Finite Group Databasebeta

← #14583083

Subgroups — #14583083

Order 2752.

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#13063372C211yesmaximal, characteristic
2#13063358C211yesmaximal, characteristic, complemented
3#13063355C211yesmaximal, characteristic, complemented
4#13063325C211yesmaximal, characteristic, complemented
5#13063253C211yesmaximal, characteristic, complemented
6#13063243C211yesmaximal, characteristic, complemented
7#104×C43C211yesmaximal, characteristic, complemented
8#41×C43C2211yescharacteristic
9Q8×D43—21no—
10#10621900—21no—
11#10621900—22no—
12#10621898—21no—
13#10621898C2211yescharacteristic
14C2×Dic86—21no—
15C2×Dic86C2211yescharacteristic
16C2×Dic86C2211yescharacteristic
17M16×C43C2211yescharacteristic
18C42×C43C2211yescharacteristic
19#10621885—21no—
20#10621883—21no—
21C4⋊Dic43—22no—
22#10621877C2211yescharacteristic
23Dic172—21no—
24#10621873—21no—
25Q8×C43D411yescharacteristic
26D4×C43—21no—
27D4×C43D411yescharacteristic
28C2×C4×C43—21no—
29C2×C4×C43—21no—
30C2×C4×C43C2311yescharacteristic
31C22⋊D43—22no—
32C22⋊D43—21no—
33C2×Dic43—22no—
34C2×Dic43—21no—
35C2×Dic43D412yes—
36D172D411yescharacteristic
37C4×D43—22no—
38C4×D43—21no—
39Dic86—22no—
40Dic86—21no—
41Dic86—21no—
42Dic86—21no—
43Dic86—21no—
44Dic86D411yescharacteristic
45C8×C43—21no—
46C43⋊C8—21no—
47C22×C43—21no—
48C22×C43C2×D411yescharacteristic
49C2×D43—21no—
50C4×C43—22no—
51C4×C43—21no—
52C4×C43C2×D411yescharacteristic
53C4×C43C2×D411yescharacteristic
54Dic43—22no—
55Dic43—21no—
56Dic43—41no—
57C2×C43—21no—
58C2×C43—41no—
59C2×C43#12011yescharacteristic
60D43—41no—
61#456—431nomaximal, Sylow
62C43#45611yescharacteristic, complemented, Sylow
632−1+4—431no—
64#137—431no—
65#137—431no—
66C4⋊Q8—431no—
67#104—431no—
68#104D4311yescharacteristic, complemented
69#101—431no—
70#41—431no—
71#41—861no—
72#41—862no—
73#41—861no—
74#41C2×D4311yescharacteristic
75C2×Q8—431no—
76C2×Q8—431no—
77C2×Q8—861no—
78C2×Q8—861no—
79Q16—861no—
80Q16—861no—
81SD16—861no—
82SD16—861no—
83M16—431no—
84M16C2×D4311yescharacteristic
85C4⋊C4—862no—
86C42C2×D4311yescharacteristic
87Q8—431no—
88Q8—862no—
89Q8—861no—
90Q8—861no—
91Q8—861no—
92Q8—861no—
93Q8D17211yescharacteristic
94D4—21no—
95D4—431no—
96D4—862no—
97D4—861no—
98D4D17211yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—432no—
102C2×C4—862no—
103C2×C4—862no—
104C2×C4—861no—
105C2×C4—861no—
106C2×C4C22×D4311yescharacteristic
107C8—21no—
108C8—861no—
109C22—21no—
110C22—861no—
111C22D4×D4311yescharacteristic
112C4—22no—
113C4—21no—
114C4—862no—
115C4—861no—
116C4—1721no—
117C4C2×D17211yescharacteristic
118C4D4×D4311yescharacteristic
119C2—21no—
120C2—41no—
121C2—1721no—
122C2#1306329511yescharacteristic
subgroupG/H
centerC2#13063295
commutator, cosocleC2×C4×C43C23
FrattiniC2×C4C22×D43
Fitting#104×C43C2
socleC2×C43#120
prime radical#13063372C2
hypercenter#104D43
hypocenterC43#456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #13063358C2semidirect
3. #13063355C2semidirect
4. #13063325C2semidirect
5. #13063253C2semidirect
6. #13063243C2semidirect
7. #104×C43C2semidirect
62. C43#456semidirect
68. #104D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130633722
#130633582
#130633552
#130633252
#130632532
#130632432
#104×C432
#45643