Finite Group Databasebeta

← #18005373

Subgroups — #18005373

Order 4736.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11924515C211yesmaximal, characteristic, complemented
2#14557874C212yesmaximal, complemented
3#14557861C211yesmaximal, characteristic, complemented
4#14557844C211yesmaximal, characteristic, complemented
5#14557772C212yesmaximal, complemented
6#14557760C212yesmaximal, complemented
7#14557695C212yesmaximal, complemented
8#14557688C211yesmaximal, characteristic, complemented
9#14557671C211yesmaximal, characteristic, complemented
10C2×C22⋊#64436C211yesmaximal, characteristic, complemented
11C37×#525C211yesmaximal, characteristic
12C22×Dic74C2211yescharacteristic
13C2×#10596942C2212yescomplemented
14C2×#10596940C2212yescomplemented
15C22×#64436C2212yes—
16#11924515—21no—
17#11924515—21no—
18#11924515C2212yes—
19#11924515C2212yes—
20C2×C4⋊Dic37C2211yescharacteristic
21C2×#10596936—21no—
22C2×C22⋊Dic37—21no—
23#11924469C2212yescomplemented
24#11924467C2212yescomplemented
25#11924460C2212yescomplemented
26#11924459C2212yescomplemented
27#11924459C2212yescomplemented
28#11924457C2212yescomplemented
29C22⋊#64436C2211yescharacteristic
30C22⋊#64436C2211yescharacteristic
31C22⋊#64436C2212yes—
32C2×#41×C37C2211yescharacteristic
33C23×C4×C37C2211yescharacteristic
34#123×C37—21no—
35C22⋊Q8×C37C2211yescharacteristic
36C22⋊Q8×C37C2211yescharacteristic
37#121×C37C2211yescharacteristic
38#121×C37C2211yescharacteristic
39#120×C37—21no—
40C4×D4×C37—21no—
41C4×D4×C37—21no—
42#117×C37C2211yescharacteristic
43C24×C37D411yescharacteristic
44#41×C37—42no—
45C2×Q8×C37C2311yescharacteristic
46C2×D4×C37—21no—
47C2×D4×C37—21no—
48C2×D4×C37—21no—
49C2×D4×C37C2311yescharacteristic
50C22×C4×C37—21no—
51C22×C4×C37—42no—
52C22×C4×C37D411yescharacteristic
53C22×C4×C37D411yescharacteristic
54C22×C4×C37D411yescharacteristic
55C22×C4×C37C2311yescharacteristic
56C22×C4×C37C2311yescharacteristic
57C22×C4×C37C2311yescharacteristic
58C22×Dic37—21no—
59C22×Dic37—21no—
60C2×Dic74—21no—
61C2×Dic74—42no—
62C2×Dic74C2312yes—
63C4⋊C4×C37—21no—
64C4⋊C4×C37—21no—
65C4⋊C4×C37C2311yescharacteristic
66C4⋊C4×C37C2311yescharacteristic
67C22⋊C4×C37—21no—
68C22⋊C4×C37—21no—
69C22⋊C4×C37—21no—
70C22⋊C4×C37—21no—
71C22⋊C4×C37—21no—
72C42×C37—21no—
73C22⋊Dic37—22no—
74C22⋊Dic37—22no—
75#10596942—42no—
76#10596940—42no—
77C4⋊Dic37—21no—
78C4⋊Dic37C2312yes—
79#10596936—22no—
80#10596936—22no—
81C2×#64436—42no—
82C2×#64436C2312yes—
83C2×#64436C2312yes—
84C23×C37—22no—
85C23×C37—22no—
86C23×C37—21no—
87C23×C37—41no—
88C23×C37C2×D411yescharacteristic
89C23×C37C2×D411yescharacteristic
90C23×C37C2×D411yescharacteristic
91Q8×C37—22no—
92D4×C37—22no—
93D4×C37—42no—
94D4×C37—42no—
95D4×C37—42no—
96C2×C4×C37—22no—
97C2×C4×C37—22no—
98C2×C4×C37—22no—
99C2×C4×C37—21no—
100C2×C4×C37—21no—
101C2×C4×C37—21no—
102C2×C4×C37—41no—
103C2×C4×C37—41no—
104C2×C4×C37—41no—
105C2×C4×C37—42no—
106C2×C4×C37C2×D411yescharacteristic
107C2×C4×C37C2×D411yescharacteristic
108C2×C4×C37C2×D411yescharacteristic
109C2×C4×C37C2411yescharacteristic
110C2×Dic37—22no—
111C2×Dic37—22no—
112C2×Dic37—42no—
113C2×Dic37—42no—
114Dic74—22no—
115Dic74—22no—
116Dic74—42no—
117#64436—22no—
118#64436—22no—
119C22×C37—21no—
120C22×C37—21no—
121C22×C37—21no—
122C22×C37—21no—
123C22×C37—21no—
124C22×C37—21no—
125C22×C37—21no—
126C22×C37—44no—
127C22×C37—41no—
128C22×C37—41no—
129C22×C37—41no—
130C22×C37#13512yes—
131C22×C37#13712yes—
132C22×C37C22×D411yescharacteristic
133C4×C37—21no—
134C4×C37—21no—
135C4×C37—21no—
136C4×C37—41no—
137C4×C37—41no—
138C4×C37—41no—
139C4×C37H(5,𝔽2)12yes—
140Dic37—42no—
141Dic37—42no—
142#3190—371nomaximal, Sylow
143C2×C37—22no—
144C2×C37—22no—
145C2×C37—41no—
146C2×C37—81no—
147C2×C37#53411yescharacteristic
148C2×C37C2×#13511yescharacteristic
149C2×C37C2×#13711yescharacteristic
150#525D3711yescharacteristic
151C2×C22⋊Q8—371no—
152#485—372no—
153#483—371no—
154#480—371no—
155#467—372no—
156#465—372no—
157#452—372no—
158#451—371no—
159#448—371no—
160C2×C22⋊C8—371no—
161C37#319011yescharacteristic, complemented, Sylow
162C2×#41C2×D3711yescharacteristic
163C22×Q8—371no—
164C23×C4C2×D3711yescharacteristic
165C2×Q16—372no—
166C2×SD16—372no—
167C22×C8—372no—
168#123—21no—
169C22⋊Q8—372no—
170C22⋊Q8—372no—
171C22⋊Q8—741no—
172C22⋊Q8—741no—
173C22⋊Q8C2×D3711yescharacteristic
174C22⋊Q8C2×D3711yescharacteristic
175#121C2×D3711yescharacteristic
176#121C2×D3711yescharacteristic
177#120—21no—
178C4×D4—21no—
179C4×D4—21no—
180#117C2×D3711yescharacteristic
181C2×C4⋊C4—371no—
182C2×C4⋊C4—741no—
183C2×C22⋊C4—741no—
184#107—372no—
185#106—372no—
186#103—372no—
187#103—372no—
188#103—372no—
189#102—372no—
190C22⋊C8—371no—
191C22⋊C8—371no—
192C22⋊C8—372no—
193C24C22⋊D3711yescharacteristic
194#41—42no—
195C2×Q8—372no—
196C2×Q8—741no—
197C2×Q8—1482no—
198C2×Q8C22×D3711yescharacteristic
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4C22×D3711yescharacteristic
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—741no—
206C22×C4—741no—
207C22×C4C22⋊D3711yescharacteristic
208C22×C4C22⋊D3711yescharacteristic
209C22×C4C22⋊D3711yescharacteristic
210C22×C4C22×D3711yescharacteristic
211C22×C4C22×D3711yescharacteristic
212C22×C4C22×D3711yescharacteristic
213Q16—1482no—
214SD16—1482no—
215C2×C8—372no—
216C2×C8—372no—
217C2×C8—1482no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—372no—
221C4⋊C4—742no—
222C4⋊C4—742no—
223C4⋊C4—741no—
224C4⋊C4C22×D3711yescharacteristic
225C4⋊C4C22×D3711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—742no—
232C22⋊C4—742no—
233C42—21no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—41no—
238C23C2×C22⋊D3711yescharacteristic
239C23C2×C22⋊D3711yescharacteristic
240C23C2×C22⋊D3711yescharacteristic
241Q8—22no—
242Q8—742no—
243Q8—742no—
244Q8—1482no—
245D4—22no—
246D4—42no—
247D4—42no—
248D4—42no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—742no—
260C2×C4—742no—
261C2×C4—1482no—
262C2×C4—1482no—
263C2×C4C2×C22⋊D3711yescharacteristic
264C2×C4C2×C22⋊D3711yescharacteristic
265C2×C4C2×C22⋊D3711yescharacteristic
266C2×C4C23×D3711yescharacteristic
267C8—742no—
268C8—742no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22#1192455612yes—
281C22#1192456612yes—
282C22C22×C22⋊D3711yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—1482no—
290C4—1482no—
291C4#1192458112yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—81no—
296C2#1455809211yescharacteristic
297C2C2×#1192455611yescharacteristic
298C2C2×#1192456611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#525C2
socleC22×C37C22×D4
hypercenter#525D37
hypocenterC37#3190
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#11924515C2semidirect
2. #14557874C2semidirect
3. #14557861C2semidirect
4. #14557844C2semidirect
5. #14557772C2semidirect
6. #14557760C2semidirect
7. #14557695C2semidirect
8. #14557688C2semidirect
9. #14557671C2semidirect
10. C2×C22⋊#64436C2semidirect
13. C2×#10596942C22semidirect
14. C2×#10596940C22semidirect
23. #11924469C22semidirect
24. #11924467C22semidirect
25. #11924460C22semidirect
26. #11924459C22semidirect
27. #11924459C22semidirect
28. #11924457C22semidirect
161. C37#3190semidirect

Maximal subgroups

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

subgroupindex
C2×#119245152
#145578742
#145578612
#145578442
#145577722
#145577602
#145576952
#145576882
#145576712
C2×C22⋊#644362
C37×#5252
#319037