Finite Group Databasebeta

← #18006569

Subgroups — #18006569

Order 4736.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558236C211yesmaximal, characteristic, complemented
2#14558187C211yesmaximal, characteristic, complemented
3#14557903C211yesmaximal, characteristic, complemented
4#14557876C211yesmaximal, characteristic, complemented
5#14557865C211yesmaximal, characteristic, complemented
6#14557780C211yesmaximal, characteristic, complemented
7#14557763C211yesmaximal, characteristic, complemented
8#14557739C211yesmaximal, characteristic, complemented
9#14557679C211yesmaximal, characteristic, complemented
10#14557679C211yesmaximal, characteristic, complemented
11#14557643C211yesmaximal, characteristic, complemented
12#14557603C211yesmaximal, characteristic, complemented
13#14557531C211yesmaximal, characteristic, complemented
14#14557526C211yesmaximal, characteristic, complemented
15C37×#478C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C2×#10596929C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic
23#11924536C2211yescharacteristic
24#11924531—21no—
25#11924521—21no—
26#11924520—21no—
27#11924520—21no—
28#11924516C2211yescharacteristic
29#11924516C2211yescharacteristic
30#11924511—21no—
31#11924511C2211yescharacteristic
32#11924511C2211yescharacteristic
33#11924510—21no—
34C4×D148C2211yescharacteristic
35C4×D148C2211yescharacteristic
36#11924498—21no—
37#11924494C2211yescharacteristic
38C2×C4⋊Dic37—21no—
39C4⋊C4×D37C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924461C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924447C2211yescharacteristic
52#125×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×D4×C37C2311yescharacteristic
60C22×C4×C37—21no—
61C2×C22⋊D37—21no—
62C2×C22⋊D37—21no—
63C22×Dic37—21no—
64C22×Dic37—21no—
65#10596964—22no—
66#10596964—22no—
67#10596964—41no—
68#10596964—41no—
69C2×D148—21no—
70C2×D148—21no—
71C2×D148D411yescharacteristic
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37C2311yescharacteristic
76C2×C4×D37C2311yescharacteristic
77C2×Dic74C2311yescharacteristic
78C2×Dic74C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37—21no—
82C4⋊C4×C37—21no—
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C22⋊C4×C37—21no—
87C42×C37C2311yescharacteristic
88#10596939—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938D411yescharacteristic
96#10596938D411yescharacteristic
97C4⋊Dic37—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37—21no—
100C4⋊Dic37—21no—
101C4⋊Dic37D411yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104C4×Dic37—21no—
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107#10596930—41no—
108#10596930—41no—
109#10596929—41no—
110C8×D37—41no—
111C23×C37—21no—
112C22×D37—21no—
113C22×D37C2×D411yescharacteristic
114C22×D37C2×D411yescharacteristic
115D4×C37—21no—
116D4×C37#4112yes—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—42no—
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2411yescharacteristic
124C22⋊D37—42no—
125C22⋊D37—42no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—42no—
130C2×Dic37—42no—
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133D148—21no—
134D148—21no—
135D148—41no—
136D148—42no—
137D148—81no—
138C4×D37—21no—
139C4×D37—21no—
140C4×D37—21no—
141C4×D37—21no—
142C4×D37—81no—
143C4×D37—81no—
144Dic74—21no—
145Dic74—21no—
146Dic74—21no—
147Dic74—21no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—22no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—21no—
160C2×D37—21no—
161C2×D37—21no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37C2×#4111yescharacteristic
171C4×C37H(5,𝔽2)11yescharacteristic
172Dic37—21no—
173Dic37—21no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3307—371nomaximal, Sylow
178C2×C37—42no—
179C2×C37#54611yescharacteristic
180C2×C37#57511yescharacteristic
181C2×C37#57711yescharacteristic
182D37—41no—
183D37—41no—
184D37—81no—
185#553—371no—
186#547—371no—
187#491—371no—
188#485—371no—
189#483—371no—
190#478D3711yescharacteristic, complemented
191#468—371no—
192#465—371no—
193#461—371no—
194#449—371no—
195#449—371no—
196#442—371no—
197#435—371no—
198#417—371no—
199#416—371no—
200C37#330711yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C2×#41—371no—
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C2×M16—371no—
207C22×C8—371no—
208C4⋊Q8—371no—
209#126—741no—
210#125C2×D3711yescharacteristic
211#123—741no—
212#123—741no—
213#123—741no—
214C22⋊Q8—371no—
215C22⋊Q8—371no—
216#121—371no—
217#121—371no—
218#121—741no—
219#121—741no—
220C4×D4—371no—
221C4×D4—371no—
222C4×D4—741no—
223C4×D4C2×D3711yescharacteristic
224#117—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—741no—
227#107C2×D3711yescharacteristic
228#106—371no—
229#106C2×D3711yescharacteristic
230C4⋊C8C2×D3711yescharacteristic
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#103—371no—
237#102—371no—
238#102—371no—
239#102C2×D3711yescharacteristic
240#102C2×D3711yescharacteristic
241C22⋊C8—371no—
242C22⋊C8—371no—
243#97—371no—
244#41—742no—
245#41—742no—
246#41—1481no—
247#41—1481no—
248C2×Q8—371no—
249C2×Q8—371no—
250C2×D4—371no—
251C2×D4—371no—
252C2×D4—741no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4C22×D3711yescharacteristic
257C22×C4—21no—
258C22×C4—371no—
259C22×C4—371no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4—741no—
264SD16—1481no—
265SD16—1481no—
266D8—742no—
267M16—1481no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—1481no—
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4C22×D3711yescharacteristic
283C4⋊C4C22×D3711yescharacteristic
284C4⋊C4C22×D3711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—371no—
287C22⋊C4—371no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—21no—
297C23—371no—
298C23—371no—
299C23—741no—
300Q8—741no—
301Q8—741no—
302Q8—741no—
303Q8—741no—
304D4—21no—
305D4—2961no—
306D4—741no—
307D4—741no—
308D4—1481no—
309D4—1482no—
310D4—1482no—
311D4—1482no—
312D4#1059696612yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—371no—
318C2×C4—371no—
319C2×C4—2961no—
320C2×C4—2961no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—1482no—
329C2×C4—1482no—
330C2×C4D4×D3711yescharacteristic
331C2×C4D4×D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—741no—
336C8—741no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—741no—
341C22—741no—
342C22—741no—
343C22—741no—
344C22—741no—
345C22—741no—
346C22—1481no—
347C22—1481no—
348C22—1481no—
349C22C2×D4×D3711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—741no—
356C4—741no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4C2×#1059696611yescharacteristic
361C4#1192458211yescharacteristic
362C2—42no—
363C2—2961no—
364C2—1481no—
365C2—1481no—
366C2#1455817411yescharacteristic
367C2#1455832911yescharacteristic
368C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#478C2
socleC22×C37C22×D4
hypercenter#478D37
hypocenterC37#3307
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. #14558236C2semidirect
2. #14558187C2semidirect
3. #14557903C2semidirect
4. #14557876C2semidirect
5. #14557865C2semidirect
6. #14557780C2semidirect
7. #14557763C2semidirect
8. #14557739C2semidirect
9. #14557679C2semidirect
10. #14557679C2semidirect
11. #14557643C2semidirect
12. #14557603C2semidirect
13. #14557531C2semidirect
14. #14557526C2semidirect
15. C37×#478C2semidirect
190. #478D37semidirect
200. C37#3307semidirect

Maximal subgroups

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

subgroupindex
#145582362
#145581872
#145579032
#145578762
#145578652
#145577802
#145577632
#145577392
#145576792
#145576432
#145576032
#145575312
#145575262
C37×#4782
#330737