Finite Group Databasebeta

← #18006449

Subgroups — #18006449

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#14558227C211yesmaximal, characteristic, complemented
2#14558180C211yesmaximal, characteristic, complemented
3#14557886C211yesmaximal, characteristic, complemented
4#14557870C211yesmaximal, characteristic, complemented
5#14557832C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557763C211yesmaximal, characteristic, complemented
8#14557747C211yesmaximal, characteristic, complemented
9#14557680C211yesmaximal, characteristic, complemented
10#14557668C211yesmaximal, characteristic, complemented
11#14557615C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557527C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#482C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596930C2211yescharacteristic, complemented
19C2×D296C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C22×#64436C2211yescharacteristic, complemented
22C2×C8×D37C2211yescharacteristic
23#11924530—21no—
24#11924527C2211yescharacteristic, complemented
25#11924523C2211yescharacteristic
26#11924518—21no—
27#11924518—21no—
28#11924516C2211yescharacteristic
29#11924511C2211yescharacteristic
30#11924510C2211yescharacteristic, complemented
31#11924509—21no—
32#11924507—21no—
33#11924504—21no—
34C4×D148—21no—
35#11924498C2211yescharacteristic
36#11924498C2211yescharacteristic, complemented
37C4×C22⋊D37C2211yescharacteristic
38C4⋊C4×D37C2211yescharacteristic
39C22⋊C4×D37—21no—
40#11924469C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924459C2211yescharacteristic, complemented
44#11924459C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic, complemented
52#121×C37C2211yescharacteristic
53#117×C37C2211yescharacteristic, complemented
54#107×C37C2211yescharacteristic, complemented
55#106×C37C2211yescharacteristic, complemented
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37D411yescharacteristic
67D4×D37—22no—
68D4×D37—41no—
69#10596962—22no—
70#10596962—41no—
71C2×D148—21no—
72C2×D148C2311yescharacteristic
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37C2311yescharacteristic
79C2×Dic74C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C2×C8×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C42×C37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37D411yescharacteristic
91#10596939—41no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938D411yescharacteristic
98C4⋊Dic37—21no—
99C4⋊Dic37—21no—
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936—21no—
103#10596936D411yescharacteristic
104C4×Dic37C2311yescharacteristic
105C2×#64436—41no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108D296—22no—
109#10596930—41no—
110C8×D37—41no—
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37—21no—
115C22×D37—42no—
116C22×D37—42no—
117C22×D37—81no—
118C22×D37C2×D411yescharacteristic
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—81no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2411yescharacteristic
129C22⋊D37—22no—
130C22⋊D37—42no—
131C22⋊D37—42no—
132C22⋊D37—81no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138D148—21no—
139D148—21no—
140D148—21no—
141D148—42no—
142D148#4112yes—
143C4×D37—21no—
144C4×D37—21no—
145C4×D37—42no—
146C4×D37—81no—
147C4×D37—81no—
148C4×D37—81no—
149Dic74—21no—
150Dic74—21no—
151C8×C37—21no—
152C8×C37—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37C22×D411yescharacteristic
162C2×D37—21no—
163C2×D37—21no—
164C2×D37—22no—
165C2×D37—41no—
166C2×D37—41no—
167C2×D37—41no—
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—84no—
171C2×D37#13512yes—
172C4×C37—21no—
173C4×C37—41no—
174C4×C37—41no—
175C4×C37—41no—
176C4×C37C2×#4111yescharacteristic
177C4×C37H(5,𝔽2)11yescharacteristic
178Dic37—21no—
179Dic37—21no—
180Dic37—21no—
181Dic37—41no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—41no—
185C2×C37—81no—
186C2×C37#54611yescharacteristic
187C2×C37C2×#13511yescharacteristic
188C2×C37#57611yescharacteristic
189D37—22no—
190D37—42no—
191D37—81no—
192#553—371no—
193#546—371no—
194#488—371no—
195#484—371no—
196#482D3711yescharacteristic, complemented
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⋊Q8—371no—
221#121—371no—
222#121—371no—
223#121—741no—
224#121—741no—
225#121C2×D3711yescharacteristic
226#120—741no—
227C4×D4—371no—
228C4×D4—371no—
229C4×D4—371no—
230C4×D4—741no—
231#117C2×D3711yescharacteristic, complemented
232C2×C4⋊C4—371no—
233C2×C22⋊C4—741no—
234#107—371no—
235#107C2×D3711yescharacteristic, complemented
236#106C2×D3711yescharacteristic, complemented
237C4⋊C8—371no—
238#103—371no—
239#103—371no—
240#103—371no—
241#102—371no—
242#102—371no—
243#102—371no—
244#102—371no—
245#102—371no—
246#102C2×D3711yescharacteristic
247#102C2×D3711yescharacteristic
248C22⋊C8—371no—
249C22⋊C8C2×D3711yescharacteristic, complemented
250C4×C8—371no—
251C24—741no—
252#41—742no—
253#41—1481no—
254C2×Q8—371no—
255C2×D4—21no—
256C2×D4—371no—
257C2×D4—371no—
258C2×D4—371no—
259C2×D4—741no—
260C2×D4—741no—
261C2×D4—742no—
262C2×D4—741no—
263C2×D4—741no—
264C2×D4—1481no—
265C2×D4C22×D3711yescharacteristic
266C22×C4—371no—
267C22×C4—741no—
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—371no—
282C4⋊C4—371no—
283C4⋊C4—741no—
284C4⋊C4—741no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4C22×D3711yescharacteristic
288C4⋊C4C22×D3711yescharacteristic
289C4⋊C4C22×D3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—371no—
293C22⋊C4—371no—
294C22⋊C4—741no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4—741no—
300C22⋊C4—741no—
301C42—21no—
302C42—371no—
303C23—21no—
304C23—371no—
305C23—2961no—
306C23—741no—
307C23—741no—
308C23—1482no—
309C23—1482no—
310C23D4×D3711yescharacteristic
311Q8—741no—
312Q8—741no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—372no—
317D4—2961no—
318D4—742no—
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—371no—
331C2×C4—371no—
332C2×C4—371no—
333C2×C4—2961no—
334C2×C4—2961no—
335C2×C4—2961no—
336C2×C4—741no—
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—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—372no—
354C22—2964no—
355C22—741no—
356C22—741no—
357C22—742no—
358C22—1481no—
359C22—1481no—
360C22—1481no—
361C22—1481no—
362C22—1481no—
363C22C2×D4×D3711yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—741no—
369C4—741no—
370C4—741no—
371C4—1481no—
372C4—1481no—
373C4#41×D3711yescharacteristic
374C4#1192458211yescharacteristic
375C2—41no—
376C2—81no—
377C2—2961no—
378C2—742no—
379C2—1482no—
380C2#1455817511yescharacteristic
381C2#135×D3711yescharacteristic
382C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#482C2
socleC22×C37C22×D4
hypercenter#482D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14558227C2semidirect
2. #14558180C2semidirect
3. #14557886C2semidirect
4. #14557870C2semidirect
5. #14557832C2semidirect
6. #14557767C2semidirect
7. #14557763C2semidirect
8. #14557747C2semidirect
9. #14557680C2semidirect
10. #14557668C2semidirect
11. #14557615C2semidirect
12. #14557596C2semidirect
13. #14557527C2semidirect
14. #102×D37C2semidirect
15. C37×#482C2semidirect
18. C2×#10596930C22semidirect
21. C22×#64436C22semidirect
24. #11924527C22semidirect
30. #11924510C22semidirect
36. #11924498C22semidirect
40. #11924469C22semidirect
41. #11924465C22semidirect
42. #11924461C22semidirect
43. #11924459C22semidirect
44. #11924459C22semidirect
49. #11924456C22semidirect
51. C8×Dic37C22semidirect
53. #117×C37C22semidirect
54. #107×C37C22semidirect
55. #106×C37C22semidirect
58. C22⋊C8×C37C22semidirect
196. #482D37semidirect
207. C37#3297semidirect
231. #117C2×D37semidirect
235. #107C2×D37semidirect
236. #106C2×D37semidirect
249. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582272
#145581802
#145578862
#145578702
#145578322
#145577672
#145577632
#145577472
#145576802
#145576682
#145576152
#145575962
#145575272
#102×D372
C37×#4822
#329737