Finite Group Databasebeta

← #18007736

Subgroups — #18007736

Order 4736.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#14558335C211yesmaximal, characteristic, complemented
2#14558334C211yesmaximal, characteristic, complemented
3#14557971C211yesmaximal, characteristic, complemented
4#14557970C212yesmaximal, complemented
5#14557967C212yesmaximal, complemented
6#14557964C212yesmaximal, complemented
7#14557963C211yesmaximal, characteristic, complemented
8C2×#11924477C211yesmaximal, characteristic, complemented
9D16×D37C212yesmaximal, complemented
10#14557951C211yesmaximal, characteristic, complemented
11C37×#509C211yesmaximal, characteristic, complemented
12#11924582—21no—
13#11924581—21no—
14#11924563—22no—
15#11924562—21no—
16#11924561—21no—
17#11924560—22no—
18#11924559C2212yescomplemented
19#11924558C2211yescharacteristic, complemented
20#11924555C2212yescomplemented
21C2×D296C2211yescharacteristic, complemented
22D8×D37C2212yescomplemented
23D8×D37C2212yescomplemented
24#11924542C2211yescharacteristic
25#11924482C2211yescharacteristic, complemented
26#11924481C2212yescomplemented
27#11924480C2211yescharacteristic, complemented
28#11924479C2211yescharacteristic, complemented
29D592C2212yescomplemented
30#11924477C2211yescharacteristic, complemented
31#11924477C2212yescomplemented
32#11924477C2212yescomplemented
33#11924475C2212yescomplemented
34C2×#10596925C2211yescharacteristic, complemented
35C16×D37C2212yescomplemented
36#135×C37C2211yescharacteristic, complemented
37C2×D8×C37C2211yescharacteristic, complemented
38SD32×C37C2212yescomplemented
39D16×C37C2212yescomplemented
40M32×C37C2211yescharacteristic, complemented
41#41×C37—21no—
42C2×D4×C37—21no—
43C2×C22⋊D37—42no—
44#10596966—22no—
45#10596964—22no—
46#10596964—41no—
47D4×D37—22no—
48D4×D37—22no—
49D4×D37—42no—
50D4×D37—41no—
51#10596962—21no—
52#10596962—41no—
53#10596962D411yescharacteristic
54C2×D148—21no—
55C2×D148—41no—
56Q16×C37C2311yescharacteristic
57SD16×C37—21no—
58D8×C37—21no—
59D8×C37C2311yescharacteristic
60D8×C37C2312yes—
61C2×C8×C37C2311yescharacteristic
62#10596941—22no—
63#10596940—22no—
64#10596939—22no—
65#10596939—22no—
66#10596934D411yescharacteristic
67Dic148C2311yescharacteristic
68D296—21no—
69D296C2312yes—
70D296C2311yescharacteristic
71#10596930—21no—
72#10596929D412yes—
73C8×D37C2312yes—
74C16×C37C2312yes—
75#10596925C2311yescharacteristic
76#10596925C2311yescharacteristic
77C23×C37—41no—
78C22×D37—41no—
79C22×D37—42no—
80C22×D37—42no—
81Q8×C37—21no—
82D4×C37—21no—
83D4×C37—22no—
84D4×C37—41no—
85D4×C37—41no—
86C2×C4×C37—41no—
87C2×C4×C37C2×D411yescharacteristic
88C22⋊D37—41no—
89C22⋊D37—42no—
90C22⋊D37—42no—
91C22⋊D37—42no—
92C22⋊D37D812yes—
93C2×Dic37—42no—
94D148—21no—
95D148—22no—
96D148—42no—
97D148—41no—
98D148D811yescharacteristic
99C4×D37—41no—
100C4×D37—42no—
101C4×D37C2×D412yes—
102Dic74—21no—
103Dic74D811yescharacteristic
104C8×C37C2×D411yescharacteristic
105C8×C37C2411yescharacteristic
106#64436C2×D412yes—
107C22×C37—42no—
108C22×C37—41no—
109C22×C37—161no—
110C22×C37C2×D811yescharacteristic
111C2×D37—42no—
112C2×D37—41no—
113C2×D37—162no—
114C2×D37—162no—
115C2×D37—161no—
116C2×D37C2×D812yes—
117C4×C37—41no—
118C4×C37C2×D811yescharacteristic
119C4×C37C22×D411yescharacteristic
120Dic37—41no—
121Dic37C2×D812yes—
122#3415—371nomaximal, Sylow
123C2×C37—21no—
124C2×C37—81no—
125C2×C37—82no—
126C2×C37C22×D811yescharacteristic
127D37—22no—
128D37—82no—
129D37—81no—
130#576—371no—
131#576—371no—
132#509—372no—
133#509—372no—
134#509—371no—
135#509D3711yescharacteristic, complemented
136#508—371no—
137#508—372no—
138C2×D16—371no—
139C2×D16—372no—
140#504—371no—
141C37#341511yescharacteristic, complemented, Sylow
142H(5,𝔽2)—741no—
143H(5,𝔽2)—741no—
144AGL(1,ℤ/8)—742no—
145AGL(1,ℤ/8)—742no—
146AGL(1,ℤ/8)—741no—
147AGL(1,ℤ/8)—741no—
148#135—372no—
149#135—372no—
150#135—371no—
151#135C2×D3711yescharacteristic, complemented
152C2×D8—372no—
153C2×D8—372no—
154C2×D8—371no—
155C2×D8C2×D3711yescharacteristic, complemented
156#131—371no—
157Q32—371no—
158SD32—371no—
159SD32—371no—
160SD32—372no—
161SD32C2×D3712yescomplemented
162D16—372no—
163D16—371no—
164D16—372no—
165D16—372no—
166D16C2×D3712yescomplemented
167M32—372no—
168M32C2×D3711yescharacteristic, complemented
169C2×C16—371no—
170C2×C16—372no—
171#41—21no—
172#41—371no—
173#41—742no—
174#41—742no—
175#41—741no—
176#41—1481no—
177#41—1481no—
178C2×D4—21no—
179C2×D4—742no—
180C2×D4—742no—
181C2×D4—741no—
182C2×D4—1481no—
183C2×D4—1482no—
184C2×D4—1481no—
185C2×D4—1482no—
186Q16—371no—
187Q16C22×D3711yescharacteristic
188SD16—21no—
189SD16—742no—
190SD16—742no—
191SD16—741no—
192D8—21no—
193D8—372no—
194D8—371no—
195D8—742no—
196D8—742no—
197D8—741no—
198D8C22×D3712yes—
199D8C22×D3711yescharacteristic
200M16—371no—
201M16—372no—
202C2×C8—372no—
203C2×C8C22×D3711yescharacteristic
204C16—371no—
205C16—371no—
206C16C22×D3712yes—
207C23—41no—
208C23—1482no—
209C23—1482no—
210C23—1481no—
211Q8—21no—
212Q8—371no—
213Q8—741no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—372no—
219D4—371no—
220D4—741no—
221D4—742no—
222D4—1482no—
223D4—1482no—
224D4—1482no—
225D4—1482no—
226D4—1481no—
227D4—1481no—
228C2×C4—41no—
229C2×C4—372no—
230C2×C4—1482no—
231C2×C4—1482no—
232C2×C4—1481no—
233C2×C4D4×D3711yescharacteristic
234C8—372no—
235C8D4×D3711yescharacteristic
236C8C23×D3711yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—372no—
241C22—5921no—
242C22—5922no—
243C22—5922no—
244C22—1482no—
245C22—1481no—
246C22D8×D3711yescharacteristic
247C4—41no—
248C4—372no—
249C4—1481no—
250C4D8×D3711yescharacteristic
251C4C2×D4×D3711yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—2962no—
256C2—2961no—
257C2—742no—
258C2C2×D8×D3711yescharacteristic
subgroupG/H
centerC2C2×D8×D37
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC37×#509C2
socleC2×C37C22×D8
hypercenter#509D37
hypocenterC37#3415
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #14558335C2semidirect
2. #14558334C2semidirect
3. #14557971C2semidirect
4. #14557970C2semidirect
5. #14557967C2semidirect
6. #14557964C2semidirect
7. #14557963C2semidirect
8. C2×#11924477C2semidirect
9. D16×D37C2semidirect
10. #14557951C2semidirect
11. C37×#509C2semidirect
18. #11924559C22semidirect
19. #11924558C22semidirect
20. #11924555C22semidirect
21. C2×D296C22semidirect
22. D8×D37C22semidirect
23. D8×D37C22semidirect
25. #11924482C22semidirect
26. #11924481C22semidirect
27. #11924480C22semidirect
28. #11924479C22semidirect
29. D592C22semidirect
30. #11924477C22semidirect
31. #11924477C22semidirect
32. #11924477C22semidirect
33. #11924475C22semidirect
34. C2×#10596925C22semidirect
35. C16×D37C22semidirect
36. #135×C37C22semidirect
37. C2×D8×C37C22semidirect
38. SD32×C37C22semidirect
39. D16×C37C22semidirect
40. M32×C37C22semidirect
135. #509D37semidirect
141. C37#3415semidirect
151. #135C2×D37semidirect
155. C2×D8C2×D37semidirect
161. SD32C2×D37semidirect
166. D16C2×D37semidirect
168. M32C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583352
#145583342
#145579712
#145579702
#145579672
#145579642
#145579632
C2×#119244772
D16×D372
#145579512
C37×#5092
#341537