Finite Group Databasebeta

← #16821437

Subgroups — #16821437

Order 3712.

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

normal subgroups only

This group has 226 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, complemented
2#14271599C212yesmaximal, complemented
3#14270972C212yesmaximal, complemented
4#14270945C211yesmaximal, characteristic, complemented
5C29×#469C211yesmaximal, characteristic, complemented
6C2×#90805—21no—
7C2×D8×C29C2211yescharacteristic, complemented
8C2×M16×C29C2211yescharacteristic
9C29×#121—21no—
10#11745271—22no—
11#11745270—22no—
12#11745266—21no—
13#11745266C2212yes—
14C29×#106C2211yescharacteristic, complemented
15C29×#102—21no—
16#11745175—22no—
17#11745174—22no—
18#11745160C2212yescomplemented
19C2×D4×C29—21no—
20C2×D4×C29—41no—
21C22×C4×C29D411yescharacteristic
22C2×C22⋊D29—41no—
23#90805—22no—
24#90805—22no—
25#90805—41no—
26#90805—41no—
27C2×D116—21no—
28C2×C4×D29—41no—
29C2×Dic58—21no—
30D8×C29—22no—
31M16×C29—22no—
32C2×C8×C29D411yescharacteristic
33C2×C8×C29C2311yescharacteristic
34C4⋊C4×C29—21no—
35C22⋊C4×C29—41no—
36Dic116—21no—
37Dic116D412yescomplemented
38D232—21no—
39D232D412yescomplemented
40#90773—22no—
41#90773—22no—
42#90768—22no—
43C23×C29—41no—
44C23×C29D811yescharacteristic
45C22×D29—41no—
46D4×C29—41no—
47D4×C29—41no—
48D4×C29—82no—
49C2×C4×C29—21no—
50C2×C4×C29—21no—
51C2×C4×C29—41no—
52C2×C4×C29D811yescharacteristic
53C2×C4×C29C2×D411yescharacteristic
54C22⋊D29—42no—
55C22⋊D29—42no—
56C2×Dic29—41no—
57D116—22no—
58D116—41no—
59C4×D29—42no—
60C4×D29—42no—
61Dic58—22no—
62Dic58—41no—
63C8×C29—21no—
64C8×C29C2×D412yes—
65#2190—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—41no—
68C22×C29—81no—
69C22×C29—81no—
70C22×C29—81no—
71C22×C29C2×D811yescharacteristic
72C2×D29—42no—
73C2×D29—82no—
74C4×C29—21no—
75C4×C29—81no—
76C4×C29#12011yescharacteristic
77C4×C29AGL(1,ℤ/8)11yescharacteristic
78Dic29—42no—
79#575—291no—
80#509—292no—
81#469D2911yescharacteristic, complemented
82#360—292no—
83#349—291no—
84C2×C29—21no—
85C2×C29—41no—
86C2×C29—161no—
87C2×C29#44711yescharacteristic
88D29—82no—
89C2×#41—581no—
90#137—582no—
91AGL(1,ℤ/8)—582no—
92#135—292no—
93#135—581no—
94C2×D8C2×D2911yescharacteristic, complemented
95C2×M16C2×D2911yescharacteristic
96#121—21no—
97SD32—582no—
98D16—582no—
99M32—292no—
100#106C2×D2911yescharacteristic, complemented
101#102—21no—
102C29#219011yescharacteristic, complemented, Sylow
103#41—582no—
104#41—582no—
105#41—1161no—
106#41—1161no—
107C2×Q8—581no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—581no—
111C2×D4—1161no—
112C22×C4—1161no—
113C22×C4C22⋊D2911yescharacteristic
114Q16—292no—
115Q16—581no—
116SD16—582no—
117SD16—582no—
118D8—22no—
119D8—292no—
120D8—581no—
121M16—22no—
122C2×C8C22⋊D2911yescharacteristic
123C2×C8C22×D2911yescharacteristic
124C4⋊C4—21no—
125C22⋊C4—41no—
126C16—582no—
127C23—41no—
128C23—1161no—
129C23#9078211yescharacteristic
130Q8—582no—
131Q8—1161no—
132D4—41no—
133D4—41no—
134D4—82no—
135D4—582no—
136D4—1161no—
137D4—1162no—
138D4—1162no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—1162no—
143C2×C4—1161no—
144C2×C4—1162no—
145C2×C4#9078211yescharacteristic
146C2×C4C2×C22⋊D2911yescharacteristic
147C8—21no—
148C8D4×D2912yes—
149C22—21no—
150C22—41no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—1162no—
155C22—2322no—
156C22C2×#9078211yescharacteristic
157C4—21no—
158C4—81no—
159C4—1162no—
160C4#1174529911yescharacteristic
161C4#1174531111yescharacteristic
162C2—21no—
163C2—41no—
164C2—161no—
165C2—2322no—
166C2#1427129611yescharacteristic
subgroupG/H
centerC2#14271296
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#469C2
socleC2×C29#447
hypercenter#469D29
hypocenterC29#2190
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14271963C2semidirect
2. #14271599C2semidirect
3. #14270972C2semidirect
4. #14270945C2semidirect
5. C29×#469C2semidirect
7. C2×D8×C29C22semidirect
14. C29×#106C22semidirect
18. #11745160C22semidirect
37. Dic116D4semidirect
39. D232D4semidirect
81. #469D29semidirect
94. C2×D8C2×D29semidirect
100. #106C2×D29semidirect
102. C29#2190semidirect

Maximal subgroups

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

subgroupindex
#142719632
#142715992
#142709722
#142709452
C29×#4692
#219029