Finite Group Databasebeta

← #18004547

Subgroups — #18004547

Order 4736.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558099C211yesmaximal, characteristic
2#14558014C211yesmaximal, characteristic, complemented
3#14557860C211yesmaximal, characteristic, complemented
4#14557858C211yesmaximal, characteristic, complemented
5#14557855C211yesmaximal, characteristic, complemented
6#14557854C211yesmaximal, characteristic, complemented
7#14557851C211yesmaximal, characteristic, complemented
8#14557850C211yesmaximal, characteristic, complemented
9#14557848C211yesmaximal, characteristic, complemented
10#14557574C211yesmaximal, characteristic, complemented
11#14557570C211yesmaximal, characteristic, complemented
12#14557536C211yesmaximal, characteristic, complemented
13#102×D37C211yesmaximal, characteristic, complemented
14#14557498C211yesmaximal, characteristic, complemented
15C37×#480C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596929C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20#11924532—21no—
21#11924522—21no—
22#11924511C2211yescharacteristic
23#11924510C2211yescharacteristic
24#11924507C2211yescharacteristic
25#11924506—21no—
26#11924504—21no—
27#11924501—21no—
28#11924498—21no—
29C4×C22⋊D37—21no—
30C4×C22⋊D37—21no—
31#11924495C2211yescharacteristic, complemented
32#11924494C2211yescharacteristic
33#11924494C2211yescharacteristic
34#11924494C2211yescharacteristic, complemented
35C4⋊C4×D37C2211yescharacteristic
36C4⋊C4×D37C2211yescharacteristic, complemented
37#11924470C2211yescharacteristic, complemented
38#11924469C2211yescharacteristic, complemented
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924467C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51#11924448C2211yescharacteristic, complemented
52#121×C37C2211yescharacteristic
53C2×C4⋊C4×C37C2211yescharacteristic, complemented
54#107×C37C2211yescharacteristic, complemented
55#107×C37C2211yescharacteristic, complemented
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37—21no—
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37D411yescharacteristic
68C2×C22⋊D37D411yescharacteristic
69D4×D37—22no—
70D4×D37—22no—
71#10596962—22no—
72#10596962—22no—
73C2×D148—21no—
74C2×D148D411yescharacteristic
75C2×D148C2311yescharacteristic
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37C2311yescharacteristic
79C2×C4×D37C2311yescharacteristic
80C2×Dic74D411yescharacteristic
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C4⋊C4×C37—21no—
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C4⋊C4×C37C2311yescharacteristic
87C22⋊C4×C37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596929—22no—
107C8×D37—22no—
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—21no—
111C22×D37—42no—
112C22×D37—81no—
113C22×D37—81no—
114C22×D37C2×D411yescharacteristic
115C22×D37C2×D411yescharacteristic
116D4×C37—21no—
117D4×C37—21no—
118D4×C37—81no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—81no—
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2411yescharacteristic
127C22⋊D37—22no—
128C22⋊D37—22no—
129C22⋊D37—42no—
130C22⋊D37—81no—
131C22⋊D37—81no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137D148—22no—
138D148—21no—
139D148—21no—
140D148—81no—
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—81no—
144C4×D37—81no—
145C4×D37#4112yes—
146C4×D37#4112yes—
147Dic74—22no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37C22×D411yescharacteristic
159C2×D37—21no—
160C2×D37—21no—
161C2×D37—21no—
162C2×D37—21no—
163C2×D37—21no—
164C2×D37—41no—
165C2×D37—41no—
166C2×D37—41no—
167C2×D37—84no—
168C2×D37#12312yes—
169C4×C37—21no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37—41no—
173C4×C37C2×#4111yescharacteristic
174C4×C37C2×#4111yescharacteristic
175Dic37—21no—
176Dic37—41no—
177Dic37—41no—
178Dic37—41no—
179Dic37#12312yes—
180#3096—371nomaximal, Sylow
181C2×C37—41no—
182C2×C37—81no—
183C2×C37C2×#12311yescharacteristic
184C2×C37#57611yescharacteristic
185C2×C37#57711yescharacteristic
186D37—22no—
187D37—41no—
188D37—81no—
189#535—371no—
190#520—371no—
191#482—371no—
192#482—371no—
193#482—371no—
194#482—371no—
195#481—371no—
196#481—371no—
197#480—371no—
198#480D3711yescharacteristic, complemented
199#428—371no—
200#427—371no—
201#418—371no—
202C2×#102—371no—
203#408—371no—
204C37#309611yescharacteristic, complemented, Sylow
205C2×#41—371no—
206C22×D4—371no—
207C2×M16—371no—
208C22×C8—371no—
209#127—741no—
210#124—741no—
211#121—371no—
212#121—371no—
213#121—371no—
214#121C2×D3711yescharacteristic
215#120—741no—
216#120—741no—
217C4×Q8—741no—
218C4×D4—741no—
219C4×D4—741no—
220C4×D4—741no—
221#117—371no—
222#117—371no—
223#117—371no—
224#117—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—371no—
227C2×C4⋊C4C2×D3711yescharacteristic, complemented
228#107—371no—
229#107—371no—
230#107C2×D3711yescharacteristic, complemented
231#107C2×D3711yescharacteristic, complemented
232#106—371no—
233#106—371no—
234#106—371no—
235#106—371no—
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241#102—371no—
242#102C2×D3711yescharacteristic
243#102C2×D3711yescharacteristic
244C22⋊C8—371no—
245C22⋊C8—371no—
246C22⋊C8—371no—
247C22⋊C8C2×D3711yescharacteristic, complemented
248C24—741no—
249#41—742no—
250#41—742no—
251C2×Q8—371no—
252C2×D4—21no—
253C2×D4—371no—
254C2×D4—371no—
255C2×D4—371no—
256C2×D4—371no—
257C2×D4—741no—
258C2×D4—742no—
259C2×D4—742no—
260C2×D4—741no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4C22×D3711yescharacteristic
264C22×C4—21no—
265C22×C4—371no—
266C22×C4—371no—
267C22×C4—741no—
268C22×C4—741no—
269C22×C4C22×D3711yescharacteristic
270M16—742no—
271C2×C8—371no—
272C2×C8—371no—
273C2×C8—742no—
274C2×C8C22×D3711yescharacteristic
275C2×C8C22×D3711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—371no—
278C4⋊C4—371no—
279C4⋊C4—371no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4C22×D3711yescharacteristic
283C4⋊C4C22×D3711yescharacteristic
284C4⋊C4C22×D3711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C42—741no—
294C42—741no—
295C42—741no—
296C42—741no—
297C23—21no—
298C23—371no—
299C23—371no—
300C23—2961no—
301C23—2961no—
302C23—741no—
303C23—1482no—
304C23D4×D3711yescharacteristic
305Q8—742no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—2961no—
310D4—2961no—
311D4—2961no—
312D4—742no—
313D4—742no—
314D4—742no—
315D4—741no—
316D4—741no—
317D4—1482no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—371no—
325C2×C4—372no—
326C2×C4—372no—
327C2×C4—371no—
328C2×C4—2961no—
329C2×C4—2961no—
330C2×C4—741no—
331C2×C4—741no—
332C2×C4—741no—
333C2×C4—741no—
334C2×C4—741no—
335C2×C4D4×D3711yescharacteristic
336C2×C4C23×D3711yescharacteristic
337C8—21no—
338C8—21no—
339C8—741no—
340C8—741no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—372no—
348C22—2964no—
349C22—741no—
350C22—741no—
351C22—741no—
352C22—741no—
353C22—741no—
354C22—1481no—
355C22—1481no—
356C22—1481no—
357C22C2×D4×D3711yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—372no—
363C4—741no—
364C4—1481no—
365C4—1481no—
366C4—1481no—
367C4#41×D3711yescharacteristic
368C4#41×D3711yescharacteristic
369C2—41no—
370C2—81no—
371C2—2961no—
372C2—742no—
373C2—1481no—
374C2#123×D3711yescharacteristic
375C2#1455833411yescharacteristic
376C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#480C2
socleC22×C37C22×D4
prime radical#14558099C2
hypercenter#480D37
hypocenterC37#3096
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #14558014C2semidirect
3. #14557860C2semidirect
4. #14557858C2semidirect
5. #14557855C2semidirect
6. #14557854C2semidirect
7. #14557851C2semidirect
8. #14557850C2semidirect
9. #14557848C2semidirect
10. #14557574C2semidirect
11. #14557570C2semidirect
12. #14557536C2semidirect
13. #102×D37C2semidirect
14. #14557498C2semidirect
15. C37×#480C2semidirect
31. #11924495C22semidirect
34. #11924494C22semidirect
36. C4⋊C4×D37C22semidirect
37. #11924470C22semidirect
38. #11924469C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924467C22semidirect
42. #11924467C22semidirect
49. C22⋊#64436C22semidirect
50. #11924448C22semidirect
51. #11924448C22semidirect
53. C2×C4⋊C4×C37C22semidirect
54. #107×C37C22semidirect
55. #107×C37C22semidirect
58. C22⋊C8×C37C22semidirect
198. #480D37semidirect
204. C37#3096semidirect
227. C2×C4⋊C4C2×D37semidirect
230. #107C2×D37semidirect
231. #107C2×D37semidirect
247. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580992
#145580142
#145578602
#145578582
#145578552
#145578542
#145578512
#145578502
#145578482
#145575742
#145575702
#145575362
#102×D372
#145574982
C37×#4802
#309637