Finite Group Databasebeta

← #18006561

Subgroups — #18006561

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#14558183C211yesmaximal, characteristic, complemented
2#14558177C211yesmaximal, characteristic, complemented
3#14557891C211yesmaximal, characteristic, complemented
4#14557864C211yesmaximal, characteristic, complemented
5#14557850C211yesmaximal, characteristic, complemented
6#14557821C211yesmaximal, characteristic, complemented
7#14557783C211yesmaximal, characteristic, complemented
8#14557760C211yesmaximal, characteristic, complemented
9#14557746C211yesmaximal, characteristic, complemented
10#14557675C211yesmaximal, characteristic, complemented
11#14557645C211yesmaximal, characteristic, complemented
12#14557601C211yesmaximal, characteristic, complemented
13#14557531C211yesmaximal, characteristic, complemented
14C2×#11924457C211yesmaximal, characteristic, complemented
15C37×#447C211yesmaximal, characteristic, complemented
16C2×#10596964—21no—
17C2×#10596964C2211yescharacteristic
18C2×#10596940C2211yescharacteristic, complemented
19C2×#10596929C2211yescharacteristic, complemented
20C22×#64436C2211yescharacteristic
21#11924535C2211yescharacteristic, complemented
22#11924523C2211yescharacteristic
23#11924518—21no—
24#11924517—21no—
25#11924517—21no—
26#11924515C2211yescharacteristic
27#11924513—21no—
28#11924508—21no—
29#11924507C2211yescharacteristic
30#11924507C2211yescharacteristic, complemented
31#11924505—21no—
32D4×Dic37C2211yescharacteristic
33D4×Dic37C2211yescharacteristic, complemented
34C4×C22⋊D37C2211yescharacteristic
35C2×C4⋊Dic37C2211yescharacteristic
36C4⋊C4×D37C2211yescharacteristic, complemented
37C2×C22⋊Dic37—21no—
38#11924468C2211yescharacteristic, complemented
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924459C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51#11924446C2211yescharacteristic, complemented
52C22×D4×C37C2211yescharacteristic
53C2×D8×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C24×C37—21no—
60C2×D4×C37—22no—
61C2×D4×C37—21no—
62C2×D4×C37—21no—
63C2×D4×C37—41no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C2×D4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37D411yescharacteristic
72C22×Dic37—21no—
73C22×Dic37—21no—
74C22×Dic37—21no—
75C22×Dic37—21no—
76#10596964—22no—
77#10596964—41no—
78#10596964—44no—
79C2×C4×D37—21no—
80C2×C4×D37C2311yescharacteristic
81C2×Dic74—21no—
82C2×Dic74C2311yescharacteristic
83D8×C37—22no—
84D8×C37—41no—
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C4⋊C4×C37C2311yescharacteristic
88C22⋊C4×C37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92C22⋊Dic37—21no—
93C22⋊Dic37—21no—
94C22⋊Dic37—21no—
95C22⋊Dic37—21no—
96C22⋊Dic37D411yescharacteristic
97#10596940—41no—
98#10596938D411yescharacteristic
99C4⋊Dic37—21no—
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106#10596936D411yescharacteristic
107C4×Dic37C2311yescharacteristic
108C2×#64436—41no—
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111#10596929—41no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—21no—
115C23×C37—42no—
116C23×C37—42no—
117C23×C37—81no—
118C23×C37C2×D411yescharacteristic
119C22×D37C2×D411yescharacteristic
120D4×C37—21no—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—21no—
124D4×C37—21no—
125D4×C37—42no—
126D4×C37—42no—
127D4×C37#4112yescomplemented
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2411yescharacteristic
133C22⋊D37—22no—
134C22⋊D37—42no—
135C22⋊D37—42no—
136C22⋊D37—81no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—42no—
142C2×Dic37—42no—
143C2×Dic37—42no—
144C2×Dic37—81no—
145C2×Dic37C2×D411yescharacteristic
146C2×Dic37C2×D411yescharacteristic
147C2×Dic37C2×D411yescharacteristic
148C4×D37—21no—
149C4×D37—21no—
150C4×D37—42no—
151Dic74—21no—
152Dic74—21no—
153Dic74—42no—
154C8×C37—21no—
155C8×C37—21no—
156#64436—21no—
157#64436—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—22no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—84no—
170C22×C37AGL(1,ℤ/8)12yes—
171C22×C37C22×D411yescharacteristic
172C2×D37—21no—
173C2×D37—21no—
174C2×D37—21no—
175C4×C37—21no—
176C4×C37—41no—
177C4×C37C2×#4111yescharacteristic
178C4×C37H(5,𝔽2)11yescharacteristic
179Dic37—21no—
180Dic37—21no—
181Dic37—21no—
182Dic37—41no—
183Dic37—41no—
184Dic37—41no—
185Dic37—41no—
186#3306—371nomaximal, Sylow
187C2×C37—22no—
188C2×C37—42no—
189C2×C37—81no—
190C2×C37—81no—
191C2×C37#54611yescharacteristic
192C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C37#57711yescharacteristic
194D37—41no—
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#447D3711yescharacteristic, complemented
206#442—371no—
207#435—371no—
208#417—371no—
209C2×#102—371no—
210C37#330611yescharacteristic, complemented, Sylow
211C2×#41—371no—
212C2×#41—741no—
213C22×D4C2×D3711yescharacteristic
214C2×SD16—371no—
215C2×D8C2×D3711yescharacteristic
216C2×D8C2×D3711yescharacteristic
217C2×M16—371no—
218C22×C8—371no—
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—741no—
229#121C2×D3711yescharacteristic
230#120—741no—
231C4×D4—371no—
232C4×D4—371no—
233C4×D4—371no—
234C2×C4⋊C4—371no—
235C2×C4⋊C4—371no—
236C2×C22⋊C4—741no—
237#106—371no—
238#106—371no—
239#106—371no—
240C4⋊C8—371no—
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#102C2×D3711yescharacteristic
250#102C2×D3711yescharacteristic
251C22⋊C8—371no—
252C22⋊C8C2×D3711yescharacteristic
253#97—371no—
254C24—21no—
255#41—742no—
256#41—1481no—
257#41—1484no—
258C2×Q8—371no—
259C2×Q8—741no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—371no—
265C2×D4—741no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4C22×D3711yescharacteristic
269C2×D4C22×D3711yescharacteristic
270C2×D4C22×D3711yescharacteristic
271C22×C4—371no—
272C22×C4—741no—
273C22×C4—741no—
274C22×C4—741no—
275C22×C4—741no—
276C22×C4—741no—
277C22×C4C22×D3711yescharacteristic
278SD16—1481no—
279D8—22no—
280D8—41no—
281M16—1481no—
282C2×C8—371no—
283C2×C8—371no—
284C2×C8—1481no—
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⋊C4C22×D3711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—371no—
298C22⋊C4—371no—
299C22⋊C4—741no—
300C22⋊C4—741no—
301C22⋊C4—741no—
302C22⋊C4—741no—
303C22⋊C4—741no—
304C22⋊C4—741no—
305C22⋊C4—741no—
306C42—371no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—371no—
314C23D4×D3711yescharacteristic
315Q8—741no—
316Q8—741no—
317Q8—1482no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—2961no—
326D4—742no—
327D4—1482no—
328D4—1482no—
329D4#1059696412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—371no—
334C2×C4—371no—
335C2×C4—371no—
336C2×C4—2961no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—741no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—1482no—
344C2×C4—1482no—
345C2×C4—1482no—
346C2×C4—1482no—
347C2×C4D4×D3711yescharacteristic
348C2×C4C23×D3711yescharacteristic
349C8—21no—
350C8—21no—
351C8—741no—
352C8—741no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—741no—
366C22—741no—
367C22—741no—
368C22#1192456012yes—
369C22C2×D4×D3711yescharacteristic
370C4—21no—
371C4—41no—
372C4—741no—
373C4—741no—
374C4—741no—
375C4—1481no—
376C4—1481no—
377C4—1481no—
378C4—1481no—
379C4C2×#1059696411yescharacteristic
380C4#1192458111yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—1481no—
386C2#1455817011yescharacteristic
387C2C2×#1192456011yescharacteristic
388C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#447C2
socleC22×C37C22×D4
hypercenter#447D37
hypocenterC37#3306
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14558183C2semidirect
2. #14558177C2semidirect
3. #14557891C2semidirect
4. #14557864C2semidirect
5. #14557850C2semidirect
6. #14557821C2semidirect
7. #14557783C2semidirect
8. #14557760C2semidirect
9. #14557746C2semidirect
10. #14557675C2semidirect
11. #14557645C2semidirect
12. #14557601C2semidirect
13. #14557531C2semidirect
14. C2×#11924457C2semidirect
15. C37×#447C2semidirect
18. C2×#10596940C22semidirect
19. C2×#10596929C22semidirect
21. #11924535C22semidirect
30. #11924507C22semidirect
33. D4×Dic37C22semidirect
36. C4⋊C4×D37C22semidirect
38. #11924468C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924461C22semidirect
43. #11924461C22semidirect
44. #11924459C22semidirect
49. #11924457C22semidirect
50. #11924448C22semidirect
51. #11924446C22semidirect
127. D4×C37#41semidirect
205. #447D37semidirect
210. C37#3306semidirect
329. D4#10596964semidirect

Maximal subgroups

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

subgroupindex
#145581832
#145581772
#145578912
#145578642
#145578502
#145578212
#145577832
#145577602
#145577462
#145576752
#145576452
#145576012
#145575312
C2×#119244572
C37×#4472
#330637