Finite Group Databasebeta

← #18007199

Subgroups — #18007199

Order 4736.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558236C211yesmaximal, characteristic, complemented
2#14558233C211yesmaximal, characteristic, complemented
3#14557932C211yesmaximal, characteristic, complemented
4#14557859C211yesmaximal, characteristic, complemented
5#14557856C211yesmaximal, characteristic, complemented
6#14557848C211yesmaximal, characteristic, complemented
7#14557845C211yesmaximal, characteristic, complemented
8#14557834C211yesmaximal, characteristic, complemented
9#14557785C211yesmaximal, characteristic, complemented
10#14557785C211yesmaximal, characteristic, complemented
11C4×#10596939C211yesmaximal, characteristic, complemented
12#14557610C211yesmaximal, characteristic, complemented
13#14557574C211yesmaximal, characteristic, complemented
14#14557572C211yesmaximal, characteristic, complemented
15C37×#478C211yesmaximal, characteristic, complemented
16C2×#10596939C2211yescharacteristic
17C2×#10596929C2211yescharacteristic
18C2×#10596929C2211yescharacteristic
19#11924531—21no—
20#11924529—21no—
21#11924528C2211yescharacteristic
22#11924521—21no—
23#11924519—21no—
24#11924511—21no—
25#11924511C2211yescharacteristic
26#11924511C2211yescharacteristic
27#11924509—21no—
28#11924507C2211yescharacteristic
29#11924507C2211yescharacteristic
30C4×D148C2211yescharacteristic
31C4×D148C2211yescharacteristic
32#11924498—21no—
33C4×C22⋊D37—21no—
34#11924494C2211yescharacteristic
35#11924494C2211yescharacteristic
36C4⋊C4×D37C2211yescharacteristic
37C4⋊C4×D37C2211yescharacteristic
38#11924470C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924469C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924467C2211yescharacteristic
44#11924467C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic
51C4×#64436C2211yescharacteristic
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—
63C2×D148—21no—
64C2×D148—21no—
65C2×D148D411yescharacteristic
66C2×D148C2311yescharacteristic
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37C2311yescharacteristic
71C2×C4×D37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C2×C8×C37C2311yescharacteristic
74C4⋊C4×C37—21no—
75C4⋊C4×C37—21no—
76C4⋊C4×C37C2311yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C42×C37C2311yescharacteristic
81C22⋊Dic37—21no—
82C22⋊Dic37—21no—
83#10596939—22no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938D411yescharacteristic
90#10596938D411yescharacteristic
91C4⋊Dic37D411yescharacteristic
92C4⋊Dic37C2311yescharacteristic
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99C4×Dic37—21no—
100C4×Dic37—21no—
101C2×#64436C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103#10596929—22no—
104#10596929—22no—
105C23×C37—21no—
106C22×D37—21no—
107C22×D37C2×D411yescharacteristic
108C22×D37C2×D411yescharacteristic
109D4×C37—21no—
110D4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—81no—
115C2×C4×C37C2×D411yescharacteristic
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2411yescharacteristic
118C22⋊D37—42no—
119C22⋊D37—81no—
120C2×Dic37—21no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37C2×D411yescharacteristic
124C2×Dic37C2×D411yescharacteristic
125D148—21no—
126D148—21no—
127D148—41no—
128D148—42no—
129D148—81no—
130C4×D37—21no—
131C4×D37—21no—
132C4×D37—21no—
133C4×D37—21no—
134C4×D37—81no—
135C4×D37—81no—
136C4×D37—81no—
137C8×C37—21no—
138C8×C37—21no—
139#64436—21no—
140#64436#4112yes—
141C22×C37—41no—
142C22×C37—41no—
143C22×C37—41no—
144C22×C37C22×D411yescharacteristic
145C2×D37—21no—
146C2×D37—21no—
147C2×D37—21no—
148C2×D37—21no—
149C2×D37—21no—
150C2×D37—21no—
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37C2×#4111yescharacteristic
160C4×C372−1+411yescharacteristic
161Dic37—21no—
162Dic37—21no—
163Dic37—41no—
164Dic37—41no—
165Dic37—41no—
166#3355—371nomaximal, Sylow
167C2×C37—81no—
168C2×C37#54711yescharacteristic
169C2×C37#57511yescharacteristic
170C2×C37#57611yescharacteristic
171D37—41no—
172D37—41no—
173D37—81no—
174#553—371no—
175#553—371no—
176#499—371no—
177#482—371no—
178#482—371no—
179#480—371no—
180#480—371no—
181#478—371no—
182#478D3711yescharacteristic, complemented
183#469—371no—
184#469—371no—
185C4×D8—371no—
186#436—371no—
187#428—371no—
188#428—371no—
189C37#335511yescharacteristic, complemented, Sylow
190C2×D8—371no—
191C2×M16—371no—
192C2×M16—371no—
193#126—741no—
194#126—741no—
195#125—371no—
196#125C2×D3711yescharacteristic
197#123—741no—
198#123—741no—
199#121—371no—
200#121—371no—
201#121—371no—
202#121—371no—
203#121—741no—
204#121—741no—
205C4×D4—371no—
206C4×D4—371no—
207C4×D4—741no—
208C4×D4—741no—
209C4×D4C2×D3711yescharacteristic
210#117—371no—
211#117—371no—
212C2×C4⋊C4—371no—
213C2×C4⋊C4—371no—
214#107—371no—
215#107—371no—
216#107—371no—
217#107—371no—
218#107C2×D3711yescharacteristic
219#106—371no—
220#106—371no—
221#106—371no—
222#106C2×D3711yescharacteristic
223C4⋊C8C2×D3711yescharacteristic
224#102—371no—
225#102—371no—
226#102—371no—
227#102—371no—
228#102C2×D3711yescharacteristic
229#102C2×D3711yescharacteristic
230C22⋊C8—371no—
231C22⋊C8—371no—
232C4×C8—371no—
233C2×D4—371no—
234C2×D4—371no—
235C2×D4—741no—
236C2×D4—741no—
237C2×D4—741no—
238C2×D4—741no—
239C2×D4C22×D3711yescharacteristic
240C22×C4—21no—
241C22×C4—371no—
242C22×C4—371no—
243C22×C4—741no—
244C22×C4—741no—
245C22×C4—741no—
246D8—742no—
247M16—742no—
248M16—742no—
249C2×C8—371no—
250C2×C8—371no—
251C2×C8C22×D3711yescharacteristic
252C2×C8C22×D3711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—371no—
256C4⋊C4—371no—
257C4⋊C4—371no—
258C4⋊C4—371no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4—741no—
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C4⋊C4C22×D3711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—371no—
268C22⋊C4—371no—
269C22⋊C4—741no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C42—741no—
277C42—741no—
278C42C22×D3711yescharacteristic
279C23—21no—
280C23—371no—
281C23—371no—
282C23—741no—
283D4—21no—
284D4—21no—
285D4—2961no—
286D4—2961no—
287D4—741no—
288D4—741no—
289D4—1481no—
290D4—1482no—
291D4—1482no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—371no—
297C2×C4—371no—
298C2×C4—2961no—
299C2×C4—2961no—
300C2×C4—2961no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4—741no—
307C2×C4—741no—
308C2×C4D4×D3711yescharacteristic
309C2×C4D4×D3711yescharacteristic
310C2×C4C23×D3711yescharacteristic
311C8—21no—
312C8—21no—
313C8—372no—
314C8—741no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—741no—
319C22—741no—
320C22—741no—
321C22—741no—
322C22—741no—
323C22—741no—
324C22—1481no—
325C22—1481no—
326C22—1481no—
327C22C2×D4×D3711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—741no—
334C4—741no—
335C4—1481no—
336C4—1481no—
337C4—1481no—
338C4#41×D3711yescharacteristic
339C4#1192458411yescharacteristic
340C2—81no—
341C2—2961no—
342C2—1481no—
343C2—1481no—
344C2#1455818511yescharacteristic
345C2#1455833011yescharacteristic
346C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#478C2
socleC22×C37C22×D4
hypercenter#478D37
hypocenterC37#3355
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. #14558233C2semidirect
3. #14557932C2semidirect
4. #14557859C2semidirect
5. #14557856C2semidirect
6. #14557848C2semidirect
7. #14557845C2semidirect
8. #14557834C2semidirect
9. #14557785C2semidirect
10. #14557785C2semidirect
11. C4×#10596939C2semidirect
12. #14557610C2semidirect
13. #14557574C2semidirect
14. #14557572C2semidirect
15. C37×#478C2semidirect
182. #478D37semidirect
189. C37#3355semidirect

Maximal subgroups

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

subgroupindex
#145582362
#145582332
#145579322
#145578592
#145578562
#145578482
#145578452
#145578342
#145577852
C4×#105969392
#145576102
#145575742
#145575722
C37×#4782
#335537