Finite Group Databasebeta

← #14583070

Subgroups — #14583070

Order 2752.

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#13063372C211yesmaximal, characteristic, complemented
2#13063351C211yesmaximal, characteristic, complemented
3#13063312C211yesmaximal, characteristic, complemented
4#13063252C211yesmaximal, characteristic, complemented
5#13063251C211yesmaximal, characteristic, complemented
6#13063243C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
8#41×C43C2211yescharacteristic
9C2×D4×C43C2211yescharacteristic
10Q8×D43—21no—
11#10621900—21no—
12#10621900—22no—
13#10621898—21no—
14#10621898C2211yescharacteristic
15C2×Dic86—21no—
16C2×Dic86C2211yescharacteristic
17SD16×C43—21no—
18D8×C43—21no—
19M16×C43C2211yescharacteristic
20C22⋊Dic43—22no—
21#10621883—21no—
22#10621882—21no—
23C4×Dic43C2211yescharacteristic
24#10621877C2211yescharacteristic
25C23×C43—21no—
26Q8×C43D411yescharacteristic
27D4×C43—21no—
28D4×C43—21no—
29D4×C43—21no—
30D4×C43D411yescharacteristic
31C2×C4×C43—21no—
32C2×C4×C43C2311yescharacteristic
33C22⋊D43—22no—
34C22⋊D43—21no—
35C2×Dic43—22no—
36C2×Dic43—21no—
37C2×Dic43D412yes—
38D172D411yescharacteristic
39C4×D43—22no—
40C4×D43—21no—
41Dic86—22no—
42Dic86—21no—
43Dic86—21no—
44Dic86D411yescharacteristic
45C8×C43—21no—
46C43⋊C8—21no—
47C22×C43—21no—
48C22×C43—42no—
49C22×C43—41no—
50C22×C43C2×D411yescharacteristic
51C2×D43—21no—
52C4×C43—21no—
53C4×C43C2×D411yescharacteristic
54C4×C43C2×D411yescharacteristic
55Dic43—22no—
56Dic43—21no—
57Dic43—41no—
58C2×C43—21no—
59C2×C43—41no—
60C2×C43—81no—
61C2×C43#12011yescharacteristic
62D43—41no—
63#454—431nomaximal, Sylow
64C43#45411yescharacteristic, complemented, Sylow
652−1+4—431no—
66AGL(1,ℤ/8)—431no—
67AGL(1,ℤ/8)D4311yescharacteristic, complemented
68#124—431no—
69#104—431no—
70#104—431no—
71#101—431no—
72#41—431no—
73#41—861no—
74#41—862no—
75#41—861no—
76#41C2×D4311yescharacteristic
77C2×Q8—431no—
78C2×Q8—861no—
79C2×Q8—861no—
80C2×D4C2×D4311yescharacteristic
81SD16—21no—
82SD16—861no—
83D8—21no—
84D8—861no—
85M16—431no—
86M16C2×D4311yescharacteristic
87C22⋊C4—862no—
88C42—431no—
89C23—21no—
90Q8—431no—
91Q8—862no—
92Q8—861no—
93Q8—861no—
94Q8C22⋊D4311yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—431no—
99D4—862no—
100D4—861no—
101D4C22⋊D4311yescharacteristic
102C2×C4—21no—
103C2×C4—432no—
104C2×C4—862no—
105C2×C4—862no—
106C2×C4—861no—
107C2×C4—861no—
108C2×C4C22×D4311yescharacteristic
109C8—21no—
110C8—861no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—861no—
115C22D4×D4311yescharacteristic
116C4—21no—
117C4—862no—
118C4—861no—
119C4—1721no—
120C4D4×D4311yescharacteristic
121C4C2×C22⋊D4311yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—1721no—
126C2#1306329311yescharacteristic
subgroupG/H
centerC2#13063293
commutator, cosocleC2×C4×C43C23
FrattiniC2×C4C22×D43
FittingAGL(1,ℤ/8)×C43C2
socleC2×C43#120
hypercenterAGL(1,ℤ/8)D43
hypocenterC43#454
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13063372C2semidirect
2. #13063351C2semidirect
3. #13063312C2semidirect
4. #13063252C2semidirect
5. #13063251C2semidirect
6. #13063243C2semidirect
7. AGL(1,ℤ/8)×C43C2semidirect
64. C43#454semidirect
67. AGL(1,ℤ/8)D43semidirect

Maximal subgroups

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

subgroupindex
#130633722
#130633512
#130633122
#130632522
#130632512
#130632432
AGL(1,ℤ/8)×C432
#45443