Finite Group Databasebeta

← #18006358

Subgroups — #18006358

Order 4736.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558341C211yesmaximal, characteristic, complemented
2#14558336C211yesmaximal, characteristic, complemented
3#14558335C211yesmaximal, characteristic, complemented
4#14557919C211yesmaximal, characteristic, complemented
5#14557803C211yesmaximal, characteristic, complemented
6#14557801C211yesmaximal, characteristic, complemented
7#14557798C211yesmaximal, characteristic, complemented
8#14557793C211yesmaximal, characteristic, complemented
9#14557709C211yesmaximal, characteristic, complemented
10#14557706C211yesmaximal, characteristic, complemented
11#14557701C211yesmaximal, characteristic, complemented
12#14557699C211yesmaximal, characteristic, complemented
13#14557655C211yesmaximal, characteristic, complemented
14#14557653C211yesmaximal, characteristic, complemented
15C37×#577C211yesmaximal, characteristic, complemented
16#11924582C2211yescharacteristic
17#11924582C2211yescharacteristic, complemented
18#11924567—21no—
19#11924567C2211yescharacteristic, complemented
20#11924563—21no—
21#11924563—21no—
22#11924562—21no—
23#11924562C2211yescharacteristic
24#11924561—21no—
25#11924561—21no—
26#11924561C2211yescharacteristic
27#11924561C2211yescharacteristic, complemented
28#11924561C2211yescharacteristic, complemented
29#11924561C2211yescharacteristic, complemented
30#11924559—21no—
31#11924556—21no—
32#11924556—21no—
33#11924556C2211yescharacteristic
34C2×#10596941—21no—
35C2×#10596941C2211yescharacteristic, complemented
36C2×D296C2211yescharacteristic, complemented
37C2×#10596939—21no—
38C2×#10596939C2211yescharacteristic, complemented
39D8×D37—21no—
40#11924543C2211yescharacteristic, complemented
41#11924543C2211yescharacteristic, complemented
42#11924542C2211yescharacteristic, complemented
43#11924532C2211yescharacteristic, complemented
44#11924525C2211yescharacteristic, complemented
45#11924472C2211yescharacteristic, complemented
46#11924471C2211yescharacteristic, complemented
47#11924463C2211yescharacteristic, complemented
48#11924463C2211yescharacteristic, complemented
49#11924463C2211yescharacteristic, complemented
50#11924462C2211yescharacteristic, complemented
51#11924455C2211yescharacteristic, complemented
52#11924453C2211yescharacteristic, complemented
53#11924452C2211yescharacteristic, complemented
54#11924452C2211yescharacteristic, complemented
55#11924446C2211yescharacteristic, complemented
562−1+4×C37C2211yescharacteristic, complemented
57H(5,𝔽2)×C37C2211yescharacteristic, complemented
58#137×C37—21no—
59#137×C37C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C37—21no—
61AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
62#135×C37—21no—
63#135×C37C2211yescharacteristic
64C2×SD16×C37—21no—
65C2×SD16×C37C2211yescharacteristic, complemented
66#131×C37C2211yescharacteristic, complemented
67#41×C37—21no—
68#41×C37—21no—
69#41×C37—21no—
70#41×C37—21no—
71#41×C37—41no—
72#41×C37C2311yescharacteristic
73#41×C37C2311yescharacteristic
74#41×C37C2311yescharacteristic
75C2×Q8×C37—21no—
76C2×Q8×C37—21no—
77C2×Q8×C37C2311yescharacteristic
78C2×D4×C37—21no—
79C2×D4×C37—21no—
80C2×D4×C37—41no—
81C2×D4×C37C2311yescharacteristic
82C2×C22⋊D37—41no—
83#10596966—21no—
84#10596966—21no—
85D4×D37—21no—
86D4×D37—21no—
87D4×D37—41no—
88D4×D37—41no—
89#10596962—21no—
90#10596962—21no—
91#10596962C2311yescharacteristic
92C2×D148—21no—
93C2×D148—21no—
94C2×D148C2311yescharacteristic
95C2×D148C2311yescharacteristic
96Q16×C37—21no—
97Q16×C37D411yescharacteristic, complemented
98SD16×C37—21no—
99SD16×C37—21no—
100SD16×C37—21no—
101SD16×C37—21no—
102SD16×C37D411yescharacteristic, complemented
103SD16×C37D411yescharacteristic, complemented
104D8×C37—21no—
105D8×C37D411yescharacteristic, complemented
106M16×C37—21no—
107M16×C37C2311yescharacteristic
108C2×C8×C37—21no—
109C2×C8×C37C2311yescharacteristic
110#10596942—21no—
111#10596942D411yescharacteristic, complemented
112#10596941—21no—
113#10596941—21no—
114#10596941—21no—
115#10596941—21no—
116#10596941—21no—
117#10596941—21no—
118#10596941—21no—
119#10596941D411yescharacteristic, complemented
120#10596940—21no—
121#10596940D411yescharacteristic, complemented
122#10596939—21no—
123#10596939—21no—
124#10596939—21no—
125#10596939—21no—
126#10596939—21no—
127#10596939—21no—
128#10596939—21no—
129#10596939D411yescharacteristic, complemented
130#10596938—41no—
131C4×Dic37C2311yescharacteristic
132#10596934—21no—
133#10596934—21no—
134#10596934C2311yescharacteristic
135#10596934C2311yescharacteristic
136#10596934C2311yescharacteristic
137C2×#64436—21no—
138C2×#64436—21no—
139C2×#64436C2311yescharacteristic
140D296—21no—
141D296—21no—
142#10596929—21no—
143C8×D37—21no—
144C23×C37—21no—
145C23×C37—41no—
146C22×D37—21no—
147C22×D37—21no—
148C22×D37—41no—
149C22×D37—41no—
150Q8×C37—21no—
151Q8×C37—21no—
152Q8×C37—41no—
153Q8×C37C2×D411yescharacteristic
154Q8×C37C2×D411yescharacteristic
155Q8×C37C2×D411yescharacteristic
156D4×C37—21no—
157D4×C37—21no—
158D4×C37—21no—
159D4×C37—21no—
160D4×C37—21no—
161D4×C37—41no—
162D4×C37—41no—
163D4×C37—41no—
164D4×C37C2×D411yescharacteristic
165D4×C37C2×D411yescharacteristic
166D4×C37C2×D411yescharacteristic
167C2×C4×C37—21no—
168C2×C4×C37—21no—
169C2×C4×C37—21no—
170C2×C4×C37—21no—
171C2×C4×C37—41no—
172C2×C4×C37—41no—
173C2×C4×C37—41no—
174C2×C4×C37C2411yescharacteristic
175C22⋊D37—21no—
176C22⋊D37—41no—
177C22⋊D37—41no—
178C22⋊D37—82no—
179C2×Dic37—21no—
180D148—21no—
181D148—21no—
182D148—21no—
183D148—21no—
184D148—41no—
185D148—41no—
186D148C2×D411yescharacteristic
187C4×D37—21no—
188C4×D37—41no—
189C4×D37—41no—
190Dic74C2×D411yescharacteristic
191C8×C37—21no—
192C8×C37C2×D411yescharacteristic
193C8×C37C2×D411yescharacteristic
194#64436—21no—
195#64436—21no—
196#64436—21no—
197#64436C2×D411yescharacteristic
198#64436C2×D411yescharacteristic
199C22×C37—21no—
200C22×C37—21no—
201C22×C37—21no—
202C22×C37—41no—
203C22×C37—81no—
204C22×C37—161no—
205C22×C37H(5,𝔽2)11yescharacteristic
206C2×D37—21no—
207C2×D37—41no—
208C2×D37—41no—
209C2×D37—81no—
210C2×D37—81no—
211C2×D37—161no—
212C2×D37—161no—
213C4×C37—21no—
214C4×C37—21no—
215C4×C37—21no—
216C4×C37—41no—
217C4×C37C22×D411yescharacteristic
218C4×C37C22×D411yescharacteristic
219Dic37—21no—
220Dic37—41no—
221#3288—371nomaximal, Sylow
222C2×C37—21no—
223C2×C37—41no—
224C2×C37—41no—
225C2×C37—41no—
226C2×C37—81no—
227C2×C37D4211yescharacteristic
228D37—41no—
229D37—81no—
230D37—81no—
231#577—371no—
232#577D3711yescharacteristic, complemented
233#576—371no—
234#576—371no—
235#496—371no—
236#472—371no—
237#472—371no—
238#471—371no—
239#471—371no—
240#455—371no—
241#454—371no—
242#453—371no—
243#453—371no—
244#444—371no—
245#444—371no—
246C37#328811yescharacteristic, complemented, Sylow
2472−1+4C2×D3711yescharacteristic, complemented
248H(5,𝔽2)—371no—
249H(5,𝔽2)—371no—
250H(5,𝔽2)C2×D3711yescharacteristic, complemented
251#137—21no—
252#137—371no—
253#137—741no—
254#137C2×D3711yescharacteristic, complemented
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—371no—
257AGL(1,ℤ/8)—371no—
258AGL(1,ℤ/8)—371no—
259AGL(1,ℤ/8)—371no—
260AGL(1,ℤ/8)—371no—
261AGL(1,ℤ/8)—741no—
262AGL(1,ℤ/8)—741no—
263AGL(1,ℤ/8)—741no—
264AGL(1,ℤ/8)—741no—
265AGL(1,ℤ/8)—741no—
266AGL(1,ℤ/8)C2×D3711yescharacteristic, complemented
267#135—21no—
268#135—371no—
269#135—741no—
270#135—741no—
271#135—741no—
272#135C2×D3711yescharacteristic
273C2×SD16—21no—
274C2×SD16—371no—
275C2×SD16—741no—
276C2×SD16C2×D3711yescharacteristic, complemented
277C2×D8—371no—
278C2×D8—371no—
279C2×D8—741no—
280C2×D8—741no—
281#131—371no—
282#131—371no—
283#131—371no—
284#131C2×D3711yescharacteristic, complemented
285#127—371no—
286#124—371no—
287#108—371no—
288#108—371no—
289#104—371no—
290#104—371no—
291#104—371no—
292#104—371no—
293#101—371no—
294#100—371no—
295#100—371no—
296#100—371no—
297#97—371no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—41no—
303#41—371no—
304#41—741no—
305#41—741no—
306#41—741no—
307#41—741no—
308#41C22×D3711yescharacteristic
309#41C22×D3711yescharacteristic
310#41C22×D3711yescharacteristic
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8C22×D3711yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—371no—
318C2×D4—371no—
319C2×D4—741no—
320C2×D4—741no—
321C2×D4—741no—
322C2×D4—741no—
323C2×D4—1481no—
324C2×D4—1481no—
325C2×D4—1481no—
326C2×D4C22×D3711yescharacteristic
327Q16—21no—
328Q16—371no—
329Q16—741no—
330Q16C22⋊D3711yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—371no—
336SD16—371no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16C22⋊D3711yescharacteristic, complemented
346SD16C22⋊D3711yescharacteristic, complemented
347D8—21no—
348D8—371no—
349D8—741no—
350D8—741no—
351D8—741no—
352D8—741no—
353D8—741no—
354D8—741no—
355D8—741no—
356D8—741no—
357D8—741no—
358D8C22⋊D3711yescharacteristic, complemented
359M16—21no—
360M16—371no—
361M16—371no—
362M16—371no—
363M16—741no—
364M16—741no—
365M16—741no—
366M16C22×D3711yescharacteristic
367C2×C8—21no—
368C2×C8—371no—
369C2×C8—741no—
370C2×C8—741no—
371C2×C8—741no—
372C2×C8C22×D3711yescharacteristic
373C22⋊C4—1481no—
374C42—371no—
375C23—21no—
376C23—41no—
377C23—741no—
378C23—741no—
379C23—1481no—
380C23—1481no—
381Q8—21no—
382Q8—21no—
383Q8—41no—
384Q8—371no—
385Q8D4×D3711yescharacteristic
386Q8C2×C22⋊D3711yescharacteristic
387Q8C2×C22⋊D3711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—371no—
397D4—2962no—
398D4—741no—
399D4—741no—
400D4—741no—
401D4—741no—
402D4—741no—
403D4—1481no—
404D4—1481no—
405D4—1481no—
406D4—1481no—
407D4D4×D3711yescharacteristic
408D4C2×C22⋊D3711yescharacteristic
409D4C2×C22⋊D3711yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—741no—
418C2×C4—741no—
419C2×C4—1481no—
420C2×C4—1481no—
421C2×C4C23×D3711yescharacteristic
422C8—21no—
423C8—371no—
424C8—371no—
425C8—741no—
426C8—741no—
427C8—741no—
428C8C2×C22⋊D3711yescharacteristic
429C8C2×C22⋊D3711yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—81no—
435C22—161no—
436C22—2961no—
437C22—2961no—
438C22—741no—
439C22—5921no—
440C22—5921no—
441C22—1481no—
442C22—1481no—
443C22#1192458111yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—741no—
449C4—1481no—
450C4C2×D4×D3711yescharacteristic
451C4C22×C22⋊D3711yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—2961no—
458C2—2961no—
459C2—1481no—
460C2D4×C22⋊D3711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#577C2
socleC2×C37D42
hypercenter#577D37
hypocenterC37#3288
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #14558341C2semidirect
2. #14558336C2semidirect
3. #14558335C2semidirect
4. #14557919C2semidirect
5. #14557803C2semidirect
6. #14557801C2semidirect
7. #14557798C2semidirect
8. #14557793C2semidirect
9. #14557709C2semidirect
10. #14557706C2semidirect
11. #14557701C2semidirect
12. #14557699C2semidirect
13. #14557655C2semidirect
14. #14557653C2semidirect
15. C37×#577C2semidirect
17. #11924582C22semidirect
19. #11924567C22semidirect
27. #11924561C22semidirect
28. #11924561C22semidirect
29. #11924561C22semidirect
35. C2×#10596941C22semidirect
36. C2×D296C22semidirect
38. C2×#10596939C22semidirect
40. #11924543C22semidirect
41. #11924543C22semidirect
42. #11924542C22semidirect
43. #11924532C22semidirect
44. #11924525C22semidirect
45. #11924472C22semidirect
46. #11924471C22semidirect
47. #11924463C22semidirect
48. #11924463C22semidirect
49. #11924463C22semidirect
50. #11924462C22semidirect
51. #11924455C22semidirect
52. #11924453C22semidirect
53. #11924452C22semidirect
54. #11924452C22semidirect
55. #11924446C22semidirect
56. 2−1+4×C37C22semidirect
57. H(5,𝔽2)×C37C22semidirect
59. #137×C37C22semidirect
61. AGL(1,ℤ/8)×C37C22semidirect
65. C2×SD16×C37C22semidirect
66. #131×C37C22semidirect
97. Q16×C37D4semidirect
102. SD16×C37D4semidirect
103. SD16×C37D4semidirect
105. D8×C37D4semidirect
111. #10596942D4semidirect
119. #10596941D4semidirect
121. #10596940D4semidirect
129. #10596939D4semidirect
232. #577D37semidirect
246. C37#3288semidirect
247. 2−1+4C2×D37semidirect
250. H(5,𝔽2)C2×D37semidirect
254. #137C2×D37semidirect
266. AGL(1,ℤ/8)C2×D37semidirect
276. C2×SD16C2×D37semidirect
284. #131C2×D37semidirect
330. Q16C22⋊D37semidirect
345. SD16C22⋊D37semidirect
346. SD16C22⋊D37semidirect
358. D8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583412
#145583362
#145583352
#145579192
#145578032
#145578012
#145577982
#145577932
#145577092
#145577062
#145577012
#145576992
#145576552
#145576532
C37×#5772
#328837