Finite Group Databasebeta

← #18004878

Subgroups — #18004878

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#14558012C211yesmaximal, characteristic, complemented
3#14557865C211yesmaximal, characteristic, complemented
4#14557853C211yesmaximal, characteristic, complemented
5#14557815C211yesmaximal, characteristic, complemented
6#14557756C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557696C211yesmaximal, characteristic, complemented
9#14557679C211yesmaximal, characteristic
10#14557642C211yesmaximal, characteristic, complemented
11#14557639C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13#14557620C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#476C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×Dic148C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21#11924531—21no—
22#11924525—21no—
23#11924524C2211yescharacteristic
24#11924521—21no—
25#11924516C2211yescharacteristic
26#11924512—21no—
27#11924511C2211yescharacteristic
28C4×Dic74C2211yescharacteristic
29#11924501C2211yescharacteristic
30#11924501C2211yescharacteristic
31D4×Dic37C2211yescharacteristic
32#11924498C2211yescharacteristic
33C4×C22⋊D37—21no—
34#11924496—21no—
35#11924493C2211yescharacteristic
36#11924492—21no—
37C2×#10596936—21no—
38C4⋊C4×D37C2211yescharacteristic
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×D4×C37C2211yescharacteristic
54#106×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C22×Dic37—21no—
64C22×Dic37—21no—
65#10596964—22no—
66#10596964—22no—
67C2×D148—21no—
68C2×D148C2311yescharacteristic
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37C2311yescharacteristic
72C2×Dic74C2311yescharacteristic
73C2×Dic74C2311yescharacteristic
74C2×C8×C37C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C4⋊C4×C37—21no—
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C22⋊C4×C37—21no—
81C42×C37C2311yescharacteristic
82C22⋊Dic37—21no—
83#10596940—22no—
84#10596939—22no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938D411yescharacteristic
91#10596938D411yescharacteristic
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936D411yescharacteristic
99#10596936D411yescharacteristic
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106Dic148—22no—
107#10596930—22no—
108C23×C37—21no—
109C22×D37—21no—
110C22×D37C2×D411yescharacteristic
111Q8×C37—81no—
112D4×C37—21no—
113D4×C37#4112yes—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—81no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2411yescharacteristic
121C22⋊D37—24no—
122C2×Dic37—24no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37—81no—
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129C2×Dic37C2×D411yescharacteristic
130D148—21no—
131D148—21no—
132D148—81no—
133C4×D37—21no—
134C4×D37—21no—
135C4×D37—81no—
136C4×D37—81no—
137Dic74—21no—
138Dic74—21no—
139Dic74—21no—
140Dic74#4112yes—
141C8×C37—21no—
142C8×C37—21no—
143#64436—21no—
144#64436—21no—
145C22×C37—22no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37C22×D411yescharacteristic
149C2×D37—21no—
150C2×D37—21no—
151C2×D37—21no—
152C2×D37—41no—
153C2×D37—41no—
154C2×D37—41no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37C2×#4111yescharacteristic
161C4×C37C2×#4111yescharacteristic
162Dic37—22no—
163Dic37—21no—
164Dic37—21no—
165Dic37—21no—
166Dic37—41no—
167Dic37—41no—
168#3125—371nomaximal, Sylow
169C2×C37—42no—
170C2×C37#52511yescharacteristic
171C2×C37#57711yescharacteristic
172C2×C37#57711yescharacteristic
173D37—41no—
174D37—81no—
175#542—371no—
176#520—371no—
177#483—371no—
178#481—371no—
179#476D3711yescharacteristic, complemented
180#475—371no—
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×Q8—371no—
207C4×D4—371no—
208C4×D4—371no—
209C4×D4—741no—
210C4×D4—741no—
211C4×D4C2×D3711yescharacteristic
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#103—371no—
225#103—371no—
226#102—371no—
227#102—371no—
228#102C2×D3711yescharacteristic
229#102C2×D3711yescharacteristic
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×Q8—371no—
239C2×D4—371no—
240C2×D4—741no—
241C2×D4—741no—
242C2×D4C22×D3711yescharacteristic
243C22×C4—21no—
244C22×C4—371no—
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—371no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—741no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4C22×D3711yescharacteristic
267C4⋊C4C22×D3711yescharacteristic
268C4⋊C4C22×D3711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—371no—
271C22⋊C4—371no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C42—371no—
279C42—741no—
280C42—741no—
281C42—741no—
282C42C22×D3711yescharacteristic
283C23—21no—
284C23—371no—
285C23—741no—
286Q8—81no—
287Q8—372no—
288Q8—741no—
289Q8—741no—
290Q8—741no—
291D4—21no—
292D4—2961no—
293D4—744no—
294D4—741no—
295D4—741no—
296D4#1059696612yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—371no—
302C2×C4—371no—
303C2×C4—371no—
304C2×C4—2961no—
305C2×C4—2961no—
306C2×C4—2961no—
307C2×C4—744no—
308C2×C4—741no—
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—22no—
321C22—41no—
322C22—41no—
323C22—741no—
324C22—741no—
325C22—741no—
326C22—1481no—
327C22—1481no—
328C22—1481no—
329C22C2×D4×D3711yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—741no—
336C4—742no—
337C4—741no—
338C4—741no—
339C4—1481no—
340C4—1481no—
341C4#41×D3711yescharacteristic
342C4C2×#1059696611yescharacteristic
343C2—42no—
344C2—2961no—
345C2—1481no—
346C2#1455804611yescharacteristic
347C2#1455833911yescharacteristic
348C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#476C2
socleC22×C37C22×D4
prime radical#14557679C2
hypercenter#476D37
hypocenterC37#3125
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #14558157C2semidirect
2. #14558012C2semidirect
3. #14557865C2semidirect
4. #14557853C2semidirect
5. #14557815C2semidirect
6. #14557756C2semidirect
7. #14557748C2semidirect
8. #14557696C2semidirect
10. #14557642C2semidirect
11. #14557639C2semidirect
12. #14557624C2semidirect
13. #14557620C2semidirect
14. #14557593C2semidirect
15. C37×#476C2semidirect
179. #476D37semidirect
190. C37#3125semidirect

Maximal subgroups

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

subgroupindex
#145581572
#145580122
#145578652
#145578532
#145578152
#145577562
#145577482
#145576962
#145576792
#145576422
#145576392
#145576242
#145576202
#145575932
C37×#4762
#312537