Finite Group Databasebeta

← #17993678

Subgroups — #17993678

Order 4736.

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

normal subgroups only

This group has 240 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#14558248C211yesmaximal, characteristic, complemented
2#14557905C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic, complemented
4#14557281C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#459C211yesmaximal, characteristic, complemented
8C2×#10596940—22no—
9C2×#10596939—21no—
10#11924536C2211yescharacteristic
11#11924522—22no—
12#11924510—21no—
13#11924507—21no—
14C4×D148C2211yescharacteristic
15#11924495—21no—
16#11924494—21no—
17C4⋊#64436C2211yescharacteristic
18#11924457—21no—
19C4×#64436C2211yescharacteristic
20C2×D8×C37—21no—
21#127×C37C2211yescharacteristic
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37D411yescharacteristic
29C22×C4×C37—21no—
30C2×C22⋊D37—22no—
31C2×D148D411yescharacteristic
32C2×C4×D37—21no—
33C2×Dic74D412yes—
34D8×C37—42no—
35C2×C8×C37—21no—
36C4⋊C4×C37D411yescharacteristic
37C22⋊C4×C37—21no—
38C42×C37C2311yescharacteristic
39C22⋊Dic37—22no—
40#10596940—44no—
41#10596939—42no—
42#10596938—22no—
43#10596938—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37D411yescharacteristic
47C4×Dic37—22no—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—21no—
51C23×C37—41no—
52C22×D37—21no—
53D4×C37—21no—
54D4×C37—21no—
55D4×C37—42no—
56D4×C37—41no—
57D4×C37—41no—
58D4×C37—41no—
59D4×C37—41no—
60C2×C4×C37—21no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C22⋊D37—82no—
67C2×Dic37—21no—
68C2×Dic37—22no—
69D148—21no—
70D148—21no—
71C4×D37—41no—
72C4×D37—41no—
73Dic74—42no—
74C8×C37—41no—
75#64436—22no—
76#64436—41no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—81no—
81C22×C37—81no—
82C22×C37—81no—
83C22×C37#12011yescharacteristic
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—41no—
87C4×C37—21no—
88C4×C37—41no—
89C4×C37#13511yescharacteristic
90C4×C37#13511yescharacteristic
91C4×C37AGL(1,ℤ/8)11yescharacteristic
92C4×C37AGL(1,ℤ/8)11yescharacteristic
93Dic37—41no—
94Dic37—42no—
95#1624—371nomaximal, Sylow
96C2×C37—81no—
97C2×C37—161no—
98C2×C37#44911yescharacteristic
99C2×C37#44911yescharacteristic
100C2×C37#45311yescharacteristic
101D37—81no—
102#555—371no—
103#492—371no—
104#459—371no—
105#459D3711yescharacteristic, complemented
106#333—371no—
107D4⋊C8—371no—
108D4⋊C8—371no—
109C37#162411yescharacteristic, complemented, Sylow
110C2×SD16—742no—
111C2×D8—21no—
112C2×D8—741no—
113C4⋊Q8—371no—
114#127C2×D3711yescharacteristic
115#124—742no—
116#121—741no—
117#121—741no—
118C4×D4—371no—
119C4×D4C2×D3711yescharacteristic
120#117—741no—
121#117—741no—
122C4⋊C8—371no—
123C4⋊C8C2×D3711yescharacteristic
124#102—21no—
125#102—741no—
126C4×C8—371no—
127C2×Q8—372no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—371no—
132C2×D4—742no—
133C2×D4C22⋊D3711yescharacteristic
134C22×C4—21no—
135C22×C4—741no—
136SD16—1484no—
137D8—42no—
138D8—1482no—
139C2×C8—21no—
140C2×C8—741no—
141C2×C8—741no—
142C4⋊C4—371no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4C22⋊D3711yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—742no—
148C22⋊C4—742no—
149C22⋊C4—741no—
150C42—742no—
151C42C22×D3711yescharacteristic
152C23—21no—
153C23—41no—
154C23—741no—
155Q8—1482no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—2962no—
164D4—741no—
165D4—741no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—741no—
170C2×C4—742no—
171C2×C4—1481no—
172C2×C4—1481no—
173C2×C4D4×D3711yescharacteristic
174C2×C4D4×D3711yescharacteristic
175C2×C4C2×C22⋊D3711yescharacteristic
176C8—41no—
177C8—742no—
178C8—1481no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—1481no—
186C22—1481no—
187C22—1481no—
188C22#1192450411yescharacteristic
189C4—21no—
190C4—41no—
191C4—1482no—
192C4—1481no—
193C4#1192455511yescharacteristic
194C4#1192455611yescharacteristic
195C4#1192456011yescharacteristic
196C4#1192456211yescharacteristic
197C2—81no—
198C2—161no—
199C2—2961no—
200C2#1455767511yescharacteristic
201C2#1455767611yescharacteristic
202C2#1455769911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#459C2
socleC22×C37#120
hypercenter#459D37
hypocenterC37#1624
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14558248C2semidirect
2. #14557905C2semidirect
3. #14557725C2semidirect
4. #14557281C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#459C2semidirect
105. #459D37semidirect
109. C37#1624semidirect

Maximal subgroups

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

subgroupindex
#145582482
#145579052
#145577252
#145572812
D4⋊#644362
#145572602
C37×#4592
#162437