Finite Group Databasebeta

← #23749694

Subgroups — #23749694

Order 9536.

124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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×C8×D149C211yesmaximal, characteristic, complemented
2C4×C22⋊D149C211yesmaximal, characteristic
3#18011840C211yesmaximal, characteristic, complemented
4C22⋊#11924746C211yesmaximal, characteristic, complemented
5#18011823C211yesmaximal, characteristic, complemented
6#18011821C211yesmaximal, characteristic, complemented
7C2×M16×C149C211yesmaximal, characteristic, complemented
8C2×C22⋊D149C411yescharacteristic
9C2×C4×D149C2211yescharacteristic
10C2×#11924746C2211yescharacteristic
11C2×#11924746C2211yescharacteristic
12C8×D149—22no—
13#14558715C411yescharacteristic
14C22⋊Dic149C411yescharacteristic
15#14558713C411yescharacteristic
16C4×Dic149C2211yescharacteristic
17C22×C4×C149C2211yescharacteristic
18M16×C149—22no—
19C2×C8×C149C2211yescharacteristic
20C2×C8×C149C2211yescharacteristic
21C22×D149C2×C411yescharacteristic
22C22⋊D149—22no—
23C2×Dic149C2×C411yescharacteristic
24C2×Dic149C2×C411yescharacteristic
25C2×Dic149C2×C411yescharacteristic
26C4×D149—21no—
27C4×D149—21no—
28#11924746—21no—
29#11924746—21no—
30C23×C149C2×C411yescharacteristic
31C2×C4×C149—21no—
32C2×C4×C149—21no—
33C2×C4×C149C2×C411yescharacteristic
34C2×C4×C149C2311yescharacteristic
35C8×C149—21no—
36C8×C149D412yescomplemented
37C22×C149—21no—
38C22×C149—21no—
39C22×C149—21no—
40C22×C149C22×C411yescharacteristic
41C2×D149—21no—
42C2×D149—21no—
43C2×D149M1612yescomplemented
44C4×C149—21no—
45C4×C149C2×D411yescharacteristic
46C4×C149#4111yescharacteristic
47Dic149—21no—
48Dic149—21no—
49Dic149—21no—
50C2×C149—41no—
51C2×C149C4×D411yescharacteristic
52C2×C149C2×M1611yescharacteristic
53C2×C149#13111yescharacteristic
54D149—22no—
55C149#43511yescharacteristic, complemented, Sylow
56#435—1491nomaximal, Sylow
57C2×M16D14911yescharacteristic, complemented
58C22×C8—1491no—
59C4×D4—1491no—
60C4⋊C8—1491no—
61C22⋊C8—1491no—
62C22⋊C8—1491no—
63#97—1491no—
64C2×D4—1491no—
65C22×C4—1491no—
66C22×C4C2×D14911yescharacteristic
67M16—22no—
68C2×C8—2982no—
69C2×C8—1491no—
70C2×C8—1491no—
71C2×C8C2×D14911yescharacteristic
72C2×C8C2×D14911yescharacteristic
73C4⋊C4—1491no—
74C22⋊C4—1491no—
75C22⋊C4—1491no—
76C42—1491no—
77C23—1491no—
78C23C4×D14911yescharacteristic
79D4—2982no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—2981no—
83C2×C4—2981no—
84C2×C4—1491no—
85C2×C4—1491no—
86C2×C4—1491no—
87C2×C4C4×D14911yescharacteristic
88C2×C4C22×D14911yescharacteristic
89C8—21no—
90C8—2981no—
91C8—2981no—
92C8C22⋊D14912yescomplemented
93C22—21no—
94C22—21no—
95C22—21no—
96C22—2981no—
97C22—2981no—
98C22—1492no—
99C22C2×C4×D14911yescharacteristic
100C4—21no—
101C4—2981no—
102C4—2981no—
103C4—2981no—
104C4C2×C22⋊D14911yescharacteristic
105C4#1455873611yescharacteristic
106C2—41no—
107C2—2982no—
108C2C4×C22⋊D14911yescharacteristic
109C2M16×D14911yescharacteristic
110C2#1801191911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D149
commutator, socleC22×C149C22×C4
FittingC2×M16×C149C2
prime radicalC2×C22⋊D149C4
cosocleC2×C4×C149C23
hypercenterC2×M16D149
hypocenterC149#435
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C8×D149C2semidirect
3. #18011840C2semidirect
4. C22⋊#11924746C2semidirect
5. #18011823C2semidirect
6. #18011821C2semidirect
7. C2×M16×C149C2semidirect
36. C8×C149D4semidirect
43. C2×D149M16semidirect
55. C149#435semidirect
57. C2×M16D149semidirect
92. C8C22⋊D149semidirect