Finite Group Databasebeta

← #18004778

Subgroups — #18004778

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#14558148C211yesmaximal, characteristic, complemented
2#14558005C211yesmaximal, characteristic, complemented
3#14557877C211yesmaximal, characteristic, complemented
4#14557855C211yesmaximal, characteristic, complemented
5#14557822C211yesmaximal, characteristic, complemented
6#14557811C211yesmaximal, characteristic, complemented
7#14557747C211yesmaximal, characteristic, complemented
8#14557746C211yesmaximal, characteristic, complemented
9#14557685C211yesmaximal, characteristic, complemented
10#14557665C211yesmaximal, characteristic
11#14557635C211yesmaximal, characteristic, complemented
12C4×#10596940C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557595C211yesmaximal, characteristic, complemented
15C37×#442C211yesmaximal, characteristic, complemented
16C2×D4×D37C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20#11924535C2211yescharacteristic, complemented
21#11924529—21no—
22#11924523C2211yescharacteristic, complemented
23#11924522—21no—
24#11924519—21no—
25#11924516C2211yescharacteristic
26#11924515—21no—
27#11924507C2211yescharacteristic
28C4×Dic74C2211yescharacteristic, complemented
29C4×D148C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31#11924498C2211yescharacteristic
32C4×C22⋊D37—21no—
33#11924496—21no—
34#11924494C2211yescharacteristic
35#11924493C2211yescharacteristic
36C2×#10596938—21no—
37C22⋊C4×D37—21no—
38#11924470C2211yescharacteristic, complemented
39#11924469C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924459C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic
51C4×#64436C2211yescharacteristic, complemented
52C2×D8×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic, complemented
55#106×C37C2211yescharacteristic, complemented
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic, complemented
58#97×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×D4×C37C2311yescharacteristic
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37—21no—
63C22×C4×C37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C22×Dic37—21no—
67D4×D37—22no—
68D4×D37—22no—
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37C2311yescharacteristic
73C2×Dic74—21no—
74C2×Dic74C2311yescharacteristic
75D8×C37—22no—
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C42×C37C2311yescharacteristic
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87#10596940—22no—
88#10596939—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938D411yescharacteristic
94#10596938D411yescharacteristic
95C4⋊Dic37—21no—
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107#10596930—22no—
108C23×C37—21no—
109C23×C37—21no—
110C22×D37—21no—
111C22×D37—24no—
112C22×D37—81no—
113C22×D37—81no—
114C22×D37C2×D411yescharacteristic
115D4×C37—21no—
116D4×C37—21no—
117D4×C37—21no—
118D4×C37#4112yes—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—81no—
122C2×C4×C37—81no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2411yescharacteristic
126C22⋊D37—24no—
127C22⋊D37—81no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—81no—
132C2×Dic37C2×D411yescharacteristic
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135D148—21no—
136D148#4112yes—
137C4×D37—21no—
138C4×D37—21no—
139C4×D37—81no—
140C4×D37—81no—
141Dic74—21no—
142Dic74—21no—
143Dic74—81no—
144C8×C37—21no—
145C8×C37—21no—
146#64436—21no—
147#64436—21no—
148C22×C37—22no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37C22×D411yescharacteristic
155C2×D37—21no—
156C2×D37—22no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—84no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37C2×#4111yescharacteristic
167C4×C37C2×#4111yescharacteristic
168Dic37—21no—
169Dic37—21no—
170Dic37—21no—
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174#3118—371nomaximal, Sylow
175C2×C37—42no—
176C2×C37—81no—
177C2×C37#52511yescharacteristic
178C2×C37#57611yescharacteristic
179C2×C37#57711yescharacteristic
180D37—41no—
181D37—42no—
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#442D3711yescharacteristic, complemented
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×D8C2×D3711yescharacteristic
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—741no—
216C4×D4—741no—
217C4×D4C2×D3711yescharacteristic
218C4×D4C2×D3711yescharacteristic, complemented
219#117—371no—
220#117—371no—
221C2×C22⋊C4—741no—
222C2×C22⋊C4—741no—
223#107—371no—
224#107—371no—
225#106—371no—
226#106C2×D3711yescharacteristic, complemented
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, complemented
237C22⋊C8—371no—
238C22⋊C8—371no—
239#97C2×D3711yescharacteristic, complemented
240C4×C8—371no—
241C24—741no—
242C2×Q8—371no—
243C2×Q8—741no—
244C2×D4—371no—
245C2×D4—741no—
246C2×D4—742no—
247C2×D4—741no—
248C2×D4—742no—
249C2×D4C22×D3711yescharacteristic
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—371no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257SD16—742no—
258SD16—742no—
259D8—22no—
260D8—742no—
261C2×C8—371no—
262C2×C8—371no—
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⋊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—371no—
287C42—741no—
288C42—741no—
289C42C22×D3711yescharacteristic
290C23—21no—
291C23—21no—
292C23—371no—
293C23—2961no—
294C23—2961no—
295C23—744no—
296C23—741no—
297Q8—2961no—
298Q8—741no—
299Q8—741no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—372no—
304D4—2961no—
305D4—744no—
306D4—741no—
307D4#1059696212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—371no—
315C2×C4—2961no—
316C2×C4—2961no—
317C2×C4—2961no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4D4×D3711yescharacteristic
324C2×C4D4×D3711yescharacteristic
325C2×C4C23×D3711yescharacteristic
326C8—21no—
327C8—21no—
328C8—741no—
329C8—741no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—2964no—
337C22—741no—
338C22—742no—
339C22—741no—
340C22—741no—
341C22—1481no—
342C22—1481no—
343C22C2×D4×D3711yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—741no—
349C4—741no—
350C4—741no—
351C4—1481no—
352C4—1481no—
353C4—1481no—
354C4#41×D3711yescharacteristic
355C4C2×#1059696211yescharacteristic
356C2—42no—
357C2—81no—
358C2—1481no—
359C2—1482no—
360C2#1455804211yescharacteristic
361C2#1455833711yescharacteristic
362C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#442C2
socleC22×C37C22×D4
prime radical#14557665C2
hypercenter#442D37
hypocenterC37#3118
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14558148C2semidirect
2. #14558005C2semidirect
3. #14557877C2semidirect
4. #14557855C2semidirect
5. #14557822C2semidirect
6. #14557811C2semidirect
7. #14557747C2semidirect
8. #14557746C2semidirect
9. #14557685C2semidirect
11. #14557635C2semidirect
12. C4×#10596940C2semidirect
13. C4×#10596939C2semidirect
14. #14557595C2semidirect
15. C37×#442C2semidirect
20. #11924535C22semidirect
22. #11924523C22semidirect
28. C4×Dic74C22semidirect
38. #11924470C22semidirect
39. #11924469C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924465C22semidirect
43. #11924461C22semidirect
44. #11924459C22semidirect
47. #11924457C22semidirect
51. C4×#64436C22semidirect
54. C4×D4×C37C22semidirect
55. #106×C37C22semidirect
57. #102×C37C22semidirect
58. #97×C37C22semidirect
192. #442D37semidirect
197. C37#3118semidirect
218. C4×D4C2×D37semidirect
226. #106C2×D37semidirect
236. #102C2×D37semidirect
239. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581482
#145580052
#145578772
#145578552
#145578222
#145578112
#145577472
#145577462
#145576852
#145576652
#145576352
C4×#105969402
C4×#105969392
#145575952
C37×#4422
#311837