Finite Group Databasebeta

← #18004875

Subgroups — #18004875

Order 4736.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558154C211yesmaximal, characteristic, complemented
2#14558013C211yesmaximal, characteristic, complemented
3#14557864C211yesmaximal, characteristic, complemented
4#14557852C211yesmaximal, characteristic, complemented
5#14557824C211yesmaximal, characteristic, complemented
6#14557819C211yesmaximal, characteristic, complemented
7#14557756C211yesmaximal, characteristic, complemented
8#14557749C211yesmaximal, characteristic, complemented
9#14557697C211yesmaximal, characteristic, complemented
10#14557680C211yesmaximal, characteristic
11#14557646C211yesmaximal, characteristic, complemented
12#14557641C211yesmaximal, characteristic, complemented
13C4×#10596930C211yesmaximal, characteristic, complemented
14C4×#10596930C211yesmaximal, characteristic, complemented
15C37×#433C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×Dic148C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924536C2211yescharacteristic
22#11924531—21no—
23#11924524C2211yescharacteristic
24#11924522—21no—
25#11924518—21no—
26#11924515C2211yescharacteristic
27#11924514—21no—
28#11924510C2211yescharacteristic
29C4×Dic74C2211yescharacteristic
30C4×Dic74C2211yescharacteristic
31C4×Dic74C2211yescharacteristic
32C4×D148C2211yescharacteristic
33C4×D148C2211yescharacteristic
34C4×D148C2211yescharacteristic
35#11924496—21no—
36#11924496—21no—
37#11924494—21no—
38C2×C4⋊Dic37C2211yescharacteristic
39C4⋊C4×D37—21no—
40#11924468C2211yescharacteristic
41#11924468C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924468C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924461C2211yescharacteristic
46#11924461C2211yescharacteristic
47#11924461C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic
52#117×C37C2211yescharacteristic
53C4⋊C8×C37C2211yescharacteristic
54C4⋊C8×C37C2211yescharacteristic
55C22⋊C8×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57#97×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C2×C22⋊D37—21no—
61C2×C22⋊D37—21no—
62C22×Dic37—21no—
63#10596962—22no—
64#10596962—22no—
65C2×D148C2311yescharacteristic
66C2×D148C2311yescharacteristic
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×Dic74—21no—
72C2×Dic74C2311yescharacteristic
73C2×Dic74C2311yescharacteristic
74C2×C8×C37C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C4⋊C4×C37D411yescharacteristic
79C4⋊C4×C37D411yescharacteristic
80C22⋊C4×C37D411yescharacteristic
81C22⋊C4×C37D411yescharacteristic
82C42×C37C2311yescharacteristic
83C42×C37C2311yescharacteristic
84C22⋊Dic37—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104Dic148—22no—
105D296—22no—
106#10596930—22no—
107#10596930—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110C22×D37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37C2×D411yescharacteristic
114C2×C4×C37C2×D411yescharacteristic
115C2×C4×C37C2×D411yescharacteristic
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2411yescharacteristic
119C22⋊D37—24no—
120C22⋊D37—81no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—81no—
128D148—21no—
129D148—21no—
130D148—21no—
131D148#4112yes—
132C4×D37—24no—
133C4×D37—81no—
134C4×D37—81no—
135C4×D37—81no—
136Dic74—21no—
137Dic74—21no—
138Dic74—21no—
139Dic74—81no—
140Dic74#4112yes—
141C8×C37—21no—
142C8×C37—21no—
143C8×C37—21no—
144C8×C37—21no—
145C22×C37—21no—
146C22×C37—21no—
147C22×C37—21no—
148C22×C37C22×D411yescharacteristic
149C2×D37—22no—
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C2×D37—41no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—21no—
158C4×C37—21no—
159C4×C37—21no—
160C4×C37C2×#4111yescharacteristic
161C4×C37C2×#4111yescharacteristic
162Dic37—22no—
163Dic37—41no—
164Dic37—41no—
165Dic37—41no—
166Dic37—41no—
167Dic37—41no—
168#3125—371nomaximal, Sylow
169C2×C37—41no—
170C2×C37#52511yescharacteristic
171C2×C37#57711yescharacteristic
172C2×C37#57711yescharacteristic
173D37—42no—
174D37—81no—
175#542—371no—
176#520—371no—
177#483—371no—
178#481—371no—
179#476—371no—
180#475—371no—
181#464—371no—
182#463—371no—
183#452—371no—
184#449—371no—
185#442—371no—
186#441—371no—
187C4×SD16—371no—
188C4×SD16—371no—
189#433D3711yescharacteristic, complemented
190C37#312511yescharacteristic, complemented, Sylow
191C2×#41—371no—
192C2×Q16—371no—
193C2×SD16—371no—
194C2×SD16—371no—
195C2×D8—371no—
196C4⋊Q8—371no—
197#126—741no—
198#124—371no—
199#124—741no—
200#123—741no—
201C22⋊Q8—371no—
202C22⋊Q8—741no—
203#121—371no—
204C4×Q8—371no—
205C4×Q8—371no—
206C4×Q8—371no—
207C4×D4—371no—
208C4×D4—371no—
209C4×D4—371no—
210C4×D4—741no—
211C4×D4—741no—
212#117—741no—
213#117C2×D3711yescharacteristic
214C2×C4⋊C4—371no—
215C2×C4⋊C4—741no—
216#106—371no—
217#106—371no—
218#106—371no—
219#106—371no—
220C4⋊C8C2×D3711yescharacteristic
221C4⋊C8C2×D3711yescharacteristic
222#103—371no—
223#103—371no—
224#103—371no—
225#103—371no—
226#102—371no—
227#102—371no—
228#102—371no—
229#102—371no—
230C22⋊C8C2×D3711yescharacteristic
231C22⋊C8C2×D3711yescharacteristic
232#97C2×D3711yescharacteristic
233C4×C8C2×D3711yescharacteristic
234#41—742no—
235#41—742no—
236C2×Q8—371no—
237C2×Q8—371no—
238C2×Q8—741no—
239C2×D4—371no—
240C2×D4—371no—
241C2×D4—741no—
242C2×D4—741no—
243C22×C4—741no—
244C22×C4—741no—
245C22×C4—741no—
246C22×C4—741no—
247C22×C4—741no—
248C22×C4C22×D3711yescharacteristic
249Q16—742no—
250SD16—742no—
251SD16—742no—
252D8—742no—
253C2×C8C22×D3711yescharacteristic
254C2×C8C22×D3711yescharacteristic
255C2×C8C22×D3711yescharacteristic
256C2×C8C22×D3711yescharacteristic
257C4⋊C4—371no—
258C4⋊C4—371no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—741no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4—741no—
267C4⋊C4D14811yescharacteristic
268C4⋊C4D14811yescharacteristic
269C22⋊C4—741no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4D14811yescharacteristic
277C22⋊C4D14811yescharacteristic
278C42—741no—
279C42—741no—
280C42—741no—
281C42C22×D3711yescharacteristic
282C42C22×D3711yescharacteristic
283C23—741no—
284C23—741no—
285C23C2×D14811yescharacteristic
286Q8—372no—
287Q8—2961no—
288Q8—741no—
289Q8—741no—
290Q8—741no—
291D4—372no—
292D4—2961no—
293D4—744no—
294D4—741no—
295D4—741no—
296D4—741no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2961no—
300C2×C4—2961no—
301C2×C4—2961no—
302C2×C4—2961no—
303C2×C4—744no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4—741no—
307C2×C4—741no—
308C2×C4—741no—
309C2×C4—741no—
310C2×C4C2×D14811yescharacteristic
311C2×C4C2×D14811yescharacteristic
312C2×C4C2×D14811yescharacteristic
313C2×C4C2×D14811yescharacteristic
314C2×C4C2×D14811yescharacteristic
315C2×C4C23×D3711yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—742no—
324C22—1481no—
325C22—1481no—
326C22—1481no—
327C22—1481no—
328C22—1481no—
329C22C22×D14811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—742no—
336C4—1481no—
337C4—1481no—
338C4—1481no—
339C4—1481no—
340C4—1481no—
341C4#41×D3711yescharacteristic
342C4#41×D3711yescharacteristic
343C2—41no—
344C2—2961no—
345C2—1482no—
346C2#1455804511yescharacteristic
347C2#1455834511yescharacteristic
348C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#433C2
socleC22×C37C22×D4
prime radical#14557680C2
hypercenter#433D37
hypocenterC37#3125
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14558013C2semidirect
3. #14557864C2semidirect
4. #14557852C2semidirect
5. #14557824C2semidirect
6. #14557819C2semidirect
7. #14557756C2semidirect
8. #14557749C2semidirect
9. #14557697C2semidirect
11. #14557646C2semidirect
12. #14557641C2semidirect
13. C4×#10596930C2semidirect
14. C4×#10596930C2semidirect
15. C37×#433C2semidirect
189. #433D37semidirect
190. C37#3125semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145580132
#145578642
#145578522
#145578242
#145578192
#145577562
#145577492
#145576972
#145576802
#145576462
#145576412
C4×#105969302
C37×#4332
#312537