Finite Group Databasebeta

← #18004781

Subgroups — #18004781

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#14558008C211yesmaximal, characteristic, complemented
3#14557871C211yesmaximal, characteristic, complemented
4#14557858C211yesmaximal, characteristic, complemented
5#14557821C211yesmaximal, characteristic, complemented
6#14557811C211yesmaximal, characteristic, complemented
7#14557750C211yesmaximal, characteristic, complemented
8#14557750C211yesmaximal, characteristic, complemented
9#14557667C211yesmaximal, characteristic
10#14557642C211yesmaximal, characteristic, complemented
11#14557634C211yesmaximal, characteristic, complemented
12SD16×Dic37C211yesmaximal, characteristic, complemented
13#14557613C211yesmaximal, characteristic, complemented
14#14557591C211yesmaximal, characteristic, complemented
15C37×#450C211yesmaximal, characteristic, complemented
16C2×#10596939C2211yescharacteristic
17C2×#10596939C2211yescharacteristic
18#11924535C2211yescharacteristic, complemented
19#11924531—21no—
20#11924525C2211yescharacteristic, complemented
21#11924522—21no—
22#11924518—21no—
23#11924516—21no—
24#11924510C2211yescharacteristic
25Q8×Dic37C2211yescharacteristic, complemented
26D4×Dic37—21no—
27D4×Dic37—21no—
28D4×Dic37C2211yescharacteristic
29D4×Dic37C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31D4×Dic37C2211yescharacteristic
32#11924498C2211yescharacteristic, complemented
33#11924495C2211yescharacteristic
34#11924495C2211yescharacteristic
35C2×C22⋊Dic37—21no—
36C2×C22⋊Dic37—21no—
37#11924470C2211yescharacteristic, complemented
38#11924469C2211yescharacteristic, complemented
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924460C2211yescharacteristic, complemented
44#11924460C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic, complemented
46#11924458C2211yescharacteristic, complemented
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924446C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22×D4×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54C2×SD16×C37C2211yescharacteristic
55C22⋊Q8×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C24×C37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37—22no—
62C2×D4×C37—22no—
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C22×Dic37—21no—
69C22×Dic37—21no—
70C22×Dic37—21no—
71C22×Dic37—21no—
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×Dic74—21no—
75SD16×C37—22no—
76SD16×C37—22no—
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C22⋊Dic37—21no—
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37D411yescharacteristic
88C22⋊Dic37D411yescharacteristic
89#10596939—22no—
90#10596939—22no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95C4⋊Dic37—21no—
96C4⋊Dic37D411yescharacteristic
97C4⋊Dic37D411yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C4×Dic37C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—24no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37—81no—
112C23×C37—81no—
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117D4×C37—24no—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37#4112yes—
121D4×C37#4112yes—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2411yescharacteristic
128C22⋊D37—81no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—81no—
133C2×Dic37—81no—
134C2×Dic37—81no—
135C2×Dic37—81no—
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138C2×Dic37C2×D411yescharacteristic
139C2×Dic37C2×D411yescharacteristic
140D148—21no—
141D148—21no—
142C4×D37—81no—
143Dic74—81no—
144C8×C37—21no—
145C8×C37—21no—
146#64436—21no—
147#64436—21no—
148C22×C37—21no—
149C22×C37—22no—
150C22×C37—22no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—84no—
158C22×C37C22×D411yescharacteristic
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C4×C37—21no—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37C2×#4111yescharacteristic
166C4×C37C2×#4111yescharacteristic
167Dic37—21no—
168Dic37—21no—
169Dic37—21no—
170Dic37—21no—
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174#3118—371nomaximal, Sylow
175C2×C37—41no—
176C2×C37—42no—
177C2×C37—42no—
178C2×C37#52511yescharacteristic
179C2×C37#57611yescharacteristic
180C2×C37#57711yescharacteristic
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#450D3711yescharacteristic, complemented
191#447—371no—
192#442—371no—
193#440—371no—
194C4×SD16—371no—
195C4×D8—371no—
196#433—371no—
197C37#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D3711yescharacteristic
199C2×SD16C2×D3711yescharacteristic
200C2×SD16C2×D3711yescharacteristic
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#117—371no—
221C2×C22⋊C4—741no—
222C2×C22⋊C4—741no—
223#107—371no—
224#107—371no—
225#106—371no—
226#106—371no—
227C4⋊C8—371no—
228C4⋊C8—371no—
229#103—371no—
230#103—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102C2×D3711yescharacteristic
236#102C2×D3711yescharacteristic
237C22⋊C8—371no—
238C22⋊C8C2×D3711yescharacteristic
239#97—371no—
240C4×C8—371no—
241C24—21no—
242C2×Q8—741no—
243C2×Q8C22×D3711yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—371no—
248C2×D4—741no—
249C2×D4C22×D3711yescharacteristic
250C2×D4C22×D3711yescharacteristic
251C22×C4—741no—
252C22×C4—741no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4C22×D3711yescharacteristic
257SD16—22no—
258SD16—22no—
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—371no—
270C4⋊C4—371no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4C22×D3711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—371no—
276C22⋊C4—371no—
277C22⋊C4—741no—
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—371no—
287C42—371no—
288C42—741no—
289C42—741no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—741no—
296C23D4×D3711yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—2961no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—2961no—
304D4—741no—
305D4—741no—
306D4#1059696412yes—
307D4#1059696412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—371no—
315C2×C4—371no—
316C2×C4—2961no—
317C2×C4—2961no—
318C2×C4—2961no—
319C2×C4—2961no—
320C2×C4—2961no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4D4×D3711yescharacteristic
325C2×C4C23×D3711yescharacteristic
326C8—21no—
327C8—21no—
328C8—741no—
329C8—741no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22C2×D4×D3711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—741no—
348C4—741no—
349C4—741no—
350C4—741no—
351C4—1481no—
352C4—1481no—
353C4—1481no—
354C4C2×#1059696411yescharacteristic
355C4C2×#1059696411yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—2961no—
360C2#1455803911yescharacteristic
361C2#1455833711yescharacteristic
362C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#450C2
socleC22×C37C22×D4
prime radical#14557667C2
hypercenter#450D37
hypocenterC37#3118
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14558156C2semidirect
2. #14558008C2semidirect
3. #14557871C2semidirect
4. #14557858C2semidirect
5. #14557821C2semidirect
6. #14557811C2semidirect
7. #14557750C2semidirect
8. #14557750C2semidirect
10. #14557642C2semidirect
11. #14557634C2semidirect
12. SD16×Dic37C2semidirect
13. #14557613C2semidirect
14. #14557591C2semidirect
15. C37×#450C2semidirect
18. #11924535C22semidirect
20. #11924525C22semidirect
25. Q8×Dic37C22semidirect
32. #11924498C22semidirect
37. #11924470C22semidirect
38. #11924469C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924465C22semidirect
43. #11924460C22semidirect
44. #11924460C22semidirect
45. #11924458C22semidirect
46. #11924458C22semidirect
50. #11924446C22semidirect
51. C8×Dic37C22semidirect
190. #450D37semidirect
197. C37#3118semidirect

Maximal subgroups

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

subgroupindex
#145581562
#145580082
#145578712
#145578582
#145578212
#145578112
#145577502
#145576672
#145576422
#145576342
SD16×Dic372
#145576132
#145575912
C37×#4502
#311837