Finite Group Databasebeta

← #18004880

Subgroups — #18004880

Order 4736.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558157C211yesmaximal, characteristic, complemented
2#14558015C211yesmaximal, characteristic, complemented
3#14557865C211yesmaximal, characteristic, complemented
4#14557853C211yesmaximal, characteristic, complemented
5#14557820C211yesmaximal, characteristic, complemented
6#14557755C211yesmaximal, characteristic, complemented
7#14557749C211yesmaximal, characteristic, complemented
8#14557698C211yesmaximal, characteristic, complemented
9#14557681C211yesmaximal, characteristic
10#14557644C211yesmaximal, characteristic, complemented
11#14557637C211yesmaximal, characteristic, complemented
12#14557620C211yesmaximal, characteristic, complemented
13#14557618C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#475C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924531—21no—
22#11924525—21no—
23#11924524C2211yescharacteristic
24#11924521—21no—
25#11924516C2211yescharacteristic
26#11924512—21no—
27#11924511C2211yescharacteristic
28Q8×Dic37C2211yescharacteristic
29#11924501C2211yescharacteristic
30C4×D148—21no—
31C4×D148C2211yescharacteristic
32#11924498—21no—
33#11924498C2211yescharacteristic
34#11924498C2211yescharacteristic
35#11924493—21no—
36#11924493C2211yescharacteristic
37C4⋊C4×D37—21no—
38C4⋊C4×D37C2211yescharacteristic
39#11924467C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
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
61#10596966—22no—
62#10596966—22no—
63C2×D148—21no—
64C2×D148—21no—
65C2×D148C2311yescharacteristic
66C2×D148C2311yescharacteristic
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37C2311yescharacteristic
73C2×Dic74C2311yescharacteristic
74C2×C8×C37C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C42×C37—21no—
82C42×C37C2311yescharacteristic
83#10596942—22no—
84#10596941—22no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938D411yescharacteristic
93#10596938D411yescharacteristic
94C4⋊Dic37—21no—
95C4⋊Dic37—21no—
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936D411yescharacteristic
100#10596936D411yescharacteristic
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106D296—22no—
107#10596930—22no—
108C22×D37—21no—
109C22×D37—21no—
110C22×D37C2×D411yescharacteristic
111Q8×C37—21no—
112Q8×C37—81no—
113Q8×C37#4112yes—
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—24no—
127D148—21no—
128D148—21no—
129D148—21no—
130D148—81no—
131D148#4112yes—
132C4×D37—24no—
133C4×D37—21no—
134C4×D37—21no—
135C4×D37—81no—
136C4×D37—81no—
137C4×D37—81no—
138C4×D37—81no—
139Dic74—21no—
140Dic74—21no—
141C8×C37—21no—
142C8×C37—21no—
143#64436—21no—
144#64436—21no—
145C22×C37C22×D411yescharacteristic
146C2×D37—21no—
147C2×D37—22no—
148C2×D37—21no—
149C2×D37—21no—
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C2×D37—41no—
155C4×C37—22no—
156C4×C37—21no—
157C4×C37—21no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37C2×#4111yescharacteristic
162C4×C37C2×#4111yescharacteristic
163Dic37—21no—
164Dic37—21no—
165Dic37—21no—
166Dic37—41no—
167Dic37—41no—
168#3125—371nomaximal, Sylow
169C2×C37#52511yescharacteristic
170C2×C37#57711yescharacteristic
171C2×C37#57711yescharacteristic
172D37—41no—
173D37—42no—
174D37—81no—
175#542—371no—
176#520—371no—
177#483—371no—
178#481—371no—
179#476—371no—
180#475D3711yescharacteristic, complemented
181#464—371no—
182#463—371no—
183#452—371no—
184#449—371no—
185#442—371no—
186#441—371no—
187C4×SD16—371no—
188C4×SD16—371no—
189#433—371no—
190C37#312511yescharacteristic, complemented, Sylow
191C2×#41—371no—
192C2×Q16—371no—
193C2×SD16—371no—
194C2×SD16—371no—
195C2×D8—371no—
196C4⋊Q8C2×D3711yescharacteristic
197#126—741no—
198#124—371no—
199#124—741no—
200#123—741no—
201C22⋊Q8—371no—
202C22⋊Q8—741no—
203#121—371no—
204C4×Q8—371no—
205C4×Q8—371no—
206C4×Q8C2×D3711yescharacteristic
207C4×D4—371no—
208C4×D4—371no—
209C4×D4—371no—
210C4×D4—741no—
211C4×D4—741no—
212#117—371no—
213#117—741no—
214C2×C4⋊C4—371no—
215C2×C4⋊C4—741no—
216#106—371no—
217#106—371no—
218#106C2×D3711yescharacteristic
219#106C2×D3711yescharacteristic
220C4⋊C8—371no—
221C4⋊C8C2×D3711yescharacteristic
222#103—371no—
223#103—371no—
224#103C2×D3711yescharacteristic
225#103C2×D3711yescharacteristic
226#102—371no—
227#102—371no—
228#102—371no—
229#102—371no—
230C22⋊C8—371no—
231C22⋊C8—371no—
232#97—371no—
233C4×C8—371no—
234#41—742no—
235#41—742no—
236C2×Q8—21no—
237C2×Q8—371no—
238C2×Q8C22×D3711yescharacteristic
239C2×D4—371no—
240C2×D4—371no—
241C2×D4—741no—
242C2×D4—741no—
243C22×C4—371no—
244C22×C4—741no—
245C22×C4—741no—
246C22×C4—741no—
247C22×C4—741no—
248C22×C4—741no—
249Q16—742no—
250SD16—742no—
251SD16—742no—
252D8—742no—
253C2×C8—371no—
254C2×C8—371no—
255C2×C8C22×D3711yescharacteristic
256C2×C8C22×D3711yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4C22×D3711yescharacteristic
267C4⋊C4C22×D3711yescharacteristic
268C4⋊C4C22×D3711yescharacteristic
269C22⋊C4—371no—
270C22⋊C4—371no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C42—21no—
279C42—371no—
280C42—741no—
281C42—741no—
282C42C22×D3711yescharacteristic
283C23—371no—
284C23—741no—
285C23—741no—
286Q8—21no—
287Q8—81no—
288Q8—741no—
289Q8—741no—
290Q8#1059696612yes—
291D4—372no—
292D4—2961no—
293D4—744no—
294D4—741no—
295D4—741no—
296D4—741no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—371no—
302C2×C4—371no—
303C2×C4—371no—
304C2×C4—2961no—
305C2×C4—2961no—
306C2×C4—2961no—
307C2×C4—2961no—
308C2×C4—744no—
309C2×C4—741no—
310C2×C4—741no—
311C2×C4—741no—
312C2×C4—741no—
313C2×C4D4×D3711yescharacteristic
314C2×C4D4×D3711yescharacteristic
315C2×C4C23×D3711yescharacteristic
316C8—21no—
317C8—21no—
318C8—741no—
319C8—741no—
320C22—742no—
321C22—741no—
322C22—741no—
323C22—741no—
324C22—1481no—
325C22—1481no—
326C22—1481no—
327C22—1481no—
328C22—1481no—
329C22C2×D4×D3711yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—741no—
337C4—741no—
338C4—741no—
339C4—1481no—
340C4—1481no—
341C4#41×D3711yescharacteristic
342C4C2×#1059696611yescharacteristic
343C2—2961no—
344C2—1481no—
345C2—1482no—
346C2#1455804611yescharacteristic
347C2#1455833911yescharacteristic
348C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#475C2
socleC22×C37C22×D4
prime radical#14557681C2
hypercenter#475D37
hypocenterC37#3125
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. #14558015C2semidirect
3. #14557865C2semidirect
4. #14557853C2semidirect
5. #14557820C2semidirect
6. #14557755C2semidirect
7. #14557749C2semidirect
8. #14557698C2semidirect
10. #14557644C2semidirect
11. #14557637C2semidirect
12. #14557620C2semidirect
13. #14557618C2semidirect
14. #14557593C2semidirect
15. C37×#475C2semidirect
180. #475D37semidirect
190. C37#3125semidirect

Maximal subgroups

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

subgroupindex
#145581572
#145580152
#145578652
#145578532
#145578202
#145577552
#145577492
#145576982
#145576812
#145576442
#145576372
#145576202
#145576182
#145575932
C37×#4752
#312537