Finite Group Databasebeta

← #14575431

Subgroups — #14575431

Order 2432.

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

normal subgroups only

This group has 476 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#11927348C212yesmaximal, complemented
2#11927347C212yesmaximal, complemented
3#11926920C211yesmaximal, characteristic, complemented
4#11926813C212yesmaximal, complemented
5#11926812C212yesmaximal, complemented
6#11926713C212yesmaximal, complemented
7#11926711C211yesmaximal, characteristic, complemented
8#11926658C212yesmaximal, complemented
9C19×#453C211yesmaximal, characteristic, complemented
10C19×H(5,𝔽2)C2211yescharacteristic, complemented
11#10597435C2212yescomplemented
12#10597430C2211yescharacteristic, complemented
13C19×AGL(1,ℤ/8)C2212yescomplemented
14C19×#127C2211yescharacteristic, complemented
15#10597396—22no—
16#10597396C2212yes—
17#10597395—22no—
18#10597395C2212yescomplemented
19#10597394C2212yescomplemented
20#10597378—22no—
21#10597378C2212yescomplemented
22C2×#64525—22no—
23C2×#64525C2212yescomplemented
24C2×#64525C2212yescomplemented
25#10597362—22no—
26#10597360—22no—
27#10597357—22no—
28D8×D19—22no—
29#10597354C2212yescomplemented
30#10597353C2212yescomplemented
31#10597320C2211yescharacteristic, complemented
32C19×#104C2212yescomplemented
33C19×#100C2211yescharacteristic, complemented
34#10597290C2211yescharacteristic, complemented
35#10597280C2212yescomplemented
36#10597279C2212yescomplemented
37#10597262C2212yescomplemented
38C4×C19⋊C8C2211yescharacteristic, complemented
39#41×C19—22no—
40#41×C19C2312yes—
41C2×D4×C19—22no—
42C2×D4×C19—41no—
43C2×D4×C19—41no—
44C2×D4×C19C2311yescharacteristic
45C2×D4×C19C2311yescharacteristic
46C2×C22⋊D19—41no—
47#64545—22no—
48#64543—22no—
49D4×D19—22no—
50D4×D19—22no—
51D4×D19—42no—
52#64541—22no—
53#64541C2312yes—
54C2×D76—22no—
55C2×D76—41no—
56C2×D76C2312yes—
57SD16×C19—22no—
58D8×C19—22no—
59M16×C19C2312yes—
60C42×C19C2311yescharacteristic
61#64528D412yescomplemented
62#64527—22no—
63#64527D412yescomplemented
64#64526—22no—
65#64526D412yescomplemented
66#64525—22no—
67#64525—22no—
68#64525—22no—
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—
82C23×C19—21no—
83C23×C19—41no—
84C22×D19—22no—
85C22×D19—41no—
86C22×D19—42no—
87Q8×C19C2×D412yes—
88D4×C19—22no—
89D4×C19—22no—
90D4×C19—22no—
91D4×C19—42no—
92D4×C19—82no—
93D4×C19C2×D412yes—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—41no—
97C2×C4×C19C2411yescharacteristic
98C22⋊D19—22no—
99C22⋊D19—42no—
100C22⋊D19—42no—
101C2×Dic19—41no—
102D76—22no—
103D76—22no—
104D76—42no—
105D76—82no—
106D76C2×D412yes—
107C4×D19—22no—
108C4×D19—42no—
109Dic38C2×D412yes—
110C8×C19—22no—
111C19⋊C8—22no—
112C19⋊C8C2×D412yes—
113C19⋊C8C2×D412yes—
114#3292—191nomaximal, Sylow
115C22×C19—22no—
116C22×C19—41no—
117C22×C19—41no—
118C22×C19—81no—
119C22×C19—81no—
120C22×C19—161no—
121C22×C19H(5,𝔽2)11yescharacteristic
122C2×D19—22no—
123C2×D19—42no—
124C2×D19—82no—
125C2×D19—161no—
126C2×D19—162no—
127C4×C19—22no—
128C4×C19—22no—
129C4×C19C22×D412yes—
130Dic19—22no—
131#576—192no—
132#576—192no—
133#493—191no—
134#472—192no—
135#472—192no—
136#453—191no—
137#453—192no—
138#453D1911yescharacteristic, complemented
139#443—192no—
140C2×C19—21no—
141C2×C19—42no—
142C2×C19—81no—
143C2×C19—81no—
144C2×C19D4211yescharacteristic
145D19—42no—
146D19—82no—
147H(5,𝔽2)—192no—
148H(5,𝔽2)—191no—
149H(5,𝔽2)C2×D1911yescharacteristic, complemented
150AGL(1,ℤ/8)—192no—
151AGL(1,ℤ/8)—192no—
152AGL(1,ℤ/8)—192no—
153AGL(1,ℤ/8)—382no—
154AGL(1,ℤ/8)—382no—
155AGL(1,ℤ/8)—382no—
156AGL(1,ℤ/8)—382no—
157AGL(1,ℤ/8)C2×D1912yescomplemented
158#135—192no—
159#135—382no—
160#135—382no—
161C2×D8—192no—
162C2×D8—192no—
163C2×D8—382no—
164C2×D8—382no—
165#131—192no—
166#131—192no—
167#127—191no—
168#127C2×D1911yescharacteristic, complemented
169#108—192no—
170#104—192no—
171#104C2×D1912yescomplemented
172#100—191no—
173#100—192no—
174#100C2×D1911yescharacteristic, complemented
175C4×C8—191no—
176C19#329211yescharacteristic, complemented, Sylow
177#41—22no—
178#41—192no—
179#41—382no—
180#41—382no—
181#41—382no—
182#41C22×D1912yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—192no—
187C2×D4—382no—
188C2×D4—382no—
189C2×D4—382no—
190C2×D4—761no—
191C2×D4—762no—
192C2×D4—761no—
193C2×D4C22×D1911yescharacteristic
194C2×D4C22×D1911yescharacteristic
195Q16—192no—
196SD16—22no—
197SD16—192no—
198SD16—192no—
199SD16—382no—
200SD16—382no—
201SD16—382no—
202D8—22no—
203D8—192no—
204D8—382no—
205D8—382no—
206D8—382no—
207D8—382no—
208D8—382no—
209D8—382no—
210D8—382no—
211M16—192no—
212M16—382no—
213M16—382no—
214M16C22×D1912yes—
215C2×C8—192no—
216C2×C8—382no—
217C2×C8—382no—
218C42C22×D1911yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—382no—
223C23—762no—
224C23—761no—
225Q8—192no—
226Q8D4×D1912yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—192no—
233D4—382no—
234D4—382no—
235D4—382no—
236D4—762no—
237D4—762no—
238D4—762no—
239D4—1522no—
240D4D4×D1912yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—382no—
245C2×C4—762no—
246C2×C4—761no—
247C2×C4C23×D1911yescharacteristic
248C8—22no—
249C8—192no—
250C8—192no—
251C8—382no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—382no—
259C22—3042no—
260C22—3041no—
261C22—762no—
262C22—1522no—
263C22#1059743011yescharacteristic
264C4—22no—
265C4—22no—
266C4—382no—
267C4C2×D4×D1912yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—762no—
273C2—1522no—
274C2#1192717611yescharacteristic
subgroupG/H
centerC2#11927176
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#453C2
socleC2×C19D42
hypercenter#453D19
hypocenterC19#3292
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #11927348C2semidirect
2. #11927347C2semidirect
3. #11926920C2semidirect
4. #11926813C2semidirect
5. #11926812C2semidirect
6. #11926713C2semidirect
7. #11926711C2semidirect
8. #11926658C2semidirect
9. C19×#453C2semidirect
10. C19×H(5,𝔽2)C22semidirect
11. #10597435C22semidirect
12. #10597430C22semidirect
13. C19×AGL(1,ℤ/8)C22semidirect
14. C19×#127C22semidirect
18. #10597395C22semidirect
19. #10597394C22semidirect
21. #10597378C22semidirect
23. C2×#64525C22semidirect
24. C2×#64525C22semidirect
29. #10597354C22semidirect
30. #10597353C22semidirect
31. #10597320C22semidirect
32. C19×#104C22semidirect
33. C19×#100C22semidirect
34. #10597290C22semidirect
35. #10597280C22semidirect
36. #10597279C22semidirect
37. #10597262C22semidirect
38. C4×C19⋊C8C22semidirect
61. #64528D4semidirect
63. #64527D4semidirect
65. #64526D4semidirect
72. #64525D4semidirect
138. #453D19semidirect
149. H(5,𝔽2)C2×D19semidirect
157. AGL(1,ℤ/8)C2×D19semidirect
168. #127C2×D19semidirect
171. #104C2×D19semidirect
174. #100C2×D19semidirect
176. C19#3292semidirect

Maximal subgroups

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

subgroupindex
#119273482
#119273472
#119269202
#119268132
#119268122
#119267132
#119267112
#119266582
C19×#4532
#329219