Finite Group Databasebeta

← #14564701

Subgroups — #14564701

Order 2432.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#11927056C211yesmaximal, characteristic, complemented
3#11927051C211yesmaximal, characteristic, complemented
4#11926560C211yesmaximal, characteristic, complemented
5#11926507C211yesmaximal, characteristic, complemented
6#11926300C211yesmaximal, characteristic, complemented
7C19×#421C211yesmaximal, characteristic, complemented
8C2×#41×C19C2211yescharacteristic
9C2×#64541C2211yescharacteristic
10C22×C4×D19C2211yescharacteristic
11C2×M16×C19C2211yescharacteristic
12C19×#117C2211yescharacteristic
13#10597397—21no—
14#10597396—22no—
15#10597395—21no—
16#10597392—21no—
17#10597388—21no—
18#10597384—21no—
19#10597383—21no—
20#10597381—21no—
21#10597378—21no—
22C4×C22⋊D19—22no—
23#10597372C2211yescharacteristic
24C2×#64520C2211yescharacteristic
25#10597343—21no—
26#10597341—21no—
27#10597332—21no—
28#10597328—21no—
29C4×D76—22no—
30C19×#104—22no—
31#10597282—22no—
32(C2×D19)⋊C8—22no—
33C23×D19D411yescharacteristic
34#41×C19—21no—
35#41×C19—21no—
36#41×C19—21no—
37#41×C19—21no—
38C2×Q8×C19D411yescharacteristic, complemented
39C2×D4×C19—21no—
40C2×D4×C19D411yescharacteristic, complemented
41C22×C4×C19—21no—
42C22×C4×C19C2311yescharacteristic
43C2×C22⋊D19—22no—
44C2×C22⋊D19—21no—
45C22×Dic19D411yescharacteristic
46#64541—21no—
47#64541—21no—
48#64541—21no—
49#64541—21no—
50C2×D76—22no—
51C2×D76D411yescharacteristic, complemented
52C2×C4×D19—21no—
53C2×C4×D19—21no—
54C2×C4×D19—21no—
55C2×C4×D19—21no—
56C2×C4×D19—21no—
57C2×C4×D19—21no—
58C2×C4×D19—21no—
59C2×Dic38D411yescharacteristic, complemented
60M16×C19—21no—
61M16×C19—21no—
62C2×C8×C19—21no—
63C4⋊C4×C19—21no—
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—
73(C2×D19)⋊C4—22no—
74(C2×D19)⋊C4—22no—
75C4⋊Dic19—22no—
76C4⋊Dic19—21no—
77Dic19⋊C4—22no—
78C4×Dic19D412yescomplemented
79#64520—21no—
80#64520—21no—
81C2×C19⋊C8D412yescomplemented
82C23×C19—21no—
83C23×C19C2×D411yescharacteristic
84C22×D19—21no—
85C22×D19—21no—
86C22×D19—21no—
87C22×D19—21no—
88C22×D19—42no—
89Q8×C19—21no—
90Q8×C19—21no—
91D4×C19—21no—
92D4×C19—21no—
93D4×C19—41no—
94D4×C19—41no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19C2×D411yescharacteristic
100C2×C4×C19C2×D411yescharacteristic
101C2×C4×C19C2×D411yescharacteristic
102C2×C4×C19C2×D411yescharacteristic
103C2×C4×C19C2×D411yescharacteristic
104C2×C4×C19#4111yescharacteristic
105C22⋊D19—44no—
106C22⋊D19—41no—
107C22⋊D19—41no—
108C2×Dic19—22no—
109C2×Dic19—21no—
110C2×Dic19—21no—
111C2×Dic19—21no—
112C2×Dic19—21no—
113D76—21no—
114D76—21no—
115D76—44no—
116C4×D19—41no—
117C4×D19—41no—
118C4×D19—41no—
119C4×D19—41no—
120C4×D19—41no—
121C4×D19—41no—
122Dic38—21no—
123Dic38—21no—
124C8×C19—41no—
125C19⋊C8—22no—
126#2010—191nomaximal, Sylow
127C22×C19—41no—
128C22×C19—42no—
129C22×C19—41no—
130C22×C19#12011yescharacteristic
131C22×C19#12011yescharacteristic
132C22×C19#12111yescharacteristic
133C2×D19—22no—
134C2×D19—22no—
135C2×D19—22no—
136C2×D19—41no—
137C2×D19—41no—
138C2×D19—41no—
139C2×D19—41no—
140C2×D19—42no—
141C2×D19—41no—
142C4×C19—42no—
143C4×C19—41no—
144C4×C19#12011yescharacteristic
145C4×C19#12111yescharacteristic
146C4×C19#12111yescharacteristic
147C4×C19#12711yescharacteristic
148Dic19—42no—
149Dic19—41no—
150Dic19—41no—
151#575—191no—
152#525—191no—
153#525—191no—
154#421—191no—
155#421D1911yescharacteristic, complemented
156#407—191no—
157H(3,ℤ/4)—191no—
158C2×C19—21no—
159C2×C19—21no—
160C2×C19—21no—
161C2×C19—81no—
162C2×C19#39211yescharacteristic
163D19—42no—
164D19—81no—
165C2×#41—191no—
166C2×#41C2×D1911yescharacteristic
167C23×C4—191no—
168#137—381no—
169#137—381no—
170AGL(1,ℤ/8)—381no—
171AGL(1,ℤ/8)—381no—
172#135—382no—
173C2×M16—191no—
174C2×M16C2×D1911yescharacteristic
175#123—381no—
176#123—381no—
177C22⋊Q8—381no—
178C22⋊Q8—381no—
179#121—381no—
180#121—381no—
181#120—381no—
182#120—381no—
183C4×D4—382no—
184C4×D4—382no—
185#117—191no—
186#117C2×D1911yescharacteristic
187#104—22no—
188#104—382no—
189C22⋊C8—382no—
190C19#201011yescharacteristic, complemented, Sylow
191C24—191no—
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×Q8D7611yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—191no—
204C2×D4—382no—
205C2×D4—382no—
206C2×D4—381no—
207C2×D4D7611yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—191no—
210C22×C4—381no—
211C22×C4—381no—
212C22×C4—381no—
213C22×C4—381no—
214C22×C4—381no—
215C22×C4—381no—
216C22×C4—381no—
217C22×C4C22×D1911yescharacteristic
218Q16—382no—
219SD16—382no—
220SD16—382no—
221D8—382no—
222M16—21no—
223M16—21no—
224M16—381no—
225M16—381no—
226C2×C8—21no—
227C2×C8—192no—
228C4⋊C4—21no—
229C4⋊C4—382no—
230C4⋊C4—382no—
231C4⋊C4—381no—
232C22⋊C4—21no—
233C22⋊C4—382no—
234C22⋊C4—382no—
235C22⋊C4—382no—
236C22⋊C4—382no—
237C22⋊C4—381no—
238C42—192no—
239C42C22⋊D1912yescomplemented
240C23—21no—
241C23—381no—
242C23—381no—
243C23—381no—
244C23—381no—
245C23—762no—
246C23D4×D1911yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—381no—
250Q8—381no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—381no—
256D4—381no—
257D4—764no—
258D4—764no—
259D4—761no—
260D4—761no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—381no—
266C2×C4—381no—
267C2×C4—382no—
268C2×C4—381no—
269C2×C4—381no—
270C2×C4—761no—
271C2×C4—761no—
272C2×C4—761no—
273C2×C4—761no—
274C2×C4—761no—
275C2×C4—761no—
276C2×C4C2×D7611yescharacteristic
277C2×C4#6454111yescharacteristic
278C2×C4D4×D1911yescharacteristic
279C2×C4D4×D1911yescharacteristic
280C2×C4D4×D1911yescharacteristic
281C2×C4C2×C22⋊D1911yescharacteristic
282C8—41no—
283C8—382no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—382no—
288C22—382no—
289C22—382no—
290C22—761no—
291C22—761no—
292C22—761no—
293C22—762no—
294C22—761no—
295C22—761no—
296C22#1059732811yescharacteristic
297C22#1059733011yescharacteristic
298C22#1059738311yescharacteristic
299C4—42no—
300C4—41no—
301C4—762no—
302C4—761no—
303C4—761no—
304C4#1059732811yescharacteristic
305C4#1059733011yescharacteristic
306C4#1059737611yescharacteristic
307C4#1059738611yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—762no—
313C2—1521no—
314C2#1192645311yescharacteristic
subgroupG/H
centerC4#10597386
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#421C2
socleC2×C19#392
hypercenter#421D19
hypocenterC19#2010
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #11927342C2semidirect
2. #11927056C2semidirect
3. #11927051C2semidirect
4. #11926560C2semidirect
5. #11926507C2semidirect
6. #11926300C2semidirect
7. C19×#421C2semidirect
38. C2×Q8×C19D4semidirect
40. C2×D4×C19D4semidirect
51. C2×D76D4semidirect
59. C2×Dic38D4semidirect
65. C42×C19D4semidirect
78. C4×Dic19D4semidirect
81. C2×C19⋊C8D4semidirect
155. #421D19semidirect
190. C19#2010semidirect
201. C2×Q8D76semidirect
207. C2×D4D76semidirect
239. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119273422
#119270562
#119270512
#119265602
#119265072
#119263002
C19×#4212
#201019