Finite Group Databasebeta

← #18004532

Subgroups — #18004532

Order 4736.

462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#11924495C211yesmaximal, characteristic, complemented
2#14557854C214yesmaximal, complemented
3#14557849C212yesmaximal, complemented
4#14557844C212yesmaximal, complemented
5#14557573C212yesmaximal, complemented
6#14557538C212yesmaximal, complemented
7#14557497C211yesmaximal, characteristic, complemented
8C2×#121×C37C211yesmaximal, characteristic
9C2×#10596934C2212yes—
10#11924495—21no—
11#11924495—21no—
12#11924495C2212yes—
13#11924495C2212yescomplemented
14C2×C4⋊Dic37C2211yescharacteristic, complemented
15C2×C4⋊Dic37C2211yescharacteristic, complemented
16C2×C22⋊Dic37—21no—
17C2×C4×Dic37—21no—
18#11924469C2214yescomplemented
19#11924467C2214yescomplemented
20#11924457C2214yescomplemented
21#11924457C2214yescomplemented
22C22⋊#64436C2212yescomplemented
23C22⋊#64436C2212yescomplemented
24C22×D4×C37—21no—
25C22×D4×C37C2211yescharacteristic
26C23×C4×C37C2211yescharacteristic
27#121×C37—21no—
28#121×C37—21no—
29#121×C37C2212yes—
30#121×C37C2212yes—
31C2×C4⋊C4×C37C2211yescharacteristic
32C2×C22⋊C4×C37—21no—
33C24×C37—21no—
34C24×C37D411yescharacteristic
35C2×D4×C37—22no—
36C2×D4×C37—22no—
37C2×D4×C37—21no—
38C2×D4×C37—24no—
39C2×D4×C37—44no—
40C2×D4×C37C2312yes—
41C22×C4×C37—24no—
42C22×C4×C37—21no—
43C22×C4×C37D411yescharacteristic
44C22×C4×C37D411yescharacteristic
45C22×C4×C37D411yescharacteristic
46C22×C4×C37C2311yescharacteristic
47C22×C4×C37C2311yescharacteristic
48C22×C4×C37C2311yescharacteristic
49C22×Dic37—21no—
50C22×Dic37—21no—
51C4⋊C4×C37—21no—
52C4⋊C4×C37C2312yes—
53C22⋊C4×C37—22no—
54C22⋊C4×C37—22no—
55C22⋊Dic37—22no—
56C22⋊Dic37—22no—
57C4⋊Dic37—21no—
58C4⋊Dic37—21no—
59C4⋊Dic37C2312yes—
60C4⋊Dic37C2312yes—
61C4×Dic37—22no—
62C4×Dic37—22no—
63#10596934—24no—
64C2×#64436C2314yes—
65C23×C37—22no—
66C23×C37—22no—
67C23×C37—22no—
68C23×C37—41no—
69C23×C37—42no—
70C23×C37—42no—
71C23×C37—42no—
72C23×C37C2×D411yescharacteristic
73C23×C37C2×D411yescharacteristic
74C23×C37C2×D411yescharacteristic
75D4×C37—24no—
76D4×C37—44no—
77D4×C37—44no—
78D4×C37—42no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—42no—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37#4114yes—
90C2×C4×C37C2411yescharacteristic
91C2×Dic37—22no—
92C2×Dic37—22no—
93C2×Dic37—42no—
94C2×Dic37—42no—
95#64436—24no—
96C22×C37—21no—
97C22×C37—21no—
98C22×C37—21no—
99C22×C37—21no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37—44no—
104C22×C37—42no—
105C22×C37—42no—
106C22×C37—42no—
107C22×C37—84no—
108C22×C37#12312yes—
109C22×C37AGL(1,ℤ/8)12yes—
110C22×C37C22×D411yescharacteristic
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—42no—
114C4×C37#12312yes—
115C4×C37C2×#4112yes—
116Dic37—42no—
117Dic37—42no—
118#3094—371nomaximal, Sylow
119C2×C37—22no—
120C2×C37—22no—
121C2×C37—41no—
122C2×C37—82no—
123C2×C37C2×#12311yescharacteristic
124C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
125C2×C37#57511yescharacteristic
126C2×#121D3711yescharacteristic
127C2×#117—371no—
128#482—374no—
129#481—372no—
130#480—372no—
131#428—372no—
132#418—372no—
133#407—371no—
134C37#309411yescharacteristic, complemented, Sylow
135C22×D4—21no—
136C22×D4C2×D3711yescharacteristic
137C23×C4C2×D3711yescharacteristic
138C2×M16—372no—
139#121—21no—
140#121—21no—
141#121C2×D3712yes—
142#121C2×D3712yes—
143#117—372no—
144#117—372no—
145#117—741no—
146#117—741no—
147C2×C4⋊C4—371no—
148C2×C4⋊C4—371no—
149C2×C4⋊C4C2×D3711yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—741no—
152C2×C42—741no—
153#107—374no—
154#106—374no—
155#102—374no—
156#102—374no—
157C22⋊C8—372no—
158C22⋊C8—372no—
159C24—21no—
160C24C22⋊D3711yescharacteristic
161C2×D4—22no—
162C2×D4—22no—
163C2×D4—24no—
164C2×D4—21no—
165C2×D4—44no—
166C2×D4C22×D3712yes—
167C22×C4—24no—
168C22×C4—21no—
169C22×C4—741no—
170C22×C4—741no—
171C22×C4C22⋊D3711yescharacteristic
172C22×C4C22⋊D3711yescharacteristic
173C22×C4C22⋊D3711yescharacteristic
174C22×C4C22×D3711yescharacteristic
175C22×C4C22×D3711yescharacteristic
176C22×C4C22×D3711yescharacteristic
177M16—744no—
178C2×C8—374no—
179C4⋊C4—21no—
180C4⋊C4—372no—
181C4⋊C4—372no—
182C4⋊C4—741no—
183C4⋊C4—741no—
184C4⋊C4C22×D3712yes—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—742no—
188C22⋊C4—742no—
189C42—742no—
190C42—742no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23C2×C22⋊D3711yescharacteristic
199C23C2×C22⋊D3711yescharacteristic
200C23C2×C22⋊D3711yescharacteristic
201D4—24no—
202D4—44no—
203D4—44no—
204D4—42no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—742no—
213C2×C4—742no—
214C2×C4—1482no—
215C2×C4—1482no—
216C2×C4#1059696414yes—
217C2×C4C2×C22⋊D3711yescharacteristic
218C2×C4C2×C22⋊D3711yescharacteristic
219C2×C4C2×C22⋊D3711yescharacteristic
220C2×C4C23×D3711yescharacteristic
221C8—744no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—84no—
234C22#1192451712yes—
235C22#1192456212yes—
236C22C22×C22⋊D3711yescharacteristic
237C4—21no—
238C4—21no—
239C4—42no—
240C4—1482no—
241C4—1482no—
242C4#1192451712yes—
243C4C2×#1059696412yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—82no—
248C2C2×#1192451711yescharacteristic
249C2C2×#1192456211yescharacteristic
250C2#1455833111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC2×#121×C37C2
socleC22×C37C22×D4
hypercenterC2×#121D37
hypocenterC37#3094
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11924495C2semidirect
2. #14557854C2semidirect
3. #14557849C2semidirect
4. #14557844C2semidirect
5. #14557573C2semidirect
6. #14557538C2semidirect
7. #14557497C2semidirect
13. #11924495C22semidirect
14. C2×C4⋊Dic37C22semidirect
15. C2×C4⋊Dic37C22semidirect
18. #11924469C22semidirect
19. #11924467C22semidirect
20. #11924457C22semidirect
21. #11924457C22semidirect
22. C22⋊#64436C22semidirect
23. C22⋊#64436C22semidirect
134. C37#3094semidirect

Maximal subgroups

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

subgroupindex
C2×#119244952
#145578542
#145578492
#145578442
#145575732
#145575382
#145574972
C2×#121×C372
#309437