Finite Group Databasebeta

← #18006424

Subgroups — #18006424

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#14558217C211yesmaximal, characteristic, complemented
2#14558171C211yesmaximal, characteristic
3#14557889C211yesmaximal, characteristic, complemented
4#14557862C211yesmaximal, characteristic, complemented
5#14557858C211yesmaximal, characteristic, complemented
6#14557831C211yesmaximal, characteristic, complemented
7#14557771C211yesmaximal, characteristic, complemented
8#14557764C211yesmaximal, characteristic, complemented
9#14557757C211yesmaximal, characteristic, complemented
10#14557682C211yesmaximal, characteristic, complemented
11SD16×Dic37C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557529C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#452C211yesmaximal, characteristic, complemented
16C2×D4×D37C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C22×#64436C2211yescharacteristic, complemented
19C2×C8×D37C2211yescharacteristic
20#11924529—21no—
21#11924527C2211yescharacteristic, complemented
22#11924526—21no—
23#11924525C2211yescharacteristic
24#11924519—21no—
25#11924518—21no—
26#11924512C2211yescharacteristic
27#11924512C2211yescharacteristic
28#11924510C2211yescharacteristic
29#11924508—21no—
30#11924504—21no—
31Q8×Dic37C2211yescharacteristic, complemented
32D4×Dic37C2211yescharacteristic
33C4×C22⋊D37C2211yescharacteristic
34#11924495C2211yescharacteristic, complemented
35#11924494—21no—
36C4⋊C4×D37C2211yescharacteristic
37C2×#10596938—21no—
38#11924470C2211yescharacteristic, complemented
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924460C2211yescharacteristic, complemented
43#11924460C2211yescharacteristic, complemented
44#11924460C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic, complemented
52C2×#41×C37C2211yescharacteristic
53C2×Q16×C37C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic
55C22⋊Q8×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60#41×C37—22no—
61#41×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37—21no—
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37D411yescharacteristic
71C22×Dic37—21no—
72D4×D37—22no—
73D4×D37—41no—
74C2×D148C2311yescharacteristic
75C2×C4×D37—21no—
76C2×C4×D37C2311yescharacteristic
77Q16×C37—41no—
78SD16×C37—22no—
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37—21no—
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37D411yescharacteristic
87#10596941—41no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938D411yescharacteristic
94C4⋊Dic37—21no—
95C4⋊Dic37—21no—
96C4⋊Dic37C2311yescharacteristic
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×#64436—41no—
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C8×D37—41no—
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37—42no—
115C22×D37—42no—
116C22×D37—81no—
117C22×D37C2×D411yescharacteristic
118Q8×C37—21no—
119Q8×C37—21no—
120Q8×C37—21no—
121Q8×C37—21no—
122D4×C37—21no—
123D4×C37—42no—
124D4×C37#4112yes—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—42no—
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2411yescharacteristic
133C22⋊D37—22no—
134C22⋊D37—42no—
135C22⋊D37—81no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—81no—
140C2×Dic37C2×D411yescharacteristic
141C2×Dic37C2×D411yescharacteristic
142C2×Dic37C2×D411yescharacteristic
143D148—21no—
144D148—21no—
145C4×D37—21no—
146C4×D37—21no—
147C4×D37—42no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—22no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37C22×D411yescharacteristic
159C2×D37—21no—
160C2×D37—21no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—84no—
165C2×D37#13512yes—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37C2×#4111yescharacteristic
171C4×C37H(5,𝔽2)11yescharacteristic
172Dic37—21no—
173Dic37—21no—
174Dic37—21no—
175Dic37—41no—
176Dic37—41no—
177Dic37—41no—
178#3296—371nomaximal, Sylow
179C2×C37—42no—
180C2×C37—41no—
181C2×C37#54611yescharacteristic
182C2×C37C2×#13511yescharacteristic
183C2×C37#57711yescharacteristic
184D37—22no—
185D37—81no—
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#452D3711yescharacteristic, complemented
196#450—371no—
197C4×SD16—371no—
198C8×D4—371no—
199#416—371no—
200C2×#102—371no—
201C37#329611yescharacteristic, complemented, Sylow
202C2×#41C2×D3711yescharacteristic
203C22×D4—371no—
204C2×Q16C2×D3711yescharacteristic, complemented
205C2×SD16—371no—
206C2×SD16C2×D3711yescharacteristic
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, complemented
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⋊C4—371no—
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#103C2×D3711yescharacteristic, complemented
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241#102C2×D3711yescharacteristic
242C22⋊C8—371no—
243C22⋊C8C2×D3711yescharacteristic, complemented
244C4×C8—371no—
245C24—741no—
246#41—22no—
247#41—41no—
248C2×Q8C22×D3711yescharacteristic
249C2×Q8C22×D3711yescharacteristic
250C2×D4—21no—
251C2×D4—371no—
252C2×D4—371no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—742no—
256C2×D4—1481no—
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—371no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263Q16—41no—
264SD16—22no—
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—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4—741no—
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—21no—
298C23—371no—
299C23—2961no—
300C23—741no—
301C23—1482no—
302C23—1482no—
303C23D4×D3711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—42no—
310D4—2961no—
311D4—742no—
312D4—741no—
313D4—741no—
314D4—1482no—
315D4#1059696412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—371no—
323C2×C4—371no—
324C2×C4—371no—
325C2×C4—2961no—
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—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—372no—
345C22—2964no—
346C22—741no—
347C22—741no—
348C22—1481no—
349C22—1481no—
350C22—1481no—
351C22C2×D4×D3711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—741no—
357C4—741no—
358C4—741no—
359C4—1481no—
360C4—1481no—
361C4—1481no—
362C4C2×#1059696411yescharacteristic
363C4#1192458111yescharacteristic
364C2—41no—
365C2—42no—
366C2—2961no—
367C2—742no—
368C2#1455817011yescharacteristic
369C2#135×D3711yescharacteristic
370C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#452C2
socleC22×C37C22×D4
prime radical#14558171C2
hypercenter#452D37
hypocenterC37#3296
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #14558217C2semidirect
3. #14557889C2semidirect
4. #14557862C2semidirect
5. #14557858C2semidirect
6. #14557831C2semidirect
7. #14557771C2semidirect
8. #14557764C2semidirect
9. #14557757C2semidirect
10. #14557682C2semidirect
11. SD16×Dic37C2semidirect
12. #14557596C2semidirect
13. #14557529C2semidirect
14. #102×D37C2semidirect
15. C37×#452C2semidirect
18. C22×#64436C22semidirect
21. #11924527C22semidirect
31. Q8×Dic37C22semidirect
34. #11924495C22semidirect
38. #11924470C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924460C22semidirect
43. #11924460C22semidirect
44. #11924460C22semidirect
51. C8×Dic37C22semidirect
53. C2×Q16×C37C22semidirect
55. C22⋊Q8×C37C22semidirect
56. #103×C37C22semidirect
58. C22⋊C8×C37C22semidirect
195. #452D37semidirect
201. C37#3296semidirect
204. C2×Q16C2×D37semidirect
217. C22⋊Q8C2×D37semidirect
235. #103C2×D37semidirect
243. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582172
#145581712
#145578892
#145578622
#145578582
#145578312
#145577712
#145577642
#145577572
#145576822
SD16×Dic372
#145575962
#145575292
#102×D372
C37×#4522
#329637