Finite Group Databasebeta

← #18006445

Subgroups — #18006445

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#14558236C211yesmaximal, characteristic, complemented
2#14558176C211yesmaximal, characteristic, complemented
3#14557867C211yesmaximal, characteristic, complemented
4#14557855C211yesmaximal, characteristic, complemented
5#14557830C211yesmaximal, characteristic, complemented
6#14557768C211yesmaximal, characteristic, complemented
7#14557765C211yesmaximal, characteristic, complemented
8#14557745C211yesmaximal, characteristic, complemented
9#14557681C211yesmaximal, characteristic, complemented
10#14557668C211yesmaximal, characteristic, complemented
11C4×D296C211yesmaximal, characteristic, complemented
12C8×D148C211yesmaximal, characteristic, complemented
13#14557528C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#488C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596941C2211yescharacteristic, complemented
19C2×D296C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic, complemented
23#11924531—21no—
24#11924521—21no—
25#11924518—21no—
26#11924512C2211yescharacteristic
27#11924511—21no—
28#11924511C2211yescharacteristic
29#11924511C2211yescharacteristic, complemented
30#11924509—21no—
31#11924507C2211yescharacteristic
32#11924506—21no—
33C4×D148C2211yescharacteristic
34C4×D148C2211yescharacteristic
35C4×D148C2211yescharacteristic, complemented
36#11924498—21no—
37#11924494C2211yescharacteristic, complemented
38C4⋊C4×D37C2211yescharacteristic
39C22⋊C4×D37—21no—
40#11924470C2211yescharacteristic, complemented
41#11924469C2211yescharacteristic, complemented
42#11924467C2211yescharacteristic, complemented
43C4⋊#64436C2211yescharacteristic, complemented
44#11924460C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924458C2211yescharacteristic, complemented
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924448C2211yescharacteristic, complemented
52#125×C37C2211yescharacteristic, complemented
53#124×C37C2211yescharacteristic
54#103×C37C2211yescharacteristic, complemented
55#103×C37C2211yescharacteristic, complemented
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64#10596966—22no—
65#10596966—41no—
66D4×D37—22no—
67D4×D37—41no—
68C2×D148—21no—
69C2×D148—21no—
70C2×D148—21no—
71C2×D148D411yescharacteristic
72C2×D148C2311yescharacteristic
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37C2311yescharacteristic
79C2×C4×D37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C2×C8×C37C2311yescharacteristic
82C4⋊C4×C37—21no—
83C4⋊C4×C37—21no—
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C42×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90#10596941—41no—
91#10596939—41no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98#10596938D411yescharacteristic
99#10596938D411yescharacteristic
100C4⋊Dic37D411yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105C4×Dic37—21no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108D296—22no—
109C8×D37—41no—
110C8×D37—41no—
111C23×C37—21no—
112C22×D37—21no—
113C22×D37—21no—
114C22×D37—42no—
115C22×D37—42no—
116C22×D37—81no—
117C22×D37C2×D411yescharacteristic
118C22×D37C2×D411yescharacteristic
119Q8×C37—21no—
120Q8×C37—21no—
121D4×C37—21no—
122D4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2411yescharacteristic
129C22⋊D37—42no—
130C22⋊D37—81no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135D148—22no—
136D148—21no—
137D148—21no—
138D148—21no—
139D148—42no—
140D148—42no—
141D148—81no—
142D148#4112yes—
143C4×D37—21no—
144C4×D37—21no—
145C4×D37—21no—
146C4×D37—21no—
147C4×D37—42no—
148C4×D37—81no—
149C4×D37—81no—
150C4×D37—81no—
151C8×C37—21no—
152C8×C37—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37C22×D411yescharacteristic
159C2×D37—21no—
160C2×D37—21no—
161C2×D37—21no—
162C2×D37—22no—
163C2×D37—21no—
164C2×D37—21no—
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—21no—
174C4×C37—41no—
175C4×C37—41no—
176C4×C37—41no—
177C4×C37C2×#4111yescharacteristic
178C4×C37H(5,𝔽2)11yescharacteristic
179Dic37—21no—
180Dic37—21no—
181Dic37—41no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—81no—
185C2×C37#54611yescharacteristic
186C2×C37C2×#13511yescharacteristic
187C2×C37#57611yescharacteristic
188D37—22no—
189D37—41no—
190D37—42no—
191D37—81no—
192#553—371no—
193#546—371no—
194#488D3711yescharacteristic, complemented
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×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#125C2×D3711yescharacteristic, complemented
217#124C2×D3711yescharacteristic
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—371no—
230C4×D4—741no—
231#117—371no—
232C2×C4⋊C4—371no—
233C2×C22⋊C4—741no—
234#107—371no—
235#107—371no—
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#102C2×D3711yescharacteristic
247#102C2×D3711yescharacteristic
248C22⋊C8—371no—
249C22⋊C8—371no—
250C4×C8C2×D3711yescharacteristic, complemented
251C24—741no—
252#41—742no—
253#41—1481no—
254C2×Q8C22×D3711yescharacteristic
255C2×D4—371no—
256C2×D4—371no—
257C2×D4—371no—
258C2×D4—741no—
259C2×D4—741no—
260C2×D4—741no—
261C2×D4—741no—
262C2×D4—742no—
263C2×D4—741no—
264C2×D4—1481no—
265C2×D4C22×D3711yescharacteristic
266C22×C4—371no—
267C22×C4—371no—
268C22×C4—741no—
269C22×C4—741no—
270C22×C4—741no—
271C22×C4—741no—
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—371no—
286C4⋊C4—741no—
287C4⋊C4—741no—
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—741no—
302C42C22×D3711yescharacteristic
303C23—21no—
304C23—371no—
305C23—371no—
306C23—2961no—
307C23—741no—
308C23—741no—
309C23—1482no—
310C23—1482no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—372no—
316D4—2961no—
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—371no—
329C2×C4—371no—
330C2×C4—2961no—
331C2×C4—2961no—
332C2×C4—2961no—
333C2×C4—741no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—1482no—
340C2×C4D4×D3711yescharacteristic
341C2×C4D4×D3711yescharacteristic
342C2×C4C23×D3711yescharacteristic
343C8—21no—
344C8—21no—
345C8—741no—
346C8—741no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—372no—
351C22—2964no—
352C22—741no—
353C22—741no—
354C22—741no—
355C22—741no—
356C22—741no—
357C22—742no—
358C22—1481no—
359C22—1481no—
360C22—1481no—
361C22—1481no—
362C22—1481no—
363C22C2×D4×D3711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—741no—
370C4—741no—
371C4—1481no—
372C4—1481no—
373C4#41×D3711yescharacteristic
374C4#1192458211yescharacteristic
375C2—81no—
376C2—2961no—
377C2—742no—
378C2—1482no—
379C2—1481no—
380C2#1455817611yescharacteristic
381C2#135×D3711yescharacteristic
382C2#1455833511yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#488C2
socleC22×C37C22×D4
hypercenter#488D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14558236C2semidirect
2. #14558176C2semidirect
3. #14557867C2semidirect
4. #14557855C2semidirect
5. #14557830C2semidirect
6. #14557768C2semidirect
7. #14557765C2semidirect
8. #14557745C2semidirect
9. #14557681C2semidirect
10. #14557668C2semidirect
11. C4×D296C2semidirect
12. C8×D148C2semidirect
13. #14557528C2semidirect
14. #102×D37C2semidirect
15. C37×#488C2semidirect
18. C2×#10596941C22semidirect
22. C2×C8×D37C22semidirect
29. #11924511C22semidirect
35. C4×D148C22semidirect
37. #11924494C22semidirect
40. #11924470C22semidirect
41. #11924469C22semidirect
42. #11924467C22semidirect
43. C4⋊#64436C22semidirect
44. #11924460C22semidirect
46. #11924458C22semidirect
51. #11924448C22semidirect
52. #125×C37C22semidirect
54. #103×C37C22semidirect
55. #103×C37C22semidirect
58. C4×C8×C37C22semidirect
194. #488D37semidirect
207. C37#3297semidirect
216. #125C2×D37semidirect
239. #103C2×D37semidirect
240. #103C2×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
#145582362
#145581762
#145578672
#145578552
#145578302
#145577682
#145577652
#145577452
#145576812
#145576682
C4×D2962
C8×D1482
#145575282
#102×D372
C37×#4882
#329737