Finite Group Databasebeta

← #17993794

Subgroups — #17993794

Order 4736.

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

normal subgroups only

This group has 250 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#14558204C211yesmaximal, characteristic
2#14557881C211yesmaximal, characteristic, complemented
3#14557815C211yesmaximal, characteristic, complemented
4#14557276C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#461C211yesmaximal, characteristic, complemented
8C2×#10596962—21no—
9#11924533C2211yescharacteristic
10#11924532—21no—
11#11924510—21no—
12#11924509—22no—
13C4×Dic74C2211yescharacteristic
14#11924498—21no—
15#11924467—21no—
16C4⋊#64436C2211yescharacteristic
17#11924459—21no—
18#11924456—22no—
19C4×#64436C2211yescharacteristic
20C2×SD16×C37—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37—21no—
28C2×C22⋊D37—22no—
29C2×C22⋊D37—22no—
30#10596962—42no—
31#10596962—42no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148D412yes—
35C2×C4×D37—22no—
36C2×Dic74D411yescharacteristic
37SD16×C37—42no—
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37—21no—
41C4⋊C4×C37D411yescharacteristic
42C22⋊C4×C37—21no—
43C42×C37C2311yescharacteristic
44#10596938—22no—
45C4⋊Dic37D411yescharacteristic
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—21no—
51C22×D37—22no—
52Q8×C37—41no—
53Q8×C37—41no—
54D4×C37—21no—
55D4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C22⋊D37—44no—
64C22⋊D37—82no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67D148—42no—
68D148—41no—
69D148—41no—
70D148—41no—
71D148—41no—
72C4×D37—44no—
73Dic74—21no—
74Dic74SD1612yescomplemented
75C8×C37—41no—
76#64436—41no—
77#64436—41no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37#12011yescharacteristic
82C2×D37—42no—
83C2×D37—42no—
84C2×D37—42no—
85C4×C37—21no—
86C4×C37—41no—
87C4×C37—81no—
88C4×C37C2×SD1611yescharacteristic
89C4×C37#13511yescharacteristic
90C4×C37AGL(1,ℤ/8)11yescharacteristic
91C4×C37AGL(1,ℤ/8)11yescharacteristic
92Dic37—22no—
93Dic37—41no—
94#1642—371nomaximal, Sylow
95C2×C37—81no—
96C2×C37#44911yescharacteristic
97C2×C37#45011yescharacteristic
98C2×C37#45511yescharacteristic
99D37—82no—
100#550—371no—
101#486—371no—
102#475—371no—
103#461D3711yescharacteristic, complemented
104#331—371no—
105Q8⋊C8—371no—
106D4⋊C8—371no—
107C37#164211yescharacteristic, complemented, Sylow
108C2×#41—741no—
109C2×SD16—21no—
110C4⋊Q8C2×D3711yescharacteristic
111#127—371no—
112#127—741no—
113#121—742no—
114#121—741no—
115C4×Q8—371no—
116C4×D4—741no—
117C4×D4C2×D3711yescharacteristic
118#106—741no—
119C4⋊C8—371no—
120C4⋊C8C2×D3711yescharacteristic
121#103—21no—
122#103—741no—
123#102—742no—
124C4×C8—371no—
125#41—1482no—
126#41—1482no—
127C2×Q8—21no—
128C2×Q8—371no—
129C2×D4—372no—
130C2×D4—742no—
131C2×D4—742no—
132C2×D4—741no—
133C2×D4—741no—
134C2×D4C22⋊D3711yescharacteristic
135C22×C4—21no—
136C22×C4—742no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—741no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—371no—
144C4⋊C4—741no—
145C4⋊C4C22⋊D3711yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—742no—
148C42—741no—
149C42C22×D3711yescharacteristic
150C23—21no—
151C23—742no—
152Q8—41no—
153Q8—41no—
154Q8—372no—
155Q8—741no—
156D4—21no—
157D4—21no—
158D4—2962no—
159D4—1482no—
160D4—1484no—
161D4—1481no—
162D4—1481no—
163D4—1481no—
164D4—1481no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—741no—
170C2×C4—741no—
171C2×C4—1484no—
172C2×C4D4×D3711yescharacteristic
173C2×C4D4×D3711yescharacteristic
174C2×C4C2×C22⋊D3711yescharacteristic
175C8—41no—
176C8—1481no—
177C8—1481no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1482no—
182C22—1482no—
183C22—1482no—
184C22#1192450411yescharacteristic
185C4—21no—
186C4—41no—
187C4—81no—
188C4—742no—
189C4—1481no—
190C4SD16×D3711yescharacteristic
191C4#1192455611yescharacteristic
192C4#1192456211yescharacteristic
193C4#1192456311yescharacteristic
194C2—81no—
195C2—2962no—
196C2#1455767611yescharacteristic
197C2#1455768211yescharacteristic
198C2#1455770911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#461C2
socleC22×C37#120
prime radical#14558204C2
hypercenter#461D37
hypocenterC37#1642
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #14557881C2semidirect
3. #14557815C2semidirect
4. #14557276C2semidirect
5. #14557263C2semidirect
6. D4⋊#64436C2semidirect
7. C37×#461C2semidirect
74. Dic74SD16semidirect
103. #461D37semidirect
107. C37#1642semidirect

Maximal subgroups

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

subgroupindex
#145582042
#145578812
#145578152
#145572762
#145572632
D4⋊#644362
C37×#4612
#164237