Finite Group Databasebeta

← #14575430

Subgroups — #14575430

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#11927355C212yesmaximal, complemented
2#11927354C212yesmaximal, complemented
3#11926916C211yesmaximal, characteristic, complemented
4#11926806C212yesmaximal, complemented
5#11926805C212yesmaximal, complemented
6#11926728C212yesmaximal, complemented
7#11926711C211yesmaximal, characteristic, complemented
8#11926658C212yesmaximal, complemented
9C19×#453C211yesmaximal, characteristic, complemented
10C19×H(5,𝔽2)C2211yescharacteristic, complemented
11#10597436C2212yes—
12#10597430C2211yescharacteristic, complemented
13C19×AGL(1,ℤ/8)C2212yes—
14C19×#127C2211yescharacteristic
15#10597397—22no—
16#10597397C2212yescomplemented
17#10597396—22no—
18#10597396C2212yes—
19#10597394C2212yescomplemented
20C2×#64526—22no—
21C2×#64526C2212yescomplemented
22C2×#64526C2212yescomplemented
23#10597378—22no—
24#10597378C2212yes—
25#10597361—22no—
26SD16×D19—22no—
27#10597358—22no—
28#10597357—22no—
29#10597355C2212yescomplemented
30#10597353C2212yescomplemented
31#10597315C2211yescharacteristic, complemented
32C19×#104C2212yescomplemented
33C19×#100C2211yescharacteristic, complemented
34#10597290C2211yescharacteristic, complemented
35#10597281C2212yescomplemented
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—
47Q8×D19—22no—
48#64543—22no—
49#64543—22no—
50#64543—42no—
51D4×D19—22no—
52#64541—22no—
53#64541C2312yes—
54C2×Dic38—22no—
55C2×Dic38C2312yes—
56SD16×C19—22no—
57D8×C19—22no—
58M16×C19C2312yes—
59C42×C19C2311yescharacteristic
60#64528—22no—
61#64528D412yescomplemented
62#64527D412yescomplemented
63#64526—22no—
64#64526—22no—
65#64526—22no—
66#64526—22no—
67#64526—22no—
68#64526—22no—
69#64526D412yescomplemented
70#64525—22no—
71#64525D412yescomplemented
72C4⋊Dic19—41no—
73#64520—22no—
74#64520C2312yes—
75C2×C19⋊C8—22no—
76C2×C19⋊C8C2312yes—
77Dic76—22no—
78#64516—22no—
79#64515—22no—
80C8×D19—22no—
81C23×C19—21no—
82C23×C19—21no—
83C23×C19—41no—
84C22×D19—41no—
85Q8×C19C2×D412yes—
86D4×C19—22no—
87D4×C19—22no—
88D4×C19—22no—
89D4×C19—42no—
90D4×C19—82no—
91D4×C19C2×D412yes—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—41no—
95C2×C4×C19C2411yescharacteristic
96C22⋊D19—22no—
97C22⋊D19—42no—
98C22⋊D19—42no—
99C2×Dic19—22no—
100C2×Dic19—41no—
101C2×Dic19—42no—
102D76C2×D412yes—
103C4×D19—22no—
104C4×D19—42no—
105Dic38—22no—
106Dic38—22no—
107Dic38—42no—
108Dic38C2×D412yes—
109C8×C19—22no—
110C19⋊C8—22no—
111C19⋊C8C2×D412yes—
112C19⋊C8C2×D412yes—
113#3291—191nomaximal, Sylow
114C22×C19—22no—
115C22×C19—41no—
116C22×C19—41no—
117C22×C19—81no—
118C22×C19—81no—
119C22×C19—161no—
120C22×C19H(5,𝔽2)11yescharacteristic
121C2×D19—22no—
122C2×D19—161no—
123C4×C19—22no—
124C4×C19—22no—
125C4×C19C22×D412yes—
126Dic19—22no—
127Dic19—42no—
128#577—192no—
129#577—192no—
130#492—191no—
131#471—192no—
132#471—192no—
133#456—192no—
134#453—191no—
135#453D1911yescharacteristic, complemented
136#443—192no—
137C2×C19—21no—
138C2×C19—42no—
139C2×C19—81no—
140C2×C19—81no—
141C2×C19D4211yescharacteristic
142D19—42no—
1432−1+4—192no—
144H(5,𝔽2)—191no—
145H(5,𝔽2)C2×D1911yescharacteristic, complemented
146#137—192no—
147#137—192no—
148#137—382no—
149#137—382no—
150AGL(1,ℤ/8)—192no—
151AGL(1,ℤ/8)—382no—
152AGL(1,ℤ/8)—382no—
153AGL(1,ℤ/8)C2×D1912yes—
154#135—192no—
155#135—382no—
156#135—382no—
157C2×SD16—192no—
158C2×SD16—192no—
159C2×SD16—382no—
160C2×SD16—382no—
161#131—192no—
162#131—192no—
163C4⋊Q8—191no—
164#127C2×D1911yescharacteristic
165#108—192no—
166#104—192no—
167#104C2×D1912yescomplemented
168#101—192no—
169#100—191no—
170#100C2×D1911yescharacteristic, complemented
171C4×C8—191no—
172C19#329111yescharacteristic, complemented, Sylow
173#41—22no—
174#41—192no—
175#41—382no—
176#41—382no—
177#41—382no—
178#41—762no—
179#41C22×D1912yes—
180C2×Q8—192no—
181C2×Q8—382no—
182C2×Q8—382no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—382no—
187C2×D4—761no—
188C2×D4C22×D1911yescharacteristic
189C2×D4C22×D1911yescharacteristic
190Q16—192no—
191Q16—382no—
192Q16—382no—
193SD16—22no—
194SD16—192no—
195SD16—192no—
196SD16—382no—
197SD16—382no—
198SD16—382no—
199SD16—382no—
200SD16—382no—
201SD16—382no—
202SD16—382no—
203D8—22no—
204D8—192no—
205D8—382no—
206M16—192no—
207M16—382no—
208M16—382no—
209M16C22×D1912yes—
210C2×C8—192no—
211C2×C8—382no—
212C2×C8—382no—
213C4⋊C4—761no—
214C42C22×D1911yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—761no—
219Q8—192no—
220Q8—382no—
221Q8—382no—
222Q8—762no—
223Q8D4×D1912yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—192no—
230D4—382no—
231D4—762no—
232D4—762no—
233D4D4×D1912yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—382no—
238C2×C4—382no—
239C2×C4—762no—
240C2×C4—761no—
241C2×C4—762no—
242C2×C4C23×D1911yescharacteristic
243C8—22no—
244C8—192no—
245C8—192no—
246C8—382no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—382no—
254C22—3041no—
255C22#1059743011yescharacteristic
256C4—22no—
257C4—22no—
258C4—382no—
259C4—762no—
260C4C2×D4×D1912yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—762no—
266C2#1192717611yescharacteristic
subgroupG/H
centerC2#11927176
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#453C2
socleC2×C19D42
hypercenter#453D19
hypocenterC19#3291
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. #11927355C2semidirect
2. #11927354C2semidirect
3. #11926916C2semidirect
4. #11926806C2semidirect
5. #11926805C2semidirect
6. #11926728C2semidirect
7. #11926711C2semidirect
8. #11926658C2semidirect
9. C19×#453C2semidirect
10. C19×H(5,𝔽2)C22semidirect
12. #10597430C22semidirect
16. #10597397C22semidirect
19. #10597394C22semidirect
21. C2×#64526C22semidirect
22. C2×#64526C22semidirect
29. #10597355C22semidirect
30. #10597353C22semidirect
31. #10597315C22semidirect
32. C19×#104C22semidirect
33. C19×#100C22semidirect
34. #10597290C22semidirect
35. #10597281C22semidirect
36. #10597279C22semidirect
37. #10597262C22semidirect
38. C4×C19⋊C8C22semidirect
61. #64528D4semidirect
62. #64527D4semidirect
69. #64526D4semidirect
71. #64525D4semidirect
135. #453D19semidirect
145. H(5,𝔽2)C2×D19semidirect
167. #104C2×D19semidirect
170. #100C2×D19semidirect
172. C19#3291semidirect

Maximal subgroups

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

subgroupindex
#119273552
#119273542
#119269162
#119268062
#119268052
#119267282
#119267112
#119266582
C19×#4532
#329119