Finite Group Databasebeta

← #14576770

Subgroups — #14576770

Order 2432.

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

normal subgroups only

This group has 364 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
1C2×#10597365C211yesmaximal, characteristic, complemented
2#135×D19C211yesmaximal, characteristic, complemented
3#11926986C212yesmaximal, complemented
4#11926985C211yesmaximal, characteristic, complemented
5#11926982C211yesmaximal, characteristic, complemented
6#11926981C212yesmaximal, complemented
7#11926979C211yesmaximal, characteristic, complemented
8#11926977C212yesmaximal, complemented
9#11926975C212yesmaximal, complemented
10M32×D19C211yesmaximal, characteristic, complemented
11C19×#510C211yesmaximal, characteristic, complemented
12#41×D19—21no—
13C2×#64545—21no—
14C19×#135C2211yescharacteristic
15C2×Q16×C19C2211yescharacteristic, complemented
16#10597396—21no—
17C2×#64527—21no—
18#10597365—21no—
19#10597365—21no—
20#10597365C2212yes—
21#10597365C2211yescharacteristic, complemented
22#10597365C2212yescomplemented
23Q16×D19C2211yescharacteristic, complemented
24#10597362—21no—
25SD16×D19—21no—
26#10597358C2211yescharacteristic, complemented
27D8×D19C2211yescharacteristic, complemented
28#10597350C2211yescharacteristic
29C2×D152C2211yescharacteristic, complemented
30C2×C8×D19C2211yescharacteristic
31C19×Q32C2212yescomplemented
32C19×SD32C2212yescomplemented
33C19×M32C2211yescharacteristic, complemented
34#10597286C2212yescomplemented
35#10597285C2212yescomplemented
36#10597285C2212yescomplemented
37#10597283C2212yescomplemented
38#10597269C2211yescharacteristic, complemented
39#10597257C2212yescomplemented
40D304C2212yescomplemented
41#10597255C2212yescomplemented
42C16×D19C2212yescomplemented
43#41×C19—21no—
44C2×Q8×C19—21no—
45#64545—22no—
46#64545—22no—
47#64545—21no—
48#64545—41no—
49#64545—41no—
50Q8×D19—21no—
51#64543—21no—
52#64543—41no—
53D4×D19—21no—
54D4×D19—41no—
55#64541—21no—
56#64541—41no—
57C2×D76—21no—
58C2×D76—41no—
59C2×C4×D19—41no—
60C2×C4×D19—41no—
61C2×C4×D19D411yescharacteristic
62Q16×C19—21no—
63Q16×C19C2312yes—
64Q16×C19C2311yescharacteristic
65SD16×C19—21no—
66D8×C19C2311yescharacteristic
67C2×C8×C19C2311yescharacteristic
68#64528—21no—
69#64527—22no—
70#64527—22no—
71#64527—21no—
72#64526—21no—
73#64525—21no—
74C2×C19⋊C8D411yescharacteristic
75Dic76C2311yescharacteristic
76D152—21no—
77D152C2311yescharacteristic
78D152C2312yes—
79#64516—21no—
80C8×D19D411yescharacteristic
81C8×D19D411yescharacteristic
82C8×D19C2311yescharacteristic
83C8×D19C2311yescharacteristic
84C16×C19C2312yes—
85C19⋊C16C2312yes—
86C22×D19—41no—
87C22×D19—41no—
88C22×D19D811yescharacteristic
89Q8×C19—22no—
90Q8×C19—21no—
91Q8×C19—41no—
92D4×C19—21no—
93D4×C19—41no—
94C2×C4×C19—41no—
95C2×C4×C19—41no—
96C2×C4×C19C2×D411yescharacteristic
97C22⋊D19—41no—
98C22⋊D19—41no—
99C22⋊D19—41no—
100C2×Dic19—41no—
101C2×Dic19D811yescharacteristic
102D76—21no—
103D76—22no—
104D76—42no—
105D76—42no—
106D76—41no—
107D76—41no—
108C4×D19—41no—
109C4×D19—41no—
110C4×D19—41no—
111C4×D19—42no—
112C4×D19—42no—
113C4×D19D811yescharacteristic
114C4×D19D811yescharacteristic
115C4×D19C2×D411yescharacteristic
116C4×D19C2×D411yescharacteristic
117Dic38—21no—
118Dic38—41no—
119C8×C19C2×D411yescharacteristic
120C8×C19C2411yescharacteristic
121C19⋊C8C2×D411yescharacteristic
122C19⋊C8C2×D411yescharacteristic
123#3414—191nomaximal, Sylow
124C22×C19—41no—
125C22×C19C2×D811yescharacteristic
126C2×D19—41no—
127C2×D19—42no—
128C2×D19—41no—
129C2×D19—82no—
130C2×D19—82no—
131C2×D19C2×D811yescharacteristic
132C2×D19C2×D811yescharacteristic
133C4×C19—41no—
134C4×C19—42no—
135C4×C19C2×D811yescharacteristic
136C4×C19C22×D411yescharacteristic
137Dic19—41no—
138Dic19C2×D811yescharacteristic
139Dic19C2×D811yescharacteristic
140C2×#135—191no—
141C2×#135—191no—
142#510—191no—
143#510—192no—
144#510D1911yescharacteristic, complemented
145#509—191no—
146#509—192no—
147#509—191no—
148#508—192no—
149#508—192no—
150C2×M32—191no—
151C2×C19—21no—
152C2×C19—81no—
153C2×C19C22×D811yescharacteristic
154D19—21no—
155D19—21no—
156D19—82no—
157D19—81no—
158C2×#41—381no—
159C2×#41—381no—
160#135—192no—
161#135—191no—
162#135—192no—
163#135—191no—
164#135—191no—
165#135—381no—
166#135—381no—
167#135—381no—
168#135—381no—
169#135C2×D1911yescharacteristic
170C2×Q16—191no—
171C2×Q16C2×D1911yescharacteristic, complemented
172C2×SD16—381no—
173C2×SD16—381no—
174C2×D8—191no—
175C2×D8—191no—
176C22×C8—191no—
177Q32—192no—
178Q32C2×D1912yescomplemented
179SD32—192no—
180SD32—192no—
181SD32—192no—
182SD32C2×D1912yescomplemented
183D16—192no—
184D16—192no—
185M32—191no—
186M32—192no—
187M32C2×D1911yescharacteristic, complemented
188C2×C16—192no—
189C19#341411yescharacteristic, complemented, Sylow
190#41—21no—
191#41—381no—
192#41—382no—
193#41—381no—
194#41—382no—
195#41—381no—
196#41—761no—
197#41—761no—
198#41—761no—
199#41—761no—
200C2×Q8—21no—
201C2×Q8—381no—
202C2×D4—381no—
203C2×D4—381no—
204C2×D4—761no—
205C2×D4—761no—
206C22×C4—191no—
207C22×C4—761no—
208C22×C4—761no—
209Q16—21no—
210Q16—191no—
211Q16—381no—
212Q16C22×D1911yescharacteristic
213Q16C22×D1912yes—
214SD16—21no—
215SD16—381no—
216SD16—382no—
217SD16—381no—
218SD16—382no—
219SD16—381no—
220D8—191no—
221D8—192no—
222D8—381no—
223D8—381no—
224D8C22×D1911yescharacteristic
225C2×C8—191no—
226C2×C8—191no—
227C2×C8—191no—
228C2×C8—191no—
229C2×C8—191no—
230C2×C8C22×D1911yescharacteristic
231C16—192no—
232C16C22×D1912yes—
233C23—191no—
234C23—761no—
235C23—761no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—381no—
240Q8—761no—
241D4—21no—
242D4—41no—
243D4—381no—
244D4—382no—
245D4—761no—
246D4—762no—
247D4—762no—
248D4—761no—
249D4—761no—
250D4—761no—
251D4—761no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—191no—
255C2×C4—191no—
256C2×C4—191no—
257C2×C4—191no—
258C2×C4—191no—
259C2×C4—761no—
260C2×C4—762no—
261C2×C4—762no—
262C2×C4—761no—
263C2×C4—761no—
264C2×C4—761no—
265C2×C4D4×D1911yescharacteristic
266C8—191no—
267C8—191no—
268C8D4×D1911yescharacteristic
269C8C23×D1911yescharacteristic
270C22—41no—
271C22—191no—
272C22—191no—
273C22—761no—
274C22—762no—
275C22—761no—
276C22—1522no—
277C22—1522no—
278C22D8×D1911yescharacteristic
279C4—41no—
280C4—42no—
281C4—191no—
282C4—191no—
283C4—761no—
284C4D8×D1911yescharacteristic
285C4C2×D4×D1911yescharacteristic
286C2—21no—
287C2—81no—
288C2—381no—
289C2—381no—
290C2—1522no—
291C2—1521no—
292C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC2C2×D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC19×#510C2
socleC2×C19C22×D8
hypercenter#510D19
hypocenterC19#3414
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#10597365C2semidirect
2. #135×D19C2semidirect
3. #11926986C2semidirect
4. #11926985C2semidirect
5. #11926982C2semidirect
6. #11926981C2semidirect
7. #11926979C2semidirect
8. #11926977C2semidirect
9. #11926975C2semidirect
10. M32×D19C2semidirect
11. C19×#510C2semidirect
15. C2×Q16×C19C22semidirect
21. #10597365C22semidirect
22. #10597365C22semidirect
23. Q16×D19C22semidirect
26. #10597358C22semidirect
27. D8×D19C22semidirect
29. C2×D152C22semidirect
31. C19×Q32C22semidirect
32. C19×SD32C22semidirect
33. C19×M32C22semidirect
34. #10597286C22semidirect
35. #10597285C22semidirect
36. #10597285C22semidirect
37. #10597283C22semidirect
38. #10597269C22semidirect
39. #10597257C22semidirect
40. D304C22semidirect
41. #10597255C22semidirect
42. C16×D19C22semidirect
144. #510D19semidirect
171. C2×Q16C2×D19semidirect
178. Q32C2×D19semidirect
182. SD32C2×D19semidirect
187. M32C2×D19semidirect
189. C19#3414semidirect

Maximal subgroups

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

subgroupindex
C2×#105973652
#135×D192
#119269862
#119269852
#119269822
#119269812
#119269792
#119269772
#119269752
M32×D192
C19×#5102
#341419