Finite Group Databasebeta

← #18006558

Subgroups — #18006558

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#14558184C211yesmaximal, characteristic, complemented
2#14558171C211yesmaximal, characteristic, complemented
3#14557894C211yesmaximal, characteristic, complemented
4#14557862C211yesmaximal, characteristic, complemented
5#14557851C211yesmaximal, characteristic, complemented
6#14557821C211yesmaximal, characteristic, complemented
7#14557786C211yesmaximal, characteristic, complemented
8#14557765C211yesmaximal, characteristic, complemented
9#14557751C211yesmaximal, characteristic, complemented
10#14557678C211yesmaximal, characteristic, complemented
11#14557668C211yesmaximal, characteristic, complemented
12#14557642C211yesmaximal, characteristic, complemented
13#14557602C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#417C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×D4×D37C2211yescharacteristic
18C2×#10596941C2211yescharacteristic, complemented
19C2×D296C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924535C2211yescharacteristic, complemented
23#11924525C2211yescharacteristic
24#11924521—21no—
25#11924519—21no—
26#11924519—21no—
27#11924514—21no—
28#11924512C2211yescharacteristic
29#11924511C2211yescharacteristic
30#11924510C2211yescharacteristic
31#11924510C2211yescharacteristic, complemented
32#11924508—21no—
33#11924504—21no—
34D4×Dic37C2211yescharacteristic
35#11924498C2211yescharacteristic, complemented
36C4×C22⋊D37C2211yescharacteristic
37C4⋊C4×D37C2211yescharacteristic
38C2×#10596938—21no—
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924460C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic, complemented
46#11924457C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic
51#11924446C2211yescharacteristic, complemented
52C2×#41×C37C2211yescharacteristic
53C2×M16×C37C2211yescharacteristic, complemented
54C2×C4⋊C4×C37C2211yescharacteristic, complemented
55#103×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C23×D37—21no—
60#41×C37—22no—
61#41×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37D411yescharacteristic
72C22×Dic37—21no—
73D4×D37—22no—
74D4×D37—41no—
75#10596962—44no—
76C2×D148—21no—
77C2×D148C2311yescharacteristic
78C2×D148C2311yescharacteristic
79C2×C4×D37—21no—
80C2×C4×D37—21no—
81C2×C4×D37C2311yescharacteristic
82C2×Dic74—21no—
83M16×C37—41no—
84C2×C8×C37C2311yescharacteristic
85C2×C8×C37C2311yescharacteristic
86C4⋊C4×C37—21no—
87C4⋊C4×C37C2311yescharacteristic
88C4⋊C4×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90C22⋊Dic37D411yescharacteristic
91#10596941—41no—
92#10596939—22no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98#10596938—21no—
99#10596938—21no—
100#10596938D411yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106#10596936D411yescharacteristic
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110D296—41no—
111C8×D37—41no—
112C23×C37—21no—
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115C22×D37—21no—
116C22×D37—42no—
117C22×D37—42no—
118C22×D37—81no—
119C22×D37C2×D411yescharacteristic
120Q8×C37—21no—
121Q8×C37—21no—
122D4×C37—21no—
123D4×C37—42no—
124D4×C37#4112yescomplemented
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×C37—42no—
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2411yescharacteristic
134C22⋊D37—22no—
135C22⋊D37—42no—
136C22⋊D37—42no—
137C22⋊D37—81no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—81no—
141C2×Dic37C2×D411yescharacteristic
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144D148—21no—
145D148—21no—
146D148—21no—
147D148—21no—
148D148—42no—
149C4×D37—21no—
150C4×D37—21no—
151C4×D37—42no—
152C4×D37—42no—
153Dic74—42no—
154C8×C37—21no—
155C8×C37—21no—
156#64436—21no—
157#64436—21no—
158C22×C37—22no—
159C22×C37—21no—
160C22×C37—21no—
161C22×C37—21no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37C22×D411yescharacteristic
165C2×D37—21no—
166C2×D37—21no—
167C2×D37—41no—
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—41no—
171C2×D37—41no—
172C2×D37—41no—
173C2×D37—84no—
174C2×D37AGL(1,ℤ/8)12yes—
175C4×C37—21no—
176C4×C37—41no—
177C4×C37—41no—
178C4×C37—41no—
179C4×C37C2×#4111yescharacteristic
180C4×C37H(5,𝔽2)11yescharacteristic
181Dic37—21no—
182Dic37—21no—
183Dic37—21no—
184Dic37—41no—
185Dic37—41no—
186#3306—371nomaximal, Sylow
187C2×C37—42no—
188C2×C37—41no—
189C2×C37#54611yescharacteristic
190C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C37#57711yescharacteristic
192D37—22no—
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#435—371no—
208#417D3711yescharacteristic, complemented
209C2×#102—371no—
210C37#330611yescharacteristic, complemented, Sylow
211C2×#41—741no—
212C2×#41C2×D3711yescharacteristic
213C22×D4—371no—
214C2×SD16—371no—
215C2×D8—371no—
216C2×D8—371no—
217C2×M16C2×D3711yescharacteristic, complemented
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—371no—
229#121—741no—
230#120—741no—
231C4×D4—371no—
232C4×D4—371no—
233C4×D4—371no—
234C2×C4⋊C4—371no—
235C2×C4⋊C4C2×D3711yescharacteristic, complemented
236C2×C22⋊C4—741no—
237#106—371no—
238#106—371no—
239#106—371no—
240C4⋊C8—371no—
241#103—371no—
242#103C2×D3711yescharacteristic, complemented
243#103C2×D3711yescharacteristic, complemented
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⋊C8—371no—
253#97—371no—
254C24—741no—
255#41—22no—
256#41—41no—
257#41—1484no—
258C2×Q8—741no—
259C2×Q8C22×D3711yescharacteristic
260C2×D4—21no—
261C2×D4—371no—
262C2×D4—371no—
263C2×D4—371no—
264C2×D4—741no—
265C2×D4—741no—
266C2×D4—741no—
267C2×D4—742no—
268C2×D4—741no—
269C2×D4—1481no—
270C2×D4C22×D3711yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—371no—
274C22×C4—741no—
275C22×C4—741no—
276C22×C4—741no—
277C22×C4C22×D3711yescharacteristic
278SD16—1481no—
279D8—742no—
280D8—1481no—
281M16—41no—
282C2×C8—371no—
283C2×C8—371no—
284C2×C8—1481no—
285C2×C8C22×D3711yescharacteristic
286C2×C8C22×D3711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—371no—
289C4⋊C4—371no—
290C4⋊C4—371no—
291C4⋊C4—741no—
292C4⋊C4—741no—
293C4⋊C4—741no—
294C4⋊C4C22×D3711yescharacteristic
295C4⋊C4C22×D3711yescharacteristic
296C22⋊C4—371no—
297C22⋊C4—371no—
298C22⋊C4—741no—
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—371no—
309C23—2961no—
310C23—741no—
311C23—741no—
312C23—1482no—
313C23—1482no—
314C23D4×D3711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1482no—
318D4—21no—
319D4—42no—
320D4—2961no—
321D4—742no—
322D4—741no—
323D4—741no—
324D4—741no—
325D4—741no—
326D4—1482no—
327D4—1482no—
328D4—1482no—
329D4#1059696212yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—371no—
338C2×C4—371no—
339C2×C4—371no—
340C2×C4—2961no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—741no—
344C2×C4—741no—
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—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—372no—
360C22—2964no—
361C22—741no—
362C22—741no—
363C22—1481no—
364C22—1481no—
365C22—1481no—
366C22—1481no—
367C22—1481no—
368C22—1481no—
369C22C2×D4×D3711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—741no—
375C4—741no—
376C4—741no—
377C4—1481no—
378C4—1481no—
379C4C2×#1059696211yescharacteristic
380C4#1192458111yescharacteristic
381C2—41no—
382C2—42no—
383C2—2961no—
384C2—2961no—
385C2—742no—
386C2#1455817311yescharacteristic
387C2AGL(1,ℤ/8)×D3711yescharacteristic
388C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#417C2
socleC22×C37C22×D4
hypercenter#417D37
hypocenterC37#3306
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #14558184C2semidirect
2. #14558171C2semidirect
3. #14557894C2semidirect
4. #14557862C2semidirect
5. #14557851C2semidirect
6. #14557821C2semidirect
7. #14557786C2semidirect
8. #14557765C2semidirect
9. #14557751C2semidirect
10. #14557678C2semidirect
11. #14557668C2semidirect
12. #14557642C2semidirect
13. #14557602C2semidirect
14. #102×D37C2semidirect
15. C37×#417C2semidirect
18. C2×#10596941C22semidirect
22. #11924535C22semidirect
31. #11924510C22semidirect
35. #11924498C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924467C22semidirect
42. #11924465C22semidirect
43. #11924460C22semidirect
45. #11924458C22semidirect
49. C22⋊#64436C22semidirect
51. #11924446C22semidirect
53. C2×M16×C37C22semidirect
54. C2×C4⋊C4×C37C22semidirect
55. #103×C37C22semidirect
56. #103×C37C22semidirect
124. D4×C37#41semidirect
208. #417D37semidirect
210. C37#3306semidirect
217. C2×M16C2×D37semidirect
235. C2×C4⋊C4C2×D37semidirect
242. #103C2×D37semidirect
243. #103C2×D37semidirect
329. D4#10596962semidirect

Maximal subgroups

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

subgroupindex
#145581842
#145581712
#145578942
#145578622
#145578512
#145578212
#145577862
#145577652
#145577512
#145576782
#145576682
#145576422
#145576022
#102×D372
C37×#4172
#330637