Finite Group Databasebeta

← #18006380

Subgroups — #18006380

Order 4736.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558349C211yesmaximal, characteristic, complemented
2#14558344C211yesmaximal, characteristic, complemented
3#14558342C211yesmaximal, characteristic, complemented
4#14558336C211yesmaximal, characteristic, complemented
5#14557915C211yesmaximal, characteristic, complemented
6#14557806C211yesmaximal, characteristic, complemented
7#14557802C211yesmaximal, characteristic, complemented
8#14557798C211yesmaximal, characteristic, complemented
9#14557795C211yesmaximal, characteristic, complemented
10#14557712C211yesmaximal, characteristic, complemented
11#14557707C211yesmaximal, characteristic, complemented
12#14557705C211yesmaximal, characteristic, complemented
13#14557647C211yesmaximal, characteristic, complemented
14#14557647C211yesmaximal, characteristic, complemented
15C37×#455C211yesmaximal, characteristic, complemented
16#11924584C2211yescharacteristic, complemented
17#11924583C2211yescharacteristic, complemented
18#11924582C2211yescharacteristic
19#11924569C2211yescharacteristic, complemented
20#11924568—21no—
21#11924568—21no—
22#11924566—21no—
23#11924566C2211yescharacteristic
24#11924565—21no—
25#11924564C2211yescharacteristic, complemented
26#11924563—21no—
27#11924562—21no—
28#11924562—21no—
29#11924562C2211yescharacteristic
30#11924562C2211yescharacteristic, complemented
31#11924561—21no—
32#11924561C2211yescharacteristic
33#11924559—21no—
34#11924557—21no—
35#11924556—21no—
36#11924556—21no—
37#11924556C2211yescharacteristic
38#11924556C2211yescharacteristic
39C2×#10596942C2211yescharacteristic, complemented
40Q16×D37—21no—
41C2×#10596940—21no—
42C2×#10596940C2211yescharacteristic, complemented
43C2×#10596941C2211yescharacteristic, complemented
44SD16×D37—21no—
45C2×#10596939—21no—
46C2×#10596939C2211yescharacteristic
47#11924544C2211yescharacteristic, complemented
48#11924544C2211yescharacteristic, complemented
49#11924543C2211yescharacteristic
50#11924543C2211yescharacteristic, complemented
51#11924524C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924464C2211yescharacteristic, complemented
55#11924464C2211yescharacteristic, complemented
56#11924455C2211yescharacteristic, complemented
57#11924454C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59C4×#64436C2211yescharacteristic, complemented
60H(5,𝔽2)×C37C2211yescharacteristic
61#137×C37C2211yescharacteristic
62#137×C37C2211yescharacteristic, complemented
63#124×C37C2211yescharacteristic, complemented
64#104×C37C2211yescharacteristic
65#104×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67#41×C37—21no—
68#41×C37—21no—
69#41×C37C2311yescharacteristic
70#41×C37C2311yescharacteristic
71C2×Q8×C37C2311yescharacteristic
72C2×D4×C37—21no—
73C2×D4×C37—21no—
74C2×D4×C37—41no—
75C2×D4×C37C2311yescharacteristic
76#10596966—21no—
77#10596966—21no—
78#10596966—21no—
79Q8×D37—21no—
80Q8×D37—21no—
81Q8×D37—21no—
82#10596964—21no—
83#10596964—41no—
84D4×D37—21no—
85D4×D37—41no—
86#10596962—21no—
87#10596962—21no—
88#10596962—41no—
89#10596962C2311yescharacteristic
90#10596962C2311yescharacteristic
91C2×D148—21no—
92C2×D148C2311yescharacteristic
93C2×Dic74—21no—
94C2×Dic74C2311yescharacteristic
95Q16×C37—21no—
96Q16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99M16×C37C2311yescharacteristic
100M16×C37C2311yescharacteristic
101C22⋊C4×C37—41no—
102C42×C37C2311yescharacteristic
103#10596942—21no—
104#10596942—21no—
105#10596942—21no—
106#10596942D411yescharacteristic
107#10596942D411yescharacteristic
108#10596941—21no—
109#10596941—21no—
110#10596941—21no—
111#10596941D411yescharacteristic
112#10596941D411yescharacteristic
113#10596940—21no—
114#10596940—21no—
115#10596940—21no—
116#10596940—21no—
117#10596940—21no—
118#10596940D411yescharacteristic
119#10596940D411yescharacteristic
120#10596939—21no—
121#10596939—21no—
122#10596939—21no—
123#10596939—21no—
124#10596939—21no—
125#10596939D411yescharacteristic
126#10596939D411yescharacteristic
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—41no—
146C22×D37—21no—
147C22×D37—41no—
148Q8×C37—21no—
149Q8×C37—21no—
150Q8×C37C2×D411yescharacteristic
151Q8×C37C2×D411yescharacteristic
152D4×C37—21no—
153D4×C37—21no—
154D4×C37—21no—
155D4×C37—21no—
156D4×C37—41no—
157D4×C37—41no—
158D4×C37C2×D411yescharacteristic
159D4×C37C2×D411yescharacteristic
160C2×C4×C37—21no—
161C2×C4×C37—21no—
162C2×C4×C37—21no—
163C2×C4×C37—21no—
164C2×C4×C37—41no—
165C2×C4×C37C2411yescharacteristic
166C22⋊D37—21no—
167C22⋊D37—21no—
168C22⋊D37—41no—
169C22⋊D37—41no—
170C2×Dic37—21no—
171C2×Dic37—41no—
172D148—21no—
173D148—21no—
174D148—41no—
175D148—41no—
176D148C2×D411yescharacteristic
177D148C2×D411yescharacteristic
178C4×D37—21no—
179C4×D37—21no—
180C4×D37—41no—
181C4×D37—41no—
182C4×D37—41no—
183C4×D37—41no—
184Dic74—21no—
185Dic74—21no—
186Dic74—41no—
187Dic74—41no—
188Dic74C2×D411yescharacteristic
189Dic74C2×D411yescharacteristic
190C8×C37—21no—
191C8×C37—21no—
192#64436—21no—
193#64436—21no—
194#64436C2×D411yescharacteristic
195#64436C2×D411yescharacteristic
196#64436C2×D411yescharacteristic
197#64436C2×D411yescharacteristic
198C22×C37—21no—
199C22×C37—21no—
200C22×C37—41no—
201C22×C37—81no—
202C22×C37—161no—
203C22×C37H(5,𝔽2)11yescharacteristic
204C2×D37—21no—
205C2×D37—21no—
206C2×D37—41no—
207C2×D37—81no—
208C2×D37—161no—
209C4×C37—21no—
210C4×C37—21no—
211C4×C37—41no—
212C4×C37—41no—
213C4×C37C22×D411yescharacteristic
214C4×C37C22×D411yescharacteristic
215Dic37—21no—
216Dic37—21no—
217Dic37—41no—
218#3290—371nomaximal, Sylow
219C2×C37—21no—
220C2×C37—41no—
221C2×C37—41no—
222C2×C37—81no—
223C2×C37D4211yescharacteristic
224D37—41no—
225D37—41no—
226D37—81no—
227#578—371no—
228#577—371no—
229#577—371no—
230#576—371no—
231#495—371no—
232#473—371no—
233#472—371no—
234#471—371no—
235#471—371no—
236#455—371no—
237#455D3711yescharacteristic, complemented
238#454—371no—
239#454—371no—
240#443—371no—
241#443—371no—
242C37#329011yescharacteristic, complemented, Sylow
2432−1+4—371no—
2442−1+4—371no—
245H(5,𝔽2)—371no—
246H(5,𝔽2)C2×D3711yescharacteristic
247#137—371no—
248#137—371no—
249#137—741no—
250#137—741no—
251#137—741no—
252#137—741no—
253#137C2×D3711yescharacteristic
254#137C2×D3711yescharacteristic, complemented
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—
263#135—371no—
264#135—371no—
265#135—741no—
266#135—741no—
267#135—741no—
268#135—741no—
269C2×Q16—371no—
270C2×Q16—741no—
271C2×SD16—371no—
272C2×SD16—371no—
273C2×SD16—741no—
274C2×SD16—741no—
275C2×D8—371no—
276C2×D8—741no—
277#131—371no—
278#131—371no—
279#131—371no—
280#131—371no—
281#124—371no—
282#124C2×D3711yescharacteristic, complemented
283#108—371no—
284#108—371no—
285#104—371no—
286#104—371no—
287#104C2×D3711yescharacteristic
288#104C2×D3711yescharacteristic, complemented
289#101—371no—
290#101—371no—
291#100—371no—
292#100C2×D3711yescharacteristic, complemented
293C4×C8—371no—
294#41—21no—
295#41—21no—
296#41—371no—
297#41—371no—
298#41—741no—
299#41—741no—
300#41—741no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—1481no—
305#41—1481no—
306#41C22×D3711yescharacteristic
307#41C22×D3711yescharacteristic
308C2×Q8—371no—
309C2×Q8—741no—
310C2×Q8—741no—
311C2×Q8—741no—
312C2×Q8—741no—
313C2×Q8C22×D3711yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—371no—
318C2×D4—741no—
319C2×D4—741no—
320C2×D4—1481no—
321C2×D4C22×D3711yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—371no—
325Q16—371no—
326Q16—741no—
327Q16—741no—
328Q16—741no—
329Q16—741no—
330SD16—21no—
331SD16—21no—
332SD16—371no—
333SD16—371no—
334SD16—371no—
335SD16—371no—
336SD16—741no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16—741no—
346D8—371no—
347D8—371no—
348D8—741no—
349D8—741no—
350D8—741no—
351D8—741no—
352D8—741no—
353D8—741no—
354M16—371no—
355M16—371no—
356M16—741no—
357M16—741no—
358M16—741no—
359M16—741no—
360M16C22×D3711yescharacteristic
361M16C22×D3711yescharacteristic
362C2×C8—371no—
363C2×C8—371no—
364C2×C8—741no—
365C2×C8—741no—
366C2×C8—741no—
367C2×C8—741no—
368C22⋊C4—41no—
369C22⋊C4—1481no—
370C42C22×D3711yescharacteristic
371C23—21no—
372C23—41no—
373C23—741no—
374C23—1481no—
375Q8—21no—
376Q8—21no—
377Q8—371no—
378Q8—371no—
379Q8—741no—
380Q8—741no—
381Q8—1481no—
382Q8—1481no—
383Q8D4×D3711yescharacteristic
384Q8D4×D3711yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—371no—
392D4—371no—
393D4—741no—
394D4—741no—
395D4—741no—
396D4—741no—
397D4—1481no—
398D4—1481no—
399D4—1481no—
400D4—1481no—
401D4D4×D3711yescharacteristic
402D4D4×D3711yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—741no—
409C2×C4—741no—
410C2×C4—741no—
411C2×C4—1481no—
412C2×C4—1481no—
413C2×C4—1481no—
414C2×C4—1481no—
415C2×C4—1481no—
416C2×C4C23×D3711yescharacteristic
417C8—21no—
418C8—21no—
419C8—371no—
420C8—371no—
421C8—371no—
422C8—371no—
423C8—741no—
424C8—741no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—161no—
430C22—2961no—
431C22—741no—
432C22—741no—
433C22—5921no—
434C22—1481no—
435C22#1192458111yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—741no—
441C4—741no—
442C4—1481no—
443C4C2×D4×D3711yescharacteristic
444C4C2×D4×D3711yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—2961no—
450C2—1481no—
451C2—1481no—
452C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#455C2
socleC2×C37D42
hypercenter#455D37
hypocenterC37#3290
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14558349C2semidirect
2. #14558344C2semidirect
3. #14558342C2semidirect
4. #14558336C2semidirect
5. #14557915C2semidirect
6. #14557806C2semidirect
7. #14557802C2semidirect
8. #14557798C2semidirect
9. #14557795C2semidirect
10. #14557712C2semidirect
11. #14557707C2semidirect
12. #14557705C2semidirect
13. #14557647C2semidirect
14. #14557647C2semidirect
15. C37×#455C2semidirect
16. #11924584C22semidirect
17. #11924583C22semidirect
19. #11924569C22semidirect
25. #11924564C22semidirect
30. #11924562C22semidirect
39. C2×#10596942C22semidirect
42. C2×#10596940C22semidirect
43. C2×#10596941C22semidirect
47. #11924544C22semidirect
48. #11924544C22semidirect
50. #11924543C22semidirect
51. #11924524C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
54. #11924464C22semidirect
55. #11924464C22semidirect
56. #11924455C22semidirect
57. #11924454C22semidirect
58. #11924452C22semidirect
59. C4×#64436C22semidirect
62. #137×C37C22semidirect
63. #124×C37C22semidirect
65. #104×C37C22semidirect
66. #100×C37C22semidirect
237. #455D37semidirect
242. C37#3290semidirect
254. #137C2×D37semidirect
282. #124C2×D37semidirect
288. #104C2×D37semidirect
292. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583492
#145583442
#145583422
#145583362
#145579152
#145578062
#145578022
#145577982
#145577952
#145577122
#145577072
#145577052
#145576472
C37×#4552
#329037