Finite Group Databasebeta

← #14564635

Subgroups — #14564635

Order 2432.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10597392C211yesmaximal, characteristic, complemented
2C2×#10597384C211yesmaximal, characteristic
3C2×#10597292C211yesmaximal, characteristic, complemented
4C2×#10597289C211yesmaximal, characteristic, complemented
5C2×(C2×D19)⋊C8C211yesmaximal, characteristic, complemented
6#11926307C211yesmaximal, characteristic, complemented
7C22×SD16×C19C211yesmaximal, characteristic, complemented
8C22×Q8×C19C2211yescharacteristic
9C22×D4×C19C2211yescharacteristic
10C22×C22⋊D19—21no—
11C22×C4×D19C2211yescharacteristic
12C2×SD16×C19—22no—
13C2×SD16×C19—22no—
14C2×SD16×C19—22no—
15C22×C8×C19C2211yescharacteristic
16C2×C22⋊Dic19—21no—
17#10597392—22no—
18#10597392—22no—
19#10597384—22no—
20#10597384—22no—
21C2×(C2×D19)⋊C4—21no—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×C4⋊Dic19C2211yescharacteristic
24C2×Dic19⋊C4—21no—
25C22×C19⋊C8C2211yescharacteristic
26#10597292—22no—
27#10597289—22no—
28(C2×D19)⋊C8—22no—
29C24×C19—21no—
30C23×D19D411yescharacteristic
31C2×Q8×C19—21no—
32C2×Q8×C19—21no—
33C2×Q8×C19—21no—
34C2×Q8×C19—21no—
35C2×Q8×C19—21no—
36C2×Q8×C19D412yescomplemented
37C2×D4×C19—21no—
38C2×D4×C19—21no—
39C2×D4×C19—21no—
40C2×D4×C19—21no—
41C2×D4×C19—21no—
42C2×D4×C19D412yes—
43C22×C4×C19—21no—
44C22×C4×C19C2311yescharacteristic
45C2×C22⋊D19—24no—
46C2×C22⋊D19—42no—
47C2×C22⋊D19—42no—
48C22×Dic19—21no—
49C22×Dic19—21no—
50C22×Dic19D411yescharacteristic
51C2×C4×D19—21no—
52C2×C4×D19—21no—
53C2×C4×D19—21no—
54C2×C4×D19—21no—
55C2×C4×D19—21no—
56C2×C4×D19—21no—
57SD16×C19—28no—
58C2×C8×C19—21no—
59C2×C8×C19—21no—
60C2×C8×C19D412yescomplemented
61C22⋊Dic19—24no—
62(C2×D19)⋊C4—24no—
63C4⋊Dic19—21no—
64C4⋊Dic19—21no—
65C4⋊Dic19D412yes—
66C4⋊Dic19D412yescomplemented
67Dic19⋊C4—24no—
68C2×C19⋊C8—21no—
69C2×C19⋊C8—21no—
70C2×C19⋊C8—21no—
71C23×C19—22no—
72C23×C19—41no—
73C23×C19—41no—
74C23×C19—41no—
75C23×C19—41no—
76C23×C19—41no—
77C23×C19—41no—
78C23×C19C2×D411yescharacteristic
79C22×D19—21no—
80C22×D19—21no—
81C22×D19—21no—
82C22×D19—21no—
83C22×D19—21no—
84C22×D19—21no—
85C22×D19SD1612yescomplemented
86Q8×C19—22no—
87Q8×C19—22no—
88Q8×C19—41no—
89Q8×C19—41no—
90D4×C19—22no—
91D4×C19—22no—
92D4×C19—41no—
93D4×C19—41no—
94C2×C4×C19—22no—
95C2×C4×C19—41no—
96C2×C4×C19—41no—
97C2×C4×C19C2×D411yescharacteristic
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2×D411yescharacteristic
100C2×C4×C19C2×D411yescharacteristic
101C2×C4×C19C2×D411yescharacteristic
102C2×C4×C19#4111yescharacteristic
103C22⋊D19—48no—
104C2×Dic19—21no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—21no—
108C2×Dic19—21no—
109C2×Dic19—41no—
110C2×Dic19—41no—
111C2×Dic19—41no—
112C2×Dic19—41no—
113C4×D19—41no—
114C4×D19—41no—
115C4×D19—41no—
116C4×D19—41no—
117C8×C19—22no—
118C19⋊C8—41no—
119#2000—191nomaximal, Sylow
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—42no—
123C22×C19—81no—
124C22×C19—81no—
125C22×C19—81no—
126C22×C19—81no—
127C22×C19#12011yescharacteristic
128C22×C19#12011yescharacteristic
129C22×C19#12111yescharacteristic
130C22×C19C2×SD1611yescharacteristic
131C22×C19#13511yescharacteristic
132C22×C19AGL(1,ℤ/8)11yescharacteristic
133C22×C19#13711yescharacteristic
134C2×D19—22no—
135C2×D19—22no—
136C2×D19—22no—
137C2×D19—41no—
138C2×D19—41no—
139C2×D19—41no—
140C2×D19—41no—
141C4×C19—42no—
142C4×C19#12011yescharacteristic
143C4×C19#12111yescharacteristic
144C4×C19#12111yescharacteristic
145C4×C19#12711yescharacteristic
146Dic19—41no—
147Dic19—42no—
148Dic19—42no—
149C22×SD16D1911yescharacteristic, complemented
150C2×C22⋊Q8—191no—
151C2×#121—191no—
152C2×#103—191no—
153C2×#102—191no—
154C2×C22⋊C8—191no—
155#340—191no—
156C2×C19—82no—
157C2×C19#39211yescharacteristic
158C2×C19#44811yescharacteristic
159C2×C19#44911yescharacteristic
160C2×C19#45011yescharacteristic
161C2×C19#45211yescharacteristic
162C2×C19#46511yescharacteristic
163C2×C19#46811yescharacteristic
164D19—42no—
165C22×Q8C2×D1911yescharacteristic
166C22×D4—381no—
167C22×D4C2×D1911yescharacteristic
168C23×C4—191no—
169C2×SD16—22no—
170C2×SD16—22no—
171C2×SD16—22no—
172C22×C8—191no—
173C22×C8C2×D1911yescharacteristic
174C22⋊Q8—382no—
175C22⋊Q8—382no—
176#121—382no—
177#121—382no—
178C2×C4⋊C4—191no—
179C2×C4⋊C4—191no—
180C2×C4⋊C4—381no—
181C2×C22⋊C4—381no—
182C2×C22⋊C4—381no—
183#103—382no—
184#102—382no—
185C22⋊C8—382no—
186C19#200011yescharacteristic, complemented, Sylow
187C24—21no—
188C24—191no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8C22⋊D1912yescomplemented
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—384no—
201C2×D4—762no—
202C2×D4—762no—
203C2×D4C22⋊D1912yes—
204C22×C4—21no—
205C22×C4—191no—
206C22×C4—381no—
207C22×C4—381no—
208C22×C4—381no—
209C22×C4—381no—
210C22×C4—381no—
211C22×C4—381no—
212C22×C4—381no—
213C22×C4—381no—
214C22×C4C22×D1911yescharacteristic
215SD16—28no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—381no—
219C2×C8—381no—
220C2×C8—381no—
221C2×C8C22⋊D1912yescomplemented
222C4⋊C4—192no—
223C4⋊C4—192no—
224C4⋊C4—384no—
225C4⋊C4—381no—
226C4⋊C4—381no—
227C22⋊C4—384no—
228C22⋊C4—384no—
229C23—22no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—192no—
237C23—381no—
238C23—381no—
239C23—381no—
240C23—381no—
241C23—381no—
242C23—381no—
243C23D4×D1911yescharacteristic
244Q8—22no—
245Q8—22no—
246Q8—41no—
247Q8—41no—
248D4—22no—
249D4—22no—
250D4—41no—
251D4—41no—
252D4—768no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—381no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—381no—
260C2×C4—381no—
261C2×C4—761no—
262C2×C4—761no—
263C2×C4—761no—
264C2×C4—761no—
265C2×C4—761no—
266C2×C4—761no—
267C2×C4—761no—
268C2×C4—761no—
269C2×C4D4×D1911yescharacteristic
270C2×C4D4×D1911yescharacteristic
271C2×C4#6454311yescharacteristic
272C2×C4C2×C22⋊D1911yescharacteristic
273C2×C4C2×C22⋊D1911yescharacteristic
274C2×C4C2×C22⋊D1911yescharacteristic
275C8—22no—
276C8—761no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—81no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22—382no—
285C22—382no—
286C22—382no—
287C22—761no—
288C22—761no—
289C22—761no—
290C22—761no—
291C22SD16×D1911yescharacteristic
292C22#1059736011yescharacteristic
293C22#1059736111yescharacteristic
294C22#1059736211yescharacteristic
295C22#1059738311yescharacteristic
296C22#1059738311yescharacteristic
297C22#1059738411yescharacteristic
298C4—42no—
299C4—762no—
300C4—762no—
301C4—761no—
302C4#1059738511yescharacteristic
303C4#1059738511yescharacteristic
304C4#1059738611yescharacteristic
305C4#1059739911yescharacteristic
306C2—82no—
307C2—762no—
308C2#1192645211yescharacteristic
309C2#1192668111yescharacteristic
310C2#1192668811yescharacteristic
311C2#1192669311yescharacteristic
312C2#1192670311yescharacteristic
313C2#1192677011yescharacteristic
314C2#1192678711yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC22×SD16×C19C2
socleC23×C19C2×D4
prime radicalC2×#10597384C2
hypercenterC22×SD16D19
hypocenterC19#2000
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10597392C2semidirect
3. C2×#10597292C2semidirect
4. C2×#10597289C2semidirect
5. C2×(C2×D19)⋊C8C2semidirect
6. #11926307C2semidirect
7. C22×SD16×C19C2semidirect
36. C2×Q8×C19D4semidirect
60. C2×C8×C19D4semidirect
66. C4⋊Dic19D4semidirect
85. C22×D19SD16semidirect
149. C22×SD16D19semidirect
186. C19#2000semidirect
194. C2×Q8C22⋊D19semidirect
221. C2×C8C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973922
C2×#105973842
C2×#105972922
C2×#105972892
C2×(C2×D19)⋊C82
#119263072
C22×SD16×C192
#200019