Finite Group Databasebeta

← #18006387

Subgroups — #18006387

Order 4736.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558344C211yesmaximal, characteristic, complemented
2#14558341C211yesmaximal, characteristic, complemented
3#14558340C211yesmaximal, characteristic, complemented
4#14557904C211yesmaximal, characteristic, complemented
5#14557798C211yesmaximal, characteristic, complemented
6#14557796C211yesmaximal, characteristic, complemented
7#14557794C211yesmaximal, characteristic, complemented
8#14557793C211yesmaximal, characteristic, complemented
9#14557716C211yesmaximal, characteristic, complemented
10#14557714C211yesmaximal, characteristic, complemented
11#14557701C211yesmaximal, characteristic, complemented
12#14557699C211yesmaximal, characteristic, complemented
13#14557650C211yesmaximal, characteristic, complemented
14#14557648C211yesmaximal, characteristic, complemented
15C37×#577C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic
17#11924582C2211yescharacteristic, complemented
18#11924568—21no—
19#11924567—21no—
20#11924567C2211yescharacteristic, complemented
21#11924566—21no—
22#11924566C2211yescharacteristic, complemented
23#11924566C2211yescharacteristic, complemented
24#11924562—21no—
25#11924562C2211yescharacteristic
26#11924561—21no—
27#11924561C2211yescharacteristic
28#11924561C2211yescharacteristic
29#11924560—21no—
30#11924557—21no—
31#11924556—21no—
32#11924556—21no—
33#11924556C2211yescharacteristic
34C2×#10596930C2211yescharacteristic, complemented
35C2×#10596940—21no—
36C2×#10596940C2211yescharacteristic, complemented
37C2×#10596941—21no—
38C2×#10596941C2211yescharacteristic, complemented
39SD16×D37—21no—
40#11924543C2211yescharacteristic, complemented
41#11924543C2211yescharacteristic, complemented
42#11924542C2211yescharacteristic, complemented
43#11924534C2211yescharacteristic, complemented
44#11924532C2211yescharacteristic
45#11924472C2211yescharacteristic, complemented
46#11924471C2211yescharacteristic, complemented
47#11924463C2211yescharacteristic, complemented
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
57H(5,𝔽2)×C37C2211yescharacteristic, complemented
58#137×C37—21no—
59#137×C37C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C37—21no—
61AGL(1,ℤ/8)×C37C2211yescharacteristic
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
82C2×C22⋊D37—41no—
83#10596966—21no—
84Q8×D37—21no—
85#10596964—21no—
86#10596964—41no—
87D4×D37—21no—
88D4×D37—41no—
89#10596962—21no—
90#10596962—21no—
91#10596962C2311yescharacteristic
92C2×D148—21no—
93C2×D148C2311yescharacteristic
94C2×Dic74—21no—
95C2×Dic74C2311yescharacteristic
96Q16×C37—21no—
97Q16×C37D411yescharacteristic, complemented
98SD16×C37—21no—
99SD16×C37—21no—
100SD16×C37—21no—
101SD16×C37—21no—
102SD16×C37D411yescharacteristic, complemented
103SD16×C37D411yescharacteristic, complemented
104D8×C37—21no—
105D8×C37D411yescharacteristic, complemented
106M16×C37—21no—
107M16×C37C2311yescharacteristic
108C2×C8×C37—21no—
109C2×C8×C37C2311yescharacteristic
110#10596942—21no—
111#10596942—21no—
112#10596942—21no—
113#10596942D411yescharacteristic, complemented
114#10596941—21no—
115#10596941—21no—
116#10596941—21no—
117#10596941—21no—
118#10596941—21no—
119#10596941D411yescharacteristic, complemented
120#10596940—21no—
121#10596940—21no—
122#10596940—21no—
123#10596940—21no—
124#10596940—21no—
125#10596940D411yescharacteristic, complemented
126#10596939—21no—
127#10596939—21no—
128#10596939—21no—
129#10596939D411yescharacteristic, complemented
130#10596936—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—
176C22⋊D37—82no—
177C2×Dic37—21no—
178C2×Dic37—21no—
179C2×Dic37—41no—
180D148—21no—
181D148—21no—
182D148—41no—
183D148C2×D411yescharacteristic
184C4×D37—21no—
185C4×D37—41no—
186C4×D37—41no—
187Dic74—21no—
188Dic74—21no—
189Dic74—41no—
190Dic74C2×D411yescharacteristic
191C8×C37—21no—
192C8×C37C2×D411yescharacteristic
193C8×C37C2×D411yescharacteristic
194#64436—21no—
195#64436—21no—
196#64436—21no—
197#64436C2×D411yescharacteristic
198#64436C2×D411yescharacteristic
199C22×C37—21no—
200C22×C37—21no—
201C22×C37—21no—
202C22×C37—41no—
203C22×C37—81no—
204C22×C37—161no—
205C22×C37H(5,𝔽2)11yescharacteristic
206C2×D37—21no—
207C2×D37—41no—
208C2×D37—81no—
209C2×D37—161no—
210C4×C37—21no—
211C4×C37—21no—
212C4×C37—21no—
213C4×C37—41no—
214C4×C37C22×D411yescharacteristic
215C4×C37C22×D411yescharacteristic
216Dic37—22no—
217Dic37—21no—
218Dic37—41no—
219#3291—371nomaximal, Sylow
220C2×C37—21no—
221C2×C37—41no—
222C2×C37—41no—
223C2×C37—41no—
224C2×C37—81no—
225C2×C37D4211yescharacteristic
226D37—41no—
227D37—81no—
228#577—371no—
229#577—371no—
230#577—371no—
231#577D3711yescharacteristic, complemented
232#492—371no—
233#471—371no—
234#471—371no—
235#471—371no—
236#471—371no—
237#456—371no—
238#456—371no—
239#453—371no—
240#453—371no—
241#443—371no—
242#443—371no—
243C37#329111yescharacteristic, complemented, Sylow
2442−1+4—371no—
2452−1+4C2×D3711yescharacteristic
246H(5,𝔽2)—371no—
247H(5,𝔽2)C2×D3711yescharacteristic, complemented
248#137—21no—
249#137—371no—
250#137—371no—
251#137—371no—
252#137—741no—
253#137—741no—
254#137—741no—
255#137C2×D3711yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—371no—
258AGL(1,ℤ/8)—371no—
259AGL(1,ℤ/8)—371no—
260AGL(1,ℤ/8)—741no—
261AGL(1,ℤ/8)—741no—
262AGL(1,ℤ/8)—741no—
263AGL(1,ℤ/8)C2×D3711yescharacteristic
264#135—21no—
265#135—371no—
266#135—741no—
267#135—741no—
268#135—741no—
269#135C2×D3711yescharacteristic
270C2×SD16—21no—
271C2×SD16—371no—
272C2×SD16—371no—
273C2×SD16—371no—
274C2×SD16—741no—
275C2×SD16—741no—
276C2×SD16—741no—
277C2×SD16C2×D3711yescharacteristic, complemented
278#131—371no—
279#131—371no—
280#131—371no—
281#131C2×D3711yescharacteristic, complemented
282C4⋊Q8—371no—
283#127—371no—
284#108—371no—
285#108—371no—
286#104—371no—
287#104—371no—
288#104—371no—
289#104—371no—
290#101—371no—
291#101—371no—
292#100—371no—
293#100—371no—
294C4×C8—371no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—371no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—741no—
305#41—1481no—
306#41C22×D3711yescharacteristic
307#41C22×D3711yescharacteristic
308#41C22×D3711yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—371no—
312C2×Q8—741no—
313C2×Q8—741no—
314C2×Q8C22×D3711yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—371no—
319C2×D4—741no—
320C2×D4—741no—
321C2×D4—1481no—
322C2×D4—1481no—
323C2×D4C22×D3711yescharacteristic
324Q16—21no—
325Q16—371no—
326Q16—741no—
327Q16—741no—
328Q16—741no—
329Q16C22⋊D3711yescharacteristic, complemented
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—
344SD16—741no—
345SD16—741no—
346SD16—741no—
347SD16—741no—
348SD16C22⋊D3711yescharacteristic, complemented
349SD16C22⋊D3711yescharacteristic, complemented
350D8—21no—
351D8—371no—
352D8—741no—
353D8—741no—
354D8—741no—
355D8C22⋊D3711yescharacteristic, complemented
356M16—21no—
357M16—371no—
358M16—371no—
359M16—371no—
360M16—741no—
361M16—741no—
362M16—741no—
363M16C22×D3711yescharacteristic
364C2×C8—21no—
365C2×C8—371no—
366C2×C8—741no—
367C2×C8—741no—
368C2×C8—741no—
369C2×C8C22×D3711yescharacteristic
370C4⋊C4—1481no—
371C42—371no—
372C23—21no—
373C23—41no—
374C23—741no—
375C23—1481no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—371no—
380Q8—741no—
381Q8—741no—
382Q8—1481no—
383Q8D4×D3711yescharacteristic
384Q8C2×C22⋊D3711yescharacteristic
385Q8C2×C22⋊D3711yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—371no—
395D4—2962no—
396D4—741no—
397D4—741no—
398D4—741no—
399D4—1481no—
400D4—1481no—
401D4—1481no—
402D4D4×D3711yescharacteristic
403D4C2×C22⋊D3711yescharacteristic
404D4C2×C22⋊D3711yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—741no—
413C2×C4—741no—
414C2×C4—741no—
415C2×C4—1481no—
416C2×C4—1481no—
417C2×C4—1481no—
418C2×C4C23×D3711yescharacteristic
419C8—21no—
420C8—371no—
421C8—371no—
422C8—741no—
423C8—741no—
424C8—741no—
425C8C2×C22⋊D3711yescharacteristic
426C8C2×C22⋊D3711yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—2961no—
434C22—741no—
435C22—5921no—
436C22—1481no—
437C22#1192458111yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—742no—
443C4—741no—
444C4—1481no—
445C4C2×D4×D3711yescharacteristic
446C4C22×C22⋊D3711yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—2961no—
453C2—1481no—
454C2D4×C22⋊D3711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#577C2
socleC2×C37D42
hypercenter#577D37
hypocenterC37#3291
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. #14558344C2semidirect
2. #14558341C2semidirect
3. #14558340C2semidirect
4. #14557904C2semidirect
5. #14557798C2semidirect
6. #14557796C2semidirect
7. #14557794C2semidirect
8. #14557793C2semidirect
9. #14557716C2semidirect
10. #14557714C2semidirect
11. #14557701C2semidirect
12. #14557699C2semidirect
13. #14557650C2semidirect
14. #14557648C2semidirect
15. C37×#577C2semidirect
17. #11924582C22semidirect
20. #11924567C22semidirect
22. #11924566C22semidirect
23. #11924566C22semidirect
34. C2×#10596930C22semidirect
36. C2×#10596940C22semidirect
38. C2×#10596941C22semidirect
40. #11924543C22semidirect
41. #11924543C22semidirect
42. #11924542C22semidirect
43. #11924534C22semidirect
45. #11924472C22semidirect
46. #11924471C22semidirect
47. #11924463C22semidirect
48. #11924463C22semidirect
49. #11924463C22semidirect
50. #11924462C22semidirect
51. #11924455C22semidirect
52. #11924454C22semidirect
53. #11924453C22semidirect
54. #11924452C22semidirect
55. C8×Dic37C22semidirect
57. H(5,𝔽2)×C37C22semidirect
59. #137×C37C22semidirect
65. C2×SD16×C37C22semidirect
66. #131×C37C22semidirect
97. Q16×C37D4semidirect
102. SD16×C37D4semidirect
103. SD16×C37D4semidirect
105. D8×C37D4semidirect
113. #10596942D4semidirect
119. #10596941D4semidirect
125. #10596940D4semidirect
129. #10596939D4semidirect
231. #577D37semidirect
243. C37#3291semidirect
247. H(5,𝔽2)C2×D37semidirect
255. #137C2×D37semidirect
277. C2×SD16C2×D37semidirect
281. #131C2×D37semidirect
329. Q16C22⋊D37semidirect
348. SD16C22⋊D37semidirect
349. SD16C22⋊D37semidirect
355. D8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583442
#145583412
#145583402
#145579042
#145577982
#145577962
#145577942
#145577932
#145577162
#145577142
#145577012
#145576992
#145576502
#145576482
C37×#5772
#329137