Finite Group Databasebeta

← #18006416

Subgroups — #18006416

Order 4736.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558238C211yesmaximal, characteristic, complemented
2D4×C22⋊D37C211yesmaximal, characteristic
3#14557878C211yesmaximal, characteristic, complemented
4#14557851C211yesmaximal, characteristic, complemented
5#14557850C211yesmaximal, characteristic, complemented
6#14557821C211yesmaximal, characteristic, complemented
7#14557762C211yesmaximal, characteristic, complemented
8#14557761C211yesmaximal, characteristic, complemented
9#14557732C211yesmaximal, characteristic, complemented
10#14557685C211yesmaximal, characteristic, complemented
11#14557684C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C2×#102×C37C211yesmaximal, characteristic, complemented
16C22×C22⋊D37—21no—
17C2×D4×D37C2211yescharacteristic
18C2×#10596930C2211yescharacteristic, complemented
19C2×#10596940C2211yescharacteristic
20C2×#10596940C2211yescharacteristic, complemented
21C2×C8×D37C2211yescharacteristic, complemented
22#11924535C2211yescharacteristic, complemented
23#11924532C2211yescharacteristic
24#11924526—21no—
25#11924516C2211yescharacteristic, complemented
26#11924515—21no—
27#11924515C2211yescharacteristic, complemented
28#11924514—21no—
29#11924510C2211yescharacteristic
30#11924508—21no—
31#11924507C2211yescharacteristic
32#11924505—21no—
33#11924504—21no—
34#11924501C2211yescharacteristic, complemented
35D4×Dic37C2211yescharacteristic
36C4×C22⋊D37—21no—
37C4×C22⋊D37C2211yescharacteristic
38C4⋊C4×D37C2211yescharacteristic, complemented
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic, complemented
47#11924456C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic, complemented
49C22⋊#64436C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22×D4×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic, complemented
54C2×C4⋊C4×C37C2211yescharacteristic, complemented
55#102×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic, complemented
59C24×C37—21no—
60C23×D37—21no—
61C2×D4×C37—22no—
62C2×D4×C37—21no—
63C2×D4×C37—41no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—44no—
74C2×C22⋊D37D411yescharacteristic
75C22×Dic37—21no—
76D4×D37—22no—
77D4×D37—41no—
78C2×D148C2311yescharacteristic
79C2×C4×D37—21no—
80C2×C4×D37C2311yescharacteristic
81C2×Dic74—21no—
82C2×Dic74C2311yescharacteristic
83C2×C8×C37—41no—
84C2×C8×C37C2311yescharacteristic
85C2×C8×C37C2311yescharacteristic
86C4⋊C4×C37—21no—
87C4⋊C4×C37C2311yescharacteristic
88C4⋊C4×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92C22⋊Dic37D411yescharacteristic
93#10596940—22no—
94#10596940—41no—
95#10596938—21no—
96#10596938—21no—
97#10596938D411yescharacteristic
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936—21no—
103#10596936—21no—
104#10596936—21no—
105#10596936D411yescharacteristic
106C4×Dic37—21no—
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110#10596930—41no—
111C8×D37—41no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—42no—
115C23×C37—42no—
116C23×C37—81no—
117C23×C37C2×D411yescharacteristic
118C22×D37—21no—
119C22×D37—42no—
120C22×D37—42no—
121C22×D37—81no—
122C22×D37C2×D411yescharacteristic
123D4×C37—21no—
124D4×C37—21no—
125D4×C37—21no—
126D4×C37—42no—
127D4×C37#4112yes—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—81no—
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2411yescharacteristic
135C22⋊D37—42no—
136C22⋊D37—42no—
137C22⋊D37—42no—
138C22⋊D37—42no—
139C22⋊D37—81no—
140C22⋊D37SD1614yescomplemented
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—42no—
145C2×Dic37C2×D411yescharacteristic
146C2×Dic37C2×D411yescharacteristic
147C2×Dic37C2×D411yescharacteristic
148D148—21no—
149D148—21no—
150C4×D37—21no—
151C4×D37—21no—
152C4×D37—81no—
153Dic74—21no—
154Dic74—21no—
155Dic74—81no—
156C8×C37—21no—
157C8×C37—21no—
158#64436—21no—
159#64436—21no—
160C22×C37—21no—
161C22×C37—21no—
162C22×C37—22no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—41no—
168C22×C37—84no—
169C22×C37C2×SD1612yes—
170C22×C37C22×D411yescharacteristic
171C2×D37—21no—
172C2×D37—21no—
173C2×D37—41no—
174C2×D37—41no—
175C2×D37—41no—
176C2×D37—84no—
177C2×D37C2×SD1612yes—
178C4×C37—21no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37C2×#4111yescharacteristic
182C4×C37H(5,𝔽2)11yescharacteristic
183Dic37—21no—
184Dic37—21no—
185Dic37—41no—
186Dic37—41no—
187Dic37—41no—
188Dic37C2×SD1612yes—
189#3295—371nomaximal, Sylow
190C2×C37—22no—
191C2×C37—42no—
192C2×C37—81no—
193C2×C37#54611yescharacteristic
194C2×C37C22×SD1611yescharacteristic
195C2×C37#57611yescharacteristic
196D37—22no—
197D37—81no—
198#554—371no—
199D42—371no—
200#486—371no—
201#481—371no—
202#481—371no—
203#476—371no—
204#465—371no—
205#465—371no—
206#460—371no—
207#450—371no—
208#450—371no—
209C4×SD16—371no—
210C8×D4—371no—
211C2×#102—371no—
212C2×#102D3711yescharacteristic, complemented
213C37#329511yescharacteristic, complemented, Sylow
214C22×D4—371no—
215C22×D4—741no—
216C22×D4C2×D3711yescharacteristic
217C2×SD16—371no—
218C2×SD16—371no—
219C2×SD16—371no—
220C22×C8—371no—
221C22×C8C2×D3711yescharacteristic, complemented
222C4⋊Q8—371no—
223#127—371no—
224#125—741no—
225C22⋊Q8—371no—
226C22⋊Q8—371no—
227C22⋊Q8—741no—
228C22⋊Q8—741no—
229#121—371no—
230#121—371no—
231#121—741no—
232#120—741no—
233#120—741no—
234C4×Q8—371no—
235C4×D4—371no—
236C4×D4—371no—
237C4×D4—741no—
238C2×C4⋊C4—371no—
239C2×C4⋊C4C2×D3711yescharacteristic, complemented
240#106—371no—
241#106—371no—
242#106—371no—
243C4⋊C8—371no—
244#103—371no—
245#102—371no—
246#102—371no—
247#102—371no—
248#102—371no—
249#102—371no—
250#102C2×D3711yescharacteristic
251#102C2×D3711yescharacteristic
252#102C2×D3711yescharacteristic, complemented
253#102C2×D3711yescharacteristic, complemented
254C22⋊C8—371no—
255C22⋊C8—371no—
256C4×C8—371no—
257C24—21no—
258C24—741no—
259C2×Q8—371no—
260C2×Q8—741no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—371no—
265C2×D4—371no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4—741no—
269C2×D4—742no—
270C2×D4—741no—
271C2×D4—741no—
272C2×D4—1481no—
273C2×D4—1484no—
274C2×D4C22×D3711yescharacteristic
275C2×D4C22×D3711yescharacteristic
276C22×C4—21no—
277C22×C4—371no—
278C22×C4—741no—
279C22×C4—741no—
280C22×C4C22×D3711yescharacteristic
281SD16—742no—
282SD16—1481no—
283SD16—1481no—
284C2×C8—41no—
285C2×C8—371no—
286C2×C8—371no—
287C2×C8—1481no—
288C2×C8C22×D3711yescharacteristic
289C2×C8C22×D3711yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—371no—
292C4⋊C4—371no—
293C4⋊C4—371no—
294C4⋊C4—741no—
295C4⋊C4—741no—
296C4⋊C4—741no—
297C4⋊C4—741no—
298C4⋊C4—741no—
299C4⋊C4C22×D3711yescharacteristic
300C4⋊C4C22×D3711yescharacteristic
301C22⋊C4—371no—
302C22⋊C4—371no—
303C22⋊C4—741no—
304C22⋊C4—741no—
305C22⋊C4—741no—
306C22⋊C4—741no—
307C22⋊C4—741no—
308C42—371no—
309C42—741no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—371no—
316C23—2961no—
317C23—741no—
318C23—1482no—
319C23—1482no—
320C23D4×D3711yescharacteristic
321Q8—2961no—
322Q8—741no—
323Q8—741no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—374no—
329D4—2961no—
330D4—741no—
331D4—741no—
332D4—1482no—
333D4—1482no—
334D4—1482no—
335D4—1482no—
336D4#1059696212yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—371no—
343C2×C4—371no—
344C2×C4—371no—
345C2×C4—2961no—
346C2×C4—741no—
347C2×C4—741no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—741no—
351C2×C4—1482no—
352C2×C4D4×D3711yescharacteristic
353C2×C4C23×D3711yescharacteristic
354C8—21no—
355C8—21no—
356C8—741no—
357C8—741no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—372no—
368C22—2964no—
369C22—741no—
370C22—741no—
371C22—1481no—
372C22—1481no—
373C22—1481no—
374C22SD16×D3712yes—
375C22C2×D4×D3711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—372no—
380C4—741no—
381C4—741no—
382C4—1481no—
383C4—1481no—
384C4—1481no—
385C4C2×#1059696211yescharacteristic
386C4#1192458111yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—2961no—
391C2—742no—
392C2#1455817311yescharacteristic
393C2C2×SD16×D3711yescharacteristic
394C2#1455833411yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#102×C37C2
socleC22×C37C22×D4
prime radicalD4×C22⋊D37C2
hypercenterC2×#102D37
hypocenterC37#3295
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. #14558238C2semidirect
3. #14557878C2semidirect
4. #14557851C2semidirect
5. #14557850C2semidirect
6. #14557821C2semidirect
7. #14557762C2semidirect
8. #14557761C2semidirect
9. #14557732C2semidirect
10. #14557685C2semidirect
11. #14557684C2semidirect
12. #14557624C2semidirect
13. C8×C22⋊D37C2semidirect
14. #102×D37C2semidirect
15. C2×#102×C37C2semidirect
18. C2×#10596930C22semidirect
20. C2×#10596940C22semidirect
21. C2×C8×D37C22semidirect
22. #11924535C22semidirect
25. #11924516C22semidirect
27. #11924515C22semidirect
34. #11924501C22semidirect
38. C4⋊C4×D37C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924467C22semidirect
42. #11924465C22semidirect
43. #11924461C22semidirect
44. #11924458C22semidirect
46. #11924457C22semidirect
47. #11924456C22semidirect
48. #11924456C22semidirect
49. C22⋊#64436C22semidirect
50. #11924448C22semidirect
51. C8×Dic37C22semidirect
53. C22×C8×C37C22semidirect
54. C2×C4⋊C4×C37C22semidirect
57. #102×C37C22semidirect
58. #102×C37C22semidirect
140. C22⋊D37SD16semidirect
212. C2×#102D37semidirect
213. C37#3295semidirect
221. C22×C8C2×D37semidirect
239. C2×C4⋊C4C2×D37semidirect
252. #102C2×D37semidirect
253. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582382
D4×C22⋊D372
#145578782
#145578512
#145578502
#145578212
#145577622
#145577612
#145577322
#145576852
#145576842
#145576242
C8×C22⋊D372
#102×D372
C2×#102×C372
#329537