Finite Group Databasebeta

← #14570013

Subgroups — #14570013

Order 2432.

688 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10597382C211yesmaximal, characteristic, complemented
2#11926472C212yesmaximal, complemented
3#11926458C212yesmaximal, complemented
4#11926456C212yesmaximal, complemented
5#11926432C212yesmaximal, complemented
6#11926424C212yesmaximal, complemented
7#11926424C211yesmaximal, characteristic, complemented
8#11926400C212yesmaximal, complemented
9C2×C19×#120C211yesmaximal, characteristic
10C25×C19C2211yescharacteristic
11C22×D4×C19C2212yes—
12C22×D4×C19C2211yescharacteristic
13C23×Dic19C2211yescharacteristic, complemented
14C22×Dic38C2211yescharacteristic, complemented
15C19×#120—24no—
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2212yescomplemented
25C2×C22⋊Dic19C2211yescharacteristic, complemented
26#10597382—24no—
27C2×Dic19⋊C4C2212yescomplemented
28C2×C4×Dic19C2211yescharacteristic, complemented
29C19⋊#95C2212yescomplemented
30C19⋊#95C2212yescomplemented
31C19⋊#95C2212yescomplemented
32C19⋊#95C2212yescomplemented
33C24×C19—22no—
34C24×C19—24no—
35C24×C19—42no—
36C24×C19—41no—
37C24×C19—41no—
38C24×C19C2311yescharacteristic
39C24×C19C2311yescharacteristic
40C24×C19C2312yes—
41C2×D4×C19—24no—
42C2×D4×C19—24no—
43C2×D4×C19—41no—
44C2×D4×C19—41no—
45C2×D4×C19—42no—
46C2×D4×C19D414yes—
47C22×C4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C22×Dic19—41no—
50C22×Dic19—42no—
51C22×Dic19C2312yes—
52C22×Dic19C2312yes—
53C22×Dic19C2312yes—
54C22×Dic19C2312yes—
55C2×Dic38—22no—
56C2×Dic38—41no—
57C2×Dic38—41no—
58C22⋊C4×C19—22no—
59C22⋊C4×C19—24no—
60C22⋊Dic19—24no—
61C22⋊Dic19—24no—
62C22⋊Dic19—24no—
63C22⋊Dic19—42no—
64C22⋊Dic19—42no—
65C22⋊Dic19—42no—
66C22⋊Dic19—42no—
67C22⋊Dic19—41no—
68Dic19⋊C4—42no—
69C4×Dic19—22no—
70C23×C19—22no—
71C23×C19—22no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—21no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19—21no—
80C23×C19—22no—
81C23×C19—21no—
82C23×C19—21no—
83C23×C19—22no—
84C23×C19—48no—
85C23×C19—44no—
86C23×C19—44no—
87C23×C19—48no—
88C23×C19—44no—
89C23×C19C2×D412yes—
90C23×C19C2×D412yes—
91C23×C19#4114yes—
92C23×C19C2411yescharacteristic
93D4×C19—44no—
94D4×C19—48no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19C2×D412yes—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—22no—
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—44no—
114Dic38—44no—
115#2684—191nomaximal, Sylow
116C22×C19—22no—
117C22×C19—22no—
118C22×C19—24no—
119C22×C19—24no—
120C22×C19—24no—
121C22×C19—24no—
122C22×C19—24no—
123C22×C19—416no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—42no—
128C22×C19—42no—
129C22×C19—41no—
130C22×C19—41no—
131C22×C19—41no—
132C22×C19—41no—
133C22×C19—42no—
134C22×C19C22×D411yescharacteristic
135C22×C19C2×#4112yes—
136C22×C19H(5,𝔽2)11yescharacteristic
137C22×C19H(5,𝔽2)11yescharacteristic
138C22×C19H(5,𝔽2)12yes—
139C4×C19—22no—
140C4×C19—42no—
141Dic19—42no—
142Dic19—42no—
143Dic19—42no—
144Dic19—42no—
145C2×#124—191no—
146C2×#120D1911yescharacteristic
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—44no—
157C2×C19#53411yescharacteristic
158C2×C19#53812yes—
159C2×C19#54612yes—
160C2×C19#55111yescharacteristic
161C2×C19H(3,𝔽4)11yescharacteristic
162C25C2×D1911yescharacteristic
163C22×Q8—191no—
164C22×D4C2×D1912yes—
165C22×D4C2×D1911yescharacteristic
166C23×C4—191no—
167#124—384no—
168#120—24no—
169C2×C4⋊C4—192no—
170C2×C22⋊C4—192no—
171C2×C22⋊C4—192no—
172C2×C22⋊C4—192no—
173C2×C22⋊C4—192no—
174C2×C22⋊C4—192no—
175C2×C22⋊C4—192no—
176C2×C22⋊C4—192no—
177C2×C22⋊C4—191no—
178C2×C22⋊C4C2×D1912yes—
179C2×C22⋊C4C2×D1911yescharacteristic
180C2×C42—191no—
181#95—192no—
182#95—192no—
183#95—192no—
184#95—192no—
185C19#268411yescharacteristic, complemented, Sylow
186C24—24no—
187C24—22no—
188C24—42no—
189C24—41no—
190C24—41no—
191C24C22×D1912yes—
192C24C22×D1911yescharacteristic
193C24C22×D1911yescharacteristic
194C2×Q8—382no—
195C2×Q8—761no—
196C2×Q8—761no—
197C2×D4—24no—
198C2×D4—24no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—42no—
202C2×D4C22⋊D1914yes—
203C22×C4—192no—
204C22×C4—192no—
205C22×C4—192no—
206C22×C4—192no—
207C22×C4—761no—
208C22×C4—762no—
209C22×C4C22×D1912yes—
210C22×C4C22×D1911yescharacteristic
211C4⋊C4—762no—
212C22⋊C4—22no—
213C22⋊C4—24no—
214C22⋊C4—384no—
215C22⋊C4—384no—
216C22⋊C4—384no—
217C22⋊C4—761no—
218C22⋊C4—762no—
219C22⋊C4—762no—
220C22⋊C4—762no—
221C22⋊C4—762no—
222C42—382no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—21no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—48no—
238C23—44no—
239C23—44no—
240C23—48no—
241C23—44no—
242C23#6454314yes—
243C23C2×C22⋊D1912yes—
244C23C2×C22⋊D1912yes—
245C23C23×D1911yescharacteristic
246Q8—764no—
247D4—44no—
248D4—48no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—382no—
255C2×C4—382no—
256C2×C4—382no—
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—24no—
273C22—24no—
274C22—24no—
275C22—416no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22C2×#6454312yes—
287C22#1059743011yescharacteristic
288C22#1059743011yescharacteristic
289C22#1059743012yes—
290C22C22×C22⋊D1911yescharacteristic
291C4—22no—
292C4—42no—
293C4—762no—
294C4—762no—
295C4—762no—
296C4—762no—
297C2—42no—
298C2—44no—
299C2—42no—
300C2#1192710311yescharacteristic
301C2#1192712912yes—
302C2#1192718812yes—
303C2#1192722511yescharacteristic
304C2#1192728711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
Fitting, prime radicalC2×C19×#120C2
hypercenterC2×#120D19
hypocenterC19#2684
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10597382C2semidirect
2. #11926472C2semidirect
3. #11926458C2semidirect
4. #11926456C2semidirect
5. #11926432C2semidirect
6. #11926424C2semidirect
7. #11926424C2semidirect
8. #11926400C2semidirect
13. C23×Dic19C22semidirect
14. C22×Dic38C22semidirect
24. C2×C22⋊Dic19C22semidirect
25. C2×C22⋊Dic19C22semidirect
27. C2×Dic19⋊C4C22semidirect
28. C2×C4×Dic19C22semidirect
29. C19⋊#95C22semidirect
30. C19⋊#95C22semidirect
31. C19⋊#95C22semidirect
32. C19⋊#95C22semidirect
185. C19#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#105973822
#119264722
#119264582
#119264562
#119264322
#119264242
#119264002
C2×C19×#1202
#268419