Finite Group Databasebeta

← #18004507

Subgroups — #18004507

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#14558040C211yesmaximal, characteristic
2#117×D37C211yesmaximal, characteristic, complemented
3#14557873C211yesmaximal, characteristic, complemented
4#14557872C211yesmaximal, characteristic, complemented
5#14557867C211yesmaximal, characteristic, complemented
6#14557862C211yesmaximal, characteristic, complemented
7#14557856C211yesmaximal, characteristic, complemented
8#14557855C211yesmaximal, characteristic, complemented
9#14557850C211yesmaximal, characteristic, complemented
10#14557845C211yesmaximal, characteristic, complemented
11#14557571C211yesmaximal, characteristic, complemented
12#14557569C211yesmaximal, characteristic, complemented
13#14557529C211yesmaximal, characteristic, complemented
14C2×#11924448C211yesmaximal, characteristic, complemented
15C37×#416C211yesmaximal, characteristic, complemented
16C22×C4×D37C2211yescharacteristic
17C22×#64436C2211yescharacteristic
18#11924517—21no—
19#11924512C2211yescharacteristic
20#11924512C2211yescharacteristic
21#11924507C2211yescharacteristic
22#11924507C2211yescharacteristic
23#11924504—21no—
24C4×C22⋊D37—21no—
25C4×C22⋊D37—21no—
26#11924495C2211yescharacteristic
27#11924495C2211yescharacteristic
28#11924494C2211yescharacteristic
29#11924494C2211yescharacteristic
30#11924493—21no—
31#11924492—21no—
32C4⋊C4×D37C2211yescharacteristic
33C4⋊C4×D37C2211yescharacteristic
34C22⋊C4×D37—21no—
35C42×D37—21no—
36#11924470C2211yescharacteristic, complemented
37#11924470C2211yescharacteristic, complemented
38#11924469C2211yescharacteristic, complemented
39#11924469C2211yescharacteristic, complemented
40#11924468C2211yescharacteristic, complemented
41#11924468C2211yescharacteristic, complemented
42#11924467C2211yescharacteristic, complemented
43#11924467C2211yescharacteristic, complemented
44#11924460C2211yescharacteristic, complemented
45#11924460C2211yescharacteristic, complemented
46#11924457C2211yescharacteristic, complemented
47#11924457C2211yescharacteristic, complemented
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924448C2211yescharacteristic
52C2×#41×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54#117×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic, complemented
59C23×D37D411yescharacteristic
60#41×C37—22no—
61#41×C37—22no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C22×Dic37D411yescharacteristic
70C2×C4×D37—22no—
71C2×C4×D37—22no—
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37D411yescharacteristic
75C2×C4×D37D411yescharacteristic
76C2×C4×D37C2311yescharacteristic
77C2×C4×D37C2311yescharacteristic
78C2×C8×C37—22no—
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C42×C37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37—21no—
105C2×#64436—22no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—22no—
111C22×D37—22no—
112C22×D37—41no—
113C22×D37C2×D411yescharacteristic
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117D4×C37—21no—
118D4×C37—21no—
119D4×C37—42no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—42no—
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37#4112yes—
126C2×C4×C37#4112yes—
127C2×C4×C37C2411yescharacteristic
128C22⋊D37—42no—
129C22⋊D37—42no—
130C2×Dic37—22no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C4×D37—22no—
138C4×D37—22no—
139C4×D37—21no—
140C4×D37—21no—
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—42no—
144C4×D37—42no—
145C8×C37—21no—
146C8×C37—21no—
147#64436—21no—
148#64436—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37#12312yes—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—21no—
160C2×D37—21no—
161C2×D37—44no—
162C2×D37#13512yes—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37#12312yes—
167C4×C37C2×#4111yescharacteristic
168C4×C37C2×#4111yescharacteristic
169Dic37—21no—
170Dic37—21no—
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174Dic37—41no—
175#3091—371nomaximal, Sylow
176C2×C37—22no—
177C2×C37—81no—
178C2×C37C2×#12311yescharacteristic
179C2×C37C2×#13511yescharacteristic
180C2×C37#57511yescharacteristic
181D37—22no—
182D37—41no—
183#525—371no—
184C2×#117—371no—
185#485—371no—
186#485—371no—
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#416D3711yescharacteristic, complemented
197C2×C22⋊C8—371no—
198C37#309111yescharacteristic, complemented, Sylow
199C2×#41C2×D3711yescharacteristic
200C23×C4—371no—
201C22×C8—371no—
202C22×C8C2×D3711yescharacteristic
203#123—741no—
204C22⋊Q8—371no—
205C22⋊Q8—371no—
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#107—371no—
226#106—371no—
227#106—371no—
228#106—371no—
229#106—371no—
230#103—371no—
231#103—371no—
232#103C2×D3711yescharacteristic, complemented
233#103C2×D3711yescharacteristic, complemented
234#102—371no—
235#102—371no—
236#102C2×D3711yescharacteristic, complemented
237#102C2×D3711yescharacteristic, complemented
238C22⋊C8—371no—
239C22⋊C8—371no—
240C22⋊C8—371no—
241C22⋊C8—371no—
242C24—371no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D3711yescharacteristic
246C2×D4—21no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4C22×D3711yescharacteristic
250C22×C4—21no—
251C22×C4—371no—
252C22×C4—371no—
253C22×C4—371no—
254C22×C4—371no—
255C22×C4—371no—
256C22×C4—741no—
257C22×C4—741no—
258C22×C4—742no—
259C22×C4—742no—
260C22×C4C22×D3711yescharacteristic
261C2×C8—22no—
262C2×C8—371no—
263C2×C8—371no—
264C2×C8—742no—
265C2×C8C22×D3711yescharacteristic
266C2×C8C22×D3711yescharacteristic
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—371no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—741no—
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—21no—
292C23—371no—
293C23—371no—
294C23—742no—
295C23—742no—
296C23—1481no—
297C23D4×D3711yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—1482no—
304D4—1482no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—371no—
310C2×C4—371no—
311C2×C4—742no—
312C2×C4—742no—
313C2×C4—742no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—1482no—
323C2×C4—1482no—
324C2×C4#1059696212yes—
325C2×C4D4×D3711yescharacteristic
326C2×C4#1059696412yes—
327C2×C4C23×D3711yescharacteristic
328C8—21no—
329C8—21no—
330C8—741no—
331C8—741no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—372no—
338C22—741no—
339C22—741no—
340C22—741no—
341C22—741no—
342C22—741no—
343C22—1484no—
344C22#1192451812yes—
345C22C2×D4×D3711yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—741no—
350C4—741no—
351C4—1481no—
352C4—1481no—
353C4—1481no—
354C4—1481no—
355C4#1192451812yes—
356C4C2×#1059696411yescharacteristic
357C4C2×#1059696211yescharacteristic
358C2—22no—
359C2—81no—
360C2—742no—
361C2—1481no—
362C2C2×#1192451811yescharacteristic
363C2#135×D3711yescharacteristic
364C2#1455833011yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
prime radical#14558040C2
hypercenter#416D37
hypocenterC37#3091
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D37C2semidirect
3. #14557873C2semidirect
4. #14557872C2semidirect
5. #14557867C2semidirect
6. #14557862C2semidirect
7. #14557856C2semidirect
8. #14557855C2semidirect
9. #14557850C2semidirect
10. #14557845C2semidirect
11. #14557571C2semidirect
12. #14557569C2semidirect
13. #14557529C2semidirect
14. C2×#11924448C2semidirect
15. C37×#416C2semidirect
36. #11924470C22semidirect
37. #11924470C22semidirect
38. #11924469C22semidirect
39. #11924469C22semidirect
40. #11924468C22semidirect
41. #11924468C22semidirect
42. #11924467C22semidirect
43. #11924467C22semidirect
44. #11924460C22semidirect
45. #11924460C22semidirect
46. #11924457C22semidirect
47. #11924457C22semidirect
55. #103×C37C22semidirect
56. #103×C37C22semidirect
57. #102×C37C22semidirect
58. #102×C37C22semidirect
196. #416D37semidirect
198. C37#3091semidirect
232. #103C2×D37semidirect
233. #103C2×D37semidirect
236. #102C2×D37semidirect
237. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580402
#117×D372
#145578732
#145578722
#145578672
#145578622
#145578562
#145578552
#145578502
#145578452
#145575712
#145575692
#145575292
C2×#119244482
C37×#4162
#309137