Finite Group Databasebeta

← #14570011

Subgroups — #14570011

Order 2432.

688 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10597383C211yesmaximal, characteristic
2#11926472C212yesmaximal, complemented
3#11926459C212yesmaximal, complemented
4#11926455C212yesmaximal, complemented
5#11926435C212yesmaximal, complemented
6#11926424C211yesmaximal, characteristic, complemented
7#11926421C212yesmaximal, complemented
8#11926399C212yesmaximal, complemented
9C2×C19×#124C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C22×Q8×C19C2211yescharacteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C23×Dic19C2211yescharacteristic, complemented
15C19×#124—24no—
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊C4×C19C2212yescomplemented
18C2×C42×C19C2211yescharacteristic, complemented
19C2×C22⋊Dic19C2211yescharacteristic
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2211yescharacteristic, complemented
22#10597383—24no—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2212yes—
27C2×(C2×D19)⋊C4C2212yes—
28C2×Dic19⋊C4C2212yescomplemented
29C19⋊#95C2212yescomplemented
30C19⋊#95C2212yescomplemented
31C19⋊#95C2212yescomplemented
32C19⋊#95C2212yescomplemented
33C24×C19C2311yescharacteristic
34C24×C19C2311yescharacteristic
35C23×D19—22no—
36C23×D19—24no—
37C23×D19—41no—
38C23×D19—41no—
39C23×D19—42no—
40C23×D19C2312yes—
41C2×Q8×C19—22no—
42C2×Q8×C19—41no—
43C2×Q8×C19—41no—
44C2×D4×C19—41no—
45C2×D4×C19—41no—
46C2×D4×C19D414yes—
47C22×C4×C19C2312yes—
48C22×C4×C19C2312yes—
49C22×C4×C19C2311yescharacteristic
50C2×C22⋊D19—24no—
51C2×C22⋊D19—24no—
52C2×C22⋊D19—42no—
53C22×Dic19—41no—
54C22×Dic19—42no—
55C22×Dic19C2312yes—
56C22×Dic19C2312yes—
57C22×Dic19C2312yes—
58C22⋊C4×C19—24no—
59C22⋊C4×C19—24no—
60C42×C19—22no—
61C22⋊Dic19—22no—
62C22⋊Dic19—42no—
63C22⋊Dic19—41no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—24no—
66(C2×D19)⋊C4—42no—
67(C2×D19)⋊C4—42no—
68(C2×D19)⋊C4—42no—
69Dic19⋊C4—42no—
70C23×C19—22no—
71C23×C19—22no—
72C23×C19—21no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—21no—
76C23×C19—21no—
77C23×C19—21no—
78C23×C19C2×D412yes—
79C23×C19C2×D412yes—
80C23×C19C2411yescharacteristic
81C22×D19—22no—
82C22×D19—22no—
83C22×D19—22no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—22no—
87C22×D19—44no—
88C22×D19—48no—
89C22×D19—48no—
90C22×D19—44no—
91C22×D19—44no—
92C22×D19#4114yes—
93Q8×C19—44no—
94D4×C19—44no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19C2×D412yes—
104C22⋊D19—48no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—44no—
115#2684—191nomaximal, Sylow
116C22×C19—22no—
117C22×C19—22no—
118C22×C19—24no—
119C22×C19—24no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—41no—
123C22×C19—41no—
124C22×C19—41no—
125C22×C19—41no—
126C22×C19C22×D411yescharacteristic
127C22×C19C2×#4112yes—
128C22×C19H(5,𝔽2)11yescharacteristic
129C22×C19H(5,𝔽2)11yescharacteristic
130C22×C19H(5,𝔽2)12yes—
131C2×D19—24no—
132C2×D19—24no—
133C2×D19—24no—
134C2×D19—416no—
135C2×D19—42no—
136C2×D19—42no—
137C2×D19—42no—
138C2×D19—42no—
139C4×C19—22no—
140C4×C19—42no—
141C4×C19—42no—
142Dic19—42no—
143Dic19—42no—
144Dic19—42no—
145C2×#124D1911yescharacteristic, complemented
146C2×#120—191no—
147#397—192no—
148#394—192no—
149#393—192no—
150#388—192no—
151#386—191no—
152#386—192no—
153#379—192no—
154C2×C19—42no—
155C2×C19—42no—
156C2×C19#53411yescharacteristic
157C2×C19#53812yes—
158C2×C19#54612yes—
159C2×C19#55111yescharacteristic
160C2×C19H(3,𝔽4)11yescharacteristic
161D19—44no—
162C25—191no—
163C22×Q8C2×D1911yescharacteristic, complemented
164C22×D4—192no—
165C22×D4C2×D1911yescharacteristic
166C23×C4—191no—
167#124—24no—
168#120—384no—
169C2×C4⋊C4—192no—
170C2×C22⋊C4—191no—
171C2×C22⋊C4—192no—
172C2×C22⋊C4—192no—
173C2×C22⋊C4—192no—
174C2×C22⋊C4—191no—
175C2×C22⋊C4—192no—
176C2×C22⋊C4—192no—
177C2×C22⋊C4—192no—
178C2×C22⋊C4C2×D1912yes—
179C2×C22⋊C4C2×D1912yescomplemented
180C2×C42C2×D1911yescharacteristic, complemented
181#95—192no—
182#95—192no—
183#95—192no—
184#95—192no—
185C19#268411yescharacteristic, complemented, Sylow
186C24—192no—
187C24—384no—
188C24—382no—
189C24—761no—
190C24—761no—
191C24—762no—
192C24C22×D1911yescharacteristic
193C24C22×D1911yescharacteristic
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4—384no—
200C2×D4—384no—
201C2×D4—762no—
202C2×D4C22⋊D1914yes—
203C22×C4—192no—
204C22×C4—192no—
205C22×C4—192no—
206C22×C4—761no—
207C22×C4—762no—
208C22×C4C22×D1912yes—
209C22×C4C22×D1912yes—
210C22×C4C22×D1911yescharacteristic
211C4⋊C4—762no—
212C22⋊C4—24no—
213C22⋊C4—24no—
214C22⋊C4—384no—
215C22⋊C4—382no—
216C22⋊C4—384no—
217C22⋊C4—762no—
218C22⋊C4—762no—
219C22⋊C4—762no—
220C22⋊C4—761no—
221C22⋊C4—762no—
222C42—22no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—194no—
232C23—382no—
233C23—382no—
234C23—382no—
235C23—382no—
236C23—382no—
237C23—382no—
238C23—768no—
239C23—764no—
240C23—764no—
241C23—768no—
242C23—764no—
243C23C2×C22⋊D1912yes—
244C23C2×C22⋊D1912yes—
245C23C23×D1911yescharacteristic
246Q8—44no—
247D4—44no—
248D4—768no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—382no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—382no—
263C2×C4—382no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—764no—
267C2×C4C2×C22⋊D1912yes—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—24no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—384no—
279C22—384no—
280C22—384no—
281C22—7616no—
282C22—762no—
283C22—762no—
284C22—762no—
285C22—762no—
286C22#1059743011yescharacteristic
287C22#1059743011yescharacteristic
288C22#41×D1912yes—
289C22#1059743512yes—
290C22C22×C22⋊D1911yescharacteristic
291C4—22no—
292C4—42no—
293C4—42no—
294C4—762no—
295C4—762no—
296C4—762no—
297C2—42no—
298C2—42no—
299C2—764no—
300C2#1192710311yescharacteristic
301C2#1192712812yes—
302C2#1192718212yes—
303C2#1192722411yescharacteristic
304C2#1192728611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#124C2
prime radicalC2×#10597383C2
hypercenterC2×#124D19
hypocenterC19#2684
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #11926472C2semidirect
3. #11926459C2semidirect
4. #11926455C2semidirect
5. #11926435C2semidirect
6. #11926424C2semidirect
7. #11926421C2semidirect
8. #11926399C2semidirect
9. C2×C19×#124C2semidirect
11. C22×Q8×C19C22semidirect
14. C23×Dic19C22semidirect
17. C2×C22⋊C4×C19C22semidirect
18. C2×C42×C19C22semidirect
21. C2×C22⋊Dic19C22semidirect
28. C2×Dic19⋊C4C22semidirect
29. C19⋊#95C22semidirect
30. C19⋊#95C22semidirect
31. C19⋊#95C22semidirect
32. C19⋊#95C22semidirect
145. C2×#124D19semidirect
163. C22×Q8C2×D19semidirect
179. C2×C22⋊C4C2×D19semidirect
180. C2×C42C2×D19semidirect
185. C19#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#105973832
#119264722
#119264592
#119264552
#119264352
#119264242
#119264212
#119263992
C2×C19×#1242
#268419