Finite Group Databasebeta

← #18003884

Subgroups — #18003884

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×#11924564C211yesmaximal, characteristic, complemented
3C22×#10596930C211yesmaximal, characteristic, complemented
4#14558097C211yesmaximal, characteristic, complemented
5#14557680C214yesmaximal, complemented
6#14557674C214yesmaximal, complemented
7#14557543C211yesmaximal, characteristic, complemented
8#14557530C211yesmaximal, characteristic, complemented
9C37×#408C211yesmaximal, 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—
19C22×D148C2211yescharacteristic
20#11924564—24no—
21C2×#10596930—24no—
22C2×#10596930C2214yes—
23C2×#10596930C2212yes—
24C2×D296C2212yes—
25#11924532—21no—
26#11924525—21no—
27#11924510C2214yes—
28#11924504—22no—
29#11924495C2211yescharacteristic
30#11924461C2212yescomplemented
31#11924461C2214yescomplemented
32#11924458C2212yescomplemented
33C2×#41×C37C2211yescharacteristic
34C2×M16×C37C2211yescharacteristic
35C22×C8×C37C2211yescharacteristic
36C22⋊C8×C37C2214yescomplemented
37C23×D37—21no—
38#41×C37—22no—
39#41×C37—22no—
40C2×Q8×C37D411yescharacteristic
41C2×D4×C37D412yes—
42C2×D4×C37D411yescharacteristic
43C22×C4×C37C2312yes—
44C22×C4×C37C2311yescharacteristic
45C2×C22⋊D37—21no—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—24no—
48C22×Dic37—21no—
49C22×Dic37—22no—
50Q8×D37—28no—
51#10596964—216no—
52#10596964—28no—
53#10596962—22no—
54#10596962—24no—
55#10596962—24no—
56#10596962D414yescomplemented
57C2×D148—22no—
58C2×D148—22no—
59C2×D148—21no—
60C2×D148C2312yes—
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
72M16×C37—22no—
73C2×C8×C37—22no—
74C2×C8×C37C2312yes—
75C2×C8×C37C2312yes—
76C22⋊Dic37—21no—
77#10596938—24no—
78C4⋊Dic37C2312yes—
79C4×Dic37—21no—
80D296—24no—
81#10596930—28no—
82#10596930—24no—
83C23×C37C2×D412yes—
84C23×C37C2×D411yescharacteristic
85C22×D37—21no—
86C22×D37—22no—
87C22×D37—42no—
88C22×D37—82no—
89Q8×C37—22no—
90D4×C37—24no—
91D4×C37—22no—
92C2×C4×C37—22no—
93C2×C4×C37—22no—
94C2×C4×C37C2×D412yes—
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D412yes—
97C2×C4×C37C2×D412yes—
98C2×C4×C37C2411yescharacteristic
99C22⋊D37—28no—
100C22⋊D37—24no—
101C22⋊D37—84no—
102C2×Dic37—28no—
103C2×Dic37—24no—
104C2×Dic37—22no—
105C2×Dic37—21no—
106C2×Dic37—22no—
107D148—21no—
108D148—22no—
109D148—22no—
110D148—42no—
111D148C2×D412yes—
112C4×D37—28no—
113C4×D37—24no—
114Dic74—28no—
115Dic74—24no—
116Dic74—22no—
117Dic74—21no—
118Dic74C2×D412yes—
119Dic74C2×D414yes—
120C8×C37—22no—
121C8×C37—22no—
122C22×C37—22no—
123C22×C37—22no—
124C22×C37—24no—
125C22×C37#12012yes—
126C22×C37C22×D411yescharacteristic
127C2×D37—22no—
128C2×D37—42no—
129C2×D37—42no—
130C2×D37—44no—
131C2×D37—84no—
132C4×C37—22no—
133C4×C37#12012yes—
134C4×C37C22×D411yescharacteristic
135C4×C37C22×D411yescharacteristic
136Dic37—22no—
137Dic37—24no—
138Dic37—42no—
139#3010—371nomaximal, Sylow
140C2×C37—22no—
141C2×C37—42no—
142C2×C37C2×#12011yescharacteristic
143C2×C37#57712yes—
144D37—42no—
145D37—82no—
146C2×2−1+4—371no—
147C2×AGL(1,ℤ/8)—371no—
148C22×SD16—371no—
149#535—371no—
150#449—374no—
151#448—374no—
152#419—371no—
153#416—371no—
154#408D3711yescharacteristic, complemented
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×D4—371no—
167AGL(1,ℤ/8)—744no—
168C2×SD16—374no—
169C2×SD16—372no—
170C2×SD16—744no—
171C2×D8—372no—
172C2×M16C2×D3711yescharacteristic
173C22×C8C2×D3711yescharacteristic
174#127—741no—
175#124—741no—
176#121—374no—
177#120—742no—
178#117—371no—
179#103—372no—
180#103—374no—
181#102—372no—
182C22⋊C8C2×D3714yescomplemented
183C24—741no—
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—741no—
200C2×Q8—742no—
201C2×Q8D14811yescharacteristic
202C2×D4—371no—
203C2×D4—372no—
204C2×D4—744no—
205C2×D4—742no—
206C2×D4—741no—
207C2×D4—741no—
208C2×D4—742no—
209C2×D4—742no—
210C2×D4D14812yes—
211C2×D4D14811yescharacteristic
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—22no—
222C2×C8—22no—
223C2×C8C22×D3712yes—
224C2×C8C22×D3712yes—
225C4⋊C4—372no—
226C22⋊C4—741no—
227C22⋊C4—744no—
228C42—741no—
229C23—2962no—
230C23—741no—
231C23—742no—
232C23—1482no—
233C23C2×D14812yes—
234C23C2×D14811yescharacteristic
235Q8—22no—
236Q8—374no—
237Q8—372no—
238Q8—748no—
239Q8—744no—
240Q8—742no—
241Q8—741no—
242D4—24no—
243D4—22no—
244D4—372no—
245D4—2964no—
246D4—748no—
247D4—744no—
248D4—741no—
249D4—742no—
250D4—742no—
251D4—1482no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—748no—
255C2×C4—748no—
256C2×C4—744no—
257C2×C4—742no—
258C2×C4—741no—
259C2×C4—744no—
260C2×C4—742no—
261C2×C4C2×D14812yes—
262C2×C4C2×D14811yescharacteristic
263C2×C4D4×D3712yes—
264C2×C4D4×D3712yes—
265C2×C4C23×D3711yescharacteristic
266C8—22no—
267C8—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—2964no—
272C22—742no—
273C22—1482no—
274C22—1484no—
275C22—1482no—
276C22#1192450612yes—
277C22C22×D14811yescharacteristic
278C4—22no—
279C4—744no—
280C4—742no—
281C4—1482no—
282C4#1192450612yes—
283C4C2×D4×D3711yescharacteristic
284C4C2×D4×D3711yescharacteristic
285C2—22no—
286C2—42no—
287C2—2962no—
288C2—1482no—
289C2C2×#1192450611yescharacteristic
290C2#1455834512yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#408C2
socleC22×C37C22×D4
hypercenter#408D37
hypocenterC37#3010
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#11924583C2semidirect
2. C2×#11924564C2semidirect
3. C22×#10596930C2semidirect
4. #14558097C2semidirect
5. #14557680C2semidirect
6. #14557674C2semidirect
7. #14557543C2semidirect
8. #14557530C2semidirect
9. C37×#408C2semidirect
13. C2×#10596962C22semidirect
17. C22×Dic74C22semidirect
30. #11924461C22semidirect
31. #11924461C22semidirect
32. #11924458C22semidirect
36. C22⋊C8×C37C22semidirect
56. #10596962D4semidirect
69. C2×Dic74D4semidirect
154. #408D37semidirect
155. C37#3010semidirect
182. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245832
C2×#119245642
C22×#105969302
#145580972
#145576802
#145576742
#145575432
#145575302
C37×#4082
#301037