Finite Group Databasebeta

← #17996541

Subgroups — #17996541

Order 4736.

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#14558333C211yesmaximal, characteristic, complemented
2#14557969C212yesmaximal, complemented
3#14557342C212yesmaximal, complemented
4#14557315C211yesmaximal, characteristic, complemented
5C37×#469C211yesmaximal, characteristic, complemented
6C2×#10596962—21no—
7#11924569—22no—
8#11924564—22no—
9#11924558—21no—
10#11924558C2212yes—
11#11924480—22no—
12#11924477—22no—
13#11924476C2212yescomplemented
14C2×D8×C37C2211yescharacteristic, complemented
15C2×M16×C37C2211yescharacteristic
16#121×C37—21no—
17#106×C37C2211yescharacteristic, complemented
18#102×C37—21no—
19C2×D4×C37—21no—
20C2×D4×C37—41no—
21C22×C4×C37D411yescharacteristic
22C2×C22⋊D37—41no—
23#10596962—22no—
24#10596962—22no—
25#10596962—41no—
26#10596962—41no—
27C2×D148—21no—
28C2×C4×D37—41no—
29C2×Dic74—21no—
30D8×C37—22no—
31M16×C37—22no—
32C2×C8×C37D411yescharacteristic
33C2×C8×C37C2311yescharacteristic
34C4⋊C4×C37—21no—
35C22⋊C4×C37—41no—
36Dic148—21no—
37Dic148D412yescomplemented
38D296—21no—
39D296D412yescomplemented
40#10596930—22no—
41#10596930—22no—
42#10596925—22no—
43C23×C37—41no—
44C23×C37D811yescharacteristic
45C22×D37—41no—
46D4×C37—41no—
47D4×C37—41no—
48D4×C37—82no—
49C2×C4×C37—21no—
50C2×C4×C37—21no—
51C2×C4×C37—41no—
52C2×C4×C37D811yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C22⋊D37—42no—
55C22⋊D37—42no—
56C2×Dic37—41no—
57D148—22no—
58D148—41no—
59C4×D37—42no—
60C4×D37—42no—
61Dic74—22no—
62Dic74—41no—
63C8×C37—21no—
64C8×C37C2×D412yes—
65C22×C37—21no—
66C22×C37—41no—
67C22×C37—81no—
68C22×C37—81no—
69C22×C37—81no—
70C22×C37C2×D811yescharacteristic
71C2×D37—42no—
72C2×D37—82no—
73C4×C37—21no—
74C4×C37—81no—
75C4×C37#12011yescharacteristic
76C4×C37AGL(1,ℤ/8)11yescharacteristic
77Dic37—42no—
78#2190—371nomaximal, Sylow
79C2×C37—21no—
80C2×C37—41no—
81C2×C37—161no—
82C2×C37#44711yescharacteristic
83D37—82no—
84#575—371no—
85#509—372no—
86#469D3711yescharacteristic, complemented
87#360—372no—
88#349—371no—
89C37#219011yescharacteristic, complemented, Sylow
90C2×#41—741no—
91#137—742no—
92AGL(1,ℤ/8)—742no—
93#135—372no—
94#135—741no—
95C2×D8C2×D3711yescharacteristic, complemented
96C2×M16C2×D3711yescharacteristic
97#121—21no—
98SD32—742no—
99D16—742no—
100M32—372no—
101#106C2×D3711yescharacteristic, complemented
102#102—21no—
103#41—742no—
104#41—742no—
105#41—1481no—
106#41—1481no—
107C2×Q8—741no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—741no—
111C2×D4—1481no—
112C22×C4—1481no—
113C22×C4C22⋊D3711yescharacteristic
114Q16—372no—
115Q16—741no—
116SD16—742no—
117SD16—742no—
118D8—22no—
119D8—372no—
120D8—741no—
121M16—22no—
122C2×C8C22⋊D3711yescharacteristic
123C2×C8C22×D3711yescharacteristic
124C4⋊C4—21no—
125C22⋊C4—41no—
126C16—742no—
127C23—41no—
128C23—1481no—
129C23#1059693911yescharacteristic
130Q8—742no—
131Q8—1481no—
132D4—41no—
133D4—41no—
134D4—82no—
135D4—742no—
136D4—1481no—
137D4—1482no—
138D4—1482no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—1482no—
143C2×C4—1481no—
144C2×C4—1482no—
145C2×C4#1059693911yescharacteristic
146C2×C4C2×C22⋊D3711yescharacteristic
147C8—21no—
148C8D4×D3712yes—
149C22—21no—
150C22—41no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—2962no—
155C22—1482no—
156C22C2×#1059693911yescharacteristic
157C4—21no—
158C4—81no—
159C4—1482no—
160C4#1192450411yescharacteristic
161C4#1192456111yescharacteristic
162C2—21no—
163C2—41no—
164C2—161no—
165C2—2962no—
166C2#1455766611yescharacteristic
subgroupG/H
centerC2#14557666
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#469C2
socleC2×C37#447
hypercenter#469D37
hypocenterC37#2190
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14558333C2semidirect
2. #14557969C2semidirect
3. #14557342C2semidirect
4. #14557315C2semidirect
5. C37×#469C2semidirect
13. #11924476C22semidirect
14. C2×D8×C37C22semidirect
17. #106×C37C22semidirect
37. Dic148D4semidirect
39. D296D4semidirect
86. #469D37semidirect
89. C37#2190semidirect
95. C2×D8C2×D37semidirect
101. #106C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145579692
#145573422
#145573152
C37×#4692
#219037