Finite Group Databasebeta

← #14575425

Subgroups — #14575425

Order 2432.

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

normal subgroups only

This group has 460 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#11927353C212yesmaximal, complemented
2#11927352C212yesmaximal, complemented
3#11926918C211yesmaximal, characteristic, complemented
4#11926810C212yesmaximal, complemented
5#11926809C212yesmaximal, complemented
6#11926726C211yesmaximal, characteristic, complemented
7#11926713C212yesmaximal, complemented
8#11926658C212yesmaximal, complemented
9C19×#456C211yesmaximal, characteristic, complemented
10C19×2−1+4C2211yescharacteristic
11#10597435C2212yescomplemented
12#10597433C2211yescharacteristic
13C19×#137C2212yescomplemented
14C19×C4⋊Q8C2211yescharacteristic, complemented
15#10597396—22no—
16#10597396C2212yes—
17#10597395—22no—
18#10597395C2212yes—
19#10597394C2212yescomplemented
20#10597388—22no—
21#10597388C2212yescomplemented
22C2×#64527—22no—
23C2×#64527C2212yescomplemented
24C2×#64527C2212yescomplemented
25#10597365—22no—
26#10597364—22no—
27#10597360—22no—
28SD16×D19—22no—
29#10597354C2212yes—
30#10597353C2212yescomplemented
31#10597320C2211yescharacteristic
32C19×#104C2212yescomplemented
33C19×#101C2211yescharacteristic, complemented
34#10597293C2211yescharacteristic, complemented
35#10597280C2212yescomplemented
36#10597279C2212yescomplemented
37#10597262C2212yescomplemented
38C4×C19⋊C8C2211yescharacteristic, complemented
39#41×C19—22no—
40#41×C19—41no—
41#41×C19C2312yes—
42C2×Q8×C19—22no—
43C2×Q8×C19C2311yescharacteristic
44C2×Q8×C19C2311yescharacteristic
45#64545—22no—
46#64545—22no—
47Q8×D19—22no—
48D4×D19—22no—
49D4×D19—42no—
50#64541—22no—
51#64541—41no—
52#64541C2312yes—
53C2×D76—22no—
54C2×D76—41no—
55C2×D76C2312yes—
56Q16×C19—22no—
57SD16×C19—22no—
58M16×C19C2312yes—
59C4⋊C4×C19—41no—
60C42×C19C2311yescharacteristic
61#64528—22no—
62#64528D412yescomplemented
63#64527—22no—
64#64527—22no—
65#64527—22no—
66#64527—22no—
67#64527—22no—
68#64527—22no—
69#64527D412yescomplemented
70#64526D412yescomplemented
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—
81C22×D19—22no—
82C22×D19—42no—
83Q8×C19—22no—
84Q8×C19—22no—
85Q8×C19—41no—
86Q8×C19C2×D412yes—
87D4×C19—22no—
88D4×C19—41no—
89D4×C19C2×D412yes—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—42no—
95C2×C4×C19C2411yescharacteristic
96C22⋊D19—22no—
97C22⋊D19—42no—
98D76—22no—
99D76—22no—
100D76—42no—
101D76—41no—
102D76—82no—
103D76C2×D412yes—
104C4×D19—22no—
105C4×D19—42no—
106C4×D19—42no—
107Dic38—41no—
108Dic38C2×D412yes—
109C8×C19—22no—
110C19⋊C8—22no—
111C19⋊C8C2×D412yes—
112C19⋊C8C2×D412yes—
113#3291—191nomaximal, Sylow
114C22×C19—22no—
115C22×C19H(5,𝔽2)11yescharacteristic
116C2×D19—22no—
117C2×D19—42no—
118C2×D19—82no—
119C2×D19—162no—
120C4×C19—22no—
121C4×C19—22no—
122C4×C19—41no—
123C4×C19—41no—
124C4×C19C22×D412yes—
125Dic19—22no—
126#577—192no—
127#577—192no—
128#492—191no—
129#471—192no—
130#471—192no—
131#456—191no—
132#456D1911yescharacteristic, complemented
133#453—192no—
134#443—192no—
135C2×C19—21no—
136C2×C19—42no—
137C2×C19D4211yescharacteristic
138D19—42no—
139D19—82no—
1402−1+4—191no—
1412−1+4C2×D1911yescharacteristic
142H(5,𝔽2)—192no—
143#137—192no—
144#137—382no—
145#137—382no—
146#137C2×D1912yescomplemented
147AGL(1,ℤ/8)—192no—
148AGL(1,ℤ/8)—192no—
149AGL(1,ℤ/8)—382no—
150AGL(1,ℤ/8)—382no—
151#135—192no—
152#135—382no—
153#135—382no—
154C2×SD16—192no—
155C2×SD16—192no—
156C2×SD16—382no—
157C2×SD16—382no—
158#131—192no—
159#131—192no—
160C4⋊Q8C2×D1911yescharacteristic, complemented
161#127—191no—
162#108—192no—
163#104—192no—
164#104C2×D1912yescomplemented
165#101—191no—
166#101C2×D1911yescharacteristic, complemented
167#100—192no—
168C4×C8—191no—
169C19#329111yescharacteristic, complemented, Sylow
170#41—22no—
171#41—41no—
172#41—192no—
173#41—382no—
174#41—382no—
175#41—382no—
176#41—761no—
177#41C22×D1912yes—
178C2×Q8—22no—
179C2×Q8—382no—
180C2×Q8C22×D1911yescharacteristic
181C2×Q8C22×D1911yescharacteristic
182C2×D4—192no—
183C2×D4—382no—
184C2×D4—382no—
185C2×D4—761no—
186C2×D4—762no—
187Q16—22no—
188Q16—192no—
189Q16—382no—
190SD16—22no—
191SD16—192no—
192SD16—192no—
193SD16—382no—
194SD16—382no—
195SD16—382no—
196SD16—382no—
197SD16—382no—
198SD16—382no—
199SD16—382no—
200D8—192no—
201D8—382no—
202D8—382no—
203M16—192no—
204M16—382no—
205M16—382no—
206M16C22×D1912yes—
207C2×C8—192no—
208C2×C8—382no—
209C2×C8—382no—
210C4⋊C4—41no—
211C42C22×D1911yescharacteristic
212C23—382no—
213C23—762no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—192no—
218Q8—761no—
219Q8D4×D1912yes—
220D4—22no—
221D4—41no—
222D4—192no—
223D4—382no—
224D4—382no—
225D4—382no—
226D4—762no—
227D4—761no—
228D4—762no—
229D4—1522no—
230D4D4×D1912yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—382no—
237C2×C4—762no—
238C2×C4—762no—
239C2×C4C23×D1911yescharacteristic
240C8—22no—
241C8—192no—
242C8—192no—
243C8—382no—
244C22—22no—
245C22—382no—
246C22—3042no—
247C22—762no—
248C22—1522no—
249C22#1059743011yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—382no—
255C4C2×D4×D1912yes—
256C2—21no—
257C2—42no—
258C2—762no—
259C2—1522no—
260C2#1192717611yescharacteristic
subgroupG/H
centerC2#11927176
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#456C2
socleC2×C19D42
hypercenter#456D19
hypocenterC19#3291
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #11927353C2semidirect
2. #11927352C2semidirect
3. #11926918C2semidirect
4. #11926810C2semidirect
5. #11926809C2semidirect
6. #11926726C2semidirect
7. #11926713C2semidirect
8. #11926658C2semidirect
9. C19×#456C2semidirect
11. #10597435C22semidirect
13. C19×#137C22semidirect
14. C19×C4⋊Q8C22semidirect
19. #10597394C22semidirect
21. #10597388C22semidirect
23. C2×#64527C22semidirect
24. C2×#64527C22semidirect
30. #10597353C22semidirect
32. C19×#104C22semidirect
33. C19×#101C22semidirect
34. #10597293C22semidirect
35. #10597280C22semidirect
36. #10597279C22semidirect
37. #10597262C22semidirect
38. C4×C19⋊C8C22semidirect
62. #64528D4semidirect
69. #64527D4semidirect
70. #64526D4semidirect
72. #64525D4semidirect
132. #456D19semidirect
146. #137C2×D19semidirect
160. C4⋊Q8C2×D19semidirect
164. #104C2×D19semidirect
166. #101C2×D19semidirect
169. C19#3291semidirect

Maximal subgroups

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

subgroupindex
#119273532
#119273522
#119269182
#119268102
#119268092
#119267262
#119267132
#119266582
C19×#4562
#329119