Finite Group Databasebeta

← #18004176

Subgroups — #18004176

Order 4736.

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

normal subgroups only

This group has 520 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×#11924556C211yesmaximal, characteristic, complemented
2C22×C8×D37C211yesmaximal, characteristic, complemented
3#14558045C211yesmaximal, characteristic, complemented
4#14558040C211yesmaximal, characteristic, complemented
5#14557773C212yesmaximal, complemented
6#14557768C212yesmaximal, complemented
7#14557765C212yesmaximal, complemented
8#14557761C212yesmaximal, complemented
9#14557569C211yesmaximal, characteristic, complemented
10#14557530C211yesmaximal, characteristic, complemented
11C37×#416C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C22×C4×D37C2211yescharacteristic
14#11924556—24no—
15C2×#10596942C2211yescharacteristic, complemented
16C2×#10596940C2211yescharacteristic, complemented
17C2×#10596941C2211yescharacteristic, complemented
18C2×#10596939C2211yescharacteristic, complemented
19C22×#64436C2211yescharacteristic
20C2×C8×D37—24no—
21C2×C8×D37C2212yes—
22C2×C8×D37C2212yes—
23#11924520—21no—
24#11924517—21no—
25#11924516C2212yes—
26#11924512C2212yes—
27#11924511C2212yes—
28#11924507C2212yes—
29#11924506—21no—
30#11924504—21no—
31C4×D148—22no—
32C4×C22⋊D37—22no—
33#11924495C2211yescharacteristic
34#11924469C2212yescomplemented
35#11924467C2212yescomplemented
36#11924461C2212yescomplemented
37#11924458C2212yescomplemented
38C2×#41×C37C2211yescharacteristic
39C22×C8×C37C2211yescharacteristic
40#117×C37C2211yescharacteristic
41#103×C37C2212yescomplemented
42#102×C37C2212yescomplemented
43C23×D37D411yescharacteristic
44#41×C37—22no—
45#41×C37—22no—
46C2×Q8×C37C2311yescharacteristic
47C2×D4×C37—21no—
48C2×D4×C37C2311yescharacteristic
49C22×C4×C37—21no—
50C22×C4×C37C2311yescharacteristic
51C2×C22⋊D37—21no—
52C2×C22⋊D37—22no—
53C22×Dic37D411yescharacteristic
54#10596962—22no—
55#10596962—22no—
56C2×D148—22no—
57C2×D148C2311yescharacteristic
58C2×C4×D37—22no—
59C2×C4×D37—22no—
60C2×C4×D37—21no—
61C2×C4×D37D412yes—
62C2×C4×D37C2312yes—
63C2×Dic74C2311yescharacteristic
64C2×C8×C37—22no—
65C2×C8×C37C2312yes—
66C4⋊C4×C37C2312yes—
67C22⋊C4×C37—21no—
68C42×C37—21no—
69C22⋊Dic37—21no—
70C22⋊Dic37—22no—
71#10596942—22no—
72#10596941—22no—
73#10596940—22no—
74#10596939—22no—
75#10596938—22no—
76#10596938—22no—
77#10596938—22no—
78C4⋊Dic37—22no—
79C4⋊Dic37C2312yes—
80#10596936—22no—
81C4×Dic37—21no—
82C2×#64436D414yescomplemented
83C2×#64436C2311yescharacteristic
84C2×#64436C2311yescharacteristic
85C8×D37—24no—
86C8×D37—24no—
87C23×C37—21no—
88C23×C37C2×D411yescharacteristic
89C22×D37—22no—
90C22×D37—24no—
91C22×D37—21no—
92C22×D37C2×D412yes—
93Q8×C37—21no—
94Q8×C37—21no—
95D4×C37—21no—
96D4×C37—21no—
97D4×C37—42no—
98C2×C4×C37—21no—
99C2×C4×C37—22no—
100C2×C4×C37—42no—
101C2×C4×C37C2×D412yes—
102C2×C4×C37C2×D411yescharacteristic
103C2×C4×C37#4112yes—
104C2×C4×C37C2411yescharacteristic
105C22⋊D37—42no—
106C22⋊D37—44no—
107C2×Dic37—22no—
108C2×Dic37—22no—
109C2×Dic37—21no—
110C2×Dic37C2×D412yes—
111D148—21no—
112D148—21no—
113D148—44no—
114C4×D37—24no—
115C4×D37—22no—
116C4×D37—22no—
117C4×D37—42no—
118Dic74—21no—
119Dic74—21no—
120C8×C37—22no—
121#64436C2×D412yes—
122#64436C2×D412yes—
123C22×C37—22no—
124C22×C37—41no—
125C22×C37—42no—
126C22×C37#12112yes—
127C22×C37C22×D411yescharacteristic
128C2×D37—28no—
129C2×D37—22no—
130C2×D37—22no—
131C2×D37—41no—
132C2×D37—42no—
133C2×D37#13514yescomplemented
134C4×C37—41no—
135C4×C37—42no—
136C4×C37#12112yes—
137C4×C37C22×D411yescharacteristic
138C4×C37C2×#4111yescharacteristic
139Dic37—22no—
140Dic37—41no—
141Dic37—42no—
142#3050—371nomaximal, Sylow
143C2×C37—22no—
144C2×C37—81no—
145C2×C37C2×#12111yescharacteristic
146C2×C37C2×#13512yes—
147D37—24no—
148D37—81no—
149C2×#135—371no—
150C23×C8—371no—
151#525—371no—
152#525—371no—
153#467—372no—
154#466—372no—
155#465—372no—
156#465—372no—
157#427—371no—
158#416—371no—
159#416D3711yescharacteristic, complemented
160C37#305011yescharacteristic, complemented, Sylow
161C2×#41—371no—
162C2×#41C2×D3711yescharacteristic
163C23×C4—371no—
164#135—744no—
165C2×Q16—371no—
166C2×SD16—371no—
167C2×SD16—371no—
168C2×D8—371no—
169C22×C8—371no—
170C22×C8—372no—
171C22×C8—372no—
172C22×C8—744no—
173C22×C8C2×D3711yescharacteristic
174#123—741no—
175#123—741no—
176C22⋊Q8—372no—
177C22⋊Q8—372no—
178#121—372no—
179#121—372no—
180#120—741no—
181#120—741no—
182C4×D4—742no—
183C4×D4—742no—
184#117—371no—
185#117C2×D3711yescharacteristic
186#107—372no—
187#106—372no—
188#103—372no—
189#103C2×D3712yescomplemented
190#102—372no—
191#102C2×D3712yescomplemented
192C24—371no—
193#41—22no—
194#41—22no—
195#41—742no—
196#41—742no—
197C2×Q8—371no—
198C2×Q8C22×D3711yescharacteristic
199C2×D4—21no—
200C2×D4—371no—
201C2×D4—742no—
202C2×D4—742no—
203C2×D4—741no—
204C2×D4C22×D3711yescharacteristic
205C22×C4—21no—
206C22×C4—371no—
207C22×C4—372no—
208C22×C4—372no—
209C22×C4—742no—
210C22×C4—742no—
211C22×C4—741no—
212C22×C4C22×D3711yescharacteristic
213Q16—742no—
214SD16—742no—
215SD16—742no—
216D8—742no—
217C2×C8—22no—
218C2×C8—374no—
219C2×C8—371no—
220C2×C8—371no—
221C2×C8—744no—
222C2×C8—744no—
223C2×C8C22×D3712yes—
224C4⋊C4—372no—
225C4⋊C4—742no—
226C4⋊C4—742no—
227C4⋊C4C22×D3712yes—
228C22⋊C4—21no—
229C22⋊C4—742no—
230C22⋊C4—742no—
231C22⋊C4—742no—
232C22⋊C4—742no—
233C22⋊C4—741no—
234C42—21no—
235C42—741no—
236C23—21no—
237C23—372no—
238C23—744no—
239C23—742no—
240C23—741no—
241C23D4×D3711yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—741no—
245Q8—741no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—741no—
250D4—741no—
251D4—1484no—
252D4—1484no—
253D4—1482no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—372no—
258C2×C4—742no—
259C2×C4—744no—
260C2×C4—742no—
261C2×C4—742no—
262C2×C4—742no—
263C2×C4—741no—
264C2×C4—1482no—
265C2×C4#1059696212yes—
266C2×C4D4×D3712yes—
267C2×C4D4×D3711yescharacteristic
268C2×C4C23×D3711yescharacteristic
269C8—22no—
270C8—372no—
271C8—372no—
272C22—22no—
273C22—41no—
274C22—42no—
275C22—374no—
276C22—748no—
277C22—742no—
278C22—742no—
279C22—1481no—
280C22—1482no—
281C22#1192450912yes—
282C22C2×D4×D3711yescharacteristic
283C4—41no—
284C4—42no—
285C4—742no—
286C4—1481no—
287C4—1482no—
288C4#1192450912yes—
289C4C2×D4×D3711yescharacteristic
290C4C2×#1059696211yescharacteristic
291C2—22no—
292C2—81no—
293C2—2961no—
294C2—744no—
295C2C2×#1192450911yescharacteristic
296C2#135×D3712yes—
subgroupG/H
centerC2×C4D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
hypercenter#416D37
hypocenterC37#3050
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#11924556C2semidirect
2. C22×C8×D37C2semidirect
3. #14558045C2semidirect
4. #14558040C2semidirect
5. #14557773C2semidirect
6. #14557768C2semidirect
7. #14557765C2semidirect
8. #14557761C2semidirect
9. #14557569C2semidirect
10. #14557530C2semidirect
11. C37×#416C2semidirect
15. C2×#10596942C22semidirect
16. C2×#10596940C22semidirect
17. C2×#10596941C22semidirect
18. C2×#10596939C22semidirect
34. #11924469C22semidirect
35. #11924467C22semidirect
36. #11924461C22semidirect
37. #11924458C22semidirect
41. #103×C37C22semidirect
42. #102×C37C22semidirect
82. C2×#64436D4semidirect
133. C2×D37#135semidirect
159. #416D37semidirect
160. C37#3050semidirect
189. #103C2×D37semidirect
191. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245562
C22×C8×D372
#145580452
#145580402
#145577732
#145577682
#145577652
#145577612
#145575692
#145575302
C37×#4162
#305037