Finite Group Databasebeta

← #18005356

Subgroups — #18005356

Order 4736.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558043C211yesmaximal, characteristic, complemented
2#121×D37C211yesmaximal, characteristic, complemented
3#14557870C211yesmaximal, characteristic, complemented
4#14557860C211yesmaximal, characteristic, complemented
5#14557856C211yesmaximal, characteristic, complemented
6#14557850C211yesmaximal, characteristic, complemented
7#14557767C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557760C211yesmaximal, characteristic, complemented
10#14557685C211yesmaximal, characteristic, complemented
11#14557679C211yesmaximal, characteristic, complemented
12#14557675C211yesmaximal, characteristic, complemented
13#14557665C211yesmaximal, characteristic, complemented
14C2×#11924448C211yesmaximal, characteristic, complemented
15C37×#466C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic, complemented
17C2×D4×D37—21no—
18C2×D4×D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20C2×#10596930C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic, complemented
22C2×#10596939C2211yescharacteristic, complemented
23C22×#64436C2211yescharacteristic, complemented
24#11924518—21no—
25#11924516C2211yescharacteristic
26#11924515C2211yescharacteristic, complemented
27#11924511C2211yescharacteristic
28#11924510C2211yescharacteristic
29#11924509—21no—
30#11924508—21no—
31#11924507C2211yescharacteristic
32#11924507C2211yescharacteristic
33#11924504—21no—
34D4×Dic37—21no—
35#11924496—21no—
36#11924494C2211yescharacteristic, complemented
37C4⋊C4×D37C2211yescharacteristic
38C22⋊C4×D37—21no—
39#11924469C2211yescharacteristic, complemented
40#11924468C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924459C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic, complemented
46#11924457C2211yescharacteristic, complemented
47#11924456C2211yescharacteristic, complemented
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic, complemented
51#11924448C2211yescharacteristic, complemented
52C2×D8×C37C2211yescharacteristic, complemented
53C22×C8×C37C2211yescharacteristic, complemented
54#121×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic, complemented
56#107×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C23×D37D411yescharacteristic
61C2×D4×C37—21no—
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C22×Dic37—21no—
72C22×Dic37D411yescharacteristic
73#10596964—41no—
74#10596964—41no—
75D4×D37—41no—
76D4×D37—41no—
77D4×D37—44no—
78C2×D148—21no—
79C2×D148C2311yescharacteristic
80C2×C4×D37—21no—
81C2×C4×D37—41no—
82C2×C4×D37—41no—
83C2×C4×D37D411yescharacteristic
84C2×C4×D37D411yescharacteristic
85C2×C4×D37C2311yescharacteristic
86C2×C4×D37C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88D8×C37—41no—
89C2×C8×C37—41no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊Dic37—21no—
97C22⋊Dic37—21no—
98C22⋊Dic37—21no—
99#10596940—41no—
100#10596939—41no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105C4⋊Dic37—21no—
106C4⋊Dic37C2311yescharacteristic
107C4⋊Dic37C2311yescharacteristic
108#10596936—21no—
109#10596936—21no—
110C4×Dic37—21no—
111C2×#64436—41no—
112C2×#64436C2311yescharacteristic
113C2×#64436C2311yescharacteristic
114#10596930—41no—
115C23×C37—21no—
116C23×C37—21no—
117C23×C37C2×D411yescharacteristic
118C22×D37—22no—
119C22×D37—22no—
120C22×D37—21no—
121C22×D37—41no—
122C22×D37—42no—
123C22×D37—42no—
124C22×D37—42no—
125C22×D37C2×D411yescharacteristic
126C22×D37C2×D411yescharacteristic
127D4×C37—21no—
128D4×C37—21no—
129D4×C37—21no—
130D4×C37—21no—
131D4×C37—42no—
132D4×C37—42no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2411yescharacteristic
139C22⋊D37—42no—
140C22⋊D37—42no—
141C22⋊D37—42no—
142C22⋊D37—42no—
143C22⋊D37—42no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—41no—
148C2×Dic37—42no—
149C2×Dic37C2×D411yescharacteristic
150C2×Dic37C2×D411yescharacteristic
151D148—21no—
152D148—21no—
153D148—42no—
154C4×D37—21no—
155C4×D37—21no—
156C4×D37—21no—
157C4×D37—21no—
158C4×D37—41no—
159C4×D37—41no—
160C4×D37—42no—
161Dic74—21no—
162Dic74—21no—
163C8×C37—21no—
164C8×C37—21no—
165#64436—21no—
166#64436—21no—
167C22×C37—21no—
168C22×C37—21no—
169C22×C37—41no—
170C22×C37—41no—
171C22×C37—41no—
172C22×C37—41no—
173C22×C37—41no—
174C22×C37—41no—
175C22×C37AGL(1,ℤ/8)12yes—
176C22×C37C22×D411yescharacteristic
177C2×D37—21no—
178C2×D37—21no—
179C2×D37—21no—
180C2×D37—21no—
181C2×D37—21no—
182C2×D37—44no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—84no—
187C2×D37#13512yes—
188C4×C37—21no—
189C4×C37—41no—
190C4×C37—41no—
191C4×C37H(5,𝔽2)11yescharacteristic
192C4×C37H(5,𝔽2)11yescharacteristic
193Dic37—21no—
194Dic37—21no—
195Dic37—41no—
196Dic37—41no—
197Dic37—41no—
198#3188—371nomaximal, Sylow
199C2×C37—22no—
200C2×C37—81no—
201C2×C37—81no—
202C2×C37#53411yescharacteristic
203C2×C37C2×#13511yescharacteristic
204C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
205D37—22no—
206D37—41no—
207D37—81no—
208#525—371no—
209C2×#121—371no—
210#484—371no—
211#482—371no—
212#482—371no—
213#481—371no—
214#466—371no—
215#466D3711yescharacteristic, complemented
216#465—371no—
217#465—371no—
218#450—371no—
219#449—371no—
220#449—371no—
221#447—371no—
222C2×C22⋊C8—371no—
223C37#318811yescharacteristic, complemented, Sylow
224C2×#41—371no—
225C22×D4—371no—
226C22×D4—741no—
227C23×C4—371no—
228C2×SD16—371no—
229C2×SD16—371no—
230C2×D8—371no—
231C2×D8C2×D3711yescharacteristic, complemented
232C22×C8—371no—
233C22×C8C2×D3711yescharacteristic, complemented
234#123—741no—
235C22⋊Q8—371no—
236C22⋊Q8—371no—
237#121—371no—
238#121—371no—
239#121—371no—
240#121—371no—
241#121—741no—
242#121—741no—
243#121C2×D3711yescharacteristic
244#121C2×D3711yescharacteristic, complemented
245#120—741no—
246C4×D4—741no—
247C4×D4—741no—
248#117—371no—
249C2×C4⋊C4—371no—
250C2×C22⋊C4—741no—
251#107—371no—
252#107C2×D3711yescharacteristic, complemented
253#106—371no—
254#106—371no—
255#103—371no—
256#103—371no—
257#102—371no—
258#102—371no—
259#102—371no—
260#102—371no—
261#102C2×D3711yescharacteristic, complemented
262#102C2×D3711yescharacteristic, complemented
263C22⋊C8—371no—
264C22⋊C8—371no—
265C22⋊C8—371no—
266C22⋊C8—371no—
267C24—371no—
268C24—741no—
269#41—1481no—
270#41—1481no—
271C2×Q8—371no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—371no—
275C2×D4—741no—
276C2×D4—741no—
277C2×D4—741no—
278C2×D4—741no—
279C2×D4—741no—
280C2×D4—741no—
281C2×D4—1481no—
282C2×D4—1481no—
283C2×D4—1484no—
284C2×D4C22×D3711yescharacteristic
285C2×D4C22×D3711yescharacteristic
286C22×C4—371no—
287C22×C4—371no—
288C22×C4—371no—
289C22×C4—371no—
290C22×C4—371no—
291C22×C4—741no—
292C22×C4—741no—
293C22×C4—1481no—
294C22×C4—1481no—
295C22×C4C22×D3711yescharacteristic
296SD16—1481no—
297SD16—1481no—
298D8—41no—
299D8—1481no—
300C2×C8—41no—
301C2×C8—371no—
302C2×C8—371no—
303C2×C8—1481no—
304C2×C8C22×D3711yescharacteristic
305C2×C8C22×D3711yescharacteristic
306C4⋊C4—371no—
307C4⋊C4—371no—
308C4⋊C4—741no—
309C4⋊C4—741no—
310C4⋊C4—741no—
311C4⋊C4C22×D3711yescharacteristic
312C4⋊C4C22×D3711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—741no—
316C22⋊C4—741no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C42—741no—
323C23—21no—
324C23—21no—
325C23—371no—
326C23—371no—
327C23—742no—
328C23—742no—
329C23—741no—
330C23—1481no—
331C23—1482no—
332C23—1482no—
333C23—1482no—
334C23D4×D3711yescharacteristic
335Q8—741no—
336Q8—741no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—741no—
344D4—741no—
345D4—1482no—
346D4—1482no—
347D4—1482no—
348D4—1482no—
349D4—1482no—
350D4—1482no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—371no—
356C2×C4—371no—
357C2×C4—741no—
358C2×C4—741no—
359C2×C4—741no—
360C2×C4—741no—
361C2×C4—741no—
362C2×C4—741no—
363C2×C4—741no—
364C2×C4—1481no—
365C2×C4—1481no—
366C2×C4—1482no—
367C2×C4—1481no—
368C2×C4—1482no—
369C2×C4D4×D3711yescharacteristic
370C2×C4C23×D3711yescharacteristic
371C8—21no—
372C8—21no—
373C8—741no—
374C8—741no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—372no—
384C22—2964no—
385C22—741no—
386C22—741no—
387C22—741no—
388C22—741no—
389C22—741no—
390C22—1484no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22#1192456012yes—
395C22C2×D4×D3711yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—741no—
400C4—741no—
401C4—1481no—
402C4—1481no—
403C4—1481no—
404C4#1192458111yescharacteristic
405C4#1192458211yescharacteristic
406C2—22no—
407C2—81no—
408C2—81no—
409C2—2961no—
410C2—742no—
411C2—1481no—
412C2#1455809111yescharacteristic
413C2#135×D3711yescharacteristic
414C2C2×#1192456011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#466C2
socleC22×C37C22×D4
hypercenter#466D37
hypocenterC37#3188
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14558043C2semidirect
2. #121×D37C2semidirect
3. #14557870C2semidirect
4. #14557860C2semidirect
5. #14557856C2semidirect
6. #14557850C2semidirect
7. #14557767C2semidirect
8. #14557762C2semidirect
9. #14557760C2semidirect
10. #14557685C2semidirect
11. #14557679C2semidirect
12. #14557675C2semidirect
13. #14557665C2semidirect
14. C2×#11924448C2semidirect
15. C37×#466C2semidirect
16. C2×#10596964C22semidirect
20. C2×#10596930C22semidirect
21. C2×#10596940C22semidirect
22. C2×#10596939C22semidirect
23. C22×#64436C22semidirect
26. #11924515C22semidirect
36. #11924494C22semidirect
39. #11924469C22semidirect
40. #11924468C22semidirect
41. #11924467C22semidirect
42. #11924461C22semidirect
43. #11924459C22semidirect
44. #11924458C22semidirect
45. #11924457C22semidirect
46. #11924457C22semidirect
47. #11924456C22semidirect
50. #11924448C22semidirect
51. #11924448C22semidirect
52. C2×D8×C37C22semidirect
53. C22×C8×C37C22semidirect
55. #121×C37C22semidirect
56. #107×C37C22semidirect
57. #102×C37C22semidirect
58. #102×C37C22semidirect
215. #466D37semidirect
223. C37#3188semidirect
231. C2×D8C2×D37semidirect
233. C22×C8C2×D37semidirect
244. #121C2×D37semidirect
252. #107C2×D37semidirect
261. #102C2×D37semidirect
262. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580432
#121×D372
#145578702
#145578602
#145578562
#145578502
#145577672
#145577622
#145577602
#145576852
#145576792
#145576752
#145576652
C2×#119244482
C37×#4662
#318837