Finite Group Databasebeta

← #16818785

Subgroups — #16818785

Order 3712.

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

normal subgroups only

This group has 230 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#14271553C212yesmaximal, complemented
2#14271529C211yesmaximal, characteristic, complemented
3#14270905C211yesmaximal, characteristic, complemented
4#14270903C212yesmaximal, complemented
5C29×#562C211yesmaximal, characteristic, complemented
6C29×#125C2211yescharacteristic
7C29×#124C2212yes—
8C29×#123—22no—
9C29×C22⋊Q8—22no—
10C29×#121—22no—
11C2×#90784—22no—
12C2×#90782—22no—
13#11745236C2211yescharacteristic
14#11745157—22no—
15#11745151C2211yescharacteristic
16#11745151C2212yes—
17C2×Q8×C29D412yes—
18C2×D4×C29—22no—
19C2×D4×C29D412yes—
20C22×C4×C29—22no—
21C2×D116—22no—
22C2×D116—21no—
23C4⋊C4×C29—22no—
24C4⋊C4×C29—22no—
25C4⋊C4×C29D412yes—
26C22⋊C4×C29—22no—
27C22⋊C4×C29—22no—
28C22⋊C4×C29—22no—
29C42×C29C2311yescharacteristic
30#90784—44no—
31#90782—44no—
32C2×#6597—22no—
33C2×#6597—21no—
34C23×C29—22no—
35C22×D29—41no—
36Q8×C29—42no—
37D4×C29—42no—
38D4×C29—82no—
39C2×C4×C29—22no—
40C2×C4×C29—22no—
41C2×C4×C29—82no—
42C2×C4×C29C2×D411yescharacteristic
43C2×C4×C29C2×D412yes—
44D116—42no—
45D116—42no—
46D116—42no—
47#6597—24no—
48#6597—41no—
49#1656—291nomaximal, Sylow
50C22×C29—42no—
51C22×C29—42no—
52C22×C29—42no—
53C22×C29#12011yescharacteristic
54C2×D29—82no—
55C2×D29—81no—
56C4×C29—22no—
57C4×C29—21no—
58C4×C29—42no—
59C4×C29—42no—
60#562D2911yescharacteristic, complemented
61#496—292no—
62#490—291no—
63#330—291no—
64#329—292no—
65C2×C29—82no—
66C2×C29#45312yes—
67C2×C29#45411yescharacteristic
68D29—161no—
69C2×SD16—582no—
70C2×D8—582no—
71#127—291no—
72#125C2×D2911yescharacteristic
73#124C2×D2912yes—
74#123—22no—
75C22⋊Q8—22no—
76#121—22no—
77#102—582no—
78#97—291no—
79#97—292no—
80C29#165611yescharacteristic, complemented, Sylow
81C2×Q8C22⋊D2912yes—
82C2×D4—22no—
83C2×D4—581no—
84C2×D4—582no—
85C2×D4C22⋊D2912yes—
86C22×C4—22no—
87SD16—1164no—
88D8—1164no—
89C2×C8—582no—
90C2×C8—581no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D2912yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D2911yescharacteristic
98C23—22no—
99C23—1161no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—1162no—
104D4—1162no—
105D4—1162no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D2911yescharacteristic
110C2×C4C2×C22⋊D2912yes—
111C8—584no—
112C8—1161no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—2322no—
117C22—2321no—
118C22#1174531511yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—4641no—
125C2#1427133112yes—
126C2#1427133611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#562C2
socleC22×C29#120
hypercenter#562D29
hypocenterC29#1656
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. #14271553C2semidirect
2. #14271529C2semidirect
3. #14270905C2semidirect
4. #14270903C2semidirect
5. C29×#562C2semidirect
60. #562D29semidirect
80. C29#1656semidirect

Maximal subgroups

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

subgroupindex
#142715532
#142715292
#142709052
#142709032
C29×#5622
#165629