Finite Group Databasebeta

← #18004833

Subgroups — #18004833

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#14558136C211yesmaximal, characteristic, complemented
2#14558008C211yesmaximal, characteristic, complemented
3#14557858C211yesmaximal, characteristic, complemented
4#14557854C211yesmaximal, characteristic, complemented
5#14557835C211yesmaximal, characteristic, complemented
6#14557831C211yesmaximal, characteristic, complemented
7#14557726C211yesmaximal, characteristic, complemented
8#14557726C211yesmaximal, characteristic, complemented
9#14557667C211yesmaximal, characteristic, complemented
10#14557645C211yesmaximal, characteristic, complemented
11#14557642C211yesmaximal, characteristic, complemented
12D8×Dic37C211yesmaximal, characteristic, complemented
13#14557613C211yesmaximal, characteristic, complemented
14#14557591C211yesmaximal, characteristic, complemented
15C37×#447C211yesmaximal, characteristic, complemented
16C2×#10596939C2211yescharacteristic
17C2×#10596939C2211yescharacteristic
18#11924532C2211yescharacteristic, complemented
19#11924527C2211yescharacteristic, complemented
20#11924520—21no—
21#11924518—21no—
22#11924510C2211yescharacteristic
23#11924508—21no—
24#11924507—21no—
25D4×Dic37—21no—
26D4×Dic37—21no—
27D4×Dic37C2211yescharacteristic
28D4×Dic37C2211yescharacteristic
29D4×Dic37C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31D4×Dic37C2211yescharacteristic, complemented
32#11924498C2211yescharacteristic, complemented
33#11924495C2211yescharacteristic
34#11924495C2211yescharacteristic
35C2×C22⋊Dic37—21no—
36C2×C22⋊Dic37—21no—
37#11924470C2211yescharacteristic, complemented
38#11924469C2211yescharacteristic, complemented
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924465C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic, complemented
48#11924457C2211yescharacteristic, complemented
49C22⋊#64436C2211yescharacteristic
50#11924446C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22×D4×C37C2211yescharacteristic
53C2×D8×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C24×C37—21no—
60C2×D4×C37—22no—
61C2×D4×C37—22no—
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C2×D4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C22×Dic37—21no—
72C22×Dic37—21no—
73C22×Dic37—21no—
74C22×Dic37—21no—
75C22×Dic37—21no—
76C2×D148C2311yescharacteristic
77C2×C4×D37—21no—
78D8×C37—22no—
79D8×C37—22no—
80C2×C8×C37C2311yescharacteristic
81C2×C8×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37D411yescharacteristic
91C22⋊Dic37D411yescharacteristic
92#10596939—22no—
93#10596939—22no—
94#10596938—21no—
95#10596938—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37D411yescharacteristic
98C4⋊Dic37D411yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C4×Dic37C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—24no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37—21no—
112C23×C37—81no—
113C23×C37—81no—
114C23×C37C2×D411yescharacteristic
115C22×D37—21no—
116D4×C37—24no—
117D4×C37—21no—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—81no—
122D4×C37#4112yes—
123D4×C37#4112yes—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2411yescharacteristic
129C22⋊D37—81no—
130C22⋊D37—81no—
131C22⋊D37—81no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—81no—
136C2×Dic37—81no—
137C2×Dic37—81no—
138C2×Dic37—81no—
139C2×Dic37—81no—
140C2×Dic37C2×D411yescharacteristic
141C2×Dic37C2×D411yescharacteristic
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144D148—21no—
145D148—21no—
146C4×D37—81no—
147C8×C37—21no—
148C8×C37—21no—
149#64436—21no—
150#64436—21no—
151C22×C37—21no—
152C22×C37—22no—
153C22×C37—22no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—84no—
164C22×C37C22×D411yescharacteristic
165C2×D37—41no—
166C2×D37—41no—
167C2×D37—41no—
168C4×C37—21no—
169C4×C37—41no—
170C4×C37C2×#4111yescharacteristic
171C4×C37C2×#4111yescharacteristic
172Dic37—21no—
173Dic37—21no—
174Dic37—21no—
175Dic37—21no—
176Dic37—41no—
177Dic37—41no—
178Dic37—41no—
179#3122—371nomaximal, Sylow
180C2×C37—41no—
181C2×C37—42no—
182C2×C37—42no—
183C2×C37—81no—
184C2×C37#52511yescharacteristic
185C2×C37#57611yescharacteristic
186C2×C37#57611yescharacteristic
187D37—81no—
188#540—371no—
189#518—371no—
190#482—371no—
191#482—371no—
192#478—371no—
193#478—371no—
194#459—371no—
195#459—371no—
196#447—371no—
197#447D3711yescharacteristic, complemented
198#442—371no—
199#442—371no—
200C4×D8—371no—
201C4×D8—371no—
202#433—371no—
203C37#312211yescharacteristic, complemented, Sylow
204C22×D4C2×D3711yescharacteristic
205C2×D8—371no—
206C2×D8—371no—
207C2×D8C2×D3711yescharacteristic
208C2×D8C2×D3711yescharacteristic
209#127—371no—
210#125—371no—
211#123—741no—
212#123—741no—
213#121—371no—
214#121—741no—
215#121—741no—
216#121C2×D3711yescharacteristic
217C4×D4—371no—
218C4×D4—371no—
219C4×D4—371no—
220C4×D4—371no—
221C4×D4—371no—
222C4×D4—371no—
223C4×D4—741no—
224C4×D4—741no—
225#117—371no—
226#117—371no—
227C2×C22⋊C4—741no—
228C2×C22⋊C4—741no—
229#107—371no—
230#107—371no—
231#106—371no—
232#106—371no—
233C4⋊C8—371no—
234C4⋊C8—371no—
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⋊C8C2×D3711yescharacteristic
245#97—371no—
246C4×C8—371no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—371no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4C22×D3711yescharacteristic
257C2×D4C22×D3711yescharacteristic
258C2×D4C22×D3711yescharacteristic
259C22×C4—741no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4—741no—
264C22×C4—741no—
265C22×C4C22×D3711yescharacteristic
266D8—22no—
267D8—22no—
268D8—742no—
269D8—742no—
270C2×C8—371no—
271C2×C8—371no—
272C2×C8C22×D3711yescharacteristic
273C2×C8C22×D3711yescharacteristic
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—371no—
278C4⋊C4—371no—
279C4⋊C4—741no—
280C4⋊C4—741no—
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—371no—
295C42—741no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—741no—
303C23D4×D3711yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—2961no—
311D4—2961no—
312D4—2961no—
313D4—741no—
314D4—741no—
315D4#1059696412yes—
316D4#1059696412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—371no—
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—2961no—
330C2×C4—741no—
331C2×C4—741no—
332C2×C4—741no—
333C2×C4D4×D3711yescharacteristic
334C2×C4C23×D3711yescharacteristic
335C8—21no—
336C8—21no—
337C8—741no—
338C8—741no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—1481no—
353C22—1481no—
354C22—1481no—
355C22C2×D4×D3711yescharacteristic
356C4—21no—
357C4—41no—
358C4—741no—
359C4—741no—
360C4—741no—
361C4—741no—
362C4—1481no—
363C4—1481no—
364C4—1481no—
365C4C2×#1059696411yescharacteristic
366C4C2×#1059696411yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—2961no—
372C2#1455803911yescharacteristic
373C2#1455833411yescharacteristic
374C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#447C2
socleC22×C37C22×D4
hypercenter#447D37
hypocenterC37#3122
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14558136C2semidirect
2. #14558008C2semidirect
3. #14557858C2semidirect
4. #14557854C2semidirect
5. #14557835C2semidirect
6. #14557831C2semidirect
7. #14557726C2semidirect
8. #14557726C2semidirect
9. #14557667C2semidirect
10. #14557645C2semidirect
11. #14557642C2semidirect
12. D8×Dic37C2semidirect
13. #14557613C2semidirect
14. #14557591C2semidirect
15. C37×#447C2semidirect
18. #11924532C22semidirect
19. #11924527C22semidirect
31. D4×Dic37C22semidirect
32. #11924498C22semidirect
37. #11924470C22semidirect
38. #11924469C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924465C22semidirect
42. #11924465C22semidirect
43. #11924458C22semidirect
44. #11924458C22semidirect
47. #11924457C22semidirect
48. #11924457C22semidirect
50. #11924446C22semidirect
51. C8×Dic37C22semidirect
197. #447D37semidirect
203. C37#3122semidirect

Maximal subgroups

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

subgroupindex
#145581362
#145580082
#145578582
#145578542
#145578352
#145578312
#145577262
#145576672
#145576452
#145576422
D8×Dic372
#145576132
#145575912
C37×#4472
#312237