Finite Group Databasebeta

← #37589148

Subgroups — #37589148

Order 24512.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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#41×D383C212yesmaximal, complemented
2#27133873C212yesmaximal, complemented
3#27133870C212yesmaximal, complemented
4#27133868C212yesmaximal, complemented
5#27133865C212yesmaximal, complemented
6#27133863C211yesmaximal, characteristic, complemented
7#27133861C212yesmaximal, complemented
8C2×#20259440C211yesmaximal, characteristic, complemented
9#135×C383C211yesmaximal, characteristic, complemented
10#20259458C2212yes—
11#20259457—22no—
12#20259457C2212yescomplemented
13#20259456—22no—
14#20259456C2212yes—
15Q8×D383C2212yescomplemented
16D4×D383—22no—
17D4×D383C2212yescomplemented
18C2×C4×D383—22no—
19C2×C4×D383C2211yescharacteristic
20Dic1532C2211yescharacteristic, complemented
21#20259447C2212yescomplemented
22#20259446C2212yescomplemented
23#20259445C2212yescomplemented
24#20259444C2212yescomplemented
25D3064C2211yescharacteristic, complemented
26#20259442C2212yescomplemented
27#20259440C2212yescomplemented
28#20259440C2212yescomplemented
29C2×C383⋊C8C2211yescharacteristic, complemented
30#41×C383C2212yescomplemented
31Q16×C383C2211yescharacteristic, complemented
32SD16×C383C2212yescomplemented
33D8×C383C2211yescharacteristic, complemented
34C2×C8×C383C2211yescharacteristic, complemented
35C22×D383—22no—
36C22×D383D411yescharacteristic
37Dic766—22no—
38Dic766C2312yes—
39D1532—22no—
40D1532C2312yes—
41C22⋊D383—22no—
42C22⋊D383—22no—
43C22⋊D383—22no—
44C2×Dic383—22no—
45C2×Dic383D411yescharacteristic
46C4×D383—22no—
47C4×D383—22no—
48C4×D383—22no—
49C4×D383D412yes—
50C4×D383C2312yes—
51C383⋊C8C2312yes—
52Q8×C383C2312yes—
53D4×C383—22no—
54D4×C383C2312yes—
55C2×C4×C383—22no—
56C2×C4×C383C2311yescharacteristic
57C8×C383C2311yescharacteristic
58C8×C383C2311yescharacteristic
59C22×C383—22no—
60C22×C383C2×D411yescharacteristic
61C2×D383—22no—
62C2×D383—41no—
63C2×D383—44no—
64C2×D383C2×D412yes—
65C4×C383—22no—
66C4×C383C2×D411yescharacteristic
67C4×C383C2411yescharacteristic
68Dic383—22no—
69Dic383C2×D412yes—
70C2×C383—21no—
71C2×C383—42no—
72C2×C383C22×D411yescharacteristic
73D383—22no—
74D383—42no—
75C383#57511yescharacteristic, complemented, Sylow
76#575—3831nomaximal, Sylow
77C2×#41—3832no—
78#137—3832no—
79#137—3832no—
80AGL(1,ℤ/8)—3832no—
81AGL(1,ℤ/8)—3832no—
82#135—3832no—
83#135—3831no—
84#135D38311yescharacteristic, complemented
85C2×M16—3831no—
86#41—3832no—
87#41—3832no—
88#41—3832no—
89#41—7662no—
90#41—7662no—
91#41C2×D38312yescomplemented
92C2×Q8—3832no—
93C2×D4—3832no—
94C2×D4—7662no—
95C22×C4—3831no—
96C22×C4—7662no—
97Q16—3832no—
98Q16—3831no—
99Q16C2×D38311yescharacteristic, complemented
100SD16—3832no—
101SD16—3832no—
102SD16—3832no—
103SD16C2×D38312yescomplemented
104D8—3832no—
105D8—3831no—
106D8C2×D38311yescharacteristic, complemented
107M16—3832no—
108M16—3832no—
109C2×C8—3831no—
110C2×C8C2×D38311yescharacteristic, complemented
111C23—3831no—
112C23—7662no—
113Q8—3832no—
114Q8—7662no—
115Q8C22×D38312yes—
116D4—22no—
117D4—3832no—
118D4—7662no—
119D4—7662no—
120D4—7662no—
121D4—7662no—
122D4C22×D38312yes—
123C2×C4—22no—
124C2×C4—3831no—
125C2×C4—3832no—
126C2×C4—3832no—
127C2×C4—7662no—
128C2×C4—7662no—
129C2×C4—7662no—
130C2×C4—7662no—
131C2×C4C22×D38311yescharacteristic
132C8—3832no—
133C8C22×D38311yescharacteristic
134C8C22×D38311yescharacteristic
135C22—22no—
136C22—3832no—
137C22—15321no—
138C22—15324no—
139C22—7662no—
140C22D4×D38311yescharacteristic
141C4—22no—
142C4—3832no—
143C4—7662no—
144C4D4×D38311yescharacteristic
145C4C23×D38311yescharacteristic
146C2—21no—
147C2—42no—
148C2—15322no—
149C2—7662no—
150C2C2×D4×D38311yescharacteristic
subgroupG/H
centerC4D4×D383
commutator, cosocleC4×C383C24
FrattiniC4C23×D383
Fitting#135×C383C2
socleC2×C383C22×D4
hypercenter#135D383
hypocenterC383#575
LCSG ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D383C2semidirect
2. #27133873C2semidirect
3. #27133870C2semidirect
4. #27133868C2semidirect
5. #27133865C2semidirect
6. #27133863C2semidirect
7. #27133861C2semidirect
8. C2×#20259440C2semidirect
9. #135×C383C2semidirect
12. #20259457C22semidirect
15. Q8×D383C22semidirect
17. D4×D383C22semidirect
20. Dic1532C22semidirect
21. #20259447C22semidirect
22. #20259446C22semidirect
23. #20259445C22semidirect
24. #20259444C22semidirect
25. D3064C22semidirect
26. #20259442C22semidirect
27. #20259440C22semidirect
28. #20259440C22semidirect
29. C2×C383⋊C8C22semidirect
30. #41×C383C22semidirect
31. Q16×C383C22semidirect
32. SD16×C383C22semidirect
33. D8×C383C22semidirect
34. C2×C8×C383C22semidirect
75. C383#575semidirect
84. #135D383semidirect
91. #41C2×D383semidirect
99. Q16C2×D383semidirect
103. SD16C2×D383semidirect
106. D8C2×D383semidirect
110. C2×C8C2×D383semidirect

Maximal subgroups

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

subgroupindex
#41×D3832
#271338732
#271338702
#271338682
#271338652
#271338632
#271338612
C2×#202594402
#135×C3832
#575383