Finite Group Databasebeta

← #28411652

Subgroups — #28411652

Order 14656.

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#20301035C211yesmaximal, characteristic, complemented
2#20301014C211yesmaximal, characteristic, complemented
3#20300975C211yesmaximal, characteristic, complemented
4#20300915C211yesmaximal, characteristic, complemented
5#20300914C211yesmaximal, characteristic, complemented
6#20300906C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C229C211yesmaximal, characteristic, complemented
8#16814666—21no—
9#16814666C2211yescharacteristic
10#16814665—22no—
11#16814665—21no—
12C2×Dic458—21no—
13C2×Dic458C2211yescharacteristic
14Q8×D229—21no—
15#16814654—21no—
16#16814651—21no—
17#16814650C2211yescharacteristic
18C22⋊Dic229—22no—
19C4×Dic229C2211yescharacteristic
20#41×C229C2211yescharacteristic
21C2×D4×C229C2211yescharacteristic
22SD16×C229—21no—
23D8×C229—21no—
24M16×C229C2211yescharacteristic
25Dic458—22no—
26Dic458—21no—
27Dic458—21no—
28Dic458D411yescharacteristic
29D916D411yescharacteristic
30C22⋊D229—22no—
31C22⋊D229—21no—
32C2×Dic229—22no—
33C2×Dic229—21no—
34C2×Dic229D412yes—
35C4×D229—22no—
36C4×D229—21no—
37#14270080—21no—
38C23×C229—21no—
39Q8×C229D411yescharacteristic
40D4×C229—21no—
41D4×C229—21no—
42D4×C229—21no—
43D4×C229D411yescharacteristic
44C2×C4×C229—21no—
45C2×C4×C229C2311yescharacteristic
46C8×C229—21no—
47C22×C229—21no—
48C22×C229—42no—
49C22×C229—41no—
50C22×C229C2×D411yescharacteristic
51C2×D229—21no—
52C4×C229—21no—
53C4×C229C2×D411yescharacteristic
54C4×C229C2×D411yescharacteristic
55Dic229—21no—
56Dic229—22no—
57Dic229—41no—
58C2×C229—21no—
59C2×C229—41no—
60C2×C229—81no—
61C2×C229#12011yescharacteristic
62D229—41no—
63C229#45411yescharacteristic, complemented, Sylow
64#454—2291nomaximal, Sylow
652−1+4—2291no—
66AGL(1,ℤ/8)—2291no—
67AGL(1,ℤ/8)D22911yescharacteristic, complemented
68#124—2291no—
69#104—2291no—
70#104—2291no—
71#101—2291no—
72#41—4581no—
73#41—4581no—
74#41—4582no—
75#41—2291no—
76#41C2×D22911yescharacteristic
77C2×Q8—4581no—
78C2×Q8—4581no—
79C2×Q8—2291no—
80C2×D4C2×D22911yescharacteristic
81SD16—21no—
82SD16—4581no—
83D8—21no—
84D8—4581no—
85M16—2291no—
86M16C2×D22911yescharacteristic
87C22⋊C4—4582no—
88C42—2291no—
89C23—21no—
90Q8—4582no—
91Q8—4581no—
92Q8—4581no—
93Q8—2291no—
94Q8C22⋊D22911yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—4582no—
99D4—4581no—
100D4—2291no—
101D4C22⋊D22911yescharacteristic
102C2×C4—21no—
103C2×C4—4582no—
104C2×C4—4581no—
105C2×C4—4582no—
106C2×C4—4581no—
107C2×C4—2292no—
108C2×C4C22×D22911yescharacteristic
109C8—21no—
110C8—4581no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—4581no—
115C22D4×D22911yescharacteristic
116C4—21no—
117C4—9161no—
118C4—4581no—
119C4—4582no—
120C4D4×D22911yescharacteristic
121C4C2×C22⋊D22911yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—9161no—
126C2#2030095611yescharacteristic
subgroupG/H
centerC2#20300956
commutator, cosocleC2×C4×C229C23
FrattiniC2×C4C22×D229
FittingAGL(1,ℤ/8)×C229C2
socleC2×C229#120
hypercenterAGL(1,ℤ/8)D229
hypocenterC229#454
LCSG ▷ C2×C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #20301035C2semidirect
2. #20301014C2semidirect
3. #20300975C2semidirect
4. #20300915C2semidirect
5. #20300914C2semidirect
6. #20300906C2semidirect
7. AGL(1,ℤ/8)×C229C2semidirect
63. C229#454semidirect
67. AGL(1,ℤ/8)D229semidirect

Maximal subgroups

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

subgroupindex
#203010352
#203010142
#203009752
#203009152
#203009142
#203009062
AGL(1,ℤ/8)×C2292
#454229