Finite Group Databasebeta

← #23749809

Subgroups — #23749809

Order 9536.

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

normal subgroups only

This group has 142 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
2#18011944C211yesmaximal, characteristic, complemented
3#18011941C211yesmaximal, characteristic, complemented
4#18011911C211yesmaximal, characteristic, complemented
5#18011839C211yesmaximal, characteristic, complemented
6#18011829C211yesmaximal, characteristic, complemented
7#104×C149C211yesmaximal, characteristic, complemented
8#14558736—21no—
9#14558736C2211yescharacteristic
10#14558735—22no—
11#14558735—21no—
12C2×Dic298—21no—
13C2×Dic298C2211yescharacteristic
14C2×Dic298C2211yescharacteristic
15Q8×D149—21no—
16Dic596—21no—
17#14558726—21no—
18#14558725—21no—
19#14558724—21no—
20#14558720C2211yescharacteristic
21C4⋊Dic149—22no—
22#41×C149C2211yescharacteristic
23M16×C149C2211yescharacteristic
24C42×C149C2211yescharacteristic
25Dic298—22no—
26Dic298—21no—
27Dic298—21no—
28Dic298—21no—
29Dic298—21no—
30Dic298D411yescharacteristic
31D596D411yescharacteristic
32C22⋊D149—22no—
33C22⋊D149—21no—
34C2×Dic149—22no—
35C2×Dic149—21no—
36C2×Dic149D412yes—
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—21no—
50C4×C149—22no—
51C4×C149—21no—
52C4×C149C2×D411yescharacteristic
53C4×C149C2×D411yescharacteristic
54Dic149—21no—
55Dic149—22no—
56Dic149—41no—
57C2×C149—21no—
58C2×C149—41no—
59C2×C149#12011yescharacteristic
60D149—41no—
61C149#45611yescharacteristic, complemented, Sylow
62#456—1491nomaximal, Sylow
632−1+4—1491no—
64#137—1491no—
65#137—1491no—
66C4⋊Q8—1491no—
67#104—1491no—
68#104D14911yescharacteristic, complemented
69#101—1491no—
70#41—2981no—
71#41—2981no—
72#41—2982no—
73#41—1491no—
74#41C2×D14911yescharacteristic
75C2×Q8—2981no—
76C2×Q8—2981no—
77C2×Q8—1491no—
78C2×Q8—1491no—
79Q16—2981no—
80Q16—2981no—
81SD16—2981no—
82SD16—2981no—
83M16—1491no—
84M16C2×D14911yescharacteristic
85C4⋊C4—2982no—
86C42C2×D14911yescharacteristic
87Q8—2982no—
88Q8—2981no—
89Q8—2981no—
90Q8—2981no—
91Q8—2981no—
92Q8—1491no—
93Q8D59611yescharacteristic
94D4—21no—
95D4—2982no—
96D4—2981no—
97D4—1491no—
98D4D59611yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—2982no—
102C2×C4—2982no—
103C2×C4—2981no—
104C2×C4—2981no—
105C2×C4—1492no—
106C2×C4C22×D14911yescharacteristic
107C8—21no—
108C8—2981no—
109C22—21no—
110C22—2981no—
111C22D4×D14911yescharacteristic
112C4—22no—
113C4—21no—
114C4—2981no—
115C4—2982no—
116C4—5961no—
117C4D4×D14911yescharacteristic
118C4C2×D59611yescharacteristic
119C2—21no—
120C2—41no—
121C2—5961no—
122C2#1801188111yescharacteristic
subgroupG/H
centerC2#18011881
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
Fitting#104×C149C2
socleC2×C149#120
prime radical#18011958C2
hypercenter#104D149
hypocenterC149#456
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. #18011911C2semidirect
5. #18011839C2semidirect
6. #18011829C2semidirect
7. #104×C149C2semidirect
61. C149#456semidirect
68. #104D149semidirect