Finite Group Databasebeta

← #18006386

Subgroups — #18006386

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#14558342C212yesmaximal, complemented
2#14558341C212yesmaximal, complemented
3#14557907C211yesmaximal, characteristic, complemented
4#14557799C212yesmaximal, complemented
5#14557798C212yesmaximal, complemented
6#14557715C211yesmaximal, characteristic, complemented
7#14557702C212yesmaximal, complemented
8#14557647C212yesmaximal, complemented
9C37×#456C211yesmaximal, characteristic, complemented
10#11924584C2211yescharacteristic
11#11924582C2212yescomplemented
12#11924568—22no—
13#11924567—22no—
14#11924567C2212yescomplemented
15#11924564C2212yes—
16#11924563—22no—
17#11924561—22no—
18#11924561C2212yes—
19#11924559—22no—
20#11924556—22no—
21#11924556C2212yes—
22C2×#10596941—22no—
23C2×#10596941C2212yescomplemented
24C2×#10596941C2212yescomplemented
25SD16×D37—22no—
26#11924544C2212yescomplemented
27#11924543C2212yescomplemented
28#11924533C2211yescharacteristic
29#11924471C2212yescomplemented
30#11924464C2212yescomplemented
31#11924455C2211yescharacteristic, complemented
32#11924452C2212yescomplemented
33C4×#64436C2211yescharacteristic, complemented
342−1+4×C37C2211yescharacteristic
35#137×C37C2212yescomplemented
36C4⋊Q8×C37C2211yescharacteristic, complemented
37#104×C37C2212yescomplemented
38#101×C37C2211yescharacteristic, complemented
39#41×C37—22no—
40#41×C37—41no—
41#41×C37C2312yes—
42C2×Q8×C37—22no—
43C2×Q8×C37C2311yescharacteristic
44C2×Q8×C37C2311yescharacteristic
45#10596966—22no—
46#10596966—22no—
47Q8×D37—22no—
48D4×D37—22no—
49D4×D37—42no—
50#10596962—22no—
51#10596962—41no—
52#10596962C2312yes—
53C2×D148—22no—
54C2×D148—41no—
55C2×D148C2312yes—
56Q16×C37—22no—
57SD16×C37—22no—
58M16×C37C2312yes—
59C4⋊C4×C37—41no—
60C42×C37C2311yescharacteristic
61#10596942—22no—
62#10596942D412yescomplemented
63#10596941—22no—
64#10596941—22no—
65#10596941—22no—
66#10596941—22no—
67#10596941—22no—
68#10596941—22no—
69#10596941D412yescomplemented
70#10596940D412yescomplemented
71#10596939—22no—
72#10596939D412yescomplemented
73#10596934—22no—
74#10596934C2312yes—
75C2×#64436—22no—
76C2×#64436C2312yes—
77D296—22no—
78#10596930—22no—
79#10596929—22no—
80C8×D37—22no—
81C22×D37—22no—
82C22×D37—42no—
83Q8×C37—22no—
84Q8×C37—22no—
85Q8×C37—41no—
86Q8×C37C2×D412yes—
87D4×C37—22no—
88D4×C37—41no—
89D4×C37C2×D412yes—
90C2×C4×C37—21no—
91C2×C4×C37—22no—
92C2×C4×C37—21no—
93C2×C4×C37—21no—
94C2×C4×C37—42no—
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—22no—
97C22⋊D37—42no—
98D148—22no—
99D148—22no—
100D148—42no—
101D148—41no—
102D148—82no—
103D148C2×D412yes—
104C4×D37—22no—
105C4×D37—42no—
106C4×D37—42no—
107Dic74—41no—
108Dic74C2×D412yes—
109C8×C37—22no—
110#64436—22no—
111#64436C2×D412yes—
112#64436C2×D412yes—
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×C37—41no—
122C4×C37—41no—
123C4×C37C22×D412yes—
124Dic37—22no—
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—371no—
137#456D3711yescharacteristic, complemented
138#453—372no—
139#443—372no—
140C37#329111yescharacteristic, complemented, Sylow
1412−1+4—371no—
1422−1+4C2×D3711yescharacteristic
143H(5,𝔽2)—372no—
144#137—372no—
145#137—742no—
146#137—742no—
147#137C2×D3712yescomplemented
148AGL(1,ℤ/8)—372no—
149AGL(1,ℤ/8)—372no—
150AGL(1,ℤ/8)—742no—
151AGL(1,ℤ/8)—742no—
152#135—372no—
153#135—742no—
154#135—742no—
155C2×SD16—372no—
156C2×SD16—372no—
157C2×SD16—742no—
158C2×SD16—742no—
159#131—372no—
160#131—372no—
161C4⋊Q8C2×D3711yescharacteristic, complemented
162#127—371no—
163#108—372no—
164#104—372no—
165#104C2×D3712yescomplemented
166#101—371no—
167#101C2×D3711yescharacteristic, complemented
168#100—372no—
169C4×C8—371no—
170#41—22no—
171#41—41no—
172#41—372no—
173#41—742no—
174#41—742no—
175#41—742no—
176#41—1481no—
177#41C22×D3712yes—
178C2×Q8—22no—
179C2×Q8—742no—
180C2×Q8C22×D3711yescharacteristic
181C2×Q8C22×D3711yescharacteristic
182C2×D4—372no—
183C2×D4—742no—
184C2×D4—742no—
185C2×D4—1481no—
186C2×D4—1482no—
187Q16—22no—
188Q16—372no—
189Q16—742no—
190SD16—22no—
191SD16—372no—
192SD16—372no—
193SD16—742no—
194SD16—742no—
195SD16—742no—
196SD16—742no—
197SD16—742no—
198SD16—742no—
199SD16—742no—
200D8—372no—
201D8—742no—
202D8—742no—
203M16—372no—
204M16—742no—
205M16—742no—
206M16C22×D3712yes—
207C2×C8—372no—
208C2×C8—742no—
209C2×C8—742no—
210C4⋊C4—41no—
211C42C22×D3711yescharacteristic
212C23—742no—
213C23—1482no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—372no—
218Q8—1481no—
219Q8D4×D3712yes—
220D4—22no—
221D4—41no—
222D4—372no—
223D4—2962no—
224D4—742no—
225D4—742no—
226D4—742no—
227D4—1482no—
228D4—1481no—
229D4—1482no—
230D4D4×D3712yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—742no—
237C2×C4—1482no—
238C2×C4—1482no—
239C2×C4C23×D3711yescharacteristic
240C8—22no—
241C8—372no—
242C8—372no—
243C8—742no—
244C22—22no—
245C22—2962no—
246C22—742no—
247C22—5922no—
248C22—1482no—
249C22#1192458111yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—742no—
255C4C2×D4×D3712yes—
256C2—21no—
257C2—42no—
258C2—2962no—
259C2—1482no—
260C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#456C2
socleC2×C37D42
hypercenter#456D37
hypocenterC37#3291
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14558342C2semidirect
2. #14558341C2semidirect
3. #14557907C2semidirect
4. #14557799C2semidirect
5. #14557798C2semidirect
6. #14557715C2semidirect
7. #14557702C2semidirect
8. #14557647C2semidirect
9. C37×#456C2semidirect
11. #11924582C22semidirect
14. #11924567C22semidirect
23. C2×#10596941C22semidirect
24. C2×#10596941C22semidirect
26. #11924544C22semidirect
27. #11924543C22semidirect
29. #11924471C22semidirect
30. #11924464C22semidirect
31. #11924455C22semidirect
32. #11924452C22semidirect
33. C4×#64436C22semidirect
35. #137×C37C22semidirect
36. C4⋊Q8×C37C22semidirect
37. #104×C37C22semidirect
38. #101×C37C22semidirect
62. #10596942D4semidirect
69. #10596941D4semidirect
70. #10596940D4semidirect
72. #10596939D4semidirect
137. #456D37semidirect
140. C37#3291semidirect
147. #137C2×D37semidirect
161. C4⋊Q8C2×D37semidirect
165. #104C2×D37semidirect
167. #101C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583422
#145583412
#145579072
#145577992
#145577982
#145577152
#145577022
#145576472
C37×#4562
#329137