Finite Group Databasebeta

← #14576767

Subgroups — #14576767

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×#10597358C211yesmaximal, characteristic, complemented
2#135×D19C211yesmaximal, characteristic, complemented
3#11926987C211yesmaximal, characteristic, complemented
4#11926984C211yesmaximal, characteristic, complemented
5#11926983C212yesmaximal, complemented
6#11926980C211yesmaximal, characteristic, complemented
7#11926978C212yesmaximal, complemented
8#11926975C212yesmaximal, complemented
9#11926973C212yesmaximal, complemented
10M32×D19C211yesmaximal, characteristic, complemented
11C19×#509C211yesmaximal, characteristic, complemented
12#41×D19—21no—
13C2×#64543—21no—
14C19×#135C2211yescharacteristic
15C2×D8×C19C2211yescharacteristic, complemented
16#10597396—21no—
17C2×#64526—21no—
18#10597365C2211yescharacteristic, complemented
19Q16×D19C2211yescharacteristic, complemented
20#10597362—21no—
21SD16×D19—21no—
22#10597358—21no—
23#10597358—21no—
24#10597358C2212yes—
25#10597358C2211yescharacteristic, complemented
26#10597358C2212yescomplemented
27D8×D19C2211yescharacteristic, complemented
28C2×Dic76C2211yescharacteristic, complemented
29#10597350C2211yescharacteristic
30C2×C8×D19C2211yescharacteristic
31C19×SD32C2212yescomplemented
32C19×D16C2212yescomplemented
33C19×M32C2211yescharacteristic, complemented
34#10597286C2212yescomplemented
35#10597284C2212yescomplemented
36#10597284C2212yescomplemented
37#10597283C2212yescomplemented
38#10597269C2211yescharacteristic, complemented
39Dic152C2212yescomplemented
40#10597257C2212yescomplemented
41#10597255C2212yescomplemented
42C16×D19C2212yescomplemented
43#41×C19—21no—
44C2×D4×C19—21no—
45C2×C22⋊D19—41no—
46C22×Dic19—41no—
47#64545—21no—
48Q8×D19—21no—
49#64543—22no—
50#64543—22no—
51#64543—21no—
52#64543—41no—
53#64543—41no—
54#64543—41no—
55D4×D19—21no—
56D4×D19—41no—
57#64541—21no—
58#64541—41no—
59C2×C4×D19—41no—
60C2×C4×D19D411yescharacteristic
61C2×Dic38—21no—
62Q16×C19C2311yescharacteristic
63SD16×C19—21no—
64D8×C19—21no—
65D8×C19C2312yes—
66D8×C19C2311yescharacteristic
67C2×C8×C19C2311yescharacteristic
68#64528—21no—
69#64527—21no—
70#64526—22no—
71#64526—22no—
72#64526—21no—
73#64525—21no—
74C2×C19⋊C8D411yescharacteristic
75Dic76—21no—
76Dic76C2312yes—
77Dic76C2311yescharacteristic
78D152C2311yescharacteristic
79#64516—21no—
80C8×D19D411yescharacteristic
81C8×D19D411yescharacteristic
82C8×D19C2311yescharacteristic
83C8×D19C2311yescharacteristic
84C16×C19C2312yes—
85C19⋊C16C2312yes—
86C23×C19—41no—
87C22×D19—41no—
88C22×D19D811yescharacteristic
89Q8×C19—21no—
90D4×C19—21no—
91D4×C19—22no—
92D4×C19—41no—
93D4×C19—41no—
94C2×C4×C19—41no—
95C2×C4×C19C2×D411yescharacteristic
96C22⋊D19—41no—
97C22⋊D19—41no—
98C22⋊D19—42no—
99C22⋊D19—42no—
100C22⋊D19—41no—
101C2×Dic19—41no—
102C2×Dic19—41no—
103C2×Dic19—42no—
104C2×Dic19—42no—
105C2×Dic19D811yescharacteristic
106D76—21no—
107D76—41no—
108C4×D19—41no—
109C4×D19—41no—
110C4×D19—41no—
111C4×D19D811yescharacteristic
112C4×D19D811yescharacteristic
113C4×D19C2×D411yescharacteristic
114C4×D19C2×D411yescharacteristic
115Dic38—21no—
116Dic38—22no—
117Dic38—41no—
118Dic38—41no—
119C8×C19C2×D411yescharacteristic
120C8×C19C2411yescharacteristic
121C19⋊C8C2×D411yescharacteristic
122C19⋊C8C2×D411yescharacteristic
123#3414—191nomaximal, Sylow
124C22×C19—42no—
125C22×C19—41no—
126C22×C19—82no—
127C22×C19C2×D811yescharacteristic
128C2×D19—41no—
129C2×D19—41no—
130C2×D19—82no—
131C2×D19C2×D811yescharacteristic
132C2×D19C2×D811yescharacteristic
133C4×C19—41no—
134C4×C19C2×D811yescharacteristic
135C4×C19C22×D411yescharacteristic
136Dic19—41no—
137Dic19—42no—
138Dic19C2×D811yescharacteristic
139Dic19C2×D811yescharacteristic
140C2×#135—191no—
141C2×#135—191no—
142#510—191no—
143#510—192no—
144#510—191no—
145#509—191no—
146#509—192no—
147#509D1911yescharacteristic, complemented
148#508—192no—
149#508—192no—
150C2×M32—191no—
151C2×C19—21no—
152C2×C19—81no—
153C2×C19—82no—
154C2×C19C22×D811yescharacteristic
155D19—21no—
156D19—21no—
157D19—81no—
158C2×#41—381no—
159C2×#41—381no—
160#135—191no—
161#135—192no—
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×Q16—191no—
172C2×SD16—381no—
173C2×SD16—381no—
174C2×D8—191no—
175C2×D8C2×D1911yescharacteristic, complemented
176C22×C8—191no—
177Q32—192no—
178Q32—192no—
179SD32—192no—
180SD32—192no—
181SD32—192no—
182SD32C2×D1912yescomplemented
183D16—192no—
184D16C2×D1912yescomplemented
185M32—191no—
186M32—192no—
187M32C2×D1911yescharacteristic, complemented
188C2×C16—192no—
189C19#341411yescharacteristic, complemented, Sylow
190#41—21no—
191#41—382no—
192#41—382no—
193#41—381no—
194#41—381no—
195#41—381no—
196#41—761no—
197#41—761no—
198#41—761no—
199#41—761no—
200C2×Q8—381no—
201C2×Q8—381no—
202C2×D4—21no—
203C2×D4—381no—
204C2×D4—761no—
205C2×D4—761no—
206C22×C4—191no—
207C22×C4—761no—
208C22×C4—761no—
209Q16—192no—
210Q16—191no—
211Q16—381no—
212Q16—381no—
213Q16C22×D1911yescharacteristic
214SD16—21no—
215SD16—382no—
216SD16—382no—
217SD16—381no—
218SD16—381no—
219SD16—381no—
220D8—21no—
221D8—191no—
222D8—381no—
223D8C22×D1912yes—
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—41no—
234C23—191no—
235C23—761no—
236Q8—21no—
237Q8—382no—
238Q8—381no—
239Q8—761no—
240Q8—761no—
241D4—22no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—381no—
246D4—761no—
247D4—761no—
248D4—761no—
249D4—762no—
250D4—762no—
251D4—761no—
252C2×C4—41no—
253C2×C4—191no—
254C2×C4—191no—
255C2×C4—191no—
256C2×C4—191no—
257C2×C4—191no—
258C2×C4—761no—
259C2×C4—761no—
260C2×C4—761no—
261C2×C4—762no—
262C2×C4—762no—
263C2×C4—761no—
264C2×C4—761no—
265C2×C4D4×D1911yescharacteristic
266C8—191no—
267C8—191no—
268C8D4×D1911yescharacteristic
269C8C23×D1911yescharacteristic
270C22—41no—
271C22—42no—
272C22—82no—
273C22—191no—
274C22—191no—
275C22—761no—
276C22—761no—
277C22—1522no—
278C22D8×D1911yescharacteristic
279C4—41no—
280C4—191no—
281C4—191no—
282C4—761no—
283C4—762no—
284C4D8×D1911yescharacteristic
285C4C2×D4×D1911yescharacteristic
286C2—21no—
287C2—82no—
288C2—81no—
289C2—381no—
290C2—381no—
291C2—1521no—
292C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC2C2×D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC19×#509C2
socleC2×C19C22×D8
hypercenter#509D19
hypocenterC19#3414
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. C2×#10597358C2semidirect
2. #135×D19C2semidirect
3. #11926987C2semidirect
4. #11926984C2semidirect
5. #11926983C2semidirect
6. #11926980C2semidirect
7. #11926978C2semidirect
8. #11926975C2semidirect
9. #11926973C2semidirect
10. M32×D19C2semidirect
11. C19×#509C2semidirect
15. C2×D8×C19C22semidirect
18. #10597365C22semidirect
19. Q16×D19C22semidirect
25. #10597358C22semidirect
26. #10597358C22semidirect
27. D8×D19C22semidirect
28. C2×Dic76C22semidirect
31. C19×SD32C22semidirect
32. C19×D16C22semidirect
33. C19×M32C22semidirect
34. #10597286C22semidirect
35. #10597284C22semidirect
36. #10597284C22semidirect
37. #10597283C22semidirect
38. #10597269C22semidirect
39. Dic152C22semidirect
40. #10597257C22semidirect
41. #10597255C22semidirect
42. C16×D19C22semidirect
147. #509D19semidirect
175. C2×D8C2×D19semidirect
182. SD32C2×D19semidirect
184. D16C2×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×#105973582
#135×D192
#119269872
#119269842
#119269832
#119269802
#119269782
#119269752
#119269732
M32×D192
C19×#5092
#341419