Finite Group Databasebeta

← #37566044

Subgroups — #37566044

Order 24256.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#20258606C212yesmaximal, complemented
2#27131364C214yesmaximal, complemented
3#27131359C214yesmaximal, complemented
4#27131353C214yesmaximal, complemented
5C2×M16×C379C211yesmaximal, characteristic, complemented
6#20258606—22no—
7#20258606—22no—
8#20258606C2214yes—
9#20258606C2214yescomplemented
10C2×Dic758C2212yescomplemented
11C2×D1516C2212yescomplemented
12C2×C22⋊D379—22no—
13C2×C4×D379—22no—
14Dic1516C2214yescomplemented
15#20258595C2218yescomplemented
16D3032C2214yescomplemented
17C22×C4×C379C2211yescharacteristic
18M16×C379C2214yescomplemented
19C2×C8×C379C2212yescomplemented
20C22×D379—22no—
21Dic758—22no—
22Dic758C2314yes—
23D1516—22no—
24D1516C2314yes—
25C22⋊D379—24no—
26C22⋊D379—24no—
27C2×Dic379—22no—
28C4×D379—24no—
29C4×D379—24no—
30C23×C379D411yescharacteristic
31C2×C4×C379D412yes—
32C2×C4×C379D411yescharacteristic
33C2×C4×C379C2311yescharacteristic
34C2×C4×C379C2312yes—
35C8×C379C2314yes—
36C22×C379—41no—
37C22×C379C2×D412yes—
38C22×C379C2×D411yescharacteristic
39C2×D379—24no—
40C2×D379—44no—
41C4×C379C2×D412yes—
42C4×C379C2×D411yescharacteristic
43C4×C379C2411yescharacteristic
44Dic379—24no—
45C2×C379—22no—
46C2×C379—21no—
47C2×C379C22×D411yescharacteristic
48D379—44no—
49C379#57511yescharacteristic, complemented, Sylow
50#575—3791nomaximal, Sylow
51C2×#41—3792no—
52#137—3794no—
53AGL(1,ℤ/8)—3794no—
54#135—3794no—
55C2×M16D37911yescharacteristic, complemented
56#41—3794no—
57#41—3794no—
58#41—7582no—
59#41—7582no—
60C2×Q8—3792no—
61C2×D4—3792no—
62C2×D4—7582no—
63C22×C4—7582no—
64C22×C4C2×D37911yescharacteristic
65Q16—3794no—
66SD16—3798no—
67D8—3794no—
68M16C2×D37914yescomplemented
69C2×C8C2×D37912yescomplemented
70C23—7582no—
71C23D151611yescharacteristic
72Q8—3794no—
73Q8—7582no—
74D4—3794no—
75D4—7584no—
76D4—7584no—
77D4—7582no—
78C2×C4—7582no—
79C2×C4—7584no—
80C2×C4—7584no—
81C2×C4D151611yescharacteristic
82C2×C4D151612yes—
83C2×C4C22×D37912yes—
84C2×C4C22×D37911yescharacteristic
85C8C22×D37914yes—
86C22—41no—
87C22—15164no—
88C22—7584no—
89C22C2×D151612yes—
90C22C2×D151611yescharacteristic
91C4—7584no—
92C4C2×D151612yes—
93C4C2×D151611yescharacteristic
94C4C23×D37911yescharacteristic
95C2—22no—
96C2—21no—
97C2—15164no—
98C2C22×D151611yescharacteristic
subgroupG/H
centerC4C2×D1516
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
FittingC2×M16×C379C2
socleC2×C379C22×D4
hypercenterC2×M16D379
hypocenterC379#575
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#20258606C2semidirect
2. #27131364C2semidirect
3. #27131359C2semidirect
4. #27131353C2semidirect
5. C2×M16×C379C2semidirect
9. #20258606C22semidirect
10. C2×Dic758C22semidirect
11. C2×D1516C22semidirect
14. Dic1516C22semidirect
15. #20258595C22semidirect
16. D3032C22semidirect
18. M16×C379C22semidirect
19. C2×C8×C379C22semidirect
49. C379#575semidirect
55. C2×M16D379semidirect
68. M16C2×D379semidirect
69. C2×C8C2×D379semidirect

Maximal subgroups

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

subgroupindex
C2×#202586062
#271313642
#271313592
#271313532
C2×M16×C3792
#575379