Finite Group Databasebeta

← #14575404

Subgroups — #14575404

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#11927353C212yesmaximal, complemented
2#11927347C212yesmaximal, complemented
3#11926934C211yesmaximal, characteristic, complemented
4#11926813C212yesmaximal, complemented
5#11926809C212yesmaximal, complemented
6#11926716C211yesmaximal, characteristic, complemented
7#11926713C212yesmaximal, complemented
8#11926663C212yesmaximal, complemented
9C19×#455C211yesmaximal, characteristic, complemented
10C19×H(5,𝔽2)C2211yescharacteristic
11#10597435C2212yescomplemented
12#10597433C2211yescharacteristic, complemented
13C19×#137C2212yescomplemented
14C19×#124C2211yescharacteristic, complemented
15#10597396—22no—
16#10597396C2212yes—
17#10597395—22no—
18#10597395C2212yes—
19#10597394C2212yescomplemented
20C2×#64527C2212yescomplemented
21#10597378—22no—
22#10597378C2212yescomplemented
23C2×#64525—22no—
24C2×#64525C2212yescomplemented
25#10597365—22no—
26#10597364—22no—
27#10597360—22no—
28SD16×D19—22no—
29#10597354C2212yescomplemented
30#10597353C2212yescomplemented
31#10597320C2211yescharacteristic, complemented
32C19×#104C2212yescomplemented
33C19×#100C2211yescharacteristic, complemented
34#10597293C2211yescharacteristic, complemented
35#10597280C2212yescomplemented
36#10597279C2212yescomplemented
37#10597262C2212yescomplemented
38#10597260C2211yescharacteristic, complemented
39#41×C19—22no—
40#41×C19C2312yes—
41C2×Q8×C19C2311yescharacteristic
42C2×D4×C19—22no—
43C2×D4×C19—41no—
44C2×D4×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—
59C22⋊C4×C19—41no—
60C42×C19C2311yescharacteristic
61#64528D412yescomplemented
62#64527—22no—
63#64527—22no—
64#64527—22no—
65#64527D412yescomplemented
66#64526—22no—
67#64526D412yescomplemented
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—41no—
83C22×D19—22no—
84C22×D19—42no—
85Q8×C19—22no—
86Q8×C19C2×D412yes—
87D4×C19—22no—
88D4×C19—22no—
89D4×C19—42no—
90D4×C19C2×D412yes—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—41no—
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#3288—191nomaximal, Sylow
114C22×C19—22no—
115C22×C19—41no—
116C22×C19—81no—
117C22×C19—161no—
118C22×C19H(5,𝔽2)11yescharacteristic
119C2×D19—22no—
120C2×D19—42no—
121C2×D19—82no—
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#455D1911yescharacteristic, complemented
134#454—191no—
135#453—192no—
136#444—192no—
137C2×C19—21no—
138C2×C19—42no—
139C2×C19—81no—
140C2×C19D4211yescharacteristic
141D19—42no—
142D19—82no—
1432−1+4—191no—
144H(5,𝔽2)—192no—
145H(5,𝔽2)C2×D1911yescharacteristic
146#137—382no—
147#137C2×D1912yescomplemented
148AGL(1,ℤ/8)—192no—
149AGL(1,ℤ/8)—192no—
150AGL(1,ℤ/8)—192no—
151AGL(1,ℤ/8)—382no—
152AGL(1,ℤ/8)—382no—
153AGL(1,ℤ/8)—382no—
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#101—191no—
169#100—192no—
170#100C2×D1911yescharacteristic, complemented
171#97—191no—
172C19#328811yescharacteristic, complemented, Sylow
173#41—22no—
174#41—192no—
175#41—382no—
176#41—382no—
177#41—382no—
178#41—761no—
179#41C22×D1912yes—
180C2×Q8—382no—
181C2×Q8C22×D1911yescharacteristic
182C2×D4—22no—
183C2×D4—41no—
184C2×D4—192no—
185C2×D4—382no—
186C2×D4—382no—
187C2×D4—761no—
188C2×D4—762no—
189C2×D4C22×D1911yescharacteristic
190Q16—22no—
191Q16—192no—
192SD16—22no—
193SD16—192no—
194SD16—192no—
195SD16—382no—
196SD16—382no—
197SD16—382no—
198SD16—382no—
199SD16—382no—
200D8—192no—
201D8—382no—
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—41no—
217C23—382no—
218C23—762no—
219Q8—22no—
220Q8—192no—
221Q8—761no—
222Q8D4×D1912yes—
223D4—22no—
224D4—22no—
225D4—42no—
226D4—192no—
227D4—382no—
228D4—382no—
229D4—382no—
230D4—762no—
231D4—761no—
232D4—762no—
233D4—1522no—
234D4D4×D1912yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—382no—
240C2×C4—762no—
241C2×C4—762no—
242C2×C4C23×D1911yescharacteristic
243C8—22no—
244C8—192no—
245C8—192no—
246C8—382no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—161no—
251C22—382no—
252C22—3042no—
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×#455C2
socleC2×C19D42
hypercenter#455D19
hypocenterC19#3288
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #11927353C2semidirect
2. #11927347C2semidirect
3. #11926934C2semidirect
4. #11926813C2semidirect
5. #11926809C2semidirect
6. #11926716C2semidirect
7. #11926713C2semidirect
8. #11926663C2semidirect
9. C19×#455C2semidirect
11. #10597435C22semidirect
12. #10597433C22semidirect
13. C19×#137C22semidirect
14. C19×#124C22semidirect
19. #10597394C22semidirect
20. C2×#64527C22semidirect
22. #10597378C22semidirect
24. C2×#64525C22semidirect
29. #10597354C22semidirect
30. #10597353C22semidirect
31. #10597320C22semidirect
32. C19×#104C22semidirect
33. C19×#100C22semidirect
34. #10597293C22semidirect
35. #10597280C22semidirect
36. #10597279C22semidirect
37. #10597262C22semidirect
38. #10597260C22semidirect
61. #64528D4semidirect
65. #64527D4semidirect
67. #64526D4semidirect
72. #64525D4semidirect
133. #455D19semidirect
147. #137C2×D19semidirect
164. #124C2×D19semidirect
167. #104C2×D19semidirect
170. #100C2×D19semidirect
172. C19#3288semidirect

Maximal subgroups

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

subgroupindex
#119273532
#119273472
#119269342
#119268132
#119268092
#119267162
#119267132
#119266632
C19×#4552
#328819