Finite Group Databasebeta

← #14574083

Subgroups — #14574083

Order 2432.

656 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10597354C211yesmaximal, characteristic, complemented
2C2×#10597378C211yesmaximal, characteristic, complemented
3C2×#10597395C211yesmaximal, characteristic, complemented
4#11927090C211yesmaximal, characteristic, complemented
5C2×#10597386C211yesmaximal, characteristic, complemented
6#11926932C212yesmaximal, complemented
7#11926930C212yesmaximal, complemented
8#11926919C212yesmaximal, complemented
9#11926915C212yesmaximal, complemented
10M16×Dic19C211yesmaximal, characteristic, complemented
11C2×C19×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
12C2×#41×C19C2211yescharacteristic
13C22×D4×C19C2211yescharacteristic
14C22×C22⋊D19—22no—
15C2×#64541C2211yescharacteristic
16C22×D76C2211yescharacteristic
17C19×AGL(1,ℤ/8)—24no—
18C2×SD16×C19C2212yescomplemented
19C2×D8×C19C2212yescomplemented
20C2×M16×C19C2211yescharacteristic
21#10597395—24no—
22#10597393C2211yescharacteristic, complemented
23#10597390C2211yescharacteristic, complemented
24C2×#64527C2212yescomplemented
25#10597386—22no—
26#10597386C2212yes—
27#10597386C2212yes—
28#10597386C2211yescharacteristic, complemented
29#10597385—22no—
30#10597382C2211yescharacteristic, complemented
31C2×#64526C2212yescomplemented
32#10597378—24no—
33C2×#64525C2212yescomplemented
34C2×#64525C2212yescomplemented
35C4×C22⋊D19—22no—
36C2×C4×Dic19C2211yescharacteristic
37C2×#64520C2211yescharacteristic
38#10597354—24no—
39C2×D152C2212yescomplemented
40C2×#64516C2212yescomplemented
41#10597272C2212yescomplemented
42C8×Dic19C2212yescomplemented
43C24×C19—21no—
44C23×D19—21no—
45#41×C19—22no—
46#41×C19—22no—
47C2×Q8×C19C2311yescharacteristic
48C2×D4×C19—21no—
49C2×D4×C19—22no—
50C2×D4×C19—22no—
51C2×D4×C19—21no—
52C2×D4×C19C2311yescharacteristic
53C2×D4×C19C2312yes—
54C22×C4×C19—21no—
55C22×C4×C19C2311yescharacteristic
56C2×C22⋊D19—21no—
57C2×C22⋊D19—22no—
58C2×C22⋊D19—24no—
59C2×C22⋊D19—24no—
60C2×C22⋊D19—48no—
61C22×Dic19D412yes—
62#64541—22no—
63#64541—22no—
64C2×D76—22no—
65C2×D76—22no—
66C2×D76—21no—
67C2×D76C2311yescharacteristic
68C2×D76C2312yes—
69C2×C4×D19—21no—
70C2×Dic38C2311yescharacteristic
71SD16×C19—24no—
72D8×C19—24no—
73M16×C19D414yescomplemented
74C2×C8×C19C2312yes—
75C22⋊Dic19—22no—
76#64527—24no—
77#64526—24no—
78#64525—24no—
79#64525—24no—
80(C2×D19)⋊C4—22no—
81Dic19⋊C4—22no—
82C4×Dic19D412yes—
83C4×Dic19C2311yescharacteristic
84C4×Dic19C2311yescharacteristic
85#64520D414yescomplemented
86C2×C19⋊C8C2312yes—
87D152—24no—
88#64516—24no—
89C23×C19—21no—
90C23×C19—22no—
91C23×C19—44no—
92C23×C19—42no—
93C23×C19C2×D411yescharacteristic
94C22×D19—21no—
95C22×D19—22no—
96C22×D19—44no—
97C22×D19—42no—
98Q8×C19—21no—
99Q8×C19—21no—
100D4×C19—21no—
101D4×C19—22no—
102D4×C19—21no—
103D4×C19—22no—
104D4×C19—42no—
105D4×C19—42no—
106C2×C4×C19—21no—
107C2×C4×C19—42no—
108C2×C4×C19C2×D411yescharacteristic
109C2×C4×C19C2×D412yes—
110C2×C4×C19C2×D412yes—
111C2×C4×C19C2411yescharacteristic
112C22⋊D19—48no—
113C22⋊D19—42no—
114C22⋊D19—44no—
115C22⋊D19—48no—
116C2×Dic19—24no—
117C2×Dic19—21no—
118C2×Dic19C2×D412yes—
119C2×Dic19C2×D412yes—
120D76—22no—
121D76—21no—
122D76—21no—
123D76—22no—
124D76—42no—
125C4×D19—42no—
126Dic38—21no—
127Dic38—21no—
128C8×C19C2×D414yescomplemented
129C19⋊C8C2×D414yescomplemented
130#3151—191nomaximal, Sylow
131C22×C19—22no—
132C22×C19—41no—
133C22×C19—42no—
134C22×C19—44no—
135C22×C19—42no—
136C22×C19—84no—
137C22×C19#12712yes—
138C22×C19C22×D411yescharacteristic
139C2×D19—41no—
140C2×D19—42no—
141C2×D19—44no—
142C2×D19—42no—
143C2×D19—84no—
144C4×C19—41no—
145C4×C19#12712yes—
146C4×C19C22×D411yescharacteristic
147C4×C19C22×D411yescharacteristic
148Dic19—22no—
149Dic19—41no—
150Dic19AGL(1,ℤ/8)14yescomplemented
151C2×AGL(1,ℤ/8)—191no—
152C2×AGL(1,ℤ/8)—191no—
153C2×AGL(1,ℤ/8)—191no—
154C2×AGL(1,ℤ/8)D1911yescharacteristic, complemented
155#532—191no—
156C2×#127—191no—
157#496—192no—
158#496—192no—
159#493—192no—
160#492—192no—
161C4×M16—191no—
162C2×C19—22no—
163C2×C19—81no—
164C2×C19—82no—
165C2×C19C2×#12711yescharacteristic
166C2×C19C2×AGL(1,ℤ/8)12yes—
167D19—81no—
168D19—82no—
169C2×#41—191no—
170C2×#41C2×D1911yescharacteristic
171C22×D4—191no—
172C22×D4—382no—
173C22×D4C2×D1911yescharacteristic
174AGL(1,ℤ/8)—24no—
175AGL(1,ℤ/8)—384no—
176AGL(1,ℤ/8)—384no—
177AGL(1,ℤ/8)—384no—
178C2×SD16—192no—
179C2×SD16—192no—
180C2×SD16—192no—
181C2×SD16C2×D1912yescomplemented
182C2×D8—192no—
183C2×D8—192no—
184C2×D8—192no—
185C2×D8C2×D1912yescomplemented
186C2×M16—191no—
187C2×M16C2×D1911yescharacteristic
188C4⋊Q8—191no—
189#127—192no—
190#127—192no—
191#127—191no—
192#127—382no—
193#124—191no—
194#124—191no—
195#121—382no—
196C4×D4—382no—
197C2×C42—191no—
198#97—192no—
199C4×C8—192no—
200C19#315111yescharacteristic, complemented, Sylow
201C24—21no—
202C24—381no—
203#41—22no—
204#41—22no—
205#41—382no—
206#41—382no—
207C2×Q8—191no—
208C2×Q8C22×D1911yescharacteristic
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—22no—
213C2×D4—191no—
214C2×D4—192no—
215C2×D4—382no—
216C2×D4—384no—
217C2×D4—384no—
218C2×D4—381no—
219C2×D4—382no—
220C2×D4—381no—
221C2×D4—382no—
222C2×D4—768no—
223C2×D4C22×D1911yescharacteristic
224C2×D4C22×D1912yes—
225C22×C4—21no—
226C22×C4—192no—
227C22×C4—381no—
228C22×C4C22×D1911yescharacteristic
229SD16—24no—
230SD16—384no—
231SD16—384no—
232SD16—384no—
233D8—24no—
234D8—384no—
235D8—384no—
236D8—384no—
237M16—194no—
238M16C22⋊D1914yescomplemented
239C2×C8—192no—
240C2×C8C22×D1912yes—
241C4⋊C4—382no—
242C22⋊C4—382no—
243C22⋊C4—382no—
244C42—192no—
245C42—191no—
246C42—191no—
247C23—21no—
248C23—22no—
249C23—44no—
250C23—42no—
251C23—381no—
252C23—382no—
253C23—764no—
254C23—762no—
255C23D4×D1911yescharacteristic
256Q8—21no—
257Q8—21no—
258Q8—381no—
259Q8—381no—
260D4—21no—
261D4—22no—
262D4—21no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—381no—
267D4—382no—
268D4—381no—
269D4—382no—
270D4—768no—
271D4—764no—
272D4—768no—
273D4—762no—
274D4—762no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—192no—
278C2×C4—192no—
279C2×C4—384no—
280C2×C4—381no—
281C2×C4—762no—
282C2×C4D4×D1911yescharacteristic
283C2×C4D4×D1912yes—
284C2×C4C2×C22⋊D1912yes—
285C2×C4C23×D1911yescharacteristic
286C8—194no—
287C8C2×C22⋊D1914yescomplemented
288C22—22no—
289C22—44no—
290C22—42no—
291C22—41no—
292C22—42no—
293C22—84no—
294C22—764no—
295C22—762no—
296C22—761no—
297C22—762no—
298C22—1524no—
299C22#1059738612yes—
300C22C2×D4×D1911yescharacteristic
301C4—41no—
302C4—194no—
303C4—382no—
304C4—761no—
305C4#1059738612yes—
306C4C2×D4×D1911yescharacteristic
307C4C22×C22⋊D1911yescharacteristic
308C2—22no—
309C2—82no—
310C2—81no—
311C2—1522no—
312C2—1521no—
313C2C2×#1059738611yescharacteristic
314C2AGL(1,ℤ/8)×D1912yes—
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#3151
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×#10597354C2semidirect
2. C2×#10597378C2semidirect
3. C2×#10597395C2semidirect
4. #11927090C2semidirect
5. C2×#10597386C2semidirect
6. #11926932C2semidirect
7. #11926930C2semidirect
8. #11926919C2semidirect
9. #11926915C2semidirect
10. M16×Dic19C2semidirect
11. C2×C19×AGL(1,ℤ/8)C2semidirect
18. C2×SD16×C19C22semidirect
19. C2×D8×C19C22semidirect
22. #10597393C22semidirect
23. #10597390C22semidirect
24. C2×#64527C22semidirect
28. #10597386C22semidirect
30. #10597382C22semidirect
31. C2×#64526C22semidirect
33. C2×#64525C22semidirect
34. C2×#64525C22semidirect
39. C2×D152C22semidirect
40. C2×#64516C22semidirect
41. #10597272C22semidirect
42. C8×Dic19C22semidirect
73. M16×C19D4semidirect
85. #64520D4semidirect
128. C8×C19C2×D4semidirect
129. C19⋊C8C2×D4semidirect
150. Dic19AGL(1,ℤ/8)semidirect
154. C2×AGL(1,ℤ/8)D19semidirect
181. C2×SD16C2×D19semidirect
185. C2×D8C2×D19semidirect
200. C19#3151semidirect
238. M16C22⋊D19semidirect
287. C8C2×C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973542
C2×#105973782
C2×#105973952
#119270902
C2×#105973862
#119269322
#119269302
#119269192
#119269152
M16×Dic192
C2×C19×AGL(1,ℤ/8)2
#315119