Finite Group Databasebeta

← #23749779

Subgroups — #23749779

Order 9536.

148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D149C211yesmaximal, characteristic
2C2×#14558726C211yesmaximal, characteristic, complemented
3#18011887C211yesmaximal, characteristic
4#18011836C211yesmaximal, characteristic, complemented
5#18011835C211yesmaximal, characteristic, complemented
6#18011823C211yesmaximal, characteristic
7C2×Q16×C149C211yesmaximal, characteristic, complemented
8C2×Dic298—21no—
9C2×Dic298C2211yescharacteristic
10Q8×D149—22no—
11Q8×D149—22no—
12C2×C4×D149—21no—
13C2×C4×D149C2211yescharacteristic
14#14558726—22no—
15C2×#11924746C2211yescharacteristic
16C4⋊Dic149C2211yescharacteristic
17#14558715—21no—
18#14558713—21no—
19C2×Q8×C149C2211yescharacteristic
20C2×Q8×C149C2211yescharacteristic
21Q16×C149—22no—
22C2×C8×C149C2211yescharacteristic
23C22×D149D411yescharacteristic
24Dic298—24no—
25Dic298—21no—
26Dic298D412yes—
27C2×Dic149—21no—
28C2×Dic149—21no—
29C2×Dic149D411yescharacteristic
30C4×D149—24no—
31C4×D149—21no—
32C4×D149—21no—
33#11924746—21no—
34Q8×C149—21no—
35Q8×C149—21no—
36Q8×C149—21no—
37Q8×C149D412yes—
38C2×C4×C149—21no—
39C2×C4×C149—21no—
40C2×C4×C149C2311yescharacteristic
41C8×C149—21no—
42C22×C149C2×D411yescharacteristic
43C2×D149—21no—
44C2×D149—21no—
45C2×D149Q1612yescomplemented
46C4×C149—22no—
47C4×C149—41no—
48C4×C149C2×D411yescharacteristic
49C4×C149C2×D411yescharacteristic
50Dic149—22no—
51Dic149—21no—
52Dic149—41no—
53C2×C149#12011yescharacteristic
54C2×C149C2×Q1611yescharacteristic
55C2×C149#13711yescharacteristic
56D149—22no—
57C149#45111yescharacteristic, complemented, Sylow
58#451—1491nomaximal, Sylow
59C22×Q8—1491no—
60C2×Q16—1491no—
61C2×Q16D14911yescharacteristic, complemented
62C22⋊Q8—1491no—
63#103—1491no—
64#103—1491no—
65C22⋊C8—1491no—
66C2×Q8—2981no—
67C2×Q8—2982no—
68C2×Q8—2982no—
69C2×Q8—1491no—
70C2×Q8C2×D14911yescharacteristic
71C2×Q8C2×D14911yescharacteristic
72C22×C4—2981no—
73C22×C4—1491no—
74Q16—22no—
75Q16—2982no—
76C2×C8—1491no—
77C2×C8C2×D14911yescharacteristic
78C4⋊C4—2981no—
79C4⋊C4—1491no—
80C22⋊C4—2981no—
81C23—1491no—
82Q8—21no—
83Q8—21no—
84Q8—21no—
85Q8—2984no—
86Q8—2981no—
87Q8—1492no—
88Q8C22⋊D14912yes—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—2984no—
92C2×C4—2981no—
93C2×C4—2981no—
94C2×C4—2981no—
95C2×C4—2981no—
96C2×C4—1491no—
97C2×C4C22×D14911yescharacteristic
98C8—21no—
99C8—2981no—
100C22—2981no—
101C22—2981no—
102C22—1492no—
103C22D4×D14911yescharacteristic
104C4—22no—
105C4—41no—
106C4—2982no—
107C4—2981no—
108C4—5961no—
109C4D4×D14911yescharacteristic
110C4C2×C22⋊D14911yescharacteristic
111C2—2982no—
112C2#1801187911yescharacteristic
113C2Q16×D14911yescharacteristic
114C2#1801194311yescharacteristic
subgroupG/H
centerC22D4×D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
FittingC2×Q16×C149C2
socleC22×C149C2×D4
prime radicalC22×D149D4
hypercenterC2×Q16D149
hypocenterC149#451
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#14558726C2semidirect
4. #18011836C2semidirect
5. #18011835C2semidirect
7. C2×Q16×C149C2semidirect
45. C2×D149Q16semidirect
57. C149#451semidirect
61. C2×Q16D149semidirect