Finite Group Databasebeta

← #37588522

Subgroups — #37588522

Order 24512.

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

normal subgroups only

This group has 146 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, complemented
2#27133867C211yesmaximal, characteristic, complemented
3#27133828C211yesmaximal, characteristic, complemented
4#27133768C211yesmaximal, characteristic, complemented
5#27133767C211yesmaximal, characteristic, complemented
6#27133759C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C383C211yesmaximal, characteristic, complemented
8#20259457—21no—
9#20259457C2211yescharacteristic
10#20259456—22no—
11#20259456—21no—
12C2×Dic766—21no—
13C2×Dic766C2211yescharacteristic
14Q8×D383—21no—
15#20259445—21no—
16#20259442—21no—
17#20259441C2211yescharacteristic
18C22⋊Dic383—22no—
19C4×Dic383C2211yescharacteristic
20#41×C383C2211yescharacteristic
21C2×D4×C383C2211yescharacteristic
22SD16×C383—21no—
23D8×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—
38C23×C383—21no—
39Q8×C383D411yescharacteristic
40D4×C383—21no—
41D4×C383—21no—
42D4×C383—21no—
43D4×C383D411yescharacteristic
44C2×C4×C383—21no—
45C2×C4×C383C2311yescharacteristic
46C8×C383—21no—
47C22×C383—21no—
48C22×C383—42no—
49C22×C383—41no—
50C22×C383C2×D411yescharacteristic
51C2×D383—21no—
52C4×C383—21no—
53C4×C383C2×D411yescharacteristic
54C4×C383C2×D411yescharacteristic
55Dic383—21no—
56Dic383—22no—
57Dic383—41no—
58C2×C383—21no—
59C2×C383—41no—
60C2×C383—81no—
61C2×C383#12011yescharacteristic
62D383—41no—
63C383#45411yescharacteristic, complemented, Sylow
64#454—3831nomaximal, Sylow
652−1+4—3831no—
66AGL(1,ℤ/8)—3831no—
67AGL(1,ℤ/8)D38311yescharacteristic, complemented
68#124—3831no—
69#104—3831no—
70#104—3831no—
71#101—3831no—
72#41—3831no—
73#41—7661no—
74#41—7662no—
75#41—7661no—
76#41C2×D38311yescharacteristic
77C2×Q8—3831no—
78C2×Q8—7661no—
79C2×Q8—7661no—
80C2×D4C2×D38311yescharacteristic
81SD16—21no—
82SD16—7661no—
83D8—21no—
84D8—7661no—
85M16—3831no—
86M16C2×D38311yescharacteristic
87C22⋊C4—7662no—
88C42—3831no—
89C23—21no—
90Q8—3831no—
91Q8—7662no—
92Q8—7661no—
93Q8—7661no—
94Q8C22⋊D38311yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—3831no—
99D4—7662no—
100D4—7661no—
101D4C22⋊D38311yescharacteristic
102C2×C4—21no—
103C2×C4—3832no—
104C2×C4—7662no—
105C2×C4—7661no—
106C2×C4—7662no—
107C2×C4—7661no—
108C2×C4C22×D38311yescharacteristic
109C8—21no—
110C8—7661no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—7661no—
115C22D4×D38311yescharacteristic
116C4—21no—
117C4—15321no—
118C4—7662no—
119C4—7661no—
120C4D4×D38311yescharacteristic
121C4C2×C22⋊D38311yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—15321no—
126C2#2713380911yescharacteristic
subgroupG/H
centerC2#27133809
commutator, cosocleC2×C4×C383C23
FrattiniC2×C4C22×D383
FittingAGL(1,ℤ/8)×C383C2
socleC2×C383#120
hypercenterAGL(1,ℤ/8)D383
hypocenterC383#454
LCSG ▷ C2×C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #27133888C2semidirect
2. #27133867C2semidirect
3. #27133828C2semidirect
4. #27133768C2semidirect
5. #27133767C2semidirect
6. #27133759C2semidirect
7. AGL(1,ℤ/8)×C383C2semidirect
63. C383#454semidirect
67. AGL(1,ℤ/8)D383semidirect

Maximal subgroups

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

subgroupindex
#271338882
#271338672
#271338282
#271337682
#271337672
#271337592
AGL(1,ℤ/8)×C3832
#454383