Finite Group Databasebeta

← #18006359

Subgroups — #18006359

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#14558345C211yesmaximal, characteristic, complemented
2#14558343C211yesmaximal, characteristic, complemented
3#14558337C211yesmaximal, characteristic, complemented
4#14558334C211yesmaximal, characteristic, complemented
5#14557921C211yesmaximal, characteristic, complemented
6#14557802C211yesmaximal, characteristic, complemented
7#14557797C211yesmaximal, characteristic, complemented
8#14557795C211yesmaximal, characteristic, complemented
9#14557713C211yesmaximal, characteristic, complemented
10#14557704C211yesmaximal, characteristic, complemented
11#14557703C211yesmaximal, characteristic, complemented
12#14557699C211yesmaximal, characteristic, complemented
13#14557654C211yesmaximal, characteristic, complemented
14#14557653C211yesmaximal, characteristic, complemented
15C37×#472C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic, complemented
17#11924582C2211yescharacteristic, complemented
18#11924581C2211yescharacteristic
19#11924581C2211yescharacteristic, complemented
20#11924569—21no—
21#11924569C2211yescharacteristic, complemented
22#11924569C2211yescharacteristic, complemented
23#11924565—21no—
24#11924564—21no—
25#11924564C2211yescharacteristic
26#11924564C2211yescharacteristic, complemented
27#11924563—21no—
28#11924562C2211yescharacteristic
29#11924562C2211yescharacteristic, complemented
30#11924560—21no—
31#11924560—21no—
32#11924560—21no—
33#11924560—21no—
34#11924558—21no—
35#11924558C2211yescharacteristic
36#11924557—21no—
37#11924556C2211yescharacteristic
38#11924555—21no—
39#11924555—21no—
40C2×#10596930—21no—
41C2×#10596930C2211yescharacteristic, complemented
42C2×#10596940C2211yescharacteristic, complemented
43SD16×D37—21no—
44C2×#10596939C2211yescharacteristic, complemented
45D8×D37—21no—
46D8×D37—21no—
47#11924544C2211yescharacteristic, complemented
48#11924544C2211yescharacteristic, complemented
49#11924542C2211yescharacteristic, complemented
50#11924532C2211yescharacteristic, complemented
51#11924523C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924463C2211yescharacteristic, complemented
54#11924462C2211yescharacteristic, complemented
55#11924462C2211yescharacteristic, complemented
56#11924462C2211yescharacteristic, complemented
57#11924454C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59#11924446C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
62C2×D8×C37C2211yescharacteristic, complemented
63#131×C37C2211yescharacteristic, complemented
64#108×C37C2211yescharacteristic, complemented
65#100×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67#41×C37C2311yescharacteristic
68C2×D4×C37C2311yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C2×C22⋊D37—41no—
71C2×C22⋊D37—41no—
72C2×C22⋊D37—41no—
73#10596966—21no—
74Q8×D37—21no—
75#10596964—21no—
76#10596964—21no—
77#10596964—21no—
78#10596964—21no—
79#10596964—21no—
80#10596964—41no—
81D4×D37—21no—
82D4×D37—21no—
83D4×D37—21no—
84D4×D37—21no—
85D4×D37—21no—
86D4×D37—41no—
87#10596962—21no—
88#10596962—21no—
89#10596962C2311yescharacteristic
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—
100D8×C37—21no—
101D8×C37—21no—
102M16×C37—21no—
103M16×C37C2311yescharacteristic
104M16×C37C2311yescharacteristic
105M16×C37C2311yescharacteristic
106C2×C8×C37—21no—
107C2×C8×C37C2311yescharacteristic
108C22⋊Dic37—41no—
109#10596942D411yescharacteristic, complemented
110#10596941D411yescharacteristic, complemented
111#10596940—21no—
112#10596940—21no—
113#10596940—21no—
114#10596940—21no—
115#10596940D411yescharacteristic, complemented
116#10596939—21no—
117#10596939—21no—
118#10596939—21no—
119#10596939—21no—
120#10596939D411yescharacteristic, complemented
121C4×Dic37C2311yescharacteristic
122#10596934C2311yescharacteristic
123C2×#64436C2311yescharacteristic
124Dic148—21no—
125Dic148—21no—
126Dic148D411yescharacteristic, complemented
127D296—21no—
128D296—21no—
129D296D411yescharacteristic, complemented
130#10596930—21no—
131#10596930—21no—
132#10596930—21no—
133#10596930—21no—
134#10596930—21no—
135#10596930—21no—
136#10596930D411yescharacteristic, complemented
137#10596930D411yescharacteristic, complemented
138#10596929—21no—
139#10596929—21no—
140#10596929—21no—
141C8×D37—21no—
142C8×D37—21no—
143C8×D37—21no—
144C23×C37—21no—
145C23×C37—21no—
146C22×D37—21no—
147C22×D37—41no—
148C22×D37—41no—
149C22×D37—41no—
150Q8×C37C2×D411yescharacteristic
151D4×C37—21no—
152D4×C37—21no—
153D4×C37—21no—
154D4×C37—21no—
155D4×C37—21no—
156D4×C37C2×D411yescharacteristic
157C2×C4×C37—21no—
158C2×C4×C37C2411yescharacteristic
159C22⋊D37—21no—
160C22⋊D37—21no—
161C22⋊D37—21no—
162C22⋊D37—41no—
163C22⋊D37—41no—
164C22⋊D37—41no—
165C22⋊D37—41no—
166C22⋊D37—41no—
167C22⋊D37—41no—
168C22⋊D37—82no—
169C2×Dic37—21no—
170C2×Dic37—21no—
171C2×Dic37—41no—
172C2×Dic37—41no—
173C2×Dic37—41no—
174D148—21no—
175D148—21no—
176D148—41no—
177D148C2×D411yescharacteristic
178D148C2×D411yescharacteristic
179D148C2×D411yescharacteristic
180C4×D37—21no—
181C4×D37—21no—
182C4×D37—21no—
183C4×D37—41no—
184C4×D37—41no—
185Dic74—21no—
186Dic74—21no—
187Dic74—41no—
188Dic74C2×D411yescharacteristic
189Dic74C2×D411yescharacteristic
190Dic74C2×D411yescharacteristic
191C8×C37—21no—
192C8×C37—21no—
193C8×C37—21no—
194C8×C37C2×D411yescharacteristic
195C8×C37C2×D411yescharacteristic
196#64436—21no—
197#64436C2×D411yescharacteristic
198#64436C2×D411yescharacteristic
199C22×C37—21no—
200C22×C37—41no—
201C22×C37—41no—
202C22×C37—81no—
203C22×C37—81no—
204C22×C37H(5,𝔽2)11yescharacteristic
205C2×D37—21no—
206C2×D37—21no—
207C2×D37—21no—
208C2×D37—41no—
209C2×D37—81no—
210C2×D37—161no—
211C2×D37—161no—
212C2×D37—161no—
213C4×C37—21no—
214C4×C37C22×D411yescharacteristic
215C4×C37C22×D411yescharacteristic
216Dic37—21no—
217Dic37—21no—
218Dic37—21no—
219Dic37—41no—
220Dic37—41no—
221#3288—371nomaximal, Sylow
222C2×C37—21no—
223C2×C37—41no—
224C2×C37—81no—
225C2×C37—81no—
226C2×C37D4211yescharacteristic
227D37—41no—
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#472D3711yescharacteristic, complemented
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+4—371no—
248H(5,𝔽2)—371no—
249H(5,𝔽2)—371no—
250H(5,𝔽2)—371no—
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, complemented
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—741no—
279C2×D8—741no—
280C2×D8C2×D3711yescharacteristic, complemented
281#131—371no—
282#131—371no—
283#131—371no—
284#131C2×D3711yescharacteristic, complemented
285#127—371no—
286#124—371no—
287#108—371no—
288#108C2×D3711yescharacteristic, complemented
289#104—371no—
290#104—371no—
291#104—371no—
292#104—371no—
293#101—371no—
294#100—371no—
295#100C2×D3711yescharacteristic, complemented
296#100C2×D3711yescharacteristic, complemented
297#97—371no—
298#41—371no—
299#41—371no—
300#41—371no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—741no—
305#41—741no—
306#41—741no—
307#41—741no—
308#41—741no—
309#41—1481no—
310#41C22×D3711yescharacteristic
311C2×Q8—371no—
312C2×Q8—741no—
313C2×Q8—741no—
314C2×D4—371no—
315C2×D4—741no—
316C2×D4—741no—
317C2×D4—741no—
318C2×D4—741no—
319C2×D4—741no—
320C2×D4—741no—
321C2×D4—1481no—
322C2×D4—1481no—
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—21no—
350D8—21no—
351D8—371no—
352D8—371no—
353D8—741no—
354D8—741no—
355D8—741no—
356D8—741no—
357D8—741no—
358D8—741no—
359M16—21no—
360M16—371no—
361M16—741no—
362M16—741no—
363M16—741no—
364M16C22×D3711yescharacteristic
365M16C22×D3711yescharacteristic
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—21no—
377C23—741no—
378C23—1481no—
379C23—1481no—
380C23—1481no—
381Q8—371no—
382Q8—371no—
383Q8—371no—
384Q8—741no—
385Q8—741no—
386Q8—1481no—
387Q8D4×D3711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—371no—
394D4—371no—
395D4—371no—
396D4—2962no—
397D4—741no—
398D4—741no—
399D4—741no—
400D4—741no—
401D4—741no—
402D4—1481no—
403D4—1481no—
404D4—1481no—
405D4—1481no—
406D4—1481no—
407D4—1481no—
408D4—1481no—
409D4D4×D3711yescharacteristic
410C2×C4—21no—
411C2×C4—741no—
412C2×C4—741no—
413C2×C4—741no—
414C2×C4—741no—
415C2×C4—741no—
416C2×C4—1481no—
417C2×C4—1481no—
418C2×C4—1481no—
419C2×C4—1481no—
420C2×C4—1481no—
421C2×C4C23×D3711yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—371no—
426C8—371no—
427C8—741no—
428C8D4×D3711yescharacteristic
429C8D4×D3711yescharacteristic
430C22—21no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22—81no—
435C22—2961no—
436C22—741no—
437C22—741no—
438C22—741no—
439C22—5921no—
440C22—5921no—
441C22—5921no—
442C22—1481no—
443C22#1192458211yescharacteristic
444C4—21no—
445C4—741no—
446C4—741no—
447C4—741no—
448C4—1481no—
449C4—1481no—
450C4C2×D4×D3711yescharacteristic
451C4C2×D4×D3711yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—81no—
456C2—2961no—
457C2—1481no—
458C2—1481no—
459C2—1481no—
460C2#1455816711yescharacteristic
subgroupG/H
centerC2#14558167
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#472C2
socleC2×C37D42
hypercenter#472D37
hypocenterC37#3288
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #14558345C2semidirect
2. #14558343C2semidirect
3. #14558337C2semidirect
4. #14558334C2semidirect
5. #14557921C2semidirect
6. #14557802C2semidirect
7. #14557797C2semidirect
8. #14557795C2semidirect
9. #14557713C2semidirect
10. #14557704C2semidirect
11. #14557703C2semidirect
12. #14557699C2semidirect
13. #14557654C2semidirect
14. #14557653C2semidirect
15. C37×#472C2semidirect
16. #11924583C22semidirect
17. #11924582C22semidirect
19. #11924581C22semidirect
21. #11924569C22semidirect
22. #11924569C22semidirect
26. #11924564C22semidirect
29. #11924562C22semidirect
41. C2×#10596930C22semidirect
42. C2×#10596940C22semidirect
44. C2×#10596939C22semidirect
47. #11924544C22semidirect
48. #11924544C22semidirect
49. #11924542C22semidirect
50. #11924532C22semidirect
51. #11924523C22semidirect
52. #11924471C22semidirect
53. #11924463C22semidirect
54. #11924462C22semidirect
55. #11924462C22semidirect
56. #11924462C22semidirect
57. #11924454C22semidirect
58. #11924452C22semidirect
59. #11924446C22semidirect
60. AGL(1,ℤ/8)×C37C22semidirect
61. AGL(1,ℤ/8)×C37C22semidirect
62. C2×D8×C37C22semidirect
63. #131×C37C22semidirect
64. #108×C37C22semidirect
65. #100×C37C22semidirect
66. #100×C37C22semidirect
109. #10596942D4semidirect
110. #10596941D4semidirect
115. #10596940D4semidirect
120. #10596939D4semidirect
126. Dic148D4semidirect
129. D296D4semidirect
136. #10596930D4semidirect
137. #10596930D4semidirect
237. #472D37semidirect
246. C37#3288semidirect
265. AGL(1,ℤ/8)C2×D37semidirect
266. AGL(1,ℤ/8)C2×D37semidirect
280. C2×D8C2×D37semidirect
284. #131C2×D37semidirect
288. #108C2×D37semidirect
295. #100C2×D37semidirect
296. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583452
#145583432
#145583372
#145583342
#145579212
#145578022
#145577972
#145577952
#145577132
#145577042
#145577032
#145576992
#145576542
#145576532
C37×#4722
#328837