Finite Group Databasebeta

← #18006415

Subgroups — #18006415

Order 4736.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558241C211yesmaximal, characteristic, complemented
2#14558167C211yesmaximal, characteristic
3#14557878C211yesmaximal, characteristic, complemented
4#14557853C211yesmaximal, characteristic, complemented
5#14557849C211yesmaximal, characteristic, complemented
6#14557822C211yesmaximal, characteristic, complemented
7#14557765C211yesmaximal, characteristic, complemented
8#14557731C211yesmaximal, characteristic, complemented
9#14557683C211yesmaximal, characteristic, complemented
10#14557682C211yesmaximal, characteristic, complemented
11#14557618C211yesmaximal, characteristic, complemented
12C8×C22⋊D37C211yesmaximal, characteristic, complemented
13C2×#11924458C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#465C211yesmaximal, characteristic, complemented
16C22×D148C2211yescharacteristic
17C2×D4×D37—21no—
18C2×D4×D37C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×#10596941C2211yescharacteristic, complemented
21C2×C8×D37C2211yescharacteristic, complemented
22#11924535C2211yescharacteristic, complemented
23#11924532C2211yescharacteristic
24#11924526—21no—
25#11924516—21no—
26#11924513—21no—
27#11924512C2211yescharacteristic, complemented
28#11924511C2211yescharacteristic
29#11924509—21no—
30#11924506—21no—
31#11924504—21no—
32Q8×Dic37C2211yescharacteristic, complemented
33#11924498C2211yescharacteristic
34C4×C22⋊D37C2211yescharacteristic
35#11924496—21no—
36C2×C4⋊Dic37C2211yescharacteristic, complemented
37C4⋊C4×D37C2211yescharacteristic, complemented
38#11924467C2211yescharacteristic, complemented
39#11924467C2211yescharacteristic, complemented
40#11924465C2211yescharacteristic, complemented
41#11924458C2211yescharacteristic
42#11924458C2211yescharacteristic
43#11924458C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic, complemented
46#11924457C2211yescharacteristic, complemented
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic, complemented
49C22⋊#64436C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C2×SD16×C37C2211yescharacteristic, complemented
53C22×C8×C37C2211yescharacteristic, complemented
54C22⋊Q8×C37C2211yescharacteristic, complemented
55#121×C37C2211yescharacteristic
56#106×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C23×D37—21no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37D411yescharacteristic
69C22×Dic37—21no—
70D4×D37—22no—
71D4×D37—41no—
72D4×D37—44no—
73C2×D148—22no—
74C2×D148—21no—
75C2×D148—21no—
76C2×D148—41no—
77C2×D148C2311yescharacteristic
78C2×D148C2311yescharacteristic
79C2×C4×D37—21no—
80C2×C4×D37—21no—
81C2×C4×D37C2311yescharacteristic
82C2×Dic74—21no—
83SD16×C37—41no—
84C2×C8×C37—41no—
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C4⋊C4×C37—21no—
88C4⋊C4×C37C2311yescharacteristic
89C4⋊C4×C37C2311yescharacteristic
90C22⋊C4×C37—21no—
91C22⋊C4×C37—21no—
92C22⋊Dic37D411yescharacteristic
93#10596941—22no—
94#10596941—41no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98#10596938D411yescharacteristic
99C4⋊Dic37—21no—
100C4⋊Dic37—21no—
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106#10596936D411yescharacteristic
107C4×Dic37—21no—
108C4×Dic37C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C8×D37—41no—
112C23×C37—21no—
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115C22×D37—21no—
116C22×D37—42no—
117C22×D37—42no—
118C22×D37—42no—
119C22×D37—42no—
120C22×D37—81no—
121C22×D37—81no—
122C22×D37C2×D411yescharacteristic
123Q8×C37—21no—
124Q8×C37—21no—
125D4×C37—21no—
126D4×C37—21no—
127D4×C37—42no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2411yescharacteristic
135C22⋊D37—42no—
136C22⋊D37—42no—
137C22⋊D37—81no—
138C22⋊D37SD1614yescomplemented
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—81no—
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144C2×Dic37C2×D411yescharacteristic
145D148—21no—
146D148—21no—
147D148—21no—
148D148—42no—
149D148—42no—
150D148#4112yes—
151C4×D37—21no—
152C4×D37—21no—
153C4×D37—42no—
154C4×D37—81no—
155Dic74—81no—
156C8×C37—21no—
157C8×C37—21no—
158#64436—21no—
159#64436—21no—
160C22×C37—21no—
161C22×C37—21no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37C2×SD1612yes—
166C22×C37C22×D411yescharacteristic
167C2×D37—21no—
168C2×D37—21no—
169C2×D37—22no—
170C2×D37—41no—
171C2×D37—41no—
172C2×D37—41no—
173C2×D37—41no—
174C2×D37—41no—
175C2×D37—84no—
176C2×D37—84no—
177C2×D37C2×SD1612yes—
178C4×C37—21no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37—41no—
182C4×C37C2×#4111yescharacteristic
183C4×C37H(5,𝔽2)11yescharacteristic
184Dic37—21no—
185Dic37—21no—
186Dic37—41no—
187Dic37—41no—
188Dic37C2×SD1612yes—
189#3295—371nomaximal, Sylow
190C2×C37—22no—
191C2×C37—81no—
192C2×C37#54611yescharacteristic
193C2×C37C22×SD1611yescharacteristic
194C2×C37#57611yescharacteristic
195D37—22no—
196D37—42no—
197D37—81no—
198#554—371no—
199D42—371no—
200#486—371no—
201#481—371no—
202#481—371no—
203#476—371no—
204#465—371no—
205#465D3711yescharacteristic, complemented
206#460—371no—
207#450—371no—
208#450—371no—
209C4×SD16—371no—
210C8×D4—371no—
211C2×#102—371no—
212C2×#102—371no—
213C37#329511yescharacteristic, complemented, Sylow
214C22×D4—371no—
215C22×D4—371no—
216C22×D4—741no—
217C2×SD16—371no—
218C2×SD16—371no—
219C2×SD16C2×D3711yescharacteristic, complemented
220C22×C8—371no—
221C22×C8C2×D3711yescharacteristic, complemented
222C4⋊Q8—371no—
223#127—371no—
224#125—741no—
225C22⋊Q8—371no—
226C22⋊Q8—741no—
227C22⋊Q8—741no—
228C22⋊Q8C2×D3711yescharacteristic, complemented
229#121—371no—
230#121—741no—
231#121C2×D3711yescharacteristic
232#120—741no—
233#120—741no—
234C4×Q8—371no—
235C4×D4—371no—
236C4×D4—371no—
237C4×D4—741no—
238C2×C4⋊C4—371no—
239C2×C4⋊C4—371no—
240#106—371no—
241#106—371no—
242#106C2×D3711yescharacteristic, complemented
243C4⋊C8—371no—
244#103C2×D3711yescharacteristic, complemented
245#102—371no—
246#102—371no—
247#102—371no—
248#102—371no—
249#102—371no—
250#102—371no—
251#102—371no—
252#102—371no—
253#102C2×D3711yescharacteristic, complemented
254C22⋊C8—371no—
255C22⋊C8—371no—
256C4×C8—371no—
257C24—741no—
258C24—741no—
259C2×Q8—741no—
260C2×Q8C22×D3711yescharacteristic
261C2×D4—21no—
262C2×D4—371no—
263C2×D4—371no—
264C2×D4—371no—
265C2×D4—742no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4—741no—
269C2×D4—741no—
270C2×D4—742no—
271C2×D4—741no—
272C2×D4—1481no—
273C2×D4—1481no—
274C2×D4—1484no—
275C2×D4C22×D3711yescharacteristic
276C22×C4—371no—
277C22×C4—741no—
278C22×C4—741no—
279C22×C4—741no—
280C22×C4C22×D3711yescharacteristic
281SD16—41no—
282SD16—742no—
283SD16—1481no—
284C2×C8—41no—
285C2×C8—371no—
286C2×C8—371no—
287C2×C8—1481no—
288C2×C8C22×D3711yescharacteristic
289C2×C8C22×D3711yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—371no—
292C4⋊C4—371no—
293C4⋊C4—371no—
294C4⋊C4—741no—
295C4⋊C4—741no—
296C4⋊C4—741no—
297C4⋊C4—741no—
298C4⋊C4—741no—
299C4⋊C4C22×D3711yescharacteristic
300C4⋊C4C22×D3711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—371no—
304C22⋊C4—371no—
305C22⋊C4—741no—
306C22⋊C4—741no—
307C22⋊C4—741no—
308C42—371no—
309C42—741no—
310C23—21no—
311C23—371no—
312C23—2961no—
313C23—2961no—
314C23—741no—
315C23—741no—
316C23—1482no—
317C23—1482no—
318C23—1482no—
319C23—1482no—
320C23D4×D3711yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—2961no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—374no—
328D4—372no—
329D4—2961no—
330D4—741no—
331D4—741no—
332D4—741no—
333D4—1482no—
334D4—1482no—
335D4—1482no—
336D4—1482no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—371no—
343C2×C4—371no—
344C2×C4—371no—
345C2×C4—2961no—
346C2×C4—2961no—
347C2×C4—741no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—741no—
351C2×C4—1482no—
352C2×C4D4×D3711yescharacteristic
353C2×C4C23×D3711yescharacteristic
354C8—21no—
355C8—21no—
356C8—741no—
357C8—741no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—372no—
364C22—2964no—
365C22—2964no—
366C22—741no—
367C22—741no—
368C22—742no—
369C22—1481no—
370C22—1481no—
371C22—1481no—
372C22—1481no—
373C22—1481no—
374C22SD16×D3712yes—
375C22C2×D4×D3711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—372no—
381C4—741no—
382C4—741no—
383C4—1481no—
384C4—1481no—
385C4#41×D3711yescharacteristic
386C4#1192458111yescharacteristic
387C2—22no—
388C2—81no—
389C2—2961no—
390C2—742no—
391C2—1482no—
392C2#1455817211yescharacteristic
393C2C2×SD16×D3711yescharacteristic
394C2#1455833511yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#465C2
socleC22×C37C22×D4
prime radical#14558167C2
hypercenter#465D37
hypocenterC37#3295
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14558241C2semidirect
3. #14557878C2semidirect
4. #14557853C2semidirect
5. #14557849C2semidirect
6. #14557822C2semidirect
7. #14557765C2semidirect
8. #14557731C2semidirect
9. #14557683C2semidirect
10. #14557682C2semidirect
11. #14557618C2semidirect
12. C8×C22⋊D37C2semidirect
13. C2×#11924458C2semidirect
14. #102×D37C2semidirect
15. C37×#465C2semidirect
20. C2×#10596941C22semidirect
21. C2×C8×D37C22semidirect
22. #11924535C22semidirect
27. #11924512C22semidirect
32. Q8×Dic37C22semidirect
36. C2×C4⋊Dic37C22semidirect
37. C4⋊C4×D37C22semidirect
38. #11924467C22semidirect
39. #11924467C22semidirect
40. #11924465C22semidirect
43. #11924458C22semidirect
44. #11924458C22semidirect
45. #11924457C22semidirect
46. #11924457C22semidirect
48. #11924456C22semidirect
49. C22⋊#64436C22semidirect
50. #11924448C22semidirect
51. C8×Dic37C22semidirect
52. C2×SD16×C37C22semidirect
53. C22×C8×C37C22semidirect
54. C22⋊Q8×C37C22semidirect
56. #106×C37C22semidirect
57. #103×C37C22semidirect
58. #102×C37C22semidirect
138. C22⋊D37SD16semidirect
205. #465D37semidirect
213. C37#3295semidirect
219. C2×SD16C2×D37semidirect
221. C22×C8C2×D37semidirect
228. C22⋊Q8C2×D37semidirect
242. #106C2×D37semidirect
244. #103C2×D37semidirect
253. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582412
#145581672
#145578782
#145578532
#145578492
#145578222
#145577652
#145577312
#145576832
#145576822
#145576182
C8×C22⋊D372
C2×#119244582
#102×D372
C37×#4652
#329537