Finite Group Databasebeta

← #18007738

Subgroups — #18007738

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#14558346C211yesmaximal, characteristic, complemented
2#14558334C211yesmaximal, characteristic, complemented
3#14557974C211yesmaximal, characteristic, complemented
4#14557972C212yesmaximal, complemented
5#14557970C212yesmaximal, complemented
6#14557969C211yesmaximal, characteristic, complemented
7#14557965C211yesmaximal, characteristic, complemented
8#14557964C212yesmaximal, complemented
9SD32×D37C212yesmaximal, complemented
10#14557949C211yesmaximal, characteristic, complemented
11C2×SD32×C37C211yesmaximal, characteristic, complemented
12#11924584—21no—
13#11924581—21no—
14#11924568—22no—
15#11924567—21no—
16#11924562—21no—
17#11924560—22no—
18#11924559C2212yescomplemented
19#11924558C2211yescharacteristic
20#11924558C2211yescharacteristic, complemented
21#11924555C2212yes—
22Q16×D37C2212yescomplemented
23D8×D37C2212yes—
24#11924542C2211yescharacteristic
25Dic296C2211yescharacteristic, complemented
26#11924482C2212yescomplemented
27#11924481C2211yescharacteristic, complemented
28#11924481C2211yescharacteristic, complemented
29#11924480C2212yescomplemented
30#11924479C2212yescomplemented
31D592C2211yescharacteristic, complemented
32#11924477C2212yescomplemented
33#11924476C2211yescharacteristic, complemented
34#11924475C2212yescomplemented
35C16×D37C2212yescomplemented
36C2×Q16×C37C2211yescharacteristic, complemented
37C2×D8×C37C2211yescharacteristic
38SD32×C37C2212yescomplemented
39SD32×C37C2212yescomplemented
40C2×C16×C37C2211yescharacteristic, complemented
41C2×Q8×C37—21no—
42C2×D4×C37—21no—
43C2×C22⋊D37—42no—
44#10596966—22no—
45#10596966—41no—
46Q8×D37—22no—
47Q8×D37—41no—
48#10596964—22no—
49#10596964—41no—
50D4×D37—22no—
51D4×D37—41no—
52#10596962—21no—
53#10596962—21no—
54#10596962—42no—
55#10596962D411yescharacteristic
56Q16×C37—21no—
57Q16×C37C2312yes—
58D8×C37—21no—
59D8×C37C2312yes—
60C2×C8×C37C2311yescharacteristic
61#10596942—22no—
62#10596941—22no—
63#10596940—22no—
64#10596939—22no—
65#10596934D411yescharacteristic
66Dic148C2311yescharacteristic
67Dic148C2311yescharacteristic
68D296C2311yescharacteristic
69D296C2311yescharacteristic
70#10596930—21no—
71#10596930—21no—
72#10596929D412yes—
73C8×D37C2312yes—
74C16×C37C2311yescharacteristic
75C16×C37C2311yescharacteristic
76#10596925C2312yes—
77C23×C37—41no—
78C22×D37—42no—
79Q8×C37—22no—
80Q8×C37—41no—
81D4×C37—22no—
82D4×C37—41no—
83C2×C4×C37—41no—
84C2×C4×C37C2×D411yescharacteristic
85C22⋊D37—41no—
86C22⋊D37—41no—
87C22⋊D37—42no—
88C22⋊D37—42no—
89C22⋊D37D812yes—
90C2×Dic37—42no—
91D148—21no—
92D148—21no—
93D148—42no—
94D148D811yescharacteristic
95C4×D37—42no—
96C4×D37—41no—
97C4×D37—41no—
98C4×D37—42no—
99C4×D37C2×D412yes—
100Dic74—21no—
101Dic74—21no—
102Dic74—42no—
103Dic74D811yescharacteristic
104C8×C37C2×D411yescharacteristic
105C8×C37C2411yescharacteristic
106#64436C2×D412yes—
107C22×C37—42no—
108C22×C37—161no—
109C22×C37C2×D811yescharacteristic
110C2×D37—41no—
111C2×D37—41no—
112C2×D37—162no—
113C2×D37C2×D812yes—
114C4×C37—42no—
115C4×C37C2×D811yescharacteristic
116C4×C37C22×D411yescharacteristic
117Dic37—41no—
118Dic37—41no—
119Dic37C2×D812yes—
120#3416—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—82no—
123C2×C37C22×D811yescharacteristic
124D37—22no—
125D37—81no—
126D37—81no—
127#578—371no—
128#576—371no—
129#510—371no—
130#510—372no—
131#509—371no—
132#509—372no—
133#508—372no—
134#508—371no—
135C2×SD32—372no—
136C2×SD32D3711yescharacteristic, complemented
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#135—371no—
149C2×Q16—372no—
150C2×Q16C2×D3711yescharacteristic, complemented
151C2×D8—372no—
152C2×D8C2×D3711yescharacteristic
153#131—371no—
154Q32—372no—
155Q32—371no—
156SD32—372no—
157SD32—372no—
158SD32—371no—
159SD32—371no—
160SD32C2×D3712yescomplemented
161SD32C2×D3712yescomplemented
162D16—372no—
163D16—371no—
164M32—371no—
165M32—372no—
166C2×C16—372no—
167C2×C16C2×D3711yescharacteristic, complemented
168#41—371no—
169#41—742no—
170#41—742no—
171#41—741no—
172#41—741no—
173#41—1482no—
174#41—1481no—
175#41—1481no—
176C2×Q8—21no—
177C2×Q8—742no—
178C2×Q8—1481no—
179C2×D4—21no—
180C2×D4—742no—
181C2×D4—1481no—
182C2×D4—1482no—
183Q16—21no—
184Q16—371no—
185Q16—371no—
186Q16—742no—
187Q16C22×D3712yes—
188SD16—742no—
189SD16—742no—
190SD16—741no—
191SD16—741no—
192D8—21no—
193D8—371no—
194D8—371no—
195D8—742no—
196D8C22×D3712yes—
197M16—371no—
198M16—372no—
199C2×C8—372no—
200C2×C8C22×D3711yescharacteristic
201C16—372no—
202C16C22×D3711yescharacteristic
203C16C22×D3711yescharacteristic
204C23—41no—
205C23—1482no—
206Q8—22no—
207Q8—41no—
208Q8—371no—
209Q8—741no—
210Q8—741no—
211Q8—1482no—
212D4—22no—
213D4—41no—
214D4—372no—
215D4—371no—
216D4—741no—
217D4—741no—
218D4—1482no—
219D4—1482no—
220D4—1482no—
221D4—1481no—
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—42no—
235C22—161no—
236C22—372no—
237C22—5922no—
238C22—1481no—
239C22—1481no—
240C22D8×D3711yescharacteristic
241C4—42no—
242C4—372no—
243C4—1481no—
244C4—1481no—
245C4D8×D3711yescharacteristic
246C4C2×D4×D3711yescharacteristic
247C2—21no—
248C2—82no—
249C2—2961no—
250C2—2961no—
251C2—742no—
252C2C2×D8×D3711yescharacteristic
subgroupG/H
centerC2C2×D8×D37
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC2×SD32×C37C2
socleC2×C37C22×D8
hypercenterC2×SD32D37
hypocenterC37#3416
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #14558346C2semidirect
2. #14558334C2semidirect
3. #14557974C2semidirect
4. #14557972C2semidirect
5. #14557970C2semidirect
6. #14557969C2semidirect
7. #14557965C2semidirect
8. #14557964C2semidirect
9. SD32×D37C2semidirect
10. #14557949C2semidirect
11. C2×SD32×C37C2semidirect
18. #11924559C22semidirect
20. #11924558C22semidirect
22. Q16×D37C22semidirect
25. Dic296C22semidirect
26. #11924482C22semidirect
27. #11924481C22semidirect
28. #11924481C22semidirect
29. #11924480C22semidirect
30. #11924479C22semidirect
31. D592C22semidirect
32. #11924477C22semidirect
33. #11924476C22semidirect
34. #11924475C22semidirect
35. C16×D37C22semidirect
36. C2×Q16×C37C22semidirect
38. SD32×C37C22semidirect
39. SD32×C37C22semidirect
40. C2×C16×C37C22semidirect
136. C2×SD32D37semidirect
138. C37#3416semidirect
150. C2×Q16C2×D37semidirect
160. SD32C2×D37semidirect
161. SD32C2×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
#145583462
#145583342
#145579742
#145579722
#145579702
#145579692
#145579652
#145579642
SD32×D372
#145579492
C2×SD32×C372
#341637