Finite Group Databasebeta

← #18006429

Subgroups — #18006429

Order 4736.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558218C211yesmaximal, characteristic, complemented
2#14558174C211yesmaximal, characteristic
3#14557889C211yesmaximal, characteristic, complemented
4#14557859C211yesmaximal, characteristic, complemented
5#14557832C211yesmaximal, characteristic, complemented
6#14557772C211yesmaximal, characteristic, complemented
7#14557763C211yesmaximal, characteristic, complemented
8#14557758C211yesmaximal, characteristic, complemented
9#14557698C211yesmaximal, characteristic, complemented
10#14557686C211yesmaximal, characteristic, complemented
11#14557620C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557528C211yesmaximal, characteristic, complemented
14C2×#11924456C211yesmaximal, characteristic, complemented
15C37×#483C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C22×D148C2211yescharacteristic
18C2×#10596942C2211yescharacteristic, complemented
19C2×#10596930C2211yescharacteristic
20C2×#10596930C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic, complemented
23#11924531—21no—
24#11924527C2211yescharacteristic, complemented
25#11924526—21no—
26#11924525C2211yescharacteristic
27#11924521—21no—
28#11924519—21no—
29#11924516C2211yescharacteristic, complemented
30#11924515C2211yescharacteristic
31#11924511—21no—
32#11924511C2211yescharacteristic
33#11924506—21no—
34#11924501C2211yescharacteristic, complemented
35#11924498C2211yescharacteristic
36C4×C22⋊D37C2211yescharacteristic
37#11924495—21no—
38#11924494C2211yescharacteristic, complemented
39C22⋊C4×D37—21no—
40#11924469C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924460C2211yescharacteristic, complemented
43#11924459C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924448C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22⋊Q8×C37C2211yescharacteristic
53C2×C4⋊C4×C37C2211yescharacteristic
54#106×C37C2211yescharacteristic, complemented
55#106×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic
59C23×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37D411yescharacteristic
64#10596966—22no—
65#10596966—41no—
66C2×D148—22no—
67C2×D148—21no—
68C2×D148—21no—
69C2×D148—21no—
70C2×D148—41no—
71C2×D148C2311yescharacteristic
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C22⋊C4×C37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37D411yescharacteristic
87#10596942—41no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938D411yescharacteristic
95C4⋊Dic37—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C2×#64436—41no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108#10596930—22no—
109#10596930—41no—
110C8×D37—41no—
111C23×C37C2×D411yescharacteristic
112C22×D37—21no—
113C22×D37—21no—
114C22×D37—42no—
115C22×D37—42no—
116C22×D37—81no—
117C22×D37C2×D411yescharacteristic
118Q8×C37—21no—
119Q8×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—42no—
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2411yescharacteristic
129C22⋊D37—22no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37C2×D411yescharacteristic
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135D148—21no—
136D148—21no—
137D148—21no—
138D148—42no—
139D148—42no—
140D148—81no—
141D148#4112yes—
142C4×D37—21no—
143C4×D37—21no—
144C4×D37—42no—
145C4×D37—81no—
146Dic74—21no—
147Dic74—21no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37#13512yes—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—22no—
158C2×D37—21no—
159C2×D37—21no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C2×D37—84no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37—41no—
171C4×C37C2×#4111yescharacteristic
172C4×C37H(5,𝔽2)11yescharacteristic
173Dic37—21no—
174Dic37—21no—
175Dic37—21no—
176Dic37—41no—
177Dic37—41no—
178#3296—371nomaximal, Sylow
179C2×C37—22no—
180C2×C37#54611yescharacteristic
181C2×C37C2×#13511yescharacteristic
182C2×C37#57711yescharacteristic
183D37—41no—
184D37—42no—
185D37—81no—
186#552—371no—
187#546—371no—
188#488—371no—
189#483D3711yescharacteristic, complemented
190#482—371no—
191#478—371no—
192#467—371no—
193#465—371no—
194#464—371no—
195#452—371no—
196#450—371no—
197C4×SD16—371no—
198C8×D4—371no—
199#416—371no—
200C2×#102—371no—
201C37#329611yescharacteristic, complemented, Sylow
202C2×#41—371no—
203C22×D4—371no—
204C2×Q16—371no—
205C2×SD16—371no—
206C2×SD16—371no—
207C22×C8—371no—
208C22×C8—371no—
209#126—741no—
210#125—371no—
211#125—741no—
212#124—371no—
213#123—741no—
214#123—741no—
215C22⋊Q8—371no—
216C22⋊Q8—371no—
217C22⋊Q8C2×D3711yescharacteristic
218#121—371no—
219#121—741no—
220#120—741no—
221C4×Q8—371no—
222C4×D4—371no—
223C4×D4—371no—
224#117—371no—
225#117—741no—
226C2×C4⋊C4C2×D3711yescharacteristic
227C2×C22⋊C4—741no—
228#107—371no—
229#106C2×D3711yescharacteristic, complemented
230#106C2×D3711yescharacteristic, complemented
231C4⋊C8—371no—
232#103—371no—
233#103—371no—
234#103C2×D3711yescharacteristic, complemented
235#103C2×D3711yescharacteristic, complemented
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241#102—371no—
242C22⋊C8—371no—
243C22⋊C8C2×D3711yescharacteristic
244C4×C8—371no—
245C24—741no—
246#41—742no—
247#41—1481no—
248C2×Q8—371no—
249C2×Q8C22×D3711yescharacteristic
250C2×D4—371no—
251C2×D4—371no—
252C2×D4—371no—
253C2×D4—742no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4—741no—
257C2×D4—1481no—
258C22×C4—21no—
259C22×C4—371no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263Q16—1481no—
264SD16—742no—
265SD16—1481no—
266C2×C8—371no—
267C2×C8—371no—
268C2×C8—1481no—
269C2×C8—1481no—
270C2×C8C22×D3711yescharacteristic
271C2×C8C22×D3711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—741no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4C22×D3711yescharacteristic
282C4⋊C4C22×D3711yescharacteristic
283C4⋊C4C22×D3711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—371no—
286C22⋊C4—371no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C42—371no—
295C42—741no—
296C42—741no—
297C23—371no—
298C23—2961no—
299C23—741no—
300C23—741no—
301C23—1482no—
302C23—1482no—
303C23D4×D3711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—741no—
307Q8—741no—
308D4—372no—
309D4—2961no—
310D4—742no—
311D4—741no—
312D4—741no—
313D4—741no—
314D4—1482no—
315D4—1482no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—371no—
324C2×C4—371no—
325C2×C4—371no—
326C2×C4—2961no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—741no—
330C2×C4—741no—
331C2×C4—1482no—
332C2×C4D4×D3711yescharacteristic
333C2×C4C23×D3711yescharacteristic
334C8—21no—
335C8—21no—
336C8—741no—
337C8—741no—
338C22—21no—
339C22—21no—
340C22—2964no—
341C22—741no—
342C22—741no—
343C22—741no—
344C22—742no—
345C22—1481no—
346C22—1481no—
347C22—1481no—
348C22—1481no—
349C22—1481no—
350C22#1192455712yes—
351C22C2×D4×D3711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—741no—
358C4—741no—
359C4—741no—
360C4—1481no—
361C4—1481no—
362C4#41×D3711yescharacteristic
363C4#1192458211yescharacteristic
364C2—22no—
365C2—2961no—
366C2—1482no—
367C2—1481no—
368C2#1455817511yescharacteristic
369C2C2×#1192455711yescharacteristic
370C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#483C2
socleC22×C37C22×D4
prime radical#14558174C2
hypercenter#483D37
hypocenterC37#3296
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #14558218C2semidirect
3. #14557889C2semidirect
4. #14557859C2semidirect
5. #14557832C2semidirect
6. #14557772C2semidirect
7. #14557763C2semidirect
8. #14557758C2semidirect
9. #14557698C2semidirect
10. #14557686C2semidirect
11. #14557620C2semidirect
12. #14557596C2semidirect
13. #14557528C2semidirect
14. C2×#11924456C2semidirect
15. C37×#483C2semidirect
18. C2×#10596942C22semidirect
22. C2×C8×D37C22semidirect
24. #11924527C22semidirect
29. #11924516C22semidirect
34. #11924501C22semidirect
38. #11924494C22semidirect
40. #11924469C22semidirect
41. #11924465C22semidirect
42. #11924460C22semidirect
43. #11924459C22semidirect
50. #11924448C22semidirect
51. C8×Dic37C22semidirect
54. #106×C37C22semidirect
55. #106×C37C22semidirect
56. #103×C37C22semidirect
57. #103×C37C22semidirect
189. #483D37semidirect
201. C37#3296semidirect
229. #106C2×D37semidirect
230. #106C2×D37semidirect
234. #103C2×D37semidirect
235. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582182
#145581742
#145578892
#145578592
#145578322
#145577722
#145577632
#145577582
#145576982
#145576862
#145576202
#145575962
#145575282
C2×#119244562
C37×#4832
#329637