Finite Group Databasebeta

← #18006559

Subgroups — #18006559

Order 4736.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558187C211yesmaximal, characteristic, complemented
2#14558179C211yesmaximal, characteristic, complemented
3#14557893C211yesmaximal, characteristic, complemented
4#14557864C211yesmaximal, characteristic, complemented
5#14557852C211yesmaximal, characteristic, complemented
6#14557824C211yesmaximal, characteristic, complemented
7#14557786C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557749C211yesmaximal, characteristic, complemented
10#14557680C211yesmaximal, characteristic, complemented
11#14557669C211yesmaximal, characteristic, complemented
12#14557646C211yesmaximal, characteristic, complemented
13#14557535C211yesmaximal, characteristic, complemented
14C2×#11924458C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596964—21no—
18C22×D148C2211yescharacteristic
19C2×#10596930C2211yescharacteristic, complemented
20C2×D296C2211yescharacteristic
21C2×D296C2211yescharacteristic
22#11924536C2211yescharacteristic, complemented
23#11924524C2211yescharacteristic
24#11924521—21no—
25#11924520—21no—
26#11924520—21no—
27#11924516—21no—
28#11924515C2211yescharacteristic
29#11924510C2211yescharacteristic
30#11924510C2211yescharacteristic
31#11924510C2211yescharacteristic, complemented
32#11924509—21no—
33#11924504—21no—
34C4×D148C2211yescharacteristic
35C4×D148C2211yescharacteristic, complemented
36C2×C4⋊Dic37C2211yescharacteristic
37C2×C4⋊Dic37C2211yescharacteristic, complemented
38C22⋊C4×D37—21no—
39#11924468C2211yescharacteristic, complemented
40#11924468C2211yescharacteristic, complemented
41#11924468C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic, complemented
52C2×M16×C37C2211yescharacteristic, complemented
53C22×C8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55C4⋊C8×C37C2211yescharacteristic, complemented
56C22⋊C8×C37C2211yescharacteristic
57C22⋊C8×C37C2211yescharacteristic, complemented
58#97×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×D4×C37D411yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C22×Dic37—21no—
69#10596964—44no—
70#10596962—22no—
71#10596962—41no—
72C2×D148—22no—
73C2×D148—21no—
74C2×D148—41no—
75C2×D148C2311yescharacteristic
76C2×D148C2311yescharacteristic
77C2×D148C2311yescharacteristic
78C2×C4×D37—21no—
79C2×C4×D37—21no—
80C2×C4×D37—21no—
81C2×Dic74—21no—
82C2×Dic74C2311yescharacteristic
83M16×C37—41no—
84C2×C8×C37—41no—
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C2×C8×C37C2311yescharacteristic
88C2×C8×C37C2311yescharacteristic
89C4⋊C4×C37D411yescharacteristic
90C22⋊C4×C37D411yescharacteristic
91C22⋊C4×C37D411yescharacteristic
92C42×C37C2311yescharacteristic
93C22⋊Dic37—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98#10596938—21no—
99#10596938—21no—
100#10596938—21no—
101C4⋊Dic37—21no—
102C4⋊Dic37—21no—
103C4⋊Dic37—21no—
104C4⋊Dic37C2311yescharacteristic
105C4⋊Dic37C2311yescharacteristic
106C4⋊Dic37C2311yescharacteristic
107C4⋊Dic37C2311yescharacteristic
108#10596936—21no—
109D296—22no—
110D296—41no—
111#10596930—41no—
112C23×C37C2×D411yescharacteristic
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115C22×D37—21no—
116C22×D37—21no—
117C22×D37—42no—
118C22×D37—42no—
119C22×D37—81no—
120D4×C37—22no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—42no—
131C22⋊D37—42no—
132C22⋊D37—42no—
133C22⋊D37—81no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—42no—
140C2×Dic37—42no—
141D148—21no—
142D148—21no—
143D148—21no—
144D148—21no—
145D148—21no—
146D148—42no—
147D148#4112yescomplemented
148C4×D37—42no—
149C4×D37—42no—
150C4×D37—81no—
151Dic74—21no—
152Dic74—21no—
153Dic74—42no—
154C8×C37—21no—
155C8×C37—21no—
156C8×C37—21no—
157C8×C37—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—21no—
161C22×C37—21no—
162C22×C37—21no—
163C22×C37AGL(1,ℤ/8)12yes—
164C22×C37C22×D411yescharacteristic
165C2×D37—22no—
166C2×D37—41no—
167C2×D37—41no—
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—41no—
171C2×D37—41no—
172C2×D37—41no—
173C2×D37—41no—
174C2×D37—84no—
175C4×C37—21no—
176C4×C37—21no—
177C4×C37—21no—
178C4×C37—21no—
179C4×C37C2×#4111yescharacteristic
180C4×C37H(5,𝔽2)11yescharacteristic
181Dic37—41no—
182Dic37—41no—
183Dic37—41no—
184Dic37—41no—
185Dic37—41no—
186#3306—371nomaximal, Sylow
187C2×C37—22no—
188C2×C37—41no—
189C2×C37#54611yescharacteristic
190C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C37#57711yescharacteristic
192D37—42no—
193D37—81no—
194D37—81no—
195#547—371no—
196#546—371no—
197#489—371no—
198#483—371no—
199#481—371no—
200#476—371no—
201#469—371no—
202#465—371no—
203#463—371no—
204#449—371no—
205#447—371no—
206#442—371no—
207#435D3711yescharacteristic, complemented
208#417—371no—
209C2×#102—371no—
210C37#330611yescharacteristic, complemented, Sylow
211C2×#41—371no—
212C2×#41—741no—
213C22×D4—371no—
214C2×SD16—371no—
215C2×D8—371no—
216C2×D8—371no—
217C2×M16C2×D3711yescharacteristic, complemented
218C22×C8C2×D3711yescharacteristic
219C4⋊Q8—371no—
220#124—371no—
221#123—741no—
222#123—741no—
223#123—741no—
224C22⋊Q8—371no—
225C22⋊Q8—741no—
226#121—371no—
227#121—371no—
228#121—371no—
229#121—741no—
230#120—741no—
231C4×D4—371no—
232C4×D4—371no—
233C4×D4C2×D3711yescharacteristic
234C2×C4⋊C4—371no—
235C2×C4⋊C4—371no—
236C2×C22⋊C4—741no—
237#106—371no—
238#106—371no—
239#106—371no—
240C4⋊C8C2×D3711yescharacteristic, complemented
241#103—371no—
242#103—371no—
243#103—371no—
244#102—371no—
245#102—371no—
246#102—371no—
247#102—371no—
248#102—371no—
249#102—371no—
250#102—371no—
251C22⋊C8C2×D3711yescharacteristic
252C22⋊C8C2×D3711yescharacteristic, complemented
253#97C2×D3711yescharacteristic, complemented
254C24—741no—
255#41—742no—
256#41—1481no—
257#41—1484no—
258C2×Q8—371no—
259C2×Q8—741no—
260C2×D4—371no—
261C2×D4—371no—
262C2×D4—371no—
263C2×D4—742no—
264C2×D4—741no—
265C2×D4—741no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4—741no—
269C2×D4—1481no—
270C2×D4D14811yescharacteristic
271C22×C4—741no—
272C22×C4—741no—
273C22×C4—741no—
274C22×C4—741no—
275C22×C4—741no—
276C22×C4C22×D3711yescharacteristic
277C22×C4C22×D3711yescharacteristic
278SD16—1481no—
279D8—742no—
280D8—1481no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D3711yescharacteristic
284C2×C8C22×D3711yescharacteristic
285C2×C8C22×D3711yescharacteristic
286C2×C8C22×D3711yescharacteristic
287C4⋊C4—371no—
288C4⋊C4—371no—
289C4⋊C4—371no—
290C4⋊C4—371no—
291C4⋊C4—741no—
292C4⋊C4—741no—
293C4⋊C4—741no—
294C4⋊C4—741no—
295C4⋊C4D14811yescharacteristic
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4—741no—
300C22⋊C4—741no—
301C22⋊C4—741no—
302C22⋊C4—741no—
303C22⋊C4—741no—
304C22⋊C4D14811yescharacteristic
305C22⋊C4D14811yescharacteristic
306C42C22×D3711yescharacteristic
307C23—2961no—
308C23—741no—
309C23—741no—
310C23—741no—
311C23—1482no—
312C23—1482no—
313C23C2×D14811yescharacteristic
314C23C2×D14811yescharacteristic
315Q8—741no—
316Q8—741no—
317Q8—1482no—
318D4—22no—
319D4—372no—
320D4—2961no—
321D4—741no—
322D4—741no—
323D4—741no—
324D4—741no—
325D4—741no—
326D4—1482no—
327D4—1482no—
328D4—1482no—
329D4—1482no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2961no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—1482no—
341C2×C4—1482no—
342C2×C4—1482no—
343C2×C4—1482no—
344C2×C4C2×D14811yescharacteristic
345C2×C4C2×D14811yescharacteristic
346C2×C4C2×D14811yescharacteristic
347C2×C4C2×D14811yescharacteristic
348C2×C4C23×D3711yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—2964no—
359C22—742no—
360C22—1481no—
361C22—1481no—
362C22—1481no—
363C22—1481no—
364C22—1481no—
365C22—1481no—
366C22—1481no—
367C22—1481no—
368C22#1192456412yes—
369C22C22×D14811yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—1481no—
375C4—1481no—
376C4—1481no—
377C4—1481no—
378C4—1481no—
379C4#41×D3711yescharacteristic
380C4#1192458111yescharacteristic
381C2—22no—
382C2—41no—
383C2—2961no—
384C2—2961no—
385C2—1482no—
386C2#1455817811yescharacteristic
387C2C2×#1192456411yescharacteristic
388C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
hypercenter#435D37
hypocenterC37#3306
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14558187C2semidirect
2. #14558179C2semidirect
3. #14557893C2semidirect
4. #14557864C2semidirect
5. #14557852C2semidirect
6. #14557824C2semidirect
7. #14557786C2semidirect
8. #14557762C2semidirect
9. #14557749C2semidirect
10. #14557680C2semidirect
11. #14557669C2semidirect
12. #14557646C2semidirect
13. #14557535C2semidirect
14. C2×#11924458C2semidirect
15. C37×#435C2semidirect
19. C2×#10596930C22semidirect
22. #11924536C22semidirect
31. #11924510C22semidirect
35. C4×D148C22semidirect
37. C2×C4⋊Dic37C22semidirect
39. #11924468C22semidirect
40. #11924468C22semidirect
41. #11924468C22semidirect
42. #11924461C22semidirect
43. #11924461C22semidirect
44. #11924461C22semidirect
51. #11924458C22semidirect
52. C2×M16×C37C22semidirect
55. C4⋊C8×C37C22semidirect
57. C22⋊C8×C37C22semidirect
58. #97×C37C22semidirect
147. D148#41semidirect
207. #435D37semidirect
210. C37#3306semidirect
217. C2×M16C2×D37semidirect
240. C4⋊C8C2×D37semidirect
252. C22⋊C8C2×D37semidirect
253. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581872
#145581792
#145578932
#145578642
#145578522
#145578242
#145577862
#145577622
#145577492
#145576802
#145576692
#145576462
#145575352
C2×#119244582
C37×#4352
#330637