Finite Group Databasebeta

← #16818787

Subgroups — #16818787

Order 3712.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#14271911C211yesmaximal, characteristic, complemented
2#14271552C212yesmaximal, complemented
3#14271529C211yesmaximal, characteristic, complemented
4#14270902C212yesmaximal, complemented
5C29×#330C211yesmaximal, characteristic, complemented
6C29×#125C2211yescharacteristic
7C2×D232—22no—
8C2×#90773—22no—
9#11745258—22no—
10#11745257—22no—
11#11745256—22no—
12#11745237C2212yes—
13#11745236C2211yescharacteristic
14C29×#97C2212yes—
15#11745157—22no—
16#11745151C2211yescharacteristic
17C2×D116—21no—
18C2×D116—22no—
19C2×D116—22no—
20C2×D116D412yes—
21C2×C4×D29—22no—
22C2×Dic58D412yes—
23C2×C8×C29—22no—
24C4⋊C4×C29—22no—
25C4⋊C4×C29D412yes—
26C42×C29C2311yescharacteristic
27#90781—22no—
28#90781—22no—
29#90781—22no—
30#90779—22no—
31C2×#6597—21no—
32D232—44no—
33#90773—44no—
34C22×D29—22no—
35C22×D29—41no—
36C2×C4×C29—22no—
37C2×C4×C29C2×D411yescharacteristic
38C2×C4×C29C2×D412yes—
39C2×Dic29—22no—
40D116—42no—
41D116—42no—
42D116—42no—
43D116—42no—
44D116—82no—
45C4×D29—82no—
46Dic58—42no—
47C8×C29—24no—
48#6597—41no—
49#1656—291nomaximal, Sylow
50C22×C29#12011yescharacteristic
51C2×D29—42no—
52C2×D29—42no—
53C2×D29—42no—
54C2×D29—82no—
55C2×D29—81no—
56C4×C29—22no—
57C4×C29—21no—
58C4×C29—42no—
59Dic29—42no—
60#562—291no—
61#496—292no—
62#490—291no—
63#330D2911yescharacteristic, complemented
64#329—292no—
65C2×C29#45312yes—
66C2×C29#45411yescharacteristic
67D29—82no—
68D29—161no—
69C2×SD16—582no—
70C2×D8—582no—
71#127—291no—
72#125C2×D2911yescharacteristic
73#124—292no—
74#123—582no—
75C22⋊Q8—582no—
76#121—582no—
77#102—582no—
78#97—291no—
79#97C2×D2912yes—
80C29#165611yescharacteristic, complemented, Sylow
81C2×Q8—292no—
82C2×D4—292no—
83C2×D4—582no—
84C2×D4—581no—
85C2×D4—582no—
86C22×C4—582no—
87SD16—1164no—
88D8—1164no—
89C2×C8—22no—
90C2×C8—581no—
91C4⋊C4—22no—
92C4⋊C4—582no—
93C4⋊C4D11612yes—
94C22⋊C4—582no—
95C22⋊C4—582no—
96C22⋊C4—582no—
97C42C22×D2911yescharacteristic
98C23—582no—
99C23—1161no—
100Q8—1162no—
101D4—1162no—
102D4—1162no—
103D4—1162no—
104D4—1162no—
105D4—2322no—
106C2×C4—22no—
107C2×C4—582no—
108C2×C4—2322no—
109C2×C4C2×D11611yescharacteristic
110C2×C4D4×D2912yes—
111C8—24no—
112C8—1161no—
113C22—1162no—
114C22—1162no—
115C22—1162no—
116C22—2322no—
117C22—2321no—
118C22#1174524411yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—1162no—
123C2—4641no—
124C2—2322no—
125C2#1427133212yes—
126C2#1427133811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#330C2
socleC22×C29#120
hypercenter#330D29
hypocenterC29#1656
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #14271911C2semidirect
2. #14271552C2semidirect
3. #14271529C2semidirect
4. #14270902C2semidirect
5. C29×#330C2semidirect
63. #330D29semidirect
80. C29#1656semidirect

Maximal subgroups

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

subgroupindex
#142719112
#142715522
#142715292
#142709022
C29×#3302
#165629