Finite Group Databasebeta

← #18007156

Subgroups — #18007156

Order 4736.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558229C211yesmaximal, characteristic
2#14557932C211yesmaximal, characteristic, complemented
3#14557871C211yesmaximal, characteristic, complemented
4#14557861C211yesmaximal, characteristic, complemented
5#14557857C211yesmaximal, characteristic, complemented
6#14557851C211yesmaximal, characteristic, complemented
7#14557840C211yesmaximal, characteristic, complemented
8#14557830C211yesmaximal, characteristic, complemented
9#14557781C211yesmaximal, characteristic, complemented
10#14557781C211yesmaximal, characteristic, complemented
11C4×#10596941C211yesmaximal, characteristic, complemented
12#14557611C211yesmaximal, characteristic, complemented
13#14557576C211yesmaximal, characteristic, complemented
14#14557573C211yesmaximal, characteristic, complemented
15C37×#552C211yesmaximal, characteristic, complemented
16C2×#10596941C2211yescharacteristic
17C2×#10596934C2211yescharacteristic
18C2×#10596934C2211yescharacteristic
19#11924531—21no—
20#11924528C2211yescharacteristic
21#11924518—21no—
22#11924510C2211yescharacteristic
23#11924510C2211yescharacteristic
24#11924508—21no—
25C4×D148C2211yescharacteristic
26#11924496—21no—
27#11924495C2211yescharacteristic
28C2×C4⋊Dic37C2211yescharacteristic
29#11924469C2211yescharacteristic
30#11924469C2211yescharacteristic
31#11924469C2211yescharacteristic
32#11924469C2211yescharacteristic
33#11924467C2211yescharacteristic
34#11924467C2211yescharacteristic
35#11924467C2211yescharacteristic
36#11924467C2211yescharacteristic
37#11924467C2211yescharacteristic
38C4⋊#64436C2211yescharacteristic
39#11924460C2211yescharacteristic
40#11924460C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924456C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48#126×C37—21no—
49#125×C37—21no—
50#125×C37C2211yescharacteristic
51#123×C37—21no—
52C22⋊Q8×C37C2211yescharacteristic
53C22⋊Q8×C37C2211yescharacteristic
54C4×Q8×C37C2211yescharacteristic
55C4×D4×C37C2211yescharacteristic
56#117×C37—21no—
57#117×C37C2211yescharacteristic
58C2×C4⋊C4×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37D411yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C22×Dic37—21no—
67C2×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C4⋊C4×C37—21no—
70C4⋊C4×C37—21no—
71C4⋊C4×C37—21no—
72C4⋊C4×C37—21no—
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
75C4⋊C4×C37D411yescharacteristic
76C4⋊C4×C37C2311yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37D411yescharacteristic
83C22⋊C4×C37D411yescharacteristic
84C42×C37—21no—
85C42×C37—21no—
86C42×C37C2311yescharacteristic
87C22⋊Dic37—21no—
88#10596941—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98C4×Dic37—21no—
99#10596934—22no—
100#10596934—22no—
101C2×#64436C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C23×C37C2×D411yescharacteristic
106C23×C37C2×D411yescharacteristic
107C22×D37—21no—
108Q8×C37—21no—
109Q8×C37—21no—
110D4×C37—41no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—42no—
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37—42no—
126C22⋊D37—81no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—81no—
131D148—21no—
132D148—21no—
133C4×D37—81no—
134#64436—21no—
135#64436—21no—
136#64436—21no—
137#64436#4112yes—
138C22×C37—21no—
139C22×C37—21no—
140C22×C37—21no—
141C22×C37—21no—
142C22×C37—21no—
143C22×C37—21no—
144C22×C37C22×D411yescharacteristic
145C2×D37—41no—
146C2×D37—41no—
147C2×D37—41no—
148C4×C37—21no—
149C4×C37—21no—
150C4×C37—21no—
151C4×C37—21no—
152C4×C37—41no—
153C4×C37—41no—
154C4×C37—41no—
155C4×C37—41no—
156C4×C37C2×#4111yescharacteristic
157C4×C372−1+411yescharacteristic
158Dic37—41no—
159Dic37—41no—
160Dic37—41no—
161#3351—371nomaximal, Sylow
162C2×C37—41no—
163C2×C37—41no—
164C2×C37#54711yescharacteristic
165C2×C37#57511yescharacteristic
166C2×C37#57711yescharacteristic
167D37—81no—
168#553—371no—
169#552D3711yescharacteristic, complemented
170#499—371no—
171#485—371no—
172#483—371no—
173#482—371no—
174#481—371no—
175#479—371no—
176#478—371no—
177#468—371no—
178#468—371no—
179C4×SD16—371no—
180#436—371no—
181#428—371no—
182#428—371no—
183C37#335111yescharacteristic, complemented, Sylow
184C2×SD16—371no—
185C2×M16—371no—
186C2×M16—371no—
187#126—21no—
188#126—741no—
189#125—21no—
190#125—371no—
191#125C2×D3711yescharacteristic
192#123—21no—
193#123—741no—
194C22⋊Q8C2×D3711yescharacteristic
195C22⋊Q8C2×D3711yescharacteristic
196#121—371no—
197#121—371no—
198#121—741no—
199C4×Q8C2×D3711yescharacteristic
200C4×D4—371no—
201C4×D4—741no—
202C4×D4C2×D3711yescharacteristic
203#117—21no—
204#117—371no—
205#117C2×D3711yescharacteristic
206C2×C4⋊C4—371no—
207C2×C4⋊C4C2×D3711yescharacteristic
208#107—371no—
209#107—371no—
210#107—371no—
211#107—371no—
212#106—371no—
213#106—371no—
214#106—371no—
215#106—371no—
216#106—371no—
217C4⋊C8—371no—
218#103—371no—
219#103—371no—
220#103—371no—
221#102—371no—
222#102—371no—
223#102—371no—
224C22⋊C8—371no—
225C22⋊C8—371no—
226C4×C8—371no—
227C2×Q8C22×D3711yescharacteristic
228C2×D4—371no—
229C2×D4—741no—
230C2×D4—741no—
231C2×D4C22⋊D3711yescharacteristic
232C22×C4—21no—
233C22×C4—741no—
234C22×C4—741no—
235C22×C4C22×D3711yescharacteristic
236C22×C4C22×D3711yescharacteristic
237SD16—742no—
238M16—742no—
239M16—742no—
240C2×C8—371no—
241C2×C8—371no—
242C2×C8—371no—
243C2×C8—371no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—371no—
251C4⋊C4—371no—
252C4⋊C4—371no—
253C4⋊C4—741no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4C22⋊D3711yescharacteristic
257C4⋊C4C22×D3711yescharacteristic
258C4⋊C4C22×D3711yescharacteristic
259C4⋊C4C22×D3711yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—741no—
264C22⋊C4—741no—
265C22⋊C4—741no—
266C22⋊C4—741no—
267C22⋊C4C22⋊D3711yescharacteristic
268C22⋊C4C22⋊D3711yescharacteristic
269C42—21no—
270C42—21no—
271C42—741no—
272C42C22×D3711yescharacteristic
273C23—741no—
274C23C2×C22⋊D3711yescharacteristic
275C23C2×C22⋊D3711yescharacteristic
276Q8—21no—
277Q8—21no—
278D4—41no—
279D4—2961no—
280D4—741no—
281D4—741no—
282D4—1482no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—2961no—
293C2×C4—2961no—
294C2×C4—741no—
295C2×C4—741no—
296C2×C4—741no—
297C2×C4C2×C22⋊D3711yescharacteristic
298C2×C4C2×C22⋊D3711yescharacteristic
299C2×C4C2×C22⋊D3711yescharacteristic
300C2×C4C2×C22⋊D3711yescharacteristic
301C2×C4C23×D3711yescharacteristic
302C8—372no—
303C8—741no—
304C8—741no—
305C8—741no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—1481no—
313C22—1481no—
314C22—1481no—
315C22C22×C22⋊D3711yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1481no—
325C4—1481no—
326C4—1481no—
327C4#41×D3711yescharacteristic
328C4#1192458311yescharacteristic
329C2—41no—
330C2—41no—
331C2—2961no—
332C2#1455818211yescharacteristic
333C2#1455833111yescharacteristic
334C2#1455834111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#552C2
socleC22×C37C22×D4
prime radical#14558229C2
hypercenter#552D37
hypocenterC37#3351
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14557932C2semidirect
3. #14557871C2semidirect
4. #14557861C2semidirect
5. #14557857C2semidirect
6. #14557851C2semidirect
7. #14557840C2semidirect
8. #14557830C2semidirect
9. #14557781C2semidirect
10. #14557781C2semidirect
11. C4×#10596941C2semidirect
12. #14557611C2semidirect
13. #14557576C2semidirect
14. #14557573C2semidirect
15. C37×#552C2semidirect
169. #552D37semidirect
183. C37#3351semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145579322
#145578712
#145578612
#145578572
#145578512
#145578402
#145578302
#145577812
C4×#105969412
#145576112
#145575762
#145575732
C37×#5522
#335137