Finite Group Databasebeta

← #14576778

Subgroups — #14576778

Order 2432.

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#11927358C211yesmaximal, characteristic, complemented
2#11927346C211yesmaximal, characteristic, complemented
3#11926986C212yesmaximal, complemented
4#11926984C211yesmaximal, characteristic, complemented
5#11926979C211yesmaximal, characteristic, complemented
6#11926978C212yesmaximal, complemented
7#11926975C212yesmaximal, complemented
8C2×#10597257C211yesmaximal, characteristic, complemented
9SD32×D19C212yesmaximal, complemented
10#11926960C211yesmaximal, characteristic, complemented
11C19×#508C211yesmaximal, characteristic, complemented
12#10597436—21no—
13#10597435—21no—
14C19×#135C2211yescharacteristic
15C19×#135C2211yescharacteristic, complemented
16#10597397—21no—
17#10597395—21no—
18#10597365C2212yes—
19Q16×D19C2212yescomplemented
20#10597361—22no—
21#10597360—22no—
22#10597358C2212yescomplemented
23D8×D19C2212yes—
24C2×Dic76C2211yescharacteristic, complemented
25C2×D152C2211yescharacteristic
26#10597347C2211yescharacteristic
27C19×Q32C2211yescharacteristic, complemented
28C19×SD32C2211yescharacteristic, complemented
29C19×SD32C2211yescharacteristic, complemented
30C19×D16C2211yescharacteristic, complemented
31C2×C16×C19C2211yescharacteristic, complemented
32#10597286C2212yescomplemented
33#10597285C2212yescomplemented
34#10597284C2212yescomplemented
35#10597283C2212yescomplemented
36#10597269C2211yescharacteristic, complemented
37#10597257C2212yescomplemented
38#10597257C2212yescomplemented
39#10597255C2212yescomplemented
40C16×D19C2212yescomplemented
41#41×C19—21no—
42#41×C19—21no—
43#64545—22no—
44Q8×D19—22no—
45#64543—22no—
46#64543—42no—
47D4×D19—22no—
48D4×D19—42no—
49#64541—41no—
50#64541—41no—
51#64541D411yescharacteristic
52C2×D76—21no—
53C2×D76—41no—
54C2×Dic38—21no—
55C2×Dic38—41no—
56Q16×C19C2311yescharacteristic
57Q16×C19C2311yescharacteristic
58SD16×C19—21no—
59SD16×C19—21no—
60D8×C19C2311yescharacteristic
61D8×C19C2311yescharacteristic
62C2×C8×C19C2311yescharacteristic
63#64528—22no—
64#64527—22no—
65#64526—22no—
66#64525—22no—
67#64520D411yescharacteristic
68Dic76—21no—
69Dic76C2312yes—
70D152—21no—
71D152C2312yes—
72#64515D412yes—
73C8×D19C2312yes—
74C16×C19C2311yescharacteristic
75C16×C19C2311yescharacteristic
76C19⋊C16C2312yes—
77C22×D19—41no—
78C22×D19—42no—
79Q8×C19—21no—
80Q8×C19—21no—
81D4×C19—21no—
82D4×C19—21no—
83D4×C19—41no—
84D4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19—41no—
87C2×C4×C19C2×D411yescharacteristic
88C22⋊D19—42no—
89C22⋊D19—42no—
90C22⋊D19D812yes—
91C2×Dic19—41no—
92C2×Dic19—42no—
93D76—22no—
94D76—42no—
95D76—41no—
96D76D811yescharacteristic
97C4×D19—42no—
98C4×D19—42no—
99C4×D19C2×D412yes—
100Dic38—22no—
101Dic38—41no—
102Dic38—42no—
103Dic38D811yescharacteristic
104C8×C19C2×D411yescharacteristic
105C8×C19C2411yescharacteristic
106C19⋊C8C2×D412yes—
107#3416—191nomaximal, Sylow
108C22×C19—41no—
109C22×C19—41no—
110C22×C19C2×D811yescharacteristic
111C2×D19—42no—
112C2×D19—162no—
113C2×D19—161no—
114C2×D19C2×D812yes—
115C4×C19—41no—
116C4×C19—41no—
117C4×C19C2×D811yescharacteristic
118C4×C19C22×D411yescharacteristic
119Dic19—42no—
120Dic19C2×D812yes—
121#578—191no—
122#576—191no—
123#510—191no—
124#510—192no—
125#509—191no—
126#509—192no—
127#508—192no—
128#508D1911yescharacteristic, complemented
129C2×SD32—192no—
130C2×SD32—191no—
131#504—191no—
132C2×C19—21no—
133C2×C19—81no—
134C2×C19—81no—
135C2×C19C22×D811yescharacteristic
136D19—22no—
137D19—82no—
1382−1+4—381no—
139H(5,𝔽2)—381no—
140#137—382no—
141#137—381no—
142AGL(1,ℤ/8)—382no—
143AGL(1,ℤ/8)—381no—
144#135—192no—
145#135—192no—
146#135C2×D1911yescharacteristic
147#135C2×D1911yescharacteristic, complemented
148C2×Q16—192no—
149C2×Q16—191no—
150C2×D8—192no—
151C2×D8—191no—
152#131—191no—
153Q32—192no—
154Q32C2×D1911yescharacteristic, complemented
155SD32—192no—
156SD32—192no—
157SD32—192no—
158SD32—192no—
159SD32C2×D1911yescharacteristic, complemented
160SD32C2×D1911yescharacteristic, complemented
161D16—192no—
162D16C2×D1911yescharacteristic, complemented
163M32—191no—
164M32—192no—
165C2×C16—192no—
166C2×C16C2×D1911yescharacteristic, complemented
167C19#341611yescharacteristic, complemented, Sylow
168#41—21no—
169#41—21no—
170#41—191no—
171#41—382no—
172#41—382no—
173#41—761no—
174#41—761no—
175#41—762no—
176C2×Q8—382no—
177C2×Q8—381no—
178C2×Q8—761no—
179C2×D4—382no—
180C2×D4—381no—
181C2×D4—761no—
182C2×D4—762no—
183Q16—192no—
184Q16—382no—
185Q16—381no—
186Q16C22×D1911yescharacteristic
187Q16C22×D1911yescharacteristic
188SD16—21no—
189SD16—21no—
190SD16—382no—
191SD16—382no—
192D8—192no—
193D8—382no—
194D8—381no—
195D8C22×D1911yescharacteristic
196D8C22×D1911yescharacteristic
197M16—191no—
198M16—192no—
199C2×C8—192no—
200C2×C8C22×D1911yescharacteristic
201C16—192no—
202C16C22×D1911yescharacteristic
203C16C22×D1911yescharacteristic
204C23—762no—
205C23—761no—
206Q8—21no—
207Q8—21no—
208Q8—191no—
209Q8—382no—
210Q8—762no—
211Q8—761no—
212D4—21no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—192no—
217D4—191no—
218D4—382no—
219D4—762no—
220D4—762no—
221D4—762no—
222D4—761no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—192no—
226C2×C4—762no—
227C2×C4—762no—
228C2×C4—762no—
229C2×C4—761no—
230C2×C4D4×D1911yescharacteristic
231C8—192no—
232C8D4×D1911yescharacteristic
233C8C23×D1911yescharacteristic
234C22—41no—
235C22—41no—
236C22—192no—
237C22—3041no—
238C22—3042no—
239C22—762no—
240C22D8×D1911yescharacteristic
241C4—41no—
242C4—41no—
243C4—192no—
244C4—762no—
245C4D8×D1911yescharacteristic
246C4C2×D4×D1911yescharacteristic
247C2—21no—
248C2—81no—
249C2—81no—
250C2—382no—
251C2—1522no—
252C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC2C2×D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC19×#508C2
socleC2×C19C22×D8
hypercenter#508D19
hypocenterC19#3416
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #11927358C2semidirect
2. #11927346C2semidirect
3. #11926986C2semidirect
4. #11926984C2semidirect
5. #11926979C2semidirect
6. #11926978C2semidirect
7. #11926975C2semidirect
8. C2×#10597257C2semidirect
9. SD32×D19C2semidirect
10. #11926960C2semidirect
11. C19×#508C2semidirect
15. C19×#135C22semidirect
19. Q16×D19C22semidirect
22. #10597358C22semidirect
24. C2×Dic76C22semidirect
27. C19×Q32C22semidirect
28. C19×SD32C22semidirect
29. C19×SD32C22semidirect
30. C19×D16C22semidirect
31. C2×C16×C19C22semidirect
32. #10597286C22semidirect
33. #10597285C22semidirect
34. #10597284C22semidirect
35. #10597283C22semidirect
36. #10597269C22semidirect
37. #10597257C22semidirect
38. #10597257C22semidirect
39. #10597255C22semidirect
40. C16×D19C22semidirect
128. #508D19semidirect
147. #135C2×D19semidirect
154. Q32C2×D19semidirect
159. SD32C2×D19semidirect
160. SD32C2×D19semidirect
162. D16C2×D19semidirect
166. C2×C16C2×D19semidirect
167. C19#3416semidirect

Maximal subgroups

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

subgroupindex
#119273582
#119273462
#119269862
#119269842
#119269792
#119269782
#119269752
C2×#105972572
SD32×D192
#119269602
C19×#5082
#341619