Finite Group Databasebeta

← #18004979

Subgroups — #18004979

Order 4736.

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

normal subgroups only

This group has 400 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#14558089C211yesmaximal, characteristic, complemented
2#124×D37C211yesmaximal, characteristic
3#14557894C212yesmaximal, complemented
4#14557891C212yesmaximal, complemented
5#14557890C211yesmaximal, characteristic, complemented
6#14557888C211yesmaximal, characteristic, complemented
7#14557887C211yesmaximal, characteristic, complemented
8#14557540C212yesmaximal, complemented
9#14557536C212yesmaximal
10C4×#10596929C211yesmaximal, characteristic, complemented
11C37×#488C211yesmaximal, characteristic, complemented
12C2×Q8×D37C2211yescharacteristic
13C2×D4×D37C2211yescharacteristic
14C2×#10596929C2212yes—
15#11924535C2212yescomplemented
16#11924528C2211yescharacteristic, complemented
17#11924525C2211yescharacteristic
18#11924524C2211yescharacteristic
19#11924523C2211yescharacteristic
20#11924522—22no—
21#11924514—22no—
22#11924501—22no—
23#11924494C2212yes—
24C22⋊C4×D37—22no—
25C42×D37C2211yescharacteristic
26#11924461C2212yescomplemented
27#11924460C2212yescomplemented
28#11924459C2212yescomplemented
29#11924458C2212yes—
30#11924457C2212yes—
31#11924456C2212yes—
32#11924446C2212yescomplemented
33C4×#64436C2211yescharacteristic, complemented
34#125×C37C2211yescharacteristic, complemented
35#124×C37C2211yescharacteristic
36#103×C37C2212yescomplemented
37#102×C37C2212yes—
38C4×C8×C37C2211yescharacteristic, complemented
39C23×D37—21no—
40C2×Q8×C37C2311yescharacteristic
41C2×D4×C37C2311yescharacteristic
42C2×C22⋊D37—21no—
43Q8×D37—24no—
44D4×D37—24no—
45C2×D148C2311yescharacteristic
46C2×C4×D37—21no—
47C2×C4×D37D412yes—
48C2×C4×D37C2311yescharacteristic
49C2×Dic74—22no—
50C2×Dic74—21no—
51C2×Dic74C2311yescharacteristic
52C2×C8×C37C2312yes—
53C4⋊C4×C37—22no—
54C4⋊C4×C37C2312yes—
55C22⋊C4×C37—22no—
56C42×C37C2311yescharacteristic
57C22⋊Dic37—22no—
58#10596938—22no—
59#10596938—22no—
60#10596938—22no—
61C4⋊Dic37C2312yes—
62#10596936—22no—
63#10596936—22no—
64C4×Dic37—22no—
65C4×Dic37D412yes—
66C4×Dic37C2311yescharacteristic
67C2×#64436C2312yes—
68#10596929—24no—
69C23×C37—21no—
70C22×D37—21no—
71C22×D37—44no—
72C22×D37—42no—
73C22×D37C2×D411yescharacteristic
74Q8×C37—22no—
75D4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—21no—
78C2×C4×C37C2×D412yes—
79C2×C4×C37C2411yescharacteristic
80C22⋊D37—42no—
81C2×Dic37—22no—
82C2×Dic37—21no—
83C2×Dic37C2×D412yes—
84C2×Dic37C2×D411yescharacteristic
85D148—22no—
86C4×D37—42no—
87C4×D37—42no—
88C4×D37#4114yes—
89Dic74—22no—
90Dic74—44no—
91Dic74—42no—
92C8×C37—22no—
93#64436—22no—
94C22×C37—41no—
95C22×C37—42no—
96C22×C37C22×D411yescharacteristic
97C2×D37—22no—
98C2×D37—41no—
99C2×D37—42no—
100C2×D37—84no—
101C2×D37#12412yes—
102C4×C37—22no—
103C4×C37—41no—
104C4×C37—42no—
105C4×C37C2×#4112yes—
106Dic37—22no—
107Dic37—41no—
108Dic37—42no—
109Dic37#12412yes—
110#3140—371nomaximal, Sylow
111C2×C37—81no—
112C2×C37C2×#12411yescharacteristic
113C2×C37#57512yes—
114D37—22no—
115D37—81no—
116#533—371no—
117C2×#124—371no—
118#489—372no—
119#489—372no—
120#488—371no—
121#488—371no—
122#488—371no—
123#488D3711yescharacteristic, complemented
124#419—372no—
125#418—372no—
126C4×M16—371no—
127C37#314011yescharacteristic, complemented, Sylow
128C22×Q8—371no—
129C22×D4—371no—
130C2×M16—372no—
131C4⋊Q8—372no—
132#125—371no—
133#125C2×D3711yescharacteristic, complemented
134#124—371no—
135#124—371no—
136#124—371no—
137#124—742no—
138#124C2×D3711yescharacteristic
139C22⋊Q8—742no—
140C4×Q8—742no—
141#117—372no—
142C2×C22⋊C4—742no—
143C2×C42—371no—
144#103—372no—
145#103—372no—
146#103—372no—
147#103C2×D3712yescomplemented
148#102—372no—
149#102—372no—
150#102—372no—
151#102C2×D3712yes—
152#97—372no—
153C4×C8—371no—
154C4×C8C2×D3711yescharacteristic, complemented
155C24—741no—
156C2×Q8—371no—
157C2×Q8—742no—
158C2×Q8—741no—
159C2×Q8—744no—
160C2×Q8C22×D3711yescharacteristic
161C2×D4—371no—
162C2×D4—744no—
163C2×D4—741no—
164C2×D4C22×D3711yescharacteristic
165C22×C4—371no—
166C22×C4—372no—
167C22×C4—741no—
168M16—744no—
169C2×C8—372no—
170C2×C8C22×D3712yes—
171C4⋊C4—22no—
172C4⋊C4—372no—
173C4⋊C4—742no—
174C4⋊C4—742no—
175C4⋊C4C22×D3712yes—
176C22⋊C4—22no—
177C22⋊C4—742no—
178C22⋊C4—742no—
179C22⋊C4—742no—
180C22⋊C4—742no—
181C42—372no—
182C42—371no—
183C42—742no—
184C42C22×D3711yescharacteristic
185C23—21no—
186C23—371no—
187C23—741no—
188C23—1482no—
189C23—1484no—
190Q8—22no—
191Q8—742no—
192Q8—1482no—
193Q8—1484no—
194D4—22no—
195D4—742no—
196D4—1482no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—371no—
200C2×C4—374no—
201C2×C4—372no—
202C2×C4—742no—
203C2×C4—741no—
204C2×C4—1482no—
205C2×C4—1482no—
206C2×C4D4×D3712yes—
207C2×C4C23×D3711yescharacteristic
208C8—22no—
209C8—742no—
210C22—41no—
211C22—42no—
212C22—372no—
213C22—2964no—
214C22—742no—
215C22—1481no—
216C22—1482no—
217C22C2×D4×D3711yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—372no—
222C4—742no—
223C4—1481no—
224C4—1482no—
225C4#41×D3712yes—
226C2—81no—
227C2—2961no—
228C2—742no—
229C2#124×D3711yescharacteristic
230C2#1455833012yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#488C2
socleC22×C37C22×D4
prime radicalC2×D4×D37C22
hypercenter#488D37
hypocenterC37#3140
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14558089C2semidirect
3. #14557894C2semidirect
4. #14557891C2semidirect
5. #14557890C2semidirect
6. #14557888C2semidirect
7. #14557887C2semidirect
8. #14557540C2semidirect
10. C4×#10596929C2semidirect
11. C37×#488C2semidirect
15. #11924535C22semidirect
16. #11924528C22semidirect
26. #11924461C22semidirect
27. #11924460C22semidirect
28. #11924459C22semidirect
32. #11924446C22semidirect
33. C4×#64436C22semidirect
34. #125×C37C22semidirect
36. #103×C37C22semidirect
38. C4×C8×C37C22semidirect
123. #488D37semidirect
127. C37#3140semidirect
133. #125C2×D37semidirect
147. #103C2×D37semidirect
154. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580892
#124×D372
#145578942
#145578912
#145578902
#145578882
#145578872
#145575402
#145575362
C4×#105969292
C37×#4882
#314037