Finite Group Databasebeta

← #18006376

Subgroups — #18006376

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#14558340C211yesmaximal, characteristic, complemented
3#14558336C211yesmaximal, characteristic, complemented
4#14557914C211yesmaximal, characteristic, complemented
5#14557806C211yesmaximal, characteristic, complemented
6#14557801C211yesmaximal, characteristic, complemented
7#14557796C211yesmaximal, characteristic, complemented
8#14557793C211yesmaximal, characteristic, complemented
9#14557711C211yesmaximal, characteristic, complemented
10#14557709C211yesmaximal, characteristic, complemented
11#14557706C211yesmaximal, characteristic, complemented
12#14557704C211yesmaximal, characteristic, complemented
13#14557650C211yesmaximal, characteristic, complemented
14#14557648C211yesmaximal, characteristic, complemented
15C37×#577C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic, complemented
17#11924582C2211yescharacteristic
18#11924568—21no—
19#11924567—21no—
20#11924567C2211yescharacteristic, complemented
21#11924566—21no—
22#11924566C2211yescharacteristic
23#11924566C2211yescharacteristic, complemented
24#11924562—21no—
25#11924562C2211yescharacteristic
26#11924561—21no—
27#11924561C2211yescharacteristic
28#11924561C2211yescharacteristic, complemented
29#11924560—21no—
30#11924557—21no—
31#11924556—21no—
32#11924556—21no—
33#11924556C2211yescharacteristic
34C2×#10596942—21no—
35C2×#10596942C2211yescharacteristic, complemented
36C2×#10596930C2211yescharacteristic, complemented
37SD16×D37—21no—
38C2×#10596939—21no—
39C2×#10596939C2211yescharacteristic
40#11924543C2211yescharacteristic
41#11924543C2211yescharacteristic, complemented
42#11924542C2211yescharacteristic, complemented
43#11924525C2211yescharacteristic, complemented
44#11924523C2211yescharacteristic, complemented
45#11924472C2211yescharacteristic, complemented
46#11924471C2211yescharacteristic, complemented
47#11924463C2211yescharacteristic
48#11924463C2211yescharacteristic, complemented
49#11924463C2211yescharacteristic, complemented
50#11924462C2211yescharacteristic, complemented
51#11924455C2211yescharacteristic, complemented
52#11924454C2211yescharacteristic, complemented
53#11924453C2211yescharacteristic, complemented
54#11924452C2211yescharacteristic, complemented
55C8×Dic37C2211yescharacteristic, complemented
562−1+4×C37C2211yescharacteristic, complemented
57H(5,𝔽2)×C37C2211yescharacteristic
58#137×C37—21no—
59#137×C37C2211yescharacteristic
60AGL(1,ℤ/8)×C37—21no—
61AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
62#135×C37—21no—
63#135×C37C2211yescharacteristic
64C2×SD16×C37—21no—
65C2×SD16×C37C2211yescharacteristic, complemented
66#131×C37C2211yescharacteristic, complemented
67#41×C37—21no—
68#41×C37—21no—
69#41×C37—21no—
70#41×C37—21no—
71#41×C37—41no—
72#41×C37C2311yescharacteristic
73#41×C37C2311yescharacteristic
74#41×C37C2311yescharacteristic
75C2×Q8×C37—21no—
76C2×Q8×C37—21no—
77C2×Q8×C37C2311yescharacteristic
78C2×D4×C37—21no—
79C2×D4×C37—21no—
80C2×D4×C37—41no—
81C2×D4×C37C2311yescharacteristic
82#10596966—21no—
83Q8×D37—21no—
84#10596964—21no—
85#10596964—41no—
86D4×D37—21no—
87D4×D37—41no—
88#10596962—21no—
89#10596962—21no—
90#10596962C2311yescharacteristic
91C2×D148—21no—
92C2×D148C2311yescharacteristic
93C2×Dic74—21no—
94C2×Dic74C2311yescharacteristic
95Q16×C37—21no—
96Q16×C37D411yescharacteristic
97SD16×C37—21no—
98SD16×C37—21no—
99SD16×C37—21no—
100SD16×C37—21no—
101SD16×C37D411yescharacteristic
102SD16×C37D411yescharacteristic
103D8×C37—21no—
104D8×C37D411yescharacteristic
105M16×C37—21no—
106M16×C37C2311yescharacteristic
107C2×C8×C37—21no—
108C2×C8×C37C2311yescharacteristic
109C22⋊Dic37—41no—
110#10596942—21no—
111#10596942—21no—
112#10596942—21no—
113#10596942—21no—
114#10596942—21no—
115#10596942D411yescharacteristic
116#10596941—21no—
117#10596941—21no—
118#10596941—21no—
119#10596941D411yescharacteristic
120#10596940—21no—
121#10596940—21no—
122#10596940—21no—
123#10596940D411yescharacteristic
124#10596939—21no—
125#10596939—21no—
126#10596939—21no—
127#10596939—21no—
128#10596939—21no—
129#10596939D411yescharacteristic
130#10596938—41no—
131C4×Dic37C2311yescharacteristic
132#10596934—21no—
133#10596934—21no—
134#10596934C2311yescharacteristic
135#10596934C2311yescharacteristic
136#10596934C2311yescharacteristic
137C2×#64436—21no—
138C2×#64436—21no—
139C2×#64436C2311yescharacteristic
140#10596930—21no—
141#10596930—21no—
142#10596929—21no—
143C8×D37—21no—
144C23×C37—21no—
145C23×C37—41no—
146C22×D37—21no—
147C22×D37—41no—
148Q8×C37—21no—
149Q8×C37—21no—
150Q8×C37—41no—
151Q8×C37C2×D411yescharacteristic
152Q8×C37C2×D411yescharacteristic
153Q8×C37C2×D411yescharacteristic
154D4×C37—21no—
155D4×C37—21no—
156D4×C37—21no—
157D4×C37—21no—
158D4×C37—21no—
159D4×C37—41no—
160D4×C37—41no—
161D4×C37—41no—
162D4×C37C2×D411yescharacteristic
163D4×C37C2×D411yescharacteristic
164D4×C37C2×D411yescharacteristic
165C2×C4×C37—21no—
166C2×C4×C37—21no—
167C2×C4×C37—21no—
168C2×C4×C37—21no—
169C2×C4×C37—41no—
170C2×C4×C37—41no—
171C2×C4×C37—41no—
172C2×C4×C37C2411yescharacteristic
173C22⋊D37—21no—
174C22⋊D37—41no—
175C22⋊D37—41no—
176C2×Dic37—21no—
177C2×Dic37—21no—
178C2×Dic37—41no—
179D148—21no—
180D148—21no—
181D148—41no—
182D148C2×D411yescharacteristic
183C4×D37—21no—
184C4×D37—41no—
185C4×D37—41no—
186Dic74—21no—
187Dic74—21no—
188Dic74—41no—
189Dic74C2×D411yescharacteristic
190C8×C37—21no—
191C8×C37C2×D411yescharacteristic
192C8×C37C2×D411yescharacteristic
193#64436—21no—
194#64436—21no—
195#64436—21no—
196#64436C2×D411yescharacteristic
197#64436C2×D411yescharacteristic
198C22×C37—21no—
199C22×C37—21no—
200C22×C37—21no—
201C22×C37—41no—
202C22×C37—81no—
203C22×C37—161no—
204C22×C37H(5,𝔽2)11yescharacteristic
205C2×D37—21no—
206C2×D37—41no—
207C2×D37—81no—
208C2×D37—161no—
209C4×C37—21no—
210C4×C37—21no—
211C4×C37—21no—
212C4×C37—41no—
213C4×C37C22×D411yescharacteristic
214C4×C37C22×D411yescharacteristic
215Dic37—21no—
216Dic37—41no—
217Dic37—41no—
218#3290—371nomaximal, Sylow
219C2×C37—21no—
220C2×C37—41no—
221C2×C37—41no—
222C2×C37—41no—
223C2×C37—81no—
224C2×C37D4211yescharacteristic
225D37—41no—
226D37—81no—
227#578—371no—
228#577—371no—
229#577D3711yescharacteristic, complemented
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#454—371no—
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)C2×D3711yescharacteristic
247#137—21no—
248#137—371no—
249#137—371no—
250#137—371no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137C2×D3711yescharacteristic
255AGL(1,ℤ/8)—21no—
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)C2×D3711yescharacteristic, complemented
263#135—21no—
264#135—371no—
265#135—741no—
266#135—741no—
267#135—741no—
268#135C2×D3711yescharacteristic
269C2×Q16—371no—
270C2×Q16—741no—
271C2×SD16—21no—
272C2×SD16—371no—
273C2×SD16—741no—
274C2×SD16C2×D3711yescharacteristic, complemented
275C2×D8—371no—
276C2×D8—741no—
277#131—371no—
278#131—371no—
279#131—371no—
280#131C2×D3711yescharacteristic, complemented
281#124—371no—
282#124—371no—
283#108—371no—
284#108—371no—
285#104—371no—
286#104—371no—
287#104—371no—
288#104—371no—
289#101—371no—
290#101—371no—
291#100—371no—
292#100—371no—
293C4×C8—371no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—371no—
300#41—741no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—1481no—
305#41C22×D3711yescharacteristic
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—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—371no—
324Q16—741no—
325Q16—741no—
326Q16—741no—
327Q16—741no—
328Q16—741no—
329Q16C22⋊D3711yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—371no—
335SD16—371no—
336SD16—741no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16C22⋊D3711yescharacteristic
345SD16C22⋊D3711yescharacteristic
346D8—21no—
347D8—371no—
348D8—741no—
349D8—741no—
350D8—741no—
351D8—741no—
352D8—741no—
353D8C22⋊D3711yescharacteristic
354M16—21no—
355M16—371no—
356M16—371no—
357M16—371no—
358M16—741no—
359M16—741no—
360M16—741no—
361M16C22×D3711yescharacteristic
362C2×C8—21no—
363C2×C8—371no—
364C2×C8—741no—
365C2×C8—741no—
366C2×C8—741no—
367C2×C8C22×D3711yescharacteristic
368C22⋊C4—1481no—
369C22⋊C4—1481no—
370C42—371no—
371C23—21no—
372C23—41no—
373C23—741no—
374C23—1481no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—371no—
379Q8—741no—
380Q8—741no—
381Q8—1481no—
382Q8D4×D3711yescharacteristic
383Q8C2×C22⋊D3711yescharacteristic
384Q8C2×C22⋊D3711yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—371no—
394D4—741no—
395D4—741no—
396D4—741no—
397D4—1481no—
398D4—1481no—
399D4—1481no—
400D4D4×D3711yescharacteristic
401D4C2×C22⋊D3711yescharacteristic
402D4C2×C22⋊D3711yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—741no—
411C2×C4—741no—
412C2×C4—741no—
413C2×C4—1481no—
414C2×C4—1481no—
415C2×C4—1481no—
416C2×C4C23×D3711yescharacteristic
417C8—21no—
418C8—371no—
419C8—371no—
420C8—741no—
421C8—741no—
422C8—741no—
423C8C2×C22⋊D3711yescharacteristic
424C8C2×C22⋊D3711yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—2961no—
432C22—741no—
433C22—5921no—
434C22—1481no—
435C22#1192458111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—741no—
441C4—1481no—
442C4—1481no—
443C4C2×D4×D3711yescharacteristic
444C4C22×C22⋊D3711yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—2961no—
451C2—1481no—
452C2D4×C22⋊D3711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#577C2
socleC2×C37D42
hypercenter#577D37
hypocenterC37#3290
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #14558348C2semidirect
2. #14558340C2semidirect
3. #14558336C2semidirect
4. #14557914C2semidirect
5. #14557806C2semidirect
6. #14557801C2semidirect
7. #14557796C2semidirect
8. #14557793C2semidirect
9. #14557711C2semidirect
10. #14557709C2semidirect
11. #14557706C2semidirect
12. #14557704C2semidirect
13. #14557650C2semidirect
14. #14557648C2semidirect
15. C37×#577C2semidirect
16. #11924583C22semidirect
20. #11924567C22semidirect
23. #11924566C22semidirect
28. #11924561C22semidirect
35. C2×#10596942C22semidirect
36. C2×#10596930C22semidirect
41. #11924543C22semidirect
42. #11924542C22semidirect
43. #11924525C22semidirect
44. #11924523C22semidirect
45. #11924472C22semidirect
46. #11924471C22semidirect
48. #11924463C22semidirect
49. #11924463C22semidirect
50. #11924462C22semidirect
51. #11924455C22semidirect
52. #11924454C22semidirect
53. #11924453C22semidirect
54. #11924452C22semidirect
55. C8×Dic37C22semidirect
56. 2−1+4×C37C22semidirect
61. AGL(1,ℤ/8)×C37C22semidirect
65. C2×SD16×C37C22semidirect
66. #131×C37C22semidirect
229. #577D37semidirect
242. C37#3290semidirect
244. 2−1+4C2×D37semidirect
262. AGL(1,ℤ/8)C2×D37semidirect
274. C2×SD16C2×D37semidirect
280. #131C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583482
#145583402
#145583362
#145579142
#145578062
#145578012
#145577962
#145577932
#145577112
#145577092
#145577062
#145577042
#145576502
#145576482
C37×#5772
#329037