Finite Group Databasebeta

← #14575442

Subgroups — #14575442

Order 2432.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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
1D4×D76C211yesmaximal, characteristic, complemented
2#11926892C211yesmaximal, characteristic, complemented
3#11926857C212yesmaximal, complemented
4#11926821C211yesmaximal, characteristic, complemented
5#11926778C212yesmaximal, complemented
6#11926739C211yesmaximal, characteristic, complemented
7#11926677C212yesmaximal, complemented
8C4×#64525C211yesmaximal, characteristic, complemented
9D4×C19⋊C8C211yesmaximal, characteristic, complemented
10C2×#10597266C212yesmaximal, complemented
11C19×#547C211yesmaximal, characteristic, complemented
12C2×#41×C19—21no—
13C2×D4×D19—21no—
14C22×D76C2212yes—
15C19×C4⋊Q8C2211yescharacteristic, complemented
16C19×#123—22no—
17C19×C22⋊Q8—21no—
18C19×#121C2212yescomplemented
19C4×D4×C19C2211yescharacteristic
20C4×D4×C19C2211yescharacteristic, complemented
21C2×C4⋊C4×C19C2212yescomplemented
22C2×#64525C2211yescharacteristic
23C2×#64525C2212yescomplemented
24#10597376C2212yes—
25C22×C19⋊C8C2212yescomplemented
26#10597341—21no—
27#10597328—22no—
28#10597320C2211yescharacteristic
29C4×D76C2211yescharacteristic
30#10597289C2211yescharacteristic, complemented
31C22⋊(C19⋊C8)C2212yescomplemented
32#10597266C2211yescharacteristic
33#10597266C2212yes—
34#10597266C2212yescomplemented
35#10597266C2212yescomplemented
36#10597266C2212yescomplemented
37#10597264C2212yescomplemented
38#10597264C2211yescharacteristic, complemented
39C4⋊(C19⋊C8)C2211yescharacteristic, complemented
40C4×C19⋊C8C2211yescharacteristic, complemented
41C23×D19—22no—
42#41×C19—44no—
43C2×Q8×C19—21no—
44C2×D4×C19—22no—
45C2×D4×C19D411yescharacteristic
46C2×D4×C19C2311yescharacteristic
47C22×C4×C19—22no—
48C22×C4×C19—21no—
49C22×C4×C19C2312yes—
50C2×C22⋊D19—22no—
51D4×D19—44no—
52C2×D76—24no—
53C2×D76—22no—
54C2×D76—21no—
55C2×D76—21no—
56C2×D76—42no—
57C2×D76C2312yes—
58C2×D76C2311yescharacteristic
59C2×C4×D19—21no—
60C4⋊C4×C19—22no—
61C4⋊C4×C19—21no—
62C4⋊C4×C19D411yescharacteristic
63C4⋊C4×C19C2311yescharacteristic
64C4⋊C4×C19C2312yes—
65C22⋊C4×C19—21no—
66C22⋊C4×C19—22no—
67C22⋊C4×C19D412yes—
68C42×C19C2311yescharacteristic
69#64525—22no—
70#64525—42no—
71(C2×D19)⋊C4—22no—
72(C2×D19)⋊C4—21no—
73C4⋊Dic19C2311yescharacteristic
74C2×C19⋊C8—42no—
75C2×C19⋊C8C2311yescharacteristic
76C2×C19⋊C8C2312yes—
77C2×C19⋊C8C2311yescharacteristic
78C23×C19—21no—
79C23×C19C2×D412yes—
80C22×D19—21no—
81C22×D19—22no—
82C22×D19—44no—
83C22×D19—44no—
84C22×D19—82no—
85Q8×C19—42no—
86D4×C19—21no—
87D4×C19—21no—
88D4×C19—44no—
89D4×C19D814yescomplemented
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—44no—
95C2×C4×C19—42no—
96C2×C4×C19C2×D411yescharacteristic
97C2×C4×C19C2×D412yes—
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2411yescharacteristic
100C22⋊D19—44no—
101C2×Dic19—21no—
102D76—22no—
103D76—21no—
104D76—22no—
105D76—44no—
106D76—42no—
107D76—81no—
108D76#4112yescomplemented
109C4×D19—42no—
110C19⋊C8—21no—
111C19⋊C8—21no—
112C19⋊C8—22no—
113#3294—191nomaximal, Sylow
114C22×C19—22no—
115C22×C19—22no—
116C22×C19—41no—
117C22×C19—41no—
118C22×C19—41no—
119C22×C19C2×D814yes—
120C22×C19C22×D411yescharacteristic
121C2×D19—22no—
122C2×D19—41no—
123C2×D19—41no—
124C2×D19—42no—
125C2×D19—42no—
126C2×D19—42no—
127C2×D19—88no—
128C4×C19—22no—
129C4×C19—21no—
130C4×C19—41no—
131C4×C19—42no—
132C4×C19C2×D812yes—
133C4×C19C2×#4111yescharacteristic
134C4×C19H(5,𝔽2)11yescharacteristic
135Dic19—41no—
136#547D1911yescharacteristic, complemented
137D42—191no—
138#486—191no—
139#480—192no—
140#474—191no—
141#466—192no—
142#459—191no—
143#447—192no—
144C4×D8—191no—
145C8×D4—191no—
146C2×#102—192no—
147C2×C19—24no—
148C2×C19—81no—
149C2×C19#54611yescharacteristic
150C2×C19C22×D811yescharacteristic
151C2×C19#57711yescharacteristic
152D19—42no—
153D19—82no—
154C2×#41—21no—
155C22×D4—192no—
156C22×D4—381no—
157C2×D8—191no—
158C2×D8—192no—
159C22×C8—192no—
160C4⋊Q8C2×D1911yescharacteristic, complemented
161#127—191no—
162#123—22no—
163C22⋊Q8—21no—
164#121—192no—
165#121—381no—
166#121C2×D1912yescomplemented
167#120—382no—
168C4×D4—191no—
169C4×D4C2×D1911yescharacteristic
170C4×D4C2×D1911yescharacteristic, complemented
171C2×C4⋊C4C2×D1912yescomplemented
172#107—191no—
173#107—192no—
174C4⋊C8—191no—
175#102—191no—
176#102—191no—
177#102—192no—
178#102—192no—
179#102—192no—
180#102—192no—
181C22⋊C8—192no—
182C4×C8—191no—
183C19#329411yescharacteristic, complemented, Sylow
184C24—382no—
185#41—44no—
186C2×Q8—21no—
187C2×D4—22no—
188C2×D4—191no—
189C2×D4—192no—
190C2×D4—384no—
191C2×D4—382no—
192C2×D4—382no—
193C2×D4—381no—
194C2×D4—381no—
195C2×D4—762no—
196C2×D4—764no—
197C2×D4C22⋊D1911yescharacteristic
198C2×D4C22×D1911yescharacteristic
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—381no—
202C22×C4C22×D1912yes—
203D8—382no—
204D8—762no—
205C2×C8—191no—
206C2×C8—191no—
207C2×C8—192no—
208C2×C8—762no—
209C4⋊C4—22no—
210C4⋊C4—21no—
211C4⋊C4—191no—
212C4⋊C4C22⋊D1911yescharacteristic
213C4⋊C4C22×D1911yescharacteristic
214C4⋊C4C22×D1912yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—381no—
218C22⋊C4—382no—
219C22⋊C4C22⋊D1912yes—
220C42C22×D1911yescharacteristic
221C23—21no—
222C23—381no—
223C23—382no—
224C23—764no—
225C23—764no—
226C23—1522no—
227C23C2×C22⋊D1912yes—
228Q8—42no—
229D4—21no—
230D4—21no—
231D4—44no—
232D4—192no—
233D4—382no—
234D4—381no—
235D4—382no—
236D4—764no—
237D4—764no—
238D4—762no—
239D4—1521no—
240D4#6452514yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—381no—
248C2×C4—762no—
249C2×C4C2×C22⋊D1911yescharacteristic
250C2×C4C2×C22⋊D1912yes—
251C2×C4C2×C22⋊D1911yescharacteristic
252C2×C4C23×D1911yescharacteristic
253C8—381no—
254C8—381no—
255C8—382no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—382no—
262C22—761no—
263C22—761no—
264C22—762no—
265C22—762no—
266C22—762no—
267C22—1528no—
268C22C2×#6452514yes—
269C22C22×C22⋊D1911yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—42no—
274C4—761no—
275C4C2×#6452512yes—
276C4#41×D1911yescharacteristic
277C4#1059743511yescharacteristic
278C2—24no—
279C2—81no—
280C2—762no—
281C2—1522no—
282C2#1192718211yescharacteristic
283C2C22×#6452511yescharacteristic
284C2#1192735211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#547C2
socleC22×C19C22×D4
hypercenter#547D19
hypocenterC19#3294
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. D4×D76C2semidirect
2. #11926892C2semidirect
3. #11926857C2semidirect
4. #11926821C2semidirect
5. #11926778C2semidirect
6. #11926739C2semidirect
7. #11926677C2semidirect
8. C4×#64525C2semidirect
9. D4×C19⋊C8C2semidirect
10. C2×#10597266C2semidirect
11. C19×#547C2semidirect
15. C19×C4⋊Q8C22semidirect
18. C19×#121C22semidirect
20. C4×D4×C19C22semidirect
21. C2×C4⋊C4×C19C22semidirect
23. C2×#64525C22semidirect
25. C22×C19⋊C8C22semidirect
30. #10597289C22semidirect
31. C22⋊(C19⋊C8)C22semidirect
34. #10597266C22semidirect
35. #10597266C22semidirect
36. #10597266C22semidirect
37. #10597264C22semidirect
38. #10597264C22semidirect
39. C4⋊(C19⋊C8)C22semidirect
40. C4×C19⋊C8C22semidirect
89. D4×C19D8semidirect
108. D76#41semidirect
136. #547D19semidirect
160. C4⋊Q8C2×D19semidirect
166. #121C2×D19semidirect
170. C4×D4C2×D19semidirect
171. C2×C4⋊C4C2×D19semidirect
183. C19#3294semidirect
240. D4#64525semidirect

Maximal subgroups

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

subgroupindex
D4×D762
#119268922
#119268572
#119268212
#119267782
#119267392
#119266772
C4×#645252
D4×C19⋊C82
C2×#105972662
C19×#5472
#329419