Finite Group Databasebeta

← #18005361

Subgroups — #18005361

Order 4736.

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

normal subgroups only

This group has 472 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
1#14558044C211yesmaximal, characteristic, complemented
2#14557868C211yesmaximal, characteristic, complemented
3#14557854C212yesmaximal, complemented
4#14557851C211yesmaximal, characteristic, complemented
5#14557767C212yesmaximal, complemented
6#14557760C212yesmaximal, complemented
7#14557684C211yesmaximal, characteristic, complemented
8#14557676C212yesmaximal, complemented
9#14557667C211yesmaximal, characteristic, complemented
10C2×C22⋊#64436C211yesmaximal, characteristic, complemented
11C2×#121×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic, complemented
13C2×#10596940C2212yescomplemented
14C2×#10596939C2212yescomplemented
15C22×#64436C2212yescomplemented
16#11924519—21no—
17#11924515C2211yescharacteristic
18#11924515C2211yescharacteristic, complemented
19#11924510C2211yescharacteristic
20#11924510C2211yescharacteristic, complemented
21#11924505—21no—
22C4×C22⋊D37—21no—
23C4×C22⋊D37—21no—
24#11924495C2211yescharacteristic, complemented
25#11924469C2212yescomplemented
26#11924467C2212yescomplemented
27#11924459C2212yescomplemented
28#11924457C2212yescomplemented
29#11924457C2212yescomplemented
30#11924456C2212yescomplemented
31C22⋊#64436C2211yescharacteristic
32C22⋊#64436C2211yescharacteristic
33C22⋊#64436C2212yescomplemented
34C22×D4×C37—21no—
35C22×D4×C37C2211yescharacteristic
36C23×C4×C37C2211yescharacteristic
37#121×C37—21no—
38#121×C37—21no—
39#121×C37C2212yes—
40#121×C37C2212yes—
41C2×C4⋊C4×C37C2211yescharacteristic
42C2×C22⋊C4×C37—21no—
43C24×C37—21no—
44C24×C37D411yescharacteristic
45C2×D4×C37—22no—
46C2×D4×C37—22no—
47C2×D4×C37—21no—
48C2×D4×C37—42no—
49C2×D4×C37—44no—
50C2×D4×C37C2312yes—
51C22×C4×C37—21no—
52C22×C4×C37—42no—
53C22×C4×C37D411yescharacteristic
54C22×C4×C37D411yescharacteristic
55C22×C4×C37D411yescharacteristic
56C22×C4×C37C2311yescharacteristic
57C22×C4×C37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C2×C22⋊D37—21no—
60C2×C22⋊D37—21no—
61C2×C22⋊D37—21no—
62#10596962—42no—
63C2×D148C2311yescharacteristic
64C2×C4×D37—21no—
65C2×Dic74C2311yescharacteristic
66C4⋊C4×C37—21no—
67C4⋊C4×C37C2312yes—
68C22⋊C4×C37—22no—
69C22⋊C4×C37—22no—
70C22⋊Dic37—21no—
71C22⋊Dic37—21no—
72C22⋊Dic37—21no—
73#10596940—42no—
74#10596939—42no—
75#10596938—21no—
76#10596938—21no—
77C4⋊Dic37C2311yescharacteristic
78C4⋊Dic37C2311yescharacteristic
79#10596936—21no—
80#10596936—21no—
81C4×Dic37—21no—
82C2×#64436—42no—
83C2×#64436C2312yes—
84C2×#64436C2312yes—
85C23×C37—22no—
86C23×C37—22no—
87C23×C37—22no—
88C23×C37—41no—
89C23×C37—42no—
90C23×C37—42no—
91C23×C37—42no—
92C23×C37C2×D411yescharacteristic
93C23×C37C2×D411yescharacteristic
94C23×C37C2×D411yescharacteristic
95C22×D37—21no—
96D4×C37—22no—
97D4×C37—22no—
98D4×C37—42no—
99D4×C37—44no—
100D4×C37—44no—
101C2×C4×C37—22no—
102C2×C4×C37—22no—
103C2×C4×C37—22no—
104C2×C4×C37—22no—
105C2×C4×C37—41no—
106C2×C4×C37—41no—
107C2×C4×C37—41no—
108C2×C4×C37—42no—
109C2×C4×C37C2×D411yescharacteristic
110C2×C4×C37C2×D411yescharacteristic
111C2×C4×C37C2×D411yescharacteristic
112C2×C4×C37C2411yescharacteristic
113C22⋊D37—42no—
114C22⋊D37—42no—
115C22⋊D37—42no—
116C2×Dic37—21no—
117C2×Dic37—21no—
118C2×Dic37—21no—
119D148—22no—
120C4×D37—42no—
121Dic74—22no—
122#64436—22no—
123#64436—22no—
124C22×C37—21no—
125C22×C37—21no—
126C22×C37—21no—
127C22×C37—21no—
128C22×C37—21no—
129C22×C37—21no—
130C22×C37—21no—
131C22×C37—44no—
132C22×C37—42no—
133C22×C37—42no—
134C22×C37—42no—
135C22×C37—84no—
136C22×C37#13512yes—
137C22×C37AGL(1,ℤ/8)12yes—
138C22×C37C22×D411yescharacteristic
139C2×D37—41no—
140C2×D37—41no—
141C2×D37—41no—
142C4×C37—21no—
143C4×C37—21no—
144C4×C37—21no—
145C4×C37—42no—
146C4×C37H(5,𝔽2)12yes—
147Dic37—41no—
148Dic37—41no—
149Dic37—41no—
150#3188—371nomaximal, Sylow
151C2×C37—22no—
152C2×C37—22no—
153C2×C37—41no—
154C2×C37—82no—
155C2×C37#53411yescharacteristic
156C2×C37C2×#13511yescharacteristic
157C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
158D37—81no—
159#525—371no—
160C2×#121D3711yescharacteristic, complemented
161#484—371no—
162#482—372no—
163#481—371no—
164#466—372no—
165#465—372no—
166#450—371no—
167#449—372no—
168#447—371no—
169C2×C22⋊C8—371no—
170C37#318811yescharacteristic, complemented, Sylow
171C2×#41—371no—
172C22×D4—21no—
173C22×D4C2×D3711yescharacteristic
174C23×C4C2×D3711yescharacteristic
175C2×SD16—372no—
176C2×D8—372no—
177C22×C8—372no—
178#123—741no—
179C22⋊Q8—371no—
180C22⋊Q8—371no—
181#121—21no—
182#121—21no—
183#121—371no—
184#121—371no—
185#121C2×D3712yes—
186#121C2×D3712yes—
187#120—741no—
188C4×D4—741no—
189C4×D4—741no—
190#117—371no—
191C2×C4⋊C4C2×D3711yescharacteristic
192C2×C22⋊C4—21no—
193#107—372no—
194#106—372no—
195#103—372no—
196#102—372no—
197#102—372no—
198#102—372no—
199C22⋊C8—371no—
200C22⋊C8—372no—
201C22⋊C8—371no—
202C24—21no—
203C24C22⋊D3711yescharacteristic
204#41—1482no—
205C2×Q8—371no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—42no—
210C2×D4—44no—
211C2×D4—371no—
212C2×D4—741no—
213C2×D4—741no—
214C2×D4—741no—
215C2×D4C22×D3712yes—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—741no—
219C22×C4C22⋊D3711yescharacteristic
220C22×C4C22⋊D3711yescharacteristic
221C22×C4C22⋊D3711yescharacteristic
222C22×C4C22×D3711yescharacteristic
223C22×C4C22×D3711yescharacteristic
224C22×C4C22×D3711yescharacteristic
225SD16—1482no—
226D8—1482no—
227C2×C8—372no—
228C2×C8—372no—
229C2×C8—1482no—
230C4⋊C4—21no—
231C4⋊C4—371no—
232C4⋊C4—371no—
233C4⋊C4—741no—
234C4⋊C4—741no—
235C4⋊C4C22×D3712yes—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—741no—
239C22⋊C4—741no—
240C22⋊C4—741no—
241C22⋊C4—741no—
242C22⋊C4—741no—
243C42—741no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—41no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—741no—
252C23C2×C22⋊D3711yescharacteristic
253C23C2×C22⋊D3711yescharacteristic
254C23C2×C22⋊D3711yescharacteristic
255Q8—742no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—44no—
260D4—44no—
261D4—742no—
262D4—1482no—
263D4—1482no—
264D4—1482no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—741no—
274C2×C4—741no—
275C2×C4—741no—
276C2×C4—1482no—
277C2×C4C2×C22⋊D3711yescharacteristic
278C2×C4C2×C22⋊D3711yescharacteristic
279C2×C4C2×C22⋊D3711yescharacteristic
280C2×C4C23×D3711yescharacteristic
281C8—742no—
282C8—742no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—84no—
295C22—1481no—
296C22—1481no—
297C22—1481no—
298C22#1192455612yes—
299C22#1192456212yes—
300C22C22×C22⋊D3711yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—1481no—
306C4—1481no—
307C4—1481no—
308C4#1192458112yes—
309C2—22no—
310C2—22no—
311C2—41no—
312C2—82no—
313C2—2961no—
314C2#1455809211yescharacteristic
315C2C2×#1192455611yescharacteristic
316C2C2×#1192456211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#121×C37C2
socleC22×C37C22×D4
hypercenterC2×#121D37
hypocenterC37#3188
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. #14558044C2semidirect
2. #14557868C2semidirect
3. #14557854C2semidirect
4. #14557851C2semidirect
5. #14557767C2semidirect
6. #14557760C2semidirect
7. #14557684C2semidirect
8. #14557676C2semidirect
9. #14557667C2semidirect
10. C2×C22⋊#64436C2semidirect
11. C2×#121×C37C2semidirect
12. C2×#10596962C22semidirect
13. C2×#10596940C22semidirect
14. C2×#10596939C22semidirect
15. C22×#64436C22semidirect
18. #11924515C22semidirect
20. #11924510C22semidirect
24. #11924495C22semidirect
25. #11924469C22semidirect
26. #11924467C22semidirect
27. #11924459C22semidirect
28. #11924457C22semidirect
29. #11924457C22semidirect
30. #11924456C22semidirect
33. C22⋊#64436C22semidirect
160. C2×#121D37semidirect
170. C37#3188semidirect

Maximal subgroups

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

subgroupindex
#145580442
#145578682
#145578542
#145578512
#145577672
#145577602
#145576842
#145576762
#145576672
C2×C22⋊#644362
C2×#121×C372
#318837