Finite Group Databasebeta

← #23749804

Subgroups — #23749804

Order 9536.

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

normal subgroups only

This group has 152 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#18011957C211yesmaximal, characteristic
2#18011944C211yesmaximal, characteristic, complemented
3#18011941C211yesmaximal, characteristic, complemented
4#18011899C211yesmaximal, characteristic, complemented
5#18011839C211yesmaximal, characteristic, complemented
6#18011827C211yesmaximal, characteristic, complemented
7#104×C149C211yesmaximal, characteristic, complemented
8#14558737—21no—
9#14558736—21no—
10#14558736C2211yescharacteristic
11C2×Dic298C2211yescharacteristic, complemented
12C2×D596—21no—
13C2×D596C2211yescharacteristic
14D4×D149—22no—
15D4×D149—21no—
16Dic596—21no—
17#14558726—21no—
18#14558725—21no—
19#14558724—21no—
20#14558720C2211yescharacteristic, complemented
21#14558713—22no—
22#41×C149C2211yescharacteristic
23M16×C149C2211yescharacteristic, complemented
24C42×C149C2211yescharacteristic, complemented
25C22×D149—22no—
26C22×D149D412yes—
27Dic298—21no—
28Dic298—21no—
29Dic298D411yescharacteristic
30D596—22no—
31D596—21no—
32D596—21no—
33D596D411yescharacteristic
34C22⋊D149—22no—
35C22⋊D149—21no—
36C2×Dic149—21no—
37C4×D149—22no—
38C4×D149—21no—
39#11924746—21no—
40Q8×C149D411yescharacteristic
41D4×C149—21no—
42D4×C149D411yescharacteristic
43C2×C4×C149—21no—
44C2×C4×C149—21no—
45C2×C4×C149C2311yescharacteristic
46C8×C149—21no—
47C22×C149—21no—
48C22×C149C2×D411yescharacteristic
49C2×D149—22no—
50C2×D149—21no—
51C2×D149—42no—
52C2×D149—82no—
53C4×C149—21no—
54C4×C149—41no—
55C4×C149C2×D411yescharacteristic
56C4×C149C2×D411yescharacteristic
57Dic149—21no—
58Dic149—41no—
59C2×C149—21no—
60C2×C149—41no—
61C2×C149#12011yescharacteristic
62D149—42no—
63D149—41no—
64C149#45511yescharacteristic, complemented, Sylow
65#455—1491nomaximal, Sylow
66H(5,𝔽2)—1491no—
67#137—1491no—
68#137—1491no—
69#124—1491no—
70#104—1491no—
71#104D14911yescharacteristic, complemented
72#100—1491no—
73#41—2981no—
74#41—2981no—
75#41—1491no—
76#41C2×D14911yescharacteristic
77C2×Q8—1491no—
78C2×D4—2981no—
79C2×D4—2982no—
80C2×D4—2981no—
81C2×D4—1491no—
82Q16—2981no—
83Q16—2981no—
84SD16—2981no—
85SD16—2981no—
86M16—1491no—
87M16C2×D14911yescharacteristic, complemented
88C22⋊C4—2982no—
89C42C2×D14911yescharacteristic, complemented
90C23—2982no—
91C23—1492no—
92Q8—2981no—
93Q8—2981no—
94Q8—1491no—
95Q8D59611yescharacteristic
96D4—21no—
97D4—2982no—
98D4—2982no—
99D4—2981no—
100D4—2981no—
101D4—2981no—
102D4—1491no—
103D4D59611yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—2982no—
107C2×C4—2981no—
108C2×C4—2981no—
109C2×C4C22×D14911yescharacteristic
110C8—21no—
111C8—2981no—
112C22—21no—
113C22—2982no—
114C22—2981no—
115C22—5962no—
116C22—11922no—
117C22D4×D14911yescharacteristic
118C4—21no—
119C4—41no—
120C4—2981no—
121C4—5961no—
122C4D4×D14911yescharacteristic
123C4C2×D59611yescharacteristic
124C2—21no—
125C2—41no—
126C2—5962no—
127C2—5961no—
128C2#1801188111yescharacteristic
subgroupG/H
centerC2#18011881
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
Fitting#104×C149C2
socleC2×C149#120
prime radical#18011957C2
hypercenter#104D149
hypocenterC149#455
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #18011944C2semidirect
3. #18011941C2semidirect
4. #18011899C2semidirect
5. #18011839C2semidirect
6. #18011827C2semidirect
7. #104×C149C2semidirect
11. C2×Dic298C22semidirect
20. #14558720C22semidirect
23. M16×C149C22semidirect
24. C42×C149C22semidirect
64. C149#455semidirect
71. #104D149semidirect
87. M16C2×D149semidirect
89. C42C2×D149semidirect