Finite Group Databasebeta

← #17993716

Subgroups — #17993716

Order 4736.

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

normal subgroups only

This group has 218 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#14558268C211yesmaximal, characteristic
2#14557907C211yesmaximal, characteristic
3#14557825C211yesmaximal, characteristic, complemented
4#14557276C211yesmaximal, characteristic
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557263C211yesmaximal, characteristic, complemented
7C37×#477C211yesmaximal, characteristic, complemented
8C2×#10596941—22no—
9#11924533C2211yescharacteristic
10#11924525—21no—
11#11924524—21no—
12#11924521—22no—
13C4×Dic74C2211yescharacteristic
14C4×D148—21no—
15#11924498—21no—
16#11924469—21no—
17C4⋊#64436C2211yescharacteristic
18#11924459—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4×Q8×C37C2211yescharacteristic
22#107×C37—21no—
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37D411yescharacteristic
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D412yes—
30C2×C4×D37—22no—
31C2×Dic74D411yescharacteristic
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37D411yescharacteristic
37C42×C37—21no—
38C42×C37C2311yescharacteristic
39#10596941—44no—
40#10596938—22no—
41#10596938—22no—
42#10596938—22no—
43C4⋊Dic37D411yescharacteristic
44#10596936—21no—
45C4×Dic37—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C22×D37—22no—
49Q8×C37—21no—
50Q8×C37—21no—
51Q8×C37—42no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—41no—
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—21no—
60D148—42no—
61D148—41no—
62D148—41no—
63D148—41no—
64D148—41no—
65C4×D37—82no—
66Dic74—21no—
67Dic74—21no—
68C8×C37—41no—
69#64436—22no—
70#64436—41no—
71C22×C37#12011yescharacteristic
72C2×D37—42no—
73C2×D37—42no—
74C2×D37—42no—
75C4×C37—21no—
76C4×C37—41no—
77C4×C37—41no—
78C4×C37—81no—
79C4×C37#13511yescharacteristic
80C4×C37#13511yescharacteristic
81C4×C37#13711yescharacteristic
82C4×C37#13711yescharacteristic
83Dic37—41no—
84Dic37—41no—
85#1630—371nomaximal, Sylow
86C2×C37#45211yescharacteristic
87C2×C37#45211yescharacteristic
88C2×C37#45311yescharacteristic
89D37—82no—
90#559—371no—
91#492—371no—
92#477—371no—
93#477D3711yescharacteristic, complemented
94#331—371no—
95Q8⋊C8—371no—
96Q8⋊C8—371no—
97C37#163011yescharacteristic, complemented, Sylow
98C2×SD16—742no—
99C4⋊Q8C2×D3711yescharacteristic
100#127—371no—
101#124—741no—
102#124—741no—
103#123—742no—
104C4×Q8—371no—
105C4×Q8C2×D3711yescharacteristic
106C4×D4—741no—
107C4×D4—741no—
108#107—21no—
109#107—741no—
110C4⋊C8—371no—
111C4⋊C8C2×D3711yescharacteristic
112#103—21no—
113#103—741no—
114C4×C8—371no—
115C2×Q8—21no—
116C2×Q8—371no—
117C2×Q8C22⋊D3711yescharacteristic
118C2×D4—372no—
119C2×D4—741no—
120C2×D4—741no—
121C22×C4—742no—
122SD16—1484no—
123C2×C8—21no—
124C2×C8—741no—
125C2×C8—741no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—371no—
130C4⋊C4—741no—
131C4⋊C4C22⋊D3711yescharacteristic
132C22⋊C4—742no—
133C22⋊C4—742no—
134C22⋊C4—742no—
135C42—21no—
136C42—741no—
137C42C22×D3711yescharacteristic
138C23—742no—
139Q8—21no—
140Q8—21no—
141Q8—42no—
142Q8—741no—
143Q8—741no—
144D4—1482no—
145D4—1481no—
146D4—1481no—
147D4—1481no—
148D4—1481no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—2962no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4D4×D3711yescharacteristic
156C2×C4D4×D3711yescharacteristic
157C2×C4C2×C22⋊D3711yescharacteristic
158C8—41no—
159C8—742no—
160C8—1481no—
161C22—1482no—
162C22—1482no—
163C22—1482no—
164C22#1192450411yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—1481no—
170C4—1481no—
171C4#1192455611yescharacteristic
172C4#1192455911yescharacteristic
173C4#1192456711yescharacteristic
174C4#1192456811yescharacteristic
175C2—2962no—
176C2#1455769311yescharacteristic
177C2#1455769411yescharacteristic
178C2#1455769911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#477C2
socleC22×C37#120
prime radical#11924533C22
hypercenter#477D37
hypocenterC37#1630
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #14557825C2semidirect
5. Q8⋊#64436C2semidirect
6. #14557263C2semidirect
7. C37×#477C2semidirect
93. #477D37semidirect
97. C37#1630semidirect

Maximal subgroups

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

subgroupindex
#145582682
#145579072
#145578252
#145572762
Q8⋊#644362
#145572632
C37×#4772
#163037