Finite Group Databasebeta

← #16821442

Subgroups — #16821442

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#14271604C212yesmaximal, complemented
3#14270972C212yesmaximal, complemented
4#14270945C211yesmaximal, characteristic, complemented
5C29×#470C211yesmaximal, characteristic, complemented
6C2×#90805—21no—
7C2×Q16×C29C2211yescharacteristic, complemented
8C2×M16×C29C2211yescharacteristic
9C29×C22⋊Q8—21no—
10#11745271—22no—
11#11745270—22no—
12#11745266—21no—
13#11745266C2212yes—
14C29×#106C2211yescharacteristic, complemented
15C29×#103—21no—
16#11745177—22no—
17#11745176—22no—
18#11745160C2212yescomplemented
19C2×Q8×C29—21no—
20C22×C4×C29D411yescharacteristic
21C2×C22⋊D29—41no—
22#90805—22no—
23#90805—22no—
24#90805—41no—
25#90805—41no—
26C2×D116—21no—
27C2×C4×D29—41no—
28C2×Dic58—21no—
29Q16×C29—22no—
30M16×C29—22no—
31C2×C8×C29D411yescharacteristic
32C2×C8×C29C2311yescharacteristic
33C4⋊C4×C29—21no—
34C4⋊C4×C29—41no—
35C22⋊C4×C29—41no—
36Dic116—21no—
37Dic116D412yes—
38D232—21no—
39D232D412yes—
40#90773—22no—
41#90773—22no—
42#90768—22no—
43C23×C29D811yescharacteristic
44C22×D29—41no—
45Q8×C29—41no—
46Q8×C29—41no—
47C2×C4×C29—21no—
48C2×C4×C29—21no—
49C2×C4×C29—41no—
50C2×C4×C29—41no—
51C2×C4×C29D811yescharacteristic
52C2×C4×C29C2×D411yescharacteristic
53C22⋊D29—42no—
54C22⋊D29—42no—
55C2×Dic29—41no—
56D116—22no—
57D116—41no—
58C4×D29—42no—
59C4×D29—42no—
60Dic58—22no—
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—81no—
72C4×C29—81no—
73C4×C29#12011yescharacteristic
74C4×C29AGL(1,ℤ/8)11yescharacteristic
75Dic29—42no—
76#575—291no—
77#510—292no—
78#470D2911yescharacteristic, complemented
79#360—292no—
80#349—291no—
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×Q16C2×D2911yescharacteristic, complemented
91C2×M16C2×D2911yescharacteristic
92C22⋊Q8—21no—
93Q32—582no—
94SD32—582no—
95M32—292no—
96#106C2×D2911yescharacteristic, complemented
97#103—21no—
98C29#219111yescharacteristic, complemented, Sylow
99#41—582no—
100#41—582no—
101#41—1161no—
102#41—1161no—
103C2×Q8—21no—
104C2×Q8—581no—
105C2×D4—581no—
106C2×D4—1161no—
107C22×C4—1161no—
108C22×C4C22⋊D2911yescharacteristic
109Q16—22no—
110Q16—292no—
111Q16—581no—
112SD16—582no—
113SD16—582no—
114D8—292no—
115D8—581no—
116M16—22no—
117C2×C8C22⋊D2911yescharacteristic
118C2×C8C22×D2911yescharacteristic
119C4⋊C4—21no—
120C4⋊C4—41no—
121C22⋊C4—41no—
122C16—582no—
123C23—1161no—
124C23#9078211yescharacteristic
125Q8—41no—
126Q8—41no—
127Q8—582no—
128Q8—1161no—
129D4—582no—
130D4—1161no—
131D4—1162no—
132D4—1162no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—1162no—
138C2×C4—1161no—
139C2×C4—1162no—
140C2×C4#9078211yescharacteristic
141C2×C4C2×C22⋊D2911yescharacteristic
142C8—21no—
143C8D4×D2912yes—
144C22—21no—
145C22—41no—
146C22—1162no—
147C22—2322no—
148C22C2×#9078211yescharacteristic
149C4—21no—
150C4—81no—
151C4—81no—
152C4—1162no—
153C4#1174529911yescharacteristic
154C4#1174531111yescharacteristic
155C2—21no—
156C2—41no—
157C2—2322no—
158C2#1427129611yescharacteristic
subgroupG/H
centerC2#14271296
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#470C2
socleC2×C29#447
prime radical#14271963C2
hypercenter#470D29
hypocenterC29#2191
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #14271604C2semidirect
3. #14270972C2semidirect
4. #14270945C2semidirect
5. C29×#470C2semidirect
7. C2×Q16×C29C22semidirect
14. C29×#106C22semidirect
18. #11745160C22semidirect
78. #470D29semidirect
90. C2×Q16C2×D29semidirect
96. #106C2×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
#142716042
#142709722
#142709452
C29×#4702
#219129