Finite Group Databasebeta

← #14567914

Subgroups — #14567914

Order 2432.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×(C2×D19)⋊C4C211yesmaximal, characteristic
2C2×C22⋊C4×D19C211yesmaximal, characteristic
3#11926473C212yesmaximal, complemented
4#11926471C212yesmaximal, complemented
5#11926419C211yesmaximal, characteristic, complemented
6#11926418C212yesmaximal, complemented
7#11926416C211yesmaximal, characteristic, complemented
8#11926407C211yesmaximal, characteristic, complemented
9#11926406C212yesmaximal, complemented
10#11926399C211yesmaximal, characteristic
11C19×#381C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C23×C4×C19C2211yescharacteristic
14C23×Dic19C2211yescharacteristic
15C22×C4×D19C2211yescharacteristic
16C22×C4×D19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C22⋊Dic19C2211yescharacteristic
20C2×C22⋊Dic19C2211yescharacteristic
21C2×(C2×D19)⋊C4—24no—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2212yes—
28C2×C4⋊Dic19C2212yescomplemented
29C2×Dic19⋊C4C2212yescomplemented
30C22⋊C4×D19—24no—
31C19×#95C2212yescomplemented
32C19×#95C2212yescomplemented
33C19⋊#95C2212yescomplemented
34C19⋊#95C2212yescomplemented
35C19⋊#95C2212yescomplemented
36C19⋊#95C2212yescomplemented
37C24×C19C2311yescharacteristic
38C23×D19—22no—
39C23×D19—22no—
40C23×D19—24no—
41C23×D19—42no—
42C23×D19D414yes—
43C23×D19C2311yescharacteristic
44C23×D19C2311yescharacteristic
45C22×C4×C19—22no—
46C22×C4×C19—22no—
47C22×C4×C19—22no—
48C22×C4×C19C2311yescharacteristic
49C22×C4×C19C2311yescharacteristic
50C22×C4×C19C2312yes—
51C22×C4×C19C2312yes—
52C22×Dic19—22no—
53C22×Dic19—42no—
54C22×Dic19C2311yescharacteristic
55C22×Dic19C2311yescharacteristic
56C22×Dic19C2312yes—
57C22×Dic19C2312yes—
58C2×C4×D19—22no—
59C2×C4×D19—22no—
60C2×C4×D19—24no—
61C2×C4×D19—42no—
62C22⋊C4×C19—22no—
63C22⋊C4×C19—22no—
64C22⋊Dic19—22no—
65C22⋊Dic19—22no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—22no—
68(C2×D19)⋊C4—24no—
69(C2×D19)⋊C4—24no—
70(C2×D19)⋊C4—24no—
71(C2×D19)⋊C4—42no—
72C4⋊Dic19—42no—
73Dic19⋊C4—42no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19C2×D412yes—
77C23×C19#4112yes—
78C23×C19#4112yes—
79C23×C19C2411yescharacteristic
80C22×D19—21no—
81C22×D19—21no—
82C22×D19—22no—
83C22×D19—28no—
84C22×D19—21no—
85C22×D19—21no—
86C22×D19—22no—
87C22×D19—22no—
88C22×D19—28no—
89C22×D19—44no—
90C22×D19—48no—
91C22×D19—48no—
92C22×D19C2×D412yes—
93C22×D19C2×D412yes—
94C22×D19#4114yes—
95C2×C4×C19—22no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—44no—
106C2×Dic19—22no—
107C2×Dic19—21no—
108C2×Dic19—21no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19—22no—
116C2×Dic19—44no—
117C4×D19—44no—
118C4×D19—44no—
119#2483—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—22no—
122C22×C19—24no—
123C22×C19—24no—
124C22×C19#12314yes—
125C22×C19C22×D411yescharacteristic
126C22×C19C2×#4111yescharacteristic
127C22×C19C2×#4111yescharacteristic
128C22×C19C2×#4112yes—
129C22×C19H(5,𝔽2)12yes—
130C2×D19—22no—
131C2×D19—22no—
132C2×D19—24no—
133C2×D19—24no—
134C2×D19—22no—
135C2×D19—22no—
136C2×D19—22no—
137C2×D19—416no—
138C2×D19—42no—
139C2×D19—42no—
140C2×D19#12314yes—
141C4×C19—41no—
142C4×C19—42no—
143C4×C19—41no—
144C4×C19—42no—
145Dic19—41no—
146Dic19—41no—
147Dic19—42no—
148Dic19—42no—
149C22×C22⋊C4—191no—
150C22×C22⋊C4—191no—
151#397—192no—
152#397—192no—
153#385—191no—
154#385—191no—
155#385—192no—
156#381—191no—
157#381—192no—
158#381D1911yescharacteristic, complemented
159#379—191no—
160C2×C19—24no—
161C2×C19C2×#12311yescharacteristic
162C2×C19C2×#12311yescharacteristic
163C2×C19#53411yescharacteristic
164C2×C19#55112yes—
165C2×C19#55112yes—
166D19—24no—
167D19—42no—
168C25—191no—
169C23×C4—191no—
170C23×C4—191no—
171C23×C4—191no—
172C23×C4C2×D1911yescharacteristic
173C2×C4⋊C4—192no—
174C2×C4⋊C4—192no—
175C2×C22⋊C4—191no—
176C2×C22⋊C4—191no—
177C2×C22⋊C4—192no—
178C2×C22⋊C4—191no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—191no—
181C2×C22⋊C4—192no—
182C2×C22⋊C4—192no—
183C2×C22⋊C4—384no—
184C2×C22⋊C4—384no—
185C2×C22⋊C4C2×D1911yescharacteristic
186C2×C22⋊C4C2×D1911yescharacteristic
187#95—192no—
188#95—192no—
189#95—192no—
190#95—192no—
191#95C2×D1912yescomplemented
192#95C2×D1912yescomplemented
193C19#248311yescharacteristic, complemented, Sylow
194C24—191no—
195C24—191no—
196C24—194no—
197C24—384no—
198C24—382no—
199C24—382no—
200C24—762no—
201C24C22×D1911yescharacteristic
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—191no—
206C22×C4—192no—
207C22×C4—191no—
208C22×C4—192no—
209C22×C4—382no—
210C22×C4—382no—
211C22×C4—384no—
212C22×C4—382no—
213C22×C4—762no—
214C22×C4—762no—
215C22×C4C22×D1912yes—
216C22×C4C22×D1911yescharacteristic
217C22×C4C22×D1912yes—
218C22×C4C22×D1911yescharacteristic
219C4⋊C4—762no—
220C4⋊C4—762no—
221C22⋊C4—22no—
222C22⋊C4—22no—
223C22⋊C4—384no—
224C22⋊C4—382no—
225C22⋊C4—382no—
226C22⋊C4—384no—
227C22⋊C4—384no—
228C22⋊C4—382no—
229C22⋊C4—382no—
230C22⋊C4—762no—
231C23—22no—
232C23—22no—
233C23—192no—
234C23—194no—
235C23—192no—
236C23—388no—
237C23—381no—
238C23—381no—
239C23—382no—
240C23—381no—
241C23—381no—
242C23—382no—
243C23—382no—
244C23—388no—
245C23—764no—
246C23—768no—
247C23—768no—
248C23#6454112yes—
249C23D4×D1912yes—
250C23#6454312yes—
251C23C23×D1911yescharacteristic
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—44no—
263C2×C4—382no—
264C2×C4—381no—
265C2×C4—382no—
266C2×C4—381no—
267C2×C4—382no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—382no—
271C2×C4—382no—
272C2×C4—382no—
273C2×C4—764no—
274C2×C4—764no—
275C2×C4—764no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—24no—
280C22—194no—
281C22—382no—
282C22—382no—
283C22—384no—
284C22—384no—
285C22—382no—
286C22—382no—
287C22—382no—
288C22—7616no—
289C22—762no—
290C22—762no—
291C22#1059732914yes—
292C22C2×#6454111yescharacteristic
293C22C2×D4×D1911yescharacteristic
294C22C2×#6454311yescharacteristic
295C22#41×D1912yes—
296C22#1059743512yes—
297C4—41no—
298C4—42no—
299C4—41no—
300C4—42no—
301C4—761no—
302C4—761no—
303C4—762no—
304C4—762no—
305C2—24no—
306C2—384no—
307C2—762no—
308C2#123×D1911yescharacteristic
309C2C2×#1059732911yescharacteristic
310C2#1192710511yescharacteristic
311C2#1192721712yes—
312C2#1192721812yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#381C2
prime radicalC24×D19C22
hypercenter#381D19
hypocenterC19#2483
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #11926473C2semidirect
4. #11926471C2semidirect
5. #11926419C2semidirect
6. #11926418C2semidirect
7. #11926416C2semidirect
8. #11926407C2semidirect
9. #11926406C2semidirect
11. C19×#381C2semidirect
28. C2×C4⋊Dic19C22semidirect
29. C2×Dic19⋊C4C22semidirect
31. C19×#95C22semidirect
32. C19×#95C22semidirect
33. C19⋊#95C22semidirect
34. C19⋊#95C22semidirect
35. C19⋊#95C22semidirect
36. C19⋊#95C22semidirect
158. #381D19semidirect
191. #95C2×D19semidirect
192. #95C2×D19semidirect
193. C19#2483semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D19)⋊C42
C2×C22⋊C4×D192
#119264732
#119264712
#119264192
#119264182
#119264162
#119264072
#119264062
#119263992
C19×#3812
#248319