Finite Group Databasebeta

← #18006357

Subgroups — #18006357

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#14558344C211yesmaximal, characteristic, complemented
2#14558343C211yesmaximal, characteristic, complemented
3#14558337C211yesmaximal, characteristic, complemented
4#14558336C211yesmaximal, characteristic, complemented
5#14557920C211yesmaximal, characteristic, complemented
6#14557802C211yesmaximal, characteristic, complemented
7#14557801C211yesmaximal, characteristic, complemented
8#14557795C211yesmaximal, characteristic, complemented
9#14557794C211yesmaximal, characteristic, complemented
10#14557712C211yesmaximal, characteristic, complemented
11#14557707C211yesmaximal, characteristic, complemented
12#14557700C211yesmaximal, characteristic, complemented
13#14557652C211yesmaximal, characteristic, complemented
14#14557652C211yesmaximal, characteristic, complemented
15C37×#453C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic, complemented
17#11924582C2211yescharacteristic
18#11924581C2211yescharacteristic, complemented
19#11924569C2211yescharacteristic, complemented
20#11924566—21no—
21#11924566C2211yescharacteristic, complemented
22#11924565—21no—
23#11924564C2211yescharacteristic, complemented
24#11924563—21no—
25#11924562—21no—
26#11924562—21no—
27#11924562C2211yescharacteristic
28#11924562C2211yescharacteristic, complemented
29#11924561—21no—
30#11924561C2211yescharacteristic, complemented
31#11924560—21no—
32#11924560—21no—
33#11924557—21no—
34#11924556—21no—
35#11924556—21no—
36#11924556C2211yescharacteristic
37#11924556C2211yescharacteristic
38#11924555—21no—
39C2×#10596940—21no—
40C2×#10596940C2211yescharacteristic, complemented
41C2×#10596940C2211yescharacteristic, complemented
42SD16×D37—21no—
43C2×#10596939—21no—
44C2×#10596939C2211yescharacteristic, complemented
45C2×#10596939C2211yescharacteristic, complemented
46D8×D37—21no—
47#11924544C2211yescharacteristic, complemented
48#11924544C2211yescharacteristic, complemented
49#11924543C2211yescharacteristic, complemented
50#11924543C2211yescharacteristic, complemented
51#11924524C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924464C2211yescharacteristic, complemented
55#11924464C2211yescharacteristic, complemented
56#11924454C2211yescharacteristic, complemented
57#11924453C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59#11924447C2211yescharacteristic, complemented
60H(5,𝔽2)×C37C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
63#127×C37C2211yescharacteristic, complemented
64#104×C37C2211yescharacteristic, complemented
65#104×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67#41×C37—21no—
68#41×C37—21no—
69#41×C37C2311yescharacteristic
70#41×C37C2311yescharacteristic
71C2×D4×C37—21no—
72C2×D4×C37—21no—
73C2×D4×C37—41no—
74C2×D4×C37—41no—
75C2×D4×C37C2311yescharacteristic
76C2×D4×C37C2311yescharacteristic
77C2×C22⋊D37—41no—
78#10596966—21no—
79Q8×D37—21no—
80#10596964—21no—
81#10596964—21no—
82#10596964—21no—
83#10596964—41no—
84D4×D37—21no—
85D4×D37—21no—
86D4×D37—21no—
87D4×D37—41no—
88#10596962—21no—
89#10596962—21no—
90#10596962C2311yescharacteristic
91#10596962C2311yescharacteristic
92C2×D148—21no—
93C2×D148C2311yescharacteristic
94C2×Dic74—21no—
95C2×Dic74C2311yescharacteristic
96SD16×C37—21no—
97SD16×C37—21no—
98D8×C37—21no—
99D8×C37—21no—
100M16×C37C2311yescharacteristic
101M16×C37C2311yescharacteristic
102C42×C37C2311yescharacteristic
103#10596942—21no—
104#10596942D411yescharacteristic, complemented
105#10596942D411yescharacteristic, complemented
106#10596941—21no—
107#10596941D411yescharacteristic, complemented
108#10596941D411yescharacteristic, complemented
109#10596940—21no—
110#10596940—21no—
111#10596940—21no—
112#10596940—21no—
113#10596940—21no—
114#10596940—21no—
115#10596940—21no—
116#10596940D411yescharacteristic, complemented
117#10596940D411yescharacteristic, complemented
118#10596939—21no—
119#10596939—21no—
120#10596939—21no—
121#10596939—21no—
122#10596939—21no—
123#10596939—21no—
124#10596939—21no—
125#10596939D411yescharacteristic, complemented
126#10596939D411yescharacteristic, complemented
127#10596938—41no—
128#10596934—21no—
129#10596934—21no—
130#10596934C2311yescharacteristic
131#10596934C2311yescharacteristic
132C2×#64436—21no—
133C2×#64436—21no—
134C2×#64436C2311yescharacteristic
135C2×#64436C2311yescharacteristic
136Dic148—21no—
137D296—21no—
138#10596930—21no—
139#10596930—21no—
140#10596929—21no—
141#10596929—21no—
142C8×D37—21no—
143C8×D37—21no—
144C23×C37—21no—
145C23×C37—21no—
146C23×C37—41no—
147C22×D37—21no—
148C22×D37—41no—
149C22×D37—41no—
150Q8×C37C2×D411yescharacteristic
151Q8×C37C2×D411yescharacteristic
152D4×C37—21no—
153D4×C37—21no—
154D4×C37—21no—
155D4×C37—21no—
156D4×C37—21no—
157D4×C37—21no—
158D4×C37—41no—
159D4×C37—41no—
160D4×C37—82no—
161D4×C37C2×D411yescharacteristic
162D4×C37C2×D411yescharacteristic
163C2×C4×C37—21no—
164C2×C4×C37—21no—
165C2×C4×C37—21no—
166C2×C4×C37—41no—
167C2×C4×C37C2411yescharacteristic
168C22⋊D37—21no—
169C22⋊D37—21no—
170C22⋊D37—41no—
171C22⋊D37—41no—
172C22⋊D37—41no—
173C22⋊D37—41no—
174C2×Dic37—21no—
175C2×Dic37—41no—
176C2×Dic37—41no—
177D148—21no—
178D148—21no—
179D148—41no—
180D148C2×D411yescharacteristic
181D148C2×D411yescharacteristic
182C4×D37—21no—
183C4×D37—21no—
184C4×D37—41no—
185C4×D37—41no—
186Dic74—21no—
187Dic74—21no—
188Dic74—41no—
189Dic74C2×D411yescharacteristic
190Dic74C2×D411yescharacteristic
191C8×C37—21no—
192C8×C37—21no—
193#64436—21no—
194#64436—21no—
195#64436C2×D411yescharacteristic
196#64436C2×D411yescharacteristic
197#64436C2×D411yescharacteristic
198#64436C2×D411yescharacteristic
199C22×C37—21no—
200C22×C37—21no—
201C22×C37—41no—
202C22×C37—41no—
203C22×C37—81no—
204C22×C37—81no—
205C22×C37—161no—
206C22×C37H(5,𝔽2)11yescharacteristic
207C2×D37—21no—
208C2×D37—21no—
209C2×D37—41no—
210C2×D37—81no—
211C2×D37—161no—
212C2×D37—161no—
213C4×C37—21no—
214C4×C37—21no—
215C4×C37—41no—
216C4×C37C22×D411yescharacteristic
217C4×C37C22×D411yescharacteristic
218Dic37—21no—
219Dic37—21no—
220Dic37—41no—
221#3288—371nomaximal, Sylow
222C2×C37—21no—
223C2×C37—41no—
224C2×C37—41no—
225C2×C37—81no—
226C2×C37—81no—
227C2×C37D4211yescharacteristic
228D37—41no—
229D37—41no—
230D37—81no—
231#577—371no—
232#577—371no—
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#453D3711yescharacteristic, complemented
244#444—371no—
245#444—371no—
246C37#328811yescharacteristic, complemented, Sylow
2472−1+4—371no—
248H(5,𝔽2)—371no—
249H(5,𝔽2)—371no—
250H(5,𝔽2)C2×D3711yescharacteristic, complemented
251#137—371no—
252#137—371no—
253#137—741no—
254#137—741no—
255AGL(1,ℤ/8)—371no—
256AGL(1,ℤ/8)—371no—
257AGL(1,ℤ/8)—371no—
258AGL(1,ℤ/8)—371no—
259AGL(1,ℤ/8)—741no—
260AGL(1,ℤ/8)—741no—
261AGL(1,ℤ/8)—741no—
262AGL(1,ℤ/8)—741no—
263AGL(1,ℤ/8)—741no—
264AGL(1,ℤ/8)—741no—
265AGL(1,ℤ/8)C2×D3711yescharacteristic
266AGL(1,ℤ/8)C2×D3711yescharacteristic, complemented
267#135—371no—
268#135—371no—
269#135—741no—
270#135—741no—
271#135—741no—
272#135—741no—
273C2×SD16—371no—
274C2×SD16—371no—
275C2×SD16—741no—
276C2×SD16—741no—
277C2×D8—371no—
278C2×D8—371no—
279C2×D8—741no—
280C2×D8—741no—
281#131—371no—
282#131—371no—
283#131—371no—
284#131—371no—
285#127C2×D3711yescharacteristic, complemented
286#124—371no—
287#108—371no—
288#108—371no—
289#104—371no—
290#104—371no—
291#104C2×D3711yescharacteristic, complemented
292#104C2×D3711yescharacteristic, complemented
293#101—371no—
294#100—371no—
295#100—371no—
296#100C2×D3711yescharacteristic, complemented
297#97—371no—
298#41—21no—
299#41—21no—
300#41—371no—
301#41—371no—
302#41—741no—
303#41—741no—
304#41—741no—
305#41—741no—
306#41—741no—
307#41—741no—
308#41—1481no—
309#41C22×D3711yescharacteristic
310#41C22×D3711yescharacteristic
311C2×Q8—371no—
312C2×Q8—741no—
313C2×Q8—741no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—371no—
319C2×D4—741no—
320C2×D4—741no—
321C2×D4—741no—
322C2×D4—741no—
323C2×D4—1481no—
324C2×D4—1481no—
325C2×D4C22×D3711yescharacteristic
326C2×D4C22×D3711yescharacteristic
327Q16—371no—
328Q16—371no—
329Q16—741no—
330Q16—741no—
331SD16—21no—
332SD16—21no—
333SD16—371no—
334SD16—371no—
335SD16—371no—
336SD16—371no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16—741no—
346SD16—741no—
347D8—21no—
348D8—21no—
349D8—371no—
350D8—371no—
351D8—741no—
352D8—741no—
353D8—741no—
354D8—741no—
355D8—741no—
356D8—741no—
357D8—741no—
358D8—741no—
359M16—371no—
360M16—371no—
361M16—741no—
362M16—741no—
363M16—741no—
364M16—741no—
365M16C22×D3711yescharacteristic
366M16C22×D3711yescharacteristic
367C2×C8—371no—
368C2×C8—371no—
369C2×C8—741no—
370C2×C8—741no—
371C2×C8—741no—
372C2×C8—741no—
373C22⋊C4—1481no—
374C42C22×D3711yescharacteristic
375C23—21no—
376C23—21no—
377C23—41no—
378C23—741no—
379C23—1481no—
380C23—1481no—
381Q8—371no—
382Q8—371no—
383Q8—741no—
384Q8—741no—
385Q8—1481no—
386Q8D4×D3711yescharacteristic
387Q8D4×D3711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—41no—
395D4—41no—
396D4—82no—
397D4—371no—
398D4—371no—
399D4—741no—
400D4—741no—
401D4—741no—
402D4—741no—
403D4—1481no—
404D4—1481no—
405D4—1481no—
406D4—1481no—
407D4—1481no—
408D4D4×D3711yescharacteristic
409D4D4×D3711yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—741no—
415C2×C4—741no—
416C2×C4—741no—
417C2×C4—1481no—
418C2×C4—1481no—
419C2×C4—1481no—
420C2×C4—1481no—
421C2×C4C23×D3711yescharacteristic
422C8—21no—
423C8—21no—
424C8—371no—
425C8—371no—
426C8—371no—
427C8—371no—
428C8—741no—
429C8—741no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—81no—
436C22—161no—
437C22—2961no—
438C22—741no—
439C22—741no—
440C22—5921no—
441C22—5921no—
442C22—1481no—
443C22#1192458111yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—741no—
448C4—741no—
449C4—1481no—
450C4C2×D4×D3711yescharacteristic
451C4C2×D4×D3711yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2—81no—
457C2—2961no—
458C2—1481no—
459C2—1481no—
460C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#453C2
socleC2×C37D42
hypercenter#453D37
hypocenterC37#3288
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14558344C2semidirect
2. #14558343C2semidirect
3. #14558337C2semidirect
4. #14558336C2semidirect
5. #14557920C2semidirect
6. #14557802C2semidirect
7. #14557801C2semidirect
8. #14557795C2semidirect
9. #14557794C2semidirect
10. #14557712C2semidirect
11. #14557707C2semidirect
12. #14557700C2semidirect
13. #14557652C2semidirect
14. #14557652C2semidirect
15. C37×#453C2semidirect
16. #11924583C22semidirect
18. #11924581C22semidirect
19. #11924569C22semidirect
21. #11924566C22semidirect
23. #11924564C22semidirect
28. #11924562C22semidirect
30. #11924561C22semidirect
40. C2×#10596940C22semidirect
41. C2×#10596940C22semidirect
44. C2×#10596939C22semidirect
45. C2×#10596939C22semidirect
47. #11924544C22semidirect
48. #11924544C22semidirect
49. #11924543C22semidirect
50. #11924543C22semidirect
51. #11924524C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
54. #11924464C22semidirect
55. #11924464C22semidirect
56. #11924454C22semidirect
57. #11924453C22semidirect
58. #11924452C22semidirect
59. #11924447C22semidirect
60. H(5,𝔽2)×C37C22semidirect
62. AGL(1,ℤ/8)×C37C22semidirect
63. #127×C37C22semidirect
64. #104×C37C22semidirect
65. #104×C37C22semidirect
66. #100×C37C22semidirect
104. #10596942D4semidirect
105. #10596942D4semidirect
107. #10596941D4semidirect
108. #10596941D4semidirect
116. #10596940D4semidirect
117. #10596940D4semidirect
125. #10596939D4semidirect
126. #10596939D4semidirect
243. #453D37semidirect
246. C37#3288semidirect
250. H(5,𝔽2)C2×D37semidirect
266. AGL(1,ℤ/8)C2×D37semidirect
285. #127C2×D37semidirect
291. #104C2×D37semidirect
292. #104C2×D37semidirect
296. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583442
#145583432
#145583372
#145583362
#145579202
#145578022
#145578012
#145577952
#145577942
#145577122
#145577072
#145577002
#145576522
C37×#4532
#328837