Finite Group Databasebeta

← #14569969

Subgroups — #14569969

Order 2432.

1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 1000 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×#10597399C212yesmaximal, complemented
2C2×#10597383C211yesmaximal, characteristic, complemented
3C2×#10597383C212yesmaximal, complemented
4#11926460C212yesmaximal, complemented
5#11926459C212yesmaximal, complemented
6#11926458C212yesmaximal, complemented
7#11926447C211yesmaximal, characteristic, complemented
8#11926444C212yesmaximal, complemented
9C2×C19×#120C211yesmaximal, characteristic, complemented
10C25×C19C2211yescharacteristic, complemented
11C24×D19C2211yescharacteristic, complemented
12C22×D4×C19C2212yes—
13C22×D4×C19C2211yescharacteristic
14C22×C22⋊D19C2212yes—
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2212yes—
17C19×#120—24no—
18C2×C22⋊C4×C19C2212yescomplemented
19C2×C22⋊C4×C19C2211yescharacteristic, complemented
20#10597399—28no—
21C2×C22⋊Dic19C2212yescomplemented
22C2×C22⋊Dic19C2212yescomplemented
23C2×C22⋊Dic19C2212yescomplemented
24C2×C22⋊Dic19C2211yescharacteristic, complemented
25C2×C22⋊Dic19C2212yescomplemented
26#10597383—24no—
27#10597383—28no—
28C2×(C2×D19)⋊C4C2212yescomplemented
29C2×(C2×D19)⋊C4C2212yescomplemented
30C2×(C2×D19)⋊C4C2212yescomplemented
31C2×C4⋊Dic19C2211yescharacteristic, complemented
32C2×Dic19⋊C4C2212yescomplemented
33C2×C4×Dic19C2211yescharacteristic, complemented
34C19⋊#95C2212yescomplemented
35C24×C19—24no—
36C24×C19—22no—
37C24×C19—42no—
38C24×C19—41no—
39C24×C19—41no—
40C24×C19C2311yescharacteristic
41C24×C19C2312yes—
42C24×C19C2311yescharacteristic
43C23×D19—22no—
44C23×D19—24no—
45C23×D19—41no—
46C23×D19—42no—
47C23×D19—41no—
48C23×D19C2312yes—
49C2×D4×C19—24no—
50C2×D4×C19—24no—
51C2×D4×C19—41no—
52C2×D4×C19—41no—
53C2×D4×C19—42no—
54C2×D4×C19D414yescomplemented
55C22×C4×C19C2312yes—
56C22×C4×C19C2311yescharacteristic
57C2×C22⋊D19—24no—
58C2×C22⋊D19—24no—
59C2×C22⋊D19—24no—
60C2×C22⋊D19—24no—
61C2×C22⋊D19—42no—
62C2×C22⋊D19—42no—
63C2×C22⋊D19—42no—
64C2×C22⋊D19—42no—
65C2×C22⋊D19D418yescomplemented
66C22×Dic19C2312yes—
67C22×Dic19C2312yes—
68C22×Dic19C2312yes—
69C22⋊C4×C19—22no—
70C22⋊C4×C19—24no—
71C22⋊Dic19—22no—
72C22⋊Dic19—24no—
73C22⋊Dic19—24no—
74C22⋊Dic19—24no—
75C22⋊Dic19—24no—
76(C2×D19)⋊C4—24no—
77(C2×D19)⋊C4—24no—
78(C2×D19)⋊C4—24no—
79C4⋊Dic19—41no—
80Dic19⋊C4—42no—
81C4×Dic19—41no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—22no—
86C23×C19—22no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19—21no—
91C23×C19—21no—
92C23×C19—22no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—22no—
96C23×C19—44no—
97C23×C19—48no—
98C23×C19—48no—
99C23×C19—44no—
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—44no—
112C22×D19—48no—
113C22×D19—48no—
114C22×D19—44no—
115C22×D19—44no—
116C22×D19C2×D414yes—
117D4×C19—44no—
118D4×C19—48no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19C2×D412yes—
125C22⋊D19—48no—
126C22⋊D19—48no—
127C22⋊D19—48no—
128C2×Dic19—22no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—22no—
132C2×Dic19—22no—
133C2×Dic19—22no—
134C2×Dic19—22no—
135C2×Dic19—22no—
136C2×Dic19C2×D414yes—
137#2679—191nomaximal, Sylow
138C22×C19—24no—
139C22×C19—22no—
140C22×C19—22no—
141C22×C19—24no—
142C22×C19—24no—
143C22×C19—24no—
144C22×C19—24no—
145C22×C19—416no—
146C22×C19—42no—
147C22×C19—42no—
148C22×C19—42no—
149C22×C19—42no—
150C22×C19—41no—
151C22×C19—41no—
152C22×C19—42no—
153C22×C19—41no—
154C22×C19—42no—
155C22×C19—41no—
156C22×C19C22×D412yes—
157C22×C19C22×D411yescharacteristic
158C22×C19H(5,𝔽2)11yescharacteristic
159C22×C19H(5,𝔽2)11yescharacteristic
160C22×C19H(5,𝔽2)12yes—
161C2×D19—24no—
162C2×D19—24no—
163C2×D19—24no—
164C2×D19—416no—
165C2×D19—42no—
166C2×D19—42no—
167C2×D19—42no—
168C2×D19—42no—
169C4×C19—22no—
170C4×C19—42no—
171Dic19—24no—
172Dic19—42no—
173Dic19—42no—
174C2×#120—192no—
175C2×#120—192no—
176C2×#120—191no—
177C2×#120D1911yescharacteristic, complemented
178#394—192no—
179#394—192no—
180#394—192no—
181#390—191no—
182#390—192no—
183C2×C19—42no—
184C2×C19—44no—
185C2×C19—42no—
186C2×C19#53411yescharacteristic
187C2×C19#53412yes—
188C2×C19D4211yescharacteristic
189C2×C19D4212yes—
190C2×C19H(3,𝔽4)11yescharacteristic
191D19—44no—
192C25—191no—
193C25C2×D1911yescharacteristic, complemented
194C22×D4—192no—
195C22×D4—192no—
196C22×D4—192no—
197C22×D4C2×D1912yes—
198C22×D4C2×D1911yescharacteristic
199#120—24no—
200#120—388no—
201#120—388no—
202#120—384no—
203C2×C4⋊C4—192no—
204C2×C4⋊C4—191no—
205C2×C22⋊C4—192no—
206C2×C22⋊C4—192no—
207C2×C22⋊C4—192no—
208C2×C22⋊C4—192no—
209C2×C22⋊C4—191no—
210C2×C22⋊C4—192no—
211C2×C22⋊C4—192no—
212C2×C22⋊C4—192no—
213C2×C22⋊C4C2×D1912yescomplemented
214C2×C22⋊C4C2×D1911yescharacteristic, complemented
215C2×C42—191no—
216#95—192no—
217C19#267911yescharacteristic, complemented, Sylow
218C24—24no—
219C24—22no—
220C24—41no—
221C24—42no—
222C24—41no—
223C24—192no—
224C24—384no—
225C24—382no—
226C24—762no—
227C24—761no—
228C24—761no—
229C24C22×D1912yes—
230C24C22×D1911yescharacteristic
231C24C22×D1911yescharacteristic
232C2×D4—24no—
233C2×D4—24no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—42no—
237C2×D4—198no—
238C2×D4—384no—
239C2×D4—384no—
240C2×D4—384no—
241C2×D4—384no—
242C2×D4—762no—
243C2×D4—762no—
244C2×D4—762no—
245C2×D4—762no—
246C2×D4C22⋊D1914yescomplemented
247C22×C4—192no—
248C22×C4—192no—
249C22×C4—192no—
250C22×C4C22×D1912yes—
251C22×C4C22×D1911yescharacteristic
252C4⋊C4—762no—
253C4⋊C4—761no—
254C22⋊C4—22no—
255C22⋊C4—24no—
256C22⋊C4—384no—
257C22⋊C4—384no—
258C22⋊C4—384no—
259C22⋊C4—384no—
260C22⋊C4—384no—
261C22⋊C4—384no—
262C22⋊C4—382no—
263C22⋊C4—384no—
264C42—761no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—21no—
269C23—21no—
270C23—22no—
271C23—21no—
272C23—21no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—44no—
280C23—48no—
281C23—44no—
282C23—48no—
283C23—44no—
284C23—194no—
285C23—382no—
286C23—382no—
287C23—382no—
288C23—382no—
289C23—382no—
290C23—382no—
291C23—768no—
292C23—764no—
293C23—764no—
294C23—768no—
295C23—764no—
296C23D4×D1914yes—
297C23C2×C22⋊D1912yes—
298C23C2×C22⋊D1912yes—
299C23C23×D1911yescharacteristic
300D4—44no—
301D4—48no—
302D4—768no—
303D4—768no—
304D4—768no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—194no—
311C2×C4—382no—
312C2×C4—382no—
313C2×C4—382no—
314C2×C4—382no—
315C2×C4—382no—
316C2×C4—382no—
317C2×C4—382no—
318C2×C4—382no—
319C2×C4C2×C22⋊D1912yes—
320C22—22no—
321C22—22no—
322C22—24no—
323C22—24no—
324C22—24no—
325C22—24no—
326C22—24no—
327C22—416no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—42no—
335C22—41no—
336C22—42no—
337C22—41no—
338C22—384no—
339C22—384no—
340C22—384no—
341C22—7616no—
342C22—762no—
343C22—762no—
344C22—762no—
345C22—762no—
346C22C2×D4×D1912yes—
347C22#1059743011yescharacteristic
348C22#1059743011yescharacteristic
349C22#1059743012yes—
350C22C22×C22⋊D1911yescharacteristic
351C4—22no—
352C4—42no—
353C4—384no—
354C4—762no—
355C4—762no—
356C2—42no—
357C2—44no—
358C2—42no—
359C2—764no—
360C2#1192710311yescharacteristic
361C2#1192710412yes—
362C2#1192717611yescharacteristic
363C2D4×C22⋊D1912yes—
364C2#1192728711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#120C2
hypercenterC2×#120D19
hypocenterC19#2679
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10597399C2semidirect
2. C2×#10597383C2semidirect
3. C2×#10597383C2semidirect
4. #11926460C2semidirect
5. #11926459C2semidirect
6. #11926458C2semidirect
7. #11926447C2semidirect
8. #11926444C2semidirect
9. C2×C19×#120C2semidirect
10. C25×C19C22semidirect
11. C24×D19C22semidirect
18. C2×C22⋊C4×C19C22semidirect
19. C2×C22⋊C4×C19C22semidirect
21. C2×C22⋊Dic19C22semidirect
22. C2×C22⋊Dic19C22semidirect
23. C2×C22⋊Dic19C22semidirect
24. C2×C22⋊Dic19C22semidirect
25. C2×C22⋊Dic19C22semidirect
28. C2×(C2×D19)⋊C4C22semidirect
29. C2×(C2×D19)⋊C4C22semidirect
30. C2×(C2×D19)⋊C4C22semidirect
31. C2×C4⋊Dic19C22semidirect
32. C2×Dic19⋊C4C22semidirect
33. C2×C4×Dic19C22semidirect
34. C19⋊#95C22semidirect
54. C2×D4×C19D4semidirect
65. C2×C22⋊D19D4semidirect
177. C2×#120D19semidirect
193. C25C2×D19semidirect
213. C2×C22⋊C4C2×D19semidirect
214. C2×C22⋊C4C2×D19semidirect
217. C19#2679semidirect
246. C2×D4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973992
C2×#105973832
#119264602
#119264592
#119264582
#119264472
#119264442
C2×C19×#1202
#267919