Finite Group Databasebeta

← #23749877

Subgroups — #23749877

Order 9536.

130 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 39 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×#14558721C211yesmaximal, characteristic, complemented
2C2×#14558719C211yesmaximal, characteristic, complemented
3#18011886C211yesmaximal, characteristic, complemented
4#18011882C211yesmaximal, characteristic, complemented
5#18011842C211yesmaximal, characteristic, complemented
6#18011833C211yesmaximal, characteristic, complemented
7#102×C149C211yesmaximal, characteristic, complemented
8C2×D596—21no—
9C2×D596C2211yescharacteristic
10C2×C22⋊D149—21no—
11C2×C4×D149C2211yescharacteristic
12#14558721—22no—
13#14558719—22no—
14C2×#11924746C2211yescharacteristic
15C4⋊Dic149C2211yescharacteristic
16C22⋊Dic149—21no—
17#14558713—21no—
18C2×D4×C149C2211yescharacteristic
19C2×C8×C149C2211yescharacteristic
20C4⋊C4×C149C2211yescharacteristic
21C22×D149—21no—
22C22×D149D411yescharacteristic
23D596—21no—
24D596—21no—
25D596—42no—
26C22⋊D149—42no—
27C2×Dic149—21no—
28C2×Dic149D411yescharacteristic
29C4×D149—21no—
30C4×D149—21no—
31#11924746D412yescomplemented
32C23×C149—21no—
33D4×C149—21no—
34D4×C149—21no—
35C2×C4×C149—21no—
36C2×C4×C149C2311yescharacteristic
37C8×C149—21no—
38C22×C149—41no—
39C22×C149—41no—
40C22×C149—41no—
41C22×C149C2×D411yescharacteristic
42C2×D149—21no—
43C2×D149—21no—
44C2×D149—21no—
45C2×D149—41no—
46C2×D149—41no—
47C2×D149—41no—
48C4×C149—41no—
49C4×C149C2×D411yescharacteristic
50C4×C149#4111yescharacteristic
51Dic149—21no—
52Dic149—41no—
53C2×C149—81no—
54C2×C149#12111yescharacteristic
55C2×C149AGL(1,ℤ/8)11yescharacteristic
56C2×C149AGL(1,ℤ/8)11yescharacteristic
57D149—41no—
58D149—81no—
59C149#46911yescharacteristic, complemented, Sylow
60#469—1491nomaximal, Sylow
61C2×D8—1491no—
62C2×M16—1491no—
63#121—1491no—
64#121—1491no—
65#106—1491no—
66#102—1491no—
67#102D14911yescharacteristic, complemented
68C2×D4—2981no—
69C2×D4—2981no—
70C2×D4—1491no—
71C2×D4C2×D14911yescharacteristic
72C22×C4—1491no—
73D8—2982no—
74M16—2982no—
75C2×C8—1491no—
76C2×C8C2×D14911yescharacteristic
77C4⋊C4—1491no—
78C4⋊C4C2×D14911yescharacteristic
79C22⋊C4—2981no—
80C22⋊C4—2981no—
81C23—21no—
82C23—2981no—
83C23—1491no—
84D4—21no—
85D4—21no—
86D4—2981no—
87D4—2981no—
88D4—5962no—
89D4—5962no—
90C2×C4—21no—
91C2×C4—2981no—
92C2×C4—2981no—
93C2×C4—2981no—
94C2×C4—1491no—
95C2×C4C22×D14911yescharacteristic
96C8—21no—
97C8—1492no—
98C22—41no—
99C22—41no—
100C22—41no—
101C22—2981no—
102C22—2981no—
103C22—2981no—
104C22—5961no—
105C22—5961no—
106C22—5961no—
107C22D4×D14911yescharacteristic
108C4—41no—
109C4—2981no—
110C4—5961no—
111C4D4×D14911yescharacteristic
112C4#1455873611yescharacteristic
113C2—81no—
114C2—5961no—
115C2—11921no—
116C2#1801188411yescharacteristic
117C2#1801193511yescharacteristic
118C2#1801193811yescharacteristic
subgroupG/H
centerC22D4×D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
Fitting#102×C149C2
socleC22×C149C2×D4
hypercenter#102D149
hypocenterC149#469
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#14558721C2semidirect
2. C2×#14558719C2semidirect
3. #18011886C2semidirect
4. #18011882C2semidirect
5. #18011842C2semidirect
6. #18011833C2semidirect
7. #102×C149C2semidirect
31. #11924746D4semidirect
59. C149#469semidirect
67. #102D149semidirect