Finite Group Databasebeta

← #18007333

Subgroups — #18007333

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#14558252C211yesmaximal, characteristic
3#14557891C211yesmaximal, characteristic
4#14557882C211yesmaximal, characteristic, complemented
5#14557821C211yesmaximal, characteristic
6#14557816C211yesmaximal, characteristic, complemented
7#14557815C211yesmaximal, characteristic, complemented
8#14557754C211yesmaximal, characteristic
9#14557752C211yesmaximal, characteristic
10#14557742C211yesmaximal, characteristic, complemented
11#14557661C211yesmaximal, characteristic, complemented
12#14557641C211yesmaximal, characteristic, complemented
13#14557637C211yesmaximal, characteristic, complemented
14#14557624C211yesmaximal, characteristic
15C37×#489C211yesmaximal, characteristic
16C2×Dic148C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19#11924535—21no—
20#11924535C2211yescharacteristic
21#11924535C2211yescharacteristic
22#11924534—21no—
23#11924534—21no—
24#11924534C2211yescharacteristic
25#11924529—21no—
26#11924529—21no—
27#11924523C2211yescharacteristic
28#11924513—21no—
29Q8×Dic37C2211yescharacteristic
30C4×Dic74C2211yescharacteristic
31C4×Dic74C2211yescharacteristic
32C4×Dic74C2211yescharacteristic
33#11924501—21no—
34#11924501C2211yescharacteristic
35#11924501C2211yescharacteristic
36D4×Dic37C2211yescharacteristic
37#11924492—21no—
38#11924468C2211yescharacteristic
39#11924467C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924465C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924461C2211yescharacteristic
46#11924460C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924459C2211yescharacteristic
49#11924457C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C4⋊Q8×C37C2211yescharacteristic
53#124×C37C2211yescharacteristic
54#103×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37C2311yescharacteristic
62C22×Dic37—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×C37C2311yescharacteristic
72C4⋊C4×C37C2311yescharacteristic
73C22⋊C4×C37—21no—
74C22⋊C4×C37—21no—
75C42×C37C2311yescharacteristic
76C22⋊Dic37—21no—
77C22⋊Dic37—21no—
78C22⋊Dic37—21no—
79#10596942—22no—
80#10596940—22no—
81C4⋊Dic37—21no—
82C4⋊Dic37D411yescharacteristic
83C4⋊Dic37C2311yescharacteristic
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×Dic37—21no—
100C4×Dic37C2311yescharacteristic
101C4×Dic37C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104Dic148—22no—
105C23×C37—21no—
106Q8×C37—21no—
107Q8×C37—21no—
108Q8×C37—81no—
109D4×C37—21no—
110D4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37C2×D411yescharacteristic
115C2×C4×C37C2×D411yescharacteristic
116C2×C4×C37C2411yescharacteristic
117C2×Dic37—21no—
118C2×Dic37—21no—
119C2×Dic37—21no—
120C2×Dic37—21no—
121C2×Dic37—42no—
122C2×Dic37C2×D411yescharacteristic
123C2×Dic37C2×D411yescharacteristic
124C2×Dic37C2×D411yescharacteristic
125C2×Dic37C2×D411yescharacteristic
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×C37—41no—
138C22×C37—41no—
139C22×C37—41no—
140C22×C37C22×D411yescharacteristic
141C4×C37—21no—
142C4×C37—21no—
143C4×C37—41no—
144C4×C37—41no—
145C4×C37—41no—
146C4×C37C2×#4111yescharacteristic
147C4×C372−1+411yescharacteristic
148Dic37—22no—
149Dic37—21no—
150Dic37—21no—
151Dic37—21no—
152Dic37—41no—
153Dic37—41no—
154Dic37—41no—
155Dic37#13712yes—
156#3369—371nomaximal, Sylow
157C2×C37—81no—
158C2×C37#54811yescharacteristic
159C2×C37C2×#13711yescharacteristic
160C2×C37#57711yescharacteristic
161Q82—371no—
162#556—371no—
163#489—371no—
164#489D3711yescharacteristic
165#487—371no—
166#476—371no—
167#475—371no—
168#475—371no—
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#124C2×D3711yescharacteristic
191C22⋊Q8—741no—
192C4×Q8—371no—
193C4×Q8—371no—
194C4×Q8—371no—
195C4×Q8—371no—
196C4×Q8—371no—
197C4×Q8—371no—
198C4×Q8—741no—
199C4×D4—371no—
200#117—741no—
201#106—371no—
202#106—371no—
203#106—371no—
204C4⋊C8—371no—
205C4⋊C8—371no—
206C4⋊C8—371no—
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#102C2×D3711yescharacteristic
216#102C2×D3711yescharacteristic
217#97—371no—
218#97C2×D3711yescharacteristic
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×D4C22×D3711yescharacteristic
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—371no—
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⋊C4—741no—
251C4⋊C4C22×D3711yescharacteristic
252C4⋊C4C22×D3711yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—741no—
256C22⋊C4—741no—
257C22⋊C4—741no—
258C42—371no—
259C42—371no—
260C42—741no—
261C42—741no—
262C42—741no—
263C42—741no—
264C42—741no—
265C42C22×D3711yescharacteristic
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—81no—
270Q8—372no—
271Q8—2961no—
272Q8—2961no—
273Q8—742no—
274Q8—741no—
275Q8—741no—
276Q8—741no—
277D4—21no—
278D4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—371no—
283C2×C4—371no—
284C2×C4—371no—
285C2×C4—371no—
286C2×C4—741no—
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—41no—
299C22—41no—
300C22—41no—
301C22C2×D4×D3711yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—372no—
308C4—741no—
309C4—741no—
310C4—741no—
311C4—742no—
312C4—1481no—
313C4—1481no—
314C4—1481no—
315C4#41×D3711yescharacteristic
316C4#1192458311yescharacteristic
317C2—81no—
318C2#1455819111yescharacteristic
319C2#137×D3711yescharacteristic
320C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#489C2
socleC22×C37C22×D4
prime radicalC2×D4×C37C23
hypercenter#489D37
hypocenterC37#3369
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #14558263C2semidirect
4. #14557882C2semidirect
6. #14557816C2semidirect
7. #14557815C2semidirect
10. #14557742C2semidirect
11. #14557661C2semidirect
12. #14557641C2semidirect
13. #14557637C2semidirect
176. C37#3369semidirect

Maximal subgroups

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

subgroupindex
#145582632
#145582522
#145578912
#145578822
#145578212
#145578162
#145578152
#145577542
#145577522
#145577422
#145576612
#145576412
#145576372
#145576242
C37×#4892
#336937