Finite Group Databasebeta

← #14575236

Subgroups — #14575236

Order 2432.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597357C212yesmaximal, complemented
2#11927198C211yesmaximal, characteristic, complemented
3D4×D76C211yesmaximal, characteristic, complemented
4#11926917C211yesmaximal, characteristic, complemented
5#11926791C212yesmaximal, complemented
6#11926749C211yesmaximal, characteristic, complemented
7#11926739C211yesmaximal, characteristic, complemented
8#11926696C212yesmaximal, complemented
9#11926690C212yesmaximal, complemented
10#11926623C211yesmaximal, characteristic, complemented
11C4×D8×C19C211yesmaximal, characteristic, complemented
12C2×#64543C2212yescomplemented
13C2×D4×D19C2212yes—
14C22×D76—21no—
15C2×D8×C19C2211yescharacteristic
16C4×D4×C19C2211yescharacteristic
17C4×D4×C19C2211yescharacteristic, complemented
18C2×#64526C2212yes—
19C2×#64525C2212yescomplemented
20#10597376—21no—
21#10597376—21no—
22C2×C4⋊Dic19—21no—
23#10597357—28no—
24C2×#64516C2212yescomplemented
25C2×#64516C2212yescomplemented
26C2×#64515C2212yescomplemented
27#10597343C2212yescomplemented
28#10597341C2212yes—
29#10597332—22no—
30#10597328—22no—
31#10597320C2211yescharacteristic
32C4×D76C2211yescharacteristic
33#10597315C2211yescharacteristic, complemented
34C19×#107C2211yescharacteristic, complemented
35C19×#102C2211yescharacteristic
36C19×#102C2211yescharacteristic, complemented
37C4×C8×C19C2211yescharacteristic, complemented
38(C2×D19)⋊C8C2212yescomplemented
39#10597267C2212yescomplemented
40#10597266C2212yescomplemented
41C4⋊(C19⋊C8)C2211yescharacteristic, complemented
42C23×D19—22no—
43C2×D4×C19C2311yescharacteristic
44C2×D4×C19C2311yescharacteristic
45C22×C4×C19—21no—
46C22×C4×C19—21no—
47C2×C22⋊D19—22no—
48C2×C22⋊D19—22no—
49C22×Dic19—22no—
50#64543—24no—
51#64543—42no—
52D4×D19—24no—
53D4×D19—42no—
54C2×D76—22no—
55C2×D76—21no—
56C2×D76—21no—
57C2×D76—44no—
58C2×D76D411yescharacteristic
59C2×D76C2312yes—
60C2×C4×D19C2312yes—
61C2×Dic38C2312yes—
62D8×C19D414yescomplemented
63C2×C8×C19C2311yescharacteristic
64C2×C8×C19C2311yescharacteristic
65C4⋊C4×C19C2311yescharacteristic
66C4⋊C4×C19C2311yescharacteristic
67C22⋊C4×C19—21no—
68C22⋊C4×C19—21no—
69C42×C19C2311yescharacteristic
70#64526—24no—
71#64525—24no—
72(C2×D19)⋊C4—22no—
73(C2×D19)⋊C4—22no—
74(C2×D19)⋊C4D412yes—
75C4⋊Dic19—21no—
76C4⋊Dic19—21no—
77C4⋊Dic19—22no—
78C4⋊Dic19D411yescharacteristic
79C2×C19⋊C8C2312yes—
80#64516—24no—
81#64516—42no—
82#64515—24no—
83C23×C19—21no—
84C23×C19—21no—
85C22×D19—22no—
86C22×D19—44no—
87C22×D19—44no—
88C22×D19—82no—
89C22×D19C2×D412yes—
90D4×C19—21no—
91D4×C19—21no—
92D4×C19C2×D412yes—
93D4×C19C2×D412yescomplemented
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2×D411yescharacteristic
100C2×C4×C19C2411yescharacteristic
101C22⋊D19—44no—
102C22⋊D19—44no—
103C2×Dic19—22no—
104C2×Dic19—44no—
105C2×Dic19C2×D412yes—
106D76—22no—
107D76—22no—
108D76—22no—
109D76—44no—
110D76—42no—
111D76—81no—
112C4×D19—22no—
113C4×D19—22no—
114Dic38—22no—
115Dic38—22no—
116C8×C19—21no—
117C8×C19C2×D412yescomplemented
118C19⋊C8—22no—
119#3272—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—22no—
122C22×C19—41no—
123C22×C19—41no—
124C22×C19—41no—
125C22×C19—41no—
126C22×C19C22×D411yescharacteristic
127C2×D19—22no—
128C2×D19—22no—
129C2×D19—22no—
130C2×D19—42no—
131C2×D19—42no—
132C2×D19—42no—
133C2×D19—88no—
134C4×C19—21no—
135C4×C19—41no—
136C4×C19—41no—
137C4×C19AGL(1,ℤ/8)12yescomplemented
138C4×C19C22×D411yescharacteristic
139C4×C19H(5,𝔽2)11yescharacteristic
140Dic19—22no—
141Dic19—42no—
142C2×AGL(1,ℤ/8)—192no—
143#547—191no—
144D42—191no—
145#492—191no—
146#468—192no—
147#461—191no—
148#459—191no—
149#450—192no—
150#449—192no—
151C4×D8D1911yescharacteristic, complemented
152#436—191no—
153C2×C19—42no—
154C2×C19—42no—
155C2×C19D4211yescharacteristic
156C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
157C2×C19#57711yescharacteristic
158D19—42no—
159D19—82no—
160C2×#41—192no—
161C22×D4—192no—
162C22×D4—381no—
163AGL(1,ℤ/8)—388no—
164C2×SD16—192no—
165C2×SD16—192no—
166C2×SD16—192no—
167C2×D8—192no—
168C2×D8C2×D1911yescharacteristic
169C2×M16—192no—
170C4⋊Q8—191no—
171#127—191no—
172#123—382no—
173C22⋊Q8—192no—
174#121—192no—
175#121—381no—
176#121—381no—
177#120—382no—
178C4×D4—191no—
179C4×D4C2×D1911yescharacteristic
180C4×D4C2×D1911yescharacteristic, complemented
181C2×C4⋊C4—381no—
182#107C2×D1911yescharacteristic, complemented
183C4⋊C8—191no—
184#103—192no—
185#102—192no—
186#102C2×D1911yescharacteristic
187#102C2×D1911yescharacteristic, complemented
188C22⋊C8—192no—
189C4×C8C2×D1911yescharacteristic, complemented
190C19#327211yescharacteristic, complemented, Sylow
191C24—382no—
192#41—384no—
193#41—762no—
194C2×Q8—192no—
195C2×D4—191no—
196C2×D4—192no—
197C2×D4—382no—
198C2×D4—382no—
199C2×D4—384no—
200C2×D4—382no—
201C2×D4—381no—
202C2×D4—381no—
203C2×D4—764no—
204C2×D4—762no—
205C2×D4C22×D1911yescharacteristic
206C2×D4C22×D1911yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—192no—
210C22×C4—382no—
211SD16—384no—
212SD16—384no—
213SD16—762no—
214D8—384no—
215D8D7614yescomplemented
216M16—384no—
217C2×C8—192no—
218C2×C8C22×D1911yescharacteristic
219C2×C8C22×D1911yescharacteristic
220C4⋊C4—191no—
221C4⋊C4—382no—
222C4⋊C4—381no—
223C4⋊C4—381no—
224C4⋊C4C22×D1911yescharacteristic
225C4⋊C4C22×D1911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—192no—
229C22⋊C4—382no—
230C22⋊C4—382no—
231C42C22×D1911yescharacteristic
232C23—21no—
233C23—21no—
234C23—192no—
235C23—382no—
236C23—764no—
237C23—764no—
238C23—1522no—
239Q8—382no—
240Q8—382no—
241D4—21no—
242D4—21no—
243D4—382no—
244D4—382no—
245D4—382no—
246D4—764no—
247D4—764no—
248D4—764no—
249D4—762no—
250D4—1521no—
251D4C2×D7612yes—
252D4C2×D7612yescomplemented
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—192no—
258C2×C4—382no—
259C2×C4—382no—
260C2×C4—382no—
261C2×C4—764no—
262C2×C4D4×D1911yescharacteristic
263C2×C4D4×D1911yescharacteristic
264C2×C4C23×D1911yescharacteristic
265C8—21no—
266C8—382no—
267C8C2×D7612yescomplemented
268C22—22no—
269C22—22no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—382no—
275C22—382no—
276C22—382no—
277C22—762no—
278C22—762no—
279C22—762no—
280C22—1528no—
281C22C2×D4×D1911yescharacteristic
282C4—21no—
283C4—41no—
284C4—41no—
285C4—382no—
286C4—762no—
287C4#1059735712yescomplemented
288C4C22×D7611yescharacteristic
289C4#1059743511yescharacteristic
290C2—42no—
291C2—42no—
292C2—762no—
293C2—1522no—
294C2D4×D7611yescharacteristic
295C2C2×#1059735711yescharacteristic
296C2#1192735111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×D8×C19C2
socleC22×C19C22×D4
hypercenterC4×D8D19
hypocenterC19#3272
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10597357C2semidirect
2. #11927198C2semidirect
3. D4×D76C2semidirect
4. #11926917C2semidirect
5. #11926791C2semidirect
6. #11926749C2semidirect
7. #11926739C2semidirect
8. #11926696C2semidirect
9. #11926690C2semidirect
10. #11926623C2semidirect
11. C4×D8×C19C2semidirect
12. C2×#64543C22semidirect
17. C4×D4×C19C22semidirect
19. C2×#64525C22semidirect
24. C2×#64516C22semidirect
25. C2×#64516C22semidirect
26. C2×#64515C22semidirect
27. #10597343C22semidirect
33. #10597315C22semidirect
34. C19×#107C22semidirect
36. C19×#102C22semidirect
37. C4×C8×C19C22semidirect
38. (C2×D19)⋊C8C22semidirect
39. #10597267C22semidirect
40. #10597266C22semidirect
41. C4⋊(C19⋊C8)C22semidirect
62. D8×C19D4semidirect
93. D4×C19C2×D4semidirect
117. C8×C19C2×D4semidirect
137. C4×C19AGL(1,ℤ/8)semidirect
151. C4×D8D19semidirect
180. C4×D4C2×D19semidirect
182. #107C2×D19semidirect
187. #102C2×D19semidirect
189. C4×C8C2×D19semidirect
190. C19#3272semidirect
215. D8D76semidirect
252. D4C2×D76semidirect
267. C8C2×D76semidirect
287. C4#10597357semidirect

Maximal subgroups

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

subgroupindex
C2×#105973572
#119271982
D4×D762
#119269172
#119267912
#119267492
#119267392
#119266962
#119266902
#119266232
C4×D8×C192
#327219