Finite Group Databasebeta

← #14572877

Subgroups — #14572877

Order 2432.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597388C211yesmaximal, characteristic, complemented
2C2×#10597378C211yesmaximal, characteristic, complemented
3#11927055C211yesmaximal, characteristic, complemented
4#11926706C214yesmaximal, complemented
5#11926689C214yesmaximal, complemented
6#11926553C211yesmaximal, characteristic, complemented
7#11926549C211yesmaximal, characteristic, complemented
8#11926508C211yesmaximal, characteristic, complemented
9C22×#41×C19C211yesmaximal, characteristic, complemented
10C2×#41×C19—24no—
11C2×#41×C19—24no—
12C2×#41×C19—22no—
13C2×#41×C19C2214yes—
14C22×Q8×C19C2211yescharacteristic
15C22×D4×C19—21no—
16C22×D4×C19C2211yescharacteristic
17C23×C4×C19—21no—
18C23×C4×C19C2211yescharacteristic
19C2×#64541C2211yescharacteristic
20#10597399—21no—
21C2×#64528C2212yescomplemented
22#10597388—24no—
23C2×#64527C2212yescomplemented
24C2×#64526C2212yescomplemented
25#10597378—24no—
26C2×#64525C2212yescomplemented
27#10597376C2212yescomplemented
28#10597375—21no—
29C4×C22⋊D19—22no—
30#10597372C2211yescharacteristic
31#10597370C2212yescomplemented
32C2×#64520C2211yescharacteristic
33C2×#64520C2211yescharacteristic
34#10597292C2214yescomplemented
35#10597289C2214yescomplemented
36C22⋊(C19⋊C8)C2214yescomplemented
37C24×C19—21no—
38C24×C19D411yescharacteristic
39#41×C19—216no—
40#41×C19—28no—
41#41×C19—28no—
42C2×Q8×C19—22no—
43C2×Q8×C19—21no—
44C2×Q8×C19D414yescomplemented
45C2×Q8×C19C2312yes—
46C2×D4×C19—28no—
47C2×D4×C19—24no—
48C2×D4×C19—21no—
49C2×D4×C19—22no—
50C2×D4×C19D414yescomplemented
51C2×D4×C19C2312yes—
52C22×C4×C19—28no—
53C22×C4×C19—21no—
54C22×C4×C19—24no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19D411yescharacteristic
58C22×C4×C19D412yes—
59C22×C4×C19C2312yes—
60C22×C4×C19C2311yescharacteristic
61C2×C22⋊D19—22no—
62C2×C22⋊D19—21no—
63#64541—22no—
64#64541—22no—
65C2×D76C2311yescharacteristic
66C2×C4×D19—21no—
67C2×Dic38C2311yescharacteristic
68C22⋊Dic19—22no—
69C22⋊Dic19—21no—
70#64528—24no—
71#64527—24no—
72#64526—24no—
73#64525—24no—
74(C2×D19)⋊C4—22no—
75C4⋊Dic19C2312yes—
76Dic19⋊C4—22no—
77C4×Dic19—21no—
78#64520—22no—
79#64520—22no—
80C2×C19⋊C8C2312yes—
81C2×C19⋊C8C2312yes—
82C23×C19—22no—
83C23×C19—24no—
84C23×C19—22no—
85C23×C19—42no—
86C23×C19—44no—
87C23×C19C2×D412yes—
88C23×C19C2×D411yescharacteristic
89C22×D19—21no—
90Q8×C19—24no—
91Q8×C19—22no—
92Q8×C19C2×D414yes—
93D4×C19—216no—
94D4×C19—24no—
95D4×C19—22no—
96D4×C19C2×D414yes—
97C2×C4×C19—216no—
98C2×C4×C19—22no—
99C2×C4×C19—24no—
100C2×C4×C19—22no—
101C2×C4×C19—24no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19C2×D412yes—
105C2×C4×C19C2×D411yescharacteristic
106C2×C4×C19C2×D412yes—
107C2×C4×C19C2×D412yes—
108C2×C4×C19C2411yescharacteristic
109C22⋊D19—44no—
110C22⋊D19—42no—
111C2×Dic19—22no—
112C2×Dic19—21no—
113D76—21no—
114D76—21no—
115C4×D19—42no—
116Dic38—21no—
117Dic38—21no—
118C19⋊C8—22no—
119C19⋊C8—22no—
120#3005—191nomaximal, Sylow
121C22×C19—22no—
122C22×C19—22no—
123C22×C19—24no—
124C22×C19—22no—
125C22×C19—22no—
126C22×C19—44no—
127C22×C19—48no—
128C22×C19—44no—
129C22×C19#12012yes—
130C22×C19C22×D411yescharacteristic
131C2×D19—41no—
132C2×D19—42no—
133C4×C19—22no—
134C4×C19—24no—
135C4×C19#12012yes—
136C4×C19C22×D411yescharacteristic
137C4×C19C22×D411yescharacteristic
138Dic19—41no—
139Dic19—42no—
140C22×#41D1911yescharacteristic, complemented
141C2×#137—191no—
142C2×AGL(1,ℤ/8)—191no—
143#525—191no—
144#452—194no—
145#449—194no—
146#419—191no—
147#418—191no—
148#407—191no—
149C2×C19—22no—
150C2×C19—42no—
151C2×C19—44no—
152C2×C19C2×#12011yescharacteristic
153C2×C19#57512yes—
154D19—81no—
155C2×#41—24no—
156C2×#41—24no—
157C2×#41—22no—
158C2×#41—191no—
159C2×#41C2×D1914yes—
160C22×Q8C2×D1911yescharacteristic
161C22×D4—21no—
162C22×D4C2×D1911yescharacteristic
163C23×C4—21no—
164C23×C4C2×D1911yescharacteristic
165#137—384no—
166AGL(1,ℤ/8)—384no—
167C2×Q16—192no—
168C2×SD16—192no—
169C2×SD16—192no—
170C2×D8—192no—
171C2×M16—191no—
172C2×M16—191no—
173#123—381no—
174C22⋊Q8—192no—
175#121—192no—
176#120—381no—
177C4×D4—382no—
178#117—191no—
179#103—194no—
180#102—194no—
181C22⋊C8—194no—
182C19#300511yescharacteristic, complemented, Sylow
183C24—21no—
184C24C22⋊D1911yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—382no—
189#41—382no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—191no—
193C2×Q8C22⋊D1914yescomplemented
194C2×Q8C22×D1912yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—191no—
200C2×D4—382no—
201C2×D4—381no—
202C2×D4C22⋊D1914yescomplemented
203C2×D4C22×D1912yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—381no—
210C22×C4C22⋊D1912yes—
211C22×C4C22⋊D1911yescharacteristic
212C22×C4C22×D1912yes—
213C22×C4C22×D1911yescharacteristic
214Q16—384no—
215SD16—384no—
216SD16—384no—
217D8—384no—
218M16—382no—
219M16—382no—
220C2×C8—192no—
221C2×C8—192no—
222C4⋊C4—192no—
223C4⋊C4—382no—
224C22⋊C4—381no—
225C22⋊C4—382no—
226C22⋊C4—382no—
227C42—381no—
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—381no—
234C23C2×C22⋊D1912yes—
235C23C2×C22⋊D1911yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—381no—
239Q8—381no—
240Q8C2×C22⋊D1914yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—381no—
245D4—381no—
246D4—764no—
247D4—762no—
248D4C2×C22⋊D1914yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—382no—
257C2×C4—381no—
258C2×C4—762no—
259C2×C4C2×C22⋊D1912yes—
260C2×C4C2×C22⋊D1911yescharacteristic
261C2×C4C2×C22⋊D1912yes—
262C2×C4C2×C22⋊D1912yes—
263C2×C4C23×D1911yescharacteristic
264C8—382no—
265C8—382no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—762no—
275C22—761no—
276C22#1059739912yes—
277C22C22×C22⋊D1911yescharacteristic
278C4—22no—
279C4—24no—
280C4—762no—
281C4—761no—
282C4#1059739912yes—
283C4C22×C22⋊D1911yescharacteristic
284C4C22×C22⋊D1911yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—1521no—
289C2C2×#1059739911yescharacteristic
290C2#1192734212yes—
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC22×#41×C19C2
socleC22×C19C22×D4
hypercenterC22×#41D19
hypocenterC19#3005
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10597388C2semidirect
2. C2×#10597378C2semidirect
3. #11927055C2semidirect
4. #11926706C2semidirect
5. #11926689C2semidirect
6. #11926553C2semidirect
7. #11926549C2semidirect
8. #11926508C2semidirect
9. C22×#41×C19C2semidirect
21. C2×#64528C22semidirect
23. C2×#64527C22semidirect
24. C2×#64526C22semidirect
26. C2×#64525C22semidirect
27. #10597376C22semidirect
31. #10597370C22semidirect
34. #10597292C22semidirect
35. #10597289C22semidirect
36. C22⋊(C19⋊C8)C22semidirect
44. C2×Q8×C19D4semidirect
50. C2×D4×C19D4semidirect
140. C22×#41D19semidirect
182. C19#3005semidirect
193. C2×Q8C22⋊D19semidirect
202. C2×D4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973882
C2×#105973782
#119270552
#119267062
#119266892
#119265532
#119265492
#119265082
C22×#41×C192
#300519