Finite Group Databasebeta

← #18004770

Subgroups — #18004770

Order 4736.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558069C211yesmaximal, characteristic
2C2×#11924501C211yesmaximal, characteristic, complemented
3#14557851C211yesmaximal, characteristic
4#14557839C212yesmaximal, complemented
5#14557758C212yesmaximal, complemented
6#14557688C211yesmaximal, characteristic, complemented
7#14557674C211yesmaximal, characteristic
8#14557637C212yesmaximal, complemented
9#14557632C212yesmaximal, complemented
10#14557587C211yesmaximal, characteristic, complemented
11C37×#484C211yesmaximal, characteristic, complemented
12C22×Dic74C2211yescharacteristic
13C2×#10596942C2212yes—
14C2×#10596930C2212yes—
15#11924531—21no—
16#11924527C2211yescharacteristic
17#11924525C2211yescharacteristic
18#11924520—21no—
19#11924510C2211yescharacteristic
20Q8×Dic37C2211yescharacteristic
21#11924501—21no—
22#11924501—21no—
23#11924501C2212yes—
24#11924501C2212yes—
25#11924498C2211yescharacteristic
26#11924496—21no—
27#11924494—21no—
28C2×#10596936—21no—
29C2×C4×Dic37—21no—
30C2×C4×Dic37C2211yescharacteristic
31#11924467C2212yes—
32#11924465C2212yes—
33#11924461C2212yes—
34#11924459C2212yes—
35#11924456C2212yes—
36C22⋊#64436C2211yescharacteristic
37#11924446C2212yes—
38C22⋊Q8×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic
40#107×C37C2212yes—
41#103×C37C2212yes—
42C22⋊C8×C37C2211yescharacteristic
43C2×Q8×C37C2311yescharacteristic
44C22×C4×C37—21no—
45C22×C4×C37C2311yescharacteristic
46C2×C22⋊D37—21no—
47C22×Dic37—21no—
48C22×Dic37D411yescharacteristic
49C22×Dic37D411yescharacteristic
50C2×D148C2311yescharacteristic
51C2×C4×D37—21no—
52C2×Dic74—21no—
53C2×Dic74—24no—
54C2×Dic74C2312yes—
55C2×C8×C37C2312yes—
56C4⋊C4×C37—21no—
57C4⋊C4×C37—21no—
58C4⋊C4×C37C2311yescharacteristic
59C4⋊C4×C37C2312yes—
60C22⋊C4×C37—21no—
61#10596942—24no—
62#10596938—21no—
63#10596938—21no—
64#10596938—21no—
65#10596938—21no—
66C4⋊Dic37—21no—
67C4⋊Dic37—21no—
68C4⋊Dic37C2311yescharacteristic
69#10596936—22no—
70#10596936—22no—
71#10596936—21no—
72C4×Dic37—22no—
73C4×Dic37—22no—
74C4×Dic37—21no—
75C4×Dic37D411yescharacteristic
76C4×Dic37D411yescharacteristic
77C4×Dic37C2311yescharacteristic
78C4×Dic37C2311yescharacteristic
79C2×#64436C2312yes—
80#10596930—24no—
81C23×C37C2×D411yescharacteristic
82C22×D37—21no—
83Q8×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—22no—
86C2×C4×C37—21no—
87C2×C4×C37—21no—
88C2×C4×C37—42no—
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2411yescharacteristic
91C22⋊D37—42no—
92C2×Dic37—24no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—21no—
96C2×Dic37—41no—
97C2×Dic37C2×D411yescharacteristic
98C2×Dic37C2×D411yescharacteristic
99C2×Dic37C2×D411yescharacteristic
100C2×Dic37C2×D411yescharacteristic
101D148—22no—
102C4×D37—42no—
103Dic74—24no—
104Dic74—22no—
105Dic74#4114yes—
106C8×C37—22no—
107#64436—22no—
108C22×C37—21no—
109C22×C37—21no—
110C22×C37#13712yes—
111C22×C37C22×D411yescharacteristic
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—41no—
115C4×C37—21no—
116C4×C37—41no—
117C4×C37—41no—
118C4×C37—42no—
119C4×C37C2×#4112yes—
120Dic37—24no—
121Dic37—21no—
122Dic37—21no—
123Dic37—21no—
124Dic37—21no—
125Dic37—41no—
126#3117—371nomaximal, Sylow
127C2×C37—22no—
128C2×C37#52511yescharacteristic
129C2×C37C2×#13711yescharacteristic
130C2×C37#57511yescharacteristic
131D37—81no—
132#529—371no—
133C2×C4×Q8—371no—
134#484D3711yescharacteristic, complemented
135#481—371no—
136#479—372no—
137#464—372no—
138#451—371no—
139#448—371no—
140#441—372no—
141#440—372no—
142#432—371no—
143C37#311711yescharacteristic, complemented, Sylow
144C22×Q8—371no—
145C2×Q16—372no—
146C2×SD16—372no—
147#126—741no—
148#125—371no—
149#124—371no—
150#123—741no—
151C22⋊Q8C2×D3711yescharacteristic
152#121—371no—
153C4×Q8—371no—
154C4×Q8—372no—
155C4×Q8—372no—
156C4×Q8—741no—
157C4×Q8—741no—
158C4×D4—371no—
159C4×D4—741no—
160#117—741no—
161C2×C4⋊C4—741no—
162C2×C4⋊C4C2×D3711yescharacteristic
163C2×C42—371no—
164C2×C42—741no—
165#107C2×D3712yes—
166#106—372no—
167C4⋊C8—372no—
168#103—372no—
169#103—372no—
170#103C2×D3712yes—
171#102—372no—
172C22⋊C8—371no—
173C22⋊C8C2×D3711yescharacteristic
174#97—372no—
175C2×Q8—372no—
176C2×Q8—744no—
177C2×Q8—741no—
178C2×Q8C22×D3711yescharacteristic
179C2×D4—371no—
180C2×D4—741no—
181C22×C4—21no—
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—741no—
185C22×C4—741no—
186C22×C4C22×D3711yescharacteristic
187Q16—744no—
188SD16—744no—
189C2×C8—372no—
190C2×C8C22×D3712yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—371no—
194C4⋊C4—742no—
195C4⋊C4—742no—
196C4⋊C4—741no—
197C4⋊C4—741no—
198C4⋊C4—741no—
199C4⋊C4C22×D3712yes—
200C4⋊C4C22×D3711yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—741no—
203C22⋊C4—741no—
204C22⋊C4—741no—
205C22⋊C4—741no—
206C42—371no—
207C42—371no—
208C42—371no—
209C42—371no—
210C42—742no—
211C42—742no—
212C42—741no—
213C23—741no—
214C23D4×D3711yescharacteristic
215Q8—22no—
216Q8—374no—
217Q8—744no—
218Q8—742no—
219D4—742no—
220D4—1482no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—371no—
227C2×C4—371no—
228C2×C4—371no—
229C2×C4—371no—
230C2×C4—744no—
231C2×C4—742no—
232C2×C4—742no—
233C2×C4—741no—
234C2×C4—1482no—
235C2×C4—1481no—
236C2×C4D4×D3711yescharacteristic
237C2×C4C23×D3711yescharacteristic
238C8—22no—
239C8—742no—
240C22—21no—
241C22—21no—
242C22—1481no—
243C22—1481no—
244C22—1481no—
245C22#1192456812yes—
246C22C2×D4×D3711yescharacteristic
247C4—21no—
248C4—41no—
249C4—42no—
250C4—41no—
251C4—744no—
252C4—741no—
253C4—741no—
254C4—741no—
255C4—741no—
256C4—1481no—
257C4#41×D3712yes—
258C2—22no—
259C2—2961no—
260C2#1455804111yescharacteristic
261C2C2×#1192456811yescharacteristic
262C2#1455832911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#484C2
socleC22×C37C22×D4
prime radical#11924510C22
hypercenter#484D37
hypocenterC37#3117
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#11924501C2semidirect
4. #14557839C2semidirect
5. #14557758C2semidirect
6. #14557688C2semidirect
8. #14557637C2semidirect
9. #14557632C2semidirect
10. #14557587C2semidirect
11. C37×#484C2semidirect
134. #484D37semidirect
143. C37#3117semidirect

Maximal subgroups

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

subgroupindex
#145580692
C2×#119245012
#145578512
#145578392
#145577582
#145576882
#145576742
#145576372
#145576322
#145575872
C37×#4842
#311737