Finite Group Databasebeta

← #18004981

Subgroups — #18004981

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#14558088C211yesmaximal, characteristic, complemented
2#124×D37C211yesmaximal, characteristic
3#14557895C211yesmaximal, characteristic, complemented
4#14557893C211yesmaximal, characteristic, complemented
5#14557892C211yesmaximal, characteristic, complemented
6#14557889C212yesmaximal, complemented
7#14557886C212yesmaximal, complemented
8#14557540C212yesmaximal, complemented
9#14557536C212yesmaximal
10#14557485C211yesmaximal, characteristic, complemented
11C37×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D37C2211yescharacteristic
13C2×D4×D37C2211yescharacteristic
14C2×#10596929C2212yes—
15#11924536C2211yescharacteristic, complemented
16#11924527C2212yescomplemented
17#11924525C2211yescharacteristic
18#11924524C2211yescharacteristic
19#11924523C2211yescharacteristic
20#11924522—21no—
21#11924522—21no—
22#11924516—21no—
23#11924512—21no—
24Q8×Dic37—21no—
25#11924501—21no—
26#11924494C2212yes—
27C22⋊C4×D37—21no—
28C22⋊C4×D37—21no—
29C42×D37C2211yescharacteristic
30#11924461C2212yescomplemented
31#11924460C2212yescomplemented
32#11924459C2212yescomplemented
33#11924458C2212yes—
34#11924457C2212yes—
35#11924456C2212yes—
36#11924447C2211yescharacteristic, complemented
37C8×Dic37C2212yescomplemented
38C4⋊Q8×C37C2211yescharacteristic, complemented
39#124×C37C2211yescharacteristic
40#103×C37C2212yescomplemented
41#102×C37C2212yes—
42#97×C37C2211yescharacteristic, complemented
43C23×D37—21no—
44C2×Q8×C37—21no—
45C2×Q8×C37C2311yescharacteristic
46C2×D4×C37C2311yescharacteristic
47C2×C22⋊D37—21no—
48Q8×D37—24no—
49D4×D37—24no—
50C2×D148C2311yescharacteristic
51C2×C4×D37—21no—
52C2×C4×D37D411yescharacteristic
53C2×C4×D37D411yescharacteristic
54C2×C4×D37C2311yescharacteristic
55C2×Dic74—21no—
56C2×Dic74—21no—
57C2×Dic74C2311yescharacteristic
58C2×C8×C37C2312yes—
59C4⋊C4×C37—21no—
60C4⋊C4×C37C2312yes—
61C22⋊C4×C37—21no—
62C22⋊C4×C37—21no—
63C42×C37C2311yescharacteristic
64C22⋊Dic37—21no—
65C22⋊Dic37—21no—
66#10596938—22no—
67#10596938—21no—
68#10596938—21no—
69#10596938—21no—
70#10596938—21no—
71C4⋊Dic37—21no—
72C4⋊Dic37—22no—
73C4⋊Dic37C2312yes—
74#10596936—22no—
75C4×Dic37—22no—
76C4×Dic37D411yescharacteristic
77C4×Dic37D411yescharacteristic
78C4×Dic37C2311yescharacteristic
79C2×#64436C2312yes—
80#10596929—24no—
81C23×C37—21no—
82C22×D37—21no—
83C22×D37—42no—
84C22×D37—42no—
85C22×D37—42no—
86C22×D37C2×D411yescharacteristic
87Q8×C37—22no—
88Q8×C37—42no—
89D4×C37—22no—
90C2×C4×C37—22no—
91C2×C4×C37—21no—
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2411yescharacteristic
95C22⋊D37—42no—
96C2×Dic37—22no—
97C2×Dic37—21no—
98C2×Dic37C2×D411yescharacteristic
99C2×Dic37C2×D411yescharacteristic
100C2×Dic37C2×D411yescharacteristic
101D148—22no—
102C4×D37—41no—
103C4×D37—41no—
104C4×D37—42no—
105C4×D37#4114yes—
106Dic74—22no—
107Dic74—42no—
108Dic74—42no—
109C8×C37—22no—
110#64436—22no—
111C22×C37—41no—
112C22×C37—41no—
113C22×C37—41no—
114C22×C37C22×D411yescharacteristic
115C2×D37—21no—
116C2×D37—21no—
117C2×D37—41no—
118C2×D37—41no—
119C2×D37—41no—
120C2×D37—84no—
121C2×D37#12412yes—
122C4×C37—21no—
123C4×C37—21no—
124C4×C37—41no—
125C4×C37—42no—
126C4×C37C2×#4112yes—
127Dic37—21no—
128Dic37—21no—
129Dic37—41no—
130Dic37—42no—
131Dic37#12412yes—
132#3140—371nomaximal, Sylow
133C2×C37—81no—
134C2×C37C2×#12411yescharacteristic
135C2×C37#57511yescharacteristic
136C2×C37#57511yescharacteristic
137D37—22no—
138D37—81no—
139#533—371no—
140C2×#124—371no—
141#489—371no—
142#489—371no—
143#489—371no—
144#489D3711yescharacteristic, complemented
145#488—372no—
146#488—372no—
147#419—372no—
148#418—372no—
149C4×M16—371no—
150C37#314011yescharacteristic, complemented, Sylow
151C22×Q8—371no—
152C22×D4—371no—
153C2×M16—372no—
154C4⋊Q8—371no—
155C4⋊Q8C2×D3711yescharacteristic, complemented
156#125—372no—
157#124—371no—
158#124—371no—
159#124—371no—
160#124—741no—
161#124—741no—
162#124C2×D3711yescharacteristic
163C22⋊Q8—741no—
164C22⋊Q8—741no—
165C4×Q8—741no—
166C4×Q8—741no—
167#117—372no—
168C2×C22⋊C4—741no—
169C2×C22⋊C4—741no—
170C2×C42—371no—
171#103—372no—
172#103—372no—
173#103—372no—
174#103C2×D3712yescomplemented
175#102—372no—
176#102—372no—
177#102—372no—
178#102C2×D3712yes—
179#97—371no—
180#97C2×D3711yescharacteristic, complemented
181C4×C8—372no—
182C24—741no—
183C2×Q8—21no—
184C2×Q8—371no—
185C2×Q8—741no—
186C2×Q8—744no—
187C2×Q8—741no—
188C2×Q8C22×D3711yescharacteristic
189C2×D4—371no—
190C2×D4—744no—
191C2×D4—741no—
192C2×D4C22×D3711yescharacteristic
193C22×C4—371no—
194C22×C4—371no—
195C22×C4—371no—
196C22×C4—741no—
197M16—744no—
198C2×C8—372no—
199C2×C8C22×D3712yes—
200C4⋊C4—21no—
201C4⋊C4—372no—
202C4⋊C4—742no—
203C4⋊C4—742no—
204C4⋊C4—741no—
205C4⋊C4C22×D3712yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—741no—
209C22⋊C4—741no—
210C22⋊C4—742no—
211C22⋊C4—741no—
212C22⋊C4—741no—
213C22⋊C4—741no—
214C22⋊C4—741no—
215C42—371no—
216C42—371no—
217C42—371no—
218C42—742no—
219C42C22×D3711yescharacteristic
220C23—21no—
221C23—371no—
222C23—741no—
223C23—1482no—
224C23—1482no—
225C23—1482no—
226Q8—22no—
227Q8—42no—
228Q8—742no—
229Q8—1482no—
230Q8—1482no—
231D4—22no—
232D4—742no—
233D4—1482no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—371no—
237C2×C4—374no—
238C2×C4—371no—
239C2×C4—371no—
240C2×C4—742no—
241C2×C4—741no—
242C2×C4—1481no—
243C2×C4—1481no—
244C2×C4—1482no—
245C2×C4D4×D3711yescharacteristic
246C2×C4D4×D3711yescharacteristic
247C2×C4C23×D3711yescharacteristic
248C8—22no—
249C8—742no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—372no—
254C22—2964no—
255C22—741no—
256C22—741no—
257C22—1481no—
258C22—1481no—
259C22—1481no—
260C22C2×D4×D3711yescharacteristic
261C4—21no—
262C4—21no—
263C4—41no—
264C4—42no—
265C4—372no—
266C4—741no—
267C4—741no—
268C4—1481no—
269C4—1482no—
270C4#41×D3712yes—
271C2—81no—
272C2—2961no—
273C2—742no—
274C2#124×D3711yescharacteristic
275C2#1455832911yescharacteristic
276C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#489C2
socleC22×C37C22×D4
prime radicalC2×D4×D37C22
hypercenter#489D37
hypocenterC37#3140
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. #14558088C2semidirect
3. #14557895C2semidirect
4. #14557893C2semidirect
5. #14557892C2semidirect
6. #14557889C2semidirect
7. #14557886C2semidirect
8. #14557540C2semidirect
10. #14557485C2semidirect
11. C37×#489C2semidirect
15. #11924536C22semidirect
16. #11924527C22semidirect
30. #11924461C22semidirect
31. #11924460C22semidirect
32. #11924459C22semidirect
36. #11924447C22semidirect
37. C8×Dic37C22semidirect
38. C4⋊Q8×C37C22semidirect
40. #103×C37C22semidirect
42. #97×C37C22semidirect
144. #489D37semidirect
150. C37#3140semidirect
155. C4⋊Q8C2×D37semidirect
174. #103C2×D37semidirect
180. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580882
#124×D372
#145578952
#145578932
#145578922
#145578892
#145578862
#145575402
#145575362
#145574852
C37×#4892
#314037