Finite Group Databasebeta

← #23749784

Subgroups — #23749784

Order 9536.

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

normal subgroups only

This group has 152 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×#14558735C211yesmaximal, characteristic
2C2×#14558726C211yesmaximal, characteristic, complemented
3#18011887C211yesmaximal, characteristic, complemented
4#18011836C211yesmaximal, characteristic, complemented
5#18011832C211yesmaximal, characteristic, complemented
6#18011823C211yesmaximal, characteristic, complemented
7C2×SD16×C149C211yesmaximal, characteristic, complemented
8#14558735—22no—
9#14558735—22no—
10C2×Dic298C2211yescharacteristic
11C2×C22⋊D149—21no—
12C22×Dic149—21no—
13C2×C4×D149C2211yescharacteristic
14#14558726—22no—
15C2×#11924746C2211yescharacteristic
16C4⋊Dic149C2211yescharacteristic
17#14558715—21no—
18#14558713—21no—
19C2×Q8×C149C2211yescharacteristic
20C2×D4×C149C2211yescharacteristic
21SD16×C149—22no—
22C2×C8×C149C2211yescharacteristic
23C22×D149D411yescharacteristic
24Dic298—21no—
25Dic298D412yes—
26C22⋊D149—24no—
27C2×Dic149—24no—
28C2×Dic149—21no—
29C2×Dic149—21no—
30C2×Dic149D411yescharacteristic
31C4×D149—21no—
32C4×D149—21no—
33#11924746—21no—
34C23×C149—21no—
35Q8×C149—21no—
36Q8×C149—21no—
37D4×C149—21no—
38D4×C149D412yes—
39C2×C4×C149—21no—
40C2×C4×C149C2311yescharacteristic
41C8×C149—21no—
42C22×C149—22no—
43C22×C149—41no—
44C22×C149—41no—
45C22×C149C2×D411yescharacteristic
46C2×D149—21no—
47C2×D149—21no—
48C2×D149—21no—
49C4×C149—41no—
50C4×C149C2×D411yescharacteristic
51C4×C149C2×D411yescharacteristic
52Dic149—21no—
53Dic149—22no—
54Dic149—41no—
55C2×C149—42no—
56C2×C149#12011yescharacteristic
57C2×C149#13511yescharacteristic
58C2×C149#13711yescharacteristic
59D149—41no—
60C149#45211yescharacteristic, complemented, Sylow
61#452—1491nomaximal, Sylow
62C2×#41—1491no—
63C2×Q16—1491no—
64C2×SD16D14911yescharacteristic, complemented
65C22⋊Q8—1491no—
66#103—1491no—
67#102—1491no—
68C22⋊C8—1491no—
69#41—2982no—
70#41—2982no—
71C2×Q8—1491no—
72C2×Q8C2×D14911yescharacteristic
73C2×D4—2981no—
74C2×D4C2×D14911yescharacteristic
75C22×C4—2981no—
76C22×C4—1491no—
77Q16—2982no—
78SD16—22no—
79C2×C8—1491no—
80C2×C8C2×D14911yescharacteristic
81C4⋊C4—2981no—
82C4⋊C4—1491no—
83C22⋊C4—2981no—
84C23—21no—
85C23—1491no—
86Q8—21no—
87Q8—21no—
88Q8—2981no—
89Q8—1492no—
90D4—21no—
91D4—2984no—
92D4C22⋊D14912yes—
93C2×C4—21no—
94C2×C4—2984no—
95C2×C4—2981no—
96C2×C4—2981no—
97C2×C4—2981no—
98C2×C4—2981no—
99C2×C4—1491no—
100C2×C4C22×D14911yescharacteristic
101C8—21no—
102C8—2981no—
103C22—22no—
104C22—41no—
105C22—41no—
106C22—2981no—
107C22—2981no—
108C22—2981no—
109C22D4×D14911yescharacteristic
110C4—41no—
111C4—2981no—
112C4—2982no—
113C4—5961no—
114C4D4×D14911yescharacteristic
115C4C2×C22⋊D14911yescharacteristic
116C2—42no—
117C2—5961no—
118C2#1801187911yescharacteristic
119C2#1801193211yescharacteristic
120C2#1801194011yescharacteristic
subgroupG/H
centerC22D4×D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
FittingC2×SD16×C149C2
socleC22×C149C2×D4
prime radicalC2×#14558735C2
hypercenterC2×SD16D149
hypocenterC149#452
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
2. C2×#14558726C2semidirect
3. #18011887C2semidirect
4. #18011836C2semidirect
5. #18011832C2semidirect
6. #18011823C2semidirect
7. C2×SD16×C149C2semidirect
60. C149#452semidirect
64. C2×SD16D149semidirect