Finite Group Databasebeta

← #18006363

Subgroups — #18006363

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#14558340C211yesmaximal, characteristic, complemented
3#14558338C211yesmaximal, characteristic, complemented
4#14558335C211yesmaximal, characteristic, complemented
5#14557922C211yesmaximal, characteristic, complemented
6#14557804C211yesmaximal, characteristic, complemented
7#14557803C211yesmaximal, characteristic, complemented
8#14557797C211yesmaximal, characteristic, complemented
9#14557796C211yesmaximal, characteristic, complemented
10#14557712C211yesmaximal, characteristic, complemented
11#14557707C211yesmaximal, characteristic, complemented
12#14557702C211yesmaximal, characteristic, complemented
13#14557702C211yesmaximal, characteristic, complemented
14#14557656C211yesmaximal, characteristic, complemented
15C37×#444C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic, complemented
17#11924582C2211yescharacteristic
18#11924582C2211yescharacteristic, complemented
19#11924582C2211yescharacteristic, complemented
20#11924569—21no—
21#11924569C2211yescharacteristic, complemented
22#11924568—21no—
23#11924566C2211yescharacteristic, complemented
24#11924564—21no—
25#11924564—21no—
26#11924564—21no—
27#11924564C2211yescharacteristic
28#11924564C2211yescharacteristic, complemented
29#11924564C2211yescharacteristic, complemented
30#11924563—21no—
31#11924563—21no—
32#11924561C2211yescharacteristic
33#11924561C2211yescharacteristic, complemented
34#11924561C2211yescharacteristic, complemented
35#11924560—21no—
36#11924559—21no—
37#11924558—21no—
38#11924558—21no—
39#11924558C2211yescharacteristic
40#11924557—21no—
41C2×#10596930—21no—
42C2×#10596930C2211yescharacteristic, complemented
43C2×#10596930C2211yescharacteristic, complemented
44SD16×D37—21no—
45C2×D296—21no—
46C2×D296C2211yescharacteristic, complemented
47C2×D296C2211yescharacteristic, complemented
48D8×D37—21no—
49#11924542C2211yescharacteristic, complemented
50#11924542C2211yescharacteristic, complemented
51#11924533C2211yescharacteristic, complemented
52#11924524C2211yescharacteristic, complemented
53#11924472C2211yescharacteristic, complemented
54#11924464C2211yescharacteristic, complemented
55#11924464C2211yescharacteristic, complemented
56#11924454C2211yescharacteristic, complemented
57#11924452C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59#11924452C2211yescharacteristic, complemented
60#135×C37C2211yescharacteristic
61#131×C37C2211yescharacteristic, complemented
62#131×C37C2211yescharacteristic, complemented
63#108×C37C2211yescharacteristic, complemented
64#104×C37C2211yescharacteristic, complemented
65#104×C37C2211yescharacteristic, complemented
66#97×C37C2211yescharacteristic, complemented
67#41×C37C2311yescharacteristic
68#41×C37C2311yescharacteristic
69#10596966—21no—
70#10596966—21no—
71#10596966—21no—
72Q8×D37—21no—
73#10596964—21no—
74#10596964—41no—
75D4×D37—21no—
76D4×D37—21no—
77D4×D37—21no—
78D4×D37—41no—
79D4×D37—41no—
80D4×D37—41no—
81#10596962—21no—
82#10596962—21no—
83#10596962—21no—
84#10596962—21no—
85#10596962C2311yescharacteristic
86#10596962C2311yescharacteristic
87C2×D148—21no—
88C2×D148—21no—
89C2×D148—21no—
90C2×D148—41no—
91C2×D148C2311yescharacteristic
92C2×D148C2311yescharacteristic
93C2×D148C2311yescharacteristic
94C2×Dic74—21no—
95C2×Dic74C2311yescharacteristic
96Q16×C37D411yescharacteristic, complemented
97SD16×C37D411yescharacteristic, complemented
98SD16×C37D411yescharacteristic, complemented
99D8×C37D411yescharacteristic, complemented
100M16×C37—21no—
101M16×C37—21no—
102M16×C37C2311yescharacteristic
103M16×C37C2311yescharacteristic
104C2×C8×C37—21no—
105C2×C8×C37—21no—
106C2×C8×C37C2311yescharacteristic
107C2×C8×C37C2311yescharacteristic
108C42×C37C2311yescharacteristic
109#10596942—21no—
110#10596941—21no—
111#10596941—21no—
112#10596941—21no—
113#10596940—21no—
114#10596939—21no—
115#10596939—21no—
116#10596939—21no—
117#10596938—41no—
118#10596934C2311yescharacteristic
119#10596934C2311yescharacteristic
120Dic148—21no—
121Dic148D411yescharacteristic, complemented
122D296—21no—
123D296—21no—
124D296—21no—
125D296—21no—
126D296—21no—
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#10596930—21no—
137#10596930—21no—
138#10596930D411yescharacteristic, complemented
139#10596930D411yescharacteristic, complemented
140#10596929—21no—
141#10596929—21no—
142C8×D37—21no—
143C8×D37—21no—
144C22×D37—21no—
145C22×D37—21no—
146C22×D37—21no—
147C22×D37—41no—
148C22×D37—41no—
149C22×D37—41no—
150Q8×C37C2×D411yescharacteristic
151Q8×C37C2×D411yescharacteristic
152D4×C37—21no—
153D4×C37—21no—
154D4×C37C2×D411yescharacteristic
155D4×C37C2×D411yescharacteristic
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37—21no—
159C2×C4×C37C2411yescharacteristic
160C22⋊D37—21no—
161C22⋊D37—21no—
162C22⋊D37—41no—
163C22⋊D37—41no—
164C22⋊D37—41no—
165C22⋊D37—41no—
166C2×Dic37—21no—
167C2×Dic37—41no—
168D148—21no—
169D148—21no—
170D148—21no—
171D148—21no—
172D148—21no—
173D148—21no—
174D148—41no—
175D148—41no—
176D148—41no—
177D148—82no—
178D148C2×D411yescharacteristic
179D148C2×D411yescharacteristic
180C4×D37—21no—
181C4×D37—21no—
182C4×D37—41no—
183C4×D37—41no—
184C4×D37—41no—
185C4×D37—41no—
186Dic74—21no—
187Dic74—21no—
188Dic74—41no—
189Dic74C2×D411yescharacteristic
190Dic74C2×D411yescharacteristic
191C8×C37—21no—
192C8×C37—21no—
193C8×C37C2×D411yescharacteristic
194C8×C37C2×D411yescharacteristic
195C8×C37C2×D411yescharacteristic
196C8×C37C2×D411yescharacteristic
197#64436—21no—
198#64436—21no—
199C22×C37—21no—
200C22×C37—21no—
201C22×C37H(5,𝔽2)11yescharacteristic
202C2×D37—21no—
203C2×D37—21no—
204C2×D37—41no—
205C2×D37—41no—
206C2×D37—41no—
207C2×D37—81no—
208C2×D37—81no—
209C2×D37—81no—
210C2×D37—161no—
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×C37D4211yescharacteristic
226D37—41no—
227D37—41no—
228D37—81no—
229D37—81no—
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#453—371no—
244#444—371no—
245#444D3711yescharacteristic, complemented
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)—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)—741no—
267#135—371no—
268#135—741no—
269#135—741no—
270#135—741no—
271#135—741no—
272#135C2×D3711yescharacteristic
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#131C2×D3711yescharacteristic, complemented
284#131C2×D3711yescharacteristic, complemented
285#127—371no—
286#124—371no—
287#108—371no—
288#108C2×D3711yescharacteristic, complemented
289#104—371no—
290#104—371no—
291#104C2×D3711yescharacteristic, complemented
292#104C2×D3711yescharacteristic, complemented
293#101—371no—
294#100—371no—
295#100—371no—
296#100—371no—
297#97C2×D3711yescharacteristic, complemented
298#41—371no—
299#41—371no—
300#41—741no—
301#41—741no—
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—371no—
315C2×D4—371no—
316C2×D4—371no—
317C2×D4—741no—
318C2×D4—741no—
319C2×D4—741no—
320C2×D4—741no—
321C2×D4—741no—
322C2×D4—741no—
323C2×D4—1481no—
324C2×D4—1481no—
325C2×D4—1481no—
326C2×D4—1481no—
327Q16—371no—
328Q16—741no—
329Q16—741no—
330Q16D14811yescharacteristic, complemented
331SD16—371no—
332SD16—371no—
333SD16—741no—
334SD16—741no—
335SD16—741no—
336SD16—741no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16D14811yescharacteristic, complemented
346SD16D14811yescharacteristic, complemented
347D8—371no—
348D8—741no—
349D8—741no—
350D8—741no—
351D8—741no—
352D8—741no—
353D8—741no—
354D8—741no—
355D8—741no—
356D8—741no—
357D8—741no—
358D8D14811yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—371no—
362M16—371no—
363M16—741no—
364M16—741no—
365M16C22×D3711yescharacteristic
366M16C22×D3711yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—741no—
370C2×C8—741no—
371C2×C8C22×D3711yescharacteristic
372C2×C8C22×D3711yescharacteristic
373C22⋊C4—1481no—
374C42C22×D3711yescharacteristic
375C23—741no—
376C23—741no—
377C23—741no—
378C23—1481no—
379C23—1481no—
380C23—1481no—
381Q8—371no—
382Q8—371no—
383Q8—741no—
384Q8—741no—
385Q8—1481no—
386Q8C2×D14811yescharacteristic
387Q8C2×D14811yescharacteristic
388D4—21no—
389D4—21no—
390D4—371no—
391D4—371no—
392D4—2962no—
393D4—741no—
394D4—741no—
395D4—741no—
396D4—741no—
397D4—741no—
398D4—741no—
399D4—741no—
400D4—741no—
401D4—1481no—
402D4—1481no—
403D4—1481no—
404D4—1481no—
405D4—1481no—
406D4—1481no—
407D4—1481no—
408D4C2×D14811yescharacteristic
409D4C2×D14811yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
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—741no—
425C8—741no—
426C8C2×D14811yescharacteristic
427C8C2×D14811yescharacteristic
428C8D4×D3711yescharacteristic
429C8D4×D3711yescharacteristic
430C22—21no—
431C22—21no—
432C22—2961no—
433C22—2961no—
434C22—2961no—
435C22—741no—
436C22—741no—
437C22—5921no—
438C22—5921no—
439C22—5921no—
440C22—1481no—
441C22—1481no—
442C22—1481no—
443C22#1192458211yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—741no—
448C4—741no—
449C4—1481no—
450C4C2×D4×D3711yescharacteristic
451C4C22×D14811yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—2961no—
456C2—2961no—
457C2—2961no—
458C2—1481no—
459C2—1481no—
460C2D4×D14811yescharacteristic
subgroupG/H
centerC2D4×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#444C2
socleC2×C37D42
hypercenter#444D37
hypocenterC37#3288
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #14558345C2semidirect
2. #14558340C2semidirect
3. #14558338C2semidirect
4. #14558335C2semidirect
5. #14557922C2semidirect
6. #14557804C2semidirect
7. #14557803C2semidirect
8. #14557797C2semidirect
9. #14557796C2semidirect
10. #14557712C2semidirect
11. #14557707C2semidirect
12. #14557702C2semidirect
13. #14557702C2semidirect
14. #14557656C2semidirect
15. C37×#444C2semidirect
16. #11924583C22semidirect
18. #11924582C22semidirect
19. #11924582C22semidirect
21. #11924569C22semidirect
23. #11924566C22semidirect
28. #11924564C22semidirect
29. #11924564C22semidirect
33. #11924561C22semidirect
34. #11924561C22semidirect
42. C2×#10596930C22semidirect
43. C2×#10596930C22semidirect
46. C2×D296C22semidirect
47. C2×D296C22semidirect
49. #11924542C22semidirect
50. #11924542C22semidirect
51. #11924533C22semidirect
52. #11924524C22semidirect
53. #11924472C22semidirect
54. #11924464C22semidirect
55. #11924464C22semidirect
56. #11924454C22semidirect
57. #11924452C22semidirect
58. #11924452C22semidirect
59. #11924452C22semidirect
61. #131×C37C22semidirect
62. #131×C37C22semidirect
63. #108×C37C22semidirect
64. #104×C37C22semidirect
65. #104×C37C22semidirect
66. #97×C37C22semidirect
96. Q16×C37D4semidirect
97. SD16×C37D4semidirect
98. SD16×C37D4semidirect
99. D8×C37D4semidirect
121. Dic148D4semidirect
129. D296D4semidirect
138. #10596930D4semidirect
139. #10596930D4semidirect
245. #444D37semidirect
246. C37#3288semidirect
283. #131C2×D37semidirect
284. #131C2×D37semidirect
288. #108C2×D37semidirect
291. #104C2×D37semidirect
292. #104C2×D37semidirect
297. #97C2×D37semidirect
330. Q16D148semidirect
345. SD16D148semidirect
346. SD16D148semidirect
358. D8D148semidirect

Maximal subgroups

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

subgroupindex
#145583452
#145583402
#145583382
#145583352
#145579222
#145578042
#145578032
#145577972
#145577962
#145577122
#145577072
#145577022
#145576562
C37×#4442
#328837