Finite Group Databasebeta

← #16818815

Subgroups — #16818815

Order 3712.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271533C211yesmaximal, characteristic, complemented
2#14271522C212yesmaximal, complemented
3#14270905C211yesmaximal, characteristic, complemented
4#14270903C212yesmaximal, complemented
5C29×#562C211yesmaximal, characteristic
6C29×#125C2211yescharacteristic
7C29×#124C2212yes—
8C29×#123—22no—
9C29×C22⋊Q8—22no—
10C29×#121—22no—
11#11745231C2211yescharacteristic
12#11745183—22no—
13#11745180—22no—
14#11745158—22no—
15#11745151C2212yes—
16#11745151C2211yescharacteristic
17C2×Q8×C29D412yes—
18C2×D4×C29—22no—
19C2×D4×C29D412yes—
20C22×C4×C29—22no—
21C2×Dic58—21no—
22C4⋊C4×C29—22no—
23C4⋊C4×C29—22no—
24C4⋊C4×C29D412yes—
25C22⋊C4×C29—22no—
26C22⋊C4×C29—22no—
27C22⋊C4×C29—22no—
28C42×C29C2311yescharacteristic
29C4⋊Dic29—22no—
30C2×#6597—21no—
31C2×#6597—22no—
32C23×C29—22no—
33Q8×C29—42no—
34D4×C29—42no—
35D4×C29—82no—
36C2×C4×C29—22no—
37C2×C4×C29—22no—
38C2×C4×C29—82no—
39C2×C4×C29C2×D412yes—
40C2×C4×C29C2×D411yescharacteristic
41C2×Dic29—41no—
42Dic58—42no—
43#6597—41no—
44#6597—42no—
45#1662—291nomaximal, Sylow
46C22×C29—42no—
47C22×C29—42no—
48C22×C29—42no—
49C22×C29#12011yescharacteristic
50C4×C29—21no—
51C4×C29—22no—
52C4×C29—42no—
53C4×C29—42no—
54Dic29—81no—
55#562D2911yescharacteristic
56#491—291no—
57#489—292no—
58#330—291no—
59#329—292no—
60C2×C29—82no—
61C2×C29#45411yescharacteristic
62C2×C29#45512yes—
63C4⋊Q8—291no—
64#125C2×D2911yescharacteristic
65#124C2×D2912yes—
66#123—22no—
67C22⋊Q8—22no—
68#121—22no—
69#103—582no—
70#103—582no—
71#102—582no—
72#97—291no—
73#97—292no—
74C29#166211yescharacteristic, complemented, Sylow
75C2×Q8—581no—
76C2×Q8C22⋊D2912yes—
77C2×D4—22no—
78C2×D4C22⋊D2912yes—
79C22×C4—22no—
80C2×C8—582no—
81C2×C8—581no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—582no—
85C4⋊C4C22⋊D2912yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D2911yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—1162no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—1161no—
99C2×C4C2×C22⋊D2911yescharacteristic
100C2×C4C2×C22⋊D2912yes—
101C8—1161no—
102C8—1162no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1174531511yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—2321no—
112C2—82no—
113C2#1427133611yescharacteristic
114C2#1427134112yes—
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
Fitting, prime radicalC29×#562C2
socleC22×C29#120
hypercenter#562D29
hypocenterC29#1662
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14271533C2semidirect
2. #14271522C2semidirect
3. #14270905C2semidirect
4. #14270903C2semidirect
74. C29#1662semidirect

Maximal subgroups

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

subgroupindex
#142715332
#142715222
#142709052
#142709032
C29×#5622
#166229