23×D34916yes—
121C22C23×D34911yescharacteristic
122C4—3492no—
123C4—3496no—
124C4C23×D34912yes—
125C4C23×D34916yes—
126C2—26no—
127C2—3494no—
128C2—6986no—
129C2#41×D34912yesdirect product factor
130C2C24×D34911yescharacteristic
subgroupG/H
centerC2×C4C22×D349
commutator, cosocleC2×C349C25
FrattiniC2C24×D349
FittingC2×#41×C349C2
socleC22×C349C24
hypercenterC2×#41D349
hypocenterC349C22×#41
LCSG ▷ C2×C349 ▷ C349
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#19150234C2semidirect
2. C2×#19150233C2semidirect
3. C2×#19150232C2semidirect
4. #41×D349C2direct (N × H)
5. C2×Q8×D349C2semidirect
6. C2×D4×D349C2semidirect
7. C22×C4×D349C2semidirect
8. C2×#41×C349C2semidirect
10. #19150234C22semidirect
11. #19150233C22semidirect
12. #19150232C22semidirect
13. C2×Dic698C22semidirect
14. Q8×D349C22semidirect
15. C2×D1396C22semidirect
16. C2×C22⋊D349C22semidirect
17. D4×D349C22semidirect
18. C22×Dic349C22semidirect
21. C2×C4×D349C22semidirect
22. C2×C4×D349C22semidirect
23. C2×C4×D349C22semidirect
24. #41×C349C22semidirect
25. C2×Q8×C349C22semidirect
26. C2×D4×C349C22semidirect
27. C22×C4×C349C22semidirect
32. Dic698C23semidirect
33. D1396C23semidirect
34. C22⋊D349C23semidirect
37. C2×Dic349C23semidirect
40. C4×D349C23semidirect
41. C4×D349C23semidirect
43. Q8×C349C23semidirect
44. D4×C349C23semidirect
47. C2×C4×C349C23semidirect
53. C2×D349#41direct (N × H)
61. C2×C349C2×#41semidirect
64. D349C2×#41direct (N × H)
65. C349C22×#41semidirect
71. C2×#41D349direct (N × H)
79. #41C2×D349direct (N × H)
82. C2×Q8C2×D349semidirect
86. C2×D4C2×D349semidirect
93. C22×C4C2×D349semidirect
100. Q8C22×D349semidirect
103. D4C22×D349semidirect
113. C2×C4C22×D349semidirect
129. C2#41×D349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191502342
C2×#191502332
C2×#191502322
#41×D3492
C2×Q8×D3492
C2×D4×D3492
C22×C4×D3492
C2×#41×C3492
C22×#41349