Finite Group Databasebeta

← #18007339

Subgroups — #18007339

Order 4736.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558263C211yesmaximal, characteristic, complemented
2#14558255C211yesmaximal, characteristic
3#14557895C211yesmaximal, characteristic
4#14557894C211yesmaximal, characteristic
5#14557882C211yesmaximal, characteristic, complemented
6#14557822C211yesmaximal, characteristic
7#14557817C211yesmaximal, characteristic, complemented
8#14557758C211yesmaximal, characteristic
9#14557756C211yesmaximal, characteristic
10#14557742C211yesmaximal, characteristic, complemented
11#14557662C211yesmaximal, characteristic, complemented
12#14557639C211yesmaximal, characteristic, complemented
13#14557638C211yesmaximal, characteristic, complemented
14#14557620C211yesmaximal, characteristic
15C37×#475C211yesmaximal, characteristic, complemented
16C2×Dic148C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19#11924535—21no—
20#11924535C2211yescharacteristic
21#11924535C2211yescharacteristic
22#11924534—21no—
23#11924534—21no—
24#11924534C2211yescharacteristic
25#11924531—21no—
26#11924530—21no—
27#11924525C2211yescharacteristic
28#11924524C2211yescharacteristic
29#11924514—21no—
30C4×Dic74C2211yescharacteristic
31C4×Dic74C2211yescharacteristic
32#11924501—21no—
33#11924501C2211yescharacteristic
34#11924501C2211yescharacteristic
35#11924501C2211yescharacteristic
36#11924498C2211yescharacteristic
37#11924493—21no—
38#11924467C2211yescharacteristic
39#11924465C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924461C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924447C2211yescharacteristic
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
61C2×D148C2311yescharacteristic
62C2×C4×D37—21no—
63C2×Dic74—21no—
64C2×Dic74—21no—
65C2×Dic74D411yescharacteristic
66C2×Dic74C2311yescharacteristic
67C2×Dic74C2311yescharacteristic
68C2×C8×C37C2311yescharacteristic
69C2×C8×C37C2311yescharacteristic
70C4⋊C4×C37—21no—
71C4⋊C4×C37—21no—
72C4⋊C4×C37C2311yescharacteristic
73C4⋊C4×C37C2311yescharacteristic
74C4⋊C4×C37C2311yescharacteristic
75C42×C37—21no—
76C42×C37C2311yescharacteristic
77#10596942—22no—
78#10596938—21no—
79#10596938—21no—
80#10596938—21no—
81#10596938—21no—
82#10596938—21no—
83C4⋊Dic37D411yescharacteristic
84C4⋊Dic37C2311yescharacteristic
85#10596936—21no—
86#10596936—21no—
87#10596936—21no—
88#10596936—21no—
89#10596936—21no—
90#10596936—21no—
91#10596936—21no—
92#10596936—21no—
93#10596936D411yescharacteristic
94#10596936D411yescharacteristic
95C4×Dic37—21no—
96C4×Dic37—21no—
97C4×Dic37—21no—
98C4×Dic37—21no—
99C4×Dic37C2311yescharacteristic
100C4×Dic37C2311yescharacteristic
101C2×#64436C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103Dic148—22no—
104#10596930—22no—
105C22×D37—21no—
106Q8×C37—21no—
107Q8×C37—21no—
108Q8×C37—81no—
109C2×C4×C37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37C2×D411yescharacteristic
114C2×C4×C37C2×D411yescharacteristic
115C2×C4×C37C2411yescharacteristic
116C2×Dic37—21no—
117C2×Dic37—21no—
118C2×Dic37—21no—
119C2×Dic37C2×D411yescharacteristic
120C2×Dic37C2×D411yescharacteristic
121C2×Dic37C2×D411yescharacteristic
122C2×Dic37C2×D411yescharacteristic
123D148—21no—
124D148—21no—
125C4×D37—42no—
126Dic74—21no—
127Dic74—22no—
128Dic74—21no—
129Dic74—21no—
130Dic74—81no—
131Dic74—81no—
132Dic74#4112yes—
133C8×C37—21no—
134C8×C37—21no—
135#64436—21no—
136#64436—21no—
137C22×C37C22×D411yescharacteristic
138C2×D37—41no—
139C2×D37—41no—
140C2×D37—41no—
141C4×C37—21no—
142C4×C37—21no—
143C4×C37—41no—
144C4×C37—41no—
145C4×C37—41no—
146C4×C37—41no—
147C4×C37C2×#4111yescharacteristic
148C4×C372−1+411yescharacteristic
149Dic37—22no—
150Dic37—21no—
151Dic37—21no—
152Dic37—21no—
153Dic37—41no—
154Dic37—41no—
155Dic37#13712yes—
156#3369—371nomaximal, Sylow
157C2×C37#54811yescharacteristic
158C2×C37C2×#13711yescharacteristic
159C2×C37#57711yescharacteristic
160D37—81no—
161Q82—371no—
162#556—371no—
163#489—371no—
164#489—371no—
165#487—371no—
166#476—371no—
167#475—371no—
168#475D3711yescharacteristic, complemented
169#464—371no—
170#464—371no—
171#462—371no—
172#446—371no—
173#441—371no—
174#441—371no—
175C4×SD16—371no—
176C37#336911yescharacteristic, complemented, Sylow
177C2×Q16—371no—
178C2×Q16—371no—
179C2×SD16—371no—
180C4⋊Q8—371no—
181C4⋊Q8—371no—
182C4⋊Q8—371no—
183C4⋊Q8—741no—
184C4⋊Q8—741no—
185C4⋊Q8—741no—
186C4⋊Q8C2×D3711yescharacteristic
187#126—741no—
188#126—741no—
189#124—371no—
190#124—371no—
191C22⋊Q8—741no—
192C4×Q8—371no—
193C4×Q8—371no—
194C4×Q8—371no—
195C4×Q8—371no—
196C4×Q8—371no—
197C4×Q8—741no—
198C4×Q8C2×D3711yescharacteristic
199C4×D4—371no—
200#117—741no—
201#106—371no—
202#106C2×D3711yescharacteristic
203#106C2×D3711yescharacteristic
204C4⋊C8—371no—
205C4⋊C8—371no—
206C4⋊C8C2×D3711yescharacteristic
207#103—371no—
208#103—371no—
209#103—371no—
210#103—371no—
211#103—371no—
212#103C2×D3711yescharacteristic
213#103C2×D3711yescharacteristic
214#102—371no—
215#102—371no—
216#102—371no—
217#97—371no—
218#97—371no—
219C4×C8—371no—
220C2×Q8—21no—
221C2×Q8—371no—
222C2×Q8—371no—
223C2×Q8—371no—
224C2×Q8—741no—
225C2×Q8—741no—
226C2×Q8C22×D3711yescharacteristic
227C2×D4—371no—
228C22×C4—741no—
229Q16—742no—
230Q16—742no—
231SD16—742no—
232C2×C8—371no—
233C2×C8—371no—
234C2×C8C22×D3711yescharacteristic
235C2×C8C22×D3711yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—371no—
239C4⋊C4—371no—
240C4⋊C4—371no—
241C4⋊C4—371no—
242C4⋊C4—741no—
243C4⋊C4—741no—
244C4⋊C4—741no—
245C4⋊C4—741no—
246C4⋊C4—741no—
247C4⋊C4—741no—
248C4⋊C4—741no—
249C4⋊C4—741no—
250C4⋊C4C22×D3711yescharacteristic
251C4⋊C4C22×D3711yescharacteristic
252C4⋊C4C22×D3711yescharacteristic
253C22⋊C4—741no—
254C22⋊C4—741no—
255C22⋊C4—741no—
256C22⋊C4—741no—
257C22⋊C4—741no—
258C42—21no—
259C42—371no—
260C42—371no—
261C42—741no—
262C42—741no—
263C42—741no—
264C42—741no—
265C42C22×D3711yescharacteristic
266C23—741no—
267Q8—21no—
268Q8—21no—
269Q8—81no—
270Q8—372no—
271Q8—2961no—
272Q8—2961no—
273Q8—742no—
274Q8—741no—
275Q8—741no—
276Q8—741no—
277D4—741no—
278D4—741no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—371no—
284C2×C4—371no—
285C2×C4—371no—
286C2×C4—371no—
287C2×C4—741no—
288C2×C4—741no—
289C2×C4—741no—
290C2×C4—1482no—
291C2×C4D4×D3711yescharacteristic
292C2×C4D4×D3711yescharacteristic
293C2×C4C23×D3711yescharacteristic
294C8—21no—
295C8—21no—
296C8—741no—
297C8—741no—
298C22—1481no—
299C22—1481no—
300C22—1481no—
301C22C2×D4×D3711yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—372no—
309C4—741no—
310C4—741no—
311C4—741no—
312C4—742no—
313C4—1481no—
314C4—1481no—
315C4#41×D3711yescharacteristic
316C4#1192458411yescharacteristic
317C2—2961no—
318C2#1455819311yescharacteristic
319C2#137×D3711yescharacteristic
320C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#475C2
socleC22×C37C22×D4
prime radicalC2×D148C23
hypercenter#475D37
hypocenterC37#3369
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. #14558263C2semidirect
5. #14557882C2semidirect
7. #14557817C2semidirect
10. #14557742C2semidirect
11. #14557662C2semidirect
12. #14557639C2semidirect
13. #14557638C2semidirect
15. C37×#475C2semidirect
168. #475D37semidirect
176. C37#3369semidirect

Maximal subgroups

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

subgroupindex
#145582632
#145582552
#145578952
#145578942
#145578822
#145578222
#145578172
#145577582
#145577562
#145577422
#145576622
#145576392
#145576382
#145576202
C37×#4752
#336937