Finite Group Databasebeta

← #23749487

Subgroups — #23749487

Order 9536.

218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22×C4×D149C211yesmaximal, characteristic
2C2×#14558713C212yesmaximal
3#18011818C211yesmaximal, characteristic, complemented
4#18011818C212yesmaximal, complemented
5#95×C149C211yesmaximal, characteristic, complemented
6C23×D149C2211yescharacteristic
7C22×Dic149C2212yes—
8C22×Dic149C2211yescharacteristic
9C2×C4×D149—24no—
10C2×C4×D149C414yescomplemented
11#14558713—24no—
12C22×C4×C149C2212yes—
13C22×C4×C149C2211yescharacteristic
14C22×D149—21no—
15C22×D149—22no—
16C22×D149—21no—
17C22×D149C2×C412yes—
18C22×D149D414yes—
19C2×Dic149—22no—
20C2×Dic149—22no—
21C2×Dic149—22no—
22C2×Dic149—22no—
23C2×Dic149C2×C412yes—
24C4×D149—28no—
25C23×C149C2311yescharacteristic
26C2×C4×C149—22no—
27C2×C4×C149—22no—
28C2×C4×C149—22no—
29C2×C4×C149—22no—
30C2×C4×C149C2×C412yes—
31C22×C149C22×C411yescharacteristic
32C22×C149C2×D412yes—
33C22×C149#4111yescharacteristic
34C22×C149#4112yes—
35C22×C149#4111yescharacteristic
36C2×D149—22no—
37C2×D149—22no—
38C2×D149—24no—
39C2×D149—24no—
40C2×D149C22⋊C414yes—
41C4×C149—22no—
42C4×C149—42no—
43Dic149—22no—
44Dic149—42no—
45C2×C149C2×C22⋊C411yescharacteristic
46C2×C149#11711yescharacteristic
47C2×C149#11711yescharacteristic
48C2×C149#12312yes—
49C2×C149#12312yes—
50D149—24no—
51C149#38111yescharacteristic, complemented, Sylow
52#381—1491nomaximal, Sylow
53C23×C4—1491no—
54C2×C22⋊C4—1492no—
55#95—1491no—
56#95—1492no—
57#95D14911yescharacteristic, complemented
58C24—1491no—
59C22×C4—2984no—
60C22×C4—1492no—
61C22×C4—1491no—
62C22×C4—1494no—
63C22×C4C2×D14912yes—
64C22×C4C2×D14911yescharacteristic
65C22⋊C4—2984no—
66C23—2981no—
67C23—2982no—
68C23—2981no—
69C23—1492no—
70C23—1494no—
71C23C22×D14911yescharacteristic
72C2×C4—22no—
73C2×C4—22no—
74C2×C4—22no—
75C2×C4—22no—
76C2×C4—2988no—
77C2×C4—2982no—
78C2×C4—2982no—
79C2×C4—2982no—
80C2×C4—2982no—
81C2×C4—1492no—
82C2×C4C4×D14912yes—
83C22—2982no—
84C22—2982no—
85C22—2984no—
86C22—2984no—
87C22—1494no—
88C22C2×C4×D14911yescharacteristic
89C22D4×D14912yes—
90C22#1455873511yescharacteristic
91C22#1455873612yes—
92C22#1455873711yescharacteristic
93C4—22no—
94C4—42no—
95C4—2982no—
96C4—5962no—
97C2—2984no—
98C2C22⋊C4×D14911yescharacteristic
99C2#1801186811yescharacteristic
100C2#1801186911yescharacteristic
101C2#1801189312yes—
102C2#1801189612yes—
subgroupG/H
center, FrattiniC23C22×D149
commutatorC22×C149C22×C4
Fitting#95×C149C2
socle, cosocleC23×C149C23
prime radicalC23×D149C22
hypercenter#95D149
hypocenterC149#381
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #18011818C2semidirect
4. #18011818C2semidirect
5. #95×C149C2semidirect
10. C2×C4×D149C4semidirect
51. C149#381semidirect
57. #95D149semidirect