Finite Group Databasebeta

← #16818606

Subgroups — #16818606

Order 3712.

314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271798C211yesmaximal, characteristic
2#14271450C212yesmaximal, complemented
3#14270907C211yesmaximal, characteristic, complemented
4#14270892C212yesmaximal, complemented
5C29×#492C211yesmaximal, characteristic, complemented
6C2×D4×D29—22no—
7C2×SD16×C29—22no—
8C29×C4⋊Q8C2211yescharacteristic, complemented
9C29×#127C2211yescharacteristic
10#11745300—22no—
11#11745299—22no—
12C4×D116C2212yes—
13C4×C8×C29C2211yescharacteristic, complemented
14#11745157—22no—
15#11745156—22no—
16C4⋊#6597C2212yescomplemented
17C23×D29—22no—
18C2×Q8×C29—21no—
19C2×D4×C29—22no—
20C2×D4×C29D412yes—
21C2×C22⋊D29—24no—
22D4×D29—44no—
23D4×D29—44no—
24C2×D116D412yes—
25C2×C4×D29—22no—
26SD16×C29—44no—
27C2×C8×C29—21no—
28C4⋊C4×C29—22no—
29C42×C29C2311yescharacteristic
30C22⋊Dic29—22no—
31#90781—22no—
32C4⋊Dic29D412yes—
33C2×#6597—22no—
34C23×C29—22no—
35C22×D29—22no—
36C22×D29—48no—
37C22×D29—82no—
38Q8×C29—42no—
39D4×C29—42no—
40D4×C29—42no—
41D4×C29—42no—
42C2×C4×C29—41no—
43C2×C4×C29C2×D412yes—
44C2×C4×C29C2×D411yescharacteristic
45C22⋊D29—48no—
46C2×Dic29—22no—
47D116—22no—
48D116SD1614yescomplemented
49C4×D29—42no—
50C4×D29—42no—
51C8×C29—22no—
52#6597—42no—
53#1629—291nomaximal, Sylow
54C22×C29—44no—
55C22×C29—42no—
56C22×C29#12011yescharacteristic
57C2×D29—24no—
58C2×D29—42no—
59C2×D29—42no—
60C2×D29—88no—
61C4×C29—21no—
62C4×C29—81no—
63C4×C29C2×SD1612yes—
64C4×C29AGL(1,ℤ/8)12yes—
65Dic29—42no—
66D42—291no—
67#492D2911yescharacteristic, complemented
68#476—292no—
69#331—291no—
70D4⋊C8—292no—
71C2×C29—82no—
72C2×C29#45012yes—
73C2×C29#45311yescharacteristic
74D29—44no—
75C22×D4—582no—
76C2×SD16—22no—
77C4⋊Q8C2×D2911yescharacteristic, complemented
78#127C2×D2911yescharacteristic
79#121—582no—
80#120—582no—
81C4×D4—292no—
82#106—582no—
83C4⋊C8—292no—
84#102—582no—
85C4×C8C2×D2911yescharacteristic, complemented
86C29#162911yescharacteristic, complemented, Sylow
87C24—582no—
88C2×Q8—21no—
89C2×D4—22no—
90C2×D4—292no—
91C2×D4—584no—
92C2×D4—1164no—
93C2×D4—1164no—
94C2×D4C22⋊D2912yes—
95C22×C4—582no—
96SD16—44no—
97C2×C8—21no—
98C2×C8—582no—
99C4⋊C4—22no—
100C4⋊C4—292no—
101C22⋊C4—582no—
102C22⋊C4—582no—
103C42C22×D2911yescharacteristic
104C23—22no—
105C23—582no—
106C23—1168no—
107C23—2322no—
108Q8—42no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—294no—
113D4—582no—
114D4—1168no—
115C2×C4—41no—
116C2×C4—582no—
117C2×C4—1162no—
118C2×C4—1162no—
119C2×C4D4×D2912yes—
120C2×C4C2×C22⋊D2911yescharacteristic
121C8—22no—
122C8—1162no—
123C22—44no—
124C22—42no—
125C22—584no—
126C22—1162no—
127C22—1162no—
128C22—2328no—
129C22#1174529911yescharacteristic
130C4—21no—
131C4—81no—
132C4—1162no—
133C4SD16×D2912yes—
134C4#1174527612yes—
135C2—82no—
136C2—1164no—
137C2#1427131212yes—
138C2#1427133011yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#492C2
socleC22×C29#120
prime radical#14271798C2
hypercenter#492D29
hypocenterC29#1629
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #14271450C2semidirect
3. #14270907C2semidirect
4. #14270892C2semidirect
5. C29×#492C2semidirect
8. C29×C4⋊Q8C22semidirect
13. C4×C8×C29C22semidirect
16. C4⋊#6597C22semidirect
48. D116SD16semidirect
67. #492D29semidirect
77. C4⋊Q8C2×D29semidirect
85. C4×C8C2×D29semidirect
86. C29#1629semidirect

Maximal subgroups

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

subgroupindex
#142717982
#142714502
#142709072
#142708922
C29×#4922
#162929