Finite Group Databasebeta

← #463×D37 #18004016

Subgroups — #463×D37 #18004016

Order 4736.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D37C211yesmaximal, characteristic, complemented
2C2×D8×D37C211yesmaximal, characteristic
3#124×D37C211yesmaximal, characteristic, complemented
4C4×D4×D37C211yesmaximal, characteristic, complemented
5#14557751C211yesmaximal, characteristic, complemented
6#14557750C211yesmaximal, characteristic, complemented
7#14557749C211yesmaximal, characteristic, complemented
8#14557748C211yesmaximal, characteristic, complemented
9#14557747C211yesmaximal, characteristic, complemented
10#14557746C211yesmaximal, characteristic, complemented
11#14557745C211yesmaximal, characteristic, complemented
12C4⋊C8×D37C211yesmaximal, characteristic, complemented
13#103×D37C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19C22×C4×D37—21no—
20C2×#10596930C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic, complemented
22C2×#10596941C2211yescharacteristic, complemented
23SD16×D37—24no—
24C2×D296C2211yescharacteristic
25C2×#10596939C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27D8×D37—24no—
28C2×C8×D37C2211yescharacteristic
29C2×C8×D37C2211yescharacteristic
30#11924525C2211yescharacteristic, complemented
31#11924524C2211yescharacteristic, complemented
32#11924523C2211yescharacteristic, complemented
33#11924522—21no—
34#11924522—21no—
35C4×D148C2211yescharacteristic, complemented
36D4×Dic37C2211yescharacteristic, complemented
37#11924498C2211yescharacteristic, complemented
38C4×C22⋊D37—21no—
39#11924496—21no—
40C4⋊C4×D37C2211yescharacteristic
41C22⋊C4×D37—21no—
42C22⋊C4×D37—21no—
43C22⋊C4×D37—21no—
44C42×D37C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic, complemented
46#11924465C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924460C2211yescharacteristic, complemented
50#11924459C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic, complemented
52#11924457C2211yescharacteristic, complemented
53#11924456C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic, complemented
55C2×D8×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic, complemented
57C4×D4×C37C2211yescharacteristic, complemented
58C4⋊C8×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37—21no—
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C22×Dic37—21no—
70Q8×D37—22no—
71Q8×D37—22no—
72D4×D37—22no—
73D4×D37—22no—
74D4×D37—22no—
75D4×D37D414yes—
76C2×D148C2311yescharacteristic
77C2×D148C2311yescharacteristic
78C2×C4×D37—21no—
79C2×C4×D37—21no—
80C2×C4×D37—21no—
81C2×C4×D37—21no—
82C2×C4×D37—44no—
83C2×C4×D37D411yescharacteristic
84C2×C4×D37D411yescharacteristic
85C2×C4×D37C2311yescharacteristic
86C2×Dic74—21no—
87C2×Dic74C2311yescharacteristic
88SD16×C37—22no—
89D8×C37—22no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C42×C37C2311yescharacteristic
97C22⋊Dic37—21no—
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100#10596941—22no—
101#10596940—22no—
102#10596939—22no—
103#10596939—22no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110C4⋊Dic37C2311yescharacteristic
111#10596936—21no—
112C4×Dic37D411yescharacteristic
113C4×Dic37D411yescharacteristic
114C4×Dic37C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116C2×#64436C2311yescharacteristic
117D296—22no—
118#10596930—22no—
119C8×D37—22no—
120C8×D37—22no—
121C23×C37—21no—
122C23×C37—21no—
123C22×D37—21no—
124C22×D37—24no—
125C22×D37—21no—
126C22×D37—42no—
127C22×D37—42no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37C2×D411yescharacteristic
132Q8×C37—21no—
133Q8×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37C2×D412yes—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—42no—
141C2×C4×C37C2×D411yescharacteristic
142C2×C4×C37C2×D411yescharacteristic
143C2×C4×C37C2411yescharacteristic
144C22⋊D37—24no—
145C22⋊D37—42no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—42no—
149C2×Dic37C2×D411yescharacteristic
150C2×Dic37C2×D411yescharacteristic
151C2×Dic37C2×D411yescharacteristic
152D148—21no—
153D148—21no—
154D148—21no—
155D148C2×D412yes—
156C4×D37—22no—
157C4×D37—22no—
158C4×D37—42no—
159C4×D37—42no—
160C4×D37—42no—
161C4×D37—42no—
162C4×D37C2×D412yes—
163C4×D37#4112yes—
164Dic74—21no—
165Dic74—21no—
166Dic74—42no—
167C8×C37—21no—
168C8×C37—21no—
169#64436—21no—
170#64436—21no—
171C22×C37—22no—
172C22×C37—41no—
173C22×C37—41no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37C22×D411yescharacteristic
178C2×D37—22no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—48no—
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—84no—
186C2×D37#12112yes—
187C2×D37#13512yes—
188C2×D37AGL(1,ℤ/8)12yes—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—41no—
192C4×C37—41no—
193C4×C37C22×D411yescharacteristic
194C4×C37C2×#4111yescharacteristic
195Dic37—21no—
196Dic37—21no—
197Dic37—41no—
198Dic37—41no—
199Dic37#12112yes—
200C2×#463—371nomaximal, Sylow
201C2×C37—42no—
202C2×C37—81no—
203C2×C37C2×#12111yescharacteristic
204C2×C37C2×#13511yescharacteristic
205C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
206D37—42no—
207D37—81no—
208D37#46314yesdirect product factor
209C22×SD16—371no—
210C22×D8—371no—
211C2×#124—371no—
212C2×C4×D4—371no—
213#463—371no—
214#463—371no—
215#463—371no—
216#463—371no—
217#463—371no—
218#463—371no—
219#463—371no—
220#463D3711yescharacteristic, direct product factor
221C2×C4⋊C8—371no—
222C2×#103—371no—
223C2×#102—371no—
224C37C2×#46311yescharacteristic, complemented, Sylow
225C22×Q8—371no—
226C22×D4—371no—
227C22×D4—371no—
228C23×C4—741no—
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16—744no—
233C2×SD16C2×D3711yescharacteristic, complemented
234C2×D8—371no—
235C2×D8—371no—
236C2×D8—371no—
237C2×D8—744no—
238C2×D8C2×D3711yescharacteristic
239C22×C8—371no—
240C22×C8—371no—
241#124—371no—
242#124—371no—
243#124—371no—
244#124—741no—
245#124—741no—
246#124C2×D3711yescharacteristic, complemented
247C4×D4—371no—
248C4×D4—371no—
249C4×D4—371no—
250C4×D4—741no—
251C4×D4—741no—
252C4×D4C2×D3711yescharacteristic, complemented
253C2×C4⋊C4—371no—
254C2×C22⋊C4—741no—
255C2×C22⋊C4—741no—
256C2×C22⋊C4—741no—
257C2×C42—371no—
258C4⋊C8—371no—
259C4⋊C8—371no—
260C4⋊C8—371no—
261C4⋊C8C2×D3711yescharacteristic, complemented
262#103—371no—
263#103—371no—
264#103—371no—
265#103C2×D3711yescharacteristic, complemented
266#102—371no—
267#102—371no—
268#102—371no—
269#102C2×D3711yescharacteristic, complemented
270C24—741no—
271C24—741no—
272C2×Q8—371no—
273C2×Q8—741no—
274C2×Q8—742no—
275C2×Q8—742no—
276C2×Q8C22×D3711yescharacteristic
277C2×D4—374no—
278C2×D4—371no—
279C2×D4—371no—
280C2×D4—742no—
281C2×D4—742no—
282C2×D4—742no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4C22×D3711yescharacteristic
286C2×D4C22×D3711yescharacteristic
287C22×C4—21no—
288C22×C4—371no—
289C22×C4—371no—
290C22×C4—371no—
291C22×C4—741no—
292C22×C4—741no—
293C22×C4—741no—
294C22×C4—741no—
295C22×C4—741no—
296C22×C4—1484no—
297SD16—22no—
298SD16—742no—
299SD16—742no—
300SD16—742no—
301D8—22no—
302D8—742no—
303D8—742no—
304D8—742no—
305C2×C8—371no—
306C2×C8—371no—
307C2×C8—742no—
308C2×C8—742no—
309C2×C8C22×D3711yescharacteristic
310C2×C8C22×D3711yescharacteristic
311C4⋊C4—371no—
312C4⋊C4—741no—
313C4⋊C4C22×D3711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C42—371no—
327C42—371no—
328C42—371no—
329C42C22×D3711yescharacteristic
330C23—21no—
331C23—21no—
332C23—371no—
333C23—744no—
334C23—741no—
335C23—741no—
336C23—1482no—
337C23—1482no—
338C23—1482no—
339C23—1482no—
340C23—1482no—
341Q8—21no—
342Q8—21no—
343Q8—741no—
344Q8—741no—
345Q8—1482no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—372no—
350D4—744no—
351D4—741no—
352D4—741no—
353D4—741no—
354D4—1482no—
355D4D4×D3712yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—371no—
360C2×C4—372no—
361C2×C4—372no—
362C2×C4—371no—
363C2×C4—371no—
364C2×C4—742no—
365C2×C4—742no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—1482no—
369C2×C4—1482no—
370C2×C4—1482no—
371C2×C4—1482no—
372C2×C4—1482no—
373C2×C4D4×D3711yescharacteristic
374C2×C4D4×D3711yescharacteristic
375C2×C4C23×D3711yescharacteristic
376C8—21no—
377C8—21no—
378C8—741no—
379C8—741no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—372no—
387C22—372no—
388C22—372no—
389C22—2964no—
390C22—742no—
391C22—1488no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22—1481no—
396C22—1481no—
397C22C2×D4×D3711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—372no—
403C4—741no—
404C4—741no—
405C4—1481no—
406C4—1481no—
407C4C2×D4×D3711yescharacteristic
408C4#41×D3711yescharacteristic
409C2—42no—
410C2—81no—
411C2—374no—
412C2—2961no—
413C2—1482no—
414C2#121×D3711yescharacteristic
415C2#135×D3711yescharacteristic
416C2AGL(1,ℤ/8)×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#463C2
socleC22×C37C22×D4
prime radicalC2×D8×D37C2
hypercenter#463D37
hypocenterC37C2×#463
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D37C2semidirect
3. #124×D37C2semidirect
4. C4×D4×D37C2semidirect
5. #14557751C2semidirect
6. #14557750C2semidirect
7. #14557749C2semidirect
8. #14557748C2semidirect
9. #14557747C2semidirect
10. #14557746C2semidirect
11. #14557745C2semidirect
12. C4⋊C8×D37C2semidirect
13. #103×D37C2semidirect
14. #102×D37C2semidirect
15. C37×#463C2semidirect
20. C2×#10596930C22semidirect
21. C2×#10596940C22semidirect
22. C2×#10596941C22semidirect
30. #11924525C22semidirect
31. #11924524C22semidirect
32. #11924523C22semidirect
35. C4×D148C22semidirect
36. D4×Dic37C22semidirect
37. #11924498C22semidirect
45. C4⋊#64436C22semidirect
46. #11924465C22semidirect
47. #11924465C22semidirect
48. #11924461C22semidirect
49. #11924460C22semidirect
50. #11924459C22semidirect
51. #11924458C22semidirect
52. #11924457C22semidirect
53. #11924456C22semidirect
54. C2×SD16×C37C22semidirect
56. #124×C37C22semidirect
57. C4×D4×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #103×C37C22semidirect
60. #102×C37C22semidirect
208. D37#463direct (N × H)
220. #463D37direct (N × H)
224. C37C2×#463semidirect
233. C2×SD16C2×D37semidirect
246. #124C2×D37semidirect
252. C4×D4C2×D37semidirect
261. C4⋊C8C2×D37semidirect
265. #103C2×D37semidirect
269. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D372
C2×D8×D372
#124×D372
C4×D4×D372
#145577512
#145577502
#145577492
#145577482
#145577472
#145577462
#145577452
C4⋊C8×D372
#103×D372
#102×D372
C37×#4632
C2×#46337