Finite Group Databasebeta

← #18007161

Subgroups — #18007161

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#14558233C211yesmaximal, characteristic
2#14558224C211yesmaximal, characteristic, complemented
3#14557935C211yesmaximal, characteristic, complemented
4#14557872C211yesmaximal, characteristic, complemented
5#14557862C211yesmaximal, characteristic, complemented
6#14557856C211yesmaximal, characteristic, complemented
7#14557850C211yesmaximal, characteristic, complemented
8#14557840C211yesmaximal, characteristic, complemented
9#14557833C211yesmaximal, characteristic, complemented
10#14557776C211yesmaximal, characteristic, complemented
11#14557776C211yesmaximal, characteristic, complemented
12#14557612C211yesmaximal, characteristic, complemented
13#14557572C211yesmaximal, characteristic, complemented
14#14557572C211yesmaximal, characteristic, complemented
15C4×SD16×C37C211yesmaximal, characteristic, complemented
16C2×#10596929C2211yescharacteristic
17C2×#10596929C2211yescharacteristic
18#11924530—21no—
19#11924529—21no—
20#11924528C2211yescharacteristic
21#11924528C2211yescharacteristic
22#11924526—21no—
23#11924521—21no—
24#11924519—21no—
25#11924512C2211yescharacteristic
26#11924512C2211yescharacteristic
27#11924509—21no—
28#11924507C2211yescharacteristic
29#11924507C2211yescharacteristic
30C4×D148C2211yescharacteristic
31C4×C22⋊D37—21no—
32#11924494C2211yescharacteristic
33#11924494C2211yescharacteristic
34#11924493—21no—
35C4⋊C4×D37C2211yescharacteristic
36C4⋊C4×D37C2211yescharacteristic
37#11924470C2211yescharacteristic
38#11924470C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924468C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924467C2211yescharacteristic
44#11924467C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic
46#11924460C2211yescharacteristic
47#11924460C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924448C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×D148D411yescharacteristic
65C2×C4×D37—21no—
66C2×C4×D37—21no—
67C2×C4×D37C2311yescharacteristic
68C2×C4×D37C2311yescharacteristic
69SD16×C37—22no—
70C2×C8×C37C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C4⋊C4×C37—21no—
73C4⋊C4×C37C2311yescharacteristic
74C4⋊C4×C37C2311yescharacteristic
75C22⋊C4×C37—21no—
76C42×C37—21no—
77C42×C37C2311yescharacteristic
78C22⋊Dic37—21no—
79C22⋊Dic37—21no—
80#10596938—21no—
81#10596938—21no—
82#10596938—21no—
83#10596938—21no—
84#10596938D411yescharacteristic
85#10596938D411yescharacteristic
86C4⋊Dic37D411yescharacteristic
87C4⋊Dic37C2311yescharacteristic
88C4⋊Dic37C2311yescharacteristic
89C4⋊Dic37C2311yescharacteristic
90C4⋊Dic37C2311yescharacteristic
91#10596936—21no—
92#10596936—21no—
93#10596936—21no—
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99C4×Dic37—21no—
100C4×Dic37—21no—
101C2×#64436C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103#10596929—22no—
104#10596929—22no—
105C23×C37—21no—
106C22×D37C2×D411yescharacteristic
107C22×D37C2×D411yescharacteristic
108Q8×C37—21no—
109Q8×C37—21no—
110D4×C37—21no—
111D4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—81no—
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2411yescharacteristic
119C22⋊D37—42no—
120C22⋊D37—81no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37C2×D411yescharacteristic
126C2×Dic37C2×D411yescharacteristic
127D148—41no—
128C4×D37—21no—
129C4×D37—21no—
130C4×D37—21no—
131C4×D37—21no—
132C4×D37—42no—
133C4×D37—81no—
134C8×C37—21no—
135C8×C37#4112yes—
136#64436—21no—
137#64436—21no—
138C22×C37—41no—
139C22×C37—41no—
140C22×C37—41no—
141C22×C37C22×D411yescharacteristic
142C2×D37—21no—
143C2×D37—21no—
144C2×D37—21no—
145C2×D37—21no—
146C2×D37—21no—
147C2×D37—21no—
148C4×C37—21no—
149C4×C37—21no—
150C4×C37—41no—
151C4×C37—41no—
152C4×C37—41no—
153C4×C37C2×#4111yescharacteristic
154C4×C372−1+411yescharacteristic
155Dic37—21no—
156Dic37—21no—
157Dic37—41no—
158Dic37—41no—
159Dic37—41no—
160Dic37—41no—
161#3351—371nomaximal, Sylow
162C2×C37—81no—
163C2×C37#54711yescharacteristic
164C2×C37#57511yescharacteristic
165C2×C37#57711yescharacteristic
166D37—41no—
167D37—41no—
168#553—371no—
169#552—371no—
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×SD16D3711yescharacteristic, complemented
180#436—371no—
181#428—371no—
182#428—371no—
183C37#335111yescharacteristic, complemented, Sylow
184C2×SD16C2×D3711yescharacteristic
185C2×M16—371no—
186C2×M16—371no—
187#126—741no—
188#126—741no—
189#125—371no—
190#125—371no—
191#125—741no—
192#123—741no—
193#123—741no—
194C22⋊Q8—371no—
195C22⋊Q8—371no—
196#121—371no—
197#121—371no—
198#121—741no—
199C4×Q8C2×D3711yescharacteristic
200C4×D4—371no—
201C4×D4—741no—
202C4×D4C2×D3711yescharacteristic
203#117—371no—
204#117—371no—
205#117—741no—
206C2×C4⋊C4—371no—
207C2×C4⋊C4—371no—
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#106C2×D3711yescharacteristic
217C4⋊C8—371no—
218#103—371no—
219#103—371no—
220#103C2×D3711yescharacteristic
221#102—371no—
222#102—371no—
223#102C2×D3711yescharacteristic
224C22⋊C8—371no—
225C22⋊C8—371no—
226C4×C8C2×D3711yescharacteristic
227C2×Q8C22×D3711yescharacteristic
228C2×D4—371no—
229C2×D4—741no—
230C2×D4—741no—
231C2×D4C22×D3711yescharacteristic
232C22×C4—21no—
233C22×C4—371no—
234C22×C4—371no—
235C22×C4—741no—
236C22×C4—741no—
237SD16—22no—
238M16—742no—
239M16—742no—
240C2×C8—371no—
241C2×C8—371no—
242C2×C8C22×D3711yescharacteristic
243C2×C8C22×D3711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—371no—
246C4⋊C4—371no—
247C4⋊C4—371no—
248C4⋊C4—371no—
249C4⋊C4—371no—
250C4⋊C4—741no—
251C4⋊C4—741no—
252C4⋊C4—741no—
253C4⋊C4—741no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4C22×D3711yescharacteristic
259C4⋊C4C22×D3711yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—371no—
262C22⋊C4—371no—
263C22⋊C4—741no—
264C22⋊C4—741no—
265C22⋊C4—741no—
266C22⋊C4—741no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C42—21no—
270C42—741no—
271C42—741no—
272C42C22×D3711yescharacteristic
273C23—21no—
274C23—371no—
275C23—371no—
276Q8—21no—
277Q8—21no—
278D4—21no—
279D4—21no—
280D4—2961no—
281D4—1481no—
282D4—1482no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—371no—
288C2×C4—371no—
289C2×C4—2961no—
290C2×C4—741no—
291C2×C4—741no—
292C2×C4—741no—
293C2×C4—741no—
294C2×C4—741no—
295C2×C4—741no—
296C2×C4—741no—
297C2×C4—741no—
298C2×C4—1482no—
299C2×C4D4×D3711yescharacteristic
300C2×C4D4×D3711yescharacteristic
301C2×C4C23×D3711yescharacteristic
302C8—21no—
303C8—741no—
304C8—741no—
305C8#1059696212yes—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—741no—
310C22—741no—
311C22—741no—
312C22—741no—
313C22—741no—
314C22—741no—
315C22C2×D4×D3711yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—741no—
322C4—741no—
323C4—1481no—
324C4—1481no—
325C4—1481no—
326C4—1481no—
327C4C2×#1059696211yescharacteristic
328C4#1192458311yescharacteristic
329C2—81no—
330C2—1481no—
331C2—1481no—
332C2#1455818811yescharacteristic
333C2#1455833011yescharacteristic
334C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×SD16×C37C2
socleC22×C37C22×D4
prime radical#14558233C2
hypercenterC4×SD16D37
hypocenterC37#3351
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #14558224C2semidirect
3. #14557935C2semidirect
4. #14557872C2semidirect
5. #14557862C2semidirect
6. #14557856C2semidirect
7. #14557850C2semidirect
8. #14557840C2semidirect
9. #14557833C2semidirect
10. #14557776C2semidirect
11. #14557776C2semidirect
12. #14557612C2semidirect
13. #14557572C2semidirect
14. #14557572C2semidirect
15. C4×SD16×C37C2semidirect
179. C4×SD16D37semidirect
183. C37#3351semidirect

Maximal subgroups

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

subgroupindex
#145582332
#145582242
#145579352
#145578722
#145578622
#145578562
#145578502
#145578402
#145578332
#145577762
#145576122
#145575722
C4×SD16×C372
#335137