Finite Group Databasebeta

← #23749796

Subgroups — #23749796

Order 9536.

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

normal subgroups only

This group has 146 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
1#18011958C211yesmaximal, characteristic, complemented
2#18011937C211yesmaximal, characteristic, complemented
3#18011898C211yesmaximal, characteristic, complemented
4#18011838C211yesmaximal, characteristic, complemented
5#18011837C211yesmaximal, characteristic, complemented
6#18011829C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C149C211yesmaximal, characteristic, complemented
8#14558736—21no—
9#14558736C2211yescharacteristic
10#14558735—22no—
11#14558735—21no—
12C2×Dic298—21no—
13C2×Dic298C2211yescharacteristic
14Q8×D149—21no—
15#14558724—21no—
16#14558721—21no—
17#14558720C2211yescharacteristic
18C22⋊Dic149—22no—
19C4×Dic149C2211yescharacteristic
20#41×C149C2211yescharacteristic
21C2×D4×C149C2211yescharacteristic
22SD16×C149—21no—
23D8×C149—21no—
24M16×C149C2211yescharacteristic
25Dic298—22no—
26Dic298—21no—
27Dic298—21no—
28Dic298D411yescharacteristic
29D596D411yescharacteristic
30C22⋊D149—22no—
31C22⋊D149—21no—
32C2×Dic149—22no—
33C2×Dic149—21no—
34C2×Dic149D412yes—
35C4×D149—22no—
36C4×D149—21no—
37#11924746—21no—
38C23×C149—21no—
39Q8×C149D411yescharacteristic
40D4×C149—21no—
41D4×C149—21no—
42D4×C149—21no—
43D4×C149D411yescharacteristic
44C2×C4×C149—21no—
45C2×C4×C149C2311yescharacteristic
46C8×C149—21no—
47C22×C149—21no—
48C22×C149—42no—
49C22×C149—41no—
50C22×C149C2×D411yescharacteristic
51C2×D149—21no—
52C4×C149—21no—
53C4×C149C2×D411yescharacteristic
54C4×C149C2×D411yescharacteristic
55Dic149—21no—
56Dic149—22no—
57Dic149—41no—
58C2×C149—21no—
59C2×C149—41no—
60C2×C149—81no—
61C2×C149#12011yescharacteristic
62D149—41no—
63C149#45411yescharacteristic, complemented, Sylow
64#454—1491nomaximal, Sylow
652−1+4—1491no—
66AGL(1,ℤ/8)—1491no—
67AGL(1,ℤ/8)D14911yescharacteristic, complemented
68#124—1491no—
69#104—1491no—
70#104—1491no—
71#101—1491no—
72#41—2981no—
73#41—2981no—
74#41—2982no—
75#41—1491no—
76#41C2×D14911yescharacteristic
77C2×Q8—2981no—
78C2×Q8—2981no—
79C2×Q8—1491no—
80C2×D4C2×D14911yescharacteristic
81SD16—21no—
82SD16—2981no—
83D8—21no—
84D8—2981no—
85M16—1491no—
86M16C2×D14911yescharacteristic
87C22⋊C4—2982no—
88C42—1491no—
89C23—21no—
90Q8—2982no—
91Q8—2981no—
92Q8—2981no—
93Q8—1491no—
94Q8C22⋊D14911yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—2982no—
99D4—2981no—
100D4—1491no—
101D4C22⋊D14911yescharacteristic
102C2×C4—21no—
103C2×C4—2982no—
104C2×C4—2982no—
105C2×C4—2981no—
106C2×C4—2981no—
107C2×C4—1492no—
108C2×C4C22×D14911yescharacteristic
109C8—21no—
110C8—2981no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—2981no—
115C22D4×D14911yescharacteristic
116C4—21no—
117C4—2981no—
118C4—2982no—
119C4—5961no—
120C4D4×D14911yescharacteristic
121C4C2×C22⋊D14911yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—5961no—
126C2#1801187911yescharacteristic
subgroupG/H
centerC2#18011879
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
FittingAGL(1,ℤ/8)×C149C2
socleC2×C149#120
hypercenterAGL(1,ℤ/8)D149
hypocenterC149#454
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #18011958C2semidirect
2. #18011937C2semidirect
3. #18011898C2semidirect
4. #18011838C2semidirect
5. #18011837C2semidirect
6. #18011829C2semidirect
7. AGL(1,ℤ/8)×C149C2semidirect
63. C149#454semidirect
67. AGL(1,ℤ/8)D149semidirect