Finite Group Databasebeta

← #18007287

Subgroups — #18007287

Order 4736.

348 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558265C211yesmaximal, characteristic
2#14558259C211yesmaximal, characteristic, complemented
3#14557889C211yesmaximal, characteristic, complemented
4#14557887C211yesmaximal, characteristic, complemented
5#14557878C211yesmaximal, characteristic
6#14557834C211yesmaximal, characteristic, complemented
7#14557831C211yesmaximal, characteristic, complemented
8#14557816C211yesmaximal, characteristic, complemented
9#14557757C211yesmaximal, characteristic, complemented
10#14557731C211yesmaximal, characteristic
11#14557657C211yesmaximal, characteristic, complemented
12Q16×Dic37C211yesmaximal, characteristic, complemented
13SD16×Dic37C211yesmaximal, characteristic, complemented
14C4×#10596941C211yesmaximal, characteristic, complemented
15C37×#464C211yesmaximal, characteristic, complemented
16C2×#10596941C2211yescharacteristic
17#11924535—21no—
18#11924535C2211yescharacteristic
19#11924532C2211yescharacteristic
20#11924528—21no—
21#11924528C2211yescharacteristic
22#11924527—21no—
23#11924527C2211yescharacteristic
24#11924525C2211yescharacteristic
25#11924522—21no—
26#11924520—21no—
27#11924518—21no—
28Q8×Dic37C2211yescharacteristic
29Q8×Dic37C2211yescharacteristic
30Q8×Dic37C2211yescharacteristic
31C4×Dic74—21no—
32C4×Dic74C2211yescharacteristic
33C4×D148C2211yescharacteristic
34D4×Dic37C2211yescharacteristic
35#11924496—21no—
36#11924470C2211yescharacteristic
37#11924468C2211yescharacteristic
38#11924467C2211yescharacteristic
39#11924465C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49C4×#64436C2211yescharacteristic
50C8×Dic37C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×Q16×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54#124×C37C2211yescharacteristic
55C4×Q8×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C22×Dic37—21no—
65C2×D148C2311yescharacteristic
66C2×C4×D37—21no—
67C2×Dic74—21no—
68C2×Dic74D411yescharacteristic
69Q16×C37—22no—
70SD16×C37—22no—
71C2×C8×C37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C4⋊C4×C37—21no—
74C4⋊C4×C37C2311yescharacteristic
75C22⋊C4×C37—21no—
76C22⋊C4×C37—21no—
77C42×C37—21no—
78C42×C37C2311yescharacteristic
79C22⋊Dic37—21no—
80#10596941—22no—
81#10596938—21no—
82#10596938—21no—
83#10596938—21no—
84C4⋊Dic37—21no—
85C4⋊Dic37—21no—
86C4⋊Dic37—21no—
87C4⋊Dic37—21no—
88C4⋊Dic37D411yescharacteristic
89C4⋊Dic37C2311yescharacteristic
90C4⋊Dic37C2311yescharacteristic
91C4⋊Dic37C2311yescharacteristic
92#10596936—21no—
93#10596936—21no—
94#10596936—21no—
95#10596936—21no—
96#10596936D411yescharacteristic
97#10596936D411yescharacteristic
98C4×Dic37—21no—
99C4×Dic37—21no—
100C4×Dic37—21no—
101C4×Dic37C2311yescharacteristic
102C4×Dic37C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C23×C37—21no—
106C22×D37—21no—
107Q8×C37—21no—
108Q8×C37—21no—
109Q8×C37—21no—
110Q8×C37#4112yes—
111D4×C37—21no—
112D4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2411yescharacteristic
119C22⋊D37—42no—
120C22⋊D37—81no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—81no—
125C2×Dic37C2×D411yescharacteristic
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129D148—21no—
130D148—21no—
131C4×D37—81no—
132Dic74—22no—
133Dic74—42no—
134C8×C37—21no—
135C8×C37—21no—
136#64436—21no—
137#64436—21no—
138C22×C37—41no—
139C22×C37—41no—
140C22×C37—41no—
141C22×C37C22×D411yescharacteristic
142C2×D37—41no—
143C2×D37—41no—
144C2×D37—41no—
145C4×C37—22no—
146C4×C37—21no—
147C4×C37—21no—
148C4×C37—41no—
149C4×C37—41no—
150C4×C37C2×#4111yescharacteristic
151C4×C372−1+411yescharacteristic
152Dic37—21no—
153Dic37—21no—
154Dic37—21no—
155Dic37—41no—
156Dic37—41no—
157Dic37—41no—
158Dic37#13512yes—
159#3365—371nomaximal, Sylow
160C2×C37—81no—
161C2×C37#54811yescharacteristic
162C2×C37C2×#13511yescharacteristic
163C2×C37#57711yescharacteristic
164D37—81no—
165#559—371no—
166#557—371no—
167#488—371no—
168#488—371no—
169#486—371no—
170#478—371no—
171#478—371no—
172#475—371no—
173#464—371no—
174#464D3711yescharacteristic, complemented
175#460—371no—
176C8×Q8—371no—
177C4×Q16—371no—
178C4×SD16—371no—
179C4×SD16—371no—
180C37#336511yescharacteristic, complemented, Sylow
181C2×Q16C2×D3711yescharacteristic
182C2×SD16—371no—
183C2×SD16C2×D3711yescharacteristic
184C4⋊Q8—371no—
185C4⋊Q8—741no—
186#127—371no—
187#125—371no—
188#125—371no—
189#125—741no—
190#125—741no—
191#124—371no—
192#124—741no—
193#124C2×D3711yescharacteristic
194#123—741no—
195#123—741no—
196C4×Q8—371no—
197C4×Q8—371no—
198C4×Q8—371no—
199C4×Q8—371no—
200C4×Q8—741no—
201C4×Q8C2×D3711yescharacteristic
202C4×D4—371no—
203C4×D4—371no—
204C4×D4—741no—
205#107—371no—
206#106—371no—
207#106—371no—
208C4⋊C8—371no—
209C4⋊C8—371no—
210C4⋊C8C2×D3711yescharacteristic
211#103—371no—
212#103—371no—
213#103—371no—
214#103C2×D3711yescharacteristic
215#102—371no—
216#102—371no—
217#102—371no—
218#102—371no—
219#102—371no—
220#102C2×D3711yescharacteristic
221C4×C8—371no—
222C4×C8—371no—
223C4×C8—371no—
224C2×Q8—371no—
225C2×Q8—741no—
226C2×Q8C22×D3711yescharacteristic
227C2×Q8C22×D3711yescharacteristic
228C2×D4—371no—
229C2×D4—741no—
230C2×D4—741no—
231C2×D4C22×D3711yescharacteristic
232C22×C4—741no—
233C22×C4—741no—
234Q16—22no—
235SD16—22no—
236SD16—742no—
237C2×C8—371no—
238C2×C8—371no—
239C2×C8C22×D3711yescharacteristic
240C2×C8C22×D3711yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—371no—
243C4⋊C4—371no—
244C4⋊C4—371no—
245C4⋊C4—371no—
246C4⋊C4—371no—
247C4⋊C4—371no—
248C4⋊C4—741no—
249C4⋊C4—741no—
250C4⋊C4—741no—
251C4⋊C4—741no—
252C4⋊C4—741no—
253C4⋊C4—741no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4C22×D3711yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—741no—
260C22⋊C4—741no—
261C22⋊C4—741no—
262C22⋊C4—741no—
263C42—21no—
264C42—371no—
265C42—371no—
266C42—741no—
267C42—741no—
268C42—741no—
269C42C22×D3711yescharacteristic
270C23—21no—
271C23—741no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—742no—
276Q8—1482no—
277Q8#1059696412yes—
278D4—21no—
279D4—21no—
280D4—2961no—
281D4—741no—
282D4—741no—
283D4—1482no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—371no—
288C2×C4—371no—
289C2×C4—371no—
290C2×C4—371no—
291C2×C4—2961no—
292C2×C4—2961no—
293C2×C4—741no—
294C2×C4—741no—
295C2×C4—741no—
296C2×C4D4×D3711yescharacteristic
297C2×C4D4×D3711yescharacteristic
298C2×C4C23×D3711yescharacteristic
299C8—21no—
300C8—21no—
301C8—741no—
302C8—741no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—1481no—
307C22—1481no—
308C22—1481no—
309C22C2×D4×D3711yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—372no—
316C4—741no—
317C4—741no—
318C4—741no—
319C4—1481no—
320C4—1481no—
321C4—1481no—
322C4C2×#1059696411yescharacteristic
323C4#1192458311yescharacteristic
324C2—81no—
325C2—2961no—
326C2#1455818911yescharacteristic
327C2#135×D3711yescharacteristic
328C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#464C2
socleC22×C37C22×D4
prime radical#11924532C22
hypercenter#464D37
hypocenterC37#3365
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #14558259C2semidirect
3. #14557889C2semidirect
4. #14557887C2semidirect
6. #14557834C2semidirect
7. #14557831C2semidirect
8. #14557816C2semidirect
9. #14557757C2semidirect
11. #14557657C2semidirect
12. Q16×Dic37C2semidirect
13. SD16×Dic37C2semidirect
14. C4×#10596941C2semidirect
15. C37×#464C2semidirect
174. #464D37semidirect
180. C37#3365semidirect

Maximal subgroups

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

subgroupindex
#145582652
#145582592
#145578892
#145578872
#145578782
#145578342
#145578312
#145578162
#145577572
#145577312
#145576572
Q16×Dic372
SD16×Dic372
C4×#105969412
C37×#4642
#336537