Finite Group Databasebeta

← #18006393

Subgroups — #18006393

Order 4736.

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

normal subgroups only

This group has 476 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#14558336C212yesmaximal, complemented
2#14558335C211yesmaximal, characteristic, complemented
3#14557908C211yesmaximal, characteristic, complemented
4#14557803C211yesmaximal, characteristic, complemented
5#14557801C212yesmaximal, complemented
6#14557800C211yesmaximal, characteristic, complemented
7#14557701C212yesmaximal, complemented
8#14557699C212yesmaximal, complemented
9#14557650C211yesmaximal, characteristic, complemented
10#14557648C211yesmaximal, characteristic, complemented
11C37×#576C211yesmaximal, characteristic, complemented
12#11924582C2212yescomplemented
13#11924563—22no—
14#11924562—22no—
15#11924562C2212yescomplemented
16#11924561—22no—
17#11924561C2212yescomplemented
18#11924561C2212yescomplemented
19#11924559—21no—
20#11924556—22no—
21#11924556C2211yescharacteristic
22C2×D296C2211yescharacteristic, complemented
23C2×#10596939—22no—
24C2×#10596939C2212yescomplemented
25D8×D37—21no—
26#11924543C2212yescomplemented
27#11924542C2211yescharacteristic, complemented
28#11924532C2212yescomplemented
29#11924472C2211yescharacteristic, complemented
30#11924471C2211yescharacteristic, complemented
31#11924463C2212yescomplemented
32#11924463C2211yescharacteristic, complemented
33#11924462C2211yescharacteristic, complemented
34#11924453C2212yescomplemented
35#11924452C2212yescomplemented
36C8×Dic37C2211yescharacteristic, complemented
37H(5,𝔽2)×C37C2212yescomplemented
38AGL(1,ℤ/8)×C37—22no—
39AGL(1,ℤ/8)×C37C2212yescomplemented
40#135×C37—21no—
41#135×C37C2211yescharacteristic
42C2×D8×C37—21no—
43C2×D8×C37C2211yescharacteristic, complemented
44#131×C37C2211yescharacteristic, complemented
45#41×C37—22no—
46#41×C37—22no—
47#41×C37C2312yes—
48#41×C37C2311yescharacteristic
49C2×D4×C37—22no—
50C2×D4×C37—22no—
51C2×D4×C37—42no—
52C2×D4×C37C2312yes—
53C2×C22⋊D37—42no—
54#10596966—22no—
55D4×D37—22no—
56D4×D37—42no—
57#10596962—22no—
58#10596962C2311yescharacteristic
59C2×D148—22no—
60C2×D148C2312yes—
61Q16×C37D411yescharacteristic, complemented
62SD16×C37—22no—
63SD16×C37D412yescomplemented
64D8×C37—22no—
65D8×C37—21no—
66D8×C37—21no—
67D8×C37D411yescharacteristic, complemented
68M16×C37—21no—
69M16×C37C2311yescharacteristic
70C2×C8×C37—21no—
71C2×C8×C37C2311yescharacteristic
72#10596942D411yescharacteristic, complemented
73#10596941—22no—
74#10596941—22no—
75#10596941D411yescharacteristic, complemented
76#10596940—22no—
77#10596940D411yescharacteristic, complemented
78#10596939—22no—
79#10596939—22no—
80#10596939—22no—
81#10596939—22no—
82#10596939—22no—
83#10596939D411yescharacteristic, complemented
84C4×Dic37C2311yescharacteristic
85#10596934—22no—
86#10596934C2311yescharacteristic
87#10596934C2312yes—
88C2×#64436—22no—
89C2×#64436C2311yescharacteristic
90D296—21no—
91D296—21no—
92#10596929—21no—
93C8×D37—21no—
94C23×C37—22no—
95C23×C37—42no—
96C22×D37—22no—
97C22×D37—42no—
98Q8×C37C2×D411yescharacteristic
99Q8×C37C2×D412yes—
100D4×C37—22no—
101D4×C37—21no—
102D4×C37—22no—
103D4×C37—22no—
104D4×C37—42no—
105D4×C37—42no—
106D4×C37C2×D411yescharacteristic
107D4×C37C2×D412yes—
108C2×C4×C37—22no—
109C2×C4×C37—21no—
110C2×C4×C37—42no—
111C2×C4×C37C2411yescharacteristic
112C22⋊D37—21no—
113C22⋊D37—42no—
114C22⋊D37—84no—
115C2×Dic37—21no—
116D148—22no—
117D148—22no—
118D148—42no—
119D148C2×D411yescharacteristic
120C4×D37—21no—
121C4×D37—42no—
122Dic74C2×D411yescharacteristic
123C8×C37—21no—
124C8×C37C2×D411yescharacteristic
125C8×C37C2×D411yescharacteristic
126#64436—21no—
127#64436—22no—
128#64436C2×D411yescharacteristic
129#64436C2×D411yescharacteristic
130C22×C37—22no—
131C22×C37—21no—
132C22×C37—42no—
133C22×C37—82no—
134C22×C37—162no—
135C22×C37H(5,𝔽2)11yescharacteristic
136C2×D37—21no—
137C2×D37—42no—
138C2×D37—82no—
139C2×D37—162no—
140C4×C37—22no—
141C4×C37—21no—
142C4×C37C22×D411yescharacteristic
143C4×C37C22×D411yescharacteristic
144Dic37—22no—
145Dic37—21no—
146#3292—371nomaximal, Sylow
147C2×C37—21no—
148C2×C37—42no—
149C2×C37—41no—
150C2×C37—82no—
151C2×C37D4211yescharacteristic
152D37—41no—
153D37—82no—
154#576—372no—
155#576—371no—
156#576D3711yescharacteristic, complemented
157#493—371no—
158#472—372no—
159#472—371no—
160#472—371no—
161#453—372no—
162#453—372no—
163#443—371no—
164#443—371no—
165C37#329211yescharacteristic, complemented, Sylow
166H(5,𝔽2)—372no—
167H(5,𝔽2)C2×D3712yescomplemented
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—372no—
170AGL(1,ℤ/8)—372no—
171AGL(1,ℤ/8)—372no—
172AGL(1,ℤ/8)—742no—
173AGL(1,ℤ/8)—742no—
174AGL(1,ℤ/8)—742no—
175AGL(1,ℤ/8)C2×D3712yescomplemented
176#135—21no—
177#135—371no—
178#135—742no—
179#135—741no—
180#135C2×D3711yescharacteristic
181C2×D8—21no—
182C2×D8—372no—
183C2×D8—371no—
184C2×D8—742no—
185C2×D8—741no—
186C2×D8C2×D3711yescharacteristic, complemented
187#131—372no—
188#131—371no—
189#131C2×D3711yescharacteristic, complemented
190#127—372no—
191#108—371no—
192#108—371no—
193#104—371no—
194#104—372no—
195#104—371no—
196#100—372no—
197#100—372no—
198C4×C8—371no—
199#41—22no—
200#41—22no—
201#41—371no—
202#41—742no—
203#41—742no—
204#41C22×D3711yescharacteristic
205#41C22×D3712yes—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—372no—
210C2×D4—742no—
211C2×D4—742no—
212C2×D4—1482no—
213C2×D4—1482no—
214C2×D4C22×D3712yes—
215Q16—371no—
216Q16C22⋊D3711yescharacteristic, complemented
217SD16—22no—
218SD16—371no—
219SD16—371no—
220SD16—742no—
221SD16—742no—
222SD16—742no—
223SD16C22⋊D3712yescomplemented
224D8—22no—
225D8—21no—
226D8—21no—
227D8—371no—
228D8—742no—
229D8—742no—
230D8—742no—
231D8—742no—
232D8—742no—
233D8—741no—
234D8—741no—
235D8C22⋊D3711yescharacteristic, complemented
236M16—21no—
237M16—372no—
238M16—371no—
239M16—742no—
240M16—741no—
241M16C22×D3711yescharacteristic
242C2×C8—21no—
243C2×C8—371no—
244C2×C8—742no—
245C2×C8—741no—
246C2×C8C22×D3711yescharacteristic
247C42—371no—
248C23—22no—
249C23—42no—
250C23—742no—
251C23—1482no—
252Q8—371no—
253Q8D4×D3711yescharacteristic
254Q8C2×C22⋊D3712yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—371no—
262D4—2964no—
263D4—741no—
264D4—742no—
265D4—742no—
266D4—1482no—
267D4—1482no—
268D4D4×D3711yescharacteristic
269D4C2×C22⋊D3712yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—741no—
274C2×C4—741no—
275C2×C4—1482no—
276C2×C4C23×D3711yescharacteristic
277C8—21no—
278C8—371no—
279C8—371no—
280C8—742no—
281C8—741no—
282C8C2×C22⋊D3711yescharacteristic
283C8C2×C22⋊D3711yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—2962no—
290C22—741no—
291C22—5922no—
292C22—1482no—
293C22#1192458111yescharacteristic
294C4—21no—
295C4—22no—
296C4—742no—
297C4—741no—
298C4C2×D4×D3711yescharacteristic
299C4C22×C22⋊D3711yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—2962no—
305C2—1481no—
306C2D4×C22⋊D3711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#576C2
socleC2×C37D42
hypercenter#576D37
hypocenterC37#3292
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #14558336C2semidirect
2. #14558335C2semidirect
3. #14557908C2semidirect
4. #14557803C2semidirect
5. #14557801C2semidirect
6. #14557800C2semidirect
7. #14557701C2semidirect
8. #14557699C2semidirect
9. #14557650C2semidirect
10. #14557648C2semidirect
11. C37×#576C2semidirect
12. #11924582C22semidirect
15. #11924562C22semidirect
17. #11924561C22semidirect
18. #11924561C22semidirect
22. C2×D296C22semidirect
24. C2×#10596939C22semidirect
26. #11924543C22semidirect
27. #11924542C22semidirect
28. #11924532C22semidirect
29. #11924472C22semidirect
30. #11924471C22semidirect
31. #11924463C22semidirect
32. #11924463C22semidirect
33. #11924462C22semidirect
34. #11924453C22semidirect
35. #11924452C22semidirect
36. C8×Dic37C22semidirect
37. H(5,𝔽2)×C37C22semidirect
39. AGL(1,ℤ/8)×C37C22semidirect
43. C2×D8×C37C22semidirect
44. #131×C37C22semidirect
61. Q16×C37D4semidirect
63. SD16×C37D4semidirect
67. D8×C37D4semidirect
72. #10596942D4semidirect
75. #10596941D4semidirect
77. #10596940D4semidirect
83. #10596939D4semidirect
156. #576D37semidirect
165. C37#3292semidirect
167. H(5,𝔽2)C2×D37semidirect
175. AGL(1,ℤ/8)C2×D37semidirect
186. C2×D8C2×D37semidirect
189. #131C2×D37semidirect
216. Q16C22⋊D37semidirect
223. SD16C22⋊D37semidirect
235. D8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583362
#145583352
#145579082
#145578032
#145578012
#145578002
#145577012
#145576992
#145576502
#145576482
C37×#5762
#329237