Finite Group Databasebeta

← #14572093

Subgroups — #14572093

Order 2432.

800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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×#10597430C211yesmaximal, characteristic
2#11927017C212yesmaximal, complemented
3#11926516C214yesmaximal, complemented
4C2×#10597291C211yesmaximal, characteristic, complemented
5C2×#10597263C212yesmaximal, complemented
6#99×D19C214yesmaximal, complemented
7C2×C19×#99C211yesmaximal, characteristic, complemented
8C22×D4×C19C2211yescharacteristic
9C22×C22⋊D19C412yescomplemented
10C22×C22⋊D19C2211yescharacteristic
11C22×C22⋊D19C2211yescharacteristic
12#10597430—24no—
13#10597430—24no—
14C2×#64543C412yescomplemented
15C2×#64543C2212yes—
16C2×D4×D19C412yescomplemented
17C2×D4×D19C2212yes—
18C2×#64541C412yescomplemented
19C2×C22⋊C4×C19C2212yescomplemented
20C2×C22⋊Dic19C2212yescomplemented
21C4×C22⋊D19—24no—
22(C22⋊D19)⋊C4—24no—
23C22⋊C4×D19C2214yescomplemented
24#10597323C2214yescomplemented
25C19×#99C2214yescomplemented
26#10597291C2214yescomplemented
27#10597263C2218yescomplemented
28C24×C19C2×C411yescharacteristic, complemented
29C24×C19C2311yescharacteristic
30C23×D19C2×C411yescharacteristic, complemented
31C23×D19C2×C412yescomplemented
32C23×D19C2311yescharacteristic
33C2×D4×C19—22no—
34C2×D4×C19—22no—
35C2×D4×C19C2×C412yescomplemented
36C2×D4×C19C2312yes—
37C22×C4×C19—22no—
38C22×C4×C19C2×C411yescharacteristic, complemented
39C2×C22⋊D19—22no—
40C2×C22⋊D19—22no—
41C2×C22⋊D19—24no—
42C2×C22⋊D19—24no—
43C2×C22⋊D19C2×C412yes—
44C2×C22⋊D19C2×C412yes—
45C2×C22⋊D19C2×C412yescomplemented
46C2×C22⋊D19C2×C412yescomplemented
47C2×C22⋊D19C2×C412yescomplemented
48C2×C22⋊D19D414yes—
49C2×C22⋊D19D414yes—
50C2×C22⋊D19C2312yes—
51C22×Dic19—22no—
52C22×Dic19C2×C411yescharacteristic, complemented
53C22×Dic19C2×C412yescomplemented
54C22×Dic19C2311yescharacteristic
55#64543—28no—
56#64543—28no—
57D4×D19—28no—
58D4×D19—28no—
59#64541—24no—
60#64541—24no—
61C2×D76C2×C412yescomplemented
62C2×C4×D19—24no—
63C2×C4×D19C2×C412yescomplemented
64C2×C4×D19C2×C412yescomplemented
65C2×Dic38C2×C412yescomplemented
66C22⋊C4×C19—22no—
67C22⋊C4×C19C2314yes—
68C22⋊Dic19—22no—
69C22⋊Dic19C2314yes—
70(C2×D19)⋊C4—24no—
71Dic19⋊C4—24no—
72C4×Dic19—24no—
73C23×C19—21no—
74C23×C19—21no—
75C23×C19—81no—
76C23×C19—81no—
77C23×C19C22×C412yes—
78C23×C19C22×C411yescharacteristic
79C23×C19C22×C411yescharacteristic
80C23×C19C2×D412yes—
81C23×C19C2×D412yes—
82C23×C19C2411yescharacteristic
83C22×D19—22no—
84C22×D19—24no—
85C22×D19—81no—
86C22×D19—82no—
87C22×D19—81no—
88C22×D19C22×C412yes—
89C22×D19C22×C412yes—
90C22×D19C2×D414yes—
91D4×C19—24no—
92D4×C19—24no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—24no—
96C2×C4×C19—82no—
97C2×C4×C19C22×C412yes—
98C22⋊D19—22no—
99C22⋊D19—22no—
100C22⋊D19—24no—
101C22⋊D19—24no—
102C22⋊D19—24no—
103C22⋊D19C22⋊C414yes—
104C22⋊D19C22⋊C414yes—
105C22⋊D19C22⋊C418yes—
106C2×Dic19—22no—
107C2×Dic19—24no—
108C2×Dic19—24no—
109C2×Dic19—82no—
110C2×Dic19C22×C412yes—
111C2×Dic19C22×C412yes—
112C2×Dic19C2×D414yes—
113D76—24no—
114C4×D19—24no—
115C4×D19—24no—
116C4×D19—84no—
117Dic38—24no—
118#2883—191nomaximal, Sylow
119C22×C19—22no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—41no—
123C22×C19—41no—
124C22×C19—41no—
125C22×C19—42no—
126C22×C19—81no—
127C22×C19—81no—
128C22×C19C2×C22⋊C412yes—
129C22×C19C2×C22⋊C411yescharacteristic
130C22×C19C2×C22⋊C411yescharacteristic
131C22×C19C23×C411yescharacteristic
132C22×C19C22×D412yes—
133C2×D19—22no—
134C2×D19—44no—
135C2×D19—42no—
136C2×D19—42no—
137C2×D19—84no—
138C2×D19—82no—
139C2×D19C2×C22⋊C414yes—
140C4×C19—22no—
141C4×C19—44no—
142Dic19—22no—
143Dic19—44no—
144Dic19C2×C22⋊C414yes—
145C2×H(5,𝔽2)—191no—
146#518—192no—
147#410—194no—
148C2×#99—191no—
149C2×#99—192no—
150C2×#99—194no—
151C2×#99D1911yescharacteristic, complemented
152C2×C19—22no—
153C2×C19—21no—
154C2×C19—22no—
155C2×C19—21no—
156C2×C19—21no—
157C2×C19—42no—
158C2×C19C22×C22⋊C411yescharacteristic
159D19—24no—
160D19—42no—
161H(5,𝔽2)—384no—
162H(5,𝔽2)—384no—
163C2×#41—192no—
164C2×#41—192no—
165C2×#41—192no—
166C22×D4—191no—
167C22×D4—192no—
168C22×D4—191no—
169C22×D4—192no—
170C22×D4—192no—
171C22×D4C2×D1911yescharacteristic
172C4×D4—384no—
173C4×D4—384no—
174#117—194no—
175C2×C22⋊C4—192no—
176C2×C22⋊C4—194no—
177C2×C22⋊C4C2×D1912yescomplemented
178#99—194no—
179#99—198no—
180#99C2×D1914yescomplemented
181C19#288311yescharacteristic, complemented, Sylow
182C24—191no—
183C24—192no—
184C24—191no—
185C24C4×D1911yescharacteristic, complemented
186C24C22×D1911yescharacteristic
187#41—384no—
188#41—384no—
189#41—388no—
190#41—388no—
191C2×Q8—192no—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—192no—
195C2×D4—192no—
196C2×D4—194no—
197C2×D4—194no—
198C2×D4—192no—
199C2×D4—192no—
200C2×D4—192no—
201C2×D4—192no—
202C2×D4—192no—
203C2×D4—388no—
204C2×D4—388no—
205C2×D4—384no—
206C2×D4—384no—
207C2×D4—382no—
208C2×D4—382no—
209C2×D4C4×D1912yescomplemented
210C2×D4C22×D1912yes—
211C22×C4—22no—
212C22×C4—191no—
213C22×C4—192no—
214C22×C4—191no—
215C22×C4—192no—
216C22×C4—192no—
217C22×C4—384no—
218C22×C4—382no—
219C22×C4C4×D1911yescharacteristic, complemented
220C4⋊C4—384no—
221C22⋊C4—22no—
222C22⋊C4—194no—
223C22⋊C4—384no—
224C22⋊C4—382no—
225C22⋊C4C22×D1914yes—
226C42—384no—
227C23—21no—
228C23—21no—
229C23—81no—
230C23—81no—
231C23—192no—
232C23—194no—
233C23—192no—
234C23—384no—
235C23—382no—
236C23—1521no—
237C23—1521no—
238C23—1522no—
239C23C2×C4×D1912yes—
240C23C2×C4×D1911yescharacteristic
241C23C2×C4×D1911yescharacteristic
242C23D4×D1912yes—
243C23D4×D1912yes—
244C23C23×D1911yescharacteristic
245Q8—384no—
246D4—24no—
247D4—24no—
248D4—194no—
249D4—194no—
250D4—198no—
251D4—384no—
252D4—384no—
253D4—384no—
254D4—384no—
255D4—382no—
256D4—382no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—24no—
260C2×C4—82no—
261C2×C4—192no—
262C2×C4—194no—
263C2×C4—192no—
264C2×C4—384no—
265C2×C4—384no—
266C2×C4—384no—
267C2×C4—382no—
268C2×C4—384no—
269C2×C4—1524no—
270C2×C4—1522no—
271C2×C4C2×C4×D1912yes—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—81no—
280C22—81no—
281C22—194no—
282C22—382no—
283C22—764no—
284C22—762no—
285C22—762no—
286C22—1522no—
287C22—1524no—
288C22C22⋊C4×D1911yescharacteristic
289C22C22⋊C4×D1911yescharacteristic
290C22C22⋊C4×D1912yes—
291C22C22×C4×D1911yescharacteristic
292C22C2×D4×D1912yes—
293C4—22no—
294C4—44no—
295C4—194no—
296C4—382no—
297C4—764no—
298C2—22no—
299C2—21no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—42no—
304C2—384no—
305C2—762no—
306C2C2×C22⋊C4×D1911yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D19
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC2×C19×#99C2
socleC2×C19C22×C22⋊C4
prime radicalC2×#10597430C2
cosocleC23×C19C24
hypercenterC2×#99D19
hypocenterC19#2883
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #11927017C2semidirect
3. #11926516C2semidirect
4. C2×#10597291C2semidirect
5. C2×#10597263C2semidirect
6. #99×D19C2semidirect
7. C2×C19×#99C2semidirect
9. C22×C22⋊D19C4semidirect
14. C2×#64543C4semidirect
16. C2×D4×D19C4semidirect
18. C2×#64541C4semidirect
19. C2×C22⋊C4×C19C22semidirect
20. C2×C22⋊Dic19C22semidirect
23. C22⋊C4×D19C22semidirect
24. #10597323C22semidirect
25. C19×#99C22semidirect
26. #10597291C22semidirect
27. #10597263C22semidirect
28. C24×C19C2×C4semidirect
30. C23×D19C2×C4semidirect
31. C23×D19C2×C4semidirect
35. C2×D4×C19C2×C4semidirect
38. C22×C4×C19C2×C4semidirect
45. C2×C22⋊D19C2×C4semidirect
46. C2×C22⋊D19C2×C4semidirect
47. C2×C22⋊D19C2×C4semidirect
52. C22×Dic19C2×C4semidirect
53. C22×Dic19C2×C4semidirect
61. C2×D76C2×C4semidirect
63. C2×C4×D19C2×C4semidirect
64. C2×C4×D19C2×C4semidirect
65. C2×Dic38C2×C4semidirect
151. C2×#99D19semidirect
177. C2×C22⋊C4C2×D19semidirect
180. #99C2×D19semidirect
181. C19#2883semidirect
185. C24C4×D19semidirect
209. C2×D4C4×D19semidirect
219. C22×C4C4×D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105974302
#119270172
#119265162
C2×#105972912
C2×#105972632
#99×D192
C2×C19×#992
#288319