Finite Group Databasebeta

← #17993802

Subgroups — #17993802

Order 4736.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558243C211yesmaximal, characteristic
2#14557885C211yesmaximal, characteristic, complemented
3#14557735C211yesmaximal, characteristic
4#14557281C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic
7C37×#475C211yesmaximal, characteristic, complemented
8C2×#10596941—21no—
9#11924536C2211yescharacteristic
10#11924528—21no—
11#11924514—22no—
12#11924512—21no—
13C4×D148—21no—
14C4×D148C2211yescharacteristic
15C4⋊C4×D37—21no—
16C4⋊#64436C2211yescharacteristic
17#11924460—21no—
18#11924459—22no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4×Q8×C37C2211yescharacteristic
22#106×C37—21no—
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37D411yescharacteristic
27C2×D148D411yescharacteristic
28C2×C4×D37—21no—
29C2×C4×D37—22no—
30C2×Dic74D412yes—
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#10596941—42no—
39#10596938—22no—
40#10596938—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44#10596936—22no—
45#10596936—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—
62D148SD1612yes—
63C4×D37—41no—
64C4×D37—41no—
65C4×D37—82no—
66Dic74—42no—
67C8×C37—41no—
68#64436—41no—
69#64436—41no—
70C22×C37#12011yescharacteristic
71C2×D37—22no—
72C2×D37—41no—
73C2×D37—41no—
74C4×C37—21no—
75C4×C37—41no—
76C4×C37—41no—
77C4×C37—81no—
78C4×C37C2×SD1611yescharacteristic
79C4×C37#13511yescharacteristic
80C4×C37#13711yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—41no—
83Dic37—42no—
84#1643—371nomaximal, Sylow
85C2×C37#44811yescharacteristic
86C2×C37#45211yescharacteristic
87C2×C37#45511yescharacteristic
88D37—42no—
89#554—371no—
90#487—371no—
91#475D3711yescharacteristic, complemented
92#461—371no—
93#333—371no—
94Q8⋊C8—371no—
95D4⋊C8—371no—
96C37#164311yescharacteristic, complemented, Sylow
97C2×SD16—741no—
98C4⋊Q8—371no—
99C4⋊Q8C2×D3711yescharacteristic
100#125—741no—
101C22⋊Q8—742no—
102C22⋊Q8—741no—
103C4×Q8C2×D3711yescharacteristic
104C4×D4—371no—
105C4×D4—741no—
106C2×C4⋊C4—741no—
107#106—21no—
108C4⋊C8—371no—
109C4⋊C8C2×D3711yescharacteristic
110#103—21no—
111#103—742no—
112#103—741no—
113C4×C8—371no—
114C2×Q8—21no—
115C2×Q8—372no—
116C2×Q8C22⋊D3711yescharacteristic
117C2×D4—371no—
118C22×C4—742no—
119C22×C4—741no—
120SD16—1482no—
121C2×C8—21no—
122C2×C8—741no—
123C2×C8—741no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—371no—
128C4⋊C4—742no—
129C4⋊C4—742no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4C22⋊D3711yescharacteristic
133C22⋊C4—742no—
134C22⋊C4—741no—
135C42—21no—
136C42C22×D3711yescharacteristic
137C23—741no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—1482no—
143D4—372no—
144D4—741no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—2962no—
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—1481no—
158C8—1481no—
159C22—742no—
160C22—1481no—
161C22—1481no—
162C22#1192450411yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—1482no—
168C4—1481no—
169C4SD16×D3711yescharacteristic
170C4#1192455611yescharacteristic
171C4#1192456511yescharacteristic
172C4#1192456711yescharacteristic
173C2—1482no—
174C2#1455767011yescharacteristic
175C2#1455769311yescharacteristic
176C2#1455770911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#475C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#475D37
hypocenterC37#1643
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #14557885C2semidirect
4. #14557281C2semidirect
5. Q8⋊#64436C2semidirect
7. C37×#475C2semidirect
91. #475D37semidirect
96. C37#1643semidirect

Maximal subgroups

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

subgroupindex
#145582432
#145578852
#145577352
#145572812
Q8⋊#644362
#145572602
C37×#4752
#164337