Finite Group Databasebeta

← #18003880

Subgroups — #18003880

Order 4736.

732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924583C211yesmaximal, characteristic, complemented
2C2×#11924562C211yesmaximal, characteristic, complemented
3C22×#10596940C211yesmaximal, characteristic, complemented
4#14557676C214yesmaximal, complemented
5#14557671C214yesmaximal, complemented
6#14557541C211yesmaximal, characteristic, complemented
7#14557527C211yesmaximal, characteristic, complemented
8#14557500C211yesmaximal, characteristic, complemented
9C37×#535C211yesmaximal, characteristic, complemented
10#11924583—24no—
11#11924583—24no—
12C2×#10596962C2211yescharacteristic
13C2×#10596962C2212yescomplemented
14C2×#10596964—21no—
15C2×#10596964—22no—
16C22×Dic74C2211yescharacteristic
17C22×Dic74C2212yescomplemented
18C2×Q8×D37—21no—
19#11924562—24no—
20C2×#10596940—24no—
21C2×#10596940C2214yes—
22C2×#10596940C2212yes—
23C2×#10596939C2212yes—
24C2×#10596934C2211yescharacteristic
25C22×#64436C2211yescharacteristic
26#11924459C2212yescomplemented
27#11924459C2214yescomplemented
28#11924456C2212yescomplemented
29C22⋊#64436C2214yescomplemented
30C2×#41×C37C2211yescharacteristic
31C22×D4×C37C2211yescharacteristic
32#127×C37—21no—
33#124×C37—21no—
34#121×C37C2214yes—
35#120×C37—22no—
36#117×C37C2211yescharacteristic
37C24×C37—21no—
38#41×C37—22no—
39#41×C37—22no—
40C2×Q8×C37D411yescharacteristic
41C2×D4×C37—24no—
42C2×D4×C37—22no—
43C2×D4×C37—22no—
44C2×D4×C37—21no—
45C2×D4×C37D412yes—
46C2×D4×C37D411yescharacteristic
47C2×D4×C37C2312yes—
48C22×C4×C37C2312yes—
49C22×C4×C37C2311yescharacteristic
50C2×C22⋊D37—21no—
51C2×C22⋊D37—22no—
52C22×Dic37—21no—
53C22×Dic37—22no—
54Q8×D37—28no—
55#10596964—216no—
56#10596964—28no—
57#10596962—22no—
58#10596962—24no—
59#10596962—24no—
60#10596962D414yescomplemented
61C2×D148C2311yescharacteristic
62C2×C4×D37—21no—
63C2×C4×D37—22no—
64C2×Dic74—21no—
65C2×Dic74—22no—
66C2×Dic74—22no—
67C2×Dic74—24no—
68C2×Dic74—24no—
69C2×Dic74D414yescomplemented
70C2×Dic74C2312yes—
71C2×Dic74C2311yescharacteristic
72C4⋊C4×C37C2312yes—
73C22⋊C4×C37—21no—
74C22⋊C4×C37—24no—
75C42×C37—21no—
76#10596940—28no—
77#10596940—24no—
78#10596939—24no—
79#10596934—22no—
80C2×#64436—22no—
81C2×#64436C2312yes—
82C2×#64436C2312yes—
83C23×C37—22no—
84C23×C37—42no—
85C23×C37—82no—
86C23×C37C2×D412yes—
87C23×C37C2×D411yescharacteristic
88C22×D37—21no—
89Q8×C37—22no—
90D4×C37—24no—
91D4×C37—22no—
92D4×C37—22no—
93D4×C37—22no—
94D4×C37—42no—
95D4×C37—84no—
96C2×C4×C37—22no—
97C2×C4×C37—22no—
98C2×C4×C37—22no—
99C2×C4×C37C2×D412yes—
100C2×C4×C37C2×D412yes—
101C2×C4×C37C2×D412yes—
102C2×C4×C37C2×D411yescharacteristic
103C2×C4×C37C2411yescharacteristic
104C22⋊D37—28no—
105C22⋊D37—24no—
106C2×Dic37—28no—
107C2×Dic37—24no—
108C2×Dic37—22no—
109C2×Dic37—21no—
110D148—21no—
111D148C2×D412yes—
112C4×D37—28no—
113C4×D37—24no—
114Dic74—28no—
115Dic74—24no—
116Dic74—22no—
117Dic74—21no—
118Dic74C2×D412yes—
119Dic74C2×D414yes—
120#64436—22no—
121#64436—22no—
122C22×C37—22no—
123C22×C37—22no—
124C22×C37—24no—
125C22×C37—42no—
126C22×C37—44no—
127C22×C37—84no—
128C22×C37#12012yes—
129C22×C37C22×D411yescharacteristic
130C2×D37—22no—
131C2×D37—42no—
132C4×C37—22no—
133C4×C37—42no—
134C4×C37#12012yes—
135C4×C37C22×D411yescharacteristic
136C4×C37C22×D411yescharacteristic
137Dic37—22no—
138Dic37—24no—
139#3010—371nomaximal, Sylow
140C2×C37—22no—
141C2×C37—42no—
142C2×C37—82no—
143C2×C37C2×#12011yescharacteristic
144C2×C37#57712yes—
145D37—42no—
146C2×2−1+4—371no—
147C2×AGL(1,ℤ/8)—371no—
148C22×SD16—371no—
149#535D3711yescharacteristic, complemented
150#449—374no—
151#448—374no—
152#419—371no—
153#416—371no—
154#408—371no—
155C37#301011yescharacteristic, complemented, Sylow
1562−1+4—744no—
1572−1+4—744no—
158C2×#41—371no—
159C2×#41—372no—
160C2×#41—742no—
161C2×#41—741no—
162C2×#41C2×D3711yescharacteristic
163C22×Q8—371no—
164C22×Q8—372no—
165C22×Q8—741no—
166C22×D4C2×D3711yescharacteristic
167AGL(1,ℤ/8)—744no—
168C2×SD16—374no—
169C2×SD16—372no—
170C2×SD16—744no—
171C2×D8—372no—
172C2×M16—371no—
173C22×C8—371no—
174#127—21no—
175#124—21no—
176#121C2×D3714yes—
177#120—22no—
178#117C2×D3711yescharacteristic
179#103—372no—
180#103—374no—
181#102—372no—
182C22⋊C8—374no—
183C24—21no—
184#41—22no—
185#41—22no—
186#41—374no—
187#41—744no—
188#41—744no—
189#41—7416no—
190#41—748no—
191#41—742no—
192C2×Q8—374no—
193C2×Q8—372no—
194C2×Q8—371no—
195C2×Q8—744no—
196C2×Q8—744no—
197C2×Q8—748no—
198C2×Q8—742no—
199C2×Q8—742no—
200C2×Q8—741no—
201C2×Q8C22⋊D3711yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—371no—
207C2×D4—742no—
208C2×D4—741no—
209C2×D4C22⋊D3712yes—
210C2×D4C22⋊D3711yescharacteristic
211C2×D4C22×D3712yes—
212C22×C4—742no—
213C22×C4—741no—
214C22×C4—742no—
215C22×C4—741no—
216C22×C4C22×D3712yes—
217C22×C4C22×D3711yescharacteristic
218SD16—748no—
219SD16—744no—
220D8—744no—
221M16—742no—
222C2×C8—372no—
223C2×C8—372no—
224C2×C8—742no—
225C4⋊C4C22×D3712yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—741no—
233C23C2×C22⋊D3712yes—
234C23C2×C22⋊D3711yescharacteristic
235Q8—22no—
236Q8—374no—
237Q8—372no—
238Q8—748no—
239Q8—744no—
240Q8—742no—
241Q8—741no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—372no—
249D4—748no—
250D4—744no—
251D4—741no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—748no—
256C2×C4—748no—
257C2×C4—744no—
258C2×C4—742no—
259C2×C4—741no—
260C2×C4—744no—
261C2×C4D4×D3712yes—
262C2×C4D4×D3712yes—
263C2×C4C2×C22⋊D3712yes—
264C2×C4C2×C22⋊D3711yescharacteristic
265C2×C4C23×D3711yescharacteristic
266C8—742no—
267C8—742no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—42no—
272C22—44no—
273C22—84no—
274C22—742no—
275C22—1482no—
276C22#1192450412yes—
277C22C22×C22⋊D3711yescharacteristic
278C4—22no—
279C4—42no—
280C4—744no—
281C4—742no—
282C4#1192450412yes—
283C4C2×D4×D3711yescharacteristic
284C4C2×D4×D3711yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—1482no—
289C2C2×#1192450411yescharacteristic
290C2#1455834412yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#535C2
socleC22×C37C22×D4
hypercenter#535D37
hypocenterC37#3010
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11924583C2semidirect
2. C2×#11924562C2semidirect
3. C22×#10596940C2semidirect
4. #14557676C2semidirect
5. #14557671C2semidirect
6. #14557541C2semidirect
7. #14557527C2semidirect
8. #14557500C2semidirect
9. C37×#535C2semidirect
13. C2×#10596962C22semidirect
17. C22×Dic74C22semidirect
26. #11924459C22semidirect
27. #11924459C22semidirect
28. #11924456C22semidirect
29. C22⋊#64436C22semidirect
60. #10596962D4semidirect
69. C2×Dic74D4semidirect
149. #535D37semidirect
155. C37#3010semidirect

Maximal subgroups

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

subgroupindex
C2×#119245832
C2×#119245622
C22×#105969402
#145576762
#145576712
#145575412
#145575272
#145575002
C37×#5352
#301037