Finite Group Databasebeta

← #17993779

Subgroups — #17993779

Order 4736.

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

normal subgroups only

This group has 212 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#14558269C211yesmaximal, characteristic
2#14557815C211yesmaximal, characteristic, complemented
3#14557740C211yesmaximal, characteristic, complemented
4#14557277C211yesmaximal, characteristic
5#14557265C211yesmaximal, characteristic, complemented
6#14557265C211yesmaximal, characteristic, complemented
7C37×#486C211yesmaximal, characteristic
8C2×#10596942—21no—
9#11924523—21no—
10#11924523—21no—
11#11924517—22no—
12C4×Dic74C2211yescharacteristic
13C4×Dic74C2211yescharacteristic
14D4×Dic37—21no—
15D4×Dic37—21no—
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924460—21no—
20#11924459—21no—
21C4⋊Q8×C37C2211yescharacteristic
22#127×C37C2211yescharacteristic
23#102×C37—22no—
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37D412yes—
29C22×Dic37—22no—
30C2×Dic74D411yescharacteristic
31C2×Dic74D411yescharacteristic
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C42×C37C2311yescharacteristic
36C22⋊Dic37—22no—
37C22⋊Dic37—22no—
38C22⋊Dic37—22no—
39#10596942—42no—
40C4⋊Dic37D411yescharacteristic
41C4⋊Dic37D411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—22no—
49Q8×C37—41no—
50Q8×C37—41no—
51D4×C37—42no—
52D4×C37—41no—
53D4×C37—41no—
54D4×C37—41no—
55D4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—82no—
65Dic74—21no—
66Dic74—21no—
67Dic74—21no—
68Dic74—21no—
69C8×C37—41no—
70#64436—41no—
71#64436—41no—
72C22×C37—42no—
73C22×C37—42no—
74C22×C37—42no—
75C22×C37#12011yescharacteristic
76C4×C37—21no—
77C4×C37—81no—
78C4×C37#13511yescharacteristic
79C4×C37#13511yescharacteristic
80C4×C37AGL(1,ℤ/8)11yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—41no—
83Dic37—41no—
84Dic37—41no—
85Dic37—41no—
86#1640—371nomaximal, Sylow
87C2×C37—82no—
88C2×C37#44911yescharacteristic
89C2×C37#45211yescharacteristic
90C2×C37#45511yescharacteristic
91#559—371no—
92#486D3711yescharacteristic
93#475—371no—
94#462—371no—
95#331—371no—
96Q8⋊C8—371no—
97Q8⋊C8—371no—
98C37#164011yescharacteristic, complemented, Sylow
99C2×Q16—741no—
100C4⋊Q8C2×D3711yescharacteristic
101#127C2×D3711yescharacteristic
102#124—741no—
103#124—741no—
104#123—742no—
105C4×Q8—371no—
106C4×Q8—371no—
107C4×D4—741no—
108C4×D4—741no—
109#106—741no—
110C4⋊C8—371no—
111C4⋊C8—371no—
112#103—741no—
113#103—741no—
114#102—22no—
115C4×C8C2×D3711yescharacteristic
116C2×Q8—21no—
117C2×Q8—371no—
118C2×Q8—371no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D3712yes—
122C22×C4—742no—
123Q16—1482no—
124C2×C8—21no—
125C2×C8—741no—
126C2×C8—741no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—371no—
130C4⋊C4—371no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C22⋊C4—742no—
134C22⋊C4—742no—
135C22⋊C4—742no—
136C42—741no—
137C42—741no—
138C42C22×D3711yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—741no—
143Q8—741no—
144Q8—741no—
145Q8—741no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—2962no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—741no—
157C2×C4D4×D3711yescharacteristic
158C2×C4D4×D3711yescharacteristic
159C2×C4C2×C22⋊D3711yescharacteristic
160C8—41no—
161C8—1481no—
162C8—1481no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1192450411yescharacteristic
167C4—21no—
168C4—81no—
169C4—1481no—
170C4—1481no—
171C4—1481no—
172C4—1481no—
173C4#1192455511yescharacteristic
174C4#1192455711yescharacteristic
175C4#1192456011yescharacteristic
176C4#1192456511yescharacteristic
177C2—82no—
178C2#1455767511yescharacteristic
179C2#1455769211yescharacteristic
180C2#1455771011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#486C2
socleC22×C37#120
prime radical#127×C37C22
hypercenter#486D37
hypocenterC37#1640
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #14557815C2semidirect
3. #14557740C2semidirect
5. #14557265C2semidirect
6. #14557265C2semidirect
98. C37#1640semidirect

Maximal subgroups

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

subgroupindex
#145582692
#145578152
#145577402
#145572772
#145572652
C37×#4862
#164037