Finite Group Databasebeta

← #17993869

Subgroups — #17993869

Order 4736.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558253C211yesmaximal, characteristic
2#14557931C211yesmaximal, characteristic, complemented
3#14557813C211yesmaximal, characteristic
4#14557744C211yesmaximal, characteristic, complemented
5#14557278C211yesmaximal, characteristic, complemented
6#14557265C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic
8C2×Dic148—21no—
9#11924536C2211yescharacteristic
10#11924536C2211yescharacteristic
11#11924529—22no—
12#11924523—21no—
13#11924515—21no—
14C4×Dic74C2211yescharacteristic
15#11924501—21no—
16#11924495—21no—
17#11924469—21no—
18#11924468—22no—
19C4⋊#64436C2211yescharacteristic
20#11924461—21no—
21#11924457—21no—
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×D4×C37D411yescharacteristic
26C22×C4×C37—21no—
27C2×Dic74—21no—
28C2×Dic74—21no—
29C2×Dic74D411yescharacteristic
30C2×C8×C37—21no—
31C2×C8×C37—21no—
32C4⋊C4×C37D411yescharacteristic
33C22⋊C4×C37—21no—
34C42×C37C2311yescharacteristic
35C22⋊Dic37—22no—
36C22⋊Dic37—22no—
37C4⋊Dic37—21no—
38C4⋊Dic37—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37D411yescharacteristic
41C4⋊Dic37D412yes—
42#10596936—22no—
43#10596936—21no—
44C4×Dic37—22no—
45C4×Dic37—21no—
46C2×#64436—21no—
47Dic148—42no—
48C23×C37—21no—
49D4×C37—21no—
50D4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—22no—
60C2×Dic37—41no—
61Dic74—21no—
62Dic74—21no—
63Dic74—41no—
64Dic74—41no—
65Dic74—41no—
66Dic74—41no—
67C8×C37—22no—
68C8×C37—41no—
69#64436—41no—
70C22×C37—41no—
71C22×C37—41no—
72C22×C37—41no—
73C22×C37#12011yescharacteristic
74C4×C37—21no—
75C4×C37—41no—
76C4×C37#13511yescharacteristic
77C4×C37#13511yescharacteristic
78C4×C37AGL(1,ℤ/8)11yescharacteristic
79C4×C37#13711yescharacteristic
80Dic37—41no—
81Dic37—42no—
82Dic37—41no—
83Dic37—81no—
84#1652—371nomaximal, Sylow
85C2×C37—81no—
86C2×C37#44911yescharacteristic
87C2×C37#45211yescharacteristic
88C2×C37#45611yescharacteristic
89#556—371no—
90#498—371no—
91#474—371no—
92#462—371no—
93#332—371no—
94Q8⋊C8—371no—
95D4⋊C8D3711yescharacteristic
96C37#165211yescharacteristic, complemented, Sylow
97C2×Q16—741no—
98C4⋊Q8—371no—
99C4⋊Q8—371no—
100#126—742no—
101#124—741no—
102C22⋊Q8—741no—
103C4×Q8—371no—
104C4×Q8—741no—
105C4×D4C2×D3711yescharacteristic
106#117—741no—
107#107—741no—
108#106—742no—
109C4⋊C8—371no—
110C4⋊C8C2×D3711yescharacteristic
111#103—741no—
112#102—741no—
113C4×C8C2×D3711yescharacteristic
114C2×Q8—371no—
115C2×Q8—741no—
116C2×Q8—741no—
117C2×D4D14811yescharacteristic
118C22×C4—21no—
119Q16—1482no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—741no—
123C4⋊C4—371no—
124C4⋊C4—372no—
125C4⋊C4—742no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4D14811yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—742no—
133C22⋊C4—742no—
134C42—742no—
135C42—741no—
136C42C22×D3711yescharacteristic
137C23—21no—
138Q8—741no—
139Q8—741no—
140Q8—1481no—
141Q8—1481no—
142Q8—1481no—
143Q8—1481no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—741no—
150C2×C4—742no—
151C2×C4—741no—
152C2×C4—1481no—
153C2×C4C2×D14811yescharacteristic
154C2×C4D4×D3711yescharacteristic
155C2×C4D4×D3711yescharacteristic
156C8—22no—
157C8—41no—
158C8—1481no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1192450611yescharacteristic
163C4—21no—
164C4—41no—
165C4—2961no—
166C4—1482no—
167C4—1481no—
168C4—1481no—
169C4#1192455711yescharacteristic
170C4#1192455811yescharacteristic
171C4#1192456011yescharacteristic
172C4#1192456911yescharacteristic
173C2—81no—
174C2#1455767911yescharacteristic
175C2#1455769711yescharacteristic
176C2#1455771711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenterD4⋊C8D37
hypocenterC37#1652
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557931C2semidirect
4. #14557744C2semidirect
5. #14557278C2semidirect
6. #14557265C2semidirect
96. C37#1652semidirect

Maximal subgroups

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

subgroupindex
#145582532
#145579312
#145578132
#145577442
#145572782
#145572652
C37×D4⋊C82
#165237