Finite Group Databasebeta

← #23749865

Subgroups — #23749865

Order 9536.

114 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 41 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×#14558726C211yesmaximal, characteristic, complemented
2C2×C8×D149C211yesmaximal, characteristic
3#18011891C211yesmaximal, characteristic
4#18011887C211yesmaximal, characteristic
5#18011844C211yesmaximal, characteristic, complemented
6#18011836C211yesmaximal, characteristic, complemented
7#103×C149C211yesmaximal, characteristic, complemented
8C2×Dic298C2211yescharacteristic
9C2×C4×D149C2211yescharacteristic
10#14558726—22no—
11C2×#11924746C2211yescharacteristic
12C8×D149—22no—
13C4⋊Dic149—21no—
14C4⋊Dic149C2211yescharacteristic
15#14558715—21no—
16#14558713—21no—
17#14558713—21no—
18C2×Q8×C149C2211yescharacteristic
19C2×C8×C149C2211yescharacteristic
20C4⋊C4×C149C2211yescharacteristic
21C22×D149D411yescharacteristic
22Dic298—21no—
23Dic298—21no—
24C2×Dic149—21no—
25C2×Dic149—21no—
26C2×Dic149D411yescharacteristic
27C4×D149—21no—
28C4×D149—21no—
29#11924746D412yes—
30Q8×C149—21no—
31Q8×C149—21no—
32C2×C4×C149—21no—
33C2×C4×C149—21no—
34C2×C4×C149C2311yescharacteristic
35C8×C149—21no—
36C22×C149C2×D411yescharacteristic
37C2×D149—21no—
38C2×D149—21no—
39C2×D149Q1612yescomplemented
40C4×C149—41no—
41C4×C149—41no—
42C4×C149C2×D411yescharacteristic
43C4×C149#4111yescharacteristic
44Dic149—21no—
45Dic149—41no—
46Dic149—41no—
47C2×C149#12111yescharacteristic
48C2×C149C2×Q1611yescharacteristic
49C2×C149#13511yescharacteristic
50D149—22no—
51C149#46711yescharacteristic, complemented, Sylow
52#467—1491nomaximal, Sylow
53C2×Q16—1491no—
54C22×C8—1491no—
55C22⋊Q8—1491no—
56C22⋊Q8—1491no—
57#107—1491no—
58#103—1491no—
59#103D14911yescharacteristic, complemented
60C2×Q8—1491no—
61C2×Q8C2×D14911yescharacteristic
62C22×C4—1491no—
63Q16—2982no—
64C2×C8—2982no—
65C2×C8—1491no—
66C2×C8C2×D14911yescharacteristic
67C4⋊C4—2981no—
68C4⋊C4—2981no—
69C4⋊C4—1491no—
70C4⋊C4C2×D14911yescharacteristic
71C22⋊C4—2981no—
72C22⋊C4—2981no—
73C23—1491no—
74Q8—21no—
75Q8—21no—
76Q8—2981no—
77Q8—2981no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—2981no—
81C2×C4—2981no—
82C2×C4—2981no—
83C2×C4—2981no—
84C2×C4—1491no—
85C2×C4C22×D14911yescharacteristic
86C8—21no—
87C8—1492no—
88C22—2981no—
89C22—2981no—
90C22—1492no—
91C22D4×D14911yescharacteristic
92C4—41no—
93C4—41no—
94C4—2981no—
95C4—5961no—
96C4—5961no—
97C4D4×D14911yescharacteristic
98C4#1455873611yescharacteristic
99C2—2982no—
100C2#1801188411yescharacteristic
101C2Q16×D14911yescharacteristic
102C2#1801193211yescharacteristic
subgroupG/H
centerC22D4×D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
Fitting#103×C149C2
socleC22×C149C2×D4
prime radicalC22×D149D4
hypercenter#103D149
hypocenterC149#467
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#14558726C2semidirect
5. #18011844C2semidirect
6. #18011836C2semidirect
7. #103×C149C2semidirect
39. C2×D149Q16semidirect
51. C149#467semidirect
59. #103D149semidirect