Finite Group Databasebeta

← #18006391

Subgroups — #18006391

Order 4736.

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

normal subgroups only

This group has 460 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#14558344C212yesmaximal, complemented
2#14558343C212yesmaximal, complemented
3#14557905C211yesmaximal, characteristic, complemented
4#14557795C212yesmaximal, complemented
5#14557794C212yesmaximal, complemented
6#14557717C212yesmaximal, complemented
7#14557700C211yesmaximal, characteristic, complemented
8#14557647C212yesmaximal, complemented
9C37×#453C211yesmaximal, characteristic, complemented
10#11924583C2212yes—
11#11924581C2211yescharacteristic, complemented
12#11924569C2212yescomplemented
13#11924566—22no—
14#11924566C2212yescomplemented
15#11924565—22no—
16#11924562—22no—
17#11924562C2212yes—
18#11924560—22no—
19#11924556—22no—
20#11924556C2212yes—
21#11924555—22no—
22C2×#10596940—22no—
23C2×#10596940C2212yescomplemented
24C2×#10596940C2212yescomplemented
25SD16×D37—22no—
26#11924544C2212yescomplemented
27#11924543C2212yescomplemented
28#11924536C2211yescharacteristic, complemented
29#11924471C2212yescomplemented
30#11924464C2212yescomplemented
31#11924454C2212yescomplemented
32#11924453C2211yescharacteristic, complemented
33C4×#64436C2211yescharacteristic, complemented
34H(5,𝔽2)×C37C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C37C2212yes—
36#127×C37C2211yescharacteristic
37#104×C37C2212yescomplemented
38#100×C37C2211yescharacteristic, complemented
39#41×C37—22no—
40#41×C37C2312yes—
41C2×D4×C37—22no—
42C2×D4×C37—41no—
43C2×D4×C37—41no—
44C2×D4×C37C2311yescharacteristic
45C2×D4×C37C2311yescharacteristic
46C2×C22⋊D37—41no—
47Q8×D37—22no—
48#10596964—22no—
49#10596964—22no—
50#10596964—42no—
51D4×D37—22no—
52#10596962—22no—
53#10596962C2312yes—
54C2×Dic74—22no—
55C2×Dic74C2312yes—
56SD16×C37—22no—
57D8×C37—22no—
58M16×C37C2312yes—
59C42×C37C2311yescharacteristic
60#10596942—22no—
61#10596942D412yescomplemented
62#10596941D412yescomplemented
63#10596940—22no—
64#10596940—22no—
65#10596940—22no—
66#10596940—22no—
67#10596940—22no—
68#10596940—22no—
69#10596940D412yescomplemented
70#10596939—22no—
71#10596939D412yescomplemented
72C4⋊Dic37—41no—
73#10596934—22no—
74#10596934C2312yes—
75C2×#64436—22no—
76C2×#64436C2312yes—
77Dic148—22no—
78#10596930—22no—
79#10596929—22no—
80C8×D37—22no—
81C23×C37—21no—
82C23×C37—21no—
83C23×C37—41no—
84C22×D37—41no—
85Q8×C37C2×D412yes—
86D4×C37—22no—
87D4×C37—22no—
88D4×C37—22no—
89D4×C37—42no—
90D4×C37—82no—
91D4×C37C2×D412yes—
92C2×C4×C37—21no—
93C2×C4×C37—22no—
94C2×C4×C37—41no—
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—22no—
97C22⋊D37—42no—
98C22⋊D37—42no—
99C2×Dic37—22no—
100C2×Dic37—41no—
101C2×Dic37—42no—
102D148C2×D412yes—
103C4×D37—22no—
104C4×D37—42no—
105Dic74—22no—
106Dic74—22no—
107Dic74—42no—
108Dic74C2×D412yes—
109C8×C37—22no—
110#64436—22no—
111#64436C2×D412yes—
112#64436C2×D412yes—
113C22×C37—22no—
114C22×C37—41no—
115C22×C37—41no—
116C22×C37—81no—
117C22×C37—81no—
118C22×C37—161no—
119C22×C37H(5,𝔽2)11yescharacteristic
120C2×D37—22no—
121C2×D37—161no—
122C4×C37—22no—
123C4×C37—22no—
124C4×C37C22×D412yes—
125Dic37—22no—
126Dic37—42no—
127#3291—371nomaximal, Sylow
128C2×C37—21no—
129C2×C37—42no—
130C2×C37—81no—
131C2×C37—81no—
132C2×C37D4211yescharacteristic
133D37—42no—
134#577—372no—
135#577—372no—
136#492—371no—
137#471—372no—
138#471—372no—
139#456—372no—
140#453—371no—
141#453D3711yescharacteristic, complemented
142#443—372no—
143C37#329111yescharacteristic, complemented, Sylow
1442−1+4—372no—
145H(5,𝔽2)—371no—
146H(5,𝔽2)C2×D3711yescharacteristic, complemented
147#137—372no—
148#137—372no—
149#137—742no—
150#137—742no—
151AGL(1,ℤ/8)—372no—
152AGL(1,ℤ/8)—742no—
153AGL(1,ℤ/8)—742no—
154AGL(1,ℤ/8)C2×D3712yes—
155#135—372no—
156#135—742no—
157#135—742no—
158C2×SD16—372no—
159C2×SD16—372no—
160C2×SD16—742no—
161C2×SD16—742no—
162#131—372no—
163#131—372no—
164C4⋊Q8—371no—
165#127C2×D3711yescharacteristic
166#108—372no—
167#104—372no—
168#104C2×D3712yescomplemented
169#101—372no—
170#100—371no—
171#100C2×D3711yescharacteristic, complemented
172C4×C8—371no—
173#41—22no—
174#41—372no—
175#41—742no—
176#41—742no—
177#41—742no—
178#41—1482no—
179#41C22×D3712yes—
180C2×Q8—372no—
181C2×Q8—742no—
182C2×Q8—742no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—742no—
187C2×D4—1481no—
188C2×D4C22×D3711yescharacteristic
189C2×D4C22×D3711yescharacteristic
190Q16—372no—
191Q16—742no—
192Q16—742no—
193SD16—22no—
194SD16—372no—
195SD16—372no—
196SD16—742no—
197SD16—742no—
198SD16—742no—
199SD16—742no—
200SD16—742no—
201SD16—742no—
202SD16—742no—
203D8—22no—
204D8—372no—
205D8—742no—
206M16—372no—
207M16—742no—
208M16—742no—
209M16C22×D3712yes—
210C2×C8—372no—
211C2×C8—742no—
212C2×C8—742no—
213C4⋊C4—1481no—
214C42C22×D3711yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—1481no—
219Q8—372no—
220Q8—742no—
221Q8—742no—
222Q8—1482no—
223Q8D4×D3712yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—372no—
230D4—742no—
231D4—1482no—
232D4—1482no—
233D4D4×D3712yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—742no—
238C2×C4—742no—
239C2×C4—1482no—
240C2×C4—1481no—
241C2×C4—1482no—
242C2×C4C23×D3711yescharacteristic
243C8—22no—
244C8—372no—
245C8—372no—
246C8—742no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—742no—
254C22—5921no—
255C22#1192458111yescharacteristic
256C4—22no—
257C4—22no—
258C4—742no—
259C4—1482no—
260C4C2×D4×D3712yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—1482no—
266C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#453C2
socleC2×C37D42
hypercenter#453D37
hypocenterC37#3291
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14558344C2semidirect
2. #14558343C2semidirect
3. #14557905C2semidirect
4. #14557795C2semidirect
5. #14557794C2semidirect
6. #14557717C2semidirect
7. #14557700C2semidirect
8. #14557647C2semidirect
9. C37×#453C2semidirect
11. #11924581C22semidirect
12. #11924569C22semidirect
14. #11924566C22semidirect
23. C2×#10596940C22semidirect
24. C2×#10596940C22semidirect
26. #11924544C22semidirect
27. #11924543C22semidirect
28. #11924536C22semidirect
29. #11924471C22semidirect
30. #11924464C22semidirect
31. #11924454C22semidirect
32. #11924453C22semidirect
33. C4×#64436C22semidirect
34. H(5,𝔽2)×C37C22semidirect
37. #104×C37C22semidirect
38. #100×C37C22semidirect
61. #10596942D4semidirect
62. #10596941D4semidirect
69. #10596940D4semidirect
71. #10596939D4semidirect
141. #453D37semidirect
143. C37#3291semidirect
146. H(5,𝔽2)C2×D37semidirect
168. #104C2×D37semidirect
171. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583442
#145583432
#145579052
#145577952
#145577942
#145577172
#145577002
#145576472
C37×#4532
#329137