Finite Group Databasebeta

← #16818710

Subgroups — #16818710

Order 3712.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271893C211yesmaximal, characteristic
2#14271445C211yesmaximal, characteristic
3#14271370C211yesmaximal, characteristic
4#14270912C211yesmaximal, characteristic
5#14270895C211yesmaximal, characteristic
6#14270895C211yesmaximal, characteristic
7C29×#487C211yesmaximal, characteristic
8C29×C4⋊Q8C2211yescharacteristic
9C29×C4⋊Q8C2211yescharacteristic
10#11745306—22no—
11C2×#90785—21no—
12#11745250—21no—
13#11745250—21no—
14#11745249—21no—
15#11745249—21no—
16C4×Dic58C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×#103—22no—
19C4×C8×C29C2211yescharacteristic
20#11745183—21no—
21#11745158—21no—
22#11745156—21no—
23C4⋊#6597C2211yescharacteristic
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×Q8×C29D412yes—
27C2×Dic58—22no—
28C2×Dic58D411yescharacteristic
29C2×Dic58D411yescharacteristic
30C2×C8×C29—21no—
31C4⋊C4×C29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C42×C29C2311yescharacteristic
36#90785—42no—
37C4⋊Dic29D411yescharacteristic
38C4⋊Dic29D411yescharacteristic
39#90779—22no—
40#90779—22no—
41#90779—21no—
42#90779—21no—
43C4×Dic29—22no—
44C4×Dic29—21no—
45C4×Dic29—21no—
46C2×#6597—21no—
47C2×#6597—21no—
48Q8×C29—42no—
49Q8×C29—41no—
50Q8×C29—41no—
51C2×C4×C29—22no—
52C2×C4×C29—41no—
53C2×C4×C29C2×D411yescharacteristic
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×Dic29—21no—
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—21no—
60Dic58—21no—
61Dic58—21no—
62Dic58—82no—
63Dic58SD1612yes—
64Dic58Q1612yescomplemented
65C8×C29—41no—
66#6597—41no—
67#6597—41no—
68#1645—291nomaximal, Sylow
69C22×C29#12011yescharacteristic
70C4×C29—21no—
71C4×C29—42no—
72C4×C29—81no—
73C4×C29C2×SD1611yescharacteristic
74C4×C29C2×Q1611yescharacteristic
75C4×C29#13711yescharacteristic
76C4×C29#13711yescharacteristic
77Dic29—22no—
78Dic29—22no—
79Dic29—41no—
80Dic29—41no—
81Q82—291no—
82#487D2911yescharacteristic
83#475—291no—
84#462—291no—
85#333—291no—
86Q8⋊C8—291no—
87Q8⋊C8—291no—
88C2×C29#44811yescharacteristic
89C2×C29#45111yescharacteristic
90C2×C29#45511yescharacteristic
91C2×Q16—581no—
92C4⋊Q8—581no—
93C4⋊Q8—581no—
94C4⋊Q8—582no—
95C4⋊Q8C2×D2911yescharacteristic
96C4⋊Q8C2×D2911yescharacteristic
97C4×Q8—291no—
98C4×Q8—291no—
99C4×Q8—581no—
100C4×Q8—581no—
101#106—581no—
102C4⋊C8—291no—
103C4⋊C8—291no—
104#103—22no—
105#103—581no—
106#103—581no—
107C4×C8C2×D2911yescharacteristic
108C29#164511yescharacteristic, complemented, Sylow
109C2×Q8—21no—
110C2×Q8—291no—
111C2×Q8—291no—
112C2×Q8—582no—
113C2×Q8C22⋊D2912yes—
114Q16—1162no—
115C2×C8—21no—
116C2×C8—581no—
117C2×C8—581no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—291no—
123C4⋊C4—291no—
124C4⋊C4—582no—
125C4⋊C4—582no—
126C4⋊C4—581no—
127C4⋊C4—581no—
128C42—582no—
129C42—581no—
130C42—581no—
131C42C22×D2911yescharacteristic
132Q8—42no—
133Q8—41no—
134Q8—41no—
135Q8—292no—
136Q8—292no—
137Q8—581no—
138Q8—581no—
139Q8—2322no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—581no—
143C2×C4—581no—
144C2×C4—581no—
145C2×C4—581no—
146C2×C4D4×D2911yescharacteristic
147C2×C4D4×D2911yescharacteristic
148C2×C4C2×C22⋊D2911yescharacteristic
149C8—41no—
150C8—1161no—
151C8—1161no—
152C22#1174529911yescharacteristic
153C4—21no—
154C4—42no—
155C4—81no—
156C4—582no—
157C4—582no—
158C4—1161no—
159C4—1161no—
160C4SD16×D2911yescharacteristic
161C4#1174527711yescharacteristic
162C4Q16×D2911yescharacteristic
163C4#1174528011yescharacteristic
164C2#1427130011yescharacteristic
165C2#1427131711yescharacteristic
166C2#1427134011yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#487C2
socle, prime radicalC22×C29#120
hypercenter#487D29
hypocenterC29#1645
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
64. Dic58Q16semidirect
108. C29#1645semidirect

Maximal subgroups

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

subgroupindex
#142718932
#142714452
#142713702
#142709122
#142708952
C29×#4872
#164529