Finite Group Databasebeta

← #23749842

Subgroups — #23749842

Order 9536.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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
2#18011900C211yesmaximal, characteristic, complemented
3D4×Dic149C211yesmaximal, characteristic, complemented
4#18011840C211yesmaximal, characteristic, complemented
5#18011835C211yesmaximal, characteristic, complemented
6#18011833C211yesmaximal, characteristic, complemented
7C2×SD16×C149C211yesmaximal, characteristic, complemented
8C2×D596C2211yescharacteristic
9C22×Dic149—21no—
10#14558721—22no—
11C2×#11924746C2211yescharacteristic
12C4⋊Dic149C2211yescharacteristic
13C22⋊Dic149—21no—
14#14558713—21no—
15#14558713—21no—
16C4×Dic149C2211yescharacteristic
17C2×Q8×C149C2211yescharacteristic
18C2×D4×C149C2211yescharacteristic
19SD16×C149—22no—
20C2×C8×C149C2211yescharacteristic
21C22×D149—21no—
22D596—21no—
23D596—21no—
24C2×Dic149—21no—
25C2×Dic149—42no—
26C2×Dic149D411yescharacteristic
27C2×Dic149D411yescharacteristic
28#11924746—21no—
29C23×C149—21no—
30Q8×C149—21no—
31Q8×C149—21no—
32D4×C149—21no—
33D4×C149D412yes—
34C2×C4×C149—21no—
35C2×C4×C149C2311yescharacteristic
36C8×C149—21no—
37C22×C149—22no—
38C22×C149—41no—
39C22×C149—41no—
40C22×C149C2×D411yescharacteristic
41C2×D149—41no—
42C2×D149—41no—
43C2×D149—41no—
44C4×C149—41no—
45C4×C149C2×D411yescharacteristic
46C4×C149#4111yescharacteristic
47Dic149—21no—
48Dic149—21no—
49Dic149—41no—
50C2×C149—42no—
51C2×C149#12111yescharacteristic
52C2×C149#13511yescharacteristic
53C2×C149AGL(1,ℤ/8)11yescharacteristic
54D149—81no—
55C149#46311yescharacteristic, complemented, Sylow
56#463—1491nomaximal, Sylow
57C2×SD16D14911yescharacteristic, complemented
58C2×D8—1491no—
59#124—1491no—
60C4×D4—1491no—
61C4⋊C8—1491no—
62#103—1491no—
63#102—1491no—
64C2×Q8C2×D14911yescharacteristic
65C2×D4—1491no—
66C2×D4C2×D14911yescharacteristic
67C22×C4—2981no—
68SD16—22no—
69D8—2982no—
70C2×C8—1491no—
71C2×C8C2×D14911yescharacteristic
72C4⋊C4—1491no—
73C22⋊C4—2981no—
74C22⋊C4—2981no—
75C22⋊C4—2981no—
76C42—1491no—
77C23—21no—
78C23—2981no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—2981no—
83D4—2981no—
84D4C22⋊D14912yes—
85C2×C4—21no—
86C2×C4—2981no—
87C2×C4—5962no—
88C2×C4—1491no—
89C2×C4—1491no—
90C2×C4C22×D14911yescharacteristic
91C8—21no—
92C8—2981no—
93C22—22no—
94C22—41no—
95C22—41no—
96C22—5961no—
97C22—5961no—
98C22—5961no—
99C22D4×D14911yescharacteristic
100C4—41no—
101C4—2981no—
102C4—2981no—
103C4—5961no—
104C4C2×C22⋊D14911yescharacteristic
105C4#1455873511yescharacteristic
106C2—42no—
107C2—11921no—
108C2#1801188311yescharacteristic
109C2#1801193211yescharacteristic
110C2#1801193811yescharacteristic
subgroupG/H
centerC22D4×D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
FittingC2×SD16×C149C2
socleC22×C149C2×D4
prime radicalC2×#14558721C2
hypercenterC2×SD16D149
hypocenterC149#463
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. #18011900C2semidirect
3. D4×Dic149C2semidirect
4. #18011840C2semidirect
5. #18011835C2semidirect
6. #18011833C2semidirect
7. C2×SD16×C149C2semidirect
55. C149#463semidirect
57. C2×SD16D149semidirect