Finite Group Databasebeta

← #17993608

Subgroups — #17993608

Order 4736.

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

normal subgroups only

This group has 232 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#14558121C211yesmaximal, characteristic
2#14557863C211yesmaximal, characteristic, complemented
3#14557846C211yesmaximal, characteristic, complemented
4#14557269C211yesmaximal, characteristic, complemented
5#14557266C211yesmaximal, characteristic, complemented
6#14557257C211yesmaximal, characteristic, complemented
7C37×#397C211yesmaximal, characteristic, complemented
8#11924529—21no—
9#11924522—21no—
10#11924518—21no—
11#11924515C2211yescharacteristic
12#11924510C2211yescharacteristic
13#11924509—21no—
14#11924505—21no—
15C4×C22⋊D37—21no—
16#11924469—21no—
17#11924467—21no—
18#11924459—21no—
19#11924456—21no—
20C22⋊#64436C2211yescharacteristic
21C22⋊#64436C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23C2×C22⋊C4×C37—21no—
24C2×C22⋊C4×C37C2211yescharacteristic
25#95×C37—21no—
26#95×C37C2211yescharacteristic
27C24×C37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37D411yescharacteristic
31C22×C4×C37C2311yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×D148D411yescharacteristic
36C2×C4×D37—21no—
37C2×Dic74D411yescharacteristic
38C4⋊C4×C37—21no—
39C4⋊C4×C37—21no—
40C22⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—42no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46#10596938—21no—
47#10596938—21no—
48C4⋊Dic37D411yescharacteristic
49C4⋊Dic37D411yescharacteristic
50#10596936—21no—
51#10596936—21no—
52C4×Dic37—21no—
53C2×#64436—21no—
54C2×#64436—21no—
55C23×C37—21no—
56C23×C37—21no—
57C23×C37—21no—
58C23×C37—41no—
59C23×C37—41no—
60C23×C37C2×D411yescharacteristic
61C22×D37—21no—
62C2×C4×C37—21no—
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×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C22⋊D37—41no—
74C22⋊D37—41no—
75C22⋊D37—81no—
76C22⋊D37—81no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80D148—41no—
81C4×D37—81no—
82Dic74—41no—
83#64436—41no—
84#64436—41no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—42no—
88C22×C37—41no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37—81no—
92C22×C37#12011yescharacteristic
93C22×C37#13511yescharacteristic
94C22×C37AGL(1,ℤ/8)11yescharacteristic
95C2×D37—41no—
96C2×D37—41no—
97C2×D37—41no—
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—41no—
101C4×C37—81no—
102C4×C37—81no—
103Dic37—41no—
104Dic37—41no—
105Dic37—41no—
106#1612—371nomaximal, Sylow
107C2×C37—21no—
108C2×C37—21no—
109C2×C37—81no—
110C2×C37#44911yescharacteristic
111C2×C37#45511yescharacteristic
112C2×C37#45811yescharacteristic
113D37—81no—
114#538—371no—
115#483—371no—
116#480—371no—
117#397D3711yescharacteristic, complemented
118#328—371no—
119#327—371no—
120#323—371no—
121C37#161211yescharacteristic, complemented, Sylow
122#126—741no—
123#124—741no—
124#123—741no—
125C22⋊Q8—371no—
126#121—371no—
127#121—741no—
128#120—741no—
129C4×D4—741no—
130C2×C4⋊C4C2×D3711yescharacteristic
131C2×C22⋊C4—21no—
132C2×C22⋊C4C2×D3711yescharacteristic
133#107—741no—
134#106—741no—
135#103—741no—
136#102—741no—
137C22⋊C8—371no—
138C22⋊C8—371no—
139#95—21no—
140#95C2×D3711yescharacteristic
141C24C22⋊D3711yescharacteristic
142C2×Q8—371no—
143C2×D4—371no—
144C2×D4—741no—
145C2×D4—741no—
146C2×D4—741no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—741no—
150C22×C4C22⋊D3711yescharacteristic
151C22×C4C22×D3711yescharacteristic
152C2×C8—741no—
153C2×C8—741no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—371no—
157C4⋊C4—371no—
158C4⋊C4—741no—
159C4⋊C4—741no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—741no—
164C22⋊C4—741no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C42—741no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—741no—
175C23C2×C22⋊D3711yescharacteristic
176Q8—1481no—
177D4—2961no—
178D4—2961no—
179D4—1481no—
180D4—1481no—
181D4—1481no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—2961no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—741no—
195C2×C4D4×D3711yescharacteristic
196C2×C4D4×D3711yescharacteristic
197C8—1481no—
198C8—1481no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—1481no—
207C22—1481no—
208C22—1481no—
209C22#1192450411yescharacteristic
210C22#1192455611yescharacteristic
211C22#1192456211yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—1481no—
218C4—1481no—
219C4—1481no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—2961no—
224C2#1455767611yescharacteristic
225C2#1455771011yescharacteristic
226C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#397C2
socleC22×C37#120
prime radical#14558121C2
hypercenter#397D37
hypocenterC37#1612
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #14557863C2semidirect
3. #14557846C2semidirect
4. #14557269C2semidirect
5. #14557266C2semidirect
6. #14557257C2semidirect
7. C37×#397C2semidirect
117. #397D37semidirect
121. C37#1612semidirect

Maximal subgroups

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

subgroupindex
#145581212
#145578632
#145578462
#145572692
#145572662
#145572572
C37×#3972
#161237