Finite Group Databasebeta

← #17993592

Subgroups — #17993592

Order 4736.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#14558132C211yesmaximal, characteristic
2#14557846C211yesmaximal, characteristic
3#14557464C211yesmaximal, characteristic, complemented
4#14557270C211yesmaximal, characteristic, complemented
5#14557268C211yesmaximal, characteristic
6#14557258C211yesmaximal, characteristic, complemented
7C37×#483C211yesmaximal, characteristic, complemented
8#11924531—21no—
9#11924527—21no—
10#11924521—21no—
11#11924520—21no—
12#11924512—21no—
13#11924510C2211yescharacteristic
14#11924496—21no—
15C2×#10596936—21no—
16C2×#10596936C2211yescharacteristic
17#11924469—21no—
18#11924456—21no—
19C22⋊#64436C2211yescharacteristic
20#11924443—21no—
21#11924443C2211yescharacteristic
22C22⋊Q8×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
24#106×C37—21no—
25#103×C37—21no—
26C22⋊C8×C37C2211yescharacteristic
27C2×Q8×C37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33C22×Dic37D411yescharacteristic
34C2×D148D411yescharacteristic
35C2×C4×D37—21no—
36C2×C8×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37D411yescharacteristic
41C22⋊C4×C37—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37D411yescharacteristic
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52#10596936—42no—
53C4×Dic37—21no—
54C2×#64436—21no—
55C23×C37C2×D411yescharacteristic
56C22×D37—21no—
57Q8×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C22⋊D37—41no—
67C22⋊D37—41no—
68C2×Dic37—22no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—21no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37—41no—
77D148—41no—
78C4×D37—81no—
79C8×C37—41no—
80#64436—41no—
81C22×C37—21no—
82C22×C37—21no—
83C22×C37#12011yescharacteristic
84C22×C37#13511yescharacteristic
85C22×C37AGL(1,ℤ/8)11yescharacteristic
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—41no—
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37—41no—
93C4×C37—81no—
94Dic37—42no—
95Dic37—41no—
96Dic37—41no—
97Dic37—41no—
98#1609—371nomaximal, Sylow
99C2×C37—21no—
100C2×C37—21no—
101C2×C37#44911yescharacteristic
102C2×C37#45611yescharacteristic
103C2×C37#45811yescharacteristic
104D37—81no—
105#539—371no—
106#483D3711yescharacteristic, complemented
107#480—371no—
108#398—371no—
109#328—371no—
110#327—371no—
111#324—371no—
112C37#160911yescharacteristic, complemented, Sylow
113#126—741no—
114#125—741no—
115#123—741no—
116#123—741no—
117C22⋊Q8—741no—
118C22⋊Q8C2×D3711yescharacteristic
119#121—371no—
120C4×D4—741no—
121C2×C4⋊C4—371no—
122C2×C4⋊C4—741no—
123C2×C4⋊C4C2×D3711yescharacteristic
124#107—741no—
125#106—21no—
126#103—21no—
127#102—741no—
128C22⋊C8—371no—
129C22⋊C8C2×D3711yescharacteristic
130#95—371no—
131#95—741no—
132C2×Q8C22⋊D3711yescharacteristic
133C2×D4—371no—
134C2×D4—741no—
135C22×C4—21no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—741no—
139C22×C4—741no—
140C22×C4C22×D3711yescharacteristic
141C2×C8—21no—
142C2×C8—741no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—371no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—1482no—
153C4⋊C4C22⋊D3711yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C22⋊C4—741no—
159C42—741no—
160C23—741no—
161C23D4×D3711yescharacteristic
162Q8—41no—
163D4—1481no—
164D4—1481no—
165D4—1481no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—2961no—
173C2×C4—742no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4D4×D3711yescharacteristic
183C2×C4C2×C22⋊D3711yescharacteristic
184C8—41no—
185C8—1481no—
186C22—21no—
187C22—21no—
188C22—1481no—
189C22—1481no—
190C22—1481no—
191C22#1192450411yescharacteristic
192C22#1192455711yescharacteristic
193C22#1192456311yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—1482no—
200C4—1481no—
201C4—1481no—
202C4—1481no—
203C2—21no—
204C2—21no—
205C2—2961no—
206C2#1455767711yescharacteristic
207C2#1455771411yescharacteristic
208C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#483C2
socleC22×C37#120
prime radical#11924510C22
hypercenter#483D37
hypocenterC37#1609
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #14557464C2semidirect
4. #14557270C2semidirect
6. #14557258C2semidirect
7. C37×#483C2semidirect
106. #483D37semidirect
112. C37#1609semidirect

Maximal subgroups

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

subgroupindex
#145581322
#145578462
#145574642
#145572702
#145572682
#145572582
C37×#4832
#160937