Finite Group Databasebeta

← #14567269

Subgroups — #14567269

Order 2432.

1348 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 193 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
1C22×D4×D19C211yesmaximal, characteristic, complemented
2C2×#10597386C211yesmaximal, characteristic, complemented
3C2×#10597384C211yesmaximal, characteristic, complemented
4C2×#10597383C214yesmaximal, complemented
5#11926452C214yesmaximal, complemented
6#11926447C211yesmaximal, characteristic, complemented
7#11926446C211yesmaximal, characteristic, complemented
8C4×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
9C2×C19×#127C211yesmaximal, characteristic, complemented
10C24×D19C2212yes—
11C22×D4×C19C2211yescharacteristic
12C22×D4×C19C2211yescharacteristic, complemented
13C22×D4×C19C2214yescomplemented
14C22×C22⋊D19C2212yes—
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2214yescomplemented
17C2×D4×D19—24no—
18C2×D4×D19—24no—
19C2×D4×D19—24no—
20C22×D76C2211yescharacteristic
21C22×C4×D19C2211yescharacteristic
22C19×#127—24no—
23C2×C42×C19C2211yescharacteristic, complemented
24C2×C22⋊Dic19C2214yescomplemented
25C2×C22⋊Dic19C2212yescomplemented
26#10597386—24no—
27#10597384—24no—
28#10597383—216no—
29C2×(C2×D19)⋊C4C2212yes—
30C2×(C2×D19)⋊C4C2214yescomplemented
31C2×C4⋊Dic19C2211yescharacteristic, complemented
32C2×C4×Dic19C2211yescharacteristic, complemented
33C19⋊#95C2212yescomplemented
34C24×C19C2312yes—
35C24×C19C2312yes—
36C23×D19—24no—
37C23×D19—24no—
38C23×D19—24no—
39C23×D19—28no—
40C23×D19—44no—
41C23×D19C2312yes—
42C23×D19C2311yescharacteristic
43C2×D4×C19—28no—
44C2×D4×C19—22no—
45C2×D4×C19—22no—
46C2×D4×C19—22no—
47C2×D4×C19—22no—
48C2×D4×C19—22no—
49C2×D4×C19—28no—
50C2×D4×C19—44no—
51C2×D4×C19D414yescomplemented
52C22×C4×C19C2312yes—
53C22×C4×C19C2311yescharacteristic
54C2×C22⋊D19—24no—
55C2×C22⋊D19—24no—
56C2×C22⋊D19—28no—
57C2×C22⋊D19—24no—
58C2×C22⋊D19—28no—
59C2×C22⋊D19—24no—
60C2×C22⋊D19—28no—
61C2×C22⋊D19—44no—
62C22×Dic19C2312yes—
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2312yes—
65D4×D19—232no—
66C2×D76—22no—
67C2×D76—22no—
68C2×D76D414yescomplemented
69C2×C4×D19—22no—
70C2×C4×D19—22no—
71C2×C4×D19D414yescomplemented
72C42×C19—22no—
73C22⋊Dic19—24no—
74C22⋊Dic19—28no—
75(C2×D19)⋊C4—28no—
76(C2×D19)⋊C4D418yescomplemented
77C4⋊Dic19—22no—
78C4×Dic19—22no—
79C23×C19—24no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—24no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—24no—
86C23×C19—22no—
87C23×C19—24no—
88C23×C19C2×D414yes—
89C23×C19C2411yescharacteristic
90C22×D19—21no—
91C22×D19—21no—
92C22×D19—22no—
93C22×D19—216no—
94C22×D19—24no—
95C22×D19—22no—
96C22×D19—22no—
97C22×D19—24no—
98C22×D19—416no—
99C22×D19—416no—
100C22×D19—48no—
101C22×D19—48no—
102C22×D19C2×D414yes—
103C22×D19C2×D414yes—
104C22×D19C2×D412yes—
105D4×C19—28no—
106D4×C19—416no—
107D4×C19—44no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19C2×D412yes—
111C2×C4×C19C2×D412yes—
112C2×C4×C19C2×D412yes—
113C2×C4×C19C2×D414yescomplemented
114C22⋊D19—216no—
115C22⋊D19—416no—
116C22⋊D19—48no—
117C2×Dic19—22no—
118C2×Dic19—21no—
119C2×Dic19—21no—
120C2×Dic19—22no—
121C2×Dic19—22no—
122C2×Dic19—24no—
123C2×Dic19C2×D412yes—
124C2×Dic19C2×D414yescomplemented
125D76—28no—
126C4×D19—28no—
127#2433—191nomaximal, Sylow
128C22×C19—24no—
129C22×C19—28no—
130C22×C19—42no—
131C22×C19—42no—
132C22×C19—44no—
133C22×C19—42no—
134C22×C19—42no—
135C22×C19—42no—
136C22×C19—44no—
137C22×C19—44no—
138C22×C19C22×D411yescharacteristic
139C22×C19C22×D411yescharacteristic
140C22×C19C22×D412yes—
141C22×C19C22×D411yescharacteristic
142C22×C19H(5,𝔽2)12yes—
143C2×D19—22no—
144C2×D19—22no—
145C2×D19—24no—
146C2×D19—24no—
147C2×D19—24no—
148C2×D19—28no—
149C2×D19—432no—
150C2×D19—42no—
151C2×D19—42no—
152C2×D19—44no—
153C2×D19#12714yescomplemented
154C4×C19—24no—
155C4×C19#12014yescomplemented
156Dic19—22no—
157Dic19—24no—
158Dic19—42no—
159C23×D4—191no—
160C2×#127—191no—
161C2×#127D1911yescharacteristic, complemented
162C2×#121—191no—
163C2×#120—194no—
164#392—194no—
165#390—191no—
166#390—191no—
167C4×C22⋊C4—191no—
168C2×C19—44no—
169C2×C19—82no—
170C2×C19C2×#12011yescharacteristic
171C2×C19C2×#12711yescharacteristic
172C2×C19#53511yescharacteristic
173C2×C19D4212yes—
174C2×C19D4212yes—
175D19—24no—
176D19—44no—
177C25—192no—
178C22×D4—192no—
179C22×D4—192no—
180C22×D4—194no—
181C22×D4—191no—
182C22×D4—384no—
183C22×D4—384no—
184C22×D4—384no—
185C22×D4C2×D1911yescharacteristic
186C22×D4C2×D1911yescharacteristic, complemented
187C22×D4C2×D1914yescomplemented
188C23×C4—191no—
189#127—24no—
190#127—384no—
191#121—384no—
192#120—3816no—
193C2×C4⋊C4—191no—
194C2×C22⋊C4—192no—
195C2×C22⋊C4—194no—
196C2×C22⋊C4—192no—
197C2×C22⋊C4—194no—
198C2×C42—191no—
199C2×C42C2×D1911yescharacteristic, complemented
200#95—192no—
201C19#243311yescharacteristic, complemented, Sylow
202C24—191no—
203C24—192no—
204C24—384no—
205C24—384no—
206C24—388no—
207C24—384no—
208C24—764no—
209C24C22×D1912yes—
210C24C22×D1912yes—
211C2×D4—28no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—28no—
217C2×D4—22no—
218C2×D4—44no—
219C2×D4—194no—
220C2×D4—384no—
221C2×D4—388no—
222C2×D4—3832no—
223C2×D4—384no—
224C2×D4—384no—
225C2×D4—388no—
226C2×D4—384no—
227C2×D4—388no—
228C2×D4—382no—
229C2×D4—382no—
230C2×D4—764no—
231C2×D4C22⋊D1914yescomplemented
232C22×C4—191no—
233C22×C4—192no—
234C22×C4—194no—
235C22×C4—192no—
236C22×C4—382no—
237C22×C4—382no—
238C22×C4C22×D1912yes—
239C22×C4C22×D1911yescharacteristic
240C4⋊C4—382no—
241C22⋊C4—198no—
242C22⋊C4—388no—
243C22⋊C4—384no—
244C22⋊C4—388no—
245C42—22no—
246C42—382no—
247C23—24no—
248C23—22no—
249C23—22no—
250C23—24no—
251C23—22no—
252C23—24no—
253C23—22no—
254C23—24no—
255C23—22no—
256C23—194no—
257C23—192no—
258C23—194no—
259C23—3816no—
260C23—381no—
261C23—382no—
262C23—381no—
263C23—384no—
264C23—382no—
265C23—384no—
266C23—382no—
267C23—7616no—
268C23—768no—
269C23—7616no—
270C23—768no—
271C23C2×C22⋊D1914yes—
272C23C23×D1911yescharacteristic
273D4—28no—
274D4—416no—
275D4—44no—
276D4—3816no—
277D4—388no—
278D4—7616no—
279D4—768no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—194no—
283C2×C4—192no—
284C2×C4—382no—
285C2×C4—381no—
286C2×C4—382no—
287C2×C4—381no—
288C2×C4—388no—
289C2×C4—384no—
290C2×C4—382no—
291C2×C4D4×D1912yes—
292C2×C4D4×D1912yes—
293C2×C4D4×D1914yescomplemented
294C2×C4C2×C22⋊D1912yes—
295C22—28no—
296C22—24no—
297C22—42no—
298C22—42no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22—44no—
303C22—44no—
304C22—42no—
305C22—194no—
306C22—382no—
307C22—384no—
308C22—384no—
309C22—382no—
310C22—388no—
311C22—384no—
312C22—7632no—
313C22—762no—
314C22—762no—
315C22—764no—
316C22C2×D4×D1911yescharacteristic
317C22C2×D4×D1912yes—
318C22C2×D4×D1911yescharacteristic
319C22#1059743012yes—
320C22C22×C22⋊D1911yescharacteristic
321C4—24no—
322C4—384no—
323C4—382no—
324C4—762no—
325C4#1059738314yescomplemented
326C2—44no—
327C2—82no—
328C2—384no—
329C2—764no—
330C2C2×#1059738311yescharacteristic
331C2#127×D1911yescharacteristic
332C2#1192710711yescharacteristic
333C2D4×C22⋊D1912yes—
334C2#1192717912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#127C2
hypercenterC2×#127D19
hypocenterC19#2433
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D19C2semidirect
2. C2×#10597386C2semidirect
3. C2×#10597384C2semidirect
4. C2×#10597383C2semidirect
5. #11926452C2semidirect
6. #11926447C2semidirect
7. #11926446C2semidirect
8. C4×(C2×D19)⋊C4C2semidirect
9. C2×C19×#127C2semidirect
12. C22×D4×C19C22semidirect
13. C22×D4×C19C22semidirect
16. C22×C22⋊D19C22semidirect
23. C2×C42×C19C22semidirect
24. C2×C22⋊Dic19C22semidirect
25. C2×C22⋊Dic19C22semidirect
30. C2×(C2×D19)⋊C4C22semidirect
31. C2×C4⋊Dic19C22semidirect
32. C2×C4×Dic19C22semidirect
33. C19⋊#95C22semidirect
51. C2×D4×C19D4semidirect
68. C2×D76D4semidirect
71. C2×C4×D19D4semidirect
76. (C2×D19)⋊C4D4semidirect
113. C2×C4×C19C2×D4semidirect
124. C2×Dic19C2×D4semidirect
153. C2×D19#127semidirect
155. C4×C19#120semidirect
161. C2×#127D19semidirect
186. C22×D4C2×D19semidirect
187. C22×D4C2×D19semidirect
199. C2×C42C2×D19semidirect
201. C19#2433semidirect
231. C2×D4C22⋊D19semidirect
293. C2×C4D4×D19semidirect
325. C4#10597383semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973862
C2×#105973842
C2×#105973832
#119264522
#119264472
#119264462
C4×(C2×D19)⋊C42
C2×C19×#1272
#243319