Finite Group Databasebeta

← #471×D37 #18004291

Subgroups — #471×D37 #18004291

Order 4736.

468 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×D37C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D37C211yesmaximal, characteristic
3C2×SD16×D37C211yesmaximal, characteristic, complemented
4#131×D37C211yesmaximal, characteristic, complemented
5#14557799C211yesmaximal, characteristic, complemented
6#14557798C211yesmaximal, characteristic, complemented
7#14557797C211yesmaximal, characteristic, complemented
8#14557796C211yesmaximal, characteristic, complemented
9#14557795C211yesmaximal, characteristic, complemented
10#14557794C211yesmaximal, characteristic, complemented
11#14557793C211yesmaximal, characteristic, complemented
12#108×D37C211yesmaximal, characteristic, complemented
13#101×D37C211yesmaximal, characteristic, complemented
14#100×D37C211yesmaximal, characteristic, complemented
15C37×#471C211yesmaximal, characteristic, complemented
16#41×D37C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19#11924569C2211yescharacteristic, complemented
20#11924568—21no—
21#11924567C2211yescharacteristic, complemented
22#11924566C2211yescharacteristic, complemented
23#11924565—21no—
24#11924564C2211yescharacteristic
25#11924563—21no—
26#11924562C2211yescharacteristic
27#11924561C2211yescharacteristic
28#11924560—21no—
29Q16×D37—21no—
30C2×#10596930C2211yescharacteristic, complemented
31C2×#10596940C2211yescharacteristic, complemented
32C2×#10596941C2211yescharacteristic, complemented
33SD16×D37—21no—
34SD16×D37—21no—
35SD16×D37—21no—
36SD16×D37—21no—
37SD16×D37—21no—
38SD16×D37—21no—
39D8×D37—21no—
40#11924544—21no—
41#11924544C2211yescharacteristic, complemented
42#11924543C2211yescharacteristic, complemented
43#11924542—21no—
44#11924542C2211yescharacteristic, complemented
45M16×D37—21no—
46M16×D37C2211yescharacteristic
47M16×D37C2211yescharacteristic
48M16×D37C2211yescharacteristic
49C2×C8×D37—21no—
50C2×C8×D37C2211yescharacteristic
51#11924472C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924455C2211yescharacteristic, complemented
55#11924454C2211yescharacteristic, complemented
56#11924454C2211yescharacteristic, complemented
57#11924453C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59#11924452C2211yescharacteristic, complemented
60#137×C37C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62C2×SD16×C37C2211yescharacteristic, complemented
63#131×C37C2211yescharacteristic, complemented
64#108×C37C2211yescharacteristic, complemented
65#101×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67C23×D37—21no—
68#41×C37C2311yescharacteristic
69C2×Q8×C37C2311yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C2×C22⋊D37—21no—
72#10596966D411yescharacteristic
73Q8×D37—21no—
74Q8×D37—21no—
75Q8×D37—21no—
76Q8×D37—21no—
77Q8×D37D411yescharacteristic
78#10596964—21no—
79#10596964D411yescharacteristic
80D4×D37—21no—
81D4×D37—21no—
82D4×D37—21no—
83D4×D37—21no—
84D4×D37—21no—
85D4×D37D411yescharacteristic
86#10596962—21no—
87#10596962C2311yescharacteristic
88C2×D148C2311yescharacteristic
89C2×C4×D37—21no—
90C2×C4×D37—21no—
91C2×C4×D37C2311yescharacteristic
92C2×Dic74—21no—
93C2×Dic74C2311yescharacteristic
94Q16×C37—21no—
95SD16×C37—21no—
96SD16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99D8×C37—21no—
100M16×C37—21no—
101M16×C37C2311yescharacteristic
102M16×C37C2311yescharacteristic
103M16×C37C2311yescharacteristic
104C2×C8×C37—21no—
105C2×C8×C37C2311yescharacteristic
106#10596942—21no—
107#10596942—21no—
108#10596941—21no—
109#10596941—21no—
110#10596941—21no—
111#10596941—21no—
112#10596940—21no—
113#10596940—21no—
114#10596940—21no—
115#10596940—21no—
116#10596939—21no—
117#10596939—21no—
118#10596934—21no—
119#10596934C2311yescharacteristic
120#10596934C2311yescharacteristic
121#10596934C2311yescharacteristic
122C2×#64436—21no—
123C2×#64436C2311yescharacteristic
124Dic148—21no—
125D296—21no—
126#10596930—21no—
127#10596930—21no—
128#10596930—21no—
129#10596930—21no—
130#10596929—21no—
131#10596929—21no—
132#10596929—21no—
133#10596929—21no—
134#10596929—21no—
135C8×D37—21no—
136C8×D37—21no—
137C8×D37—21no—
138C8×D37—21no—
139C8×D37—21no—
140C8×D37D411yescharacteristic
141C8×D37D411yescharacteristic
142C8×D37D411yescharacteristic
143C8×D37D411yescharacteristic
144C23×C37—21no—
145C22×D37—21no—
146C22×D37—21no—
147C22×D37—41no—
148C22×D37—41no—
149C22×D37—82no—
150C22×D37#4111yescharacteristic
151Q8×C37—21no—
152Q8×C37—21no—
153Q8×C37C2×D411yescharacteristic
154D4×C37—21no—
155D4×C37—21no—
156D4×C37—21no—
157D4×C37C2×D411yescharacteristic
158C2×C4×C37—21no—
159C2×C4×C37—21no—
160C2×C4×C37C2411yescharacteristic
161C22⋊D37—21no—
162C22⋊D37—21no—
163C22⋊D37—21no—
164C22⋊D37—41no—
165C22⋊D37—41no—
166C2×Dic37—21no—
167C2×Dic37—21no—
168C2×Dic37#4111yescharacteristic
169D148—21no—
170D148—21no—
171D148—21no—
172D148C2×D411yescharacteristic
173C4×D37—21no—
174C4×D37—21no—
175C4×D37—21no—
176C4×D37—41no—
177C4×D37—41no—
178C4×D37C2×D411yescharacteristic
179C4×D37C2×D411yescharacteristic
180C4×D37C2×D411yescharacteristic
181C4×D37C2×D411yescharacteristic
182Dic74—21no—
183Dic74—21no—
184Dic74—21no—
185Dic74—41no—
186Dic74—41no—
187Dic74C2×D411yescharacteristic
188C8×C37—21no—
189C8×C37—21no—
190C8×C37—21no—
191C8×C37C2×D411yescharacteristic
192C8×C37C2×D411yescharacteristic
193#64436—21no—
194#64436—21no—
195#64436—21no—
196#64436C2×D411yescharacteristic
197#64436C2×D411yescharacteristic
198C22×C37—21no—
199C22×C37—41no—
200C22×C37—81no—
201C22×C37C2×#4111yescharacteristic
202C2×D37—22no—
203C2×D37—21no—
204C2×D37—42no—
205C2×D37—41no—
206C2×D37—82no—
207C2×D37—82no—
208C2×D37—81no—
209C2×D37#12111yescharacteristic
210C2×D37#12111yescharacteristic
211C4×C37—21no—
212C4×C37—41no—
213C4×C37C22×D411yescharacteristic
214C4×C37C22×D411yescharacteristic
215Dic37—21no—
216Dic37—41no—
217Dic37#12111yescharacteristic
218Dic37#12111yescharacteristic
219C2×#471—371nomaximal, Sylow
220C2×C37—21no—
221C2×C37—41no—
222C2×C37—81no—
223C2×C37C2×#12111yescharacteristic
224D37—21no—
225D37—41no—
226D37—81no—
227D37#47112yesdirect product factor
228C2×#137—371no—
229C2×AGL(1,ℤ/8)—371no—
230C22×SD16—371no—
231C2×#131—371no—
232#471—371no—
233#471—371no—
234#471—371no—
235#471—371no—
236#471—371no—
237#471—371no—
238#471—371no—
239#471D3711yescharacteristic, direct product factor
240C2×#108—371no—
241C2×#101—371no—
242C2×#100—371no—
243C37C2×#47111yescharacteristic, complemented, Sylow
244C2×#41—371no—
245C22×Q8—371no—
246C22×D4—371no—
247#137—371no—
248#137—371no—
249#137—371no—
250#137—741no—
251#137—741no—
252#137C2×D3711yescharacteristic, complemented
253AGL(1,ℤ/8)—371no—
254AGL(1,ℤ/8)—371no—
255AGL(1,ℤ/8)—371no—
256AGL(1,ℤ/8)—741no—
257AGL(1,ℤ/8)—741no—
258AGL(1,ℤ/8)C2×D3711yescharacteristic
259C2×Q16—741no—
260C2×SD16—371no—
261C2×SD16—371no—
262C2×SD16—371no—
263C2×SD16—741no—
264C2×SD16—741no—
265C2×SD16—741no—
266C2×SD16—741no—
267C2×SD16—741no—
268C2×SD16—741no—
269C2×SD16C2×D3711yescharacteristic, complemented
270C2×D8—741no—
271#131—371no—
272#131—371no—
273#131—371no—
274#131—741no—
275#131—741no—
276#131C2×D3711yescharacteristic, complemented
277C2×M16—371no—
278C2×M16—371no—
279C2×M16—371no—
280C2×M16—741no—
281C22×C8—371no—
282C22×C8—741no—
283#108—371no—
284#108—371no—
285#108—371no—
286#108C2×D3711yescharacteristic, complemented
287#101—371no—
288#101—371no—
289#101—371no—
290#101C2×D3711yescharacteristic, complemented
291#100—371no—
292#100—371no—
293#100—371no—
294#100C2×D3711yescharacteristic, complemented
295C24—741no—
296#41—371no—
297#41—371no—
298#41—371no—
299#41—741no—
300#41—741no—
301#41C22×D3711yescharacteristic
302C2×Q8—371no—
303C2×Q8—371no—
304C2×Q8—741no—
305C2×Q8—741no—
306C2×Q8—741no—
307C2×Q8—741no—
308C2×Q8—741no—
309C2×Q8C22×D3711yescharacteristic
310C2×D4—371no—
311C2×D4—371no—
312C2×D4—741no—
313C2×D4—741no—
314C2×D4—741no—
315C2×D4—741no—
316C2×D4—741no—
317C2×D4—741no—
318C2×D4C22×D3711yescharacteristic
319C22×C4—371no—
320C22×C4—741no—
321C22×C4—741no—
322Q16—21no—
323Q16—741no—
324Q16—741no—
325Q16—741no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—741no—
331SD16—741no—
332SD16—741no—
333SD16—741no—
334SD16—741no—
335SD16—741no—
336SD16—741no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342D8—21no—
343D8—741no—
344D8—741no—
345D8—741no—
346M16—21no—
347M16—371no—
348M16—371no—
349M16—371no—
350M16—741no—
351M16—741no—
352M16—741no—
353M16—741no—
354M16—741no—
355M16—741no—
356M16C22×D3711yescharacteristic
357M16C22×D3711yescharacteristic
358M16C22×D3711yescharacteristic
359C2×C8—21no—
360C2×C8—371no—
361C2×C8—371no—
362C2×C8—371no—
363C2×C8—371no—
364C2×C8—371no—
365C2×C8—741no—
366C2×C8—741no—
367C2×C8—741no—
368C2×C8—741no—
369C2×C8—741no—
370C2×C8—741no—
371C2×C8C22×D3711yescharacteristic
372C23—21no—
373C23—371no—
374C23—2962no—
375C23—741no—
376C23—741no—
377C23—1481no—
378C23—1481no—
379Q8—21no—
380Q8—21no—
381Q8—371no—
382Q8—741no—
383Q8—741no—
384Q8—741no—
385Q8—1481no—
386Q8—1481no—
387Q8D4×D3711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—371no—
392D4—741no—
393D4—741no—
394D4—741no—
395D4—741no—
396D4—741no—
397D4—741no—
398D4—1481no—
399D4—1481no—
400D4D4×D3711yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—371no—
404C2×C4—371no—
405C2×C4—371no—
406C2×C4—371no—
407C2×C4—371no—
408C2×C4—741no—
409C2×C4—741no—
410C2×C4—741no—
411C2×C4—741no—
412C2×C4—741no—
413C2×C4—1481no—
414C2×C4—1481no—
415C2×C4C23×D3711yescharacteristic
416C8—21no—
417C8—21no—
418C8—21no—
419C8—371no—
420C8—371no—
421C8—741no—
422C8—741no—
423C8—741no—
424C8D4×D3711yescharacteristic
425C8D4×D3711yescharacteristic
426C22—21no—
427C22—41no—
428C22—81no—
429C22—371no—
430C22—371no—
431C22—2961no—
432C22—2962no—
433C22—2962no—
434C22—742no—
435C22—741no—
436C22—1482no—
437C22—1481no—
438C22#41×D3711yescharacteristic
439C4—21no—
440C4—41no—
441C4—371no—
442C4—371no—
443C4—741no—
444C4—1481no—
445C4C2×D4×D3711yescharacteristic
446C4C2×D4×D3711yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—372no—
451C2—2961no—
452C2—741no—
453C2—1481no—
454C2#121×D3711yescharacteristic
subgroupG/H
centerC2#121×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#471C2
socleC2×C37C2×#121
prime radicalAGL(1,ℤ/8)×D37C2
hypercenter#471D37
hypocenterC37C2×#471
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #137×D37C2semidirect
3. C2×SD16×D37C2semidirect
4. #131×D37C2semidirect
5. #14557799C2semidirect
6. #14557798C2semidirect
7. #14557797C2semidirect
8. #14557796C2semidirect
9. #14557795C2semidirect
10. #14557794C2semidirect
11. #14557793C2semidirect
12. #108×D37C2semidirect
13. #101×D37C2semidirect
14. #100×D37C2semidirect
15. C37×#471C2semidirect
19. #11924569C22semidirect
21. #11924567C22semidirect
22. #11924566C22semidirect
30. C2×#10596930C22semidirect
31. C2×#10596940C22semidirect
32. C2×#10596941C22semidirect
41. #11924544C22semidirect
42. #11924543C22semidirect
44. #11924542C22semidirect
51. #11924472C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
54. #11924455C22semidirect
55. #11924454C22semidirect
56. #11924454C22semidirect
57. #11924453C22semidirect
58. #11924452C22semidirect
59. #11924452C22semidirect
60. #137×C37C22semidirect
62. C2×SD16×C37C22semidirect
63. #131×C37C22semidirect
64. #108×C37C22semidirect
65. #101×C37C22semidirect
66. #100×C37C22semidirect
227. D37#471direct (N × H)
239. #471D37direct (N × H)
243. C37C2×#471semidirect
252. #137C2×D37semidirect
269. C2×SD16C2×D37semidirect
276. #131C2×D37semidirect
286. #108C2×D37semidirect
290. #101C2×D37semidirect
294. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#137×D372
AGL(1,ℤ/8)×D372
C2×SD16×D372
#131×D372
#145577992
#145577982
#145577972
#145577962
#145577952
#145577942
#145577932
#108×D372
#101×D372
#100×D372
C37×#4712
C2×#47137