Finite Group Databasebeta

← #18004782

Subgroups — #18004782

Order 4736.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558154C211yesmaximal, characteristic, complemented
2#14558007C211yesmaximal, characteristic, complemented
3#14557875C211yesmaximal, characteristic, complemented
4#14557858C211yesmaximal, characteristic, complemented
5#14557824C211yesmaximal, characteristic, complemented
6#14557814C211yesmaximal, characteristic, complemented
7#14557749C211yesmaximal, characteristic, complemented
8#14557749C211yesmaximal, characteristic, complemented
9#14557686C211yesmaximal, characteristic, complemented
10#14557669C211yesmaximal, characteristic
11#14557646C211yesmaximal, characteristic, complemented
12#14557635C211yesmaximal, characteristic, complemented
13C4×#10596930C211yesmaximal, characteristic, complemented
14C4×D296C211yesmaximal, characteristic, complemented
15C37×#433C211yesmaximal, characteristic, complemented
16C22×D148C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924536C2211yescharacteristic, complemented
22#11924531—21no—
23#11924524C2211yescharacteristic, complemented
24#11924522—21no—
25#11924518—21no—
26#11924515C2211yescharacteristic
27#11924514—21no—
28#11924510C2211yescharacteristic
29C4×Dic74C2211yescharacteristic, complemented
30C4×D148C2211yescharacteristic
31C4×D148C2211yescharacteristic
32C4×D148C2211yescharacteristic
33C4×D148C2211yescharacteristic
34C4×D148C2211yescharacteristic, complemented
35#11924498—21no—
36#11924498—21no—
37#11924495C2211yescharacteristic
38C22⋊C4×D37—21no—
39C22⋊C4×D37—21no—
40#11924470C2211yescharacteristic, complemented
41#11924470C2211yescharacteristic, complemented
42#11924468C2211yescharacteristic, complemented
43#11924468C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924461C2211yescharacteristic, complemented
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic, complemented
52#117×C37C2211yescharacteristic
53C4⋊C8×C37C2211yescharacteristic, complemented
54C4⋊C8×C37C2211yescharacteristic, complemented
55C22⋊C8×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57#97×C37C2211yescharacteristic, complemented
58C4×C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C22×C4×C37C2311yescharacteristic
61C2×C22⋊D37—21no—
62C2×D148—21no—
63C2×D148—22no—
64C2×D148—22no—
65C2×D148C2311yescharacteristic
66C2×D148C2311yescharacteristic
67C2×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×Dic74—21no—
74C2×Dic74C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37D411yescharacteristic
80C4⋊C4×C37D411yescharacteristic
81C22⋊C4×C37D411yescharacteristic
82C22⋊C4×C37D411yescharacteristic
83C42×C37C2311yescharacteristic
84C42×C37C2311yescharacteristic
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95C4⋊Dic37—21no—
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100#10596936—21no—
101#10596936—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104D296—22no—
105D296—22no—
106#10596930—22no—
107#10596930—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—24no—
112C22×D37—21no—
113C22×D37—81no—
114C22×D37—81no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2411yescharacteristic
123C22⋊D37—81no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129D148—24no—
130D148—21no—
131D148—21no—
132D148—21no—
133D148—21no—
134D148#4112yes—
135D148#4112yes—
136C4×D37—81no—
137C4×D37—81no—
138C4×D37—81no—
139C4×D37—81no—
140C4×D37—81no—
141Dic74—21no—
142Dic74—21no—
143Dic74—81no—
144C8×C37—21no—
145C8×C37—21no—
146C8×C37—21no—
147C8×C37—21no—
148C22×C37—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37C22×D411yescharacteristic
152C2×D37—22no—
153C2×D37—22no—
154C2×D37—41no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—84no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37C2×#4111yescharacteristic
168C4×C37C2×#4111yescharacteristic
169Dic37—41no—
170Dic37—41no—
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174#3118—371nomaximal, Sylow
175C2×C37—41no—
176C2×C37#52511yescharacteristic
177C2×C37#57611yescharacteristic
178C2×C37#57711yescharacteristic
179D37—42no—
180D37—42no—
181D37—81no—
182#542—371no—
183#518—371no—
184#485—371no—
185#482—371no—
186#476—371no—
187#474—371no—
188#463—371no—
189#463—371no—
190#450—371no—
191#447—371no—
192#442—371no—
193#440—371no—
194C4×SD16—371no—
195C4×D8—371no—
196#433D3711yescharacteristic, complemented
197C37#311811yescharacteristic, complemented, Sylow
198C22×D4—371no—
199C2×SD16—371no—
200C2×SD16—371no—
201C2×D8—371no—
202C2×D8—371no—
203C4⋊Q8—371no—
204#126—741no—
205#124—371no—
206#124—741no—
207#123—741no—
208C22⋊Q8—371no—
209C22⋊Q8—741no—
210#121—371no—
211C4×Q8—371no—
212C4×D4—371no—
213C4×D4—371no—
214C4×D4—371no—
215C4×D4—371no—
216C4×D4—371no—
217C4×D4—741no—
218C4×D4—741no—
219#117—371no—
220#117C2×D3711yescharacteristic
221C2×C22⋊C4—741no—
222C2×C22⋊C4—741no—
223#107—371no—
224#107—371no—
225#106—371no—
226#106—371no—
227C4⋊C8C2×D3711yescharacteristic, complemented
228C4⋊C8C2×D3711yescharacteristic, complemented
229#103—371no—
230#103—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102—371no—
236#102—371no—
237C22⋊C8C2×D3711yescharacteristic
238C22⋊C8C2×D3711yescharacteristic
239#97C2×D3711yescharacteristic, complemented
240C4×C8C2×D3711yescharacteristic, complemented
241C24—741no—
242C2×Q8—371no—
243C2×Q8—741no—
244C2×D4—371no—
245C2×D4—371no—
246C2×D4—371no—
247C2×D4—742no—
248C2×D4—742no—
249C2×D4—741no—
250C2×D4—741no—
251C22×C4—741no—
252C22×C4—741no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4C22×D3711yescharacteristic
257SD16—742no—
258SD16—742no—
259D8—742no—
260D8—742no—
261C2×C8C22×D3711yescharacteristic
262C2×C8C22×D3711yescharacteristic
263C2×C8C22×D3711yescharacteristic
264C2×C8C22×D3711yescharacteristic
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—741no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4D14811yescharacteristic
273C4⋊C4D14811yescharacteristic
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4D14811yescharacteristic
285C22⋊C4D14811yescharacteristic
286C42—741no—
287C42—741no—
288C42C22×D3711yescharacteristic
289C42C22×D3711yescharacteristic
290C23—2961no—
291C23—2961no—
292C23—744no—
293C23—741no—
294C23—741no—
295C23—741no—
296C23C2×D14811yescharacteristic
297Q8—2961no—
298Q8—741no—
299Q8—741no—
300D4—372no—
301D4—372no—
302D4—2961no—
303D4—744no—
304D4—741no—
305D4—741no—
306D4—741no—
307D4—741no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2961no—
311C2×C4—2961no—
312C2×C4—2961no—
313C2×C4—2961no—
314C2×C4—2961no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4C2×D14811yescharacteristic
321C2×C4C2×D14811yescharacteristic
322C2×C4C2×D14811yescharacteristic
323C2×C4C2×D14811yescharacteristic
324C2×C4C2×D14811yescharacteristic
325C2×C4C23×D3711yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—2964no—
334C22—742no—
335C22—742no—
336C22—1481no—
337C22—1481no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22C22×D14811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—1481no—
350C4—1481no—
351C4—1481no—
352C4—1481no—
353C4—1481no—
354C4#41×D3711yescharacteristic
355C4#41×D3711yescharacteristic
356C2—41no—
357C2—2961no—
358C2—1482no—
359C2—1482no—
360C2#1455804511yescharacteristic
361C2#1455833811yescharacteristic
362C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#433C2
socleC22×C37C22×D4
prime radical#14557669C2
hypercenter#433D37
hypocenterC37#3118
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14558007C2semidirect
3. #14557875C2semidirect
4. #14557858C2semidirect
5. #14557824C2semidirect
6. #14557814C2semidirect
7. #14557749C2semidirect
8. #14557749C2semidirect
9. #14557686C2semidirect
11. #14557646C2semidirect
12. #14557635C2semidirect
13. C4×#10596930C2semidirect
14. C4×D296C2semidirect
15. C37×#433C2semidirect
21. #11924536C22semidirect
23. #11924524C22semidirect
29. C4×Dic74C22semidirect
34. C4×D148C22semidirect
40. #11924470C22semidirect
41. #11924470C22semidirect
42. #11924468C22semidirect
43. #11924468C22semidirect
44. #11924461C22semidirect
45. #11924461C22semidirect
50. #11924458C22semidirect
51. #11924458C22semidirect
53. C4⋊C8×C37C22semidirect
54. C4⋊C8×C37C22semidirect
57. #97×C37C22semidirect
58. C4×C8×C37C22semidirect
196. #433D37semidirect
197. C37#3118semidirect
227. C4⋊C8C2×D37semidirect
228. C4⋊C8C2×D37semidirect
239. #97C2×D37semidirect
240. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145580072
#145578752
#145578582
#145578242
#145578142
#145577492
#145576862
#145576692
#145576462
#145576352
C4×#105969302
C4×D2962
C37×#4332
#311837