Finite Group Databasebeta

← #23749787

Subgroups — #23749787

Order 9536.

152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 47 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×#14558724C211yesmaximal, characteristic, complemented
3#18011890C211yesmaximal, characteristic, complemented
4#18011835C211yesmaximal, characteristic, complemented
5#18011832C211yesmaximal, characteristic, complemented
6C22⋊#11924746C211yesmaximal, characteristic, complemented
7C2×#41×C149C211yesmaximal, characteristic
8C2×Dic298C2211yescharacteristic
9#14558726—22no—
10#14558724—22no—
11C2×#11924746C2211yescharacteristic
12C2×#11924746C2211yescharacteristic
13C4⋊Dic149C2211yescharacteristic
14#14558715—21no—
15C22⋊Dic149—21no—
16#41×C149—22no—
17#41×C149—22no—
18C2×Q8×C149C2211yescharacteristic
19C2×D4×C149—21no—
20C2×D4×C149C2211yescharacteristic
21C22×C4×C149—21no—
22C22×C4×C149C2211yescharacteristic
23Dic298—21no—
24Dic298—21no—
25C2×Dic149—21no—
26C2×Dic149—21no—
27#11924746—21no—
28#11924746—21no—
29C23×C149—21no—
30C23×C149D411yescharacteristic
31Q8×C149—21no—
32Q8×C149D412yes—
33D4×C149—24no—
34D4×C149—21no—
35D4×C149D412yes—
36C2×C4×C149—24no—
37C2×C4×C149—21no—
38C2×C4×C149—21no—
39C2×C4×C149—21no—
40C2×C4×C149D411yescharacteristic
41C2×C4×C149C2311yescharacteristic
42C22×C149—21no—
43C22×C149—22no—
44C22×C149—21no—
45C22×C149—21no—
46C22×C149—41no—
47C22×C149—41no—
48C22×C149C2×D411yescharacteristic
49C4×C149—21no—
50C4×C149—22no—
51C4×C149C2×D411yescharacteristic
52C4×C149C2×D411yescharacteristic
53Dic149—41no—
54Dic149—41no—
55C2×C149—41no—
56C2×C149—42no—
57C2×C149#12011yescharacteristic
58C2×C149#13511yescharacteristic
59C2×C149#13711yescharacteristic
60C149#45211yescharacteristic, complemented, Sylow
61#452—1491nomaximal, Sylow
62C2×#41D14911yescharacteristic
63C2×Q16—1491no—
64C2×SD16—1491no—
65C22⋊Q8—1491no—
66#103—1491no—
67#102—1491no—
68C22⋊C8—1491no—
69#41—22no—
70#41—22no—
71C2×Q8—1491no—
72C2×Q8C2×D14911yescharacteristic
73C2×D4—21no—
74C2×D4C2×D14911yescharacteristic
75C22×C4—21no—
76C22×C4C2×D14911yescharacteristic
77Q16—2982no—
78SD16—2982no—
79C2×C8—1491no—
80C2×C8—1491no—
81C4⋊C4—2981no—
82C4⋊C4—1491no—
83C22⋊C4—2981no—
84C23—21no—
85C23C22⋊D14911yescharacteristic
86Q8—21no—
87Q8—2981no—
88Q8—2981no—
89Q8C22⋊D14912yes—
90D4—24no—
91D4—21no—
92D4C22⋊D14912yes—
93C2×C4—24no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—2981no—
98C2×C4—2981no—
99C2×C4C22⋊D14911yescharacteristic
100C2×C4C22×D14911yescharacteristic
101C8—2981no—
102C8—2981no—
103C22—21no—
104C22—21no—
105C22—21no—
106C22—22no—
107C22—41no—
108C22—41no—
109C22C2×C22⋊D14911yescharacteristic
110C4—21no—
111C4—22no—
112C4—5961no—
113C4—5961no—
114C4C2×C22⋊D14911yescharacteristic
115C4C2×C22⋊D14911yescharacteristic
116C2—41no—
117C2—42no—
118C2#1801188011yescharacteristic
119C2#1801193111yescharacteristic
120C2#1801194111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
Fitting, prime radicalC2×#41×C149C2
socleC22×C149C2×D4
hypercenterC2×#41D149
hypocenterC149#452
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14558726C2semidirect
2. C2×#14558724C2semidirect
3. #18011890C2semidirect
4. #18011835C2semidirect
5. #18011832C2semidirect
6. C22⋊#11924746C2semidirect
60. C149#452semidirect