Finite Group Databasebeta

← #14564700

Subgroups — #14564700

Order 2432.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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
1#11927342C211yesmaximal, characteristic, complemented
2#11927055C211yesmaximal, characteristic, complemented
3#11926562C211yesmaximal, characteristic, complemented
4#11926561C211yesmaximal, characteristic, complemented
5#11926508C211yesmaximal, characteristic, complemented
6#11926300C211yesmaximal, characteristic, complemented
7C19×#525C211yesmaximal, characteristic, complemented
8C2×#41×C19C2211yescharacteristic
9C23×C4×C19C2211yescharacteristic
10C2×#64541C2211yescharacteristic
11C19×#123—21no—
12C19×C22⋊Q8—21no—
13C19×#121—21no—
14C19×#120—21no—
15C4×D4×C19—22no—
16C19×#117C2211yescharacteristic
17#10597399—21no—
18#10597397—21no—
19#10597396—22no—
20#10597395—21no—
21#10597388—21no—
22#10597378—21no—
23#10597376—21no—
24#10597375—21no—
25C4×C22⋊D19—22no—
26#10597372C2211yescharacteristic
27#10597370—21no—
28C2×#64520C2211yescharacteristic
29C2×#64520C2211yescharacteristic
30#10597294—22no—
31C22⋊(C19⋊C8)—22no—
32#10597262—22no—
33C24×C19D411yescharacteristic
34#41×C19—21no—
35#41×C19—21no—
36#41×C19—21no—
37#41×C19—21no—
38C2×Q8×C19D411yescharacteristic, complemented
39C2×D4×C19—22no—
40C2×D4×C19—21no—
41C2×D4×C19D411yescharacteristic, complemented
42C22×C4×C19—21no—
43C22×C4×C19—21no—
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19—21no—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19D411yescharacteristic
50C22×C4×C19C2311yescharacteristic
51C2×C22⋊D19—22no—
52C2×C22⋊D19—21no—
53#64541—21no—
54#64541—21no—
55#64541—21no—
56#64541—21no—
57C2×D76D411yescharacteristic, complemented
58C2×C4×D19—21no—
59C2×Dic38D411yescharacteristic, complemented
60C4⋊C4×C19—22no—
61C4⋊C4×C19—21no—
62C22⋊C4×C19—22no—
63C22⋊C4×C19—22no—
64C22⋊C4×C19—21no—
65C42×C19D412yescomplemented
66C22⋊Dic19—22no—
67C22⋊Dic19—21no—
68#64528—22no—
69#64527—22no—
70#64526—22no—
71#64525—22no—
72(C2×D19)⋊C4—22no—
73C4⋊Dic19—21no—
74Dic19⋊C4—22no—
75C4×Dic19D412yescomplemented
76#64520—21no—
77#64520—21no—
78#64520—21no—
79#64520—21no—
80C2×C19⋊C8—21no—
81C2×C19⋊C8D412yescomplemented
82C23×C19—21no—
83C23×C19—21no—
84C23×C19—21no—
85C23×C19—21no—
86C23×C19—42no—
87C23×C19C2×D411yescharacteristic
88C22×D19—21no—
89Q8×C19—21no—
90Q8×C19—21no—
91D4×C19—21no—
92D4×C19—21no—
93D4×C19—44no—
94D4×C19—41no—
95D4×C19—41no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19C2×D411yescharacteristic
108C2×C4×C19C2×D411yescharacteristic
109C2×C4×C19C2×D411yescharacteristic
110C2×C4×C19C2×D411yescharacteristic
111C2×C4×C19C2×D411yescharacteristic
112C2×C4×C19#4111yescharacteristic
113C22⋊D19—44no—
114C22⋊D19—41no—
115C22⋊D19—41no—
116C2×Dic19—22no—
117C2×Dic19—21no—
118D76—21no—
119D76—21no—
120C4×D19—41no—
121C4×D19—41no—
122Dic38—21no—
123Dic38—21no—
124C19⋊C8—22no—
125C19⋊C8—41no—
126#2010—191nomaximal, Sylow
127C22×C19—22no—
128C22×C19—22no—
129C22×C19—22no—
130C22×C19—41no—
131C22×C19—41no—
132C22×C19—41no—
133C22×C19—41no—
134C22×C19—42no—
135C22×C19—41no—
136C22×C19—41no—
137C22×C19#12011yescharacteristic
138C22×C19#12011yescharacteristic
139C22×C19#12111yescharacteristic
140C2×D19—42no—
141C2×D19—41no—
142C4×C19—42no—
143C4×C19—41no—
144C4×C19—41no—
145C4×C19#12011yescharacteristic
146C4×C19#12111yescharacteristic
147C4×C19#12111yescharacteristic
148C4×C19#12711yescharacteristic
149Dic19—42no—
150Dic19—41no—
151#575—191no—
152#525—191no—
153#525D1911yescharacteristic, complemented
154#421—191no—
155#421—191no—
156#407—191no—
157H(3,ℤ/4)—191no—
158C2×C19—21no—
159C2×C19—21no—
160C2×C19—21no—
161C2×C19—42no—
162C2×C19—81no—
163C2×C19#39211yescharacteristic
164D19—81no—
165C2×#41—191no—
166C2×#41C2×D1911yescharacteristic
167C23×C4C2×D1911yescharacteristic
168#137—381no—
169#137—381no—
170AGL(1,ℤ/8)—381no—
171AGL(1,ℤ/8)—381no—
172#135—382no—
173C2×M16—191no—
174C2×M16—191no—
175#123—21no—
176#123—381no—
177C22⋊Q8—21no—
178C22⋊Q8—381no—
179#121—21no—
180#121—381no—
181#120—21no—
182#120—381no—
183C4×D4—22no—
184C4×D4—382no—
185#117—191no—
186#117C2×D1911yescharacteristic
187#104—382no—
188#104—382no—
189C22⋊C8—382no—
190C19#201011yescharacteristic, complemented, Sylow
191C24C22⋊D1911yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—381no—
197#41—381no—
198#41—381no—
199#41—381no—
200C2×Q8—191no—
201C2×Q8C22⋊D1911yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—191no—
205C2×D4—382no—
206C2×D4—381no—
207C2×D4C22⋊D1911yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—381no—
216C22×C4C22⋊D1911yescharacteristic
217C22×C4C22×D1911yescharacteristic
218Q16—382no—
219SD16—382no—
220SD16—382no—
221D8—382no—
222M16—381no—
223M16—381no—
224M16—381no—
225M16—381no—
226C2×C8—192no—
227C2×C8—381no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—382no—
231C4⋊C4—381no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—382no—
236C22⋊C4—382no—
237C22⋊C4—381no—
238C42—192no—
239C42C22⋊D1912yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—381no—
246C23C2×C22⋊D1911yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—381no—
250Q8—381no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—381no—
257D4—381no—
258D4—764no—
259D4—761no—
260D4—761no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—382no—
273C2×C4—381no—
274C2×C4—761no—
275C2×C4—761no—
276C2×C4D4×D1911yescharacteristic
277C2×C4D4×D1911yescharacteristic
278C2×C4D4×D1911yescharacteristic
279C2×C4#6454311yescharacteristic
280C2×C4C2×C22⋊D1911yescharacteristic
281C2×C4C2×C22⋊D1911yescharacteristic
282C8—382no—
283C8—761no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—762no—
295C22—761no—
296C22#1059738311yescharacteristic
297C22#1059738511yescharacteristic
298C22#1059739911yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—762no—
303C4—761no—
304C4#1059738311yescharacteristic
305C4#1059738411yescharacteristic
306C4#1059738511yescharacteristic
307C4#1059738611yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—1521no—
314C2#1192645211yescharacteristic
subgroupG/H
centerC4#10597386
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#525C2
socleC2×C19#392
hypercenter#525D19
hypocenterC19#2010
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #11927342C2semidirect
2. #11927055C2semidirect
3. #11926562C2semidirect
4. #11926561C2semidirect
5. #11926508C2semidirect
6. #11926300C2semidirect
7. C19×#525C2semidirect
38. C2×Q8×C19D4semidirect
41. C2×D4×C19D4semidirect
57. C2×D76D4semidirect
59. C2×Dic38D4semidirect
65. C42×C19D4semidirect
75. C4×Dic19D4semidirect
81. C2×C19⋊C8D4semidirect
153. #525D19semidirect
190. C19#2010semidirect
201. C2×Q8C22⋊D19semidirect
207. C2×D4C22⋊D19semidirect
239. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119273422
#119270552
#119265622
#119265612
#119265082
#119263002
C19×#5252
#201019