Finite Group Databasebeta

← #18006444

Subgroups — #18006444

Order 4736.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558231C211yesmaximal, characteristic, complemented
2#14558174C211yesmaximal, characteristic, complemented
3#14557889C211yesmaximal, characteristic, complemented
4#14557860C211yesmaximal, characteristic, complemented
5#14557836C211yesmaximal, characteristic, complemented
6#14557770C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557751C211yesmaximal, characteristic, complemented
9#14557681C211yesmaximal, characteristic, complemented
10#14557669C211yesmaximal, characteristic, complemented
11#14557615C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557528C211yesmaximal, characteristic, complemented
14C2×#11924456C211yesmaximal, characteristic, complemented
15C37×#484C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C22×D148C2211yescharacteristic
18C2×#10596941C2211yescharacteristic, complemented
19C2×D296C2211yescharacteristic
20C2×D296C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic, complemented
23#11924531—21no—
24#11924527C2211yescharacteristic, complemented
25#11924525C2211yescharacteristic
26#11924521—21no—
27#11924521—21no—
28#11924511—21no—
29#11924511C2211yescharacteristic
30#11924511C2211yescharacteristic, complemented
31#11924510—21no—
32#11924510C2211yescharacteristic
33#11924506—21no—
34#11924498C2211yescharacteristic
35#11924498C2211yescharacteristic, complemented
36C4×C22⋊D37—21no—
37C4×C22⋊D37C2211yescharacteristic
38#11924494C2211yescharacteristic, complemented
39C22⋊C4×D37—21no—
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924460C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22⋊Q8×C37C2211yescharacteristic
53C2×C4⋊C4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic, complemented
55#107×C37C2211yescharacteristic, complemented
56#103×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic
59C23×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37D411yescharacteristic
65#10596966—22no—
66#10596966—41no—
67C2×D148—22no—
68C2×D148—21no—
69C2×D148—21no—
70C2×D148—21no—
71C2×D148—21no—
72C2×D148—41no—
73C2×D148C2311yescharacteristic
74C2×D148C2311yescharacteristic
75C2×D148C2311yescharacteristic
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C2×C8×C37C2311yescharacteristic
82C4⋊C4×C37—21no—
83C4⋊C4×C37—21no—
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C4⋊C4×C37C2311yescharacteristic
87C22⋊C4×C37—21no—
88C22⋊Dic37D411yescharacteristic
89#10596941—41no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98#10596938D411yescharacteristic
99C4⋊Dic37—21no—
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936D411yescharacteristic
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C2×#64436—41no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108D296—22no—
109D296—41no—
110C8×D37—41no—
111C23×C37C2×D411yescharacteristic
112C22×D37—21no—
113C22×D37—21no—
114C22×D37—21no—
115C22×D37—42no—
116C22×D37—42no—
117C22×D37—81no—
118C22×D37C2×D411yescharacteristic
119Q8×C37—21no—
120Q8×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—81no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—22no—
131C22⋊D37—42no—
132C2×Dic37—21no—
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135C2×Dic37C2×D411yescharacteristic
136D148—21no—
137D148—21no—
138D148—21no—
139D148—21no—
140D148—21no—
141D148—42no—
142D148—42no—
143D148—81no—
144D148—81no—
145D148#4112yes—
146C4×D37—21no—
147C4×D37—21no—
148C4×D37—42no—
149C4×D37—81no—
150C4×D37—81no—
151C8×C37—21no—
152C8×C37—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37#13512yes—
158C22×C37C22×D411yescharacteristic
159C2×D37—21no—
160C2×D37—22no—
161C2×D37—21no—
162C2×D37—21no—
163C2×D37—41no—
164C2×D37—41no—
165C2×D37—41no—
166C2×D37—41no—
167C2×D37—41no—
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—41no—
171C2×D37—84no—
172C4×C37—21no—
173C4×C37—41no—
174C4×C37—41no—
175C4×C37—41no—
176C4×C37—41no—
177C4×C37C2×#4111yescharacteristic
178C4×C37H(5,𝔽2)11yescharacteristic
179Dic37—21no—
180Dic37—21no—
181Dic37—21no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—22no—
185C2×C37#54611yescharacteristic
186C2×C37C2×#13511yescharacteristic
187C2×C37#57611yescharacteristic
188D37—41no—
189D37—42no—
190D37—81no—
191D37—81no—
192#553—371no—
193#546—371no—
194#488—371no—
195#484D3711yescharacteristic, complemented
196#482—371no—
197#478—371no—
198#466—371no—
199#465—371no—
200#463—371no—
201#449—371no—
202#447—371no—
203C4×D8—371no—
204C8×D4—371no—
205#416—371no—
206C2×#102—371no—
207C37#329711yescharacteristic, complemented, Sylow
208C2×#41—371no—
209C22×D4—371no—
210C2×SD16—371no—
211C2×D8—371no—
212C2×D8—371no—
213C22×C8—371no—
214C22×C8—371no—
215#126—741no—
216#125—371no—
217#124—371no—
218#123—741no—
219#123—741no—
220C22⋊Q8C2×D3711yescharacteristic
221#121—371no—
222#121—371no—
223#121—371no—
224#121—741no—
225#121—741no—
226#120—741no—
227C4×D4—371no—
228C4×D4—371no—
229C4×D4—371no—
230C4×D4—741no—
231#117—371no—
232C2×C4⋊C4C2×D3711yescharacteristic
233C2×C22⋊C4—741no—
234#107C2×D3711yescharacteristic, complemented
235#107C2×D3711yescharacteristic, complemented
236#106—371no—
237C4⋊C8—371no—
238#103—371no—
239#103C2×D3711yescharacteristic, complemented
240#103C2×D3711yescharacteristic, complemented
241#102—371no—
242#102—371no—
243#102—371no—
244#102—371no—
245#102—371no—
246#102—371no—
247#102—371no—
248C22⋊C8—371no—
249C22⋊C8C2×D3711yescharacteristic
250C4×C8—371no—
251C24—741no—
252#41—742no—
253#41—1481no—
254C2×Q8C22×D3711yescharacteristic
255C2×D4—371no—
256C2×D4—371no—
257C2×D4—371no—
258C2×D4—371no—
259C2×D4—742no—
260C2×D4—741no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4—741no—
264C2×D4—741no—
265C2×D4—1481no—
266C22×C4—21no—
267C22×C4—371no—
268C22×C4—741no—
269C22×C4—741no—
270C22×C4—741no—
271C22×C4C22×D3711yescharacteristic
272SD16—1481no—
273D8—742no—
274D8—1481no—
275C2×C8—371no—
276C2×C8—371no—
277C2×C8—1481no—
278C2×C8—1481no—
279C2×C8C22×D3711yescharacteristic
280C2×C8C22×D3711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—371no—
284C4⋊C4—371no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4C22×D3711yescharacteristic
288C4⋊C4C22×D3711yescharacteristic
289C4⋊C4C22×D3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—371no—
292C22⋊C4—371no—
293C22⋊C4—741no—
294C22⋊C4—741no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4—741no—
300C22⋊C4—741no—
301C42—371no—
302C42—741no—
303C23—371no—
304C23—2961no—
305C23—741no—
306C23—741no—
307C23—741no—
308C23—1482no—
309C23—1482no—
310C23D4×D3711yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—372no—
314D4—2961no—
315D4—2961no—
316D4—742no—
317D4—741no—
318D4—741no—
319D4—741no—
320D4—741no—
321D4—741no—
322D4—1482no—
323D4—1482no—
324D4—1482no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—371no—
333C2×C4—371no—
334C2×C4—371no—
335C2×C4—2961no—
336C2×C4—2961no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—1482no—
341C2×C4D4×D3711yescharacteristic
342C2×C4C23×D3711yescharacteristic
343C8—21no—
344C8—21no—
345C8—741no—
346C8—741no—
347C22—21no—
348C22—21no—
349C22—2964no—
350C22—741no—
351C22—741no—
352C22—741no—
353C22—742no—
354C22—1481no—
355C22—1481no—
356C22—1481no—
357C22—1481no—
358C22—1481no—
359C22—1481no—
360C22—1481no—
361C22—1481no—
362C22#1192455912yes—
363C22C2×D4×D3711yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—741no—
370C4—741no—
371C4—741no—
372C4—1481no—
373C4#41×D3711yescharacteristic
374C4#1192458211yescharacteristic
375C2—22no—
376C2—2961no—
377C2—2961no—
378C2—1482no—
379C2—1481no—
380C2#1455817511yescharacteristic
381C2C2×#1192455911yescharacteristic
382C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#484C2
socleC22×C37C22×D4
hypercenter#484D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #14558231C2semidirect
2. #14558174C2semidirect
3. #14557889C2semidirect
4. #14557860C2semidirect
5. #14557836C2semidirect
6. #14557770C2semidirect
7. #14557764C2semidirect
8. #14557751C2semidirect
9. #14557681C2semidirect
10. #14557669C2semidirect
11. #14557615C2semidirect
12. #14557596C2semidirect
13. #14557528C2semidirect
14. C2×#11924456C2semidirect
15. C37×#484C2semidirect
18. C2×#10596941C22semidirect
22. C2×C8×D37C22semidirect
24. #11924527C22semidirect
30. #11924511C22semidirect
35. #11924498C22semidirect
38. #11924494C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924460C22semidirect
49. #11924456C22semidirect
50. #11924448C22semidirect
51. C8×Dic37C22semidirect
54. #107×C37C22semidirect
55. #107×C37C22semidirect
56. #103×C37C22semidirect
57. #103×C37C22semidirect
195. #484D37semidirect
207. C37#3297semidirect
234. #107C2×D37semidirect
235. #107C2×D37semidirect
239. #103C2×D37semidirect
240. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582312
#145581742
#145578892
#145578602
#145578362
#145577702
#145577642
#145577512
#145576812
#145576692
#145576152
#145575962
#145575282
C2×#119244562
C37×#4842
#329737