Finite Group Databasebeta

← #18006189

Subgroups — #18006189

Order 4736.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924561C211yesmaximal, characteristic, complemented
2C2×#11924560C211yesmaximal, characteristic, complemented
3#14558182C211yesmaximal, characteristic, complemented
4#14558167C211yesmaximal, characteristic, complemented
5#14557904C211yesmaximal, characteristic, complemented
6#14557782C211yesmaximal, characteristic, complemented
7#14557777C211yesmaximal, characteristic, complemented
8#14557737C211yesmaximal, characteristic, complemented
9#14557726C211yesmaximal, characteristic, complemented
10#14557686C211yesmaximal, characteristic, complemented
11#14557682C211yesmaximal, characteristic, complemented
12#14557679C211yesmaximal, characteristic, complemented
13#14557613C211yesmaximal, characteristic, complemented
14#14557608C211yesmaximal, characteristic, complemented
15C37×#449C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic, complemented
17C22×D148C2211yescharacteristic
18C2×D4×D37—21no—
19C2×D4×D37C2211yescharacteristic
20#11924561—24no—
21#11924560—24no—
22C2×#10596930C2211yescharacteristic
23C2×#10596930C2211yescharacteristic, complemented
24C2×#10596940C2211yescharacteristic, complemented
25C2×#10596941C2211yescharacteristic
26C2×#10596941C2211yescharacteristic, complemented
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic, complemented
29C2×#10596934C2211yescharacteristic, complemented
30C2×#10596929C2211yescharacteristic, complemented
31#11924534C2211yescharacteristic, complemented
32#11924532C2211yescharacteristic
33#11924519—21no—
34#11924517—21no—
35#11924515C2211yescharacteristic, complemented
36#11924512C2211yescharacteristic, complemented
37#11924511C2211yescharacteristic
38#11924509—21no—
39#11924508—21no—
40#11924506—21no—
41#11924504—21no—
42D4×Dic37C2211yescharacteristic, complemented
43#11924498C2211yescharacteristic
44C4×C22⋊D37C2211yescharacteristic
45C2×#10596936—21no—
46#11924469C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924459C2211yescharacteristic, complemented
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic, complemented
51#11924457C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53C8×Dic37C2211yescharacteristic, complemented
54C2×#41×C37C2211yescharacteristic, complemented
55C2×SD16×C37C2211yescharacteristic, complemented
56C2×D8×C37C2211yescharacteristic, complemented
57#121×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic, complemented
60C22⋊C8×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37—21no—
63#41×C37—22no—
64#41×C37—41no—
65C2×Q8×C37C2311yescharacteristic
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37C2311yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C22×C4×C37—21no—
71C22×C4×C37C2311yescharacteristic
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37D411yescharacteristic
77C22×Dic37—21no—
78C22×Dic37—21no—
79#10596964—22no—
80#10596964—41no—
81D4×D37—22no—
82D4×D37—41no—
83D4×D37—44no—
84C2×D148—22no—
85C2×D148—21no—
86C2×D148—21no—
87C2×D148—41no—
88C2×D148C2311yescharacteristic
89C2×D148C2311yescharacteristic
90C2×C4×D37—21no—
91C2×C4×D37C2311yescharacteristic
92C2×Dic74C2311yescharacteristic
93SD16×C37—41no—
94D8×C37—22no—
95C2×C8×C37C2311yescharacteristic
96C2×C8×C37C2311yescharacteristic
97C4⋊C4×C37C2311yescharacteristic
98C22⋊C4×C37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37D411yescharacteristic
102#10596941—22no—
103#10596941—22no—
104#10596940—22no—
105#10596939—22no—
106#10596939D414yescomplemented
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110#10596938D411yescharacteristic
111C4⋊Dic37C2311yescharacteristic
112#10596936—21no—
113#10596936—21no—
114#10596936—21no—
115#10596936—21no—
116#10596936D411yescharacteristic
117C4×Dic37C2311yescharacteristic
118#10596934—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121#10596930—22no—
122#10596930—41no—
123#10596929—22no—
124C23×C37—21no—
125C23×C37—21no—
126C23×C37C2×D411yescharacteristic
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37—42no—
132C22×D37—42no—
133C22×D37—81no—
134C22×D37—81no—
135C22×D37C2×D411yescharacteristic
136Q8×C37—21no—
137Q8×C37—21no—
138D4×C37—21no—
139D4×C37—21no—
140D4×C37—21no—
141D4×C37—42no—
142D4×C37—42no—
143D4×C37C2×D412yescomplemented
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—42no—
149C2×C4×C37C2×D411yescharacteristic
150C2×C4×C37C2411yescharacteristic
151C22⋊D37—22no—
152C22⋊D37—42no—
153C22⋊D37—42no—
154C22⋊D37—42no—
155C22⋊D37—81no—
156C2×Dic37—21no—
157C2×Dic37—21no—
158C2×Dic37—42no—
159C2×Dic37—42no—
160C2×Dic37C2×D411yescharacteristic
161C2×Dic37C2×D411yescharacteristic
162C2×Dic37C2×D411yescharacteristic
163D148—21no—
164D148—21no—
165D148—21no—
166D148—42no—
167D148—42no—
168D148C2×D412yes—
169C4×D37—21no—
170C4×D37—21no—
171C4×D37—42no—
172Dic74—21no—
173Dic74—21no—
174C8×C37—21no—
175C8×C37—21no—
176#64436—21no—
177#64436C2×D412yescomplemented
178C22×C37—22no—
179C22×C37—21no—
180C22×C37—21no—
181C22×C37—21no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37C22×D411yescharacteristic
188C2×D37—21no—
189C2×D37—22no—
190C2×D37—21no—
191C2×D37—21no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—41no—
195C2×D37—41no—
196C2×D37—41no—
197C2×D37—84no—
198C2×D37—84no—
199C4×C37—21no—
200C4×C37—41no—
201C4×C37—41no—
202C4×C37C22×D411yescharacteristic
203C4×C37H(5,𝔽2)11yescharacteristic
204Dic37—21no—
205Dic37—21no—
206Dic37—41no—
207Dic37—41no—
208Dic37AGL(1,ℤ/8)12yescomplemented
209#3272—371nomaximal, Sylow
210C2×C37—41no—
211C2×C37—42no—
212C2×C37—81no—
213C2×C37D4211yescharacteristic
214C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C37#57711yescharacteristic
216D37—41no—
217D37—42no—
218D37—81no—
219C2×AGL(1,ℤ/8)—371no—
220C2×AGL(1,ℤ/8)—371no—
221#547—371no—
222D42—371no—
223#492—371no—
224#468—371no—
225#468—371no—
226#461—371no—
227#459—371no—
228#450—371no—
229#450—371no—
230#449—371no—
231#449D3711yescharacteristic, complemented
232C4×D8—371no—
233#436—371no—
234C37#327211yescharacteristic, complemented, Sylow
235C2×#41—371no—
236C2×#41C2×D3711yescharacteristic, complemented
237C22×D4—371no—
238C22×D4—371no—
239C22×D4—741no—
240AGL(1,ℤ/8)—744no—
241AGL(1,ℤ/8)—744no—
242C2×SD16—371no—
243C2×SD16—371no—
244C2×SD16—371no—
245C2×SD16—371no—
246C2×SD16—371no—
247C2×SD16C2×D3711yescharacteristic, complemented
248C2×D8—371no—
249C2×D8—371no—
250C2×D8C2×D3711yescharacteristic, complemented
251C2×M16—371no—
252C2×M16—371no—
253C4⋊Q8—371no—
254#127—371no—
255#123—741no—
256#123—741no—
257C22⋊Q8—371no—
258C22⋊Q8—371no—
259#121—371no—
260#121—741no—
261#121—741no—
262#121C2×D3711yescharacteristic
263#120—741no—
264#120—741no—
265C4×D4—371no—
266C4×D4—371no—
267C4×D4—371no—
268C2×C4⋊C4—741no—
269#107—371no—
270C4⋊C8—371no—
271#103—371no—
272#103C2×D3711yescharacteristic, complemented
273#102—371no—
274#102—371no—
275#102—371no—
276#102C2×D3711yescharacteristic, complemented
277C22⋊C8—371no—
278C22⋊C8C2×D3711yescharacteristic, complemented
279C4×C8—371no—
280C24—741no—
281C24—741no—
282#41—22no—
283#41—41no—
284#41—742no—
285#41—1481no—
286C2×Q8—371no—
287C2×Q8C22×D3711yescharacteristic
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—371no—
291C2×D4—371no—
292C2×D4—371no—
293C2×D4—742no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—741no—
298C2×D4—742no—
299C2×D4—741no—
300C2×D4—741no—
301C2×D4—1481no—
302C2×D4—1481no—
303C2×D4—1484no—
304C2×D4C22×D3711yescharacteristic
305C2×D4C22×D3711yescharacteristic
306C22×C4—21no—
307C22×C4—371no—
308C22×C4—741no—
309C22×C4—741no—
310C22×C4—741no—
311C22×C4C22×D3711yescharacteristic
312SD16—41no—
313SD16—742no—
314SD16—742no—
315SD16—742no—
316SD16—742no—
317SD16—1481no—
318D8—22no—
319D8—374no—
320D8—742no—
321M16—742no—
322M16—742no—
323C2×C8—371no—
324C2×C8—371no—
325C2×C8C22×D3711yescharacteristic
326C2×C8C22×D3711yescharacteristic
327C4⋊C4—371no—
328C4⋊C4—371no—
329C4⋊C4—741no—
330C4⋊C4—741no—
331C4⋊C4—741no—
332C4⋊C4—741no—
333C4⋊C4C22×D3711yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—371no—
336C22⋊C4—371no—
337C22⋊C4—741no—
338C22⋊C4—741no—
339C22⋊C4—741no—
340C22⋊C4—741no—
341C22⋊C4—741no—
342C42—371no—
343C23—21no—
344C23—21no—
345C23—371no—
346C23—2961no—
347C23—2961no—
348C23—741no—
349C23—741no—
350C23—1482no—
351C23—1482no—
352C23—1482no—
353C23—1482no—
354C23D4×D3711yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—741no—
358Q8—741no—
359D4—21no—
360D4—21no—
361D4—21no—
362D4—42no—
363D4—42no—
364D4—372no—
365D4—2961no—
366D4—742no—
367D4—741no—
368D4—741no—
369D4—741no—
370D4—1482no—
371D4—1482no—
372D4—1482no—
373D4—1482no—
374D4—1482no—
375D4D4×D3712yescomplemented
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—371no—
382C2×C4—371no—
383C2×C4—371no—
384C2×C4—741no—
385C2×C4—741no—
386C2×C4—741no—
387C2×C4—741no—
388C2×C4—1482no—
389C2×C4—1482no—
390C2×C4—1482no—
391C2×C4D4×D3711yescharacteristic
392C2×C4C23×D3711yescharacteristic
393C8—21no—
394C8—21no—
395C8—372no—
396C8—741no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—2964no—
407C22—2964no—
408C22—741no—
409C22—741no—
410C22—741no—
411C22—742no—
412C22—1481no—
413C22—1481no—
414C22—1481no—
415C22—1481no—
416C22—1481no—
417C22C2×D4×D3711yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—372no—
422C4—741no—
423C4—741no—
424C4—1481no—
425C4—1481no—
426C4C2×D4×D3711yescharacteristic
427C4#1192458111yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—2961no—
432C2—1481no—
433C2—1482no—
434C2#1455816511yescharacteristic
435C2AGL(1,ℤ/8)×D3711yescharacteristic
436C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#449C2
socleC22×C37C22×D4
hypercenter#449D37
hypocenterC37#3272
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11924561C2semidirect
2. C2×#11924560C2semidirect
3. #14558182C2semidirect
4. #14558167C2semidirect
5. #14557904C2semidirect
6. #14557782C2semidirect
7. #14557777C2semidirect
8. #14557737C2semidirect
9. #14557726C2semidirect
10. #14557686C2semidirect
11. #14557682C2semidirect
12. #14557679C2semidirect
13. #14557613C2semidirect
14. #14557608C2semidirect
15. C37×#449C2semidirect
16. C2×#10596964C22semidirect
23. C2×#10596930C22semidirect
24. C2×#10596940C22semidirect
26. C2×#10596941C22semidirect
28. C2×#10596939C22semidirect
29. C2×#10596934C22semidirect
30. C2×#10596929C22semidirect
31. #11924534C22semidirect
35. #11924515C22semidirect
36. #11924512C22semidirect
42. D4×Dic37C22semidirect
46. #11924469C22semidirect
47. #11924465C22semidirect
48. #11924459C22semidirect
50. #11924458C22semidirect
51. #11924457C22semidirect
52. #11924448C22semidirect
53. C8×Dic37C22semidirect
54. C2×#41×C37C22semidirect
55. C2×SD16×C37C22semidirect
56. C2×D8×C37C22semidirect
58. #103×C37C22semidirect
59. #102×C37C22semidirect
60. C22⋊C8×C37C22semidirect
106. #10596939D4semidirect
143. D4×C37C2×D4semidirect
177. #64436C2×D4semidirect
208. Dic37AGL(1,ℤ/8)semidirect
231. #449D37semidirect
234. C37#3272semidirect
236. C2×#41C2×D37semidirect
247. C2×SD16C2×D37semidirect
250. C2×D8C2×D37semidirect
272. #103C2×D37semidirect
276. #102C2×D37semidirect
278. C22⋊C8C2×D37semidirect
375. D4D4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245612
C2×#119245602
#145581822
#145581672
#145579042
#145577822
#145577772
#145577372
#145577262
#145576862
#145576822
#145576792
#145576132
#145576082
C37×#4492
#327237