Finite Group Databasebeta

← #16834616

Subgroups — #16834616

Order 3712.

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

normal subgroups only

This group has 112 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#14272069C211yesmaximal, characteristic, complemented
2#14272019C211yesmaximal, characteristic, complemented
3#14271338C211yesmaximal, characteristic
4#11745362C411yescharacteristic, complemented
5#11745309C2211yescharacteristic
6#11745270—21no—
7#11745218—21no—
8#11745215—21no—
9C29×#101C411yescharacteristic, complemented
10#11745173—21no—
11C2×Q8×C29C2×C411yescharacteristic
12#90809—41no—
13Q8×D29—41no—
14#90805—21no—
15#90805—41no—
16C2×D116D411yescharacteristic
17C22⋊#1181—41no—
18C2×#6599—41no—
19M16×C29—21no—
20#90781—41no—
21C4×Dic29D411yescharacteristic
22D232—41no—
23#90773—41no—
24C22×D29—21no—
25C2×#1181—81no—
26Q8×C29—41no—
27C2×C4×C29—21no—
28C2×C4×C29C22⋊C411yescharacteristic
29C22⋊D29—41no—
30C2×Dic29—21no—
31D116—21no—
32D116—41no—
33D116—41no—
34C4×D29—41no—
35C4×D29—42no—
36Dic58—21no—
37Dic58—41no—
38#6599—42no—
39C8×C29—41no—
40#1404—291nomaximal, Sylow
41C22×C29#9911yescharacteristic
42C2×D29—41no—
43C2×D29—41no—
44C2×D29—81no—
45#1181—161no—
46C4×C29—21no—
47C4×C29—41no—
48Dic29—41no—
49Dic29—41no—
50#454—291no—
51#354—291no—
52#329—291no—
53C2×C29—21no—
54C2×C29AΣL(1,𝔽16)11yescharacteristic
55D29—81no—
56D29—81no—
572−1+4—291no—
58AGL(1,ℤ/8)—581no—
59#124—291no—
60#104—581no—
61#101#118111yescharacteristic, complemented
62#99—581no—
63#97—581no—
64C29#140411yescharacteristic, complemented, Sylow
65#41—581no—
66#41—1161no—
67#41—1161no—
68C2×Q8—1161no—
69C2×Q8C2×#118111yescharacteristic
70C2×D4—291no—
71SD16—1161no—
72D8—1161no—
73M16—21no—
74C2×C8—1161no—
75C22⋊C4—1161no—
76C22⋊C4—1161no—
77C42—291no—
78C23—581no—
79Q8—41no—
80Q8—581no—
81Q8—1161no—
82D4—581no—
83D4—1161no—
84D4—1161no—
85D4—1161no—
86C2×C4—21no—
87C2×C4—581no—
88C2×C4—1161no—
89C2×C4—1162no—
90C2×C4—2321no—
91C2×C4C22⋊#118111yescharacteristic
92C8—41no—
93C8—1162no—
94C22—1161no—
95C22—1161no—
96C22—2321no—
97C22#1174521511yescharacteristic
98C4—21no—
99C4—41no—
100C4—1161no—
101C4—1161no—
102C4—4641no—
103C2—21no—
104C2—2321no—
105C2—2321no—
106C2#1427206411yescharacteristic
subgroupG/H
centerC2#14272064
commutatorC2×Q8×C29C2×C4
FrattiniC2×Q8C2×#1181
FittingC29×#101C4
socleC2×C29AΣL(1,𝔽16)
prime radical#14271338C2
cosocle#11745309C22
hypercenter#101#1181
hypocenterC29#1404
LCSG ▷ C2×Q8×C29 ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
1. #14272069C2semidirect
2. #14272019C2semidirect
4. #11745362C4semidirect
9. C29×#101C4semidirect
61. #101#1181semidirect
64. C29#1404semidirect

Maximal subgroups

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

subgroupindex
#142720692
#142720192
#142713382
#140429