Finite Group Databasebeta

← #18006364

Subgroups — #18006364

Order 4736.

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

normal subgroups only

This group has 464 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#14558341C212yesmaximal, complemented
2#14558337C212yesmaximal, complemented
3#14557923C211yesmaximal, characteristic, complemented
4#14557801C212yesmaximal, complemented
5#14557799C212yesmaximal, complemented
6#14557710C211yesmaximal, characteristic, complemented
7#14557702C212yesmaximal, complemented
8#14557652C212yesmaximal, complemented
9C37×#454C211yesmaximal, characteristic, complemented
10#11924582C2212yescomplemented
11#11924581C2211yescharacteristic
12#11924567—22no—
13#11924567C2212yescomplemented
14#11924564C2212yes—
15#11924563—22no—
16#11924561—22no—
17#11924561C2212yescomplemented
18#11924560—22no—
19#11924557—22no—
20#11924556—22no—
21#11924556C2212yes—
22C2×#10596941—22no—
23C2×#10596941C2212yescomplemented
24C2×#10596939C2212yescomplemented
25D8×D37—22no—
26#11924544C2212yescomplemented
27#11924543C2212yescomplemented
28#11924533C2211yescharacteristic, complemented
29#11924471C2212yescomplemented
30#11924464C2212yescomplemented
31#11924453C2211yescharacteristic, complemented
32#11924452C2212yescomplemented
33#11924447C2211yescharacteristic, complemented
342−1+4×C37C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C37C2212yescomplemented
36#124×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×D4×C37C2311yescharacteristic
45C2×C22⋊D37—41no—
46#10596966—22no—
47#10596964—22no—
48D4×D37—22no—
49D4×D37—22no—
50D4×D37—42no—
51#10596962—22no—
52#10596962C2312yes—
53C2×D148—22no—
54C2×D148—41no—
55C2×D148C2312yes—
56SD16×C37—22no—
57D8×C37—22no—
58M16×C37C2312yes—
59C22⋊C4×C37—41no—
60C42×C37C2311yescharacteristic
61#10596942—22no—
62#10596942D412yescomplemented
63#10596941—22no—
64#10596941—22no—
65#10596941—22no—
66#10596941—22no—
67#10596941D412yescomplemented
68#10596940D412yescomplemented
69#10596939—22no—
70#10596939—22no—
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—
81C23×C37—21no—
82C22×D37—22no—
83C22×D37—41no—
84C22×D37—42no—
85Q8×C37—22no—
86Q8×C37—41no—
87Q8×C37C2×D412yes—
88D4×C37—22no—
89D4×C37—22no—
90D4×C37—41no—
91D4×C37C2×D412yes—
92C2×C4×C37—22no—
93C2×C4×C37—21no—
94C2×C4×C37—21no—
95C2×C4×C37—42no—
96C2×C4×C37C2411yescharacteristic
97C22⋊D37—22no—
98C22⋊D37—42no—
99C22⋊D37—42no—
100C2×Dic37—41no—
101D148—22no—
102D148—22no—
103D148—42no—
104D148—82no—
105D148C2×D412yes—
106C4×D37—22no—
107C4×D37—42no—
108Dic74C2×D412yes—
109C8×C37—22no—
110#64436—22no—
111#64436C2×D412yes—
112#64436C2×D412yes—
113C22×C37—22no—
114C22×C37—41no—
115C22×C37—81no—
116C22×C37H(5,𝔽2)11yescharacteristic
117C2×D37—22no—
118C2×D37—42no—
119C2×D37—82no—
120C2×D37—161no—
121C2×D37—162no—
122C4×C37—22no—
123C4×C37—41no—
124C4×C37—41no—
125C4×C37C22×D412yes—
126Dic37—22no—
127#3288—371nomaximal, Sylow
128C2×C37—21no—
129C2×C37—42no—
130C2×C37—81no—
131C2×C37D4211yescharacteristic
132D37—42no—
133D37—82no—
134#577—372no—
135#576—372no—
136#496—371no—
137#472—372no—
138#471—372no—
139#455—371no—
140#454D3711yescharacteristic, complemented
141#453—372no—
142#444—372no—
143C37#328811yescharacteristic, complemented, Sylow
1442−1+4C2×D3711yescharacteristic, complemented
145H(5,𝔽2)—372no—
146H(5,𝔽2)—371no—
147#137—372no—
148#137—742no—
149AGL(1,ℤ/8)—372no—
150AGL(1,ℤ/8)—372no—
151AGL(1,ℤ/8)—742no—
152AGL(1,ℤ/8)—742no—
153AGL(1,ℤ/8)—742no—
154AGL(1,ℤ/8)C2×D3712yescomplemented
155#135—372no—
156#135—742no—
157#135—742no—
158C2×SD16—372no—
159C2×SD16—742no—
160C2×D8—372no—
161C2×D8—742no—
162#131—372no—
163#131—372no—
164#127—371no—
165#124C2×D3711yescharacteristic, complemented
166#108—372no—
167#104—372no—
168#104C2×D3712yescomplemented
169#101C2×D3711yescharacteristic, complemented
170#100—371no—
171#100—372no—
172#97—371no—
173#41—22no—
174#41—41no—
175#41—372no—
176#41—742no—
177#41—742no—
178#41—742no—
179#41C22×D3712yes—
180C2×Q8—22no—
181C2×Q8C22×D3711yescharacteristic
182C2×D4—372no—
183C2×D4—742no—
184C2×D4—742no—
185C2×D4—742no—
186C2×D4—1481no—
187C2×D4—1482no—
188C2×D4—1481no—
189C2×D4C22×D3711yescharacteristic
190Q16—372no—
191Q16—742no—
192SD16—22no—
193SD16—372no—
194SD16—372no—
195SD16—742no—
196SD16—742no—
197SD16—742no—
198SD16—742no—
199SD16—742no—
200D8—22no—
201D8—372no—
202D8—742no—
203D8—742no—
204D8—742no—
205D8—742no—
206M16—372no—
207M16—742no—
208M16—742no—
209M16C22×D3712yes—
210C2×C8—372no—
211C2×C8—742no—
212C2×C8—742no—
213C22⋊C4—41no—
214C42C22×D3711yescharacteristic
215C23—21no—
216C23—742no—
217C23—1482no—
218C23—1481no—
219Q8—22no—
220Q8—41no—
221Q8—372no—
222Q8D4×D3712yes—
223D4—22no—
224D4—22no—
225D4—41no—
226D4—372no—
227D4—2962no—
228D4—742no—
229D4—742no—
230D4—742no—
231D4—1482no—
232D4—1482no—
233D4—1482no—
234D4D4×D3712yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—742no—
240C2×C4—1482no—
241C2×C4—1481no—
242C2×C4C23×D3711yescharacteristic
243C8—22no—
244C8—372no—
245C8—372no—
246C8—742no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—2962no—
251C22—742no—
252C22—5922no—
253C22—5921no—
254C22—1482no—
255C22#1192458111yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—742no—
260C4C2×D4×D3712yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—2962no—
265C2—1482no—
266C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#454C2
socleC2×C37D42
hypercenter#454D37
hypocenterC37#3288
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14558341C2semidirect
2. #14558337C2semidirect
3. #14557923C2semidirect
4. #14557801C2semidirect
5. #14557799C2semidirect
6. #14557710C2semidirect
7. #14557702C2semidirect
8. #14557652C2semidirect
9. C37×#454C2semidirect
10. #11924582C22semidirect
13. #11924567C22semidirect
17. #11924561C22semidirect
23. C2×#10596941C22semidirect
24. C2×#10596939C22semidirect
26. #11924544C22semidirect
27. #11924543C22semidirect
28. #11924533C22semidirect
29. #11924471C22semidirect
30. #11924464C22semidirect
31. #11924453C22semidirect
32. #11924452C22semidirect
33. #11924447C22semidirect
34. 2−1+4×C37C22semidirect
35. AGL(1,ℤ/8)×C37C22semidirect
36. #124×C37C22semidirect
37. #104×C37C22semidirect
38. #101×C37C22semidirect
62. #10596942D4semidirect
67. #10596941D4semidirect
68. #10596940D4semidirect
72. #10596939D4semidirect
140. #454D37semidirect
143. C37#3288semidirect
144. 2−1+4C2×D37semidirect
154. AGL(1,ℤ/8)C2×D37semidirect
165. #124C2×D37semidirect
168. #104C2×D37semidirect
169. #101C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583412
#145583372
#145579232
#145578012
#145577992
#145577102
#145577022
#145576522
C37×#4542
#328837