Finite Group Databasebeta

← #18006381

Subgroups — #18006381

Order 4736.

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

normal subgroups only

This group has 454 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#14558346C211yesmaximal, characteristic, complemented
2#14558339C212yesmaximal, complemented
3#14558334C211yesmaximal, characteristic, complemented
4#14557805C211yesmaximal, characteristic, complemented
5#14557800C211yesmaximal, characteristic, complemented
6#14557793C212yesmaximal, complemented
7#14557710C212yesmaximal, complemented
8#14557705C212yesmaximal, complemented
9#14557651C211yesmaximal, characteristic, complemented
10#14557651C211yesmaximal, characteristic, complemented
11C37×#495C211yesmaximal, characteristic, complemented
12#11924584C2212yescomplemented
13#11924581C2212yes—
14#11924568—22no—
15#11924567C2212yes—
16#11924567C2212yescomplemented
17#11924565—22no—
18#11924563—22no—
19#11924562C2212yes—
20#11924562C2212yescomplemented
21#11924560—22no—
22#11924559—21no—
23#11924558C2211yescharacteristic
24#11924558C2211yescharacteristic
25#11924557—22no—
26#11924555—21no—
27Q16×D37—21no—
28SD16×D37—22no—
29D8×D37—21no—
30#11924542C2211yescharacteristic
31#11924542C2212yescomplemented
32#11924542C2211yescharacteristic, complemented
33#11924472C2211yescharacteristic, complemented
34#11924472C2211yescharacteristic, complemented
35#11924464C2211yescharacteristic
36#11924464C2211yescharacteristic, complemented
37#11924464C2212yescomplemented
38#11924455C2212yescomplemented
39#11924453C2212yescomplemented
40C2×Q16×C37C2211yescharacteristic, complemented
41C2×SD16×C37C2212yescomplemented
42C2×D8×C37C2211yescharacteristic
43#124×C37C2212yescomplemented
44C4×C8×C37C2211yescharacteristic, complemented
45C2×Q8×C37C2312yes—
46C2×D4×C37C2312yes—
47C2×C22⋊D37—42no—
48#10596966—22no—
49#10596966—22no—
50Q8×D37—22no—
51Q8×D37—22no—
52#10596964—22no—
53#10596964—22no—
54D4×D37—22no—
55D4×D37—22no—
56#10596962—42no—
57#10596962C2311yescharacteristic
58#10596962C2312yes—
59#10596962C2311yescharacteristic
60Q16×C37—21no—
61Q16×C37—21no—
62SD16×C37—22no—
63SD16×C37—22no—
64D8×C37—21no—
65D8×C37—21no—
66C2×C8×C37C2311yescharacteristic
67C2×C8×C37C2311yescharacteristic
68C22⋊C4×C37—42no—
69C42×C37C2311yescharacteristic
70#10596942—22no—
71#10596942—22no—
72#10596941—22no—
73#10596941—22no—
74#10596940—22no—
75#10596940—22no—
76#10596939—22no—
77#10596939—22no—
78#10596934C2311yescharacteristic
79#10596934C2312yes—
80#10596934C2311yescharacteristic
81Dic148D411yescharacteristic
82Dic148D411yescharacteristic
83D296D411yescharacteristic
84D296D411yescharacteristic
85#10596930D411yescharacteristic
86#10596930D411yescharacteristic
87#10596930D412yes—
88#10596929—21no—
89#10596929—22no—
90#10596929—21no—
91C8×D37—21no—
92C8×D37—22no—
93C8×D37—21no—
94C23×C37—22no—
95C22×D37—42no—
96Q8×C37—22no—
97Q8×C37—22no—
98D4×C37—22no—
99D4×C37—22no—
100C2×C4×C37—21no—
101C2×C4×C37—22no—
102C2×C4×C37C2411yescharacteristic
103C22⋊D37—21no—
104C22⋊D37—22no—
105C22⋊D37—21no—
106C22⋊D37—42no—
107C22⋊D37—42no—
108C2×Dic37—42no—
109D148—42no—
110D148C2×D411yescharacteristic
111D148C2×D412yes—
112D148C2×D411yescharacteristic
113C4×D37—21no—
114C4×D37—22no—
115C4×D37—21no—
116C4×D37—42no—
117C4×D37—42no—
118Dic74—42no—
119Dic74C2×D411yescharacteristic
120Dic74C2×D412yes—
121Dic74C2×D411yescharacteristic
122C8×C37C2×D411yescharacteristic
123C8×C37C2×D411yescharacteristic
124C8×C37C2×D411yescharacteristic
125C8×C37C2×D411yescharacteristic
126#64436—21no—
127#64436—22no—
128#64436—21no—
129C22×C37—42no—
130C22×C37—82no—
131C22×C37H(5,𝔽2)11yescharacteristic
132C2×D37—21no—
133C2×D37—22no—
134C2×D37—21no—
135C2×D37—162no—
136C4×C37—41no—
137C4×C37—42no—
138C4×C37C22×D411yescharacteristic
139C4×C37C22×D411yescharacteristic
140Dic37—21no—
141Dic37—22no—
142Dic37—21no—
143#3290—371nomaximal, Sylow
144C2×C37—21no—
145C2×C37—82no—
146C2×C37D4211yescharacteristic
147D37—41no—
148D37—42no—
149D37—41no—
150#578—371no—
151#577—372no—
152#576—371no—
153#495D3711yescharacteristic, complemented
154#473—371no—
155#472—371no—
156#471—372no—
157#455—372no—
158#454—372no—
159#443—371no—
160#443—371no—
161C37#329011yescharacteristic, complemented, Sylow
1622−1+4—372no—
163H(5,𝔽2)—372no—
164#137—372no—
165#137—372no—
166#137—742no—
167#137—742no—
168AGL(1,ℤ/8)—372no—
169AGL(1,ℤ/8)—372no—
170AGL(1,ℤ/8)—742no—
171AGL(1,ℤ/8)—742no—
172#135—371no—
173#135—371no—
174#135—741no—
175#135—741no—
176#135—742no—
177C2×Q16—741no—
178C2×Q16C2×D3711yescharacteristic, complemented
179C2×SD16—742no—
180C2×SD16C2×D3712yescomplemented
181C2×D8—741no—
182C2×D8C2×D3711yescharacteristic
183#131—371no—
184#131—372no—
185#131—371no—
186#124C2×D3712yescomplemented
187#108—371no—
188#108—371no—
189#104—371no—
190#104—372no—
191#104—371no—
192#101—372no—
193#100—372no—
194C4×C8C2×D3711yescharacteristic, complemented
195#41—371no—
196#41—372no—
197#41—371no—
198#41—742no—
199#41—742no—
200#41—742no—
201#41—742no—
202#41—1482no—
203C2×Q8—742no—
204C2×Q8—742no—
205C2×Q8C22×D3712yes—
206C2×D4—742no—
207C2×D4—742no—
208C2×D4—1482no—
209C2×D4C22×D3712yes—
210Q16—21no—
211Q16—21no—
212Q16—371no—
213Q16—371no—
214Q16—742no—
215Q16—742no—
216SD16—22no—
217SD16—22no—
218SD16—371no—
219SD16—371no—
220SD16—372no—
221SD16—742no—
222SD16—742no—
223SD16—742no—
224SD16—742no—
225D8—21no—
226D8—21no—
227D8—371no—
228D8—371no—
229D8—742no—
230D8—742no—
231M16—371no—
232M16—372no—
233M16—371no—
234M16—741no—
235M16—742no—
236M16—741no—
237C2×C8—741no—
238C2×C8—742no—
239C2×C8—741no—
240C2×C8C22×D3711yescharacteristic
241C2×C8C22×D3711yescharacteristic
242C22⋊C4—42no—
243C42C22×D3711yescharacteristic
244C23—22no—
245C23—1482no—
246Q8—22no—
247Q8—22no—
248Q8—371no—
249Q8—372no—
250Q8—371no—
251Q8—1482no—
252D4—22no—
253D4—22no—
254D4—371no—
255D4—372no—
256D4—371no—
257D4—741no—
258D4—742no—
259D4—741no—
260D4—1482no—
261D4—1482no—
262D4—1482no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—741no—
266C2×C4—742no—
267C2×C4—741no—
268C2×C4—1482no—
269C2×C4—1482no—
270C2×C4—1482no—
271C2×C4C23×D3711yescharacteristic
272C8—741no—
273C8—742no—
274C8—741no—
275C8D4×D3711yescharacteristic
276C8D4×D3711yescharacteristic
277C8D4×D3711yescharacteristic
278C8D4×D3711yescharacteristic
279C22—42no—
280C22—82no—
281C22—741no—
282C22—742no—
283C22—741no—
284C22—5922no—
285C22#1192458111yescharacteristic
286C4—41no—
287C4—42no—
288C4—741no—
289C4—742no—
290C4—741no—
291C4C2×D4×D3711yescharacteristic
292C4C2×D4×D3711yescharacteristic
293C2—21no—
294C2—82no—
295C2—1481no—
296C2—1482no—
297C2—1481no—
298C2#1455816811yescharacteristic
subgroupG/H
centerC2#14558168
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#495C2
socleC2×C37D42
hypercenter#495D37
hypocenterC37#3290
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14558346C2semidirect
2. #14558339C2semidirect
3. #14558334C2semidirect
4. #14557805C2semidirect
5. #14557800C2semidirect
6. #14557793C2semidirect
7. #14557710C2semidirect
8. #14557705C2semidirect
9. #14557651C2semidirect
10. #14557651C2semidirect
11. C37×#495C2semidirect
12. #11924584C22semidirect
16. #11924567C22semidirect
20. #11924562C22semidirect
31. #11924542C22semidirect
32. #11924542C22semidirect
33. #11924472C22semidirect
34. #11924472C22semidirect
36. #11924464C22semidirect
37. #11924464C22semidirect
38. #11924455C22semidirect
39. #11924453C22semidirect
40. C2×Q16×C37C22semidirect
41. C2×SD16×C37C22semidirect
43. #124×C37C22semidirect
44. C4×C8×C37C22semidirect
153. #495D37semidirect
161. C37#3290semidirect
178. C2×Q16C2×D37semidirect
180. C2×SD16C2×D37semidirect
186. #124C2×D37semidirect
194. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583462
#145583392
#145583342
#145578052
#145578002
#145577932
#145577102
#145577052
#145576512
C37×#4952
#329037