Finite Group Databasebeta

← #14569968

Subgroups — #14569968

Order 2432.

1000 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1000 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
1C2×#10597328C212yesmaximal, complemented
2C2×#10597328C212yesmaximal, complemented
3C2×#10597383C212yesmaximal, complemented
4#11926462C212yesmaximal, complemented
5#11926461C211yesmaximal, characteristic, complemented
6#11926459C212yesmaximal, complemented
7#11926445C211yesmaximal, characteristic, complemented
8#11926444C212yesmaximal, complemented
9C19×#394C211yesmaximal, characteristic, complemented
10C24×D19C2212yescomplemented
11C22×D4×C19C2211yescharacteristic
12C22×C22⋊D19C2212yes—
13C22×C22⋊D19C2212yes—
14C22×D76C2211yescharacteristic
15C22×D76C2212yes—
16C22×D76C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic, complemented
18C2×C22⋊C4×C19C2212yescomplemented
19C2×C22⋊C4×C19C2212yescomplemented
20C2×C22⋊Dic19C2212yescomplemented
21#10597383—28no—
22C2×(C2×D19)⋊C4C2212yescomplemented
23C2×(C2×D19)⋊C4C2212yescomplemented
24C2×(C2×D19)⋊C4C2212yescomplemented
25C2×(C2×D19)⋊C4C2212yescomplemented
26C2×(C2×D19)⋊C4C2212yescomplemented
27C2×(C2×D19)⋊C4C2212yescomplemented
28C2×Dic19⋊C4C2212yescomplemented
29C2×C4×Dic19C2211yescharacteristic, complemented
30#10597328—28no—
31#10597328—28no—
32C19×#95C2211yescharacteristic, complemented
33C19⋊#95C2211yescharacteristic, complemented
34C24×C19C2312yes—
35C23×D19—24no—
36C23×D19—24no—
37C23×D19—24no—
38C23×D19—42no—
39C23×D19—42no—
40C23×D19—42no—
41C23×D19—42no—
42C23×D19C2312yes—
43C23×D19C2312yes—
44C2×D4×C19—24no—
45C2×D4×C19—41no—
46C22×C4×C19C2311yescharacteristic
47C22×C4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C22×C4×C19C2311yescharacteristic
50C2×C22⋊D19—24no—
51C2×C22⋊D19—24no—
52C2×C22⋊D19—42no—
53C2×C22⋊D19—42no—
54C2×C22⋊D19—42no—
55C2×C22⋊D19D418yescomplemented
56C22×Dic19C2312yes—
57C22×Dic19C2312yes—
58C2×D76—24no—
59C2×D76—24no—
60C2×D76—24no—
61C2×D76—41no—
62C2×D76—41no—
63C2×D76—42no—
64C2×D76—41no—
65C2×D76D414yescomplemented
66C4⋊C4×C19—41no—
67C22⋊C4×C19—24no—
68C22⋊C4×C19—24no—
69C22⋊Dic19—24no—
70(C2×D19)⋊C4—24no—
71(C2×D19)⋊C4—24no—
72(C2×D19)⋊C4—24no—
73(C2×D19)⋊C4—24no—
74(C2×D19)⋊C4—24no—
75(C2×D19)⋊C4—24no—
76Dic19⋊C4—42no—
77C4×Dic19—41no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19C2×D414yes—
85C23×C19C2411yescharacteristic
86C22×D19—22no—
87C22×D19—22no—
88C22×D19—22no—
89C22×D19—22no—
90C22×D19—22no—
91C22×D19—22no—
92C22×D19—22no—
93C22×D19—22no—
94C22×D19—22no—
95C22×D19—22no—
96C22×D19—22no—
97C22×D19—22no—
98C22×D19—48no—
99C22×D19—48no—
100C22×D19—48no—
101C22×D19—48no—
102C22×D19—48no—
103C22×D19—48no—
104C22×D19—48no—
105C22×D19C2×D414yes—
106C22×D19C2×D414yes—
107D4×C19—44no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19C2×D412yes—
118C22⋊D19—48no—
119C22⋊D19—48no—
120C2×Dic19—22no—
121C2×Dic19—22no—
122C2×Dic19—22no—
123C2×Dic19—22no—
124C2×Dic19—22no—
125C2×Dic19C2×D414yes—
126D76—44no—
127D76—44no—
128D76—48no—
129#2679—191nomaximal, Sylow
130C22×C19—24no—
131C22×C19—24no—
132C22×C19—24no—
133C22×C19—42no—
134C22×C19—42no—
135C22×C19—42no—
136C22×C19—42no—
137C22×C19C22×D411yescharacteristic
138C22×C19C22×D412yes—
139C22×C19H(5,𝔽2)11yescharacteristic
140C22×C19H(5,𝔽2)11yescharacteristic
141C22×C19H(5,𝔽2)12yes—
142C2×D19—24no—
143C2×D19—24no—
144C2×D19—24no—
145C2×D19—24no—
146C2×D19—24no—
147C2×D19—24no—
148C2×D19—432no—
149C2×D19—42no—
150C2×D19—42no—
151C2×D19—42no—
152C2×D19—42no—
153C2×D19—42no—
154C2×D19—42no—
155C2×D19—42no—
156C2×D19—42no—
157C4×C19—22no—
158C4×C19—41no—
159C4×C19—42no—
160C4×C19—41no—
161Dic19—24no—
162Dic19—42no—
163C2×#120—192no—
164C2×#120—192no—
165C2×#120—192no—
166#394—191no—
167#394—192no—
168#394—192no—
169#394D1911yescharacteristic, complemented
170#390—191no—
171#390—192no—
172C2×C19—44no—
173C2×C19#53411yescharacteristic
174C2×C19#53412yes—
175C2×C19D4211yescharacteristic
176C2×C19D4212yes—
177C2×C19H(3,𝔽4)11yescharacteristic
178D19—44no—
179D19—44no—
180C25—192no—
181C22×D4—192no—
182C22×D4—192no—
183C22×D4—191no—
184C22×D4—191no—
185C22×D4—192no—
186C22×D4C2×D1911yescharacteristic
187#120—388no—
188#120—388no—
189#120—388no—
190C2×C4⋊C4—192no—
191C2×C4⋊C4C2×D1911yescharacteristic, complemented
192C2×C22⋊C4—192no—
193C2×C22⋊C4—192no—
194C2×C22⋊C4—192no—
195C2×C22⋊C4—192no—
196C2×C22⋊C4—192no—
197C2×C22⋊C4—192no—
198C2×C22⋊C4—192no—
199C2×C22⋊C4C2×D1912yescomplemented
200C2×C22⋊C4C2×D1912yescomplemented
201C2×C42—191no—
202#95—191no—
203#95C2×D1911yescharacteristic, complemented
204C19#267911yescharacteristic, complemented, Sylow
205C24—192no—
206C24—192no—
207C24—384no—
208C24—384no—
209C24—384no—
210C24—762no—
211C24—762no—
212C24—762no—
213C24—762no—
214C24C22×D1912yes—
215C2×D4—24no—
216C2×D4—41no—
217C2×D4—198no—
218C2×D4—194no—
219C2×D4—384no—
220C2×D4—384no—
221C2×D4—384no—
222C2×D4—384no—
223C2×D4—384no—
224C2×D4—761no—
225C2×D4—761no—
226C2×D4—761no—
227C2×D4—762no—
228C2×D4—762no—
229C2×D4—762no—
230C2×D4—762no—
231C22×C4—192no—
232C22×C4—192no—
233C22×C4C22×D1911yescharacteristic
234C22×C4C22×D1911yescharacteristic
235C22×C4C22×D1912yes—
236C22×C4C22×D1911yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—762no—
239C22⋊C4—24no—
240C22⋊C4—24no—
241C22⋊C4—384no—
242C22⋊C4—384no—
243C22⋊C4—384no—
244C22⋊C4—384no—
245C22⋊C4—384no—
246C22⋊C4—384no—
247C22⋊C4—384no—
248C42—761no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—194no—
256C23—194no—
257C23—382no—
258C23—382no—
259C23—382no—
260C23—382no—
261C23—382no—
262C23—382no—
263C23—382no—
264C23—382no—
265C23—382no—
266C23—382no—
267C23—382no—
268C23—382no—
269C23—768no—
270C23—768no—
271C23—768no—
272C23—768no—
273C23—768no—
274C23—768no—
275C23—768no—
276C23D4×D1914yes—
277C23C23×D1911yescharacteristic
278D4—44no—
279D4—764no—
280D4—764no—
281D4—768no—
282D4—768no—
283D4—768no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—194no—
294C2×C4—382no—
295C2×C4—382no—
296C2×C4—382no—
297C2×C4—382no—
298C2×C4—382no—
299C2×C4D4×D1912yes—
300C22—24no—
301C22—24no—
302C22—24no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—384no—
308C22—384no—
309C22—384no—
310C22—384no—
311C22—384no—
312C22—384no—
313C22—7632no—
314C22—762no—
315C22—762no—
316C22—762no—
317C22—762no—
318C22—762no—
319C22—762no—
320C22—762no—
321C22—762no—
322C22C2×D4×D1911yescharacteristic
323C22C2×D4×D1912yes—
324C22#1059743011yescharacteristic
325C22#1059743511yescharacteristic
326C22#1059743512yes—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—42no—
331C4—384no—
332C4—762no—
333C2—44no—
334C2—764no—
335C2—764no—
336C2#1192710211yescharacteristic
337C2#1192710512yes—
338C2#1192717611yescharacteristic
339C2#1192717812yes—
340C2#1192728611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
hypercenter#394D19
hypocenterC19#2679
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597328C2semidirect
2. C2×#10597328C2semidirect
3. C2×#10597383C2semidirect
4. #11926462C2semidirect
5. #11926461C2semidirect
6. #11926459C2semidirect
7. #11926445C2semidirect
8. #11926444C2semidirect
9. C19×#394C2semidirect
10. C24×D19C22semidirect
17. C2×C4⋊C4×C19C22semidirect
18. C2×C22⋊C4×C19C22semidirect
19. C2×C22⋊C4×C19C22semidirect
20. C2×C22⋊Dic19C22semidirect
22. C2×(C2×D19)⋊C4C22semidirect
23. C2×(C2×D19)⋊C4C22semidirect
24. C2×(C2×D19)⋊C4C22semidirect
25. C2×(C2×D19)⋊C4C22semidirect
26. C2×(C2×D19)⋊C4C22semidirect
27. C2×(C2×D19)⋊C4C22semidirect
28. C2×Dic19⋊C4C22semidirect
29. C2×C4×Dic19C22semidirect
32. C19×#95C22semidirect
33. C19⋊#95C22semidirect
55. C2×C22⋊D19D4semidirect
65. C2×D76D4semidirect
169. #394D19semidirect
191. C2×C4⋊C4C2×D19semidirect
199. C2×C22⋊C4C2×D19semidirect
200. C2×C22⋊C4C2×D19semidirect
203. #95C2×D19semidirect
204. C19#2679semidirect

Maximal subgroups

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

subgroupindex
C2×#105973282
C2×#105973832
#119264622
#119264612
#119264592
#119264452
#119264442
C19×#3942
#267919