Finite Group Databasebeta

← #23749769

Subgroups — #23749769

Order 9536.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×#14558737C211yesmaximal, characteristic, complemented
2C2×#14558721C211yesmaximal, characteristic, complemented
3#18011882C211yesmaximal, characteristic, complemented
4#18011835C211yesmaximal, characteristic, complemented
5#18011833C211yesmaximal, characteristic, complemented
6#18011823C211yesmaximal, characteristic, complemented
7C2×SD16×C149C211yesmaximal, characteristic, complemented
8#14558737—22no—
9#14558737—22no—
10C2×D596—21no—
11C2×D596C2211yescharacteristic
12C2×C22⋊D149—21no—
13C2×C4×D149—21no—
14C2×C4×D149C2211yescharacteristic
15#14558721—22no—
16C2×#11924746C2211yescharacteristic
17C4⋊Dic149C2211yescharacteristic
18C22⋊Dic149—21no—
19C2×Q8×C149C2211yescharacteristic
20C2×D4×C149C2211yescharacteristic
21SD16×C149—22no—
22C2×C8×C149C2211yescharacteristic
23C22×D149—21no—
24C22×D149D411yescharacteristic
25D596—24no—
26D596—21no—
27D596D412yescomplemented
28C22⋊D149—42no—
29C2×Dic149—21no—
30C2×Dic149D411yescharacteristic
31C4×D149—24no—
32C4×D149—21no—
33C4×D149—21no—
34#11924746—21no—
35C23×C149—21no—
36Q8×C149—21no—
37Q8×C149D412yescomplemented
38D4×C149—21no—
39D4×C149—21no—
40C2×C4×C149—21no—
41C2×C4×C149C2311yescharacteristic
42C8×C149—21no—
43C22×C149—41no—
44C22×C149—41no—
45C22×C149—41no—
46C22×C149C2×D411yescharacteristic
47C2×D149—21no—
48C2×D149—22no—
49C2×D149—21no—
50C2×D149—21no—
51C2×D149—41no—
52C2×D149—41no—
53C4×C149—22no—
54C4×C149C2×D411yescharacteristic
55C4×C149C2×D411yescharacteristic
56Dic149—21no—
57Dic149—41no—
58C2×C149—81no—
59C2×C149#12011yescharacteristic
60C2×C149#13511yescharacteristic
61C2×C149AGL(1,ℤ/8)11yescharacteristic
62D149—41no—
63D149—42no—
64C149#44911yescharacteristic, complemented, Sylow
65#449—1491nomaximal, Sylow
66C2×#41—1491no—
67C2×SD16D14911yescharacteristic, complemented
68C2×D8—1491no—
69#121—1491no—
70#103—1491no—
71#102—1491no—
72C22⋊C8—1491no—
73#41—2982no—
74#41—2982no—
75C2×Q8C2×D14911yescharacteristic
76C2×D4—2981no—
77C2×D4—2981no—
78C2×D4—1491no—
79C2×D4C2×D14911yescharacteristic
80C22×C4—2981no—
81C22×C4—1491no—
82SD16—22no—
83D8—2982no—
84C2×C8—1491no—
85C2×C8C2×D14911yescharacteristic
86C4⋊C4—1491no—
87C22⋊C4—2981no—
88C23—21no—
89C23—2981no—
90C23—1491no—
91Q8—21no—
92Q8C22⋊D14912yescomplemented
93D4—21no—
94D4—21no—
95D4—2984no—
96D4—2981no—
97D4—5962no—
98D4—1492no—
99C2×C4—21no—
100C2×C4—2984no—
101C2×C4—2981no—
102C2×C4—2981no—
103C2×C4—2981no—
104C2×C4—1491no—
105C2×C4C22×D14911yescharacteristic
106C8—21no—
107C8—2981no—
108C22—41no—
109C22—41no—
110C22—41no—
111C22—2981no—
112C22—2981no—
113C22—2981no—
114C22—2982no—
115C22—5961no—
116C22—5961no—
117C22D4×D14911yescharacteristic
118C4—22no—
119C4—2981no—
120C4—5961no—
121C4D4×D14911yescharacteristic
122C4C2×C22⋊D14911yescharacteristic
123C2—81no—
124C2—5961no—
125C2—5962no—
126C2#1801187911yescharacteristic
127C2#1801193211yescharacteristic
128C2#1801193811yescharacteristic
subgroupG/H
centerC22D4×D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
FittingC2×SD16×C149C2
socleC22×C149C2×D4
hypercenterC2×SD16D149
hypocenterC149#449
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14558737C2semidirect
2. C2×#14558721C2semidirect
3. #18011882C2semidirect
4. #18011835C2semidirect
5. #18011833C2semidirect
6. #18011823C2semidirect
7. C2×SD16×C149C2semidirect
27. D596D4semidirect
37. Q8×C149D4semidirect
64. C149#449semidirect
67. C2×SD16D149semidirect
92. Q8C22⋊D149semidirect