Finite Group Databasebeta

← #18007681

Subgroups — #18007681

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#14558269C211yesmaximal, characteristic, complemented
2#14558265C211yesmaximal, characteristic, complemented
3#14557921C211yesmaximal, characteristic, complemented
4#14557914C211yesmaximal, characteristic, complemented
5#14557753C211yesmaximal, characteristic, complemented
6#14557752C211yesmaximal, characteristic, complemented
7#14557750C211yesmaximal, characteristic, complemented
8#14557746C211yesmaximal, characteristic, complemented
9#14557726C211yesmaximal, characteristic, complemented
10#14557725C211yesmaximal, characteristic, complemented
11#14557661C211yesmaximal, characteristic, complemented
12#14557635C211yesmaximal, characteristic, complemented
13#14557634C211yesmaximal, characteristic, complemented
14D8×Dic37C211yesmaximal, characteristic, complemented
15C37×#496C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21#11924532C2211yescharacteristic
22#11924525C2211yescharacteristic
23#11924523—21no—
24#11924523C2211yescharacteristic
25#11924523C2211yescharacteristic
26#11924522—21no—
27#11924520—21no—
28#11924518—21no—
29#11924517—21no—
30#11924517—21no—
31Q8×Dic37C2211yescharacteristic
32C4×Dic74C2211yescharacteristic
33C4×Dic74C2211yescharacteristic
34C4×D148C2211yescharacteristic
35D4×Dic37—21no—
36D4×Dic37C2211yescharacteristic
37D4×Dic37C2211yescharacteristic
38D4×Dic37C2211yescharacteristic
39#11924496—21no—
40#11924470C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924465C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic
56#127×C37C2211yescharacteristic
57#124×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37—21no—
61C2×D4×C37—21no—
62C2×D4×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C22×Dic37—21no—
69C22×Dic37—21no—
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×Dic74D411yescharacteristic
73C2×Dic74C2311yescharacteristic
74SD16×C37—22no—
75SD16×C37—41no—
76D8×C37—22no—
77D8×C37—41no—
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C42×C37C2311yescharacteristic
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90#10596942—41no—
91#10596940—41no—
92#10596939—41no—
93#10596939—41no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97C4⋊Dic37—21no—
98C4⋊Dic37D411yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936D411yescharacteristic
103#10596936D411yescharacteristic
104C4×Dic37—21no—
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110#10596930—22no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C22×D37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117D4×C37—21no—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—42no—
124D4×C37—81no—
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×Dic37—21no—
134C2×Dic37—81no—
135C2×Dic37—81no—
136C2×Dic37—81no—
137C2×Dic37C2×D411yescharacteristic
138C2×Dic37C2×D411yescharacteristic
139C2×Dic37C2×D411yescharacteristic
140C2×Dic37C2×D411yescharacteristic
141D148—21no—
142D148—21no—
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×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37C22×D411yescharacteristic
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37C2×#4111yescharacteristic
168C4×C37H(5,𝔽2)11yescharacteristic
169Dic37—21no—
170Dic37—21no—
171Dic37—21no—
172Dic37—21no—
173Dic37—41no—
174Dic37—41no—
175Dic37—41no—
176#3403—371nomaximal, Sylow
177C2×C37—81no—
178C2×C37—81no—
179C2×C37—81no—
180C2×C37#55011yescharacteristic
181C2×C37#57511yescharacteristic
182C2×C37#57611yescharacteristic
183D37—81no—
184#559—371no—
185#559—371no—
186#496—371no—
187#496D3711yescharacteristic, complemented
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#440—371no—
198C4×D8—371no—
199C37#340311yescharacteristic, complemented, Sylow
200C2×Q16—371no—
201C2×SD16—371no—
202C2×SD16—371no—
203C2×SD16C2×D3711yescharacteristic
204C2×SD16C2×D3711yescharacteristic
205C2×D8—371no—
206C2×D8—371no—
207C2×D8C2×D3711yescharacteristic
208C2×D8C2×D3711yescharacteristic
209#127—371no—
210#127C2×D3711yescharacteristic
211#124—371no—
212#124—371no—
213#124—371no—
214#124—741no—
215#124—741no—
216#124C2×D3711yescharacteristic
217#123—741no—
218#123—741no—
219#123—741no—
220#123—741no—
221C4×Q8—371no—
222C4×Q8—371no—
223C4×Q8—371no—
224C4×D4—371no—
225C4×D4—371no—
226C4×D4—371no—
227C4×D4—371no—
228C4×D4—741no—
229C4×D4—741no—
230#107—371no—
231C4⋊C8—371no—
232C4⋊C8—371no—
233C4⋊C8—371no—
234#103—371no—
235#103—371no—
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#97—371no—
241#97C2×D3711yescharacteristic
242C4×C8—371no—
243C2×Q8—371no—
244C2×Q8—371no—
245C2×Q8C22×D3711yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—371no—
249C2×D4—741no—
250C2×D4—741no—
251C2×D4C22×D3711yescharacteristic
252C2×D4C22×D3711yescharacteristic
253C2×D4C22×D3711yescharacteristic
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4—741no—
258Q16—1481no—
259SD16—22no—
260SD16—41no—
261SD16—742no—
262SD16—1481no—
263D8—22no—
264D8—41no—
265D8—1481no—
266D8—1481no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8C22×D3711yescharacteristic
270C2×C8C22×D3711yescharacteristic
271C4⋊C4—371no—
272C4⋊C4—371no—
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—741no—
277C4⋊C4—741no—
278C22⋊C4—21no—
279C22⋊C4—21no—
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—371no—
291C42—371no—
292C42—741no—
293C42—741no—
294C42C22×D3711yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—741no—
299Q8—21no—
300Q8—21no—
301Q8—741no—
302Q8—741no—
303Q8—1481no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—2961no—
313D4—741no—
314D4—741no—
315D4—1482no—
316C2×C4—21no—
317C2×C4—371no—
318C2×C4—371no—
319C2×C4—371no—
320C2×C4—371no—
321C2×C4—2961no—
322C2×C4—2961no—
323C2×C4—2961no—
324C2×C4—2961no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4D4×D3711yescharacteristic
329C2×C4D4×D3711yescharacteristic
330C2×C4C23×D3711yescharacteristic
331C8—21no—
332C8—741no—
333C8—741no—
334C8#1059696412yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22C2×D4×D3711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—741no—
352C4—741no—
353C4—741no—
354C4—741no—
355C4—1481no—
356C4—1481no—
357C4—1481no—
358C4C2×#1059696411yescharacteristic
359C4#1192458111yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—2961no—
364C2#1455820311yescharacteristic
365C2#1455832911yescharacteristic
366C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#496C2
socleC22×C37C22×D4
hypercenter#496D37
hypocenterC37#3403
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14558269C2semidirect
2. #14558265C2semidirect
3. #14557921C2semidirect
4. #14557914C2semidirect
5. #14557753C2semidirect
6. #14557752C2semidirect
7. #14557750C2semidirect
8. #14557746C2semidirect
9. #14557726C2semidirect
10. #14557725C2semidirect
11. #14557661C2semidirect
12. #14557635C2semidirect
13. #14557634C2semidirect
14. D8×Dic37C2semidirect
15. C37×#496C2semidirect
187. #496D37semidirect
199. C37#3403semidirect

Maximal subgroups

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

subgroupindex
#145582692
#145582652
#145579212
#145579142
#145577532
#145577522
#145577502
#145577462
#145577262
#145577252
#145576612
#145576352
#145576342
D8×Dic372
C37×#4962
#340337