Finite Group Databasebeta

← #17993591

Subgroups — #17993591

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#14558130C211yesmaximal, characteristic
2#14557863C211yesmaximal, characteristic, complemented
3#14557846C211yesmaximal, characteristic
4#14557269C211yesmaximal, characteristic, complemented
5#14557266C211yesmaximal, characteristic
6#14557259C211yesmaximal, characteristic, complemented
7C37×#398C211yesmaximal, characteristic, complemented
8#11924531—21no—
9#11924526—21no—
10#11924521—21no—
11#11924519—21no—
12#11924515C2211yescharacteristic
13#11924514—21no—
14#11924510C2211yescharacteristic
15C4×C22⋊D37—21no—
16#11924469—21no—
17#11924467—21no—
18#11924459—21no—
19#11924456—21no—
20C22⋊#64436C2211yescharacteristic
21C22⋊#64436C2211yescharacteristic
22C2×C4⋊C4×C37—21no—
23C2×C4⋊C4×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25#95×C37—21no—
26#95×C37C2211yescharacteristic
27C22×C4×C37—21no—
28C22×C4×C37—21no—
29C22×C4×C37D411yescharacteristic
30C22×C4×C37D411yescharacteristic
31C22×C4×C37C2311yescharacteristic
32C2×C22⋊D37—21no—
33C2×D148D411yescharacteristic
34C2×C4×D37—21no—
35C2×Dic74D411yescharacteristic
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37—42no—
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37D411yescharacteristic
47C4⋊Dic37D411yescharacteristic
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52C4×Dic37—21no—
53C2×#64436—21no—
54C2×#64436—21no—
55C23×C37C2×D411yescharacteristic
56C22×D37—21no—
57C2×C4×C37—22no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C22⋊D37—41no—
72C22⋊D37—41no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76D148—41no—
77C4×D37—81no—
78Dic74—41no—
79#64436—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—42no—
92C4×C37—41no—
93C4×C37—41no—
94C4×C37—81no—
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#483—371no—
107#480—371no—
108#398D3711yescharacteristic, complemented
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—371no—
118C22⋊Q8—741no—
119#121—371no—
120C4×D4—741no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D3711yescharacteristic
123C2×C4⋊C4C2×D3711yescharacteristic
124#107—741no—
125#106—741no—
126#103—741no—
127#102—741no—
128C22⋊C8—371no—
129C22⋊C8—371no—
130#95—21no—
131#95C2×D3711yescharacteristic
132C2×Q8—371no—
133C2×D4—371no—
134C2×D4—741no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—741no—
138C22×C4C22⋊D3711yescharacteristic
139C22×C4C22⋊D3711yescharacteristic
140C22×C4C22×D3711yescharacteristic
141C2×C8—741no—
142C2×C8—741no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—371no—
149C4⋊C4—371no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4—741no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C22⋊C4—741no—
159C42—741no—
160C23—741no—
161C23C2×C22⋊D3711yescharacteristic
162Q8—1481no—
163D4—1481no—
164D4—1481no—
165D4—1481no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—2961no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4D4×D3711yescharacteristic
183C2×C4D4×D3711yescharacteristic
184C8—1481no—
185C8—1481no—
186C22—21no—
187C22—21no—
188C22—1481no—
189C22—1481no—
190C22—1481no—
191C22#1192450411yescharacteristic
192C22#1192455611yescharacteristic
193C22#1192456211yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—1481no—
201C4—1481no—
202C4—1481no—
203C2—21no—
204C2—21no—
205C2—2961no—
206C2#1455767611yescharacteristic
207C2#1455771511yescharacteristic
208C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#398C2
socleC22×C37#120
prime radical#11924510C22
hypercenter#398D37
hypocenterC37#1609
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #14557863C2semidirect
4. #14557269C2semidirect
6. #14557259C2semidirect
7. C37×#398C2semidirect
108. #398D37semidirect
112. C37#1609semidirect

Maximal subgroups

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

subgroupindex
#145581302
#145578632
#145578462
#145572692
#145572662
#145572592
C37×#3982
#160937