Finite Group Databasebeta

← #18004830

Subgroups — #18004830

Order 4736.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558157C211yesmaximal, characteristic
2#14558009C211yesmaximal, characteristic, complemented
3#14557876C211yesmaximal, characteristic, complemented
4#14557860C211yesmaximal, characteristic
5#14557815C211yesmaximal, characteristic, complemented
6#14557756C211yesmaximal, characteristic, complemented
7#14557755C211yesmaximal, characteristic, complemented
8#14557690C211yesmaximal, characteristic, complemented
9#14557673C211yesmaximal, characteristic
10#14557637C211yesmaximal, characteristic, complemented
11#14557632C211yesmaximal, characteristic, complemented
12#14557627C211yesmaximal, characteristic, complemented
13#14557618C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#477C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×Dic148C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×#10596941C2211yescharacteristic
21#11924531—21no—
22#11924525—21no—
23#11924524C2211yescharacteristic
24#11924521—21no—
25#11924516C2211yescharacteristic
26#11924512—21no—
27#11924511C2211yescharacteristic
28Q8×Dic37C2211yescharacteristic
29C4×Dic74—21no—
30C4×Dic74C2211yescharacteristic
31#11924501—21no—
32#11924501C2211yescharacteristic
33#11924501C2211yescharacteristic
34#11924498C2211yescharacteristic
35#11924494—21no—
36#11924494C2211yescharacteristic
37#11924493—21no—
38#11924493C2211yescharacteristic
39#11924467C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C4⋊Q8×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×Q8×C37C2311yescharacteristic
61Q8×D37—22no—
62Q8×D37—22no—
63C2×D148—21no—
64C2×D148C2311yescharacteristic
65C2×C4×D37—21no—
66C2×C4×D37—21no—
67C2×C4×D37C2311yescharacteristic
68C2×Dic74—21no—
69C2×Dic74C2311yescharacteristic
70C2×Dic74C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
75C4⋊C4×C37C2311yescharacteristic
76C4⋊C4×C37C2311yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C42×C37—21no—
79C42×C37C2311yescharacteristic
80#10596942—22no—
81#10596941—22no—
82#10596938—21no—
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938D411yescharacteristic
89#10596938D411yescharacteristic
90C4⋊Dic37—21no—
91C4⋊Dic37—21no—
92C4⋊Dic37C2311yescharacteristic
93#10596936—21no—
94#10596936—21no—
95#10596936—21no—
96#10596936D411yescharacteristic
97#10596936D411yescharacteristic
98C4×Dic37—21no—
99C4×Dic37—21no—
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106Dic148—22no—
107#10596930—22no—
108C22×D37—21no—
109C22×D37C2×D411yescharacteristic
110Q8×C37—21no—
111Q8×C37—81no—
112Q8×C37#4112yes—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2411yescharacteristic
120C2×Dic37—21no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37C2×D411yescharacteristic
124C2×Dic37C2×D411yescharacteristic
125C2×Dic37C2×D411yescharacteristic
126D148—21no—
127D148—21no—
128D148—81no—
129C4×D37—24no—
130C4×D37—21no—
131C4×D37—21no—
132C4×D37—81no—
133Dic74—24no—
134Dic74—21no—
135Dic74—21no—
136Dic74—21no—
137Dic74#4112yes—
138C8×C37—21no—
139C8×C37—21no—
140#64436—21no—
141#64436—21no—
142C22×C37C22×D411yescharacteristic
143C2×D37—21no—
144C2×D37—21no—
145C2×D37—21no—
146C2×D37—41no—
147C2×D37—41no—
148C2×D37—41no—
149C4×C37—22no—
150C4×C37—21no—
151C4×C37—21no—
152C4×C37—41no—
153C4×C37—41no—
154C4×C37—41no—
155C4×C37C2×#4111yescharacteristic
156C4×C37C2×#4111yescharacteristic
157Dic37—21no—
158Dic37—22no—
159Dic37—21no—
160Dic37—21no—
161Dic37—41no—
162Dic37—41no—
163#3121—371nomaximal, Sylow
164C2×C37#52511yescharacteristic
165C2×C37#57711yescharacteristic
166C2×C37#57811yescharacteristic
167D37—41no—
168D37—81no—
169#542—371no—
170#519—371no—
171#485—371no—
172#482—371no—
173#477D3711yescharacteristic, complemented
174#475—371no—
175#464—371no—
176#464—371no—
177#451—371no—
178#448—371no—
179#441—371no—
180#440—371no—
181C4×Q16—371no—
182C4×SD16—371no—
183#433—371no—
184C37#312111yescharacteristic, complemented, Sylow
185C22×Q8—371no—
186C2×Q16—371no—
187C2×Q16—371no—
188C2×SD16—371no—
189C2×SD16—371no—
190C4⋊Q8C2×D3711yescharacteristic
191#126—741no—
192#124—371no—
193#124—741no—
194#123—741no—
195C22⋊Q8—371no—
196C22⋊Q8—741no—
197#121—371no—
198C4×Q8—371no—
199C4×Q8—371no—
200C4×Q8—371no—
201C4×Q8—371no—
202C4×Q8—741no—
203C4×Q8—741no—
204C4×Q8C2×D3711yescharacteristic
205C4×D4—371no—
206#117—371no—
207#117—371no—
208#117—741no—
209#117—741no—
210#107C2×D3711yescharacteristic
211#107C2×D3711yescharacteristic
212#106—371no—
213#106—371no—
214C4⋊C8—371no—
215C4⋊C8C2×D3711yescharacteristic
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#103C2×D3711yescharacteristic
221#103C2×D3711yescharacteristic
222#102—371no—
223#102—371no—
224C22⋊C8—371no—
225C22⋊C8—371no—
226#97—371no—
227C4×C8—371no—
228C2×Q8—21no—
229C2×Q8—371no—
230C2×Q8—371no—
231C2×Q8—741no—
232C2×Q8—742no—
233C2×Q8—742no—
234C2×Q8C22×D3711yescharacteristic
235C2×D4—371no—
236C2×D4—741no—
237C22×C4—371no—
238C22×C4—741no—
239C22×C4—741no—
240Q16—742no—
241Q16—742no—
242SD16—742no—
243SD16—742no—
244C2×C8—371no—
245C2×C8—371no—
246C2×C8C22×D3711yescharacteristic
247C2×C8C22×D3711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—371no—
251C4⋊C4—371no—
252C4⋊C4—371no—
253C4⋊C4—741no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4C22×D3711yescharacteristic
259C4⋊C4C22×D3711yescharacteristic
260C4⋊C4C22×D3711yescharacteristic
261C22⋊C4—371no—
262C22⋊C4—371no—
263C22⋊C4—741no—
264C22⋊C4—741no—
265C22⋊C4—741no—
266C22⋊C4—741no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C42—21no—
270C42—371no—
271C42—741no—
272C42—741no—
273C42—741no—
274C42—741no—
275C42—741no—
276C42C22×D3711yescharacteristic
277C23—371no—
278C23—741no—
279Q8—21no—
280Q8—81no—
281Q8—372no—
282Q8—744no—
283Q8—741no—
284Q8—741no—
285Q8—741no—
286Q8#1059696612yes—
287D4—2961no—
288D4—741no—
289D4—741no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—371no—
295C2×C4—371no—
296C2×C4—371no—
297C2×C4—2961no—
298C2×C4—744no—
299C2×C4—741no—
300C2×C4—741no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4D4×D3711yescharacteristic
305C2×C4D4×D3711yescharacteristic
306C2×C4C23×D3711yescharacteristic
307C8—21no—
308C8—21no—
309C8—741no—
310C8—741no—
311C22—741no—
312C22—741no—
313C22—741no—
314C22—1481no—
315C22—1481no—
316C22—1481no—
317C22C2×D4×D3711yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—741no—
325C4—742no—
326C4—741no—
327C4—741no—
328C4—1481no—
329C4—1481no—
330C4#41×D3711yescharacteristic
331C4C2×#1059696611yescharacteristic
332C2—2961no—
333C2—1481no—
334C2#1455804611yescharacteristic
335C2#1455834311yescharacteristic
336C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#477C2
socleC22×C37C22×D4
prime radical#11924511C22
hypercenter#477D37
hypocenterC37#3121
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #14558009C2semidirect
3. #14557876C2semidirect
5. #14557815C2semidirect
6. #14557756C2semidirect
7. #14557755C2semidirect
8. #14557690C2semidirect
10. #14557637C2semidirect
11. #14557632C2semidirect
12. #14557627C2semidirect
13. #14557618C2semidirect
14. #14557593C2semidirect
15. C37×#477C2semidirect
173. #477D37semidirect
184. C37#3121semidirect

Maximal subgroups

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

subgroupindex
#145581572
#145580092
#145578762
#145578602
#145578152
#145577562
#145577552
#145576902
#145576732
#145576372
#145576322
#145576272
#145576182
#145575932
C37×#4772
#312137