Finite Group Databasebeta

← #37588535

Subgroups — #37588535

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#27133874C211yesmaximal, characteristic, complemented
3#27133871C211yesmaximal, characteristic, complemented
4#27133841C211yesmaximal, characteristic, complemented
5#27133769C211yesmaximal, characteristic, complemented
6#27133759C211yesmaximal, characteristic, complemented
7#104×C383C211yesmaximal, characteristic, complemented
8#20259457—21no—
9#20259457C2211yescharacteristic
10#20259456—22no—
11#20259456—21no—
12C2×Dic766—21no—
13C2×Dic766C2211yescharacteristic
14C2×Dic766C2211yescharacteristic
15Q8×D383—21no—
16Dic1532—21no—
17#20259447—21no—
18#20259446—21no—
19#20259445—21no—
20#20259441C2211yescharacteristic
21C4⋊Dic383—22no—
22#41×C383C2211yescharacteristic
23M16×C383C2211yescharacteristic
24C42×C383C2211yescharacteristic
25Dic766—22no—
26Dic766—21no—
27Dic766—21no—
28Dic766—21no—
29Dic766—21no—
30Dic766D411yescharacteristic
31D1532D411yescharacteristic
32C22⋊D383—22no—
33C22⋊D383—21no—
34C2×Dic383—22no—
35C2×Dic383—21no—
36C2×Dic383D412yes—
37C4×D383—22no—
38C4×D383—21no—
39C383⋊C8—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—22no—
51C4×C383—21no—
52C4×C383C2×D411yescharacteristic
53C4×C383C2×D411yescharacteristic
54Dic383—21no—
55Dic383—22no—
56Dic383—41no—
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#137—3831no—
66C4⋊Q8—3831no—
67#104—3831no—
68#104D38311yescharacteristic, complemented
69#101—3831no—
70#41—3831no—
71#41—7661no—
72#41—7662no—
73#41—7661no—
74#41C2×D38311yescharacteristic
75C2×Q8—3831no—
76C2×Q8—3831no—
77C2×Q8—7661no—
78C2×Q8—7661no—
79Q16—7661no—
80Q16—7661no—
81SD16—7661no—
82SD16—7661no—
83M16—3831no—
84M16C2×D38311yescharacteristic
85C4⋊C4—7662no—
86C42C2×D38311yescharacteristic
87Q8—3831no—
88Q8—7662no—
89Q8—7661no—
90Q8—7661no—
91Q8—7661no—
92Q8—7661no—
93Q8D153211yescharacteristic
94D4—21no—
95D4—3831no—
96D4—7662no—
97D4—7661no—
98D4D153211yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3832no—
102C2×C4—7662no—
103C2×C4—7661no—
104C2×C4—7662no—
105C2×C4—7661no—
106C2×C4C22×D38311yescharacteristic
107C8—21no—
108C8—7661no—
109C22—21no—
110C22—7661no—
111C22D4×D38311yescharacteristic
112C4—22no—
113C4—21no—
114C4—15321no—
115C4—7662no—
116C4—7661no—
117C4D4×D38311yescharacteristic
118C4C2×D153211yescharacteristic
119C2—21no—
120C2—41no—
121C2—15321no—
122C2#2713381111yescharacteristic
subgroupG/H
centerC2#27133811
commutator, cosocleC2×C4×C383C23
FrattiniC2×C4C22×D383
Fitting#104×C383C2
socleC2×C383#120
prime radical#27133888C2
hypercenter#104D383
hypocenterC383#456
LCSG ▷ C2×C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #27133874C2semidirect
3. #27133871C2semidirect
4. #27133841C2semidirect
5. #27133769C2semidirect
6. #27133759C2semidirect
7. #104×C383C2semidirect
61. C383#456semidirect
68. #104D383semidirect

Maximal subgroups

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

subgroupindex
#271338882
#271338742
#271338712
#271338412
#271337692
#271337592
#104×C3832
#456383