Finite Group Databasebeta

← #17993120

Subgroups — #17993120

Order 4736.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#14558069C211yesmaximal, characteristic
2#14557587C211yesmaximal, characteristic, complemented
3#14557384C211yesmaximal, characteristic, complemented
4#14557270C211yesmaximal, characteristic, complemented
5#14557268C211yesmaximal, characteristic
6#14557266C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic, complemented
8#11924531—21no—
9#11924527C411yescharacteristic, complemented
10#11924525C411yescharacteristic, complemented
11#11924520—21no—
12#11924510C2211yescharacteristic
13Q8×Dic37C411yescharacteristic, complemented
14#11924498C411yescharacteristic, complemented
15#11924496—21no—
16#11924494—21no—
17C2×#10596936—21no—
18C2×C4×Dic37—21no—
19C2×C4×Dic37C2211yescharacteristic
20#11924465—21no—
21C22⋊#64436C2211yescharacteristic
22#11924446—21no—
23#11924443C2211yescharacteristic
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33C22×Dic37D411yescharacteristic
34C2×D148C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×C8×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37C2×C411yescharacteristic
39C22⋊C4×C37—21no—
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—24no—
48#10596936—21no—
49C4×Dic37—21no—
50C4×Dic37—42no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37C2×C411yescharacteristic
53C4×Dic37D411yescharacteristic
54C4×Dic37D411yescharacteristic
55C2×#64436—21no—
56C23×C37C2×D411yescharacteristic
57C22×D37—21no—
58Q8×C37—41no—
59C2×C4×C37—22no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37C22×C411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C22⋊D37—41no—
68C22⋊D37—41no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—22no—
72C2×Dic37—22no—
73C2×Dic37—21no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37C22⋊C411yescharacteristic
77C2×Dic37C22⋊C411yescharacteristic
78C2×Dic37C22⋊C411yescharacteristic
79C2×Dic37C22⋊C411yescharacteristic
80D148—41no—
81C4×D37—42no—
82C8×C37—41no—
83#64436—41no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37C2×C22⋊C411yescharacteristic
87C22×C37AGL(1,ℤ/8)11yescharacteristic
88C22×C37#13711yescharacteristic
89C2×D37—41no—
90C2×D37—41no—
91C2×D37—41no—
92C4×C37—21no—
93C4×C37—21no—
94C4×C37—42no—
95C4×C37—41no—
96C4×C37—41no—
97Dic37—21no—
98Dic37—21no—
99Dic37—21no—
100Dic37—42no—
101Dic37—41no—
102Dic37#10412yes—
103#1509—371nomaximal, Sylow
104C2×C37—21no—
105C2×C37—21no—
106C2×C37#41011yescharacteristic
107C2×C37#41711yescharacteristic
108C2×C37C2×#10411yescharacteristic
109D37—81no—
110#529—371no—
111#432—371no—
112C4×C4⋊C4—371no—
113#328—371no—
114#328D3711yescharacteristic, complemented
115#327—371no—
116#327—371no—
117C37#150911yescharacteristic, complemented, Sylow
118#126—741no—
119#125—371no—
120#124—371no—
121#123—741no—
122C22⋊Q8C2×D3711yescharacteristic
123#121—371no—
124C4×Q8—371no—
125C4×D4—371no—
126C4×D4—741no—
127#117—741no—
128C2×C4⋊C4—741no—
129C2×C42—371no—
130C2×C42—741no—
131C4⋊C8—741no—
132C22⋊C8—371no—
133C22⋊C8C2×D3711yescharacteristic
134#97—741no—
135#95—371no—
136#95C2×D3711yescharacteristic
137C2×Q8C4×D3711yescharacteristic
138C2×D4—371no—
139C2×D4—741no—
140C22×C4—21no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—741no—
144C22×C4—741no—
145C22×C4C22×D3711yescharacteristic
146C2×C8—21no—
147C2×C8—741no—
148C4⋊C4—21no—
149C4⋊C4—371no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4—744no—
154C4⋊C4C4×D3711yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C42—371no—
161C42—371no—
162C42—371no—
163C42—371no—
164C42—741no—
165C42—1482no—
166C23—741no—
167C23D4×D3711yescharacteristic
168Q8—41no—
169D4—1481no—
170D4—1481no—
171D4—1481no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—371no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—742no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—742no—
186C2×C4—741no—
187C2×C4—1482no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4C2×C4×D3711yescharacteristic
191C2×C4D4×D3711yescharacteristic
192C8—41no—
193C8—1481no—
194C22—21no—
195C22—21no—
196C22—1481no—
197C22—1481no—
198C22—1481no—
199C22C22⋊C4×D3711yescharacteristic
200C22#1192456311yescharacteristic
201C22#1192456811yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—372no—
208C4—741no—
209C4—741no—
210C4—741no—
211C4—1482no—
212C4—1481no—
213C2—21no—
214C2—21no—
215C2—2961no—
216C2#1455750511yescharacteristic
217C2#1455753311yescharacteristic
218C2#104×D3711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37C2×C22⋊C4
prime radical#11924510C22
cosocleC22×C4×C37C23
hypercenter#328D37
hypocenterC37#1509
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14557587C2semidirect
3. #14557384C2semidirect
4. #14557270C2semidirect
7. C37×#328C2semidirect
9. #11924527C4semidirect
10. #11924525C4semidirect
13. Q8×Dic37C4semidirect
14. #11924498C4semidirect
114. #328D37semidirect
117. C37#1509semidirect

Maximal subgroups

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

subgroupindex
#145580692
#145575872
#145573842
#145572702
#145572682
#145572662
C37×#3282
#150937