Finite Group Databasebeta

← #18006388

Subgroups — #18006388

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#14558345C211yesmaximal, characteristic, complemented
2#14558343C211yesmaximal, characteristic, complemented
3#14558342C211yesmaximal, characteristic, complemented
4#14558339C211yesmaximal, characteristic, complemented
5#14557904C211yesmaximal, characteristic, complemented
6#14557799C211yesmaximal, characteristic, complemented
7#14557797C211yesmaximal, characteristic, complemented
8#14557795C211yesmaximal, characteristic, complemented
9#14557718C211yesmaximal, characteristic, complemented
10#14557714C211yesmaximal, characteristic, complemented
11#14557703C211yesmaximal, characteristic, complemented
12#14557699C211yesmaximal, characteristic, complemented
13#14557649C211yesmaximal, characteristic, complemented
14#14557648C211yesmaximal, characteristic, complemented
15C37×#471C211yesmaximal, characteristic, complemented
16#11924584C2211yescharacteristic
17#11924583C2211yescharacteristic
18#11924582C2211yescharacteristic, complemented
19#11924581C2211yescharacteristic, complemented
20#11924569—21no—
21#11924569C2211yescharacteristic, complemented
22#11924569C2211yescharacteristic, complemented
23#11924568—21no—
24#11924567C2211yescharacteristic, complemented
25#11924565—21no—
26#11924565—21no—
27#11924564—21no—
28#11924564C2211yescharacteristic
29#11924564C2211yescharacteristic
30#11924563—21no—
31#11924563—21no—
32#11924562C2211yescharacteristic
33#11924560—21no—
34#11924559—21no—
35#11924558—21no—
36#11924558C2211yescharacteristic
37#11924557—21no—
38#11924556C2211yescharacteristic
39#11924555—21no—
40C2×#10596930—21no—
41C2×#10596930C2211yescharacteristic, complemented
42C2×#10596940C2211yescharacteristic, complemented
43C2×#10596941C2211yescharacteristic, complemented
44SD16×D37—21no—
45SD16×D37—21no—
46SD16×D37—21no—
47#11924544C2211yescharacteristic, complemented
48#11924544C2211yescharacteristic, complemented
49#11924542C2211yescharacteristic, complemented
50#11924534C2211yescharacteristic, complemented
51#11924532C2211yescharacteristic
52#11924471C2211yescharacteristic, complemented
53#11924463C2211yescharacteristic, complemented
54#11924462C2211yescharacteristic, complemented
55#11924462C2211yescharacteristic, complemented
56#11924462C2211yescharacteristic, complemented
57#11924454C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59C8×Dic37C2211yescharacteristic, complemented
60#137×C37C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62C2×SD16×C37C2211yescharacteristic, complemented
63#131×C37C2211yescharacteristic, complemented
64#108×C37C2211yescharacteristic, complemented
65#101×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67#41×C37C2311yescharacteristic
68C2×Q8×C37C2311yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C2×C22⋊D37—41no—
71C2×C22⋊D37—41no—
72#10596966—21no—
73#10596966—21no—
74#10596966—21no—
75Q8×D37—21no—
76Q8×D37—21no—
77Q8×D37—21no—
78#10596964—21no—
79#10596964—21no—
80#10596964—21no—
81#10596964—41no—
82D4×D37—21no—
83D4×D37—21no—
84D4×D37—21no—
85D4×D37—41no—
86#10596962—21no—
87#10596962—21no—
88#10596962—41no—
89#10596962C2311yescharacteristic
90#10596962C2311yescharacteristic
91#10596962C2311yescharacteristic
92C2×D148—21no—
93C2×D148C2311yescharacteristic
94C2×Dic74—21no—
95C2×Dic74C2311yescharacteristic
96Q16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99SD16×C37—21no—
100SD16×C37—21no—
101D8×C37—21no—
102M16×C37—21no—
103M16×C37C2311yescharacteristic
104M16×C37C2311yescharacteristic
105M16×C37C2311yescharacteristic
106C2×C8×C37—21no—
107C2×C8×C37C2311yescharacteristic
108#10596942—21no—
109#10596942D411yescharacteristic, complemented
110#10596941—21no—
111#10596941—21no—
112#10596941—21no—
113#10596941D411yescharacteristic, complemented
114#10596940—21no—
115#10596940—21no—
116#10596940—21no—
117#10596940D411yescharacteristic, complemented
118#10596939—21no—
119#10596939D411yescharacteristic, complemented
120#10596936—41no—
121C4×Dic37C2311yescharacteristic
122#10596934C2311yescharacteristic
123C2×#64436C2311yescharacteristic
124Dic148—21no—
125Dic148—21no—
126Dic148D411yescharacteristic, complemented
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#10596930D411yescharacteristic, complemented
137#10596930D411yescharacteristic, complemented
138#10596929—21no—
139#10596929—21no—
140#10596929—21no—
141C8×D37—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×C37C2×D411yescharacteristic
151D4×C37—21no—
152D4×C37—21no—
153D4×C37—21no—
154D4×C37C2×D411yescharacteristic
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37C2411yescharacteristic
158C22⋊D37—21no—
159C22⋊D37—21no—
160C22⋊D37—21no—
161C22⋊D37—41no—
162C22⋊D37—41no—
163C22⋊D37—41no—
164C22⋊D37—41no—
165C22⋊D37—82no—
166C2×Dic37—21no—
167C2×Dic37—21no—
168C2×Dic37—41no—
169C2×Dic37—41no—
170D148—21no—
171D148—21no—
172D148—41no—
173D148—41no—
174D148C2×D411yescharacteristic
175D148C2×D411yescharacteristic
176D148C2×D411yescharacteristic
177C4×D37—21no—
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
190Dic74C2×D411yescharacteristic
191C8×C37—21no—
192C8×C37—21no—
193C8×C37—21no—
194C8×C37C2×D411yescharacteristic
195C8×C37C2×D411yescharacteristic
196#64436—21no—
197#64436C2×D411yescharacteristic
198#64436C2×D411yescharacteristic
199C22×C37—21no—
200C22×C37—41no—
201C22×C37—81no—
202C22×C37H(5,𝔽2)11yescharacteristic
203C2×D37—21no—
204C2×D37—21no—
205C2×D37—21no—
206C2×D37—41no—
207C2×D37—81no—
208C2×D37—161no—
209C2×D37—161no—
210C4×C37—21no—
211C4×C37—41no—
212C4×C37C22×D411yescharacteristic
213C4×C37C22×D411yescharacteristic
214Dic37—22no—
215Dic37—21no—
216Dic37—21no—
217Dic37—21no—
218Dic37—41no—
219#3291—371nomaximal, Sylow
220C2×C37—21no—
221C2×C37—41no—
222C2×C37—81no—
223C2×C37D4211yescharacteristic
224D37—41no—
225D37—41no—
226D37—41no—
227D37—81no—
228#577—371no—
229#577—371no—
230#577—371no—
231#577—371no—
232#492—371no—
233#471—371no—
234#471—371no—
235#471—371no—
236#471D3711yescharacteristic, complemented
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+4—371no—
246H(5,𝔽2)—371no—
247H(5,𝔽2)—371no—
248#137—371no—
249#137—371no—
250#137—371no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137—741no—
255#137C2×D3711yescharacteristic, complemented
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—
263AGL(1,ℤ/8)C2×D3711yescharacteristic
264#135—371no—
265#135—371no—
266#135—741no—
267#135—741no—
268#135—741no—
269#135—741no—
270C2×SD16—371no—
271C2×SD16—371no—
272C2×SD16—371no—
273C2×SD16—741no—
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#108C2×D3711yescharacteristic, complemented
286#104—371no—
287#104—371no—
288#104—371no—
289#104—371no—
290#101—371no—
291#101C2×D3711yescharacteristic, complemented
292#100—371no—
293#100C2×D3711yescharacteristic, complemented
294C4×C8—371no—
295#41—371no—
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—741no—
305#41—741no—
306#41—1481no—
307#41—1481no—
308#41C22×D3711yescharacteristic
309C2×Q8—371no—
310C2×Q8—741no—
311C2×Q8—741no—
312C2×Q8—741no—
313C2×Q8—741no—
314C2×Q8C22×D3711yescharacteristic
315C2×D4—371no—
316C2×D4—741no—
317C2×D4—741no—
318C2×D4—741no—
319C2×D4—741no—
320C2×D4—1481no—
321C2×D4—1481no—
322C2×D4—1481no—
323C2×D4C22×D3711yescharacteristic
324Q16—21no—
325Q16—371no—
326Q16—371no—
327Q16—741no—
328Q16—741no—
329Q16—741no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—371no—
335SD16—371no—
336SD16—371no—
337SD16—371no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16—741no—
346SD16—741no—
347SD16—741no—
348SD16—741no—
349SD16—741no—
350D8—21no—
351D8—371no—
352D8—371no—
353D8—741no—
354D8—741no—
355D8—741no—
356M16—21no—
357M16—371no—
358M16—741no—
359M16—741no—
360M16—741no—
361M16C22×D3711yescharacteristic
362M16C22×D3711yescharacteristic
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—741no—
374C23—1481no—
375C23—1481no—
376Q8—21no—
377Q8—21no—
378Q8—371no—
379Q8—371no—
380Q8—371no—
381Q8—741no—
382Q8—741no—
383Q8—1481no—
384Q8—1481no—
385Q8D4×D3711yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—371no—
390D4—371no—
391D4—371no—
392D4—2962no—
393D4—741no—
394D4—741no—
395D4—741no—
396D4—741no—
397D4—741no—
398D4—1481no—
399D4—1481no—
400D4—1481no—
401D4—1481no—
402D4—1481no—
403D4—1481no—
404D4D4×D3711yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—741no—
408C2×C4—741no—
409C2×C4—741no—
410C2×C4—741no—
411C2×C4—741no—
412C2×C4—1481no—
413C2×C4—1481no—
414C2×C4—1481no—
415C2×C4—1481no—
416C2×C4—1481no—
417C2×C4—1481no—
418C2×C4C23×D3711yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—371no—
423C8—371no—
424C8—741no—
425C8D4×D3711yescharacteristic
426C8D4×D3711yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—2961no—
431C22—741no—
432C22—741no—
433C22—741no—
434C22—5921no—
435C22—5921no—
436C22—1481no—
437C22#1192458211yescharacteristic
438C4—21no—
439C4—41no—
440C4—742no—
441C4—741no—
442C4—741no—
443C4—741no—
444C4—1481no—
445C4C2×D4×D3711yescharacteristic
446C4C2×D4×D3711yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—2961no—
451C2—1481no—
452C2—1481no—
453C2—1481no—
454C2#1455816711yescharacteristic
subgroupG/H
centerC2#14558167
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#471C2
socleC2×C37D42
hypercenter#471D37
hypocenterC37#3291
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #14558345C2semidirect
2. #14558343C2semidirect
3. #14558342C2semidirect
4. #14558339C2semidirect
5. #14557904C2semidirect
6. #14557799C2semidirect
7. #14557797C2semidirect
8. #14557795C2semidirect
9. #14557718C2semidirect
10. #14557714C2semidirect
11. #14557703C2semidirect
12. #14557699C2semidirect
13. #14557649C2semidirect
14. #14557648C2semidirect
15. C37×#471C2semidirect
18. #11924582C22semidirect
19. #11924581C22semidirect
21. #11924569C22semidirect
22. #11924569C22semidirect
24. #11924567C22semidirect
41. C2×#10596930C22semidirect
42. C2×#10596940C22semidirect
43. C2×#10596941C22semidirect
47. #11924544C22semidirect
48. #11924544C22semidirect
49. #11924542C22semidirect
50. #11924534C22semidirect
52. #11924471C22semidirect
53. #11924463C22semidirect
54. #11924462C22semidirect
55. #11924462C22semidirect
56. #11924462C22semidirect
57. #11924454C22semidirect
58. #11924452C22semidirect
59. C8×Dic37C22semidirect
60. #137×C37C22semidirect
62. C2×SD16×C37C22semidirect
63. #131×C37C22semidirect
64. #108×C37C22semidirect
65. #101×C37C22semidirect
66. #100×C37C22semidirect
109. #10596942D4semidirect
113. #10596941D4semidirect
117. #10596940D4semidirect
119. #10596939D4semidirect
126. Dic148D4semidirect
129. D296D4semidirect
136. #10596930D4semidirect
137. #10596930D4semidirect
236. #471D37semidirect
243. C37#3291semidirect
255. #137C2×D37semidirect
277. C2×SD16C2×D37semidirect
281. #131C2×D37semidirect
285. #108C2×D37semidirect
291. #101C2×D37semidirect
293. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583452
#145583432
#145583422
#145583392
#145579042
#145577992
#145577972
#145577952
#145577182
#145577142
#145577032
#145576992
#145576492
#145576482
C37×#4712
#329137