Finite Group Databasebeta

← #14569852

Subgroups — #14569852

Order 2432.

932 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597386C211yesmaximal, characteristic, complemented
2C2×#10597385C212yesmaximal, complemented
3C2×#10597399C212yesmaximal, complemented
4#11926459C212yesmaximal, complemented
5#11926453C212yesmaximal, complemented
6#11926452C212yesmaximal, complemented
7#11926432C212yesmaximal, complemented
8#11926424C211yesmaximal, characteristic, complemented
9C2×C19×#120C211yesmaximal, characteristic, complemented
10C25×C19C2211yescharacteristic
11C22×D4×C19C2212yes—
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C22×C22⋊D19C2212yes—
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2212yescomplemented
17C23×Dic19C2211yescharacteristic, complemented
18C22×D76C2211yescharacteristic, complemented
19C19×#120—24no—
20C2×C22⋊C4×C19C2212yes—
21C2×C22⋊C4×C19C2211yescharacteristic
22#10597399—28no—
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2212yes—
25C2×C22⋊Dic19C2212yes—
26C2×C22⋊Dic19C2211yescharacteristic, complemented
27#10597386—24no—
28#10597385—28no—
29C2×(C2×D19)⋊C4C2212yescomplemented
30C2×(C2×D19)⋊C4C2212yescomplemented
31C2×Dic19⋊C4C2212yescomplemented
32C2×C4×Dic19C2211yescharacteristic, complemented
33C19⋊#95C2212yescomplemented
34C19⋊#95C2212yescomplemented
35C24×C19—24no—
36C24×C19—22no—
37C24×C19—42no—
38C24×C19—41no—
39C24×C19—41no—
40C24×C19C2312yes—
41C24×C19C2311yescharacteristic
42C24×C19C2311yescharacteristic
43C23×D19C2312yes—
44C2×D4×C19—24no—
45C2×D4×C19—24no—
46C2×D4×C19—41no—
47C2×D4×C19—41no—
48C2×D4×C19—42no—
49C2×D4×C19D414yescomplemented
50C22×C4×C19C2312yes—
51C22×C4×C19C2311yescharacteristic
52C2×C22⋊D19—24no—
53C2×C22⋊D19—24no—
54C2×C22⋊D19—24no—
55C2×C22⋊D19—24no—
56C2×C22⋊D19—24no—
57C2×C22⋊D19—24no—
58C2×C22⋊D19—24no—
59C2×C22⋊D19—42no—
60C2×C22⋊D19—42no—
61C2×C22⋊D19—42no—
62C2×C22⋊D19—42no—
63C2×C22⋊D19—42no—
64C22×Dic19—24no—
65C22×Dic19—41no—
66C22×Dic19C2312yes—
67C22×Dic19C2312yes—
68C22×Dic19C2312yes—
69C2×D76—22no—
70C2×D76—41no—
71C2×D76—41no—
72C22⋊C4×C19—22no—
73C22⋊C4×C19—24no—
74C22⋊Dic19—24no—
75C22⋊Dic19—24no—
76C22⋊Dic19—41no—
77C22⋊Dic19D418yescomplemented
78(C2×D19)⋊C4—24no—
79(C2×D19)⋊C4—42no—
80Dic19⋊C4—24no—
81C4×Dic19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—22no—
86C23×C19—21no—
87C23×C19—21no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—22no—
96C23×C19—44no—
97C23×C19—48no—
98C23×C19—44no—
99C23×C19—48no—
100C23×C19—44no—
101C23×C19C2×D414yes—
102C23×C19C2×D412yes—
103C23×C19C2×D412yes—
104C23×C19C2411yescharacteristic
105C22×D19—22no—
106C22×D19—22no—
107C22×D19—22no—
108C22×D19—22no—
109C22×D19—22no—
110C22×D19—22no—
111C22×D19—22no—
112D4×C19—44no—
113D4×C19—48no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19C2×D412yes—
120C22⋊D19—48no—
121C22⋊D19—48no—
122C22⋊D19—48no—
123C22⋊D19—48no—
124C2×Dic19—22no—
125C2×Dic19—22no—
126C2×Dic19—22no—
127C2×Dic19—22no—
128C2×Dic19—22no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—44no—
132C2×Dic19C2×D414yes—
133C2×Dic19C2×D414yes—
134D76—44no—
135#2669—191nomaximal, Sylow
136C22×C19—22no—
137C22×C19—22no—
138C22×C19—24no—
139C22×C19—24no—
140C22×C19—24no—
141C22×C19—24no—
142C22×C19—24no—
143C22×C19—416no—
144C22×C19—42no—
145C22×C19—42no—
146C22×C19—42no—
147C22×C19—42no—
148C22×C19—41no—
149C22×C19—41no—
150C22×C19—42no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19—42no—
154C22×C19C22×D412yes—
155C22×C19C22×D411yescharacteristic
156C22×C19H(5,𝔽2)11yescharacteristic
157C22×C19H(5,𝔽2)11yescharacteristic
158C22×C19H(5,𝔽2)12yes—
159C2×D19—42no—
160C2×D19—42no—
161C2×D19—42no—
162C2×D19—42no—
163C2×D19—42no—
164C2×D19—42no—
165C2×D19—42no—
166C4×C19—22no—
167C4×C19—42no—
168Dic19—24no—
169Dic19—24no—
170Dic19—42no—
171C2×#127—191no—
172C2×#121—192no—
173C2×#120—192no—
174C2×#120D1911yescharacteristic, complemented
175#394—192no—
176#392—192no—
177#392—192no—
178#388—192no—
179#386—191no—
180C2×C19—42no—
181C2×C19—42no—
182C2×C19—44no—
183C2×C19#53411yescharacteristic
184C2×C19#53512yes—
185C2×C19D4211yescharacteristic
186C2×C19D4212yes—
187C2×C19#56011yescharacteristic
188D19—82no—
189C25C2×D1911yescharacteristic
190C22×D4—192no—
191C22×D4—192no—
192C22×D4—192no—
193C22×D4—192no—
194C22×D4—191no—
195C22×D4C2×D1912yes—
196C22×D4C2×D1911yescharacteristic
197C23×C4—191no—
198#127—384no—
199#121—388no—
200#120—24no—
201#120—388no—
202C2×C4⋊C4—192no—
203C2×C22⋊C4—192no—
204C2×C22⋊C4—192no—
205C2×C22⋊C4—192no—
206C2×C22⋊C4—192no—
207C2×C22⋊C4—191no—
208C2×C22⋊C4—192no—
209C2×C22⋊C4C2×D1912yes—
210C2×C22⋊C4C2×D1911yescharacteristic
211C2×C42—191no—
212#95—192no—
213#95—192no—
214C19#266911yescharacteristic, complemented, Sylow
215C24—24no—
216C24—22no—
217C24—41no—
218C24—42no—
219C24—41no—
220C24—192no—
221C24C22×D1912yes—
222C24C22×D1911yescharacteristic
223C24C22×D1911yescharacteristic
224C2×D4—24no—
225C2×D4—24no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—42no—
229C2×D4—384no—
230C2×D4—384no—
231C2×D4—384no—
232C2×D4—384no—
233C2×D4—384no—
234C2×D4—384no—
235C2×D4—384no—
236C2×D4—382no—
237C2×D4—761no—
238C2×D4—761no—
239C2×D4—762no—
240C2×D4—762no—
241C2×D4—762no—
242C2×D4—762no—
243C2×D4—762no—
244C2×D4C22⋊D1914yescomplemented
245C22×C4—192no—
246C22×C4—192no—
247C22×C4—192no—
248C22×C4—384no—
249C22×C4—761no—
250C22×C4C22×D1912yes—
251C22×C4C22×D1911yescharacteristic
252C4⋊C4—384no—
253C22⋊C4—22no—
254C22⋊C4—24no—
255C22⋊C4—198no—
256C22⋊C4—384no—
257C22⋊C4—384no—
258C22⋊C4—384no—
259C22⋊C4—762no—
260C22⋊C4—761no—
261C42—382no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—21no—
266C23—21no—
267C23—22no—
268C23—21no—
269C23—21no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—44no—
277C23—48no—
278C23—44no—
279C23—48no—
280C23—44no—
281C23—382no—
282C23—382no—
283C23—382no—
284C23—382no—
285C23—382no—
286C23—382no—
287C23—382no—
288C23D4×D1914yes—
289C23C2×C22⋊D1912yes—
290C23C2×C22⋊D1912yes—
291C23C23×D1911yescharacteristic
292D4—44no—
293D4—48no—
294D4—764no—
295D4—768no—
296D4—768no—
297D4—768no—
298D4—768no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—194no—
305C2×C4—194no—
306C2×C4—382no—
307C2×C4—382no—
308C2×C4—382no—
309C2×C4—382no—
310C2×C4—382no—
311C2×C4—382no—
312C2×C4—382no—
313C2×C4—764no—
314C2×C4C2×C22⋊D1912yes—
315C22—22no—
316C22—22no—
317C22—24no—
318C22—24no—
319C22—24no—
320C22—24no—
321C22—24no—
322C22—416no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—42no—
330C22—41no—
331C22—42no—
332C22—41no—
333C22—762no—
334C22—762no—
335C22—762no—
336C22—762no—
337C22—762no—
338C22—762no—
339C22—762no—
340C22C2×D4×D1912yes—
341C22#1059743011yescharacteristic
342C22#1059743011yescharacteristic
343C22#1059743012yes—
344C22C22×C22⋊D1911yescharacteristic
345C4—22no—
346C4—42no—
347C4—384no—
348C4—384no—
349C4—762no—
350C2—42no—
351C2—44no—
352C2—42no—
353C2—1522no—
354C2#1192710311yescharacteristic
355C2#1192710912yes—
356C2#1192717611yescharacteristic
357C2D4×C22⋊D1912yes—
358C2#1192728311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#120C2
hypercenterC2×#120D19
hypocenterC19#2669
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10597386C2semidirect
2. C2×#10597385C2semidirect
3. C2×#10597399C2semidirect
4. #11926459C2semidirect
5. #11926453C2semidirect
6. #11926452C2semidirect
7. #11926432C2semidirect
8. #11926424C2semidirect
9. C2×C19×#120C2semidirect
16. C22×C22⋊D19C22semidirect
17. C23×Dic19C22semidirect
18. C22×D76C22semidirect
26. C2×C22⋊Dic19C22semidirect
29. C2×(C2×D19)⋊C4C22semidirect
30. C2×(C2×D19)⋊C4C22semidirect
31. C2×Dic19⋊C4C22semidirect
32. C2×C4×Dic19C22semidirect
33. C19⋊#95C22semidirect
34. C19⋊#95C22semidirect
49. C2×D4×C19D4semidirect
77. C22⋊Dic19D4semidirect
174. C2×#120D19semidirect
214. C19#2669semidirect
244. C2×D4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973862
C2×#105973852
C2×#105973992
#119264592
#119264532
#119264522
#119264322
#119264242
C2×C19×#1202
#266919