Finite Group Databasebeta

← #483×D37 #18004470

Subgroups — #483×D37 #18004470

Order 4736.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C22⋊Q8×D37C211yesmaximal, characteristic
2C2×C4⋊C4×D37C211yesmaximal, characteristic
3#14557865C212yesmaximal, complemented
4#14557864C211yesmaximal, characteristic, complemented
5#14557863C211yesmaximal, characteristic, complemented
6#14557862C212yesmaximal, complemented
7#14557861C211yesmaximal, characteristic, complemented
8#106×D37C212yesmaximal, complemented
9#103×D37C212yesmaximal, complemented
10C22⋊C8×D37C211yesmaximal, characteristic
11C37×#483C211yesmaximal, characteristic, complemented
12C2×Q8×D37C2211yescharacteristic
13C22×C4×D37—21no—
14C22×C4×D37C2211yescharacteristic
15C2×C8×D37C2212yes—
16#11924516C2211yescharacteristic
17#11924515C2211yescharacteristic
18#11924514—21no—
19#11924513—21no—
20#11924512C2211yescharacteristic
21C2×C4⋊Dic37C2211yescharacteristic
22C2×#10596936—21no—
23C4⋊C4×D37—21no—
24C4⋊C4×D37—21no—
25C4⋊C4×D37—21no—
26C4⋊C4×D37C2212yes—
27C4⋊C4×D37C2212yes—
28C4⋊C4×D37C2211yescharacteristic
29C22⋊C4×D37—21no—
30#11924468C2212yescomplemented
31#11924467C2212yescomplemented
32#11924467C2212yescomplemented
33#11924461C2212yescomplemented
34#11924460C2212yescomplemented
35#11924459C2212yescomplemented
36C22⋊#64436C2211yescharacteristic
37#11924448C2212yes—
38C22⋊Q8×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic
40#106×C37C2212yescomplemented
41#103×C37C2212yescomplemented
42C22⋊C8×C37C2211yescharacteristic
43C23×D37D411yescharacteristic
44C2×Q8×C37C2311yescharacteristic
45C22×C4×C37—21no—
46C22×C4×C37C2311yescharacteristic
47C22×Dic37—21no—
48C22×Dic37D411yescharacteristic
49Q8×D37—24no—
50C2×C4×D37—24no—
51C2×C4×D37—21no—
52C2×C4×D37—21no—
53C2×C4×D37—22no—
54C2×C4×D37—22no—
55C2×C4×D37—44no—
56C2×C4×D37D411yescharacteristic
57C2×C4×D37D411yescharacteristic
58C2×C4×D37C2311yescharacteristic
59C2×C4×D37C2311yescharacteristic
60C2×Dic74—21no—
61C2×Dic74C2311yescharacteristic
62C2×C8×C37C2312yes—
63C4⋊C4×C37—21no—
64C4⋊C4×C37—21no—
65C4⋊C4×C37C2312yes—
66C4⋊C4×C37C2311yescharacteristic
67C22⋊C4×C37—21no—
68C22⋊Dic37—21no—
69#10596938—21no—
70#10596938—21no—
71C4⋊Dic37—21no—
72C4⋊Dic37—21no—
73C4⋊Dic37C2312yes—
74C4⋊Dic37C2311yescharacteristic
75#10596936—21no—
76#10596936—22no—
77#10596936—22no—
78#10596936—21no—
79#10596936—21no—
80C2×#64436C2312yes—
81C8×D37—24no—
82C23×C37C2×D411yescharacteristic
83C22×D37—22no—
84C22×D37—22no—
85C22×D37SD1614yes—
86C22×D37C2×D411yescharacteristic
87C22×D37C2×D411yescharacteristic
88Q8×C37—22no—
89C2×C4×C37—22no—
90C2×C4×C37—22no—
91C2×C4×C37—21no—
92C2×C4×C37—21no—
93C2×C4×C37—42no—
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2411yescharacteristic
96C2×Dic37—22no—
97C2×Dic37—21no—
98C2×Dic37—22no—
99C2×Dic37—21no—
100C2×Dic37—42no—
101C2×Dic37C2×D411yescharacteristic
102C2×Dic37C2×D411yescharacteristic
103C4×D37—22no—
104C4×D37—22no—
105C4×D37—22no—
106C4×D37—42no—
107C4×D37—44no—
108C4×D37—44no—
109C4×D37—42no—
110C4×D37#4114yes—
111Dic74—22no—
112Dic74—42no—
113C8×C37—22no—
114#64436—22no—
115C22×C37—21no—
116C22×C37—21no—
117C22×C37C2×SD1612yes—
118C22×C37C22×D411yescharacteristic
119C2×D37—21no—
120C2×D37—21no—
121C2×D37—28no—
122C2×D37#12312yes—
123C2×D37C2×SD1612yes—
124C2×D37C2×SD1612yes—
125C2×D37#13712yes—
126C4×C37—21no—
127C4×C37—41no—
128C4×C37—42no—
129C4×C37—41no—
130C4×C37C2×#4112yes—
131Dic37—21no—
132Dic37—41no—
133Dic37—42no—
134Dic37—41no—
135Dic37#12312yes—
136C2×#483—371nomaximal, Sylow
137C2×C37—22no—
138C2×C37C2×#12311yescharacteristic
139C2×C37C22×SD1611yescharacteristic
140C2×C37C2×#13711yescharacteristic
141D37—22no—
142D37#48314yesdirect product factor
143C2×C22⋊Q8—371no—
144C22×C4⋊C4—371no—
145#483—371no—
146#483—371no—
147#483—372no—
148#483—372no—
149#483—371no—
150#483D3711yescharacteristic, direct product factor
151C2×#106—372no—
152C2×#103—372no—
153C2×C22⋊C8—371no—
154C37C2×#48311yescharacteristic, complemented, Sylow
155C22×Q8—371no—
156C23×C4—371no—
157C23×C4—741no—
158C22×C8—372no—
159C22⋊Q8—371no—
160C22⋊Q8—371no—
161C22⋊Q8—371no—
162C22⋊Q8—741no—
163C22⋊Q8—741no—
164C22⋊Q8C2×D3711yescharacteristic
165C2×C4⋊C4—371no—
166C2×C4⋊C4—372no—
167C2×C4⋊C4—372no—
168C2×C4⋊C4—371no—
169C2×C4⋊C4—741no—
170C2×C4⋊C4—741no—
171C2×C4⋊C4—741no—
172C2×C4⋊C4—741no—
173C2×C4⋊C4C2×D3711yescharacteristic
174C2×C22⋊C4—741no—
175#106—372no—
176#106—372no—
177#106—372no—
178#106C2×D3712yescomplemented
179#103—372no—
180#103—372no—
181#103—372no—
182#103C2×D3712yescomplemented
183C22⋊C8—371no—
184C22⋊C8—372no—
185C22⋊C8C2×D3711yescharacteristic
186C24—371no—
187C2×Q8—371no—
188C2×Q8—741no—
189C2×Q8—744no—
190C2×Q8C22×D3711yescharacteristic
191C22×C4—21no—
192C22×C4—371no—
193C22×C4—371no—
194C22×C4—371no—
195C22×C4—371no—
196C22×C4—371no—
197C22×C4—744no—
198C22×C4—741no—
199C22×C4—741no—
200C22×C4—742no—
201C22×C4—742no—
202C22×C4—741no—
203C22×C4—1484no—
204C22×C4C22×D3711yescharacteristic
205C2×C8—372no—
206C2×C8—744no—
207C2×C8C22×D3712yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—372no—
211C4⋊C4—371no—
212C4⋊C4—742no—
213C4⋊C4—742no—
214C4⋊C4—741no—
215C4⋊C4—741no—
216C4⋊C4—741no—
217C4⋊C4—741no—
218C4⋊C4—741no—
219C4⋊C4C22×D3712yes—
220C4⋊C4C22×D3711yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—741no—
223C22⋊C4—741no—
224C22⋊C4—741no—
225C23—371no—
226C23—374no—
227C23—371no—
228C23—742no—
229C23—742no—
230C23D4×D3711yescharacteristic
231Q8—22no—
232Q8—742no—
233Q8—1482no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—371no—
240C2×C4—374no—
241C2×C4—371no—
242C2×C4—742no—
243C2×C4—742no—
244C2×C4—742no—
245C2×C4—742no—
246C2×C4—741no—
247C2×C4—741no—
248C2×C4—742no—
249C2×C4—1484no—
250C2×C4—1484no—
251C2×C4—1482no—
252C2×C4—1482no—
253C2×C4—1482no—
254C2×C4D4×D3711yescharacteristic
255C2×C4C23×D3711yescharacteristic
256C8—22no—
257C8—742no—
258C22—21no—
259C22—21no—
260C22—372no—
261C22—372no—
262C22—372no—
263C22—372no—
264C22—748no—
265C22—741no—
266C22—741no—
267C22SD16×D3712yes—
268C22C2×D4×D3711yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—372no—
274C4—741no—
275C4—1481no—
276C4—1482no—
277C4—1481no—
278C4#41×D3712yes—
279C2—22no—
280C2—374no—
281C2—742no—
282C2#123×D3711yescharacteristic
283C2C2×SD16×D3711yescharacteristic
284C2#137×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#483C2
socleC22×C37C22×D4
prime radicalC23×D37D4
hypercenter#483D37
hypocenterC37C2×#483
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #14557865C2semidirect
4. #14557864C2semidirect
5. #14557863C2semidirect
6. #14557862C2semidirect
7. #14557861C2semidirect
8. #106×D37C2semidirect
9. #103×D37C2semidirect
11. C37×#483C2semidirect
30. #11924468C22semidirect
31. #11924467C22semidirect
32. #11924467C22semidirect
33. #11924461C22semidirect
34. #11924460C22semidirect
35. #11924459C22semidirect
40. #106×C37C22semidirect
41. #103×C37C22semidirect
142. D37#483direct (N × H)
150. #483D37direct (N × H)
154. C37C2×#483semidirect
178. #106C2×D37semidirect
182. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D372
C2×C4⋊C4×D372
#145578652
#145578642
#145578632
#145578622
#145578612
#106×D372
#103×D372
C22⋊C8×D372
C37×#4832
C2×#48337