Finite Group Databasebeta

← #37588532

Subgroups — #37588532

Order 24512.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#27133888C211yesmaximal, characteristic
2#27133872C211yesmaximal, characteristic, complemented
3#27133839C211yesmaximal, characteristic, complemented
4#27133768C211yesmaximal, characteristic, complemented
5#27133767C211yesmaximal, characteristic, complemented
6#27133759C211yesmaximal, characteristic, complemented
7#137×C383C211yesmaximal, characteristic, complemented
8#20259457—21no—
9#20259457C2211yescharacteristic
10#20259456—22no—
11#20259456—21no—
12C2×Dic766—21no—
13C2×Dic766C2211yescharacteristic
14Q8×D383—21no—
15#20259447—21no—
16#20259444—21no—
17#20259441C2211yescharacteristic
18Dic383⋊C4—22no—
19C4×Dic383C2211yescharacteristic
20#41×C383C2211yescharacteristic
21C2×Q8×C383C2211yescharacteristic
22Q16×C383—21no—
23SD16×C383—21no—
24M16×C383C2211yescharacteristic
25Dic766—22no—
26Dic766—21no—
27Dic766—21no—
28Dic766D411yescharacteristic
29D1532D411yescharacteristic
30C22⋊D383—22no—
31C22⋊D383—21no—
32C2×Dic383—22no—
33C2×Dic383—21no—
34C2×Dic383D412yes—
35C4×D383—22no—
36C4×D383—21no—
37C383⋊C8—21no—
38Q8×C383—21no—
39Q8×C383—21no—
40Q8×C383D411yescharacteristic
41D4×C383—21no—
42D4×C383D411yescharacteristic
43C2×C4×C383—21no—
44C2×C4×C383—21no—
45C2×C4×C383C2311yescharacteristic
46C8×C383—21no—
47C22×C383—21no—
48C22×C383C2×D411yescharacteristic
49C2×D383—21no—
50C4×C383—21no—
51C4×C383—41no—
52C4×C383C2×D411yescharacteristic
53C4×C383C2×D411yescharacteristic
54Dic383—22no—
55Dic383—21no—
56Dic383—22no—
57C2×C383—21no—
58C2×C383—41no—
59C2×C383#12011yescharacteristic
60D383—41no—
61C383#45611yescharacteristic, complemented, Sylow
62#456—3831nomaximal, Sylow
632−1+4—3831no—
64#137—3831no—
65#137D38311yescharacteristic, complemented
66C4⋊Q8—3831no—
67#104—3831no—
68#104—3831no—
69#101—3831no—
70#41—3831no—
71#41—7661no—
72#41—7662no—
73#41—7661no—
74#41C2×D38311yescharacteristic
75C2×Q8—3831no—
76C2×Q8—7661no—
77C2×Q8—7661no—
78C2×Q8C2×D38311yescharacteristic
79Q16—21no—
80Q16—7661no—
81SD16—21no—
82SD16—7661no—
83M16—3831no—
84M16C2×D38311yescharacteristic
85C4⋊C4—7662no—
86C42—3831no—
87Q8—21no—
88Q8—21no—
89Q8—3831no—
90Q8—7662no—
91Q8—7661no—
92Q8—7661no—
93Q8C22⋊D38311yescharacteristic
94D4—21no—
95D4—3831no—
96D4—7662no—
97D4—7661no—
98D4C22⋊D38311yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3832no—
102C2×C4—7662no—
103C2×C4—7662no—
104C2×C4—7661no—
105C2×C4—7661no—
106C2×C4C22×D38311yescharacteristic
107C8—21no—
108C8—7661no—
109C22—21no—
110C22—7661no—
111C22D4×D38311yescharacteristic
112C4—21no—
113C4—41no—
114C4—7662no—
115C4—7662no—
116C4—7661no—
117C4D4×D38311yescharacteristic
118C4C2×C22⋊D38311yescharacteristic
119C2—21no—
120C2—41no—
121C2—15321no—
122C2#2713380911yescharacteristic
subgroupG/H
centerC2#27133809
commutator, cosocleC2×C4×C383C23
FrattiniC2×C4C22×D383
Fitting#137×C383C2
socleC2×C383#120
prime radical#27133888C2
hypercenter#137D383
hypocenterC383#456
LCSG ▷ C2×C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #27133872C2semidirect
3. #27133839C2semidirect
4. #27133768C2semidirect
5. #27133767C2semidirect
6. #27133759C2semidirect
7. #137×C383C2semidirect
61. C383#456semidirect
65. #137D383semidirect

Maximal subgroups

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

subgroupindex
#271338882
#271338722
#271338392
#271337682
#271337672
#271337592
#137×C3832
#456383