Finite Group Databasebeta

← #23749772

Subgroups — #23749772

Order 9536.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14558736C211yesmaximal, characteristic, complemented
2C2×#14558725C211yesmaximal, characteristic, complemented
3C2×D1192C211yesmaximal, characteristic, complemented
4#18011885C211yesmaximal, characteristic, complemented
5#18011836C211yesmaximal, characteristic, complemented
6#18011833C211yesmaximal, characteristic, complemented
7C22⋊C8×C149C211yesmaximal, characteristic, complemented
8#14558736—22no—
9#14558736—22no—
10C2×Dic298C2211yescharacteristic
11C2×D596C2211yescharacteristic
12C2×D596C2211yescharacteristic
13C2×C22⋊D149—21no—
14C2×C22⋊D149—21no—
15C2×C4×D149—21no—
16#14558725—22no—
17D1192—22no—
18C4⋊Dic149C2211yescharacteristic
19#14558713—21no—
20C22×C4×C149C2211yescharacteristic
21C2×C8×C149C2211yescharacteristic
22C2×C8×C149C2211yescharacteristic
23C22×D149—21no—
24C22×D149—21no—
25Dic298—21no—
26Dic298D412yescomplemented
27D596—21no—
28D596—21no—
29D596—21no—
30D596D412yescomplemented
31C22⋊D149—24no—
32C22⋊D149—42no—
33C2×Dic149—21no—
34C2×Dic149—21no—
35C4×D149—24no—
36C23×C149D411yescharacteristic
37C2×C4×C149—21no—
38C2×C4×C149—21no—
39C2×C4×C149D411yescharacteristic
40C2×C4×C149C2311yescharacteristic
41C8×C149—21no—
42C8×C149—21no—
43C22×C149—21no—
44C22×C149—21no—
45C22×C149—21no—
46C22×C149C2×D411yescharacteristic
47C2×D149—22no—
48C2×D149—41no—
49C2×D149—41no—
50C2×D149—41no—
51C2×D149—41no—
52C2×D149—41no—
53C4×C149—21no—
54C4×C149C2×D411yescharacteristic
55C4×C149C2×D411yescharacteristic
56Dic149—22no—
57Dic149—41no—
58C2×C149—41no—
59C2×C149#12011yescharacteristic
60C2×C149#13511yescharacteristic
61C2×C149AGL(1,ℤ/8)11yescharacteristic
62D149—42no—
63D149—81no—
64C149#44911yescharacteristic, complemented, Sylow
65#449—1491nomaximal, Sylow
66C2×#41—1491no—
67C2×SD16—1491no—
68C2×D8—1491no—
69#121—1491no—
70#103—1491no—
71#102—1491no—
72C22⋊C8D14911yescharacteristic, complemented
73#41—2982no—
74#41—2982no—
75C2×Q8—1491no—
76C2×D4—2981no—
77C2×D4—2981no—
78C2×D4—1491no—
79C2×D4—1491no—
80C22×C4—2981no—
81C22×C4C2×D14911yescharacteristic
82SD16—2982no—
83D8—2982no—
84C2×C8C2×D14911yescharacteristic
85C2×C8C2×D14911yescharacteristic
86C4⋊C4—1491no—
87C22⋊C4—2981no—
88C23—2981no—
89C23—2981no—
90C23D59611yescharacteristic
91Q8—2981no—
92Q8—1492no—
93D4—2984no—
94D4—2981no—
95D4—2981no—
96D4—2981no—
97D4—5962no—
98D4—1492no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—2984no—
102C2×C4—2981no—
103C2×C4—2981no—
104C2×C4D59611yescharacteristic
105C2×C4C22×D14911yescharacteristic
106C8—21no—
107C8—21no—
108C22—21no—
109C22—21no—
110C22—21no—
111C22—2982no—
112C22—5961no—
113C22—5961no—
114C22—5961no—
115C22—5961no—
116C22—5961no—
117C22C2×D59611yescharacteristic
118C4—21no—
119C4—2982no—
120C4—5961no—
121C4D4×D14911yescharacteristic
122C4D4×D14911yescharacteristic
123C2—41no—
124C2—5962no—
125C2—11921no—
126C2#1801188111yescharacteristic
127C2#1801193311yescharacteristic
128C2#1801193911yescharacteristic
subgroupG/H
centerC22C2×D596
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
FittingC22⋊C8×C149C2
socleC22×C149C2×D4
hypercenterC22⋊C8D149
hypocenterC149#449
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14558736C2semidirect
2. C2×#14558725C2semidirect
3. C2×D1192C2semidirect
4. #18011885C2semidirect
5. #18011836C2semidirect
6. #18011833C2semidirect
7. C22⋊C8×C149C2semidirect
26. Dic298D4semidirect
30. D596D4semidirect
64. C149#449semidirect
72. C22⋊C8D149semidirect