Finite Group Databasebeta

← #18004783

Subgroups — #18004783

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#14558156C211yesmaximal, characteristic, complemented
2#14558007C211yesmaximal, characteristic, complemented
3#14557857C211yesmaximal, characteristic, complemented
4#14557822C211yesmaximal, characteristic, complemented
5#14557812C211yesmaximal, characteristic, complemented
6#14557751C211yesmaximal, characteristic, complemented
7#14557751C211yesmaximal, characteristic, complemented
8#14557683C211yesmaximal, characteristic, complemented
9#14557669C211yesmaximal, characteristic
10#14557644C211yesmaximal, characteristic, complemented
11#14557636C211yesmaximal, characteristic, complemented
12#14557618C211yesmaximal, characteristic, complemented
13#14557615C211yesmaximal, characteristic, complemented
14#14557591C211yesmaximal, characteristic, complemented
15C37×#485C211yesmaximal, characteristic, complemented
16C22×D148C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924535C2211yescharacteristic, complemented
22#11924531—21no—
23#11924525C2211yescharacteristic, complemented
24#11924522—21no—
25#11924518—21no—
26#11924516—21no—
27#11924510C2211yescharacteristic
28Q8×Dic37C2211yescharacteristic, complemented
29C4×D148—21no—
30C4×D148—21no—
31#11924498C2211yescharacteristic
32#11924498C2211yescharacteristic
33#11924498C2211yescharacteristic
34#11924498C2211yescharacteristic
35#11924498C2211yescharacteristic, complemented
36#11924495C2211yescharacteristic
37C22⋊C4×D37—21no—
38C22⋊C4×D37—21no—
39#11924469C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic, complemented
49C22⋊#64436C2211yescharacteristic
50#11924446C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
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×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C2×D148—21no—
64C2×D148—22no—
65C2×D148—22no—
66C2×D148C2311yescharacteristic
67C2×D148C2311yescharacteristic
68C2×D148C2311yescharacteristic
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×Dic74—21no—
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C42×C37—21no—
84C22⋊Dic37D411yescharacteristic
85C22⋊Dic37D411yescharacteristic
86#10596941—22no—
87#10596941—22no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37D411yescharacteristic
98C4⋊Dic37D411yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100#10596936—21no—
101C4×Dic37—21no—
102C4×Dic37C2311yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106D296—22no—
107D296—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—24no—
112C22×D37—21no—
113C22×D37—81no—
114C22×D37—81no—
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—81no—
126C2×Dic37—21no—
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131D148—24no—
132D148—21no—
133D148—21no—
134D148—21no—
135D148—21no—
136D148#4112yes—
137D148#4112yes—
138C4×D37—81no—
139C4×D37—81no—
140C4×D37—81no—
141C4×D37—81no—
142C4×D37—81no—
143Dic74—81no—
144C8×C37—21no—
145C8×C37—21no—
146#64436—21no—
147#64436—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—41no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37—41no—
167C4×C37C2×#4111yescharacteristic
168C4×C37C2×#4111yescharacteristic
169Dic37—21no—
170Dic37—21no—
171Dic37—21no—
172Dic37—21no—
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#485D3711yescharacteristic, complemented
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#433—371no—
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—741no—
209C22⋊Q8C2×D3711yescharacteristic
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#107C2×D3711yescharacteristic, complemented
225#106—371no—
226#106C2×D3711yescharacteristic, complemented
227C4⋊C8—371no—
228C4⋊C8—371no—
229#103C2×D3711yescharacteristic, complemented
230#103C2×D3711yescharacteristic, complemented
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102—371no—
236#102—371no—
237C22⋊C8—371no—
238C22⋊C8C2×D3711yescharacteristic
239#97—371no—
240C4×C8—371no—
241C24—741no—
242C2×Q8—741no—
243C2×Q8C22×D3711yescharacteristic
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×C8—371no—
262C2×C8—371no—
263C2×C8C22×D3711yescharacteristic
264C2×C8C22×D3711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—371no—
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—741no—
270C4⋊C4—741no—
271C4⋊C4C22×D3711yescharacteristic
272C4⋊C4C22×D3711yescharacteristic
273C4⋊C4C22×D3711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—371no—
277C22⋊C4—371no—
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—371no—
288C42—371no—
289C42—741no—
290C23—2961no—
291C23—2961no—
292C23—744no—
293C23—741no—
294C23—741no—
295C23—741no—
296C23D4×D3711yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—2961no—
300D4—372no—
301D4—372no—
302D4—2961no—
303D4—744no—
304D4—741no—
305D4—741no—
306D4—741no—
307D4—741no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—371no—
315C2×C4—371no—
316C2×C4—371no—
317C2×C4—371no—
318C2×C4—2961no—
319C2×C4—2961no—
320C2×C4—2961no—
321C2×C4—2961no—
322C2×C4—2961no—
323C2×C4—741no—
324C2×C4D4×D3711yescharacteristic
325C2×C4C23×D3711yescharacteristic
326C8—21no—
327C8—21no—
328C8—741no—
329C8—741no—
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—
343C22C2×D4×D3711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—741no—
350C4—741no—
351C4—741no—
352C4—741no—
353C4—1481no—
354C4#41×D3711yescharacteristic
355C4#41×D3711yescharacteristic
356C2—41no—
357C2—2961no—
358C2—1482no—
359C2—1482no—
360C2#1455804111yescharacteristic
361C2#1455833511yescharacteristic
362C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#485C2
socleC22×C37C22×D4
prime radical#14557669C2
hypercenter#485D37
hypocenterC37#3118
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
1. #14558156C2semidirect
2. #14558007C2semidirect
3. #14557857C2semidirect
4. #14557822C2semidirect
5. #14557812C2semidirect
6. #14557751C2semidirect
7. #14557751C2semidirect
8. #14557683C2semidirect
10. #14557644C2semidirect
11. #14557636C2semidirect
12. #14557618C2semidirect
13. #14557615C2semidirect
14. #14557591C2semidirect
15. C37×#485C2semidirect
21. #11924535C22semidirect
23. #11924525C22semidirect
28. Q8×Dic37C22semidirect
35. #11924498C22semidirect
39. #11924469C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924465C22semidirect
47. #11924456C22semidirect
48. #11924456C22semidirect
50. #11924446C22semidirect
51. C8×Dic37C22semidirect
54. #107×C37C22semidirect
55. #106×C37C22semidirect
56. #103×C37C22semidirect
57. #103×C37C22semidirect
184. #485D37semidirect
197. C37#3118semidirect
224. #107C2×D37semidirect
226. #106C2×D37semidirect
229. #103C2×D37semidirect
230. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581562
#145580072
#145578572
#145578222
#145578122
#145577512
#145576832
#145576692
#145576442
#145576362
#145576182
#145576152
#145575912
C37×#4852
#311837