Finite Group Databasebeta

← #18005198

Subgroups — #18005198

Order 4736.

364 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558087C211yesmaximal, characteristic, complemented
2#14558065C211yesmaximal, characteristic
3#14557940C211yesmaximal, characteristic, complemented
4#14557924C211yesmaximal, characteristic, complemented
5#14557900C211yesmaximal, characteristic, complemented
6#14557891C211yesmaximal, characteristic, complemented
7#14557792C211yesmaximal, characteristic, complemented
8#14557790C211yesmaximal, characteristic, complemented
9#14557778C211yesmaximal, characteristic
10#14557776C211yesmaximal, characteristic
11C4×Dic148C211yesmaximal, characteristic, complemented
12C4×#10596942C211yesmaximal, characteristic, complemented
13C4×#10596940C211yesmaximal, characteristic, complemented
14C4×#10596929C211yesmaximal, characteristic, complemented
15C4×SD16×C37C211yesmaximal, characteristic, complemented
16C2×Dic148C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596929C2211yescharacteristic
20C2×#10596929C2211yescharacteristic
21#11924535C2211yescharacteristic
22#11924534C2211yescharacteristic
23#11924529—21no—
24#11924527C2211yescharacteristic
25#11924526—21no—
26#11924523C2211yescharacteristic
27#11924518—21no—
28#11924516C2211yescharacteristic
29#11924516C2211yescharacteristic
30#11924514—21no—
31#11924512C2211yescharacteristic
32#11924507C2211yescharacteristic
33C4×Dic74—21no—
34C4×Dic74C2211yescharacteristic
35C4×Dic74C2211yescharacteristic
36C4×C22⋊D37—21no—
37#11924495—21no—
38#11924493—21no—
39C42×D37C2211yescharacteristic
40#11924470C2211yescharacteristic
41#11924469C2211yescharacteristic
42#11924467C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924446C2211yescharacteristic
50#11924446C2211yescharacteristic
51C4×#64436C2211yescharacteristic
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×C4×D37D411yescharacteristic
64C2×C4×D37D411yescharacteristic
65C2×C4×D37C2311yescharacteristic
66C2×Dic74—21no—
67C2×Dic74C2311yescharacteristic
68C2×Dic74C2311yescharacteristic
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—
80C22⋊Dic37—21no—
81#10596942—22no—
82#10596940—22no—
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86C4⋊Dic37—21no—
87C4⋊Dic37—21no—
88C4⋊Dic37—21no—
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—
98C4×Dic37—21no—
99C4×Dic37—21no—
100C4×Dic37D411yescharacteristic
101C4×Dic37D411yescharacteristic
102C4×Dic37C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105Dic148—22no—
106#10596929—22no—
107#10596929—22no—
108C23×C37—21no—
109C22×D37C2×D411yescharacteristic
110Q8×C37—21no—
111Q8×C37—21no—
112D4×C37—21no—
113D4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—42no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2411yescharacteristic
121C22⋊D37—42no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129C4×D37—22no—
130C4×D37—21no—
131C4×D37—21no—
132C4×D37—41no—
133Dic74—21no—
134Dic74—21no—
135Dic74—21no—
136Dic74—21no—
137Dic74—42no—
138C8×C37—21no—
139C8×C37#4112yes—
140#64436—21no—
141#64436#4112yes—
142C22×C37—41no—
143C22×C37—41no—
144C22×C37—41no—
145C22×C37C22×D411yescharacteristic
146C2×D37—21no—
147C2×D37—21no—
148C2×D37—21no—
149C4×C37—21no—
150C4×C37—41no—
151C4×C37—41no—
152C4×C37—41no—
153C4×C37#13712yes—
154C4×C37C2×#4111yescharacteristic
155C4×C37C2×#4111yescharacteristic
156Dic37—21no—
157Dic37—21no—
158Dic37—21no—
159Dic37—41no—
160Dic37—41no—
161Dic37—41no—
162Dic37—41no—
163#3172—371nomaximal, Sylow
164C2×C37—81no—
165C2×C37#53211yescharacteristic
166C2×C37C2×#13711yescharacteristic
167C2×C37#57511yescharacteristic
168D37—41no—
169#533—371no—
170#529—371no—
171#501—371no—
172#497—371no—
173#491—371no—
174#489—371no—
175#470—371no—
176#470—371no—
177#468—371no—
178#468—371no—
179C4×Q16—371no—
180C4×Q16—371no—
181C4×SD16—371no—
182C4×SD16D3711yescharacteristic, complemented
183C4×M16—371no—
184C37#317211yescharacteristic, complemented, Sylow
185C2×Q16—371no—
186C2×Q16—371no—
187C2×SD16—371no—
188C2×SD16C2×D3711yescharacteristic
189C2×M16—371no—
190C2×M16—371no—
191C4⋊Q8—371no—
192C4⋊Q8—371no—
193#126—741no—
194#125—371no—
195#125—741no—
196#124—371no—
197#123—741no—
198C22⋊Q8—371no—
199C22⋊Q8—371no—
200C22⋊Q8—371no—
201C22⋊Q8—741no—
202#121—371no—
203C4×Q8—371no—
204C4×Q8—371no—
205C4×Q8—741no—
206C4×Q8C2×D3711yescharacteristic
207C4×D4—741no—
208C4×D4C2×D3711yescharacteristic
209#117—741no—
210#117—741no—
211C2×C42—371no—
212#107—371no—
213#107—371no—
214#106—371no—
215#106C2×D3711yescharacteristic
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#103—371no—
221#103C2×D3711yescharacteristic
222#102—371no—
223#102C2×D3711yescharacteristic
224#97—371no—
225#97—371no—
226C4×C8—371no—
227C4×C8C2×D3711yescharacteristic
228C2×Q8—371no—
229C2×Q8—371no—
230C2×Q8—741no—
231C2×Q8C22×D3711yescharacteristic
232C2×D4—741no—
233C2×D4C22×D3711yescharacteristic
234C22×C4—21no—
235C22×C4—371no—
236C22×C4—371no—
237C22×C4—371no—
238Q16—742no—
239Q16—742no—
240SD16—22no—
241SD16—742no—
242M16—742no—
243M16—742no—
244C2×C8—371no—
245C2×C8—371no—
246C2×C8C22×D3711yescharacteristic
247C2×C8C22×D3711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—371no—
250C4⋊C4—371no—
251C4⋊C4—741no—
252C4⋊C4—741no—
253C4⋊C4—741no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4C22×D3711yescharacteristic
262C4⋊C4C22×D3711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—741no—
265C22⋊C4—741no—
266C22⋊C4—741no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C22⋊C4—741no—
270C42—21no—
271C42—371no—
272C42—371no—
273C42—371no—
274C42—741no—
275C42—741no—
276C42C22×D3711yescharacteristic
277C23—21no—
278C23—371no—
279Q8—21no—
280Q8—21no—
281Q8—741no—
282Q8—741no—
283Q8—741no—
284Q8—741no—
285Q8—1482no—
286D4—21no—
287D4—21no—
288D4—1482no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—371no—
294C2×C4—371no—
295C2×C4—371no—
296C2×C4—742no—
297C2×C4—741no—
298C2×C4—741no—
299C2×C4—741no—
300C2×C4—741no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—1481no—
304C2×C4D4×D3711yescharacteristic
305C2×C4D4×D3711yescharacteristic
306C2×C4C23×D3711yescharacteristic
307C8—21no—
308C8—372no—
309C8—741no—
310C8#1059696212yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—741no—
315C22—741no—
316C22—741no—
317C22C2×D4×D3711yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—741no—
323C4—741no—
324C4—741no—
325C4—1481no—
326C4—1481no—
327C4—1481no—
328C4—1481no—
329C4#1192456512yes—
330C4#41×D3711yescharacteristic
331C4C2×#1059696211yescharacteristic
332C2—81no—
333C2—1481no—
334C2#1455808011yescharacteristic
335C2C2×#1192456511yescharacteristic
336C2#1455833011yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×SD16×C37C2
socleC22×C37C22×D4
prime radical#11924507C22
hypercenterC4×SD16D37
hypocenterC37#3172
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14558087C2semidirect
3. #14557940C2semidirect
4. #14557924C2semidirect
5. #14557900C2semidirect
6. #14557891C2semidirect
7. #14557792C2semidirect
8. #14557790C2semidirect
11. C4×Dic148C2semidirect
12. C4×#10596942C2semidirect
13. C4×#10596940C2semidirect
14. C4×#10596929C2semidirect
15. C4×SD16×C37C2semidirect
182. C4×SD16D37semidirect
184. C37#3172semidirect

Maximal subgroups

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

subgroupindex
#145580872
#145580652
#145579402
#145579242
#145579002
#145578912
#145577922
#145577902
#145577782
#145577762
C4×Dic1482
C4×#105969422
C4×#105969402
C4×#105969292
C4×SD16×C372
#317237