Finite Group Databasebeta

← #18006379

Subgroups — #18006379

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#14558345C211yesmaximal, characteristic, complemented
3#14558339C211yesmaximal, characteristic, complemented
4#14558337C211yesmaximal, characteristic, complemented
5#14557914C211yesmaximal, characteristic, complemented
6#14557807C211yesmaximal, characteristic, complemented
7#14557802C211yesmaximal, characteristic, complemented
8#14557797C211yesmaximal, characteristic, complemented
9#14557713C211yesmaximal, characteristic, complemented
10#14557709C211yesmaximal, characteristic, complemented
11#14557708C211yesmaximal, characteristic, complemented
12#14557704C211yesmaximal, characteristic, complemented
13#14557649C211yesmaximal, characteristic, complemented
14#14557648C211yesmaximal, characteristic, complemented
15C37×#471C211yesmaximal, characteristic, complemented
16#11924584C2211yescharacteristic, complemented
17#11924583C2211yescharacteristic, complemented
18#11924582C2211yescharacteristic
19#11924581C2211yescharacteristic
20#11924569—21no—
21#11924569C2211yescharacteristic
22#11924569C2211yescharacteristic, complemented
23#11924568—21no—
24#11924567C2211yescharacteristic
25#11924565—21no—
26#11924565—21no—
27#11924564—21no—
28#11924564C2211yescharacteristic
29#11924564C2211yescharacteristic, complemented
30#11924563—21no—
31#11924563—21no—
32#11924562C2211yescharacteristic, complemented
33#11924560—21no—
34#11924558—21no—
35#11924558C2211yescharacteristic
36#11924557—21no—
37#11924557—21no—
38#11924557—21no—
39#11924556C2211yescharacteristic
40C2×#10596942C2211yescharacteristic, complemented
41Q16×D37—21no—
42C2×#10596930—21no—
43C2×#10596930C2211yescharacteristic, complemented
44SD16×D37—21no—
45C2×#10596939C2211yescharacteristic
46D8×D37—21no—
47#11924544C2211yescharacteristic
48#11924544C2211yescharacteristic, complemented
49#11924542C2211yescharacteristic, complemented
50#11924525C2211yescharacteristic, complemented
51#11924523C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924463C2211yescharacteristic, complemented
54#11924462C2211yescharacteristic
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—
71#10596966—21no—
72#10596966—21no—
73#10596966—21no—
74Q8×D37—21no—
75Q8×D37—21no—
76Q8×D37—21no—
77#10596964—21no—
78#10596964—21no—
79#10596964—21no—
80#10596964—41no—
81D4×D37—21no—
82D4×D37—21no—
83D4×D37—21no—
84D4×D37—41no—
85#10596962—21no—
86#10596962—21no—
87#10596962—41no—
88#10596962C2311yescharacteristic
89#10596962C2311yescharacteristic
90#10596962C2311yescharacteristic
91C2×D148—21no—
92C2×D148C2311yescharacteristic
93C2×Dic74—21no—
94C2×Dic74C2311yescharacteristic
95Q16×C37—21no—
96SD16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99SD16×C37—21no—
100D8×C37—21no—
101M16×C37—21no—
102M16×C37C2311yescharacteristic
103M16×C37C2311yescharacteristic
104M16×C37C2311yescharacteristic
105C2×C8×C37—21no—
106C2×C8×C37C2311yescharacteristic
107C22⋊Dic37—41no—
108#10596942—21no—
109#10596942—21no—
110#10596942—21no—
111#10596942D411yescharacteristic
112#10596941—21no—
113#10596941D411yescharacteristic
114#10596940—21no—
115#10596940D411yescharacteristic
116#10596939—21no—
117#10596939—21no—
118#10596939—21no—
119#10596939D411yescharacteristic
120#10596938—41no—
121C4×Dic37C2311yescharacteristic
122#10596934C2311yescharacteristic
123C2×#64436C2311yescharacteristic
124Dic148—21no—
125Dic148—21no—
126Dic148D411yescharacteristic
127D296—21no—
128D296—21no—
129D296D411yescharacteristic
130#10596930—21no—
131#10596930—21no—
132#10596930—21no—
133#10596930—21no—
134#10596930—21no—
135#10596930—21no—
136#10596930D411yescharacteristic
137#10596930D411yescharacteristic
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—
165C2×Dic37—21no—
166C2×Dic37—21no—
167C2×Dic37—41no—
168C2×Dic37—41no—
169D148—21no—
170D148—21no—
171D148—41no—
172D148—41no—
173D148C2×D411yescharacteristic
174D148C2×D411yescharacteristic
175D148C2×D411yescharacteristic
176C4×D37—21no—
177C4×D37—21no—
178C4×D37—21no—
179C4×D37—41no—
180C4×D37—41no—
181C4×D37—41no—
182C4×D37—41no—
183Dic74—21no—
184Dic74—21no—
185Dic74—41no—
186Dic74—41no—
187Dic74C2×D411yescharacteristic
188Dic74C2×D411yescharacteristic
189Dic74C2×D411yescharacteristic
190C8×C37—21no—
191C8×C37—21no—
192C8×C37—21no—
193C8×C37C2×D411yescharacteristic
194C8×C37C2×D411yescharacteristic
195#64436—21no—
196#64436C2×D411yescharacteristic
197#64436C2×D411yescharacteristic
198C22×C37—21no—
199C22×C37—41no—
200C22×C37—81no—
201C22×C37H(5,𝔽2)11yescharacteristic
202C2×D37—21no—
203C2×D37—21no—
204C2×D37—21no—
205C2×D37—41no—
206C2×D37—81no—
207C2×D37—161no—
208C2×D37—161no—
209C4×C37—21no—
210C4×C37—41no—
211C4×C37C22×D411yescharacteristic
212C4×C37C22×D411yescharacteristic
213Dic37—21no—
214Dic37—21no—
215Dic37—21no—
216Dic37—41no—
217Dic37—41no—
218#3290—371nomaximal, Sylow
219C2×C37—21no—
220C2×C37—41no—
221C2×C37—81no—
222C2×C37D4211yescharacteristic
223D37—41no—
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#471D3711yescharacteristic, complemented
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+4—371no—
245H(5,𝔽2)—371no—
246H(5,𝔽2)—371no—
247#137—371no—
248#137—371no—
249#137—371no—
250#137—741no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137C2×D3711yescharacteristic, complemented
255AGL(1,ℤ/8)—371no—
256AGL(1,ℤ/8)—371no—
257AGL(1,ℤ/8)—371no—
258AGL(1,ℤ/8)—741no—
259AGL(1,ℤ/8)—741no—
260AGL(1,ℤ/8)—741no—
261AGL(1,ℤ/8)—741no—
262AGL(1,ℤ/8)C2×D3711yescharacteristic
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—741no—
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#108C2×D3711yescharacteristic, complemented
285#104—371no—
286#104—371no—
287#104—371no—
288#104—371no—
289#101—371no—
290#101C2×D3711yescharacteristic, complemented
291#100—371no—
292#100C2×D3711yescharacteristic, complemented
293C4×C8—371no—
294#41—371no—
295#41—371no—
296#41—371no—
297#41—741no—
298#41—741no—
299#41—741no—
300#41—741no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—741no—
305#41—1481no—
306#41—1481no—
307#41C22×D3711yescharacteristic
308C2×Q8—371no—
309C2×Q8—741no—
310C2×Q8—741no—
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—21no—
323Q16—371no—
324Q16—371no—
325Q16—741no—
326Q16—741no—
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—
346D8—21no—
347D8—371no—
348D8—371no—
349D8—741no—
350D8—741no—
351D8—741no—
352D8—741no—
353D8—741no—
354M16—21no—
355M16—371no—
356M16—741no—
357M16—741no—
358M16—741no—
359M16C22×D3711yescharacteristic
360M16C22×D3711yescharacteristic
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—741no—
373C23—1481no—
374C23—1481no—
375Q8—21no—
376Q8—21no—
377Q8—371no—
378Q8—371no—
379Q8—371no—
380Q8—741no—
381Q8—741no—
382Q8—1481no—
383Q8—1481no—
384Q8D4×D3711yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—371no—
389D4—371no—
390D4—371no—
391D4—741no—
392D4—741no—
393D4—741no—
394D4—741no—
395D4—741no—
396D4—1481no—
397D4—1481no—
398D4—1481no—
399D4—1481no—
400D4—1481no—
401D4—1481no—
402D4D4×D3711yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—741no—
406C2×C4—741no—
407C2×C4—741no—
408C2×C4—741no—
409C2×C4—741no—
410C2×C4—1481no—
411C2×C4—1481no—
412C2×C4—1481no—
413C2×C4—1481no—
414C2×C4—1481no—
415C2×C4—1481no—
416C2×C4C23×D3711yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—371no—
421C8—371no—
422C8—741no—
423C8D4×D3711yescharacteristic
424C8D4×D3711yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—2961no—
429C22—741no—
430C22—741no—
431C22—741no—
432C22—5921no—
433C22—5921no—
434C22—1481no—
435C22#1192458211yescharacteristic
436C4—21no—
437C4—41no—
438C4—741no—
439C4—741no—
440C4—741no—
441C4—1481no—
442C4—1481no—
443C4C2×D4×D3711yescharacteristic
444C4C2×D4×D3711yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—2961no—
449C2—1481no—
450C2—1481no—
451C2—1481no—
452C2#1455816711yescharacteristic
subgroupG/H
centerC2#14558167
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#471C2
socleC2×C37D42
hypercenter#471D37
hypocenterC37#3290
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. #14558349C2semidirect
2. #14558345C2semidirect
3. #14558339C2semidirect
4. #14558337C2semidirect
5. #14557914C2semidirect
6. #14557807C2semidirect
7. #14557802C2semidirect
8. #14557797C2semidirect
9. #14557713C2semidirect
10. #14557709C2semidirect
11. #14557708C2semidirect
12. #14557704C2semidirect
13. #14557649C2semidirect
14. #14557648C2semidirect
15. C37×#471C2semidirect
16. #11924584C22semidirect
17. #11924583C22semidirect
22. #11924569C22semidirect
29. #11924564C22semidirect
32. #11924562C22semidirect
40. C2×#10596942C22semidirect
43. C2×#10596930C22semidirect
48. #11924544C22semidirect
49. #11924542C22semidirect
50. #11924525C22semidirect
51. #11924523C22semidirect
52. #11924471C22semidirect
53. #11924463C22semidirect
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
235. #471D37semidirect
242. C37#3290semidirect
254. #137C2×D37semidirect
274. C2×SD16C2×D37semidirect
280. #131C2×D37semidirect
284. #108C2×D37semidirect
290. #101C2×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
#145583452
#145583392
#145583372
#145579142
#145578072
#145578022
#145577972
#145577132
#145577092
#145577082
#145577042
#145576492
#145576482
C37×#4712
#329037