Finite Group Databasebeta

← C2×#30628383 #44537556

Subgroups — C2×#30628383 #44537556

Order 31424.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 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
1#30628383C2116yesmaximal, direct product factor
2C2×#21463329C212yesmaximal, complemented
3C2×#21463328C213yesmaximal, complemented
4C22×D1964C213yesmaximal, complemented
5C2×D4×D491C216yesmaximal, complemented
6C2×#41×C491C211yesmaximal, characteristic, complemented
7C23×D491C2216yescomplemented
8#21463329C22116yescomplemented
9#21463328C22124yescomplemented
10C2×Dic982C2211yescharacteristic, complemented
11C2×D1964C2216yescomplemented
12C2×D1964C2213yescomplemented
13C2×D1964C22124yescomplemented
14C2×C22⋊D491C2216yescomplemented
15D4×D491C22148yescomplemented
16C2×C4×D491C2216yescomplemented
17#41×C491C2218yescomplemented
18C2×Q8×C491C2211yescharacteristic, complemented
19C2×D4×C491C2213yescomplemented
20C22×C4×C491C2213yescomplemented
21C22×D491—412no—
22C22×D491C2316yes—
23C22×D491C23124yescomplemented
24Dic982C2314yescomplemented
25D1964C23124yescomplemented
26D1964C23112yescomplemented
27C22⋊D491C23124yescomplemented
28C2×Dic491C2312yes—
29C4×D491C23124yescomplemented
30C23×C491C2313yes—
31Q8×C491C2314yescomplemented
32D4×C491C23112yescomplemented
33C2×C4×C491C2311yescharacteristic
34C2×C4×C491C2313yes—
35C2×C4×C491C23112yescomplemented
36C22×C491—26no—
37C22×C491C2416yes—
38C22×C491C2411yescharacteristic
39C2×D491—212no—
40C2×D491—424no—
41C2×D491C24112yes—
42C4×C491C2412yes—
43C4×C491C2416yes—
44Dic491C2414yes—
45C2×C491—26no—
46C2×C491H(5,𝔽2)12yescomplemented
47C2×C491C2511yescharacteristic
48D491—212no—
49C491C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
50C2×H(5,𝔽2)—4911nomaximal, Sylow
51H(5,𝔽2)—49116no—
52C2×#41—4912no—
53C2×#41—4913no—
54C2×#41D49111yescharacteristic, complemented
55C22×D4—4916no—
56C22×D4—4913no—
57C24—4916no—
58#41—49116no—
59#41—49124no—
60#41C2×D49118yescomplemented
61C2×Q8—4911no—
62C2×Q8C2×D49111yescharacteristic, complemented
63C2×D4—4916no—
64C2×D4—49148no—
65C2×D4—4916no—
66C2×D4—4913no—
67C2×D4—49124no—
68C2×D4C2×D49113yescomplemented
69C22×C4—4916no—
70C22×C4C2×D49113yescomplemented
71C23—196412no—
72C23—49124no—
73C23—4916no—
74C23C22×D49113yes—
75Q8—4914no—
76Q8C22×D49114yescomplemented
77D4—49124no—
78D4—49124no—
79D4—49112no—
80D4C22×D491112yescomplemented
81C2×C4—4912no—
82C2×C4—49124no—
83C2×C4C22×D49113yes—
84C2×C4C22×D49111yescharacteristic
85C2×C4C22×D491112yescomplemented
86C22—26no—
87C22—196424no—
88C22—98212no—
89C22—49112no—
90C22C23×D49116yes—
91C22C23×D49111yescharacteristic
92C4—4914no—
93C4C23×D49116yes—
94C4C23×D49112yes—
95C2—26no—
96C2—98212no—
97C2#3062838312yesdirect product factor
98C2C24×D49111yescharacteristic
subgroupG/H
centerC22C23×D491
commutator, cosocleC2×C491C25
FrattiniC2C24×D491
FittingC2×#41×C491C2
socleC22×C491C24
hypercenterC2×#41D491
hypocenterC491C2×H(5,𝔽2)
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #30628383C2direct (N × H)
2. C2×#21463329C2semidirect
3. C2×#21463328C2semidirect
4. C22×D1964C2semidirect
5. C2×D4×D491C2semidirect
6. C2×#41×C491C2semidirect
7. C23×D491C22semidirect
8. #21463329C22semidirect
9. #21463328C22semidirect
10. C2×Dic982C22semidirect
11. C2×D1964C22semidirect
12. C2×D1964C22semidirect
13. C2×D1964C22semidirect
14. C2×C22⋊D491C22semidirect
15. D4×D491C22semidirect
16. C2×C4×D491C22semidirect
17. #41×C491C22semidirect
18. C2×Q8×C491C22semidirect
19. C2×D4×C491C22semidirect
20. C22×C4×C491C22semidirect
23. C22×D491C23semidirect
24. Dic982C23semidirect
25. D1964C23semidirect
26. D1964C23semidirect
27. C22⋊D491C23semidirect
29. C4×D491C23semidirect
31. Q8×C491C23semidirect
32. D4×C491C23semidirect
35. C2×C4×C491C23semidirect
46. C2×C491H(5,𝔽2)semidirect
49. C491C2×H(5,𝔽2)semidirect
54. C2×#41D491semidirect
60. #41C2×D491semidirect
62. C2×Q8C2×D491semidirect
68. C2×D4C2×D491semidirect
70. C22×C4C2×D491semidirect
76. Q8C22×D491semidirect
80. D4C22×D491semidirect
85. C2×C4C22×D491semidirect
97. C2#30628383direct (N × H)

Maximal subgroups

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

subgroupindex
#306283832
C2×#214633292
C2×#214633282
C22×D19642
C2×D4×D4912
C2×#41×C4912
C2×H(5,𝔽2)491