Finite Group Databasebeta

← #17993798

Subgroups — #17993798

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#14557880C211yesmaximal, characteristic, complemented
3#14557819C211yesmaximal, characteristic, complemented
4#14557738C211yesmaximal, characteristic, complemented
5#14557276C211yesmaximal, characteristic, complemented
6#14557265C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596962—21no—
9C2×#10596940—21no—
10#11924536C2211yescharacteristic
11#11924533C2211yescharacteristic
12#11924532—21no—
13#11924510—21no—
14#11924509—22no—
15C4×Dic74C2211yescharacteristic
16#11924498—21no—
17#11924468—21no—
18C4⋊#64436C2211yescharacteristic
19#11924461—21no—
20#11924459—21no—
21#11924458—22no—
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×D4×C37D411yescharacteristic
26C22×C4×C37—21no—
27C2×C22⋊D37—22no—
28C2×C22⋊D37—22no—
29#10596962—42no—
30#10596962—42no—
31C2×D148—21no—
32C2×D148—21no—
33C2×D148D412yes—
34C2×C4×D37—22no—
35C2×Dic74—21no—
36C2×Dic74D411yescharacteristic
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C22⋊C4×C37—21no—
41C42×C37C2311yescharacteristic
42#10596940—42no—
43#10596938—22no—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37D411yescharacteristic
47#10596936—21no—
48C4×Dic37—21no—
49C2×#64436—21no—
50C23×C37—21no—
51C22×D37—22no—
52D4×C37—21no—
53D4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C22⋊D37—44no—
61C22⋊D37—82no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—41no—
65D148—42no—
66D148—41no—
67D148—41no—
68D148—41no—
69D148—41no—
70C4×D37—44no—
71Dic74—21no—
72Dic74—41no—
73Dic74—41no—
74Dic74SD1612yescomplemented
75C8×C37—41no—
76C8×C37—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×C37C2×SD1611yescharacteristic
88C4×C37#13511yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90C4×C37AGL(1,ℤ/8)11yescharacteristic
91Dic37—22no—
92Dic37—41no—
93Dic37—81no—
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#461—371no—
104#331—371no—
105Q8⋊C8—371no—
106D4⋊C8D3711yescharacteristic, complemented
107C37#164211yescharacteristic, complemented, Sylow
108C2×#41—741no—
109C2×SD16—741no—
110C4⋊Q8—371no—
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—741no—
122#103—741no—
123#102—742no—
124C4×C8C2×D3711yescharacteristic
125#41—1482no—
126#41—1482no—
127C2×Q8—371no—
128C2×Q8—741no—
129C2×D4—372no—
130C2×D4—742no—
131C2×D4—742no—
132C2×D4—741no—
133C2×D4—741no—
134C2×D4D14811yescharacteristic
135C22×C4—21no—
136C22×C4—742no—
137SD16—1482no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—741no—
141C4⋊C4—371no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4D14811yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—742no—
148C42—741no—
149C42C22×D3711yescharacteristic
150C23—21no—
151C23—742no—
152Q8—372no—
153Q8—741no—
154Q8—1481no—
155Q8—1481no—
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—741no—
169C2×C4—741no—
170C2×C4—1484no—
171C2×C4—1481no—
172C2×C4C2×D14811yescharacteristic
173C2×C4D4×D3711yescharacteristic
174C2×C4D4×D3711yescharacteristic
175C8—41no—
176C8—41no—
177C8—1481no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1482no—
182C22—1482no—
183C22—1482no—
184C22#1192450611yescharacteristic
185C4—21no—
186C4—41no—
187C4—2961no—
188C4—742no—
189C4—1481no—
190C4SD16×D3711yescharacteristic
191C4#1192455811yescharacteristic
192C4#1192456011yescharacteristic
193C4#1192456411yescharacteristic
194C2—81no—
195C2—2962no—
196C2#1455768011yescharacteristic
197C2#1455768511yescharacteristic
198C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37#120
prime radical#14558204C2
hypercenterD4⋊C8D37
hypocenterC37#1642
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557880C2semidirect
3. #14557819C2semidirect
4. #14557738C2semidirect
5. #14557276C2semidirect
6. #14557265C2semidirect
7. C37×D4⋊C8C2semidirect
74. Dic74SD16semidirect
106. D4⋊C8D37semidirect
107. C37#1642semidirect

Maximal subgroups

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

subgroupindex
#145582042
#145578802
#145578192
#145577382
#145572762
#145572652
C37×D4⋊C82
#164237