Finite Group Databasebeta

← #18007742

Subgroups — #18007742

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#14558334C211yesmaximal, characteristic, complemented
3#14557976C211yesmaximal, characteristic, complemented
4#14557972C212yesmaximal, complemented
5#14557967C212yesmaximal, complemented
6#14557963C211yesmaximal, characteristic, complemented
7#14557962C212yesmaximal, complemented
8C2×#11924480C211yesmaximal, characteristic, complemented
9SD32×D37C212yesmaximal, complemented
10#14557951C211yesmaximal, characteristic, complemented
11C37×#509C211yesmaximal, characteristic, complemented
12#11924583—21no—
13#11924581—21no—
14#11924566—21no—
15#11924565—22no—
16#11924562—21no—
17#11924560—22no—
18#11924558C2211yescharacteristic
19#11924555C2212yes—
20#11924555C2212yescomplemented
21C2×Dic148C2211yescharacteristic, complemented
22Q16×D37C2212yescomplemented
23D8×D37C2212yes—
24#11924542C2211yescharacteristic
25Dic296C2212yescomplemented
26#11924482C2211yescharacteristic, complemented
27#11924481C2212yescomplemented
28#11924480C2212yescomplemented
29#11924480C2212yescomplemented
30#11924480C2211yescharacteristic, complemented
31#11924479C2211yescharacteristic, complemented
32#11924477C2211yescharacteristic, complemented
33#11924475C2212yescomplemented
34C2×#10596925C2211yescharacteristic, complemented
35C16×D37C2212yescomplemented
36#135×C37C2211yescharacteristic, complemented
37C2×D8×C37C2211yescharacteristic
38SD32×C37C2212yescomplemented
39D16×C37C2212yescomplemented
40M32×C37C2211yescharacteristic, complemented
41#41×C37—21no—
42C2×D4×C37—21no—
43C2×C22⋊D37—42no—
44Q8×D37—22no—
45#10596964—22no—
46#10596964—22no—
47#10596964—42no—
48#10596964—41no—
49D4×D37—22no—
50D4×D37—41no—
51#10596962—21no—
52#10596962—41no—
53#10596962D411yescharacteristic
54C2×Dic74—21no—
55C2×Dic74—41no—
56Q16×C37C2311yescharacteristic
57SD16×C37—21no—
58D8×C37—21no—
59D8×C37C2312yes—
60D8×C37C2311yescharacteristic
61C2×C8×C37C2311yescharacteristic
62#10596942—22no—
63#10596940—22no—
64#10596940—22no—
65#10596939—22no—
66#10596934D411yescharacteristic
67Dic148—21no—
68Dic148C2312yes—
69Dic148C2311yescharacteristic
70D296C2311yescharacteristic
71#10596930—21no—
72#10596929D412yes—
73C8×D37C2312yes—
74C16×C37C2312yes—
75#10596925C2311yescharacteristic
76#10596925C2311yescharacteristic
77C23×C37—41no—
78C22×D37—42no—
79Q8×C37—21no—
80D4×C37—22no—
81D4×C37—21no—
82D4×C37—41no—
83D4×C37—41no—
84C2×C4×C37—41no—
85C2×C4×C37C2×D411yescharacteristic
86C22⋊D37—41no—
87C22⋊D37—42no—
88C22⋊D37—42no—
89C22⋊D37—42no—
90C22⋊D37D812yes—
91C2×Dic37—41no—
92C2×Dic37—42no—
93C2×Dic37—42no—
94D148—21no—
95D148D811yescharacteristic
96C4×D37—42no—
97C4×D37—41no—
98C4×D37C2×D412yes—
99Dic74—21no—
100Dic74—22no—
101Dic74—41no—
102Dic74—42no—
103Dic74D811yescharacteristic
104C8×C37C2×D411yescharacteristic
105C8×C37C2411yescharacteristic
106#64436C2×D412yes—
107C22×C37—41no—
108C22×C37—42no—
109C22×C37—161no—
110C22×C37C2×D811yescharacteristic
111C2×D37—41no—
112C2×D37—162no—
113C2×D37C2×D812yes—
114C4×C37—41no—
115C4×C37C2×D811yescharacteristic
116C4×C37C22×D411yescharacteristic
117Dic37—42no—
118Dic37—41no—
119Dic37C2×D812yes—
120#3416—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—82no—
123C2×C37—81no—
124C2×C37C22×D811yescharacteristic
125D37—22no—
126D37—81no—
127#578—371no—
128#576—371no—
129#510—372no—
130#510—371no—
131#509—372no—
132#509D3711yescharacteristic, complemented
133#508—371no—
134#508—372no—
135C2×SD32—371no—
136C2×SD32—372no—
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#135—371no—
148#135C2×D3711yescharacteristic, complemented
149C2×Q16—372no—
150C2×Q16—371no—
151C2×D8—372no—
152C2×D8C2×D3711yescharacteristic
153#131—371no—
154Q32—371no—
155Q32—372no—
156SD32—371no—
157SD32—372no—
158SD32—372no—
159SD32—371no—
160SD32—372no—
161SD32C2×D3712yescomplemented
162D16—371no—
163D16C2×D3712yescomplemented
164M32—372no—
165M32C2×D3711yescharacteristic, complemented
166C2×C16—371no—
167C2×C16—372no—
168#41—21no—
169#41—371no—
170#41—742no—
171#41—742no—
172#41—741no—
173#41—1481no—
174#41—1482no—
175#41—1481no—
176C2×Q8—742no—
177C2×Q8—741no—
178C2×Q8—1481no—
179C2×D4—21no—
180C2×D4—742no—
181C2×D4—1481no—
182C2×D4—1482no—
183Q16—372no—
184Q16—371no—
185Q16—742no—
186Q16—741no—
187Q16C22×D3711yescharacteristic
188SD16—21no—
189SD16—742no—
190SD16—742no—
191SD16—741no—
192D8—21no—
193D8—371no—
194D8—742no—
195D8C22×D3711yescharacteristic
196D8C22×D3712yes—
197M16—371no—
198M16—372no—
199C2×C8—372no—
200C2×C8C22×D3711yescharacteristic
201C16—371no—
202C16—371no—
203C16C22×D3712yes—
204C23—41no—
205C23—1482no—
206Q8—21no—
207Q8—371no—
208Q8—741no—
209Q8—742no—
210Q8—1482no—
211Q8—1481no—
212D4—22no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—372no—
217D4—371no—
218D4—741no—
219D4—1482no—
220D4—1482no—
221D4—1482no—
222D4—1481no—
223C2×C4—41no—
224C2×C4—372no—
225C2×C4—1482no—
226C2×C4—1482no—
227C2×C4—1482no—
228C2×C4—1481no—
229C2×C4—1481no—
230C2×C4D4×D3711yescharacteristic
231C8—372no—
232C8D4×D3711yescharacteristic
233C8C23×D3711yescharacteristic
234C22—41no—
235C22—42no—
236C22—161no—
237C22—372no—
238C22—5922no—
239C22—1481no—
240C22D8×D3711yescharacteristic
241C4—41no—
242C4—372no—
243C4—1481no—
244C4—1482no—
245C4D8×D3711yescharacteristic
246C4C2×D4×D3711yescharacteristic
247C2—21no—
248C2—82no—
249C2—81no—
250C2—2961no—
251C2—742no—
252C2C2×D8×D3711yescharacteristic
subgroupG/H
centerC2C2×D8×D37
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC37×#509C2
socleC2×C37C22×D8
hypercenter#509D37
hypocenterC37#3416
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. #14558347C2semidirect
2. #14558334C2semidirect
3. #14557976C2semidirect
4. #14557972C2semidirect
5. #14557967C2semidirect
6. #14557963C2semidirect
7. #14557962C2semidirect
8. C2×#11924480C2semidirect
9. SD32×D37C2semidirect
10. #14557951C2semidirect
11. C37×#509C2semidirect
20. #11924555C22semidirect
21. C2×Dic148C22semidirect
22. Q16×D37C22semidirect
25. Dic296C22semidirect
26. #11924482C22semidirect
27. #11924481C22semidirect
28. #11924480C22semidirect
29. #11924480C22semidirect
30. #11924480C22semidirect
31. #11924479C22semidirect
32. #11924477C22semidirect
33. #11924475C22semidirect
34. C2×#10596925C22semidirect
35. C16×D37C22semidirect
36. #135×C37C22semidirect
38. SD32×C37C22semidirect
39. D16×C37C22semidirect
40. M32×C37C22semidirect
132. #509D37semidirect
138. C37#3416semidirect
148. #135C2×D37semidirect
161. SD32C2×D37semidirect
163. D16C2×D37semidirect
165. M32C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583472
#145583342
#145579762
#145579722
#145579672
#145579632
#145579622
C2×#119244802
SD32×D372
#145579512
C37×#5092
#341637