Finite Group Databasebeta

← #18004841

Subgroups — #18004841

Order 4736.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558139C211yesmaximal, characteristic, complemented
2#14558005C211yesmaximal, characteristic, complemented
3#14557860C211yesmaximal, characteristic, complemented
4#14557859C211yesmaximal, characteristic, complemented
5#14557830C211yesmaximal, characteristic, complemented
6#14557729C211yesmaximal, characteristic, complemented
7#14557728C211yesmaximal, characteristic, complemented
8#14557668C211yesmaximal, characteristic, complemented
9#14557668C211yesmaximal, characteristic, complemented
10#14557644C211yesmaximal, characteristic, complemented
11#14557642C211yesmaximal, characteristic, complemented
12#14557615C211yesmaximal, characteristic, complemented
13#14557613C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#478C211yesmaximal, characteristic, complemented
16C2×D4×D37C2211yescharacteristic
17C2×D296C2211yescharacteristic
18C2×D296C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21#11924533C2211yescharacteristic, complemented
22#11924521—21no—
23#11924521—21no—
24#11924511—21no—
25#11924511—21no—
26#11924511C2211yescharacteristic
27#11924511C2211yescharacteristic
28C4×D148C2211yescharacteristic
29D4×Dic37C2211yescharacteristic
30#11924498C2211yescharacteristic
31#11924498C2211yescharacteristic, complemented
32#11924498C2211yescharacteristic, complemented
33C4×C22⋊D37—21no—
34#11924496—21no—
35#11924494C2211yescharacteristic
36#11924493C2211yescharacteristic
37C2×#10596938—21no—
38C22⋊C4×D37—21no—
39#11924469C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41C4⋊#64436C2211yescharacteristic, complemented
42#11924458C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic, complemented
44#11924456C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic, complemented
47#11924456C2211yescharacteristic, complemented
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52#125×C37C2211yescharacteristic, complemented
53C4×D4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic, complemented
55#106×C37C2211yescharacteristic, complemented
56C4⋊C8×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C23×D37—21no—
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C22×Dic37—21no—
64D4×D37—22no—
65D4×D37—22no—
66C2×D148—21no—
67C2×D148—21no—
68C2×D148—21no—
69C2×D148—21no—
70C2×D148C2311yescharacteristic
71C2×D148C2311yescharacteristic
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C4⋊C4×C37—21no—
81C4⋊C4×C37—21no—
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C42×C37C2311yescharacteristic
87C22⋊Dic37—21no—
88#10596939—22no—
89#10596939—22no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938D411yescharacteristic
98#10596938D411yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106D296—22no—
107D296—22no—
108C23×C37—21no—
109C22×D37—21no—
110C22×D37—24no—
111C22×D37—21no—
112C22×D37—21no—
113C22×D37—81no—
114C22×D37—81no—
115C22×D37C2×D411yescharacteristic
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—81no—
128C2×Dic37C2×D411yescharacteristic
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131D148—21no—
132D148—21no—
133D148—21no—
134D148—21no—
135D148—21no—
136D148—81no—
137D148—81no—
138D148—81no—
139D148—81no—
140D148#4112yes—
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—81no—
144C4×D37—81no—
145C4×D37—81no—
146C4×D37—81no—
147C8×C37—21no—
148C8×C37—21no—
149#64436—21no—
150#64436—21no—
151C22×C37—22no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37C22×D411yescharacteristic
155C2×D37—21no—
156C2×D37—22no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C2×D37—41no—
166C2×D37—41no—
167C2×D37—84no—
168C4×C37—21no—
169C4×C37—21no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37—41no—
173C4×C37C2×#4111yescharacteristic
174C4×C37C2×#4111yescharacteristic
175Dic37—21no—
176Dic37—21no—
177Dic37—21no—
178Dic37—41no—
179#3122—371nomaximal, Sylow
180C2×C37—42no—
181C2×C37#52511yescharacteristic
182C2×C37#57611yescharacteristic
183C2×C37#57611yescharacteristic
184D37—41no—
185D37—42no—
186D37—81no—
187D37—81no—
188#540—371no—
189#518—371no—
190#482—371no—
191#482—371no—
192#478—371no—
193#478D3711yescharacteristic, complemented
194#459—371no—
195#459—371no—
196#447—371no—
197#447—371no—
198#442—371no—
199#442—371no—
200C4×D8—371no—
201C4×D8—371no—
202#433—371no—
203C37#312211yescharacteristic, complemented, Sylow
204C22×D4—371no—
205C2×D8—371no—
206C2×D8—371no—
207C2×D8—371no—
208C2×D8—371no—
209#127—371no—
210#125C2×D3711yescharacteristic, complemented
211#123—741no—
212#123—741no—
213#121—371no—
214#121—371no—
215#121—741no—
216#121—741no—
217C4×D4—371no—
218C4×D4—371no—
219C4×D4—371no—
220C4×D4—371no—
221C4×D4—371no—
222C4×D4—741no—
223C4×D4—741no—
224C4×D4C2×D3711yescharacteristic
225#117—371no—
226#117—371no—
227C2×C22⋊C4—741no—
228C2×C22⋊C4—741no—
229#107—371no—
230#107C2×D3711yescharacteristic, complemented
231#106—371no—
232#106C2×D3711yescharacteristic, complemented
233C4⋊C8—371no—
234C4⋊C8C2×D3711yescharacteristic, complemented
235#102—371no—
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241#102C2×D3711yescharacteristic
242#102C2×D3711yescharacteristic
243C22⋊C8—371no—
244C22⋊C8—371no—
245#97—371no—
246C4×C8—371no—
247C24—741no—
248C2×D4—371no—
249C2×D4—371no—
250C2×D4—371no—
251C2×D4—741no—
252C2×D4—741no—
253C2×D4—741no—
254C2×D4—742no—
255C2×D4—742no—
256C2×D4—741no—
257C2×D4—741no—
258C2×D4C22×D3711yescharacteristic
259C22×C4—21no—
260C22×C4—371no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4—741no—
264C22×C4—741no—
265C22×C4—741no—
266D8—742no—
267D8—742no—
268D8—742no—
269D8—742no—
270C2×C8—371no—
271C2×C8—371no—
272C2×C8C22×D3711yescharacteristic
273C2×C8C22×D3711yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—371no—
277C4⋊C4—371no—
278C4⋊C4—371no—
279C4⋊C4C22×D3711yescharacteristic
280C4⋊C4C22×D3711yescharacteristic
281C4⋊C4C22×D3711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—371no—
284C22⋊C4—371no—
285C22⋊C4—741no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C42—371no—
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—21no—
297C23—371no—
298C23—2961no—
299C23—2961no—
300C23—744no—
301C23—741no—
302C23—741no—
303C23—741no—
304D4—21no—
305D4—372no—
306D4—2961no—
307D4—2961no—
308D4—2961no—
309D4—2961no—
310D4—744no—
311D4—741no—
312D4—741no—
313D4—741no—
314D4—741no—
315D4—741no—
316D4#1059696612yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—371no—
322C2×C4—371no—
323C2×C4—371no—
324C2×C4—2961no—
325C2×C4—2961no—
326C2×C4—2961no—
327C2×C4—2961no—
328C2×C4—2961no—
329C2×C4—741no—
330C2×C4—741no—
331C2×C4—741no—
332C2×C4D4×D3711yescharacteristic
333C2×C4D4×D3711yescharacteristic
334C2×C4C23×D3711yescharacteristic
335C8—21no—
336C8—21no—
337C8—741no—
338C8—741no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—2964no—
343C22—741no—
344C22—742no—
345C22—741no—
346C22—741no—
347C22—1481no—
348C22—1481no—
349C22—1481no—
350C22—1481no—
351C22—1481no—
352C22—1481no—
353C22—1481no—
354C22—1481no—
355C22C2×D4×D3711yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—741no—
362C4—741no—
363C4—741no—
364C4—1481no—
365C4#41×D3711yescharacteristic
366C4C2×#1059696611yescharacteristic
367C2—42no—
368C2—2961no—
369C2—2961no—
370C2—1481no—
371C2—1482no—
372C2#1455804611yescharacteristic
373C2#1455833511yescharacteristic
374C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#478C2
socleC22×C37C22×D4
hypercenter#478D37
hypocenterC37#3122
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14558139C2semidirect
2. #14558005C2semidirect
3. #14557860C2semidirect
4. #14557859C2semidirect
5. #14557830C2semidirect
6. #14557729C2semidirect
7. #14557728C2semidirect
8. #14557668C2semidirect
9. #14557668C2semidirect
10. #14557644C2semidirect
11. #14557642C2semidirect
12. #14557615C2semidirect
13. #14557613C2semidirect
14. #14557593C2semidirect
15. C37×#478C2semidirect
21. #11924533C22semidirect
31. #11924498C22semidirect
32. #11924498C22semidirect
39. #11924469C22semidirect
40. #11924467C22semidirect
41. C4⋊#64436C22semidirect
42. #11924458C22semidirect
43. #11924458C22semidirect
46. #11924456C22semidirect
47. #11924456C22semidirect
50. #11924446C22semidirect
51. C8×Dic37C22semidirect
52. #125×C37C22semidirect
54. #107×C37C22semidirect
55. #106×C37C22semidirect
56. C4⋊C8×C37C22semidirect
193. #478D37semidirect
203. C37#3122semidirect
210. #125C2×D37semidirect
230. #107C2×D37semidirect
232. #106C2×D37semidirect
234. C4⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581392
#145580052
#145578602
#145578592
#145578302
#145577292
#145577282
#145576682
#145576442
#145576422
#145576152
#145576132
#145575932
C37×#4782
#312237