Finite Group Databasebeta

← #18005160

Subgroups — #18005160

Order 4736.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558067C211yesmaximal, characteristic, complemented
2#14557932C211yesmaximal, characteristic, complemented
3#14557915C211yesmaximal, characteristic, complemented
4#14557890C211yesmaximal, characteristic, complemented
5#14557887C211yesmaximal, characteristic, complemented
6#14557772C211yesmaximal, characteristic, complemented
7#14557767C211yesmaximal, characteristic
8#14557764C211yesmaximal, characteristic, complemented
9#14557760C211yesmaximal, characteristic, complemented
10C4×#10596942C211yesmaximal, characteristic, complemented
11C4×#10596941C211yesmaximal, characteristic, complemented
12C4×#10596940C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14C2×C4×#64436C211yesmaximal, characteristic, complemented
15C37×#529C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C22×#64436C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22#11924530—21no—
23#11924528C2211yescharacteristic
24#11924524C2211yescharacteristic
25#11924519—21no—
26#11924515C2211yescharacteristic
27#11924510C2211yescharacteristic
28C4×Dic74C2211yescharacteristic
29C4×D148C2211yescharacteristic
30C4×C22⋊D37—21no—
31#11924493—21no—
32#11924469C2211yescharacteristic
33#11924469C2211yescharacteristic
34#11924467C2211yescharacteristic
35#11924467C2211yescharacteristic
36#11924460C2211yescharacteristic
37#11924460C2211yescharacteristic
38#11924459C2211yescharacteristic
39#11924459C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44C4×#64436C2211yescharacteristic
45C4×#64436C2211yescharacteristic
46C4×#64436C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48#126×C37—21no—
49#125×C37C2211yescharacteristic
50#124×C37C2211yescharacteristic
51#123×C37—21no—
52C22⋊Q8×C37C2211yescharacteristic
53#121×C37C2211yescharacteristic
54C4×Q8×C37C2211yescharacteristic
55C4×D4×C37—21no—
56C4×D4×C37C2211yescharacteristic
57#117×C37—21no—
58C2×C42×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37—21no—
63C22×C4×C37D411yescharacteristic
64C22×C4×C37D411yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C2×C22⋊D37—21no—
67C2×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C2×Dic74C2311yescharacteristic
70C4⋊C4×C37—21no—
71C4⋊C4×C37—21no—
72C4⋊C4×C37—21no—
73C4⋊C4×C37—21no—
74C4⋊C4×C37C2311yescharacteristic
75C4⋊C4×C37C2311yescharacteristic
76C22⋊C4×C37—21no—
77C22⋊C4×C37—21no—
78C22⋊C4×C37—21no—
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C42×C37—21no—
82C42×C37D411yescharacteristic
83C42×C37D411yescharacteristic
84C42×C37C2311yescharacteristic
85C42×C37C2311yescharacteristic
86C22⋊Dic37—21no—
87#10596942—22no—
88#10596941—22no—
89#10596940—22no—
90#10596939—22no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102C2×#64436—22no—
103C2×#64436—22no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—21no—
111Q8×C37—21no—
112Q8×C37—21no—
113D4×C37—21no—
114D4×C37—21no—
115D4×C37—42no—
116C2×C4×C37—22no—
117C2×C4×C37—22no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—42no—
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—42no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134D148—21no—
135D148—21no—
136C4×D37—42no—
137Dic74—21no—
138Dic74—21no—
139#64436—21no—
140#64436—21no—
141#64436#4112yes—
142#64436#4112yes—
143C22×C37—21no—
144C22×C37—21no—
145C22×C37—41no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37#13512yes—
149C22×C37C22×D411yescharacteristic
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37#13512yes—
161C4×C37C2×#4111yescharacteristic
162C4×C37C2×#4111yescharacteristic
163Dic37—41no—
164Dic37—41no—
165Dic37—41no—
166#3168—371nomaximal, Sylow
167C2×C37—22no—
168C2×C37—81no—
169C2×C37#53211yescharacteristic
170C2×C37C2×#13511yescharacteristic
171C2×C37C2×#13511yescharacteristic
172D37—81no—
173#529—371no—
174#529D3711yescharacteristic, complemented
175#499—371no—
176#495—371no—
177#488—371no—
178#488—371no—
179#467—371no—
180#466—371no—
181#465—371no—
182#465—371no—
183C4×Q16—371no—
184C4×SD16—371no—
185C4×SD16—371no—
186C4×D8—371no—
187C2×C4×C8—371no—
188C37#316811yescharacteristic, complemented, Sylow
189C2×Q16—371no—
190C2×SD16—371no—
191C2×SD16—371no—
192C2×D8—371no—
193C22×C8—371no—
194C22×C8—371no—
195#126—21no—
196#126—741no—
197#125—371no—
198#125C2×D3711yescharacteristic
199#124—371no—
200#124C2×D3711yescharacteristic
201#123—21no—
202#123—741no—
203C22⋊Q8—371no—
204C22⋊Q8C2×D3711yescharacteristic
205#121—371no—
206#121C2×D3711yescharacteristic
207C4×Q8—371no—
208C4×Q8C2×D3711yescharacteristic
209C4×D4—21no—
210C4×D4—371no—
211C4×D4—741no—
212C4×D4C2×D3711yescharacteristic
213#117—21no—
214#117—741no—
215C2×C42C2×D3711yescharacteristic
216#107—371no—
217#107—371no—
218#106—371no—
219#106—371no—
220#103—371no—
221#103—371no—
222#103—371no—
223#103—371no—
224#102—371no—
225#102—371no—
226#102—371no—
227#102—371no—
228C4×C8—371no—
229C4×C8—371no—
230C4×C8—371no—
231C4×C8—371no—
232C2×Q8—371no—
233C2×Q8C22×D3711yescharacteristic
234C2×D4—21no—
235C2×D4—371no—
236C2×D4—741no—
237C2×D4C22×D3711yescharacteristic
238C22×C4—21no—
239C22×C4—741no—
240C22×C4C22⋊D3711yescharacteristic
241C22×C4C22⋊D3711yescharacteristic
242C22×C4C22×D3711yescharacteristic
243Q16—742no—
244SD16—742no—
245SD16—742no—
246D8—742no—
247C2×C8—371no—
248C2×C8—371no—
249C2×C8—371no—
250C2×C8—371no—
251C2×C8—742no—
252C2×C8—742no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—371no—
258C4⋊C4—371no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4—741no—
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C42—21no—
276C42—741no—
277C42C22⋊D3711yescharacteristic
278C42C22⋊D3711yescharacteristic
279C42C22×D3711yescharacteristic
280C42C22×D3711yescharacteristic
281C23—21no—
282C23—741no—
283C23C2×C22⋊D3711yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—741no—
287Q8—741no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—741no—
292D4—741no—
293D4—1482no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—1482no—
306C2×C4C2×C22⋊D3711yescharacteristic
307C2×C4C2×C22⋊D3711yescharacteristic
308C2×C4C2×C22⋊D3711yescharacteristic
309C2×C4C2×C22⋊D3711yescharacteristic
310C2×C4C2×C22⋊D3711yescharacteristic
311C2×C4C23×D3711yescharacteristic
312C8—372no—
313C8—372no—
314C8—741no—
315C8—741no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1481no—
322C22—1481no—
323C22—1481no—
324C22#1192455612yes—
325C22C22×C22⋊D3711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1481no—
334C4—1481no—
335C4—1481no—
336C4#1192455612yes—
337C4#41×D3711yescharacteristic
338C4#41×D3711yescharacteristic
339C2—22no—
340C2—81no—
341C2—2961no—
342C2#1455807911yescharacteristic
343C2C2×#1192455611yescharacteristic
344C2C2×#1192455611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#529C2
socleC22×C37C22×D4
prime radical#14557767C2
hypercenter#529D37
hypocenterC37#3168
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14558067C2semidirect
2. #14557932C2semidirect
3. #14557915C2semidirect
4. #14557890C2semidirect
5. #14557887C2semidirect
6. #14557772C2semidirect
8. #14557764C2semidirect
9. #14557760C2semidirect
10. C4×#10596942C2semidirect
11. C4×#10596941C2semidirect
12. C4×#10596940C2semidirect
13. C4×#10596939C2semidirect
14. C2×C4×#64436C2semidirect
15. C37×#529C2semidirect
174. #529D37semidirect
188. C37#3168semidirect

Maximal subgroups

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

subgroupindex
#145580672
#145579322
#145579152
#145578902
#145578872
#145577722
#145577672
#145577642
#145577602
C4×#105969422
C4×#105969412
C4×#105969402
C4×#105969392
C2×C4×#644362
C37×#5292
#316837