Finite Group Databasebeta

← #16818608

Subgroups — #16818608

Order 3712.

314 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 65 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#14271535C211yesmaximal, characteristic, complemented
2#14271453C212yesmaximal, complemented
3#14270907C211yesmaximal, characteristic, complemented
4D4⋊#6597C212yesmaximal, complemented
5D42×C29C211yesmaximal, characteristic
6C22×D4×C29—22no—
7C29×#127C2211yescharacteristic
8C29×#121—22no—
9C29×#120—22no—
10C4×D4×C29C2212yes—
11C2×#90783—22no—
12#11745231C2211yescharacteristic, complemented
13#11745180—22no—
14#11745156—22no—
15C4⋊#6597C2212yescomplemented
16C4×#6597C2211yescharacteristic, complemented
17C24×C29—22no—
18C2×D4×C29—24no—
19C2×D4×C29—22no—
20C2×D4×C29—44no—
21C2×D4×C29—44no—
22C2×D4×C29D412yes—
23C2×D4×C29D412yes—
24C22×C4×C29—22no—
25C2×Dic58—21no—
26C4⋊C4×C29D412yes—
27C22⋊C4×C29—22no—
28C22⋊C4×C29—22no—
29C42×C29C2311yescharacteristic
30#90783—44no—
31C4⋊Dic29—22no—
32C2×#6597—21no—
33C2×#6597—22no—
34C23×C29—22no—
35C23×C29—22no—
36C23×C29—48no—
37C23×C29—82no—
38D4×C29—22no—
39D4×C29—42no—
40D4×C29—48no—
41D4×C29—42no—
42D4×C29—42no—
43D4×C29SD1614yescomplemented
44C2×C4×C29—22no—
45C2×C4×C29—42no—
46C2×C4×C29—42no—
47C2×C4×C29C2×D411yescharacteristic
48C2×C4×C29C2×D412yes—
49C2×Dic29—41no—
50Dic58—42no—
51#6597—22no—
52#6597—42no—
53#1629—291nomaximal, Sylow
54C22×C29—24no—
55C22×C29—42no—
56C22×C29—42no—
57C22×C29—44no—
58C22×C29—42no—
59C22×C29—88no—
60C22×C29#12011yescharacteristic
61C4×C29—21no—
62C4×C29—42no—
63C4×C29C2×SD1612yes—
64C4×C29AGL(1,ℤ/8)12yes—
65Dic29—81no—
66D42D2911yescharacteristic
67#492—291no—
68#476—292no—
69#331—291no—
70D4⋊C8—292no—
71C2×C29—44no—
72C2×C29—82no—
73C2×C29#45012yes—
74C2×C29#45311yescharacteristic
75C22×D4—22no—
76C2×SD16—582no—
77C4⋊Q8—291no—
78#127C2×D2911yescharacteristic
79#121—22no—
80#120—22no—
81C4×D4C2×D2912yes—
82#106—582no—
83C4⋊C8—292no—
84#102—582no—
85C4×C8—291no—
86C29#162911yescharacteristic, complemented, Sylow
87C24—22no—
88C2×Q8—581no—
89C2×D4—24no—
90C2×D4—22no—
91C2×D4—44no—
92C2×D4—44no—
93C2×D4C22⋊D2912yes—
94C2×D4C22⋊D2912yes—
95C22×C4—22no—
96SD16—1164no—
97C2×C8—581no—
98C2×C8—582no—
99C4⋊C4—582no—
100C4⋊C4C22⋊D2912yes—
101C22⋊C4—22no—
102C22⋊C4—22no—
103C42C22×D2911yescharacteristic
104C23—22no—
105C23—22no—
106C23—48no—
107C23—82no—
108Q8—1162no—
109D4—22no—
110D4—42no—
111D4—48no—
112D4—42no—
113D4—42no—
114D4#9078314yescomplemented
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—1161no—
119C2×C4C2×C22⋊D2911yescharacteristic
120C2×C4C2×C22⋊D2912yes—
121C8—582no—
122C8—1162no—
123C22—24no—
124C22—42no—
125C22—42no—
126C22—44no—
127C22—42no—
128C22—88no—
129C22#1174531511yescharacteristic
130C4—21no—
131C4—42no—
132C4—2321no—
133C4#1174529412yes—
134C4C2×#9078312yes—
135C2—44no—
136C2—82no—
137C2#1427131412yes—
138C2#1427133111yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
Fitting, prime radicalD42×C29C2
socleC22×C29#120
hypercenterD42D29
hypocenterC29#1629
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14271535C2semidirect
2. #14271453C2semidirect
3. #14270907C2semidirect
4. D4⋊#6597C2semidirect
12. #11745231C22semidirect
15. C4⋊#6597C22semidirect
16. C4×#6597C22semidirect
43. D4×C29SD16semidirect
86. C29#1629semidirect
114. D4#90783semidirect

Maximal subgroups

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

subgroupindex
#142715352
#142714532
#142709072
D4⋊#65972
D42×C292
#162929