Finite Group Databasebeta

← #18006390

Subgroups — #18006390

Order 4736.

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

normal subgroups only

This group has 460 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
1#14558345C212yesmaximal, complemented
2#14558340C212yesmaximal, complemented
3#14557906C211yesmaximal, characteristic, complemented
4#14557797C212yesmaximal, complemented
5#14557796C212yesmaximal, complemented
6#14557717C212yesmaximal, complemented
7#14557702C212yesmaximal, complemented
8#14557651C211yesmaximal, characteristic, complemented
9C37×#443C211yesmaximal, characteristic, complemented
10#11924583C2212yes—
11#11924582C2212yescomplemented
12#11924569—22no—
13#11924569C2212yescomplemented
14#11924568—22no—
15#11924566C2212yescomplemented
16#11924564—22no—
17#11924564C2212yes—
18#11924561C2212yes—
19#11924560—22no—
20#11924558—22no—
21#11924558C2211yescharacteristic
22#11924557—22no—
23C2×#10596930—22no—
24C2×#10596930C2212yescomplemented
25C2×#10596930C2212yescomplemented
26SD16×D37—22no—
27#11924542C2212yescomplemented
28#11924536C2211yescharacteristic, complemented
29#11924533C2211yescharacteristic
30#11924472C2211yescharacteristic, complemented
31#11924464C2212yescomplemented
32#11924454C2212yescomplemented
33#11924452C2212yescomplemented
34#135×C37C2211yescharacteristic
35#131×C37C2212yescomplemented
36#108×C37C2211yescharacteristic, complemented
37#104×C37C2212yescomplemented
38C4×C8×C37C2211yescharacteristic, complemented
39#41×C37C2312yes—
40#10596966—22no—
41Q8×D37—22no—
42#10596964—22no—
43#10596964—42no—
44D4×D37—22no—
45D4×D37—42no—
46#10596962—22no—
47#10596962—22no—
48#10596962C2312yes—
49C2×D148—22no—
50C2×D148—41no—
51C2×D148C2312yes—
52C2×Dic74—22no—
53C2×Dic74C2312yes—
54Q16×C37D411yescharacteristic, complemented
55SD16×C37D412yescomplemented
56D8×C37D411yescharacteristic, complemented
57M16×C37—22no—
58M16×C37C2312yes—
59C2×C8×C37—22no—
60C2×C8×C37C2311yescharacteristic
61C2×C8×C37C2311yescharacteristic
62C42×C37C2311yescharacteristic
63#10596942—22no—
64#10596941—22no—
65#10596940—22no—
66#10596939—22no—
67C4⋊Dic37—41no—
68#10596934C2312yes—
69Dic148—22no—
70Dic148D411yescharacteristic, complemented
71D296—22no—
72D296D411yescharacteristic, complemented
73#10596930—22no—
74#10596930—22no—
75#10596930—22no—
76#10596930—22no—
77#10596930—22no—
78#10596930—22no—
79#10596930D412yescomplemented
80#10596929—22no—
81C8×D37—22no—
82C22×D37—22no—
83C22×D37—42no—
84Q8×C37C2×D412yes—
85D4×C37—22no—
86D4×C37C2×D412yes—
87C2×C4×C37—21no—
88C2×C4×C37—22no—
89C2×C4×C37C2411yescharacteristic
90C22⋊D37—22no—
91C22⋊D37—42no—
92C22⋊D37—42no—
93C2×Dic37—22no—
94C2×Dic37—42no—
95D148—22no—
96D148—22no—
97D148—42no—
98D148—82no—
99D148C2×D412yes—
100C4×D37—22no—
101C4×D37—42no—
102C4×D37—42no—
103Dic74—22no—
104Dic74—22no—
105Dic74—42no—
106Dic74C2×D412yes—
107C8×C37—22no—
108C8×C37C2×D411yescharacteristic
109C8×C37C2×D411yescharacteristic
110C8×C37C2×D411yescharacteristic
111C8×C37C2×D411yescharacteristic
112#64436—22no—
113C22×C37—22no—
114C22×C37H(5,𝔽2)11yescharacteristic
115C2×D37—22no—
116C2×D37—42no—
117C2×D37—82no—
118C2×D37—162no—
119C4×C37—22no—
120C4×C37—22no—
121C4×C37C22×D411yescharacteristic
122C4×C37C22×D411yescharacteristic
123Dic37—22no—
124Dic37—42no—
125#3291—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—42no—
128C2×C37D4211yescharacteristic
129D37—42no—
130D37—82no—
131#577—372no—
132#577—372no—
133#492—371no—
134#471—372no—
135#471—372no—
136#456—372no—
137#453—372no—
138#443—371no—
139#443D3711yescharacteristic, complemented
140C37#329111yescharacteristic, complemented, Sylow
1412−1+4—372no—
142H(5,𝔽2)—372no—
143#137—372no—
144#137—372no—
145#137—742no—
146#137—742no—
147AGL(1,ℤ/8)—372no—
148AGL(1,ℤ/8)—372no—
149AGL(1,ℤ/8)—742no—
150AGL(1,ℤ/8)—742no—
151#135—371no—
152#135—742no—
153#135—742no—
154#135C2×D3711yescharacteristic
155C2×SD16—372no—
156C2×SD16—372no—
157C2×SD16—742no—
158C2×SD16—742no—
159#131—372no—
160#131C2×D3712yescomplemented
161C4⋊Q8—371no—
162#127—371no—
163#108—371no—
164#108C2×D3711yescharacteristic, complemented
165#104—372no—
166#104C2×D3712yescomplemented
167#101—372no—
168#100—372no—
169C4×C8C2×D3711yescharacteristic, complemented
170#41—372no—
171#41—742no—
172#41—742no—
173#41—742no—
174#41—742no—
175#41—1482no—
176#41C22×D3712yes—
177C2×Q8—372no—
178C2×Q8—742no—
179C2×Q8—742no—
180C2×D4—372no—
181C2×D4—742no—
182C2×D4—742no—
183C2×D4—1481no—
184C2×D4—1482no—
185Q16—371no—
186Q16—742no—
187Q16—742no—
188Q16D14811yescharacteristic, complemented
189SD16—372no—
190SD16—742no—
191SD16—742no—
192SD16—742no—
193SD16—742no—
194SD16—742no—
195SD16—742no—
196SD16—742no—
197SD16—742no—
198SD16D14812yescomplemented
199D8—371no—
200D8—742no—
201D8—742no—
202D8D14811yescharacteristic, complemented
203M16—22no—
204M16—372no—
205M16—742no—
206M16C22×D3712yes—
207C2×C8—22no—
208C2×C8—742no—
209C2×C8C22×D3711yescharacteristic
210C2×C8C22×D3711yescharacteristic
211C4⋊C4—1481no—
212C42C22×D3711yescharacteristic
213C23—742no—
214C23—1482no—
215Q8—372no—
216Q8—742no—
217Q8—742no—
218Q8—1482no—
219Q8C2×D14812yes—
220D4—22no—
221D4—372no—
222D4—2962no—
223D4—742no—
224D4—742no—
225D4—742no—
226D4—1482no—
227D4—1482no—
228D4—1482no—
229D4C2×D14812yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—742no—
233C2×C4—742no—
234C2×C4—1482no—
235C2×C4—1482no—
236C2×C4—1482no—
237C2×C4C23×D3711yescharacteristic
238C8—22no—
239C8—742no—
240C8C2×D14811yescharacteristic
241C8C2×D14811yescharacteristic
242C8D4×D3711yescharacteristic
243C8D4×D3711yescharacteristic
244C22—22no—
245C22—2962no—
246C22—742no—
247C22—5922no—
248C22—1482no—
249C22#1192458211yescharacteristic
250C4—22no—
251C4—22no—
252C4—742no—
253C4—1482no—
254C4C2×D4×D3711yescharacteristic
255C4C22×D14811yescharacteristic
256C2—21no—
257C2—42no—
258C2—2962no—
259C2—1482no—
260C2D4×D14811yescharacteristic
subgroupG/H
centerC2D4×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#443C2
socleC2×C37D42
hypercenter#443D37
hypocenterC37#3291
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #14558345C2semidirect
2. #14558340C2semidirect
3. #14557906C2semidirect
4. #14557797C2semidirect
5. #14557796C2semidirect
6. #14557717C2semidirect
7. #14557702C2semidirect
8. #14557651C2semidirect
9. C37×#443C2semidirect
11. #11924582C22semidirect
13. #11924569C22semidirect
15. #11924566C22semidirect
24. C2×#10596930C22semidirect
25. C2×#10596930C22semidirect
27. #11924542C22semidirect
28. #11924536C22semidirect
30. #11924472C22semidirect
31. #11924464C22semidirect
32. #11924454C22semidirect
33. #11924452C22semidirect
35. #131×C37C22semidirect
36. #108×C37C22semidirect
37. #104×C37C22semidirect
38. C4×C8×C37C22semidirect
54. Q16×C37D4semidirect
55. SD16×C37D4semidirect
56. D8×C37D4semidirect
70. Dic148D4semidirect
72. D296D4semidirect
79. #10596930D4semidirect
139. #443D37semidirect
140. C37#3291semidirect
160. #131C2×D37semidirect
164. #108C2×D37semidirect
166. #104C2×D37semidirect
169. C4×C8C2×D37semidirect
188. Q16D148semidirect
198. SD16D148semidirect
202. D8D148semidirect

Maximal subgroups

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

subgroupindex
#145583452
#145583402
#145579062
#145577972
#145577962
#145577172
#145577022
#145576512
C37×#4432
#329137