Finite Group Databasebeta

← #16821445

Subgroups — #16821445

Order 3712.

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

normal subgroups only

This group has 216 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#14271963C211yesmaximal, characteristic
2#14271606C212yesmaximal, complemented
3#14271421C211yesmaximal, characteristic, complemented
4#14270974C212yesmaximal, complemented
5C29×#349C211yesmaximal, characteristic, complemented
6C2×#90805—21no—
7C2×M16×C29C2211yescharacteristic
8#11745286—21no—
9#11745271—22no—
10#11745270—22no—
11C2×Dic116C2211yescharacteristic, complemented
12#11745266—21no—
13#11745266C2212yes—
14C29×M32C2212yescomplemented
15#11745165C2211yescharacteristic, complemented
16#11745164—21no—
17Dic232—22no—
18#11745148—22no—
19C22×C4×C29D411yescharacteristic
20C2×C22⋊D29—41no—
21#90805—22no—
22#90805—22no—
23#90805—41no—
24#90805—41no—
25C2×D116—21no—
26C2×C4×D29—41no—
27C2×Dic58—21no—
28C2×Dic58—21no—
29M16×C29—22no—
30C2×C8×C29D411yescharacteristic
31C2×C8×C29C2311yescharacteristic
32C22⋊Dic29—41no—
33C4⋊Dic29—21no—
34#90779—41no—
35Dic116—21no—
36Dic116—22no—
37Dic116D412yes—
38D232—21no—
39D232D412yes—
40#90773—22no—
41#90773—22no—
42C16×C29—22no—
43C23×C29D811yescharacteristic
44C22×D29—41no—
45C2×C4×C29—21no—
46C2×C4×C29—21no—
47C2×C4×C29D811yescharacteristic
48C2×C4×C29C2×D411yescharacteristic
49C22⋊D29—42no—
50C22⋊D29—42no—
51C2×Dic29—41no—
52C2×Dic29—41no—
53C2×Dic29—41no—
54D116—22no—
55D116—41no—
56C4×D29—42no—
57C4×D29—42no—
58Dic58—22no—
59Dic58—41no—
60Dic58—41no—
61Dic58—41no—
62C8×C29—21no—
63C8×C29C2×D412yes—
64#2191—291nomaximal, Sylow
65C22×C29—21no—
66C22×C29—41no—
67C22×C29C2×D811yescharacteristic
68C2×D29—42no—
69C2×D29—82no—
70C4×C29—21no—
71C4×C29#12011yescharacteristic
72C4×C29AGL(1,ℤ/8)11yescharacteristic
73Dic29—42no—
74Dic29—81no—
75Dic29—81no—
76#575—291no—
77#510—292no—
78#470—291no—
79#360—292no—
80#349D2911yescharacteristic, complemented
81C2×C29—21no—
82C2×C29—41no—
83C2×C29#44711yescharacteristic
84D29—82no—
85C2×#41—581no—
86#137—582no—
87AGL(1,ℤ/8)—582no—
88#135—292no—
89#135—581no—
90C2×Q16—291no—
91C2×M16C2×D2911yescharacteristic
92C22⋊Q8—581no—
93Q32—582no—
94SD32—582no—
95M32C2×D2912yescomplemented
96#106—291no—
97#103—581no—
98C29#219111yescharacteristic, complemented, Sylow
99#41—582no—
100#41—582no—
101#41—1161no—
102#41—1161no—
103C2×Q8—581no—
104C2×Q8—581no—
105C2×D4—581no—
106C2×D4—1161no—
107C22×C4—1161no—
108C22×C4D11611yescharacteristic
109Q16—292no—
110Q16—581no—
111Q16—582no—
112SD16—582no—
113SD16—582no—
114D8—292no—
115D8—581no—
116M16—22no—
117C2×C8D11611yescharacteristic
118C2×C8C22×D2911yescharacteristic
119C4⋊C4—581no—
120C4⋊C4—1161no—
121C22⋊C4—1161no—
122C16—22no—
123C23—1161no—
124C23D23211yescharacteristic
125Q8—582no—
126Q8—1161no—
127Q8—1161no—
128Q8—1161no—
129D4—582no—
130D4—1161no—
131D4—1162no—
132D4—1162no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—1162no—
136C2×C4—1161no—
137C2×C4—1162no—
138C2×C4—1161no—
139C2×C4—1161no—
140C2×C4D23211yescharacteristic
141C2×C4C2×D11611yescharacteristic
142C8—21no—
143C8D4×D2912yes—
144C22—21no—
145C22—41no—
146C22—1162no—
147C22—2322no—
148C22C2×D23211yescharacteristic
149C4—21no—
150C4—1162no—
151C4—2321no—
152C4—2321no—
153C4#1174524411yescharacteristic
154C4#1174527011yescharacteristic
155C2—21no—
156C2—41no—
157C2—2322no—
158C2#1427129911yescharacteristic
subgroupG/H
centerC2#14271299
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#349C2
socleC2×C29#447
prime radical#14271963C2
hypercenter#349D29
hypocenterC29#2191
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #14271606C2semidirect
3. #14271421C2semidirect
4. #14270974C2semidirect
5. C29×#349C2semidirect
11. C2×Dic116C22semidirect
14. C29×M32C22semidirect
15. #11745165C22semidirect
80. #349D29semidirect
95. M32C2×D29semidirect
98. C29#2191semidirect

Maximal subgroups

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

subgroupindex
#142719632
#142716062
#142714212
#142709742
C29×#3492
#219129