Finite Group Databasebeta

← #14575403

Subgroups — #14575403

Order 2432.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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#11927352C212yesmaximal, complemented
2#11927348C212yesmaximal, complemented
3#11926934C211yesmaximal, characteristic, complemented
4#11926812C212yesmaximal, complemented
5#11926810C212yesmaximal, complemented
6#11926721C211yesmaximal, characteristic, complemented
7#11926713C212yesmaximal, complemented
8#11926663C212yesmaximal, complemented
9C19×#454C211yesmaximal, characteristic, complemented
10C19×2−1+4C2211yescharacteristic, complemented
11#10597435C2212yescomplemented
12#10597430C2211yescharacteristic
13C19×AGL(1,ℤ/8)C2212yescomplemented
14C19×#124C2211yescharacteristic, complemented
15#10597396—22no—
16#10597396C2212yes—
17#10597395—22no—
18#10597395C2212yescomplemented
19#10597394C2212yescomplemented
20#10597388—22no—
21#10597388C2212yescomplemented
22C2×#64527—22no—
23C2×#64527C2212yescomplemented
24C2×#64525C2212yescomplemented
25#10597362—22no—
26#10597360—22no—
27#10597357—22no—
28D8×D19—22no—
29#10597354C2212yes—
30#10597353C2212yescomplemented
31#10597320C2211yescharacteristic, complemented
32C19×#104C2212yescomplemented
33C19×#101C2211yescharacteristic, complemented
34#10597290C2211yescharacteristic, complemented
35#10597280C2212yescomplemented
36#10597279C2212yescomplemented
37#10597262C2212yescomplemented
38#10597260C2211yescharacteristic, complemented
39#41×C19—22no—
40#41×C19—41no—
41#41×C19C2312yes—
42C2×Q8×C19—22no—
43C2×Q8×C19C2311yescharacteristic
44C2×D4×C19C2311yescharacteristic
45C2×C22⋊D19—41no—
46#64545—22no—
47#64543—22no—
48D4×D19—22no—
49D4×D19—22no—
50D4×D19—42no—
51#64541—22no—
52#64541C2312yes—
53C2×D76—22no—
54C2×D76—41no—
55C2×D76C2312yes—
56SD16×C19—22no—
57D8×C19—22no—
58M16×C19C2312yes—
59C22⋊C4×C19—41no—
60C42×C19C2311yescharacteristic
61#64528—22no—
62#64528D412yescomplemented
63#64527—22no—
64#64527—22no—
65#64527—22no—
66#64527—22no—
67#64527D412yescomplemented
68#64526D412yescomplemented
69#64525—22no—
70#64525—22no—
71#64525—22no—
72#64525D412yescomplemented
73#64520—22no—
74#64520C2312yes—
75C2×C19⋊C8—22no—
76C2×C19⋊C8C2312yes—
77D152—22no—
78#64516—22no—
79#64515—22no—
80C8×D19—22no—
81C23×C19—21no—
82C22×D19—22no—
83C22×D19—41no—
84C22×D19—42no—
85Q8×C19—22no—
86Q8×C19—41no—
87Q8×C19C2×D412yes—
88D4×C19—22no—
89D4×C19—22no—
90D4×C19—41no—
91D4×C19C2×D412yes—
92C2×C4×C19—22no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—42no—
96C2×C4×C19C2411yescharacteristic
97C22⋊D19—22no—
98C22⋊D19—42no—
99C22⋊D19—42no—
100C2×Dic19—41no—
101D76—22no—
102D76—22no—
103D76—42no—
104D76—82no—
105D76C2×D412yes—
106C4×D19—22no—
107C4×D19—42no—
108Dic38C2×D412yes—
109C8×C19—22no—
110C19⋊C8—22no—
111C19⋊C8C2×D412yes—
112C19⋊C8C2×D412yes—
113#3288—191nomaximal, Sylow
114C22×C19—22no—
115C22×C19—41no—
116C22×C19—81no—
117C22×C19H(5,𝔽2)11yescharacteristic
118C2×D19—22no—
119C2×D19—42no—
120C2×D19—82no—
121C2×D19—161no—
122C2×D19—162no—
123C4×C19—22no—
124C4×C19—41no—
125C4×C19—41no—
126C4×C19C22×D412yes—
127Dic19—22no—
128#577—192no—
129#576—192no—
130#496—191no—
131#472—192no—
132#471—192no—
133#455—191no—
134#454D1911yescharacteristic, complemented
135#453—192no—
136#444—192no—
137C2×C19—21no—
138C2×C19—42no—
139C2×C19—81no—
140C2×C19D4211yescharacteristic
141D19—42no—
142D19—82no—
1432−1+4C2×D1911yescharacteristic, complemented
144H(5,𝔽2)—192no—
145H(5,𝔽2)—191no—
146#137—192no—
147#137—382no—
148AGL(1,ℤ/8)—192no—
149AGL(1,ℤ/8)—192no—
150AGL(1,ℤ/8)—382no—
151AGL(1,ℤ/8)—382no—
152AGL(1,ℤ/8)—382no—
153AGL(1,ℤ/8)C2×D1912yescomplemented
154#135—192no—
155#135—382no—
156#135—382no—
157C2×SD16—192no—
158C2×SD16—382no—
159C2×D8—192no—
160C2×D8—382no—
161#131—192no—
162#131—192no—
163#127—191no—
164#124C2×D1911yescharacteristic, complemented
165#108—192no—
166#104—192no—
167#104C2×D1912yescomplemented
168#101C2×D1911yescharacteristic, complemented
169#100—191no—
170#100—192no—
171#97—191no—
172C19#328811yescharacteristic, complemented, Sylow
173#41—22no—
174#41—41no—
175#41—192no—
176#41—382no—
177#41—382no—
178#41—382no—
179#41C22×D1912yes—
180C2×Q8—22no—
181C2×Q8C22×D1911yescharacteristic
182C2×D4—192no—
183C2×D4—382no—
184C2×D4—382no—
185C2×D4—382no—
186C2×D4—761no—
187C2×D4—762no—
188C2×D4—761no—
189C2×D4C22×D1911yescharacteristic
190Q16—192no—
191Q16—382no—
192SD16—22no—
193SD16—192no—
194SD16—192no—
195SD16—382no—
196SD16—382no—
197SD16—382no—
198SD16—382no—
199SD16—382no—
200D8—22no—
201D8—192no—
202D8—382no—
203D8—382no—
204D8—382no—
205D8—382no—
206M16—192no—
207M16—382no—
208M16—382no—
209M16C22×D1912yes—
210C2×C8—192no—
211C2×C8—382no—
212C2×C8—382no—
213C22⋊C4—41no—
214C42C22×D1911yescharacteristic
215C23—21no—
216C23—382no—
217C23—762no—
218C23—761no—
219Q8—22no—
220Q8—41no—
221Q8—192no—
222Q8D4×D1912yes—
223D4—22no—
224D4—22no—
225D4—41no—
226D4—192no—
227D4—382no—
228D4—382no—
229D4—382no—
230D4—762no—
231D4—762no—
232D4—762no—
233D4—1522no—
234D4D4×D1912yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—382no—
240C2×C4—762no—
241C2×C4—761no—
242C2×C4C23×D1911yescharacteristic
243C8—22no—
244C8—192no—
245C8—192no—
246C8—382no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—382no—
251C22—3042no—
252C22—3041no—
253C22—762no—
254C22—1522no—
255C22#1059743011yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—382no—
260C4C2×D4×D1912yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—762no—
265C2—1522no—
266C2#1192717611yescharacteristic
subgroupG/H
centerC2#11927176
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#454C2
socleC2×C19D42
hypercenter#454D19
hypocenterC19#3288
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #11927352C2semidirect
2. #11927348C2semidirect
3. #11926934C2semidirect
4. #11926812C2semidirect
5. #11926810C2semidirect
6. #11926721C2semidirect
7. #11926713C2semidirect
8. #11926663C2semidirect
9. C19×#454C2semidirect
10. C19×2−1+4C22semidirect
11. #10597435C22semidirect
13. C19×AGL(1,ℤ/8)C22semidirect
14. C19×#124C22semidirect
18. #10597395C22semidirect
19. #10597394C22semidirect
21. #10597388C22semidirect
23. C2×#64527C22semidirect
24. C2×#64525C22semidirect
30. #10597353C22semidirect
31. #10597320C22semidirect
32. C19×#104C22semidirect
33. C19×#101C22semidirect
34. #10597290C22semidirect
35. #10597280C22semidirect
36. #10597279C22semidirect
37. #10597262C22semidirect
38. #10597260C22semidirect
62. #64528D4semidirect
67. #64527D4semidirect
68. #64526D4semidirect
72. #64525D4semidirect
134. #454D19semidirect
143. 2−1+4C2×D19semidirect
153. AGL(1,ℤ/8)C2×D19semidirect
164. #124C2×D19semidirect
167. #104C2×D19semidirect
168. #101C2×D19semidirect
172. C19#3288semidirect

Maximal subgroups

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

subgroupindex
#119273522
#119273482
#119269342
#119268122
#119268102
#119267212
#119267132
#119266632
C19×#4542
#328819