Finite Group Databasebeta

← #16818804

Subgroups — #16818804

Order 3712.

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

normal subgroups only

This group has 196 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#14271913C211yesmaximal, characteristic
2#14271572C212yesmaximal, complemented
3#14271558C211yesmaximal, characteristic
4#14270904C212yesmaximal, complemented
5C29×#329C211yesmaximal, characteristic
6C29×#124C2211yescharacteristic
7#11745306—21no—
8C2×#90785—21no—
9#11745297—21no—
10C2×#90783—21no—
11#11745241—22no—
12#11745240—22no—
13#11745232C2212yes—
14#11745231C2211yescharacteristic
15C29×#97C2212yes—
16#11745166—22no—
17#11745165—22no—
18#11745151C2211yescharacteristic
19C2×Q8×C29D411yescharacteristic
20C2×D4×C29D411yescharacteristic
21C22×Dic29—21no—
22C2×Dic58—21no—
23C2×Dic58—21no—
24C2×C8×C29—22no—
25C22⋊C4×C29—22no—
26C42×C29C2311yescharacteristic
27C22⋊Dic29—22no—
28C22⋊Dic29—21no—
29#90785—42no—
30#90783—42no—
31C4⋊Dic29—22no—
32C4⋊Dic29D412yes—
33C4⋊Dic29D412yes—
34#90779—22no—
35#90779—22no—
36#90779—22no—
37C4×Dic29—21no—
38C2×#6597—21no—
39C23×C29—21no—
40Q8×C29—41no—
41D4×C29—41no—
42C2×C4×C29—21no—
43C2×C4×C29C2×D411yescharacteristic
44C2×C4×C29C2×D412yes—
45C2×Dic29—22no—
46C2×Dic29—22no—
47C2×Dic29—41no—
48C2×Dic29—81no—
49Dic58—41no—
50Dic58—41no—
51Dic58—81no—
52C8×C29—24no—
53#6597—22no—
54#1660—291nomaximal, Sylow
55C22×C29—41no—
56C22×C29—42no—
57C22×C29#12011yescharacteristic
58C4×C29—21no—
59C4×C29—22no—
60C4×C29—41no—
61Dic29—42no—
62Dic29—42no—
63Dic29—81no—
64#563—291no—
65#501—292no—
66#497—291no—
67#330—292no—
68#329D2911yescharacteristic
69C2×C29—81no—
70C2×C29#45311yescharacteristic
71C2×C29#45612yes—
72C2×Q16—581no—
73C2×SD16—581no—
74C4⋊Q8—291no—
75C4⋊Q8—581no—
76#126—582no—
77#125—292no—
78#124C2×D2911yescharacteristic
79#123—581no—
80C22⋊Q8—582no—
81#107—582no—
82#106—582no—
83#97—291no—
84#97C2×D2912yes—
85C29#166011yescharacteristic, complemented, Sylow
86C2×Q8—581no—
87C2×Q8—581no—
88C2×Q8D11611yescharacteristic
89C2×D4D11611yescharacteristic
90C22×C4—581no—
91Q16—1162no—
92SD16—1162no—
93C2×C8—22no—
94C2×C8—581no—
95C4⋊C4—292no—
96C4⋊C4—292no—
97C4⋊C4—582no—
98C4⋊C4—582no—
99C4⋊C4—582no—
100C4⋊C4—582no—
101C22⋊C4—22no—
102C22⋊C4—582no—
103C22⋊C4—581no—
104C42—581no—
105C42C22×D2911yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—1161no—
109Q8—1161no—
110Q8—2321no—
111D4—41no—
112C2×C4—21no—
113C2×C4—582no—
114C2×C4—582no—
115C2×C4—1161no—
116C2×C4—2321no—
117C2×C4C2×D11611yescharacteristic
118C2×C4D4×D2912yes—
119C8—24no—
120C8—582no—
121C22—41no—
122C22—42no—
123C22#1174524411yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—1162no—
128C4—1162no—
129C4—2321no—
130C2—81no—
131C2#1427133311yescharacteristic
132C2#1427134712yes—
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#329C2
socleC22×C29#120
prime radicalC2×D4×C29D4
hypercenter#329D29
hypocenterC29#1660
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14271572C2semidirect
4. #14270904C2semidirect
85. C29#1660semidirect

Maximal subgroups

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

subgroupindex
#142719132
#142715722
#142715582
#142709042
C29×#3292
#166029