Finite Group Databasebeta

← #18006065

Subgroups — #18006065

Order 4736.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558157C211yesmaximal, characteristic, complemented
2#14558155C211yesmaximal, characteristic, complemented
3#14557822C211yesmaximal, characteristic, complemented
4#14557820C211yesmaximal, characteristic, complemented
5#14557817C211yesmaximal, characteristic, complemented
6#14557790C211yesmaximal, characteristic, complemented
7#14557787C211yesmaximal, characteristic
8#14557765C211yesmaximal, characteristic, complemented
9#14557763C211yesmaximal, characteristic, complemented
10#14557758C211yesmaximal, characteristic, complemented
11#14557755C211yesmaximal, characteristic, complemented
12#14557751C211yesmaximal, characteristic, complemented
13#14557749C211yesmaximal, characteristic, complemented
14#14557558C211yesmaximal, characteristic, complemented
15C37×#475C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×#10596929C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924535C2211yescharacteristic
23#11924531—21no—
24#11924530—21no—
25#11924525—21no—
26#11924525C2211yescharacteristic
27#11924524—21no—
28#11924524C2211yescharacteristic
29#11924521—21no—
30#11924521—21no—
31#11924516C2211yescharacteristic
32#11924514—21no—
33#11924512—21no—
34#11924512C2211yescharacteristic
35#11924511C2211yescharacteristic
36#11924511C2211yescharacteristic
37#11924501C2211yescharacteristic
38C4×D148C2211yescharacteristic
39#11924498C2211yescharacteristic
40#11924493C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924467C2211yescharacteristic
43C4⋊#64436C2211yescharacteristic
44#11924465C2211yescharacteristic
45#11924465C2211yescharacteristic
46#11924461C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924456C2211yescharacteristic
51#11924456C2211yescharacteristic
52C4⋊Q8×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54#106×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×D148—21no—
62C2×D148—21no—
63C2×D148C2311yescharacteristic
64C2×D148C2311yescharacteristic
65C2×C4×D37—21no—
66C2×C4×D37—21no—
67C2×C4×D37C2311yescharacteristic
68C2×Dic74—21no—
69C2×Dic74C2311yescharacteristic
70C2×C8×C37C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C4⋊C4×C37—21no—
73C4⋊C4×C37—21no—
74C4⋊C4×C37C2311yescharacteristic
75C4⋊C4×C37C2311yescharacteristic
76C4⋊C4×C37C2311yescharacteristic
77C42×C37—21no—
78C42×C37C2311yescharacteristic
79#10596942—41no—
80#10596941—41no—
81#10596938—21no—
82#10596938—21no—
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938D411yescharacteristic
92#10596938D411yescharacteristic
93C4⋊Dic37—21no—
94C4⋊Dic37C2311yescharacteristic
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936D411yescharacteristic
99#10596936D411yescharacteristic
100C4×Dic37—21no—
101C4×Dic37C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104D296—41no—
105#10596930—41no—
106#10596929—41no—
107C8×D37—41no—
108C22×D37—21no—
109C22×D37—21no—
110C22×D37C2×D411yescharacteristic
111Q8×C37—21no—
112Q8×C37—21no—
113Q8×C37—81no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2411yescharacteristic
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37C2×D411yescharacteristic
124C2×Dic37C2×D411yescharacteristic
125C2×Dic37C2×D411yescharacteristic
126D148—21no—
127D148—21no—
128D148—21no—
129D148—21no—
130D148—81no—
131D148—81no—
132C4×D37—21no—
133C4×D37—21no—
134C4×D37—81no—
135C4×D37—81no—
136Dic74—21no—
137Dic74—21no—
138Dic74—81no—
139C8×C37—21no—
140C8×C37—21no—
141#64436—21no—
142#64436—21no—
143C22×C37C22×D411yescharacteristic
144C2×D37—21no—
145C2×D37—21no—
146C2×D37—21no—
147C2×D37—41no—
148C2×D37—41no—
149C2×D37—41no—
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—41no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37H(5,𝔽2)11yescharacteristic
160C4×C372−1+411yescharacteristic
161Dic37—21no—
162Dic37—21no—
163Dic37—21no—
164Dic37—41no—
165Dic37—41no—
166#3263—371nomaximal, Sylow
167C2×C37#53711yescharacteristic
168C2×C37#57711yescharacteristic
169C2×C37#57711yescharacteristic
170D37—41no—
171D37—81no—
172D37—81no—
173#542—371no—
174#542—371no—
175#476—371no—
176#476—371no—
177#475—371no—
178#475D3711yescharacteristic, complemented
179#470—371no—
180#469—371no—
181#465—371no—
182#465—371no—
183#464—371no—
184#464—371no—
185#463—371no—
186#463—371no—
187#424—371no—
188C37#326311yescharacteristic, complemented, Sylow
189C2×Q16—371no—
190C2×SD16—371no—
191C2×SD16—371no—
192C2×D8—371no—
193C2×M16—371no—
194C22×C8—371no—
195C4⋊Q8—371no—
196C4⋊Q8C2×D3711yescharacteristic
197#126—741no—
198#126—741no—
199#124—371no—
200#124—371no—
201#124—741no—
202#124—741no—
203#123—741no—
204#123—741no—
205C22⋊Q8—371no—
206C22⋊Q8—371no—
207C22⋊Q8—741no—
208C22⋊Q8—741no—
209#121—371no—
210#121—371no—
211C4×Q8—371no—
212C4×Q8C2×D3711yescharacteristic
213C4×D4—371no—
214C4×D4—371no—
215#117—371no—
216#106—371no—
217#106—371no—
218#106C2×D3711yescharacteristic
219#106C2×D3711yescharacteristic
220C4⋊C8—371no—
221C4⋊C8—371no—
222C4⋊C8—371no—
223C4⋊C8C2×D3711yescharacteristic
224#103—371no—
225#103—371no—
226#103C2×D3711yescharacteristic
227#103C2×D3711yescharacteristic
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232C2×Q8—21no—
233C2×Q8—371no—
234C2×Q8—741no—
235C2×Q8C22×D3711yescharacteristic
236C2×D4—371no—
237C2×D4—371no—
238C2×D4—741no—
239C2×D4—741no—
240C22×C4—371no—
241C22×C4—741no—
242C22×C4—741no—
243Q16—1481no—
244SD16—1481no—
245SD16—1481no—
246D8—1481no—
247M16—1481no—
248C2×C8—371no—
249C2×C8—371no—
250C2×C8—1481no—
251C2×C8C22×D3711yescharacteristic
252C2×C8C22×D3711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—371no—
256C4⋊C4—371no—
257C4⋊C4—371no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4C22×D3711yescharacteristic
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—371no—
266C22⋊C4—371no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C22⋊C4—741no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C42—21no—
278C42—371no—
279C42—741no—
280C42C22×D3711yescharacteristic
281C23—371no—
282C23—741no—
283C23—741no—
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—2961no—
288Q8—741no—
289Q8—741no—
290D4—2961no—
291D4—2961no—
292D4—741no—
293D4—741no—
294D4—741no—
295D4—741no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—371no—
301C2×C4—371no—
302C2×C4—371no—
303C2×C4—2961no—
304C2×C4—2961no—
305C2×C4—741no—
306C2×C4—741no—
307C2×C4—741no—
308C2×C4—741no—
309C2×C4D4×D3711yescharacteristic
310C2×C4D4×D3711yescharacteristic
311C2×C4C23×D3711yescharacteristic
312C8—21no—
313C8—21no—
314C8—741no—
315C8—741no—
316C22—741no—
317C22—741no—
318C22—741no—
319C22—1481no—
320C22—1481no—
321C22—1481no—
322C22—1481no—
323C22—1481no—
324C22—1481no—
325C22C2×D4×D3711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—741no—
333C4—741no—
334C4—741no—
335C4—1481no—
336C4—1481no—
337C4#1192458211yescharacteristic
338C4#1192458411yescharacteristic
339C2—2961no—
340C2—2961no—
341C2—1481no—
342C2#1455811311yescharacteristic
343C2#1455833911yescharacteristic
344C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#475C2
socleC22×C37C22×D4
prime radical#14557787C2
hypercenter#475D37
hypocenterC37#3263
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #14558157C2semidirect
2. #14558155C2semidirect
3. #14557822C2semidirect
4. #14557820C2semidirect
5. #14557817C2semidirect
6. #14557790C2semidirect
8. #14557765C2semidirect
9. #14557763C2semidirect
10. #14557758C2semidirect
11. #14557755C2semidirect
12. #14557751C2semidirect
13. #14557749C2semidirect
14. #14557558C2semidirect
15. C37×#475C2semidirect
178. #475D37semidirect
188. C37#3263semidirect

Maximal subgroups

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

subgroupindex
#145581572
#145581552
#145578222
#145578202
#145578172
#145577902
#145577872
#145577652
#145577632
#145577582
#145577552
#145577512
#145577492
#145575582
C37×#4752
#326337