Finite Group Databasebeta

← #18007685

Subgroups — #18007685

Order 4736.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558268C211yesmaximal, characteristic, complemented
2#14558266C211yesmaximal, characteristic, complemented
3#14557922C211yesmaximal, characteristic, complemented
4#14557919C211yesmaximal, characteristic, complemented
5#14557914C211yesmaximal, characteristic, complemented
6#14557758C211yesmaximal, characteristic, complemented
7#14557755C211yesmaximal, characteristic, complemented
8#14557751C211yesmaximal, characteristic, complemented
9#14557747C211yesmaximal, characteristic, complemented
10#14557728C211yesmaximal, characteristic, complemented
11#14557727C211yesmaximal, characteristic, complemented
12#14557661C211yesmaximal, characteristic, complemented
13#14557632C211yesmaximal, characteristic, complemented
14#14557615C211yesmaximal, characteristic, complemented
15C37×#440C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×D296C2211yescharacteristic
21C2×D296C2211yescharacteristic
22C2×#10596939C2211yescharacteristic
23C2×#10596939C2211yescharacteristic
24#11924533C2211yescharacteristic
25#11924532C2211yescharacteristic
26#11924525C2211yescharacteristic
27#11924525C2211yescharacteristic
28#11924524—21no—
29#11924524C2211yescharacteristic
30#11924523C2211yescharacteristic
31#11924522—21no—
32#11924521—21no—
33#11924521—21no—
34#11924519—21no—
35#11924518—21no—
36C4×Dic74C2211yescharacteristic
37#11924501C2211yescharacteristic
38C4×D148—21no—
39#11924498C2211yescharacteristic
40#11924498C2211yescharacteristic
41#11924498C2211yescharacteristic
42C4×C22⋊D37—21no—
43C4⋊#64436C2211yescharacteristic
44#11924465C2211yescharacteristic
45#11924465C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×D148—21no—
65C2×D148—21no—
66C2×D148C2311yescharacteristic
67C2×D148C2311yescharacteristic
68C2×D148C2311yescharacteristic
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×Dic74D411yescharacteristic
73C2×Dic74C2311yescharacteristic
74SD16×C37—22no—
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C22⋊C4×C37—21no—
81C42×C37—21no—
82C42×C37C2311yescharacteristic
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85#10596942—41no—
86#10596941—41no—
87#10596939—41no—
88#10596939—41no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98C4⋊Dic37D411yescharacteristic
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C4×Dic37C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107D296—22no—
108D296—41no—
109#10596930—22no—
110#10596930—41no—
111C23×C37—21no—
112C22×D37—21no—
113C22×D37—21no—
114C22×D37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117D4×C37—21no—
118D4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—81no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2411yescharacteristic
126C22⋊D37—42no—
127C22⋊D37—81no—
128C2×Dic37—21no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133D148—21no—
134D148—21no—
135D148—21no—
136D148—21no—
137D148—21no—
138D148—21no—
139D148—42no—
140D148—81no—
141C4×D37—81no—
142C4×D37—81no—
143C4×D37—81no—
144Dic74—21no—
145Dic74—21no—
146Dic74—41no—
147C8×C37—21no—
148C8×C37#4112yes—
149#64436—21no—
150#64436—21no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37C22×D411yescharacteristic
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37C2×#4111yescharacteristic
170C4×C37H(5,𝔽2)11yescharacteristic
171Dic37—21no—
172Dic37—21no—
173Dic37—21no—
174Dic37—21no—
175Dic37—41no—
176#3403—371nomaximal, Sylow
177C2×C37—81no—
178C2×C37#55011yescharacteristic
179C2×C37#57511yescharacteristic
180C2×C37#57611yescharacteristic
181D37—81no—
182D37—81no—
183D37—81no—
184#559—371no—
185#559—371no—
186#496—371no—
187#496—371no—
188#495—371no—
189#464—371no—
190#464—371no—
191#463—371no—
192#463—371no—
193#459—371no—
194#459—371no—
195#446—371no—
196#440—371no—
197#440D3711yescharacteristic, complemented
198C4×D8—371no—
199C37#340311yescharacteristic, complemented, Sylow
200C2×Q16—371no—
201C2×SD16—371no—
202C2×SD16—371no—
203C2×SD16—371no—
204C2×SD16C2×D3711yescharacteristic
205C2×D8—371no—
206C2×D8—371no—
207C2×D8—371no—
208C2×D8—371no—
209#127—371no—
210#127—371no—
211#124—371no—
212#124—371no—
213#124—371no—
214#124—371no—
215#124—741no—
216#124—741no—
217#123—741no—
218#123—741no—
219#123—741no—
220#123—741no—
221C4×Q8—371no—
222C4×Q8—371no—
223C4×Q8C2×D3711yescharacteristic
224C4×D4—371no—
225C4×D4—371no—
226C4×D4—371no—
227C4×D4—741no—
228C4×D4—741no—
229C4×D4C2×D3711yescharacteristic
230#107C2×D3711yescharacteristic
231C4⋊C8—371no—
232C4⋊C8—371no—
233C4⋊C8—371no—
234#103—371no—
235#103C2×D3711yescharacteristic
236#102—371no—
237#102—371no—
238#102—371no—
239#102C2×D3711yescharacteristic
240#97—371no—
241#97C2×D3711yescharacteristic
242C4×C8—371no—
243C2×Q8—371no—
244C2×Q8—371no—
245C2×Q8C22×D3711yescharacteristic
246C2×D4—371no—
247C2×D4—371no—
248C2×D4—371no—
249C2×D4—741no—
250C2×D4—741no—
251C2×D4—741no—
252C2×D4—741no—
253C2×D4C22×D3711yescharacteristic
254C22×C4—21no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4—741no—
258Q16—1481no—
259SD16—22no—
260SD16—742no—
261SD16—1481no—
262SD16—1481no—
263D8—742no—
264D8—1481no—
265D8—1481no—
266D8—1481no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8C22×D3711yescharacteristic
270C2×C8C22×D3711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—371no—
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—741no—
276C4⋊C4C22×D3711yescharacteristic
277C4⋊C4C22×D3711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C42—21no—
291C42—371no—
292C42—371no—
293C42—741no—
294C42C22×D3711yescharacteristic
295C23—21no—
296C23—741no—
297C23—741no—
298C23—741no—
299Q8—21no—
300Q8—21no—
301Q8—741no—
302Q8—741no—
303Q8—1481no—
304D4—21no—
305D4—21no—
306D4—2961no—
307D4—2961no—
308D4—741no—
309D4—741no—
310D4—741no—
311D4—741no—
312D4—741no—
313D4—741no—
314D4—1482no—
315D4—1482no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—371no—
321C2×C4—371no—
322C2×C4—371no—
323C2×C4—371no—
324C2×C4—2961no—
325C2×C4—2961no—
326C2×C4—2961no—
327C2×C4—741no—
328C2×C4D4×D3711yescharacteristic
329C2×C4D4×D3711yescharacteristic
330C2×C4C23×D3711yescharacteristic
331C8—21no—
332C8—741no—
333C8—741no—
334C8#1059696212yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22—1481no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22C2×D4×D3711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—741no—
354C4—741no—
355C4—741no—
356C4—741no—
357C4—1481no—
358C4C2×#1059696211yescharacteristic
359C4#1192458211yescharacteristic
360C2—81no—
361C2—2961no—
362C2—2961no—
363C2—2961no—
364C2#1455820411yescharacteristic
365C2#1455833211yescharacteristic
366C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#440C2
socleC22×C37C22×D4
hypercenter#440D37
hypocenterC37#3403
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14558268C2semidirect
2. #14558266C2semidirect
3. #14557922C2semidirect
4. #14557919C2semidirect
5. #14557914C2semidirect
6. #14557758C2semidirect
7. #14557755C2semidirect
8. #14557751C2semidirect
9. #14557747C2semidirect
10. #14557728C2semidirect
11. #14557727C2semidirect
12. #14557661C2semidirect
13. #14557632C2semidirect
14. #14557615C2semidirect
15. C37×#440C2semidirect
197. #440D37semidirect
199. C37#3403semidirect

Maximal subgroups

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

subgroupindex
#145582682
#145582662
#145579222
#145579192
#145579142
#145577582
#145577552
#145577512
#145577472
#145577282
#145577272
#145576612
#145576322
#145576152
C37×#4402
#340337