Finite Group Databasebeta

← #18006427

Subgroups — #18006427

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#14558177C211yesmaximal, characteristic
3#14557886C211yesmaximal, characteristic, complemented
4#14557863C211yesmaximal, characteristic, complemented
5#14557855C211yesmaximal, characteristic, complemented
6#14557831C211yesmaximal, characteristic, complemented
7#14557774C211yesmaximal, characteristic, complemented
8#14557761C211yesmaximal, characteristic, complemented
9#14557754C211yesmaximal, characteristic, complemented
10#14557696C211yesmaximal, characteristic, complemented
11#14557684C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#14557526C211yesmaximal, characteristic, complemented
15C2×#102×C37C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×Dic148C2211yescharacteristic, complemented
18C2×#10596940C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic, complemented
21#11924531—21no—
22#11924527C2211yescharacteristic, complemented
23#11924526—21no—
24#11924523C2211yescharacteristic
25#11924519—21no—
26#11924517—21no—
27#11924516C2211yescharacteristic, complemented
28#11924515C2211yescharacteristic
29#11924515C2211yescharacteristic
30#11924508—21no—
31#11924507C2211yescharacteristic
32#11924505—21no—
33#11924501C2211yescharacteristic, complemented
34D4×Dic37C2211yescharacteristic
35C4×C22⋊D37C2211yescharacteristic
36#11924495—21no—
37#11924494C2211yescharacteristic, complemented
38C2×C22⋊Dic37—21no—
39#11924470C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924459C2211yescharacteristic, complemented
46#11924459C2211yescharacteristic, complemented
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22×D4×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54C2×C4⋊C4×C37C2211yescharacteristic
55#102×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C24×C37—21no—
60C2×D4×C37—22no—
61C2×D4×C37—21no—
62C2×D4×C37—41no—
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37D411yescharacteristic
70C22×Dic37—21no—
71C22×Dic37—21no—
72#10596964—22no—
73#10596964—41no—
74C2×C4×D37C2311yescharacteristic
75C2×Dic74C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77C2×C8×C37—41no—
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C4⋊C4×C37—21no—
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37D411yescharacteristic
90#10596940—22no—
91#10596940—41no—
92#10596938—21no—
93#10596938—21no—
94#10596938D411yescharacteristic
95C4⋊Dic37—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103#10596936D411yescharacteristic
104C4×Dic37—21no—
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109Dic148—41no—
110C8×D37—41no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—42no—
114C23×C37—42no—
115C23×C37—81no—
116C23×C37C2×D411yescharacteristic
117C22×D37C2×D411yescharacteristic
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—42no—
122D4×C37#4112yes—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—42no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—22no—
131C22⋊D37—42no—
132C22⋊D37—81no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—42no—
138C2×Dic37—81no—
139C2×Dic37C2×D411yescharacteristic
140C2×Dic37C2×D411yescharacteristic
141C2×Dic37C2×D411yescharacteristic
142C4×D37—21no—
143C4×D37—21no—
144Dic74—21no—
145Dic74—21no—
146Dic74—21no—
147Dic74—21no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—22no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—84no—
161C22×C37#13512yes—
162C22×C37C22×D411yescharacteristic
163C2×D37—21no—
164C2×D37—21no—
165C2×D37—21no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37C2×#4111yescharacteristic
170C4×C37H(5,𝔽2)11yescharacteristic
171Dic37—21no—
172Dic37—21no—
173Dic37—21no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177Dic37—41no—
178#3296—371nomaximal, Sylow
179C2×C37—22no—
180C2×C37—42no—
181C2×C37—81no—
182C2×C37#54611yescharacteristic
183C2×C37C2×#13511yescharacteristic
184C2×C37#57711yescharacteristic
185D37—41no—
186#552—371no—
187#546—371no—
188#488—371no—
189#483—371no—
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×#102D3711yescharacteristic, complemented
201C37#329611yescharacteristic, complemented, Sylow
202C2×#41—371no—
203C22×D4C2×D3711yescharacteristic
204C2×Q16—371no—
205C2×SD16—371no—
206C2×SD16—371no—
207C22×C8—371no—
208C22×C8C2×D3711yescharacteristic
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⋊Q8—371no—
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#106—371no—
230#106—371no—
231C4⋊C8—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#102—371no—
237#102—371no—
238#102C2×D3711yescharacteristic
239#102C2×D3711yescharacteristic
240#102C2×D3711yescharacteristic
241#102C2×D3711yescharacteristic
242C22⋊C8—371no—
243C22⋊C8—371no—
244C4×C8—371no—
245C24—21no—
246#41—742no—
247#41—1481no—
248C2×Q8—371no—
249C2×Q8—371no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—371no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4C22×D3711yescharacteristic
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—371no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263Q16—1481no—
264SD16—742no—
265SD16—1481no—
266C2×C8—41no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8—1481no—
270C2×C8C22×D3711yescharacteristic
271C2×C8C22×D3711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—741no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4C22×D3711yescharacteristic
283C4⋊C4C22×D3711yescharacteristic
284C22⋊C4—371no—
285C22⋊C4—371no—
286C22⋊C4—741no—
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—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—371no—
303C23D4×D3711yescharacteristic
304Q8—741no—
305Q8—741no—
306Q8—741no—
307Q8—741no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—2961no—
313D4—742no—
314D4—1482no—
315D4#1059696212yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—371no—
322C2×C4—371no—
323C2×C4—371no—
324C2×C4—2961no—
325C2×C4—741no—
326C2×C4—741no—
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—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—741no—
348C22—741no—
349C22—741no—
350C22#1192455512yes—
351C22C2×D4×D3711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—741no—
356C4—741no—
357C4—741no—
358C4—1481no—
359C4—1481no—
360C4—1481no—
361C4—1481no—
362C4C2×#1059696211yescharacteristic
363C4#1192458111yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—1481no—
368C2#1455817311yescharacteristic
369C2C2×#1192455511yescharacteristic
370C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#102×C37C2
socleC22×C37C22×D4
prime radical#14558177C2
hypercenterC2×#102D37
hypocenterC37#3296
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14558218C2semidirect
3. #14557886C2semidirect
4. #14557863C2semidirect
5. #14557855C2semidirect
6. #14557831C2semidirect
7. #14557774C2semidirect
8. #14557761C2semidirect
9. #14557754C2semidirect
10. #14557696C2semidirect
11. #14557684C2semidirect
12. #14557624C2semidirect
13. C8×C22⋊D37C2semidirect
14. #14557526C2semidirect
15. C2×#102×C37C2semidirect
17. C2×Dic148C22semidirect
20. C2×C8×D37C22semidirect
22. #11924527C22semidirect
27. #11924516C22semidirect
33. #11924501C22semidirect
37. #11924494C22semidirect
39. #11924470C22semidirect
40. #11924467C22semidirect
41. #11924467C22semidirect
42. #11924465C22semidirect
43. #11924461C22semidirect
44. #11924461C22semidirect
45. #11924459C22semidirect
46. #11924459C22semidirect
50. #11924448C22semidirect
51. C8×Dic37C22semidirect
200. C2×#102D37semidirect
201. C37#3296semidirect

Maximal subgroups

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

subgroupindex
#145582182
#145581772
#145578862
#145578632
#145578552
#145578312
#145577742
#145577612
#145577542
#145576962
#145576842
#145576242
C8×C22⋊D372
#145575262
C2×#102×C372
#329637