Finite Group Databasebeta

← #18004514

Subgroups — #18004514

Order 4736.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558046C211yesmaximal, characteristic
2#117×D37C211yesmaximal, characteristic, complemented
3#14557871C211yesmaximal, characteristic, complemented
4#14557867C211yesmaximal, characteristic, complemented
5#14557862C211yesmaximal, characteristic, complemented
6#14557858C211yesmaximal, characteristic, complemented
7#14557857C211yesmaximal, characteristic, complemented
8#14557853C211yesmaximal, characteristic, complemented
9#14557848C211yesmaximal, characteristic, complemented
10#14557570C211yesmaximal, characteristic, complemented
11#14557568C211yesmaximal, characteristic, complemented
12#14557528C211yesmaximal, characteristic, complemented
13#14557528C211yesmaximal, characteristic, complemented
14C22⋊C8×D37C211yesmaximal, characteristic, complemented
15C37×#485C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18C2×C8×D37C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20#11924521—21no—
21#11924512C2211yescharacteristic
22#11924511C2211yescharacteristic
23#11924510C2211yescharacteristic
24#11924506—21no—
25#11924498—21no—
26#11924496—21no—
27#11924495C2211yescharacteristic
28#11924494C2211yescharacteristic
29#11924494C2211yescharacteristic
30#11924494C2211yescharacteristic
31#11924493—21no—
32#11924492—21no—
33C4⋊C4×D37C2211yescharacteristic
34C4⋊C4×D37C2211yescharacteristic
35C22⋊C4×D37—21no—
36C42×D37—21no—
37#11924470C2211yescharacteristic, complemented
38#11924469C2211yescharacteristic, complemented
39#11924469C2211yescharacteristic, complemented
40#11924468C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924467C2211yescharacteristic, complemented
43#11924460C2211yescharacteristic, complemented
44#11924460C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic, complemented
46#11924458C2211yescharacteristic, complemented
47#11924456C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic, complemented
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924448C2211yescharacteristic
52C22⋊Q8×C37C2211yescharacteristic
53#117×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic, complemented
55#106×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic
59C23×D37D411yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C22×Dic37D411yescharacteristic
64#10596966—22no—
65#10596966—22no—
66C2×D148—21no—
67C2×D148—21no—
68C2×D148C2311yescharacteristic
69C2×C4×D37—22no—
70C2×C4×D37—22no—
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37D411yescharacteristic
75C2×C4×D37D411yescharacteristic
76C2×C4×D37C2311yescharacteristic
77C2×C4×D37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C4⋊C4×C37—21no—
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C22⋊C4×C37—21no—
85C22⋊C4×C37—21no—
86C42×C37—21no—
87C22⋊Dic37—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C8×D37—22no—
107C8×D37—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—22no—
110C22×D37—22no—
111C22×D37—21no—
112C22×D37—41no—
113C22×D37C2×D411yescharacteristic
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37—42no—
126C2×Dic37—22no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132D148—21no—
133D148—21no—
134D148—42no—
135D148—42no—
136C4×D37—22no—
137C4×D37—21no—
138C4×D37—21no—
139C4×D37—22no—
140C4×D37—42no—
141C4×D37—42no—
142C4×D37—42no—
143C4×D37#4112yes—
144C4×D37#4112yes—
145C8×C37—21no—
146C8×C37—21no—
147#64436—21no—
148#64436—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37C22×D411yescharacteristic
153C2×D37—21no—
154C2×D37—21no—
155C2×D37—21no—
156C2×D37—21no—
157C2×D37—44no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37#12312yes—
162C2×D37#13512yes—
163C4×C37—21no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37C2×#4111yescharacteristic
169C4×C37C2×#4111yescharacteristic
170Dic37—21no—
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174Dic37#12312yes—
175#3091—371nomaximal, Sylow
176C2×C37—41no—
177C2×C37C2×#12311yescharacteristic
178C2×C37C2×#13511yescharacteristic
179C2×C37#57511yescharacteristic
180D37—22no—
181D37—22no—
182D37—81no—
183#525—371no—
184C2×#117—371no—
185#485—371no—
186#485D3711yescharacteristic, complemented
187#484—371no—
188#483—371no—
189#482—371no—
190#482—371no—
191#481—371no—
192#480—371no—
193#427—371no—
194#427—371no—
195#416—371no—
196#416—371no—
197C2×C22⋊C8—371no—
198C37#309111yescharacteristic, complemented, Sylow
199C2×#41—371no—
200C23×C4—371no—
201C22×C8—371no—
202C22×C8—371no—
203#123—741no—
204C22⋊Q8—371no—
205C22⋊Q8C2×D3711yescharacteristic
206#121—371no—
207#121—371no—
208#120—741no—
209C4×D4—741no—
210C4×D4—741no—
211#117—371no—
212#117—371no—
213#117—371no—
214#117—371no—
215#117—741no—
216#117—741no—
217#117C2×D3711yescharacteristic
218C2×C4⋊C4—371no—
219C2×C4⋊C4—371no—
220C2×C22⋊C4—741no—
221C2×C42—741no—
222#107—371no—
223#107—371no—
224#107—371no—
225#107C2×D3711yescharacteristic, complemented
226#106—371no—
227#106—371no—
228#106—371no—
229#106C2×D3711yescharacteristic, complemented
230#103—371no—
231#103—371no—
232#103C2×D3711yescharacteristic, complemented
233#103C2×D3711yescharacteristic, complemented
234#102—371no—
235#102—371no—
236#102—371no—
237#102—371no—
238C22⋊C8—371no—
239C22⋊C8—371no—
240C22⋊C8—371no—
241C22⋊C8C2×D3711yescharacteristic
242C24—371no—
243#41—742no—
244#41—742no—
245C2×Q8C22×D3711yescharacteristic
246C2×D4—371no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C22×C4—371no—
251C22×C4—371no—
252C22×C4—371no—
253C22×C4—371no—
254C22×C4—371no—
255C22×C4—742no—
256C22×C4—742no—
257C22×C4—741no—
258C22×C4—741no—
259C22×C4—741no—
260C22×C4C22×D3711yescharacteristic
261C2×C8—371no—
262C2×C8—371no—
263C2×C8—742no—
264C2×C8—742no—
265C2×C8C22×D3711yescharacteristic
266C2×C8C22×D3711yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—371no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4C22×D3711yescharacteristic
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C42—21no—
287C42—741no—
288C42—741no—
289C42—741no—
290C42—741no—
291C23—371no—
292C23—371no—
293C23—742no—
294C23—742no—
295C23—741no—
296C23—1481no—
297C23D4×D3711yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—741no—
301D4—741no—
302D4—1482no—
303D4—1482no—
304D4—1482no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—371no—
312C2×C4—372no—
313C2×C4—372no—
314C2×C4—371no—
315C2×C4—742no—
316C2×C4—742no—
317C2×C4—742no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—1482no—
324C2×C4—1482no—
325C2×C4—1482no—
326C2×C4D4×D3711yescharacteristic
327C2×C4C23×D3711yescharacteristic
328C8—21no—
329C8—21no—
330C8—741no—
331C8—741no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—372no—
336C22—372no—
337C22—741no—
338C22—741no—
339C22—741no—
340C22—741no—
341C22—1484no—
342C22—1481no—
343C22—1481no—
344C22—1481no—
345C22C2×D4×D3711yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—372no—
352C4—741no—
353C4—1481no—
354C4—1481no—
355C4—1481no—
356C4#41×D3711yescharacteristic
357C4#41×D3711yescharacteristic
358C2—41no—
359C2—2961no—
360C2—742no—
361C2—742no—
362C2#123×D3711yescharacteristic
363C2#135×D3711yescharacteristic
364C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#485C2
socleC22×C37C22×D4
prime radical#14558046C2
hypercenter#485D37
hypocenterC37#3091
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #117×D37C2semidirect
3. #14557871C2semidirect
4. #14557867C2semidirect
5. #14557862C2semidirect
6. #14557858C2semidirect
7. #14557857C2semidirect
8. #14557853C2semidirect
9. #14557848C2semidirect
10. #14557570C2semidirect
11. #14557568C2semidirect
12. #14557528C2semidirect
13. #14557528C2semidirect
14. C22⋊C8×D37C2semidirect
15. C37×#485C2semidirect
37. #11924470C22semidirect
38. #11924469C22semidirect
39. #11924469C22semidirect
40. #11924468C22semidirect
41. #11924467C22semidirect
42. #11924467C22semidirect
43. #11924460C22semidirect
44. #11924460C22semidirect
45. #11924458C22semidirect
46. #11924458C22semidirect
47. #11924456C22semidirect
48. #11924456C22semidirect
54. #107×C37C22semidirect
55. #106×C37C22semidirect
56. #103×C37C22semidirect
57. #103×C37C22semidirect
186. #485D37semidirect
198. C37#3091semidirect
225. #107C2×D37semidirect
229. #106C2×D37semidirect
232. #103C2×D37semidirect
233. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580462
#117×D372
#145578712
#145578672
#145578622
#145578582
#145578572
#145578532
#145578482
#145575702
#145575682
#145575282
C22⋊C8×D372
C37×#4852
#309137