Finite Group Databasebeta

← D4×#64525 #14575308

Subgroups — D4×#64525 #14575308

Order 2432.

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

normal subgroups only

This group has 620 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
1C22×#64525C212yesmaximal, complemented
2D4×D76C211yesmaximal, characteristic, complemented
3#11926920C211yesmaximal, characteristic, complemented
4#11926778C212yesmaximal, complemented
5#11926739C211yesmaximal, characteristic, complemented
6#11926736C211yesmaximal, characteristic, complemented
7#11926678C212yesmaximal, complemented
8#11926677C212yesmaximal, complemented
9C4×#64525C211yesmaximal, characteristic, complemented
10D4×C19⋊C8C211yesmaximal, characteristic, complemented
11D42×C19C211yesmaximal, characteristic, complemented
12C22×D4×C19—21no—
13C22×D4×C19C2212yescomplemented
14C2×D4×D19—21no—
15C22×D76C2212yescomplemented
16C19×#127C2211yescharacteristic, complemented
17C19×#121—21no—
18C19×#121C2212yescomplemented
19C19×#120—22no—
20C4×D4×C19C2211yescharacteristic
21C4×D4×C19C2211yescharacteristic, complemented
22C2×#64525—28no—
23C2×#64525C2211yescharacteristic
24C2×#64525C2212yescomplemented
25C2×#64525C2212yescomplemented
26C2×#64525C2212yescomplemented
27C2×#64525C2212yescomplemented
28#10597376C2212yescomplemented
29C22×C19⋊C8C2212yescomplemented
30#10597341—21no—
31#10597328—22no—
32#10597320C2211yescharacteristic, complemented
33C4×D76C2211yescharacteristic, complemented
34#10597289C2211yescharacteristic, complemented
35#10597289C2212yescomplemented
36C22⋊(C19⋊C8)C2212yescomplemented
37#10597266C2211yescharacteristic, complemented
38#10597266C2212yescomplemented
39#10597264C2211yescharacteristic, complemented
40C4⋊(C19⋊C8)C2211yescharacteristic, complemented
41C4×C19⋊C8C2211yescharacteristic, complemented
42C24×C19—22no—
43C23×D19—22no—
44C2×D4×C19—24no—
45C2×D4×C19—22no—
46C2×D4×C19—22no—
47C2×D4×C19—21no—
48C2×D4×C19—21no—
49C2×D4×C19—42no—
50C2×D4×C19—44no—
51C2×D4×C19D411yescharacteristic
52C2×D4×C19C2312yes—
53C2×D4×C19C2311yescharacteristic
54C22×C4×C19—21no—
55C22×C4×C19C2312yes—
56C2×C22⋊D19—22no—
57D4×D19—44no—
58C2×D76—24no—
59C2×D76—22no—
60C2×D76—21no—
61C2×D76—21no—
62C2×D76—42no—
63C2×D76C2312yes—
64C2×D76C2311yescharacteristic
65C2×C4×D19—21no—
66C4⋊C4×C19D411yescharacteristic
67C4⋊C4×C19C2311yescharacteristic
68C22⋊C4×C19—21no—
69C22⋊C4×C19—22no—
70C22⋊C4×C19D412yes—
71C42×C19C2311yescharacteristic
72#64525—24no—
73#64525—24no—
74#64525—24no—
75#64525—42no—
76#64525D414yesdirect product factor
77(C2×D19)⋊C4—22no—
78(C2×D19)⋊C4—21no—
79C4⋊Dic19C2311yescharacteristic
80C2×C19⋊C8—24no—
81C2×C19⋊C8C2311yescharacteristic
82C2×C19⋊C8C2312yes—
83C2×C19⋊C8C2311yescharacteristic
84C23×C19—21no—
85C23×C19—22no—
86C23×C19—44no—
87C23×C19—44no—
88C23×C19—82no—
89C23×C19C2×D412yes—
90C22×D19—21no—
91C22×D19—22no—
92C22×D19—44no—
93C22×D19—44no—
94C22×D19—82no—
95D4×C19—22no—
96D4×C19—21no—
97D4×C19—22no—
98D4×C19—44no—
99D4×C19—44no—
100D4×C19—42no—
101D4×C19—81no—
102D4×C19D814yescomplemented
103D4×C19C2×D412yescomplemented
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—21no—
107C2×C4×C19—42no—
108C2×C4×C19C2×D411yescharacteristic
109C2×C4×C19C2×D412yes—
110C2×C4×C19C2×D411yescharacteristic
111C2×C4×C19C2411yescharacteristic
112C22⋊D19—44no—
113C2×Dic19—21no—
114D76—22no—
115D76—21no—
116D76—22no—
117D76—44no—
118D76—42no—
119D76—81no—
120D76C2×D412yescomplemented
121C4×D19—42no—
122C19⋊C8—22no—
123C19⋊C8—21no—
124C19⋊C8C2×D412yescomplemented
125D4×D8—191nomaximal, Sylow
126C22×C19—22no—
127C22×C19—22no—
128C22×C19—22no—
129C22×C19—41no—
130C22×C19—41no—
131C22×C19—42no—
132C22×C19—42no—
133C22×C19—42no—
134C22×C19—88no—
135C22×C19C2×D814yescomplemented
136C22×C19C22×D411yescharacteristic
137C2×D19—22no—
138C2×D19—41no—
139C2×D19—41no—
140C2×D19—42no—
141C2×D19—42no—
142C2×D19—42no—
143C2×D19—88no—
144C4×C19—22no—
145C4×C19—21no—
146C4×C19—41no—
147C4×C19C2×D812yescomplemented
148C4×C19C22×D411yescharacteristic
149C4×C19H(5,𝔽2)11yescharacteristic
150Dic19—41no—
151C22×D8—192no—
152D42—191no—
153D42D1911yescharacteristic, complemented
154#493—191no—
155#466—192no—
156#459—191no—
157#459—191no—
158#447—192no—
159#447—192no—
160C4×D8—191no—
161C8×D4—191no—
162C2×C19—24no—
163C2×C19—42no—
164C2×C19—82no—
165C2×C19D4211yescharacteristic
166C2×C19C22×D811yescharacteristic
167C2×C19#57611yescharacteristic
168D19—42no—
169D19—82no—
170C22×D4—21no—
171C22×D4—192no—
172C22×D4—381no—
173C22×D4C2×D1912yescomplemented
174C2×D8—191no—
175C2×D8—192no—
176C2×D8—192no—
177C2×D8—192no—
178C2×D8—192no—
179C2×D8—388no—
180C22×C8—192no—
181#127—191no—
182#127C2×D1911yescharacteristic, complemented
183#121—21no—
184#121—192no—
185#121—381no—
186#121C2×D1912yescomplemented
187#120—22no—
188#120—382no—
189C4×D4—191no—
190C4×D4C2×D1911yescharacteristic
191C4×D4C2×D1911yescharacteristic, complemented
192#107—191no—
193C4⋊C8—191no—
194#102—191no—
195#102—192no—
196#102—191no—
197#102—192no—
198C22⋊C8—192no—
199C4×C8—191no—
200C19D4×D811yescharacteristic, complemented, Sylow
201C24—22no—
202C24—382no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—191no—
211C2×D4—192no—
212C2×D4—384no—
213C2×D4—382no—
214C2×D4—382no—
215C2×D4—381no—
216C2×D4—381no—
217C2×D4—762no—
218C2×D4—764no—
219C2×D4C22⋊D1911yescharacteristic
220C2×D4C22×D1912yes—
221C2×D4C22×D1911yescharacteristic
222C22×C4—21no—
223C22×C4—381no—
224C22×C4C22×D1912yes—
225D8—194no—
226D8—384no—
227D8—384no—
228D8—384no—
229D8—762no—
230C2×C8—191no—
231C2×C8—191no—
232C2×C8—192no—
233C2×C8—384no—
234C4⋊C4—191no—
235C4⋊C4C22⋊D1911yescharacteristic
236C4⋊C4C22×D1911yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—381no—
240C22⋊C4—382no—
241C22⋊C4C22⋊D1912yes—
242C42C22×D1911yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—381no—
249C23—382no—
250C23—764no—
251C23—764no—
252C23—1522no—
253C23C2×C22⋊D1912yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—192no—
262D4—382no—
263D4—381no—
264D4—382no—
265D4—764no—
266D4—764no—
267D4—762no—
268D4—1521no—
269D4#6452514yesdirect product factor
270D4D4×D1912yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—381no—
276C2×C4—762no—
277C2×C4C2×C22⋊D1911yescharacteristic
278C2×C4C2×C22⋊D1912yes—
279C2×C4C2×C22⋊D1911yescharacteristic
280C2×C4C23×D1911yescharacteristic
281C8—192no—
282C8—382no—
283C8—381no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—382no—
294C22—761no—
295C22—761no—
296C22—762no—
297C22—762no—
298C22—762no—
299C22—1528no—
300C22C2×#6452514yescomplemented
301C22C22×C22⋊D1911yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—761no—
306C4C2×#6452512yescomplemented
307C4C2×D4×D1911yescharacteristic
308C4#1059743011yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—762no—
313C2—1522no—
314C2D4×C22⋊D1911yescharacteristic
315C2C22×#6452511yescharacteristic
316C2#1192734711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingD42×C19C2
socleC22×C19C22×D4
hypercenterD42D19
hypocenterC19D4×D8
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#64525C2semidirect
2. D4×D76C2semidirect
3. #11926920C2semidirect
4. #11926778C2semidirect
5. #11926739C2semidirect
6. #11926736C2semidirect
7. #11926678C2semidirect
8. #11926677C2semidirect
9. C4×#64525C2semidirect
10. D4×C19⋊C8C2semidirect
11. D42×C19C2semidirect
13. C22×D4×C19C22semidirect
15. C22×D76C22semidirect
16. C19×#127C22semidirect
18. C19×#121C22semidirect
21. C4×D4×C19C22semidirect
24. C2×#64525C22semidirect
25. C2×#64525C22semidirect
26. C2×#64525C22semidirect
27. C2×#64525C22semidirect
28. #10597376C22semidirect
29. C22×C19⋊C8C22semidirect
32. #10597320C22semidirect
33. C4×D76C22semidirect
34. #10597289C22semidirect
35. #10597289C22semidirect
36. C22⋊(C19⋊C8)C22semidirect
37. #10597266C22semidirect
38. #10597266C22semidirect
39. #10597264C22semidirect
40. C4⋊(C19⋊C8)C22semidirect
41. C4×C19⋊C8C22semidirect
76. #64525D4direct (N × H)
102. D4×C19D8semidirect
103. D4×C19C2×D4semidirect
120. D76C2×D4semidirect
124. C19⋊C8C2×D4semidirect
135. C22×C19C2×D8semidirect
147. C4×C19C2×D8semidirect
153. D42D19semidirect
173. C22×D4C2×D19semidirect
182. #127C2×D19semidirect
186. #121C2×D19semidirect
191. C4×D4C2×D19semidirect
200. C19D4×D8semidirect
269. D4#64525direct (N × H)
270. D4D4×D19semidirect
300. C22C2×#64525semidirect
306. C4C2×#64525semidirect

Maximal subgroups

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

subgroupindex
C22×#645252
D4×D762
#119269202
#119267782
#119267392
#119267362
#119266782
#119266772
C4×#645252
D4×C19⋊C82
D42×C192
D4×D819