Finite Group Databasebeta

← #18006375

Subgroups — #18006375

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#14558348C211yesmaximal, characteristic, complemented
2#14558343C211yesmaximal, characteristic, complemented
3#14558341C211yesmaximal, characteristic, complemented
4#14558337C211yesmaximal, characteristic, complemented
5#14557915C211yesmaximal, characteristic, complemented
6#14557807C211yesmaximal, characteristic, complemented
7#14557801C211yesmaximal, characteristic, complemented
8#14557799C211yesmaximal, characteristic, complemented
9#14557794C211yesmaximal, characteristic, complemented
10#14557712C211yesmaximal, characteristic, complemented
11#14557710C211yesmaximal, characteristic, complemented
12#14557707C211yesmaximal, characteristic, complemented
13#14557647C211yesmaximal, characteristic, complemented
14#14557647C211yesmaximal, characteristic, complemented
15C37×#454C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic, complemented
17#11924582C2211yescharacteristic
18#11924581C2211yescharacteristic
19#11924569C2211yescharacteristic
20#11924567—21no—
21#11924567—21no—
22#11924567C2211yescharacteristic
23#11924567C2211yescharacteristic, complemented
24#11924566—21no—
25#11924566C2211yescharacteristic, complemented
26#11924565—21no—
27#11924564C2211yescharacteristic
28#11924563—21no—
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×#10596942—21no—
40C2×#10596942C2211yescharacteristic, complemented
41C2×#10596940C2211yescharacteristic, complemented
42C2×#10596941—21no—
43C2×#10596941C2211yescharacteristic, complemented
44SD16×D37—21no—
45C2×#10596939C2211yescharacteristic
46D8×D37—21no—
47#11924544C2211yescharacteristic
48#11924544C2211yescharacteristic, complemented
49#11924543C2211yescharacteristic, complemented
50#11924543C2211yescharacteristic, complemented
51#11924524C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924464C2211yescharacteristic
55#11924464C2211yescharacteristic, complemented
56#11924454C2211yescharacteristic, complemented
57#11924453C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59C4×#64436C2211yescharacteristic, complemented
602−1+4×C37C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
63#124×C37C2211yescharacteristic, complemented
64#104×C37C2211yescharacteristic, complemented
65#104×C37C2211yescharacteristic, complemented
66#101×C37C2211yescharacteristic, complemented
67#41×C37—21no—
68#41×C37—21no—
69#41×C37—41no—
70#41×C37C2311yescharacteristic
71#41×C37C2311yescharacteristic
72C2×Q8×C37—21no—
73C2×Q8×C37—21no—
74C2×Q8×C37C2311yescharacteristic
75C2×D4×C37C2311yescharacteristic
76C2×C22⋊D37—41no—
77#10596966—21no—
78Q8×D37—21no—
79#10596964—21no—
80#10596964—21no—
81#10596964—21no—
82#10596964—41no—
83D4×D37—21no—
84D4×D37—21no—
85D4×D37—21no—
86D4×D37—41no—
87#10596962—21no—
88#10596962—21no—
89#10596962C2311yescharacteristic
90#10596962C2311yescharacteristic
91C2×D148—21no—
92C2×D148C2311yescharacteristic
93C2×Dic74—21no—
94C2×Dic74C2311yescharacteristic
95SD16×C37—21no—
96SD16×C37—21no—
97D8×C37—21no—
98D8×C37—21no—
99M16×C37C2311yescharacteristic
100M16×C37C2311yescharacteristic
101C22⋊C4×C37—41no—
102C42×C37C2311yescharacteristic
103#10596942—21no—
104#10596942—21no—
105#10596942—21no—
106#10596942—21no—
107#10596942—21no—
108#10596942D411yescharacteristic
109#10596942D411yescharacteristic
110#10596941—21no—
111#10596941—21no—
112#10596941—21no—
113#10596941—21no—
114#10596941—21no—
115#10596941D411yescharacteristic
116#10596941D411yescharacteristic
117#10596940—21no—
118#10596940—21no—
119#10596940—21no—
120#10596940D411yescharacteristic
121#10596940D411yescharacteristic
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—
145C22×D37—21no—
146C22×D37—41no—
147C22×D37—41no—
148Q8×C37—21no—
149Q8×C37—21no—
150Q8×C37—41no—
151Q8×C37C2×D411yescharacteristic
152Q8×C37C2×D411yescharacteristic
153D4×C37—21no—
154D4×C37—21no—
155D4×C37—21no—
156D4×C37—21no—
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×C37—41no—
166C2×C4×C37C2411yescharacteristic
167C22⋊D37—21no—
168C22⋊D37—21no—
169C22⋊D37—41no—
170C22⋊D37—41no—
171C22⋊D37—41no—
172C22⋊D37—41no—
173C2×Dic37—21no—
174C2×Dic37—41no—
175C2×Dic37—41no—
176D148—21no—
177D148—21no—
178D148—41no—
179D148C2×D411yescharacteristic
180D148C2×D411yescharacteristic
181C4×D37—21no—
182C4×D37—21no—
183C4×D37—41no—
184C4×D37—41no—
185Dic74—21no—
186Dic74—21no—
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×C37H(5,𝔽2)11yescharacteristic
203C2×D37—21no—
204C2×D37—21no—
205C2×D37—41no—
206C2×D37—81no—
207C2×D37—161no—
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#455—371no—
238#454—371no—
239#454D3711yescharacteristic, complemented
240#443—371no—
241#443—371no—
242C37#329011yescharacteristic, complemented, Sylow
2432−1+4—371no—
2442−1+4C2×D3711yescharacteristic, complemented
245H(5,𝔽2)—371no—
246H(5,𝔽2)—371no—
247#137—371no—
248#137—371no—
249#137—371no—
250#137—371no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137—741no—
255AGL(1,ℤ/8)—371no—
256AGL(1,ℤ/8)—371no—
257AGL(1,ℤ/8)—741no—
258AGL(1,ℤ/8)—741no—
259AGL(1,ℤ/8)—741no—
260AGL(1,ℤ/8)—741no—
261AGL(1,ℤ/8)C2×D3711yescharacteristic
262AGL(1,ℤ/8)C2×D3711yescharacteristic, complemented
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, complemented
288#104C2×D3711yescharacteristic, complemented
289#101—371no—
290#101C2×D3711yescharacteristic, complemented
291#100—371no—
292#100—371no—
293C4×C8—371no—
294#41—21no—
295#41—21no—
296#41—41no—
297#41—371no—
298#41—371no—
299#41—741no—
300#41—741no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—741no—
305#41—1481no—
306#41C22×D3711yescharacteristic
307#41C22×D3711yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—371no—
311C2×Q8—741no—
312C2×Q8—741no—
313C2×Q8C22×D3711yescharacteristic
314C2×D4—371no—
315C2×D4—741no—
316C2×D4—741no—
317C2×D4—741no—
318C2×D4—741no—
319C2×D4—1481no—
320C2×D4—1481no—
321C2×D4C22×D3711yescharacteristic
322Q16—371no—
323Q16—371no—
324Q16—741no—
325Q16—741no—
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—21no—
347D8—21no—
348D8—371no—
349D8—371no—
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—741no—
373C23—1481no—
374C23—1481no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—371no—
379Q8—371no—
380Q8—741no—
381Q8—741no—
382Q8—1481no—
383Q8D4×D3711yescharacteristic
384Q8D4×D3711yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—371no—
391D4—371no—
392D4—741no—
393D4—741no—
394D4—741no—
395D4—741no—
396D4—1481no—
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—41no—
409C2×C4—741no—
410C2×C4—741no—
411C2×C4—741no—
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—2961no—
430C22—741no—
431C22—741no—
432C22—5921no—
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×#454C2
socleC2×C37D42
hypercenter#454D37
hypocenterC37#3290
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14558348C2semidirect
2. #14558343C2semidirect
3. #14558341C2semidirect
4. #14558337C2semidirect
5. #14557915C2semidirect
6. #14557807C2semidirect
7. #14557801C2semidirect
8. #14557799C2semidirect
9. #14557794C2semidirect
10. #14557712C2semidirect
11. #14557710C2semidirect
12. #14557707C2semidirect
13. #14557647C2semidirect
14. #14557647C2semidirect
15. C37×#454C2semidirect
16. #11924583C22semidirect
23. #11924567C22semidirect
25. #11924566C22semidirect
30. #11924561C22semidirect
40. C2×#10596942C22semidirect
41. C2×#10596940C22semidirect
43. C2×#10596941C22semidirect
48. #11924544C22semidirect
49. #11924543C22semidirect
50. #11924543C22semidirect
51. #11924524C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
55. #11924464C22semidirect
56. #11924454C22semidirect
57. #11924453C22semidirect
58. #11924452C22semidirect
59. C4×#64436C22semidirect
60. 2−1+4×C37C22semidirect
62. AGL(1,ℤ/8)×C37C22semidirect
63. #124×C37C22semidirect
64. #104×C37C22semidirect
65. #104×C37C22semidirect
66. #101×C37C22semidirect
239. #454D37semidirect
242. C37#3290semidirect
244. 2−1+4C2×D37semidirect
262. AGL(1,ℤ/8)C2×D37semidirect
282. #124C2×D37semidirect
287. #104C2×D37semidirect
288. #104C2×D37semidirect
290. #101C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583482
#145583432
#145583412
#145583372
#145579152
#145578072
#145578012
#145577992
#145577942
#145577122
#145577102
#145577072
#145576472
C37×#4542
#329037