Finite Group Databasebeta

← #18006555

Subgroups — #18006555

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#14558174C211yesmaximal, characteristic, complemented
3#14557894C211yesmaximal, characteristic, complemented
4#14557853C211yesmaximal, characteristic, complemented
5#14557822C211yesmaximal, characteristic, complemented
6#14557787C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557751C211yesmaximal, characteristic, complemented
9#14557681C211yesmaximal, characteristic, complemented
10#14557669C211yesmaximal, characteristic, complemented
11#14557644C211yesmaximal, characteristic, complemented
12#14557601C211yesmaximal, characteristic, complemented
13#14557533C211yesmaximal, characteristic, complemented
14C2×#11924456C211yesmaximal, characteristic, complemented
15C37×#483C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596962—21no—
18C22×D148C2211yescharacteristic
19C2×#10596941C2211yescharacteristic, complemented
20C2×D296C2211yescharacteristic
21C2×D296C2211yescharacteristic
22C2×#10596929C2211yescharacteristic, complemented
23C22×#64436C2211yescharacteristic
24#11924535C2211yescharacteristic, complemented
25#11924525C2211yescharacteristic
26#11924521—21no—
27#11924521—21no—
28#11924519—21no—
29#11924514—21no—
30#11924511—21no—
31#11924511C2211yescharacteristic
32#11924511C2211yescharacteristic, complemented
33#11924510C2211yescharacteristic
34#11924506—21no—
35#11924498C2211yescharacteristic
36#11924498C2211yescharacteristic, complemented
37C4×C22⋊D37C2211yescharacteristic
38C4⋊C4×D37C2211yescharacteristic, complemented
39C22⋊C4×D37—21no—
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924460C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51#11924446C2211yescharacteristic, complemented
52C22⋊Q8×C37C2211yescharacteristic
53C2×C4⋊C4×C37C2211yescharacteristic
54#106×C37C2211yescharacteristic, complemented
55#106×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic
59C23×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37D411yescharacteristic
65#10596966—22no—
66#10596966—41no—
67#10596962—44no—
68C2×D148—22no—
69C2×D148—21no—
70C2×D148—21no—
71C2×D148—21no—
72C2×D148—21no—
73C2×D148—41no—
74C2×D148C2311yescharacteristic
75C2×D148C2311yescharacteristic
76C2×D148C2311yescharacteristic
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37—21no—
80C2×C4×D37—21no—
81C2×C4×D37C2311yescharacteristic
82C2×Dic74—21no—
83C2×C8×C37C2311yescharacteristic
84C2×C8×C37C2311yescharacteristic
85C4⋊C4×C37—21no—
86C4⋊C4×C37—21no—
87C4⋊C4×C37C2311yescharacteristic
88C4⋊C4×C37C2311yescharacteristic
89C4⋊C4×C37C2311yescharacteristic
90C22⋊C4×C37—21no—
91C22⋊Dic37D411yescharacteristic
92#10596941—41no—
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
102#10596936—21no—
103#10596936—21no—
104#10596936D411yescharacteristic
105C4×Dic37C2311yescharacteristic
106C2×#64436—41no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109D296—22no—
110D296—41no—
111#10596929—41no—
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37—21no—
115C22×D37—21no—
116C22×D37—42no—
117C22×D37—42no—
118C22×D37—81no—
119C22×D37C2×D411yescharacteristic
120Q8×C37—21no—
121Q8×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—42no—
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2411yescharacteristic
131C22⋊D37—22no—
132C22⋊D37—42no—
133C2×Dic37—21no—
134C2×Dic37C2×D411yescharacteristic
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137D148—21no—
138D148—21no—
139D148—21no—
140D148—21no—
141D148—21no—
142D148—42no—
143D148—42no—
144D148—42no—
145D148—81no—
146D148#4112yescomplemented
147C4×D37—21no—
148C4×D37—21no—
149C4×D37—42no—
150C4×D37—42no—
151C4×D37—42no—
152C4×D37—81no—
153Dic74—42no—
154C8×C37—21no—
155C8×C37—21no—
156#64436—21no—
157#64436—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37AGL(1,ℤ/8)12yes—
161C22×C37C22×D411yescharacteristic
162C2×D37—21no—
163C2×D37—22no—
164C2×D37—21no—
165C2×D37—21no—
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—41no—
177C4×C37—41no—
178C4×C37—41no—
179C4×C37—41no—
180C4×C37C2×#4111yescharacteristic
181C4×C37H(5,𝔽2)11yescharacteristic
182Dic37—21no—
183Dic37—21no—
184Dic37—21no—
185Dic37—41no—
186#3306—371nomaximal, Sylow
187C2×C37—22no—
188C2×C37#54611yescharacteristic
189C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C37#57711yescharacteristic
191D37—41no—
192D37—42no—
193D37—81no—
194D37—81no—
195#547—371no—
196#546—371no—
197#489—371no—
198#483D3711yescharacteristic, complemented
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#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×M16—371no—
218C22×C8—371no—
219C4⋊Q8—371no—
220#124—371no—
221#123—741no—
222#123—741no—
223#123—741no—
224C22⋊Q8—741no—
225C22⋊Q8C2×D3711yescharacteristic
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
236C2×C22⋊C4—741no—
237#106—371no—
238#106C2×D3711yescharacteristic, complemented
239#106C2×D3711yescharacteristic, complemented
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#102—371no—
250#102—371no—
251C22⋊C8—371no—
252C22⋊C8C2×D3711yescharacteristic
253#97—371no—
254C24—741no—
255#41—742no—
256#41—1484no—
257#41—1481no—
258C2×Q8—741no—
259C2×Q8C22×D3711yescharacteristic
260C2×D4—371no—
261C2×D4—371no—
262C2×D4—371no—
263C2×D4—371no—
264C2×D4—742no—
265C2×D4—741no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4—741no—
269C2×D4—741no—
270C2×D4—1481no—
271C22×C4—21no—
272C22×C4—371no—
273C22×C4—741no—
274C22×C4—741no—
275C22×C4—741no—
276C22×C4—741no—
277C22×C4C22×D3711yescharacteristic
278SD16—1481no—
279D8—742no—
280D8—1481no—
281M16—1481no—
282C2×C8—371no—
283C2×C8—371no—
284C2×C8—1481no—
285C2×C8C22×D3711yescharacteristic
286C2×C8C22×D3711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—371no—
290C4⋊C4—371no—
291C4⋊C4—741no—
292C4⋊C4—741no—
293C4⋊C4C22×D3711yescharacteristic
294C4⋊C4C22×D3711yescharacteristic
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—371no—
308C23—2961no—
309C23—741no—
310C23—741no—
311C23—741no—
312C23—1482no—
313C23—1482no—
314C23D4×D3711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1482no—
318D4—372no—
319D4—2961no—
320D4—742no—
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—21no—
335C2×C4—21no—
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—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—2964no—
356C22—741no—
357C22—741no—
358C22—741no—
359C22—742no—
360C22—1481no—
361C22—1481no—
362C22—1481no—
363C22—1481no—
364C22—1481no—
365C22—1481no—
366C22—1481no—
367C22—1481no—
368C22#1192456312yes—
369C22C2×D4×D3711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—741no—
376C4—741no—
377C4—741no—
378C4—1481no—
379C4#41×D3711yescharacteristic
380C4#1192458211yescharacteristic
381C2—22no—
382C2—2961no—
383C2—2961no—
384C2—1482no—
385C2—1481no—
386C2#1455817511yescharacteristic
387C2C2×#1192456311yescharacteristic
388C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#483C2
socleC22×C37C22×D4
hypercenter#483D37
hypocenterC37#3306
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #14558184C2semidirect
2. #14558174C2semidirect
3. #14557894C2semidirect
4. #14557853C2semidirect
5. #14557822C2semidirect
6. #14557787C2semidirect
7. #14557764C2semidirect
8. #14557751C2semidirect
9. #14557681C2semidirect
10. #14557669C2semidirect
11. #14557644C2semidirect
12. #14557601C2semidirect
13. #14557533C2semidirect
14. C2×#11924456C2semidirect
15. C37×#483C2semidirect
19. C2×#10596941C22semidirect
22. C2×#10596929C22semidirect
24. #11924535C22semidirect
32. #11924511C22semidirect
36. #11924498C22semidirect
38. C4⋊C4×D37C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924460C22semidirect
49. #11924456C22semidirect
50. #11924448C22semidirect
51. #11924446C22semidirect
54. #106×C37C22semidirect
55. #106×C37C22semidirect
56. #103×C37C22semidirect
57. #103×C37C22semidirect
146. D148#41semidirect
198. #483D37semidirect
210. C37#3306semidirect
238. #106C2×D37semidirect
239. #106C2×D37semidirect
242. #103C2×D37semidirect
243. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581842
#145581742
#145578942
#145578532
#145578222
#145577872
#145577642
#145577512
#145576812
#145576692
#145576442
#145576012
#145575332
C2×#119244562
C37×#4832
#330637