Finite Group Databasebeta

← #14574097

Subgroups — #14574097

Order 2432.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#10597355C211yesmaximal, characteristic, complemented
2C2×#10597397C211yesmaximal, characteristic, complemented
3C2×#10597378C211yesmaximal, characteristic, complemented
4#11927090C211yesmaximal, characteristic, complemented
5C2×#10597382C211yesmaximal, characteristic, complemented
6#11926935C212yesmaximal, complemented
7#11926932C212yesmaximal, complemented
8#11926927C212yesmaximal, complemented
9#11926925C212yesmaximal, complemented
10M16×Dic19C211yesmaximal, characteristic, complemented
11C2×C19×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
12C2×#41×C19C2211yescharacteristic
13C22×D4×C19C2211yescharacteristic
14C2×#64541C2211yescharacteristic
15C22×Dic38C2211yescharacteristic
16C19×AGL(1,ℤ/8)—24no—
17C2×SD16×C19C2212yes—
18C2×D8×C19C2212yes—
19C2×M16×C19C2211yescharacteristic
20C2×C22⋊Dic19—22no—
21#10597397—24no—
22#10597393C2211yescharacteristic, complemented
23#10597390C2211yescharacteristic, complemented
24C2×#64528C2212yescomplemented
25#10597386C2211yescharacteristic, complemented
26#10597385—22no—
27#10597382—22no—
28#10597382C2212yes—
29#10597382C2212yes—
30#10597382C2211yescharacteristic, complemented
31C2×#64526C2212yes—
32C2×#64526C2212yescomplemented
33#10597378—24no—
34C2×#64525C2212yes—
35C4×C22⋊D19—22no—
36C2×C4×Dic19C2211yescharacteristic
37C2×#64520C2211yescharacteristic
38#10597355—24no—
39C2×Dic76C2212yescomplemented
40C2×#64516C2212yescomplemented
41#10597272C2212yescomplemented
42C8×Dic19C2212yescomplemented
43C24×C19—21no—
44#41×C19—22no—
45#41×C19—22no—
46C2×Q8×C19C2311yescharacteristic
47C2×D4×C19—21no—
48C2×D4×C19—22no—
49C2×D4×C19—22no—
50C2×D4×C19—21no—
51C2×D4×C19C2312yes—
52C2×D4×C19C2311yescharacteristic
53C22×C4×C19—21no—
54C22×C4×C19C2311yescharacteristic
55C2×C22⋊D19—21no—
56C2×C22⋊D19—22no—
57C22×Dic19—21no—
58C22×Dic19D412yes—
59#64541—22no—
60#64541—22no—
61C2×D76C2311yescharacteristic
62C2×C4×D19—21no—
63C2×Dic38—22no—
64C2×Dic38—22no—
65C2×Dic38—21no—
66C2×Dic38C2311yescharacteristic
67C2×Dic38C2312yes—
68SD16×C19—24no—
69D8×C19—24no—
70M16×C19D414yescomplemented
71C2×C8×C19C2312yes—
72C22⋊Dic19—24no—
73C22⋊Dic19—24no—
74C22⋊Dic19—22no—
75#64528—24no—
76#64526—24no—
77#64526—24no—
78#64525—24no—
79(C2×D19)⋊C4—22no—
80Dic19⋊C4—22no—
81C4×Dic19D412yes—
82C4×Dic19C2311yescharacteristic
83C4×Dic19C2311yescharacteristic
84#64520D414yescomplemented
85C2×C19⋊C8C2312yes—
86Dic76—24no—
87#64516—24no—
88C23×C19—22no—
89C23×C19—21no—
90C23×C19—44no—
91C23×C19—42no—
92C23×C19C2×D411yescharacteristic
93C22×D19—21no—
94Q8×C19—21no—
95Q8×C19—21no—
96D4×C19—22no—
97D4×C19—21no—
98D4×C19—21no—
99D4×C19—22no—
100D4×C19—42no—
101D4×C19—42no—
102C2×C4×C19—21no—
103C2×C4×C19—42no—
104C2×C4×C19C2×D411yescharacteristic
105C2×C4×C19C2×D412yes—
106C2×C4×C19C2×D412yes—
107C2×C4×C19C2411yescharacteristic
108C22⋊D19—44no—
109C22⋊D19—42no—
110C2×Dic19—21no—
111C2×Dic19—22no—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19C2×D412yes—
115C2×Dic19C2×D412yes—
116D76—21no—
117D76—21no—
118C4×D19—42no—
119Dic38—22no—
120Dic38—21no—
121Dic38—21no—
122Dic38—22no—
123Dic38—42no—
124C8×C19C2×D414yes—
125C19⋊C8C2×D414yes—
126#3153—191nomaximal, Sylow
127C22×C19—22no—
128C22×C19—41no—
129C22×C19—42no—
130C22×C19—42no—
131C22×C19—44no—
132C22×C19—84no—
133C22×C19#12712yes—
134C22×C19C22×D411yescharacteristic
135C2×D19—41no—
136C2×D19—42no—
137C4×C19—41no—
138C4×C19#12712yes—
139C4×C19C22×D411yescharacteristic
140C4×C19C22×D411yescharacteristic
141Dic19—22no—
142Dic19—22no—
143Dic19—42no—
144Dic19—41no—
145C2×#137—191no—
146C2×#137—191no—
147C2×AGL(1,ℤ/8)—191no—
148C2×AGL(1,ℤ/8)D1911yescharacteristic, complemented
149#532—191no—
150C2×#124—191no—
151#497—192no—
152#496—192no—
153#495—192no—
154#495—192no—
155C4×M16—191no—
156C2×C19—22no—
157C2×C19—81no—
158C2×C19—82no—
159C2×C19C2×#12711yescharacteristic
160C2×C19#57512yes—
161D19—81no—
162C2×#41—191no—
163C2×#41C2×D1911yescharacteristic
164C22×Q8—191no—
165C22×D4C2×D1911yescharacteristic
166#137—384no—
167#137—384no—
168AGL(1,ℤ/8)—24no—
169AGL(1,ℤ/8)—384no—
170C2×Q16—192no—
171C2×Q16—192no—
172C2×SD16—192no—
173C2×SD16—192no—
174C2×SD16—192no—
175C2×SD16C2×D1912yes—
176C2×D8—192no—
177C2×D8C2×D1912yes—
178C2×M16—191no—
179C2×M16C2×D1911yescharacteristic
180C4⋊Q8—191no—
181#127—191no—
182#124—191no—
183#124—192no—
184#124—192no—
185#124—191no—
186#124—382no—
187#121—382no—
188C4×D4—382no—
189C2×C22⋊C4—382no—
190C2×C42—191no—
191#97—192no—
192C4×C8—192no—
193C19#315311yescharacteristic, complemented, Sylow
194C24—21no—
195#41—22no—
196#41—22no—
197#41—382no—
198#41—382no—
199C2×Q8—192no—
200C2×Q8—191no—
201C2×Q8—381no—
202C2×Q8—382no—
203C2×Q8—382no—
204C2×Q8C22×D1911yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—22no—
209C2×D4—191no—
210C2×D4—382no—
211C2×D4—381no—
212C2×D4C22×D1912yes—
213C2×D4C22×D1911yescharacteristic
214C22×C4—21no—
215C22×C4—192no—
216C22×C4—381no—
217C22×C4—381no—
218C22×C4C22×D1911yescharacteristic
219Q16—384no—
220Q16—384no—
221SD16—24no—
222SD16—384no—
223SD16—384no—
224SD16—384no—
225D8—24no—
226D8—384no—
227M16—194no—
228M16C22⋊D1914yescomplemented
229C2×C8—192no—
230C2×C8C22×D1912yes—
231C4⋊C4—382no—
232C22⋊C4—382no—
233C22⋊C4—384no—
234C22⋊C4—384no—
235C22⋊C4—382no—
236C42—192no—
237C42—191no—
238C42—191no—
239C23—22no—
240C23—21no—
241C23—44no—
242C23—42no—
243C23—381no—
244C23D4×D1911yescharacteristic
245Q8—21no—
246Q8—21no—
247Q8—381no—
248Q8—382no—
249Q8—382no—
250Q8—381no—
251Q8—762no—
252D4—22no—
253D4—21no—
254D4—21no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—381no—
259D4—381no—
260D4—764no—
261D4—762no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—192no—
265C2×C4—192no—
266C2×C4—382no—
267C2×C4—381no—
268C2×C4—762no—
269C2×C4—762no—
270C2×C4—762no—
271C2×C4D4×D1911yescharacteristic
272C2×C4D4×D1912yes—
273C2×C4C2×C22⋊D1912yes—
274C2×C4C23×D1911yescharacteristic
275C8—194no—
276C8C2×C22⋊D1914yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—44no—
282C22—84no—
283C22—761no—
284C22—762no—
285C22#1059738612yes—
286C22C2×D4×D1911yescharacteristic
287C4—41no—
288C4—382no—
289C4—382no—
290C4—761no—
291C4—762no—
292C4#1059738612yes—
293C4C2×D4×D1911yescharacteristic
294C4C22×C22⋊D1911yescharacteristic
295C2—22no—
296C2—82no—
297C2—81no—
298C2—1521no—
299C2C2×#1059738611yescharacteristic
300C2#1192734012yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×AGL(1,ℤ/8)C2
socleC22×C19C22×D4
hypercenterC2×AGL(1,ℤ/8)D19
hypocenterC19#3153
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#10597355C2semidirect
2. C2×#10597397C2semidirect
3. C2×#10597378C2semidirect
4. #11927090C2semidirect
5. C2×#10597382C2semidirect
6. #11926935C2semidirect
7. #11926932C2semidirect
8. #11926927C2semidirect
9. #11926925C2semidirect
10. M16×Dic19C2semidirect
11. C2×C19×AGL(1,ℤ/8)C2semidirect
22. #10597393C22semidirect
23. #10597390C22semidirect
24. C2×#64528C22semidirect
25. #10597386C22semidirect
30. #10597382C22semidirect
32. C2×#64526C22semidirect
39. C2×Dic76C22semidirect
40. C2×#64516C22semidirect
41. #10597272C22semidirect
42. C8×Dic19C22semidirect
70. M16×C19D4semidirect
84. #64520D4semidirect
148. C2×AGL(1,ℤ/8)D19semidirect
193. C19#3153semidirect
228. M16C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973552
C2×#105973972
C2×#105973782
#119270902
C2×#105973822
#119269352
#119269322
#119269272
#119269252
M16×Dic192
C2×C19×AGL(1,ℤ/8)2
#315319