Finite Group Databasebeta

← #18004787

Subgroups — #18004787

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#14558157C211yesmaximal, characteristic, complemented
2#14558005C211yesmaximal, characteristic, complemented
3#14557876C211yesmaximal, characteristic, complemented
4#14557860C211yesmaximal, characteristic, complemented
5#14557820C211yesmaximal, characteristic, complemented
6#14557749C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557685C211yesmaximal, characteristic, complemented
9#14557668C211yesmaximal, characteristic
10#14557642C211yesmaximal, characteristic, complemented
11#14557632C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13#14557615C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#474C211yesmaximal, characteristic, complemented
16C2×D4×D37C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21#11924531—21no—
22#11924525—21no—
23#11924524C2211yescharacteristic, complemented
24#11924521—21no—
25#11924516C2211yescharacteristic
26#11924512—21no—
27#11924511C2211yescharacteristic
28#11924501C2211yescharacteristic, complemented
29C4×D148C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31#11924498C2211yescharacteristic
32#11924498C2211yescharacteristic, complemented
33C4×C22⋊D37—21no—
34#11924496—21no—
35#11924494C2211yescharacteristic
36#11924493C2211yescharacteristic
37C2×#10596938—21no—
38C22⋊C4×D37—21no—
39#11924467C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41C4⋊#64436C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924459C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic, complemented
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic, complemented
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C4⋊Q8×C37C2211yescharacteristic, complemented
53C4×D4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic, complemented
55#107×C37C2211yescharacteristic, complemented
56C4⋊C8×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C23×D37—21no—
60C2×Q8×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37—21no—
63C2×C22⋊D37—21no—
64C22×Dic37—21no—
65D4×D37—22no—
66D4×D37—22no—
67C2×D148—21no—
68C2×D148C2311yescharacteristic
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×C4×D37C2311yescharacteristic
74C2×Dic74C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C42×C37C2311yescharacteristic
83C22⋊Dic37—21no—
84#10596940—22no—
85#10596939—22no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938D411yescharacteristic
95#10596938D411yescharacteristic
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936D411yescharacteristic
100#10596936D411yescharacteristic
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106D296—22no—
107#10596930—22no—
108C23×C37—21no—
109C22×D37—21no—
110C22×D37—24no—
111C22×D37—21no—
112C22×D37—81no—
113C22×D37—81no—
114C22×D37C2×D411yescharacteristic
115Q8×C37—81no—
116D4×C37—21no—
117D4×C37#4112yes—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—81no—
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37—24no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—81no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132D148—21no—
133D148—21no—
134D148—21no—
135D148—81no—
136D148#4112yes—
137C4×D37—21no—
138C4×D37—21no—
139C4×D37—81no—
140C4×D37—81no—
141C4×D37—81no—
142Dic74—21no—
143Dic74—21no—
144C8×C37—21no—
145C8×C37—21no—
146#64436—21no—
147#64436—21no—
148C22×C37—22no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37C22×D411yescharacteristic
152C2×D37—21no—
153C2×D37—22no—
154C2×D37—21no—
155C2×D37—21no—
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—41no—
165C4×C37—41no—
166C4×C37—41no—
167C4×C37C2×#4111yescharacteristic
168C4×C37C2×#4111yescharacteristic
169Dic37—21no—
170Dic37—21no—
171Dic37—21no—
172Dic37—41no—
173Dic37—41no—
174#3118—371nomaximal, Sylow
175C2×C37—42no—
176C2×C37#52511yescharacteristic
177C2×C37#57611yescharacteristic
178C2×C37#57711yescharacteristic
179D37—41no—
180D37—42no—
181D37—81no—
182#542—371no—
183#518—371no—
184#485—371no—
185#482—371no—
186#476—371no—
187#474D3711yescharacteristic, complemented
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⋊Q8C2×D3711yescharacteristic, complemented
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—741no—
217C4×D4—741no—
218C4×D4C2×D3711yescharacteristic
219#117—371no—
220#117—371no—
221C2×C22⋊C4—741no—
222C2×C22⋊C4—741no—
223#107C2×D3711yescharacteristic, complemented
224#107C2×D3711yescharacteristic, complemented
225#106—371no—
226#106—371no—
227C4⋊C8—371no—
228C4⋊C8C2×D3711yescharacteristic, complemented
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⋊C8—371no—
239#97—371no—
240C4×C8—371no—
241C24—741no—
242C2×Q8—21no—
243C2×Q8—371no—
244C2×D4—371no—
245C2×D4—371no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—742no—
249C2×D4—742no—
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—371no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
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—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—741no—
288C42—741no—
289C42C22×D3711yescharacteristic
290C23—21no—
291C23—371no—
292C23—2961no—
293C23—2961no—
294C23—744no—
295C23—741no—
296C23—741no—
297Q8—81no—
298Q8—741no—
299Q8—741no—
300D4—21no—
301D4—372no—
302D4—2961no—
303D4—744no—
304D4—741no—
305D4—741no—
306D4—741no—
307D4#1059696612yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—371no—
315C2×C4—2961no—
316C2×C4—2961no—
317C2×C4—2961no—
318C2×C4—2961no—
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—2964no—
334C22—741no—
335C22—742no—
336C22—741no—
337C22—741no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22C2×D4×D3711yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—741no—
350C4—741no—
351C4—741no—
352C4—1481no—
353C4—1481no—
354C4#41×D3711yescharacteristic
355C4C2×#1059696611yescharacteristic
356C2—42no—
357C2—2961no—
358C2—1481no—
359C2—1482no—
360C2#1455804611yescharacteristic
361C2#1455833411yescharacteristic
362C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#474C2
socleC22×C37C22×D4
prime radical#14557668C2
hypercenter#474D37
hypocenterC37#3118
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14558157C2semidirect
2. #14558005C2semidirect
3. #14557876C2semidirect
4. #14557860C2semidirect
5. #14557820C2semidirect
6. #14557749C2semidirect
7. #14557748C2semidirect
8. #14557685C2semidirect
10. #14557642C2semidirect
11. #14557632C2semidirect
12. #14557624C2semidirect
13. #14557615C2semidirect
14. #14557593C2semidirect
15. C37×#474C2semidirect
23. #11924524C22semidirect
28. #11924501C22semidirect
32. #11924498C22semidirect
39. #11924467C22semidirect
40. #11924467C22semidirect
41. C4⋊#64436C22semidirect
42. #11924461C22semidirect
43. #11924459C22semidirect
44. #11924458C22semidirect
47. #11924456C22semidirect
50. #11924446C22semidirect
51. C8×Dic37C22semidirect
52. C4⋊Q8×C37C22semidirect
54. #107×C37C22semidirect
55. #107×C37C22semidirect
56. C4⋊C8×C37C22semidirect
187. #474D37semidirect
197. C37#3118semidirect
203. C4⋊Q8C2×D37semidirect
223. #107C2×D37semidirect
224. #107C2×D37semidirect
228. C4⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581572
#145580052
#145578762
#145578602
#145578202
#145577492
#145577482
#145576852
#145576682
#145576422
#145576322
#145576242
#145576152
#145575932
C37×#4742
#311837