Finite Group Databasebeta

← #18006448

Subgroups — #18006448

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#14558229C211yesmaximal, characteristic, complemented
2#14558179C211yesmaximal, characteristic, complemented
3#14557888C211yesmaximal, characteristic, complemented
4#14557869C211yesmaximal, characteristic, complemented
5#14557858C211yesmaximal, characteristic, complemented
6#14557834C211yesmaximal, characteristic, complemented
7#14557769C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557749C211yesmaximal, characteristic, complemented
10#14557680C211yesmaximal, characteristic, complemented
11#14557669C211yesmaximal, characteristic, complemented
12C4×D296C211yesmaximal, characteristic, complemented
13#14557530C211yesmaximal, characteristic, complemented
14C2×#11924458C211yesmaximal, characteristic, complemented
15C8×D4×C37C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×D148C2211yescharacteristic
18C2×#10596930C2211yescharacteristic, complemented
19C2×D296C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924531—21no—
22#11924528C2211yescharacteristic, complemented
23#11924524C2211yescharacteristic
24#11924521—21no—
25#11924518—21no—
26#11924515C2211yescharacteristic
27#11924510C2211yescharacteristic
28#11924510C2211yescharacteristic
29#11924510C2211yescharacteristic, complemented
30#11924509—21no—
31#11924508—21no—
32#11924504—21no—
33C4×D148C2211yescharacteristic
34C4×D148C2211yescharacteristic, complemented
35#11924496—21no—
36#11924495C2211yescharacteristic, complemented
37C2×C4⋊Dic37C2211yescharacteristic
38C22⋊C4×D37—21no—
39#11924470C2211yescharacteristic, complemented
40#11924470C2211yescharacteristic, complemented
41#11924468C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924461C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic, complemented
52C22×C8×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic, complemented
54C4×D4×C37C2211yescharacteristic
55C4⋊C8×C37C2211yescharacteristic, complemented
56C22⋊C8×C37C2211yescharacteristic
57C22⋊C8×C37C2211yescharacteristic, complemented
58C4×C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×D4×C37D411yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68#10596962—22no—
69#10596962—41no—
70C2×D148—22no—
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×Dic74C2311yescharacteristic
80C2×C8×C37—41no—
81C2×C8×C37—41no—
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C2×C8×C37C2311yescharacteristic
85C2×C8×C37C2311yescharacteristic
86C4⋊C4×C37D411yescharacteristic
87C22⋊C4×C37D411yescharacteristic
88C22⋊C4×C37D411yescharacteristic
89C42×C37C2311yescharacteristic
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98#10596938—21no—
99C4⋊Dic37—21no—
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103C4⋊Dic37C2311yescharacteristic
104#10596936—21no—
105#10596936—21no—
106#10596936—21no—
107C4×Dic37—21no—
108D296—22no—
109D296—41no—
110#10596930—41no—
111C23×C37C2×D411yescharacteristic
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37—21no—
115C22×D37—21no—
116C22×D37—42no—
117C22×D37—42no—
118C22×D37—81no—
119D4×C37—22no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2411yescharacteristic
129C22⋊D37—42no—
130C22⋊D37—42no—
131C22⋊D37—81no—
132C22⋊D37—81no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—81no—
139D148—21no—
140D148—21no—
141D148—21no—
142D148—21no—
143D148—21no—
144D148—42no—
145D148#4112yes—
146C4×D37—42no—
147C4×D37—81no—
148C4×D37—81no—
149Dic74—21no—
150Dic74—21no—
151C8×C37—21no—
152C8×C37—21no—
153C8×C37—21no—
154C8×C37—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37#13512yes—
161C22×C37C22×D411yescharacteristic
162C2×D37—22no—
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—21no—
174C4×C37—21no—
175C4×C37—21no—
176C4×C37C2×#4111yescharacteristic
177C4×C37H(5,𝔽2)11yescharacteristic
178Dic37—41no—
179Dic37—41no—
180Dic37—41no—
181Dic37—41no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—22no—
185C2×C37—41no—
186C2×C37#54611yescharacteristic
187C2×C37C2×#13511yescharacteristic
188C2×C37#57611yescharacteristic
189D37—42no—
190D37—81no—
191D37—81no—
192#553—371no—
193#546—371no—
194#488—371no—
195#484—371no—
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×D4D3711yescharacteristic, complemented
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×C8C2×D3711yescharacteristic
214C22×C8C2×D3711yescharacteristic, complemented
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—371no—
224#121—741no—
225#121—741no—
226#120—741no—
227C4×D4—371no—
228C4×D4—371no—
229C4×D4—741no—
230C4×D4C2×D3711yescharacteristic
231#117—371no—
232C2×C4⋊C4—371no—
233C2×C22⋊C4—741no—
234#107—371no—
235#107—371no—
236#106—371no—
237C4⋊C8C2×D3711yescharacteristic, complemented
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#102—371no—
247#102—371no—
248C22⋊C8C2×D3711yescharacteristic
249C22⋊C8C2×D3711yescharacteristic, complemented
250C4×C8C2×D3711yescharacteristic, complemented
251C24—741no—
252#41—742no—
253#41—1481no—
254C2×Q8—371no—
255C2×D4—371no—
256C2×D4—371no—
257C2×D4—371no—
258C2×D4—742no—
259C2×D4—741no—
260C2×D4—741no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4—741no—
264C2×D4—1481no—
265C2×D4D14811yescharacteristic
266C22×C4—741no—
267C22×C4—741no—
268C22×C4—741no—
269C22×C4—741no—
270C22×C4C22×D3711yescharacteristic
271C22×C4C22×D3711yescharacteristic
272SD16—1481no—
273D8—742no—
274D8—1481no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D3711yescharacteristic
278C2×C8C22×D3711yescharacteristic
279C2×C8C22×D3711yescharacteristic
280C2×C8C22×D3711yescharacteristic
281C4⋊C4—371no—
282C4⋊C4—371no—
283C4⋊C4—371no—
284C4⋊C4—371no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4—741no—
288C4⋊C4—741no—
289C4⋊C4D14811yescharacteristic
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C22⋊C4—741no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4D14811yescharacteristic
300C22⋊C4D14811yescharacteristic
301C42—741no—
302C42C22×D3711yescharacteristic
303C23—2961no—
304C23—741no—
305C23—741no—
306C23—741no—
307C23—1482no—
308C23—1482no—
309C23C2×D14811yescharacteristic
310C23C2×D14811yescharacteristic
311Q8—741no—
312Q8—741no—
313D4—22no—
314D4—372no—
315D4—2961no—
316D4—2961no—
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—2961no—
330C2×C4—2961no—
331C2×C4—2961no—
332C2×C4—741no—
333C2×C4—741no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—1482no—
338C2×C4C2×D14811yescharacteristic
339C2×C4C2×D14811yescharacteristic
340C2×C4C2×D14811yescharacteristic
341C2×C4C2×D14811yescharacteristic
342C2×C4C23×D3711yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—2964no—
353C22—742no—
354C22—1481no—
355C22—1481no—
356C22—1481no—
357C22—1481no—
358C22—1481no—
359C22—1481no—
360C22—1481no—
361C22—1481no—
362C22#1192455812yes—
363C22C22×D14811yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—1481no—
369C4—1481no—
370C4—1481no—
371C4—1481no—
372C4—1481no—
373C4#41×D3711yescharacteristic
374C4#1192458111yescharacteristic
375C2—22no—
376C2—41no—
377C2—2961no—
378C2—2961no—
379C2—1482no—
380C2#1455817811yescharacteristic
381C2C2×#1192455811yescharacteristic
382C2#1455833811yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC8×D4×C37C2
socleC22×C37C22×D4
hypercenterC8×D4D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14558229C2semidirect
2. #14558179C2semidirect
3. #14557888C2semidirect
4. #14557869C2semidirect
5. #14557858C2semidirect
6. #14557834C2semidirect
7. #14557769C2semidirect
8. #14557762C2semidirect
9. #14557749C2semidirect
10. #14557680C2semidirect
11. #14557669C2semidirect
12. C4×D296C2semidirect
13. #14557530C2semidirect
14. C2×#11924458C2semidirect
15. C8×D4×C37C2semidirect
18. C2×#10596930C22semidirect
22. #11924528C22semidirect
29. #11924510C22semidirect
34. C4×D148C22semidirect
36. #11924495C22semidirect
39. #11924470C22semidirect
40. #11924470C22semidirect
41. #11924468C22semidirect
42. #11924461C22semidirect
43. #11924461C22semidirect
44. #11924461C22semidirect
51. #11924458C22semidirect
53. C22×C8×C37C22semidirect
55. C4⋊C8×C37C22semidirect
57. C22⋊C8×C37C22semidirect
58. C4×C8×C37C22semidirect
204. C8×D4D37semidirect
207. C37#3297semidirect
214. C22×C8C2×D37semidirect
237. C4⋊C8C2×D37semidirect
249. C22⋊C8C2×D37semidirect
250. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145581792
#145578882
#145578692
#145578582
#145578342
#145577692
#145577622
#145577492
#145576802
#145576692
C4×D2962
#145575302
C2×#119244582
C8×D4×C372
#329737