Finite Group Databasebeta

← #23749899

Subgroups — #23749899

Order 9536.

100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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#18011944C211yesmaximal, characteristic
2#18011942C211yesmaximal, characteristic
3C2×#14558726C211yesmaximal, characteristic, complemented
4#18011919C211yesmaximal, characteristic
5#18011846C211yesmaximal, characteristic, complemented
6#18011829C211yesmaximal, characteristic, complemented
7#101×C149C211yesmaximal, characteristic, complemented
8#14558736C2211yescharacteristic
9C2×Dic298C2211yescharacteristic
10Dic596—21no—
11#14558726—21no—
12#14558726—21no—
13#14558726—21no—
14#14558725—21no—
15#14558723—21no—
16#14558720C2211yescharacteristic
17#14558719—21no—
18C2×#11924746C2211yescharacteristic
19C8×D149—21no—
20C2×Q8×C149C2211yescharacteristic
21M16×C149C2211yescharacteristic
22M16×C149C2211yescharacteristic
23Dic298—21no—
24Dic298—21no—
25Dic298D411yescharacteristic
26D596D411yescharacteristic
27C22⋊D149—21no—
28C2×Dic149—21no—
29C4×D149—21no—
30#11924746—21no—
31#11924746D411yescharacteristic
32#11924746D411yescharacteristic
33Q8×C149—21no—
34Q8×C149—21no—
35C2×C4×C149—21no—
36C2×C4×C149C2311yescharacteristic
37C8×C149—21no—
38C8×C149—21no—
39C22×C149#4111yescharacteristic
40C2×D149—21no—
41C4×C149—41no—
42C4×C149C2×D411yescharacteristic
43C4×C149C2×D411yescharacteristic
44Dic149—21no—
45Dic149—41no—
46C2×C149—21no—
47C2×C149#12111yescharacteristic
48D149—41no—
49C149#47311yescharacteristic, complemented, Sylow
50#473—1491nomaximal, Sylow
51#137—1491no—
52#137—1491no—
53C2×Q16—1491no—
54#131—1491no—
55#108—1491no—
56#101—1491no—
57#101D14911yescharacteristic, complemented
58#41—1491no—
59C2×Q8—1491no—
60C2×Q8C2×D14911yescharacteristic
61Q16—2981no—
62Q16—2981no—
63Q16—2981no—
64Q16—2981no—
65SD16—2981no—
66SD16—2981no—
67M16—2981no—
68M16—1491no—
69M16C2×D14911yescharacteristic
70M16C2×D14911yescharacteristic
71C2×C8—2981no—
72C2×C8—1491no—
73Q8—21no—
74Q8—21no—
75Q8—2981no—
76Q8—2981no—
77Q8—1491no—
78D4—2981no—
79D4—1491no—
80C2×C4—21no—
81C2×C4—2981no—
82C2×C4—2981no—
83C2×C4C22×D14911yescharacteristic
84C8—21no—
85C8—21no—
86C8—2981no—
87C8—1491no—
88C8—1491no—
89C22—2981no—
90C22#1455873611yescharacteristic
91C4—41no—
92C4—2981no—
93C4—5961no—
94C4D4×D14911yescharacteristic
95C4D4×D14911yescharacteristic
96C2—21no—
97C2—5961no—
98C2#1801188411yescharacteristic
subgroupG/H
centerC2#18011884
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
Fitting#101×C149C2
socleC2×C149#121
prime radical#14558736C22
hypercenter#101D149
hypocenterC149#473
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. C2×#14558726C2semidirect
5. #18011846C2semidirect
6. #18011829C2semidirect
7. #101×C149C2semidirect
49. C149#473semidirect
57. #101D149semidirect