Finite Group Databasebeta

← #18007739

Subgroups — #18007739

Order 4736.

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

normal subgroups only

This group has 360 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#14558347C211yesmaximal, characteristic, complemented
2#14558335C211yesmaximal, characteristic, complemented
3#14557975C212yesmaximal, complemented
4#14557973C211yesmaximal, characteristic, complemented
5#14557968C211yesmaximal, characteristic, complemented
6#14557967C212yesmaximal, complemented
7#14557964C212yesmaximal, complemented
8C2×#11924481C211yesmaximal, characteristic, complemented
9SD32×D37C212yesmaximal, complemented
10#14557949C211yesmaximal, characteristic, complemented
11C37×#508C211yesmaximal, characteristic, complemented
12#11924583—21no—
13#11924582—21no—
14#11924566—21no—
15#11924565—22no—
16#11924563—22no—
17#11924561—21no—
18#11924559C2212yes—
19#11924555C2212yescomplemented
20C2×Dic148C2211yescharacteristic, complemented
21Q16×D37C2212yescomplemented
22C2×D296C2211yescharacteristic
23D8×D37C2212yes—
24#11924542C2211yescharacteristic
25#11924482C2212yescomplemented
26#11924481C2212yescomplemented
27#11924481C2212yescomplemented
28#11924480C2212yescomplemented
29#11924479C2212yescomplemented
30#11924477C2212yescomplemented
31#11924476C2211yescharacteristic, complemented
32#11924475C2212yescomplemented
33C16×D37C2212yescomplemented
34#135×C37C2211yescharacteristic
35#135×C37C2211yescharacteristic, complemented
36Q32×C37C2211yescharacteristic, complemented
37SD32×C37C2211yescharacteristic, complemented
38SD32×C37C2211yescharacteristic, complemented
39D16×C37C2211yescharacteristic, complemented
40C2×C16×C37C2211yescharacteristic, complemented
41#41×C37—21no—
42#41×C37—21no—
43#10596966—22no—
44Q8×D37—22no—
45#10596964—22no—
46#10596964—42no—
47D4×D37—22no—
48D4×D37—42no—
49#10596962—41no—
50#10596962—41no—
51#10596962D411yescharacteristic
52C2×D148—21no—
53C2×D148—41no—
54C2×Dic74—21no—
55C2×Dic74—41no—
56Q16×C37C2311yescharacteristic
57Q16×C37C2311yescharacteristic
58SD16×C37—21no—
59SD16×C37—21no—
60D8×C37C2311yescharacteristic
61D8×C37C2311yescharacteristic
62C2×C8×C37C2311yescharacteristic
63#10596942—22no—
64#10596941—22no—
65#10596940—22no—
66#10596939—22no—
67#10596934D411yescharacteristic
68Dic148—21no—
69Dic148C2312yes—
70D296—21no—
71D296C2312yes—
72#10596929D412yes—
73C8×D37C2312yes—
74C16×C37C2311yescharacteristic
75C16×C37C2311yescharacteristic
76#10596925C2312yes—
77C22×D37—41no—
78C22×D37—42no—
79Q8×C37—21no—
80Q8×C37—21no—
81D4×C37—21no—
82D4×C37—21no—
83D4×C37—41no—
84D4×C37—41no—
85C2×C4×C37—41no—
86C2×C4×C37—41no—
87C2×C4×C37C2×D411yescharacteristic
88C22⋊D37—42no—
89C22⋊D37—42no—
90C22⋊D37D812yes—
91C2×Dic37—41no—
92C2×Dic37—42no—
93D148—22no—
94D148—42no—
95D148—41no—
96D148D811yescharacteristic
97C4×D37—42no—
98C4×D37—42no—
99C4×D37C2×D412yes—
100Dic74—22no—
101Dic74—41no—
102Dic74—42no—
103Dic74D811yescharacteristic
104C8×C37C2×D411yescharacteristic
105C8×C37C2411yescharacteristic
106#64436C2×D412yes—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37C2×D811yescharacteristic
110C2×D37—42no—
111C2×D37—162no—
112C2×D37—161no—
113C2×D37C2×D812yes—
114C4×C37—41no—
115C4×C37—41no—
116C4×C37C2×D811yescharacteristic
117C4×C37C22×D411yescharacteristic
118Dic37—42no—
119Dic37C2×D812yes—
120#3416—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—81no—
123C2×C37—81no—
124C2×C37C22×D811yescharacteristic
125D37—22no—
126D37—82no—
127#578—371no—
128#576—371no—
129#510—371no—
130#510—372no—
131#509—371no—
132#509—372no—
133#508—372no—
134#508D3711yescharacteristic, complemented
135C2×SD32—372no—
136C2×SD32—371no—
137#504—371no—
138C37#341611yescharacteristic, complemented, Sylow
1392−1+4—741no—
140H(5,𝔽2)—741no—
141#137—742no—
142#137—741no—
143AGL(1,ℤ/8)—742no—
144AGL(1,ℤ/8)—741no—
145#135—372no—
146#135—372no—
147#135C2×D3711yescharacteristic
148#135C2×D3711yescharacteristic, complemented
149C2×Q16—372no—
150C2×Q16—371no—
151C2×D8—372no—
152C2×D8—371no—
153#131—371no—
154Q32—372no—
155Q32C2×D3711yescharacteristic, complemented
156SD32—372no—
157SD32—372no—
158SD32—372no—
159SD32—372no—
160SD32C2×D3711yescharacteristic, complemented
161SD32C2×D3711yescharacteristic, complemented
162D16—372no—
163D16C2×D3711yescharacteristic, complemented
164M32—371no—
165M32—372no—
166C2×C16—372no—
167C2×C16C2×D3711yescharacteristic, complemented
168#41—21no—
169#41—21no—
170#41—371no—
171#41—742no—
172#41—742no—
173#41—1481no—
174#41—1481no—
175#41—1482no—
176C2×Q8—742no—
177C2×Q8—741no—
178C2×Q8—1481no—
179C2×D4—742no—
180C2×D4—741no—
181C2×D4—1481no—
182C2×D4—1482no—
183Q16—372no—
184Q16—742no—
185Q16—741no—
186Q16C22×D3711yescharacteristic
187Q16C22×D3711yescharacteristic
188SD16—21no—
189SD16—21no—
190SD16—742no—
191SD16—742no—
192D8—372no—
193D8—742no—
194D8—741no—
195D8C22×D3711yescharacteristic
196D8C22×D3711yescharacteristic
197M16—371no—
198M16—372no—
199C2×C8—372no—
200C2×C8C22×D3711yescharacteristic
201C16—372no—
202C16C22×D3711yescharacteristic
203C16C22×D3711yescharacteristic
204C23—1482no—
205C23—1481no—
206Q8—21no—
207Q8—21no—
208Q8—371no—
209Q8—742no—
210Q8—1482no—
211Q8—1481no—
212D4—21no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—372no—
217D4—371no—
218D4—742no—
219D4—1482no—
220D4—1482no—
221D4—1482no—
222D4—1481no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—372no—
226C2×C4—1482no—
227C2×C4—1482no—
228C2×C4—1482no—
229C2×C4—1481no—
230C2×C4D4×D3711yescharacteristic
231C8—372no—
232C8D4×D3711yescharacteristic
233C8C23×D3711yescharacteristic
234C22—41no—
235C22—41no—
236C22—372no—
237C22—5921no—
238C22—5922no—
239C22—1482no—
240C22D8×D3711yescharacteristic
241C4—41no—
242C4—41no—
243C4—372no—
244C4—1482no—
245C4D8×D3711yescharacteristic
246C4C2×D4×D3711yescharacteristic
247C2—21no—
248C2—81no—
249C2—81no—
250C2—2962no—
251C2—742no—
252C2C2×D8×D3711yescharacteristic
subgroupG/H
centerC2C2×D8×D37
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC37×#508C2
socleC2×C37C22×D8
hypercenter#508D37
hypocenterC37#3416
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #14558347C2semidirect
2. #14558335C2semidirect
3. #14557975C2semidirect
4. #14557973C2semidirect
5. #14557968C2semidirect
6. #14557967C2semidirect
7. #14557964C2semidirect
8. C2×#11924481C2semidirect
9. SD32×D37C2semidirect
10. #14557949C2semidirect
11. C37×#508C2semidirect
19. #11924555C22semidirect
20. C2×Dic148C22semidirect
21. Q16×D37C22semidirect
25. #11924482C22semidirect
26. #11924481C22semidirect
27. #11924481C22semidirect
28. #11924480C22semidirect
29. #11924479C22semidirect
30. #11924477C22semidirect
31. #11924476C22semidirect
32. #11924475C22semidirect
33. C16×D37C22semidirect
35. #135×C37C22semidirect
36. Q32×C37C22semidirect
37. SD32×C37C22semidirect
38. SD32×C37C22semidirect
39. D16×C37C22semidirect
40. C2×C16×C37C22semidirect
134. #508D37semidirect
138. C37#3416semidirect
148. #135C2×D37semidirect
155. Q32C2×D37semidirect
160. SD32C2×D37semidirect
161. SD32C2×D37semidirect
163. D16C2×D37semidirect
167. C2×C16C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583472
#145583352
#145579752
#145579732
#145579682
#145579672
#145579642
C2×#119244812
SD32×D372
#145579492
C37×#5082
#341637