Finite Group Databasebeta

← #14576777

Subgroups — #14576777

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#11927357C211yesmaximal, characteristic, complemented
2#11927345C211yesmaximal, characteristic, complemented
3#11926985C211yesmaximal, characteristic, complemented
4#11926983C212yesmaximal, complemented
5#11926981C212yesmaximal, complemented
6#11926980C211yesmaximal, characteristic, complemented
7#11926976C211yesmaximal, characteristic, complemented
8#11926975C212yesmaximal, complemented
9SD32×D19C212yesmaximal, complemented
10#11926960C211yesmaximal, characteristic, complemented
11C2×C19×SD32C211yesmaximal, characteristic, complemented
12#10597433—21no—
13#10597430—21no—
14C2×Q16×C19C2211yescharacteristic, complemented
15C2×D8×C19C2211yescharacteristic
16#10597388—21no—
17#10597378—21no—
18#10597365C2212yescomplemented
19#10597364—22no—
20Q16×D19C2212yescomplemented
21#10597358C2212yes—
22#10597357—22no—
23D8×D19C2212yes—
24#10597350C2211yescharacteristic
25#10597350C2211yescharacteristic, complemented
26#10597347C2211yescharacteristic
27C19×SD32C2212yescomplemented
28C19×SD32C2212yescomplemented
29C2×C16×C19C2211yescharacteristic, complemented
30#10597286C2212yescomplemented
31#10597285C2212yescomplemented
32#10597284C2212yescomplemented
33#10597283C2212yescomplemented
34#10597269C2211yescharacteristic, complemented
35Dic152C2211yescharacteristic, complemented
36#10597257C2211yescharacteristic, complemented
37#10597257C2211yescharacteristic, complemented
38D304C2211yescharacteristic, complemented
39#10597255C2212yescomplemented
40C16×D19C2212yescomplemented
41C2×Q8×C19—21no—
42C2×D4×C19—21no—
43C2×C22⋊D19—42no—
44#64545—22no—
45#64545—41no—
46Q8×D19—22no—
47Q8×D19—41no—
48#64543—22no—
49#64543—41no—
50D4×D19—22no—
51D4×D19—41no—
52#64541—21no—
53#64541—21no—
54#64541—42no—
55#64541D411yescharacteristic
56Q16×C19—21no—
57Q16×C19C2312yes—
58D8×C19—21no—
59D8×C19C2312yes—
60C2×C8×C19C2311yescharacteristic
61#64528—22no—
62#64527—22no—
63#64526—22no—
64#64525—22no—
65#64520D411yescharacteristic
66Dic76C2311yescharacteristic
67Dic76C2311yescharacteristic
68D152C2311yescharacteristic
69D152C2311yescharacteristic
70#64516—21no—
71#64516—21no—
72#64515D412yes—
73C8×D19C2312yes—
74C16×C19C2311yescharacteristic
75C16×C19C2311yescharacteristic
76C19⋊C16C2312yes—
77C23×C19—41no—
78C22×D19—42no—
79Q8×C19—22no—
80Q8×C19—41no—
81D4×C19—22no—
82D4×C19—41no—
83C2×C4×C19—41no—
84C2×C4×C19C2×D411yescharacteristic
85C22⋊D19—41no—
86C22⋊D19—41no—
87C22⋊D19—42no—
88C22⋊D19—42no—
89C22⋊D19D812yes—
90C2×Dic19—42no—
91D76—21no—
92D76—21no—
93D76—42no—
94D76D811yescharacteristic
95C4×D19—42no—
96C4×D19—41no—
97C4×D19—41no—
98C4×D19—42no—
99C4×D19C2×D412yes—
100Dic38—21no—
101Dic38—21no—
102Dic38—42no—
103Dic38D811yescharacteristic
104C8×C19C2×D411yescharacteristic
105C8×C19C2411yescharacteristic
106C19⋊C8C2×D412yes—
107#3416—191nomaximal, Sylow
108C22×C19—42no—
109C22×C19—161no—
110C22×C19C2×D811yescharacteristic
111C2×D19—41no—
112C2×D19—41no—
113C2×D19—162no—
114C2×D19C2×D812yes—
115C4×C19—42no—
116C4×C19C2×D811yescharacteristic
117C4×C19C22×D411yescharacteristic
118Dic19—41no—
119Dic19—41no—
120Dic19C2×D812yes—
121#578—191no—
122#576—191no—
123#510—191no—
124#510—192no—
125#509—191no—
126#509—192no—
127#508—192no—
128#508—191no—
129C2×SD32—192no—
130C2×SD32D1911yescharacteristic, complemented
131#504—191no—
132C2×C19—21no—
133C2×C19—82no—
134C2×C19C22×D811yescharacteristic
135D19—22no—
136D19—81no—
137D19—81no—
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#135—191no—
147#135—191no—
148C2×Q16—192no—
149C2×Q16C2×D1911yescharacteristic, complemented
150C2×D8—192no—
151C2×D8C2×D1911yescharacteristic
152#131—191no—
153Q32—192no—
154Q32—191no—
155SD32—192no—
156SD32—192no—
157SD32—191no—
158SD32—191no—
159SD32C2×D1912yescomplemented
160SD32C2×D1912yescomplemented
161D16—192no—
162D16—191no—
163M32—191no—
164M32—192no—
165C2×C16—192no—
166C2×C16C2×D1911yescharacteristic, complemented
167C19#341611yescharacteristic, complemented, Sylow
168#41—191no—
169#41—382no—
170#41—382no—
171#41—381no—
172#41—381no—
173#41—762no—
174#41—761no—
175#41—761no—
176C2×Q8—21no—
177C2×Q8—382no—
178C2×Q8—761no—
179C2×D4—21no—
180C2×D4—382no—
181C2×D4—761no—
182C2×D4—762no—
183Q16—21no—
184Q16—191no—
185Q16—191no—
186Q16—382no—
187Q16C22×D1912yes—
188SD16—382no—
189SD16—382no—
190SD16—381no—
191SD16—381no—
192D8—21no—
193D8—191no—
194D8—191no—
195D8—382no—
196D8C22×D1912yes—
197M16—191no—
198M16—192no—
199C2×C8—192no—
200C2×C8C22×D1911yescharacteristic
201C16—192no—
202C16C22×D1911yescharacteristic
203C16C22×D1911yescharacteristic
204C23—41no—
205C23—762no—
206Q8—22no—
207Q8—41no—
208Q8—191no—
209Q8—381no—
210Q8—381no—
211Q8—762no—
212D4—22no—
213D4—41no—
214D4—192no—
215D4—191no—
216D4—381no—
217D4—381no—
218D4—762no—
219D4—762no—
220D4—762no—
221D4—761no—
222D4—761no—
223C2×C4—41no—
224C2×C4—192no—
225C2×C4—762no—
226C2×C4—762no—
227C2×C4—762no—
228C2×C4—761no—
229C2×C4—761no—
230C2×C4D4×D1911yescharacteristic
231C8—192no—
232C8D4×D1911yescharacteristic
233C8C23×D1911yescharacteristic
234C22—42no—
235C22—161no—
236C22—192no—
237C22—3042no—
238C22—761no—
239C22—761no—
240C22D8×D1911yescharacteristic
241C4—42no—
242C4—192no—
243C4—761no—
244C4—761no—
245C4D8×D1911yescharacteristic
246C4C2×D4×D1911yescharacteristic
247C2—21no—
248C2—82no—
249C2—382no—
250C2—1521no—
251C2—1521no—
252C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC2C2×D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC2×C19×SD32C2
socleC2×C19C22×D8
hypercenterC2×SD32D19
hypocenterC19#3416
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #11927357C2semidirect
2. #11927345C2semidirect
3. #11926985C2semidirect
4. #11926983C2semidirect
5. #11926981C2semidirect
6. #11926980C2semidirect
7. #11926976C2semidirect
8. #11926975C2semidirect
9. SD32×D19C2semidirect
10. #11926960C2semidirect
11. C2×C19×SD32C2semidirect
14. C2×Q16×C19C22semidirect
18. #10597365C22semidirect
20. Q16×D19C22semidirect
25. #10597350C22semidirect
27. C19×SD32C22semidirect
28. C19×SD32C22semidirect
29. C2×C16×C19C22semidirect
30. #10597286C22semidirect
31. #10597285C22semidirect
32. #10597284C22semidirect
33. #10597283C22semidirect
34. #10597269C22semidirect
35. Dic152C22semidirect
36. #10597257C22semidirect
37. #10597257C22semidirect
38. D304C22semidirect
39. #10597255C22semidirect
40. C16×D19C22semidirect
130. C2×SD32D19semidirect
149. C2×Q16C2×D19semidirect
159. SD32C2×D19semidirect
160. SD32C2×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
#119273572
#119273452
#119269852
#119269832
#119269812
#119269802
#119269762
#119269752
SD32×D192
#119269602
C2×C19×SD322
#341619