Finite Group Databasebeta

← #16818801

Subgroups — #16818801

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#14271569C212yesmaximal, complemented
3#14270904C212yesmaximal, complemented
4#14270903C211yesmaximal, characteristic
5C29×#497C211yesmaximal, characteristic
6C2×Q16×C29—21no—
7C2×SD16×C29—21no—
8C29×C4⋊Q8C2211yescharacteristic
9C29×#124C2211yescharacteristic
10#11745306—21no—
11#11745297—21no—
12#11745241—22no—
13#11745240—22no—
14#11745232C2212yes—
15C29×#97C2211yescharacteristic
16#11745156—22no—
17#11745155—22no—
18#11745151C2212yes—
19C2×Q8×C29—21no—
20C2×Q8×C29D411yescharacteristic
21C2×D4×C29D411yescharacteristic
22C22×Dic29—21no—
23C2×Dic58—21no—
24Q16×C29—42no—
25SD16×C29—42no—
26C2×C8×C29—21no—
27C4⋊C4×C29—22no—
28C22⋊C4×C29—22no—
29C42×C29C2311yescharacteristic
30C22⋊Dic29—22no—
31C22⋊Dic29—21no—
32C4⋊Dic29D412yes—
33C4⋊Dic29D412yes—
34#90779—22no—
35#90779—22no—
36#90779—22no—
37C4×Dic29—21no—
38C2×#6597—22no—
39C23×C29—21no—
40Q8×C29—41no—
41Q8×C29—41no—
42Q8×C29—41no—
43D4×C29—41no—
44C2×C4×C29—21no—
45C2×C4×C29—41no—
46C2×C4×C29C2×D412yes—
47C2×C4×C29C2×D411yescharacteristic
48C2×Dic29—22no—
49C2×Dic29—22no—
50C2×Dic29—81no—
51Dic58—81no—
52C8×C29—22no—
53#6597—24no—
54#1660—291nomaximal, Sylow
55C22×C29—41no—
56C22×C29—42no—
57C22×C29#12011yescharacteristic
58C4×C29—21no—
59C4×C29—22no—
60C4×C29—41no—
61C4×C29—81no—
62Dic29—42no—
63Dic29—42no—
64#563—291no—
65#501—292no—
66#497D2911yescharacteristic
67#330—292no—
68#329—291no—
69C2×C29—81no—
70C2×C29#45311yescharacteristic
71C2×C29#45612yes—
72C2×Q16—21no—
73C2×SD16—21no—
74C4⋊Q8—581no—
75C4⋊Q8C2×D2911yescharacteristic
76#126—582no—
77#125—292no—
78#124C2×D2911yescharacteristic
79#123—581no—
80C22⋊Q8—582no—
81#107—582no—
82#106—582no—
83#97—292no—
84#97C2×D2911yescharacteristic
85C29#166011yescharacteristic, complemented, Sylow
86C2×Q8—21no—
87C2×Q8—581no—
88C2×Q8C22⋊D2911yescharacteristic
89C2×D4C22⋊D2911yescharacteristic
90C22×C4—581no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—582no—
95C4⋊C4—22no—
96C4⋊C4—292no—
97C4⋊C4—292no—
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—41no—
109Q8—41no—
110Q8—2321no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—582no—
115C2×C4—582no—
116C2×C4—2321no—
117C2×C4D4×D2912yes—
118C2×C4C2×C22⋊D2911yescharacteristic
119C8—22no—
120C8—584no—
121C22—41no—
122C22—42no—
123C22#1174529911yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—81no—
128C4—1162no—
129C4—1162no—
130C2—81no—
131C2#1427133011yescharacteristic
132C2#1427134412yes—
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#497C2
socleC22×C29#120
prime radicalC2×D4×C29D4
hypercenter#497D29
hypocenterC29#1660
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #14271569C2semidirect
3. #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
#142715692
#142709042
#142709032
C29×#4972
#166029