Finite Group Databasebeta

← #18004509

Subgroups — #18004509

Order 4736.

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

normal subgroups only

This group has 420 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
1#14558044C211yesmaximal, characteristic
2#14557874C212yesmaximal, complemented
3#14557868C211yesmaximal, characteristic, complemented
4#14557863C211yesmaximal, characteristic, complemented
5#14557857C212yesmaximal, complemented
6#14557851C211yesmaximal, characteristic, complemented
7#14557846C211yesmaximal, characteristic, complemented
8#14557569C212yesmaximal, complemented
9#14557527C212yesmaximal, complemented
10C2×C22⋊#64436C211yesmaximal, characteristic, complemented
11C2×#117×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C22×#64436C2212yes—
14#11924519—21no—
15#11924515C2211yescharacteristic
16#11924515C2211yescharacteristic
17#11924510C2211yescharacteristic
18#11924510C2211yescharacteristic
19#11924505—21no—
20C4×C22⋊D37—21no—
21C4×C22⋊D37—21no—
22#11924495C2211yescharacteristic
23#11924469C2212yescomplemented
24#11924469C2212yescomplemented
25#11924467C2212yescomplemented
26#11924467C2212yescomplemented
27#11924459C2212yescomplemented
28#11924459C2212yescomplemented
29#11924456C2212yescomplemented
30#11924456C2212yescomplemented
31C22⋊#64436C2211yescharacteristic
32C22⋊#64436C2211yescharacteristic
33C22⋊#64436C2212yes—
34C23×C4×C37C2211yescharacteristic
35#117×C37—21no—
36#117×C37—21no—
37#117×C37C2212yes—
38#117×C37C2212yes—
39C2×C4⋊C4×C37C2211yescharacteristic
40C2×C4⋊C4×C37C2211yescharacteristic
41C2×C22⋊C4×C37—21no—
42C2×C42×C37—21no—
43C24×C37D411yescharacteristic
44C22×C4×C37—24no—
45C22×C4×C37—21no—
46C22×C4×C37—21no—
47C22×C4×C37D411yescharacteristic
48C22×C4×C37D411yescharacteristic
49C22×C4×C37D411yescharacteristic
50C22×C4×C37C2311yescharacteristic
51C22×C4×C37C2311yescharacteristic
52C22×C4×C37C2311yescharacteristic
53C2×C22⋊D37—21no—
54C2×C22⋊D37—21no—
55C2×C22⋊D37—21no—
56#10596962—24no—
57C2×D148C2311yescharacteristic
58C2×C4×D37—21no—
59C2×Dic74C2311yescharacteristic
60C4⋊C4×C37—21no—
61C4⋊C4×C37—21no—
62C4⋊C4×C37C2312yes—
63C4⋊C4×C37C2312yes—
64C22⋊C4×C37—22no—
65C22⋊C4×C37—22no—
66C42×C37—22no—
67C42×C37—22no—
68C22⋊Dic37—21no—
69C22⋊Dic37—21no—
70C22⋊Dic37—21no—
71#10596938—21no—
72#10596938—21no—
73C4⋊Dic37C2311yescharacteristic
74C4⋊Dic37C2311yescharacteristic
75#10596936—21no—
76#10596936—21no—
77C4×Dic37—21no—
78C2×#64436—24no—
79C2×#64436C2312yes—
80C2×#64436C2312yes—
81C23×C37—22no—
82C23×C37—22no—
83C23×C37—41no—
84C23×C37C2×D411yescharacteristic
85C23×C37C2×D411yescharacteristic
86C23×C37C2×D411yescharacteristic
87C22×D37—21no—
88C2×C4×C37—22no—
89C2×C4×C37—22no—
90C2×C4×C37—22no—
91C2×C4×C37—22no—
92C2×C4×C37—22no—
93C2×C4×C37—22no—
94C2×C4×C37—22no—
95C2×C4×C37—42no—
96C2×C4×C37—42no—
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37#4114yes—
101C2×C4×C37C2411yescharacteristic
102C22⋊D37—42no—
103C22⋊D37—42no—
104C22⋊D37—42no—
105C2×Dic37—21no—
106C2×Dic37—21no—
107C2×Dic37—21no—
108D148—22no—
109C4×D37—42no—
110Dic74—22no—
111#64436—22no—
112#64436—22no—
113C22×C37—21no—
114C22×C37—21no—
115C22×C37—21no—
116C22×C37—21no—
117C22×C37—21no—
118C22×C37—21no—
119C22×C37—21no—
120C22×C37—44no—
121C22×C37#12312yes—
122C22×C37#13512yes—
123C22×C37C22×D411yescharacteristic
124C2×D37—41no—
125C2×D37—41no—
126C2×D37—41no—
127C4×C37—21no—
128C4×C37—21no—
129C4×C37—42no—
130C4×C37—42no—
131C4×C37#12312yes—
132C4×C37C2×#4112yes—
133Dic37—41no—
134Dic37—41no—
135Dic37—41no—
136#3091—371nomaximal, Sylow
137C2×C37—22no—
138C2×C37—22no—
139C2×C37—41no—
140C2×C37C2×#12311yescharacteristic
141C2×C37C2×#13511yescharacteristic
142C2×C37#57511yescharacteristic
143D37—81no—
144#525—371no—
145C2×#117D3711yescharacteristic, complemented
146#485—372no—
147#484—371no—
148#483—371no—
149#482—372no—
150#481—371no—
151#480—371no—
152#427—372no—
153#416—372no—
154C2×C22⋊C8—371no—
155C37#309111yescharacteristic, complemented, Sylow
156C2×#41—371no—
157C23×C4C2×D3711yescharacteristic
158C22×C8—372no—
159#123—741no—
160C22⋊Q8—371no—
161C22⋊Q8—371no—
162#121—371no—
163#121—371no—
164#120—741no—
165C4×D4—741no—
166C4×D4—741no—
167#117—21no—
168#117—21no—
169#117—371no—
170#117C2×D3712yes—
171#117C2×D3712yes—
172C2×C4⋊C4C2×D3711yescharacteristic
173C2×C4⋊C4C2×D3711yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42—21no—
176#107—372no—
177#107—372no—
178#106—372no—
179#106—372no—
180#103—372no—
181#103—372no—
182#102—372no—
183#102—372no—
184C22⋊C8—371no—
185C22⋊C8—371no—
186C22⋊C8—372no—
187C24C22⋊D3711yescharacteristic
188#41—744no—
189C2×Q8—371no—
190C2×D4—371no—
191C2×D4—741no—
192C2×D4—741no—
193C2×D4—741no—
194C22×C4—24no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—741no—
198C22×C4C22⋊D3711yescharacteristic
199C22×C4C22⋊D3711yescharacteristic
200C22×C4C22⋊D3711yescharacteristic
201C22×C4C22×D3711yescharacteristic
202C22×C4C22×D3711yescharacteristic
203C22×C4C22×D3711yescharacteristic
204C2×C8—372no—
205C2×C8—372no—
206C2×C8—744no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—371no—
210C4⋊C4—371no—
211C4⋊C4—741no—
212C4⋊C4—741no—
213C4⋊C4C22×D3712yes—
214C4⋊C4C22×D3712yes—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—741no—
218C22⋊C4—741no—
219C22⋊C4—741no—
220C22⋊C4—741no—
221C22⋊C4—741no—
222C42—22no—
223C42—22no—
224C42—741no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—741no—
229C23C2×C22⋊D3711yescharacteristic
230C23C2×C22⋊D3711yescharacteristic
231C23C2×C22⋊D3711yescharacteristic
232Q8—742no—
233D4—742no—
234D4—1482no—
235D4—1482no—
236D4—1482no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—741no—
247C2×C4—741no—
248C2×C4—741no—
249C2×C4—1482no—
250C2×C4#1059696214yes—
251C2×C4C2×C22⋊D3711yescharacteristic
252C2×C4C2×C22⋊D3711yescharacteristic
253C2×C4C2×C22⋊D3711yescharacteristic
254C2×C4C23×D3711yescharacteristic
255C8—742no—
256C8—742no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—1481no—
266C22—1481no—
267C22—1481no—
268C22#1192451912yes—
269C22#1192455612yes—
270C22C22×C22⋊D3711yescharacteristic
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—1481no—
276C4—1481no—
277C4—1481no—
278C4#1192451912yes—
279C4C2×#1059696212yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—2961no—
284C2C2×#1192451911yescharacteristic
285C2C2×#1192455611yescharacteristic
286C2#1455833111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#117×C37C2
socleC22×C37C22×D4
prime radical#14558044C2
hypercenterC2×#117D37
hypocenterC37#3091
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14557874C2semidirect
3. #14557868C2semidirect
4. #14557863C2semidirect
5. #14557857C2semidirect
6. #14557851C2semidirect
7. #14557846C2semidirect
8. #14557569C2semidirect
9. #14557527C2semidirect
10. C2×C22⋊#64436C2semidirect
11. C2×#117×C37C2semidirect
23. #11924469C22semidirect
24. #11924469C22semidirect
25. #11924467C22semidirect
26. #11924467C22semidirect
27. #11924459C22semidirect
28. #11924459C22semidirect
29. #11924456C22semidirect
30. #11924456C22semidirect
145. C2×#117D37semidirect
155. C37#3091semidirect

Maximal subgroups

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

subgroupindex
#145580442
#145578742
#145578682
#145578632
#145578572
#145578512
#145578462
#145575692
#145575272
C2×C22⋊#644362
C2×#117×C372
#309137