Finite Group Databasebeta

← #16834617

Subgroups — #16834617

Order 3712.

106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 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#14272073C211yesmaximal, characteristic, complemented
2#14272023C211yesmaximal, characteristic, complemented
3#14271346C211yesmaximal, characteristic
4C29×2−1+4C411yescharacteristic
5#11745313—21no—
6#11745306C2211yescharacteristic
7#11745221—21no—
8#11745220—21no—
9#11745185—21no—
10#11745184C411yescharacteristic
11#41×C29—21no—
12#41×C29—41no—
13#41×C29—41no—
14C2×Q8×C29—41no—
15C2×Q8×C29C2×C411yescharacteristic
16C2×Dic58D411yescharacteristic
17#90800—41no—
18C2×#6599—41no—
19#90785—41no—
20#90783—41no—
21#90779—41no—
22C4×Dic29D411yescharacteristic
23#90777—21no—
24Q8×C29—21no—
25Q8×C29—41no—
26Q8×C29—41no—
27D4×C29—21no—
28D4×C29—41no—
29D4×C29—41no—
30C2×C4×C29—21no—
31C2×C4×C29—41no—
32C2×C4×C29—42no—
33C2×C4×C29C22⋊C411yescharacteristic
34C2×Dic29—21no—
35C2×Dic29—21no—
36Dic58—41no—
37#6599—81no—
38#6599—81no—
39#6597—41no—
40#1405—291nomaximal, Sylow
41C22×C29—41no—
42C22×C29#9911yescharacteristic
43C4×C29—21no—
44C4×C29—41no—
45C4×C29—41no—
46Dic29—21no—
47Dic29—21no—
48Dic29—41no—
49#456—291no—
50#356—291no—
51#333—291no—
52C2×C29—21no—
53C2×C29—81no—
54C2×C29AΣL(1,𝔽16)11yescharacteristic
552−1+4#118111yescharacteristic
56#137—581no—
57C4⋊Q8—291no—
58C4⋊C8—581no—
59#104—581no—
60#101—291no—
61#101—581no—
62C29#140511yescharacteristic, complemented, Sylow
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—291no—
68C2×Q8C2×#118111yescharacteristic
69Q16—1161no—
70SD16—1161no—
71M16—581no—
72M16—1161no—
73C2×C8—1161no—
74C4⋊C4—1161no—
75C42—291no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—1161no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—581no—
87C2×C4—581no—
88C2×C4C22⋊#118111yescharacteristic
89C8—1161no—
90C8—2321no—
91C8—2321no—
92C22—41no—
93C22#1174522711yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—581no—
98C4—581no—
99C4—1161no—
100C2—21no—
101C2—81no—
102C2#1427206311yescharacteristic
subgroupG/H
centerC2#14272063
commutatorC2×Q8×C29C2×C4
FrattiniC2×Q8C2×#1181
Fitting, prime radicalC29×2−1+4C4
socleC2×C29AΣL(1,𝔽16)
cosocle#11745306C22
hypercenter2−1+4#1181
hypocenterC29#1405
LCSG ▷ C2×Q8×C29 ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #14272073C2semidirect
2. #14272023C2semidirect
62. C29#1405semidirect

Maximal subgroups

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

subgroupindex
#142720732
#142720232
#142713462
#140529