Finite Group Databasebeta

← #17993864

Subgroups — #17993864

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#14558256C211yesmaximal, characteristic
2#14557929C211yesmaximal, characteristic, complemented
3#14557810C211yesmaximal, characteristic
4#14557278C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic
7C37×#462C211yesmaximal, characteristic, complemented
8#11924536C2211yescharacteristic
9#11924531—22no—
10#11924524—21no—
11#11924512—21no—
12C4×Dic74—21no—
13C4×D148C2211yescharacteristic
14#11924494—21no—
15#11924469—21no—
16#11924467—22no—
17C4⋊#64436C2211yescharacteristic
18#11924456—21no—
19C4×#64436C2211yescharacteristic
20C2×Q16×C37—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37D411yescharacteristic
27C2×D148D411yescharacteristic
28C2×C4×D37—21no—
29C2×Dic74—21no—
30Q16×C37—42no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37D411yescharacteristic
36C42×C37—21no—
37C42×C37C2311yescharacteristic
38#10596938—22no—
39#10596938—22no—
40#10596938—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37D411yescharacteristic
43C4⋊Dic37D412yes—
44#10596936—22no—
45C4×Dic37—22no—
46C2×#64436—21no—
47C2×#64436—21no—
48C22×D37—21no—
49Q8×C37—21no—
50Q8×C37—21no—
51Q8×C37—41no—
52Q8×C37—41no—
53C2×C4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37—41no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—22no—
61D148—21no—
62D148—21no—
63C4×D37—41no—
64C4×D37—41no—
65Dic74—41no—
66Dic74—41no—
67C8×C37—41no—
68#64436—22no—
69#64436—41no—
70C22×C37#12011yescharacteristic
71C2×D37—41no—
72C2×D37—41no—
73C2×D37—41no—
74C4×C37—21no—
75C4×C37—41no—
76C4×C37—41no—
77C4×C37—81no—
78C4×C37#13511yescharacteristic
79C4×C37#13511yescharacteristic
80C4×C37AGL(1,ℤ/8)11yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—41no—
83Dic37—42no—
84#1652—371nomaximal, Sylow
85C2×C37#44911yescharacteristic
86C2×C37#45211yescharacteristic
87C2×C37#45611yescharacteristic
88D37—81no—
89#556—371no—
90#498—371no—
91#474—371no—
92#462D3711yescharacteristic, complemented
93#332—371no—
94Q8⋊C8—371no—
95D4⋊C8—371no—
96C37#165211yescharacteristic, complemented, Sylow
97C2×Q16—21no—
98C4⋊Q8—371no—
99C4⋊Q8C2×D3711yescharacteristic
100#126—742no—
101#124—741no—
102C22⋊Q8—741no—
103C4×Q8—741no—
104C4×Q8C2×D3711yescharacteristic
105C4×D4—371no—
106#117—741no—
107#107—741no—
108#106—742no—
109C4⋊C8—371no—
110C4⋊C8C2×D3711yescharacteristic
111#103—21no—
112#102—741no—
113C4×C8—371no—
114C2×Q8—21no—
115C2×Q8—741no—
116C2×Q8C22⋊D3711yescharacteristic
117C2×D4—371no—
118C22×C4—741no—
119Q16—42no—
120C2×C8—21no—
121C2×C8—741no—
122C2×C8—741no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—372no—
127C4⋊C4—371no—
128C4⋊C4—742no—
129C4⋊C4—741no—
130C4⋊C4C22⋊D3711yescharacteristic
131C22⋊C4—742no—
132C22⋊C4—742no—
133C22⋊C4—741no—
134C42—21no—
135C42—742no—
136C42C22×D3711yescharacteristic
137C23—741no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—1481no—
143Q8—1481no—
144D4—741no—
145D4—741no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—741no—
150C2×C4—742no—
151C2×C4—1481no—
152C2×C4—1481no—
153C2×C4D4×D3711yescharacteristic
154C2×C4D4×D3711yescharacteristic
155C2×C4C2×C22⋊D3711yescharacteristic
156C8—41no—
157C8—742no—
158C8—1481no—
159C22—1481no—
160C22—1481no—
161C22—1481no—
162C22#1192450411yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—1481no—
168C4—1482no—
169C4#1192455611yescharacteristic
170C4#1192455911yescharacteristic
171C4#1192456211yescharacteristic
172C4#1192456811yescharacteristic
173C2—2961no—
174C2#1455767611yescharacteristic
175C2#1455769411yescharacteristic
176C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#462C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#462D37
hypocenterC37#1652
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #14557929C2semidirect
4. #14557278C2semidirect
5. Q8⋊#64436C2semidirect
7. C37×#462C2semidirect
92. #462D37semidirect
96. C37#1652semidirect

Maximal subgroups

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

subgroupindex
#145582562
#145579292
#145578102
#145572782
Q8⋊#644362
#145572602
C37×#4622
#165237