Finite Group Databasebeta

← #489×D37 #18004922

Subgroups — #489×D37 #18004922

Order 4736.

436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D37C211yesmaximal, characteristic, complemented
2#124×D37C211yesmaximal, characteristic
3#14557895C211yesmaximal, characteristic, complemented
4#14557894C212yesmaximal, complemented
5#14557893C211yesmaximal, characteristic, complemented
6#14557892C211yesmaximal, characteristic, complemented
7#14557891C212yesmaximal, complemented
8#103×D37C212yesmaximal, complemented
9#102×D37C212yesmaximal
10#97×D37C211yesmaximal, characteristic, complemented
11C37×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D37—21no—
13C2×Q8×D37C2211yescharacteristic
14C2×D4×D37C2211yescharacteristic
15C2×C8×D37C2212yes—
16#11924536C2211yescharacteristic, complemented
17#11924535—21no—
18#11924535C2212yescomplemented
19#11924534—21no—
20#11924525C2211yescharacteristic
21#11924524C2211yescharacteristic
22#11924523C2211yescharacteristic
23#11924522—21no—
24#11924522—21no—
25C4⋊C4×D37—21no—
26C4⋊C4×D37C2212yes—
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
37#11924446C2212yescomplemented
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—
49Q8×D37—44no—
50D4×D37—24no—
51C2×D148C2311yescharacteristic
52C2×C4×D37—21no—
53C2×C4×D37—22no—
54C2×C4×D37D411yescharacteristic
55C2×C4×D37D411yescharacteristic
56C2×C4×D37C2311yescharacteristic
57C2×Dic74—21no—
58C2×Dic74—21no—
59C2×Dic74—22no—
60C2×Dic74C2311yescharacteristic
61C2×C8×C37C2312yes—
62C4⋊C4×C37—21no—
63C4⋊C4×C37C2312yes—
64C22⋊C4×C37—21no—
65C22⋊C4×C37—21no—
66C42×C37C2311yescharacteristic
67C22⋊Dic37—21no—
68C22⋊Dic37—21no—
69#10596938—21no—
70#10596938—21no—
71#10596938—21no—
72#10596938—21no—
73C4⋊Dic37—21no—
74C4⋊Dic37C2312yes—
75#10596936—22no—
76#10596936—22no—
77C4×Dic37D411yescharacteristic
78C4×Dic37D411yescharacteristic
79C4×Dic37C2311yescharacteristic
80C2×#64436C2312yes—
81C8×D37—24no—
82C23×C37—21no—
83C22×D37—21no—
84C22×D37—42no—
85C22×D37—42no—
86C22×D37—42no—
87C22×D37C2×D411yescharacteristic
88Q8×C37—22no—
89Q8×C37—42no—
90D4×C37—22no—
91C2×C4×C37—22no—
92C2×C4×C37—21no—
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—42no—
97C2×Dic37—22no—
98C2×Dic37—21no—
99C2×Dic37C2×D411yescharacteristic
100C2×Dic37C2×D411yescharacteristic
101C2×Dic37C2×D411yescharacteristic
102D148—22no—
103C4×D37—22no—
104C4×D37—22no—
105C4×D37—42no—
106C4×D37—44no—
107C4×D37#4114yes—
108Dic74—22no—
109Dic74—44no—
110Dic74—42no—
111Dic74—42no—
112C8×C37—22no—
113#64436—22no—
114C22×C37—41no—
115C22×C37—41no—
116C22×C37—41no—
117C22×C37C22×D411yescharacteristic
118C2×D37—41no—
119C2×D37—41no—
120C2×D37—41no—
121C2×D37—84no—
122C2×D37#12412yes—
123C2×D37AGL(1,ℤ/8)12yes—
124C2×D37#13712yes—
125C4×C37—21no—
126C4×C37—21no—
127C4×C37—41no—
128C4×C37—42no—
129C4×C37C2×#4112yes—
130Dic37—21no—
131Dic37—21no—
132Dic37—41no—
133Dic37—42no—
134Dic37#12412yes—
135C2×#489—371nomaximal, Sylow
136C2×C37—81no—
137C2×C37C2×#12411yescharacteristic
138C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C37C2×#13711yescharacteristic
140D37—81no—
141D37#48914yesdirect product factor
142C2×C4⋊Q8—371no—
143C2×#124—371no—
144#489—371no—
145#489—371no—
146#489—372no—
147#489—372no—
148#489—371no—
149#489D3711yescharacteristic, direct product factor
150C2×#103—372no—
151C2×#102—372no—
152C2×#97—371no—
153C37C2×#48911yescharacteristic, complemented, Sylow
154C22×Q8—371no—
155C22×Q8—741no—
156C22×D4—371no—
157C22×C8—372no—
158C4⋊Q8—372no—
159C4⋊Q8—371no—
160C4⋊Q8—741no—
161C4⋊Q8—741no—
162C4⋊Q8C2×D3711yescharacteristic, complemented
163#124—371no—
164#124—371no—
165#124—371no—
166#124—741no—
167#124—741no—
168#124C2×D3711yescharacteristic
169C2×C4⋊C4—372no—
170C2×C4⋊C4—741no—
171C2×C22⋊C4—741no—
172C2×C22⋊C4—741no—
173C2×C42—371no—
174#103—372no—
175#103—372no—
176#103—372no—
177#103C2×D3712yescomplemented
178#102—372no—
179#102—372no—
180#102—372no—
181#102C2×D3712yes—
182#97—372no—
183#97—371no—
184#97C2×D3711yescharacteristic, complemented
185C24—741no—
186C2×Q8—21no—
187C2×Q8—371no—
188C2×Q8—741no—
189C2×Q8—742no—
190C2×Q8—744no—
191C2×Q8—741no—
192C2×Q8—1484no—
193C2×Q8C22×D3711yescharacteristic
194C2×D4—371no—
195C2×D4—744no—
196C2×D4—741no—
197C2×D4C22×D3711yescharacteristic
198C22×C4—371no—
199C22×C4—371no—
200C22×C4—371no—
201C22×C4—741no—
202C22×C4—742no—
203C2×C8—372no—
204C2×C8—744no—
205C2×C8C22×D3712yes—
206C4⋊C4—21no—
207C4⋊C4—372no—
208C4⋊C4—742no—
209C4⋊C4—742no—
210C4⋊C4—741no—
211C4⋊C4C22×D3712yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—741no—
215C22⋊C4—741no—
216C22⋊C4—741no—
217C22⋊C4—741no—
218C22⋊C4—741no—
219C22⋊C4—741no—
220C42—371no—
221C42—371no—
222C42—371no—
223C42C22×D3711yescharacteristic
224C23—21no—
225C23—371no—
226C23—741no—
227C23—1482no—
228C23—1482no—
229C23—1482no—
230Q8—22no—
231Q8—42no—
232Q8—742no—
233Q8—1482no—
234Q8—1482no—
235Q8—1484no—
236D4—22no—
237D4—742no—
238D4—1482no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—371no—
242C2×C4—374no—
243C2×C4—371no—
244C2×C4—371no—
245C2×C4—742no—
246C2×C4—742no—
247C2×C4—741no—
248C2×C4—742no—
249C2×C4—1482no—
250C2×C4—1484no—
251C2×C4D4×D3711yescharacteristic
252C2×C4D4×D3711yescharacteristic
253C2×C4C23×D3711yescharacteristic
254C8—22no—
255C8—742no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—372no—
260C22—372no—
261C22—372no—
262C22—2964no—
263C22—1481no—
264C22—1481no—
265C22—1481no—
266C22C2×D4×D3711yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—372no—
272C4—741no—
273C4—741no—
274C4—1481no—
275C4—1482no—
276C4#41×D3712yes—
277C2—81no—
278C2—374no—
279C2—2961no—
280C2#124×D3711yescharacteristic
281C2AGL(1,ℤ/8)×D3711yescharacteristic
282C2#137×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#489C2
socleC22×C37C22×D4
prime radicalC2×D4×D37C22
hypercenter#489D37
hypocenterC37C2×#489
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. C4⋊Q8×D37C2semidirect
3. #14557895C2semidirect
4. #14557894C2semidirect
5. #14557893C2semidirect
6. #14557892C2semidirect
7. #14557891C2semidirect
8. #103×D37C2semidirect
10. #97×D37C2semidirect
11. C37×#489C2semidirect
16. #11924536C22semidirect
18. #11924535C22semidirect
30. #11924461C22semidirect
31. #11924460C22semidirect
32. #11924459C22semidirect
36. #11924447C22semidirect
37. #11924446C22semidirect
38. C4⋊Q8×C37C22semidirect
40. #103×C37C22semidirect
42. #97×C37C22semidirect
141. D37#489direct (N × H)
149. #489D37direct (N × H)
153. C37C2×#489semidirect
162. C4⋊Q8C2×D37semidirect
177. #103C2×D37semidirect
184. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D372
#124×D372
#145578952
#145578942
#145578932
#145578922
#145578912
#103×D372
#102×D372
#97×D372
C37×#4892
C2×#48937